-
Notifications
You must be signed in to change notification settings - Fork 0
Expand file tree
/
Copy pathkvantitativa-variabler.html
More file actions
1135 lines (1093 loc) · 310 KB
/
kvantitativa-variabler.html
File metadata and controls
1135 lines (1093 loc) · 310 KB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
<!DOCTYPE html>
<html lang="" xml:lang="">
<head>
<meta charset="utf-8" />
<meta http-equiv="X-UA-Compatible" content="IE=edge" />
<title>Kapitel 6 Kvantitativa variabler | Tillämpad Statistik</title>
<meta name="description" content="Kapitel 6 Kvantitativa variabler | Tillämpad Statistik" />
<meta name="generator" content="bookdown 0.29 and GitBook 2.6.7" />
<meta property="og:title" content="Kapitel 6 Kvantitativa variabler | Tillämpad Statistik" />
<meta property="og:type" content="book" />
<meta name="twitter:card" content="summary" />
<meta name="twitter:title" content="Kapitel 6 Kvantitativa variabler | Tillämpad Statistik" />
<meta name="author" content="Ronnie Pingel, Valentin Zulj" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<meta name="apple-mobile-web-app-capable" content="yes" />
<meta name="apple-mobile-web-app-status-bar-style" content="black" />
<link rel="prev" href="kategorivariabler.html"/>
<link rel="next" href="tabeller-1.html"/>
<script src="libs/jquery-3.6.0/jquery-3.6.0.min.js"></script>
<script src="https://cdn.jsdelivr.net/npm/fuse.js@6.4.6/dist/fuse.min.js"></script>
<link href="libs/gitbook-2.6.7/css/style.css" rel="stylesheet" />
<link href="libs/gitbook-2.6.7/css/plugin-table.css" rel="stylesheet" />
<link href="libs/gitbook-2.6.7/css/plugin-bookdown.css" rel="stylesheet" />
<link href="libs/gitbook-2.6.7/css/plugin-highlight.css" rel="stylesheet" />
<link href="libs/gitbook-2.6.7/css/plugin-search.css" rel="stylesheet" />
<link href="libs/gitbook-2.6.7/css/plugin-fontsettings.css" rel="stylesheet" />
<link href="libs/gitbook-2.6.7/css/plugin-clipboard.css" rel="stylesheet" />
<link href="libs/anchor-sections-1.1.0/anchor-sections.css" rel="stylesheet" />
<link href="libs/anchor-sections-1.1.0/anchor-sections-hash.css" rel="stylesheet" />
<script src="libs/anchor-sections-1.1.0/anchor-sections.js"></script>
<script src="libs/kePrint-0.0.1/kePrint.js"></script>
<link href="libs/lightable-0.0.1/lightable.css" rel="stylesheet" />
<style type="text/css">
pre > code.sourceCode { white-space: pre; position: relative; }
pre > code.sourceCode > span { display: inline-block; line-height: 1.25; }
pre > code.sourceCode > span:empty { height: 1.2em; }
.sourceCode { overflow: visible; }
code.sourceCode > span { color: inherit; text-decoration: inherit; }
pre.sourceCode { margin: 0; }
@media screen {
div.sourceCode { overflow: auto; }
}
@media print {
pre > code.sourceCode { white-space: pre-wrap; }
pre > code.sourceCode > span { text-indent: -5em; padding-left: 5em; }
}
pre.numberSource code
{ counter-reset: source-line 0; }
pre.numberSource code > span
{ position: relative; left: -4em; counter-increment: source-line; }
pre.numberSource code > span > a:first-child::before
{ content: counter(source-line);
position: relative; left: -1em; text-align: right; vertical-align: baseline;
border: none; display: inline-block;
-webkit-touch-callout: none; -webkit-user-select: none;
-khtml-user-select: none; -moz-user-select: none;
-ms-user-select: none; user-select: none;
padding: 0 4px; width: 4em;
color: #aaaaaa;
}
pre.numberSource { margin-left: 3em; border-left: 1px solid #aaaaaa; padding-left: 4px; }
div.sourceCode
{ }
@media screen {
pre > code.sourceCode > span > a:first-child::before { text-decoration: underline; }
}
code span.al { color: #ff0000; font-weight: bold; } /* Alert */
code span.an { color: #60a0b0; font-weight: bold; font-style: italic; } /* Annotation */
code span.at { color: #7d9029; } /* Attribute */
code span.bn { color: #40a070; } /* BaseN */
code span.bu { } /* BuiltIn */
code span.cf { color: #007020; font-weight: bold; } /* ControlFlow */
code span.ch { color: #4070a0; } /* Char */
code span.cn { color: #880000; } /* Constant */
code span.co { color: #60a0b0; font-style: italic; } /* Comment */
code span.cv { color: #60a0b0; font-weight: bold; font-style: italic; } /* CommentVar */
code span.do { color: #ba2121; font-style: italic; } /* Documentation */
code span.dt { color: #902000; } /* DataType */
code span.dv { color: #40a070; } /* DecVal */
code span.er { color: #ff0000; font-weight: bold; } /* Error */
code span.ex { } /* Extension */
code span.fl { color: #40a070; } /* Float */
code span.fu { color: #06287e; } /* Function */
code span.im { } /* Import */
code span.in { color: #60a0b0; font-weight: bold; font-style: italic; } /* Information */
code span.kw { color: #007020; font-weight: bold; } /* Keyword */
code span.op { color: #666666; } /* Operator */
code span.ot { color: #007020; } /* Other */
code span.pp { color: #bc7a00; } /* Preprocessor */
code span.sc { color: #4070a0; } /* SpecialChar */
code span.ss { color: #bb6688; } /* SpecialString */
code span.st { color: #4070a0; } /* String */
code span.va { color: #19177c; } /* Variable */
code span.vs { color: #4070a0; } /* VerbatimString */
code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
</style>
<link rel="stylesheet" href="style.css" type="text/css" />
</head>
<body>
<div class="book without-animation with-summary font-size-2 font-family-1" data-basepath=".">
<div class="book-summary">
<nav role="navigation">
<ul class="summary">
<li><a href="./">Tillämpad statistik</a></li>
<li class="divider"></li>
<li class="chapter" data-level="1" data-path="index.html"><a href="index.html"><i class="fa fa-check"></i><b>1</b> Introduktion</a>
<ul>
<li class="chapter" data-level="1.1" data-path="index.html"><a href="index.html#om-statistisk-programmering-med-r"><i class="fa fa-check"></i><b>1.1</b> Om statistisk programmering med R</a></li>
<li class="chapter" data-level="1.2" data-path="index.html"><a href="index.html#allmänna-tips-om-r-på-kursen"><i class="fa fa-check"></i><b>1.2</b> Allmänna tips om R på kursen</a></li>
<li class="chapter" data-level="1.3" data-path="index.html"><a href="index.html#sammanfattning"><i class="fa fa-check"></i><b>1.3</b> Sammanfattning</a></li>
<li class="chapter" data-level="1.4" data-path="index.html"><a href="index.html#referenser"><i class="fa fa-check"></i><b>1.4</b> Referenser</a></li>
</ul></li>
<li class="chapter" data-level="2" data-path="att-börja-använda-r.html"><a href="att-börja-använda-r.html"><i class="fa fa-check"></i><b>2</b> Att börja använda R</a>
<ul>
<li class="chapter" data-level="2.1" data-path="att-börja-använda-r.html"><a href="att-börja-använda-r.html#installation-av-r-och-rstudio"><i class="fa fa-check"></i><b>2.1</b> Installation av R och RStudio</a>
<ul>
<li class="chapter" data-level="2.1.1" data-path="att-börja-använda-r.html"><a href="att-börja-använda-r.html#installation-av-r-på-macos"><i class="fa fa-check"></i><b>2.1.1</b> Installation av R på MacOS</a></li>
<li class="chapter" data-level="2.1.2" data-path="att-börja-använda-r.html"><a href="att-börja-använda-r.html#installation-av-r-på-windows"><i class="fa fa-check"></i><b>2.1.2</b> Installation av R på Windows</a></li>
</ul></li>
<li class="chapter" data-level="2.2" data-path="att-börja-använda-r.html"><a href="att-börja-använda-r.html#installation-av-rstudio"><i class="fa fa-check"></i><b>2.2</b> Installation av RStudio</a></li>
<li class="chapter" data-level="2.3" data-path="att-börja-använda-r.html"><a href="att-börja-använda-r.html#första-sessionen"><i class="fa fa-check"></i><b>2.3</b> Första sessionen</a></li>
<li class="chapter" data-level="2.4" data-path="att-börja-använda-r.html"><a href="att-börja-använda-r.html#working-directory-ett-smidigt-sätt-att-spara-arbete"><i class="fa fa-check"></i><b>2.4</b> Working directory – ett smidigt sätt att spara arbete</a></li>
<li class="chapter" data-level="2.5" data-path="att-börja-använda-r.html"><a href="att-börja-använda-r.html#paket"><i class="fa fa-check"></i><b>2.5</b> Paket</a></li>
<li class="chapter" data-level="2.6" data-path="att-börja-använda-r.html"><a href="att-börja-använda-r.html#sammanfattning-1"><i class="fa fa-check"></i><b>2.6</b> Sammanfattning</a></li>
<li class="chapter" data-level="2.7" data-path="att-börja-använda-r.html"><a href="att-börja-använda-r.html#övningar"><i class="fa fa-check"></i><b>2.7</b> Övningar</a>
<ul>
<li class="chapter" data-level="" data-path="att-börja-använda-r.html"><a href="att-börja-använda-r.html#övning-2.1"><i class="fa fa-check"></i>Övning 2.1</a></li>
<li class="chapter" data-level="" data-path="att-börja-använda-r.html"><a href="att-börja-använda-r.html#övning-2.2"><i class="fa fa-check"></i>Övning 2.2</a></li>
<li class="chapter" data-level="" data-path="att-börja-använda-r.html"><a href="att-börja-använda-r.html#övning-2.3"><i class="fa fa-check"></i>Övning 2.3</a></li>
<li class="chapter" data-level="" data-path="att-börja-använda-r.html"><a href="att-börja-använda-r.html#övning-2.4"><i class="fa fa-check"></i>Övning 2.4</a></li>
<li class="chapter" data-level="" data-path="att-börja-använda-r.html"><a href="att-börja-använda-r.html#övning-2.5"><i class="fa fa-check"></i>Övning 2.5</a></li>
<li class="chapter" data-level="" data-path="att-börja-använda-r.html"><a href="att-börja-använda-r.html#övning-2.6"><i class="fa fa-check"></i>Övning 2.6</a></li>
<li class="chapter" data-level="" data-path="att-börja-använda-r.html"><a href="att-börja-använda-r.html#övning-2.7"><i class="fa fa-check"></i>Övning 2.7</a></li>
<li class="chapter" data-level="" data-path="att-börja-använda-r.html"><a href="att-börja-använda-r.html#övning-2.8"><i class="fa fa-check"></i>Övning 2.8</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="3" data-path="data-objekt-och-funktioner.html"><a href="data-objekt-och-funktioner.html"><i class="fa fa-check"></i><b>3</b> Data, objekt och funktioner</a>
<ul>
<li class="chapter" data-level="3.1" data-path="data-objekt-och-funktioner.html"><a href="data-objekt-och-funktioner.html#data-och-objekt"><i class="fa fa-check"></i><b>3.1</b> Data och objekt</a></li>
<li class="chapter" data-level="3.2" data-path="data-objekt-och-funktioner.html"><a href="data-objekt-och-funktioner.html#vektorer"><i class="fa fa-check"></i><b>3.2</b> Vektorer</a>
<ul>
<li class="chapter" data-level="3.2.1" data-path="data-objekt-och-funktioner.html"><a href="data-objekt-och-funktioner.html#vektorer-och-indexering"><i class="fa fa-check"></i><b>3.2.1</b> Vektorer och indexering</a></li>
<li class="chapter" data-level="3.2.2" data-path="data-objekt-och-funktioner.html"><a href="data-objekt-och-funktioner.html#vektorer-och-logiska-operatorer"><i class="fa fa-check"></i><b>3.2.2</b> Vektorer och logiska operatorer</a></li>
</ul></li>
<li class="chapter" data-level="3.3" data-path="data-objekt-och-funktioner.html"><a href="data-objekt-och-funktioner.html#matriser"><i class="fa fa-check"></i><b>3.3</b> Matriser</a></li>
<li class="chapter" data-level="3.4" data-path="data-objekt-och-funktioner.html"><a href="data-objekt-och-funktioner.html#data-frames"><i class="fa fa-check"></i><b>3.4</b> Data frames</a></li>
<li class="chapter" data-level="3.5" data-path="data-objekt-och-funktioner.html"><a href="data-objekt-och-funktioner.html#funktioner"><i class="fa fa-check"></i><b>3.5</b> Funktioner</a></li>
<li class="chapter" data-level="3.6" data-path="data-objekt-och-funktioner.html"><a href="data-objekt-och-funktioner.html#sammanfattning-2"><i class="fa fa-check"></i><b>3.6</b> Sammanfattning</a></li>
<li class="chapter" data-level="3.7" data-path="data-objekt-och-funktioner.html"><a href="data-objekt-och-funktioner.html#övningar-1"><i class="fa fa-check"></i><b>3.7</b> Övningar</a>
<ul>
<li class="chapter" data-level="" data-path="data-objekt-och-funktioner.html"><a href="data-objekt-och-funktioner.html#övning-3.1"><i class="fa fa-check"></i>Övning 3.1</a></li>
<li class="chapter" data-level="" data-path="data-objekt-och-funktioner.html"><a href="data-objekt-och-funktioner.html#övning-3.2"><i class="fa fa-check"></i>Övning 3.2</a></li>
<li class="chapter" data-level="" data-path="data-objekt-och-funktioner.html"><a href="data-objekt-och-funktioner.html#övning-3.3"><i class="fa fa-check"></i>Övning 3.3</a></li>
<li class="chapter" data-level="" data-path="data-objekt-och-funktioner.html"><a href="data-objekt-och-funktioner.html#övning-3.4"><i class="fa fa-check"></i>Övning 3.4</a></li>
<li class="chapter" data-level="" data-path="data-objekt-och-funktioner.html"><a href="data-objekt-och-funktioner.html#övning-3.5"><i class="fa fa-check"></i>Övning 3.5</a></li>
<li class="chapter" data-level="" data-path="data-objekt-och-funktioner.html"><a href="data-objekt-och-funktioner.html#övning-3.6"><i class="fa fa-check"></i>Övning 3.6</a></li>
<li class="chapter" data-level="" data-path="data-objekt-och-funktioner.html"><a href="data-objekt-och-funktioner.html#övning-3.7"><i class="fa fa-check"></i>Övning 3.7</a></li>
<li class="chapter" data-level="" data-path="data-objekt-och-funktioner.html"><a href="data-objekt-och-funktioner.html#övning-3.8"><i class="fa fa-check"></i>Övning 3.8</a></li>
<li class="chapter" data-level="" data-path="data-objekt-och-funktioner.html"><a href="data-objekt-och-funktioner.html#övning-3.9"><i class="fa fa-check"></i>Övning 3.9</a></li>
<li class="chapter" data-level="" data-path="data-objekt-och-funktioner.html"><a href="data-objekt-och-funktioner.html#övning-3.10"><i class="fa fa-check"></i>Övning 3.10</a></li>
<li class="chapter" data-level="" data-path="data-objekt-och-funktioner.html"><a href="data-objekt-och-funktioner.html#övning-3.11"><i class="fa fa-check"></i>Övning 3.11</a></li>
<li class="chapter" data-level="" data-path="data-objekt-och-funktioner.html"><a href="data-objekt-och-funktioner.html#övning-3.12"><i class="fa fa-check"></i>Övning 3.12</a></li>
<li class="chapter" data-level="" data-path="data-objekt-och-funktioner.html"><a href="data-objekt-och-funktioner.html#övning-3.13"><i class="fa fa-check"></i>Övning 3.13</a></li>
<li class="chapter" data-level="" data-path="data-objekt-och-funktioner.html"><a href="data-objekt-och-funktioner.html#övning-3.14"><i class="fa fa-check"></i>Övning 3.14</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="4" data-path="läsa-in-och-spara-data.html"><a href="läsa-in-och-spara-data.html"><i class="fa fa-check"></i><b>4</b> Läsa in och spara data</a>
<ul>
<li class="chapter" data-level="4.1" data-path="läsa-in-och-spara-data.html"><a href="läsa-in-och-spara-data.html#principer-för-organiserade-datamaterial"><i class="fa fa-check"></i><b>4.1</b> Principer för organiserade datamaterial</a></li>
<li class="chapter" data-level="4.2" data-path="läsa-in-och-spara-data.html"><a href="läsa-in-och-spara-data.html#läsa-in-datamaterial-med-hjälp-av-kod"><i class="fa fa-check"></i><b>4.2</b> Läsa in datamaterial med hjälp av kod</a>
<ul>
<li class="chapter" data-level="4.2.1" data-path="läsa-in-och-spara-data.html"><a href="läsa-in-och-spara-data.html#text--och-csv-filer"><i class="fa fa-check"></i><b>4.2.1</b> Text- och CSV-filer</a></li>
<li class="chapter" data-level="4.2.2" data-path="läsa-in-och-spara-data.html"><a href="läsa-in-och-spara-data.html#excel-filer"><i class="fa fa-check"></i><b>4.2.2</b> Excel-filer</a></li>
<li class="chapter" data-level="4.2.3" data-path="läsa-in-och-spara-data.html"><a href="läsa-in-och-spara-data.html#övriga-format"><i class="fa fa-check"></i><b>4.2.3</b> Övriga format</a></li>
</ul></li>
<li class="chapter" data-level="4.3" data-path="läsa-in-och-spara-data.html"><a href="läsa-in-och-spara-data.html#läsa-in-datamaterial-med-hjälp-av-menyerna-i-rstudio"><i class="fa fa-check"></i><b>4.3</b> Läsa in datamaterial med hjälp av menyerna i RStudio</a>
<ul>
<li class="chapter" data-level="4.3.1" data-path="läsa-in-och-spara-data.html"><a href="läsa-in-och-spara-data.html#läsa-in-data-från-working-directory"><i class="fa fa-check"></i><b>4.3.1</b> Läsa in data från working directory</a></li>
<li class="chapter" data-level="4.3.2" data-path="läsa-in-och-spara-data.html"><a href="läsa-in-och-spara-data.html#läsa-in-data-med-import-dataset"><i class="fa fa-check"></i><b>4.3.2</b> Läsa in data med “Import Dataset”</a></li>
</ul></li>
<li class="chapter" data-level="4.4" data-path="läsa-in-och-spara-data.html"><a href="läsa-in-och-spara-data.html#spara-datamaterial-med-hjälp-av-r"><i class="fa fa-check"></i><b>4.4</b> Spara datamaterial med hjälp av R</a></li>
<li class="chapter" data-level="4.5" data-path="läsa-in-och-spara-data.html"><a href="läsa-in-och-spara-data.html#övningar-2"><i class="fa fa-check"></i><b>4.5</b> Övningar</a>
<ul>
<li class="chapter" data-level="" data-path="läsa-in-och-spara-data.html"><a href="läsa-in-och-spara-data.html#övning-4.1"><i class="fa fa-check"></i>Övning 4.1</a></li>
<li class="chapter" data-level="" data-path="läsa-in-och-spara-data.html"><a href="läsa-in-och-spara-data.html#övning-4.2"><i class="fa fa-check"></i>Övning 4.2</a></li>
<li class="chapter" data-level="" data-path="läsa-in-och-spara-data.html"><a href="läsa-in-och-spara-data.html#övning-4.3"><i class="fa fa-check"></i>Övning 4.3</a></li>
<li class="chapter" data-level="" data-path="läsa-in-och-spara-data.html"><a href="läsa-in-och-spara-data.html#övning-4.4"><i class="fa fa-check"></i>Övning 4.4</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="5" data-path="kategorivariabler.html"><a href="kategorivariabler.html"><i class="fa fa-check"></i><b>5</b> Kategorivariabler</a>
<ul>
<li class="chapter" data-level="5.1" data-path="kategorivariabler.html"><a href="kategorivariabler.html#en-binär-variabel"><i class="fa fa-check"></i><b>5.1</b> En binär variabel</a>
<ul>
<li class="chapter" data-level="5.1.1" data-path="kategorivariabler.html"><a href="kategorivariabler.html#kodning"><i class="fa fa-check"></i><b>5.1.1</b> Kodning</a></li>
<li class="chapter" data-level="5.1.2" data-path="kategorivariabler.html"><a href="kategorivariabler.html#tabeller-och-figurer"><i class="fa fa-check"></i><b>5.1.2</b> Tabeller och figurer</a></li>
<li class="chapter" data-level="5.1.3" data-path="kategorivariabler.html"><a href="kategorivariabler.html#inferens"><i class="fa fa-check"></i><b>5.1.3</b> Inferens</a></li>
</ul></li>
<li class="chapter" data-level="5.2" data-path="kategorivariabler.html"><a href="kategorivariabler.html#två-binära-variabler"><i class="fa fa-check"></i><b>5.2</b> Två binära variabler</a>
<ul>
<li class="chapter" data-level="5.2.1" data-path="kategorivariabler.html"><a href="kategorivariabler.html#tabeller"><i class="fa fa-check"></i><b>5.2.1</b> Tabeller</a></li>
<li class="chapter" data-level="5.2.2" data-path="kategorivariabler.html"><a href="kategorivariabler.html#kvantifiering-av-samband"><i class="fa fa-check"></i><b>5.2.2</b> Kvantifiering av samband</a></li>
<li class="chapter" data-level="5.2.3" data-path="kategorivariabler.html"><a href="kategorivariabler.html#figurer"><i class="fa fa-check"></i><b>5.2.3</b> Figurer</a></li>
<li class="chapter" data-level="5.2.4" data-path="kategorivariabler.html"><a href="kategorivariabler.html#inferens-1"><i class="fa fa-check"></i><b>5.2.4</b> Inferens</a></li>
</ul></li>
<li class="chapter" data-level="5.3" data-path="kategorivariabler.html"><a href="kategorivariabler.html#tre-kategorier-eller-fler"><i class="fa fa-check"></i><b>5.3</b> Tre kategorier eller fler</a>
<ul>
<li class="chapter" data-level="5.3.1" data-path="kategorivariabler.html"><a href="kategorivariabler.html#kodning-1"><i class="fa fa-check"></i><b>5.3.1</b> Kodning</a></li>
<li class="chapter" data-level="5.3.2" data-path="kategorivariabler.html"><a href="kategorivariabler.html#tabeller-och-figurer-1"><i class="fa fa-check"></i><b>5.3.2</b> Tabeller och figurer</a></li>
<li class="chapter" data-level="5.3.3" data-path="kategorivariabler.html"><a href="kategorivariabler.html#inferens-2"><i class="fa fa-check"></i><b>5.3.3</b> Inferens</a></li>
</ul></li>
<li class="chapter" data-level="5.4" data-path="kategorivariabler.html"><a href="kategorivariabler.html#samband-mellan-kategorivariabler"><i class="fa fa-check"></i><b>5.4</b> Samband mellan kategorivariabler</a>
<ul>
<li class="chapter" data-level="5.4.1" data-path="kategorivariabler.html"><a href="kategorivariabler.html#tabeller-och-figurer-2"><i class="fa fa-check"></i><b>5.4.1</b> Tabeller och figurer</a></li>
<li class="chapter" data-level="5.4.2" data-path="kategorivariabler.html"><a href="kategorivariabler.html#inferens-3"><i class="fa fa-check"></i><b>5.4.2</b> Inferens</a></li>
</ul></li>
<li class="chapter" data-level="5.5" data-path="kategorivariabler.html"><a href="kategorivariabler.html#programmeringsuppgifter"><i class="fa fa-check"></i><b>5.5</b> Programmeringsuppgifter</a>
<ul>
<li class="chapter" data-level="5.5.1" data-path="kategorivariabler.html"><a href="kategorivariabler.html#uppgift-1"><i class="fa fa-check"></i><b>5.5.1</b> Uppgift 1</a></li>
<li class="chapter" data-level="5.5.2" data-path="kategorivariabler.html"><a href="kategorivariabler.html#uppgift-2"><i class="fa fa-check"></i><b>5.5.2</b> Uppgift 2</a></li>
<li class="chapter" data-level="5.5.3" data-path="kategorivariabler.html"><a href="kategorivariabler.html#uppgift-3"><i class="fa fa-check"></i><b>5.5.3</b> Uppgift 3</a></li>
</ul></li>
<li class="chapter" data-level="5.6" data-path="kategorivariabler.html"><a href="kategorivariabler.html#referenser-1"><i class="fa fa-check"></i><b>5.6</b> Referenser</a></li>
</ul></li>
<li class="chapter" data-level="6" data-path="kvantitativa-variabler.html"><a href="kvantitativa-variabler.html"><i class="fa fa-check"></i><b>6</b> Kvantitativa variabler</a>
<ul>
<li class="chapter" data-level="6.1" data-path="kvantitativa-variabler.html"><a href="kvantitativa-variabler.html#analys-av-en-kvantitativ-variabel"><i class="fa fa-check"></i><b>6.1</b> Analys av en kvantitativ variabel</a>
<ul>
<li class="chapter" data-level="6.1.1" data-path="kvantitativa-variabler.html"><a href="kvantitativa-variabler.html#enklare-deskriptiva-mått"><i class="fa fa-check"></i><b>6.1.1</b> Enklare deskriptiva mått</a></li>
<li class="chapter" data-level="6.1.2" data-path="kvantitativa-variabler.html"><a href="kvantitativa-variabler.html#frekvenstabeller"><i class="fa fa-check"></i><b>6.1.2</b> Frekvenstabeller</a></li>
<li class="chapter" data-level="6.1.3" data-path="kvantitativa-variabler.html"><a href="kvantitativa-variabler.html#histogram"><i class="fa fa-check"></i><b>6.1.3</b> Histogram</a></li>
</ul></li>
<li class="chapter" data-level="6.2" data-path="kvantitativa-variabler.html"><a href="kvantitativa-variabler.html#analys-av-två-kvantitativa-variabler"><i class="fa fa-check"></i><b>6.2</b> Analys av två kvantitativa variabler</a>
<ul>
<li class="chapter" data-level="6.2.1" data-path="kvantitativa-variabler.html"><a href="kvantitativa-variabler.html#två-kontinuerliga-variabler"><i class="fa fa-check"></i><b>6.2.1</b> Två kontinuerliga variabler</a></li>
<li class="chapter" data-level="6.2.2" data-path="kvantitativa-variabler.html"><a href="kvantitativa-variabler.html#en-kontinuerlig-och-en-diskret-variabel"><i class="fa fa-check"></i><b>6.2.2</b> En kontinuerlig och en diskret variabel</a></li>
</ul></li>
<li class="chapter" data-level="6.3" data-path="kvantitativa-variabler.html"><a href="kvantitativa-variabler.html#övningsuppgifter"><i class="fa fa-check"></i><b>6.3</b> Övningsuppgifter</a>
<ul>
<li class="chapter" data-level="6.3.1" data-path="kvantitativa-variabler.html"><a href="kvantitativa-variabler.html#uppgift-1-1"><i class="fa fa-check"></i><b>6.3.1</b> Uppgift 1</a></li>
<li class="chapter" data-level="6.3.2" data-path="kvantitativa-variabler.html"><a href="kvantitativa-variabler.html#uppgift-2-1"><i class="fa fa-check"></i><b>6.3.2</b> Uppgift 2</a></li>
<li class="chapter" data-level="6.3.3" data-path="kvantitativa-variabler.html"><a href="kvantitativa-variabler.html#uppgift-3-1"><i class="fa fa-check"></i><b>6.3.3</b> Uppgift 3</a></li>
</ul></li>
<li class="chapter" data-level="6.4" data-path="kvantitativa-variabler.html"><a href="kvantitativa-variabler.html#referenser-2"><i class="fa fa-check"></i><b>6.4</b> Referenser</a></li>
</ul></li>
<li class="chapter" data-level="7" data-path="tabeller-1.html"><a href="tabeller-1.html"><i class="fa fa-check"></i><b>7</b> Tabeller</a>
<ul>
<li class="chapter" data-level="7.1" data-path="tabeller-1.html"><a href="tabeller-1.html#principer-för-tabeller"><i class="fa fa-check"></i><b>7.1</b> Principer för tabeller</a></li>
<li class="chapter" data-level="7.2" data-path="tabeller-1.html"><a href="tabeller-1.html#exportera-tabell-till-html-fil"><i class="fa fa-check"></i><b>7.2</b> Exportera tabell till HTML-fil</a></li>
<li class="chapter" data-level="7.3" data-path="tabeller-1.html"><a href="tabeller-1.html#paket-för-tabeller"><i class="fa fa-check"></i><b>7.3</b> Paket för tabeller</a></li>
<li class="chapter" data-level="7.4" data-path="tabeller-1.html"><a href="tabeller-1.html#övningsuppgifter-1"><i class="fa fa-check"></i><b>7.4</b> Övningsuppgifter</a>
<ul>
<li class="chapter" data-level="7.4.1" data-path="tabeller-1.html"><a href="tabeller-1.html#uppgift-1-2"><i class="fa fa-check"></i><b>7.4.1</b> Uppgift 1</a></li>
<li class="chapter" data-level="7.4.2" data-path="tabeller-1.html"><a href="tabeller-1.html#uppgift-2-2"><i class="fa fa-check"></i><b>7.4.2</b> Uppgift 2</a></li>
<li class="chapter" data-level="7.4.3" data-path="tabeller-1.html"><a href="tabeller-1.html#uppgift-3-2"><i class="fa fa-check"></i><b>7.4.3</b> Uppgift 3</a></li>
<li class="chapter" data-level="7.4.4" data-path="tabeller-1.html"><a href="tabeller-1.html#uppgift-4"><i class="fa fa-check"></i><b>7.4.4</b> Uppgift 4</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="8" data-path="figurer-1.html"><a href="figurer-1.html"><i class="fa fa-check"></i><b>8</b> Figurer</a>
<ul>
<li class="chapter" data-level="8.1" data-path="figurer-1.html"><a href="figurer-1.html#estetik"><i class="fa fa-check"></i><b>8.1</b> Estetik</a></li>
<li class="chapter" data-level="8.2" data-path="figurer-1.html"><a href="figurer-1.html#grundläggande-figurhantering"><i class="fa fa-check"></i><b>8.2</b> Grundläggande figurhantering</a></li>
<li class="chapter" data-level="8.3" data-path="figurer-1.html"><a href="figurer-1.html#färger-och-figurer"><i class="fa fa-check"></i><b>8.3</b> Färger och figurer</a>
<ul>
<li class="chapter" data-level="8.3.1" data-path="figurer-1.html"><a href="figurer-1.html#presentation-av-aggregerade-data"><i class="fa fa-check"></i><b>8.3.1</b> Presentation av aggregerade data</a></li>
</ul></li>
<li class="chapter" data-level="8.4" data-path="figurer-1.html"><a href="figurer-1.html#cirkeldigram"><i class="fa fa-check"></i><b>8.4</b> Cirkeldigram</a></li>
<li class="chapter" data-level="8.5" data-path="figurer-1.html"><a href="figurer-1.html#figurer-för-fördelningar"><i class="fa fa-check"></i><b>8.5</b> Figurer för fördelningar</a></li>
<li class="chapter" data-level="8.6" data-path="figurer-1.html"><a href="figurer-1.html#lådagram-1"><i class="fa fa-check"></i><b>8.6</b> Lådagram</a></li>
<li class="chapter" data-level="8.7" data-path="figurer-1.html"><a href="figurer-1.html#spridningsdiagram-1"><i class="fa fa-check"></i><b>8.7</b> Spridningsdiagram</a></li>
<li class="chapter" data-level="8.8" data-path="figurer-1.html"><a href="figurer-1.html#exportera-figurer"><i class="fa fa-check"></i><b>8.8</b> Exportera figurer</a></li>
</ul></li>
</ul>
</nav>
</div>
<div class="book-body">
<div class="body-inner">
<div class="book-header" role="navigation">
<h1>
<i class="fa fa-circle-o-notch fa-spin"></i><a href="./">Tillämpad Statistik</a>
</h1>
</div>
<div class="page-wrapper" tabindex="-1" role="main">
<div class="page-inner">
<section class="normal" id="section-">
<div id="kvantitativa-variabler" class="section level1 hasAnchor" number="6">
<h1><span class="header-section-number">Kapitel 6</span> Kvantitativa variabler<a href="kvantitativa-variabler.html#kvantitativa-variabler" class="anchor-section" aria-label="Anchor link to header"></a></h1>
<style>
body {
text-align: justify}
</style>
<p>En kvantitativ variabel är en variabel vars variabelvärden är tal. Till exempel skulle en kvantitativ variabel kunna mäta</p>
<ul>
<li>Ålder: 0, 1, 2, 3, … (I detta fall anges ålder som ett siffervärde, och inte en åldergrupp som i Kapitel 5.)</li>
<li>Antal barn i en förskoleklass: 35, 36, 37, …</li>
<li>Avstånd till närmsta tunnelbanestation: Kan mätas i meter, kilometer, eller någon annan avståndsenhet.</li>
<li>Nederbörd under en given dag: Förslagsvis mätt i milimeter.</li>
</ul>
<p>Vad som tyligt framgår av variablerna ovan är att varje enskilt variabelvärde har numerisk betydelse, och inte enbart betecknar en kategori, grupp, eller klass. Variablerna mäts alltså på intervall- eller kvotskala.</p>
<p>Kvantitativa variabler delas vanligtvis in i två underkategorier, nämligen <strong>diskreta</strong> och <strong>kontinuerliga</strong> variabler. Kontinuerliga variabler kan anta värden på hela den reella tallinjen (t.ex. 1 , <span class="math inline">\(\sqrt{2}\)</span>, <span class="math inline">\(\pi\)</span>, eller vilket annat värde som helst), medan diskreta variabler brukar begränsas till sådana variabler som bara kan anta heltalsvärden (alltså 0, 1, 2, osv. Notera att 0 inte alltid räknas med). De fyra exempelvariablerna ovan kan självfallet klassificeras som antingen diskreta eller kontinuerliga. Ålder och antal barn klassas här som diskreta variabler (givet att ålder bara mäts i hela år, och att barn bara räknas i heltal), samtidigt som avstånd till tunnelbana och nederbörd betraktas som kontinuerliga (eftersom varken avstånd eller nederbörn nödvändigtvis behöver vara heltal. Ett avstånd kan vara 0.57 km, till exempel).</p>
<p>Notera att de båda kontinuerliga variablerna i detta fall måste vara positiva, eftersom vare sig negativ nederbörd eller negativa avstånd finns i verkligheten. En sak som är viktig att komma ihåg är dock att denna begränsning inte gäller generellt för kontinuerliga variabler, utan de kan också vara negativa. Ta som exempel temperatur eller årlig vinst för ett visst företag (givet att förlust ses som negativ vinst).</p>
<p>Detta kapitel handlar om hur kontinuerliga variabler kommer hanteras i <code>R</code> under kursens gång, och tanken är att det ska ge information om hur kontinuerliga variabler kan beskrivas med hjälp av <code>R</code> (beskrivande statistik, tabeller och figurer). För att visa tydliga och illustrativa exempel kommer ett och samma datamaterial användas i hela kapitlet. Datamaterialet kommer från en studie om lungkapacitet, och är hämtat från Rosner (2006). I materialet finns 654 observationer (alla från olika individer) i tre variabler</p>
<ul>
<li><code>fev</code>: forcerad utandningsvolym (forced expiratory volume). Mäter den största luftmängd som kan avges vid forcerad utandning inom ett givet antal sekunder. Värdet anges i liter per sekund (kontinuerlig).</li>
<li><code>age</code>: varje individs ålder då mätningen gjordes (diskret).</li>
<li><code>heights</code>: varje individs längd (i tum) då mätningen gjordes (kontinuerlig).</li>
</ul>
<p>Datamaterialet finns gömt under fliken här nedanför, och för att följa med i de exempel som demonstreras är det bra att kopiera variablerna och klistra in dem i ett eget <code>R</code>-script.</p>
<button title="data_rosner" type="button" onclick="if(document.getElementById('data_rosner') .style.display=='none')
{document.getElementById('data_rosner') .style.display=''}
else{document.getElementById('data_rosner') .style.display='none'}">
Visa datamaterial
</button>
<div id="data_rosner" style="display:none">
<div class="alert alert-info">
<div class="sourceCode" id="cb315"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb315-1"><a href="kvantitativa-variabler.html#cb315-1" aria-hidden="true" tabindex="-1"></a>fev <span class="ot"><-</span> <span class="fu">c</span>(<span class="fl">1.708</span>, <span class="fl">1.724</span>, <span class="fl">1.72</span>, <span class="fl">1.558</span>, <span class="fl">1.895</span>, <span class="fl">2.336</span>, <span class="fl">1.919</span>, <span class="fl">1.415</span>, <span class="fl">1.987</span>, <span class="fl">1.942</span>, <span class="fl">1.602</span>, <span class="fl">1.735</span>, <span class="fl">2.193</span>, <span class="fl">2.118</span>, <span class="fl">2.258</span>, <span class="fl">1.932</span>, <span class="fl">1.472</span>, <span class="fl">1.878</span>, <span class="fl">2.352</span>, <span class="fl">2.604</span>, <span class="fl">1.4</span>, <span class="fl">1.256</span>, <span class="fl">0.839</span>, <span class="fl">2.578</span>, <span class="fl">2.988</span>, <span class="fl">1.404</span>, <span class="fl">2.348</span>, <span class="fl">1.755</span>, <span class="fl">2.98</span>, <span class="fl">2.1</span>, <span class="fl">1.282</span>, <span class="dv">3</span>, <span class="fl">2.673</span>, <span class="fl">2.093</span>, <span class="fl">1.612</span>, <span class="fl">2.175</span>, <span class="fl">2.725</span>, <span class="fl">2.071</span>, <span class="fl">1.547</span>, <span class="fl">2.004</span>, <span class="fl">3.135</span>, <span class="fl">2.42</span>, <span class="fl">1.776</span>, <span class="fl">1.931</span>, <span class="fl">1.343</span>, <span class="fl">2.076</span>, <span class="fl">1.624</span>, <span class="fl">1.344</span>, <span class="fl">1.65</span>, <span class="fl">2.732</span>, <span class="fl">2.017</span>, <span class="fl">2.797</span>, <span class="fl">3.556</span>, <span class="fl">1.703</span>, <span class="fl">1.634</span>, <span class="fl">2.57</span>, <span class="fl">3.016</span>, <span class="fl">2.419</span>, <span class="fl">1.569</span>, <span class="fl">1.698</span>, <span class="fl">2.123</span>, <span class="fl">2.481</span>, <span class="fl">1.481</span>, <span class="fl">1.577</span>, <span class="fl">1.94</span>, <span class="fl">1.747</span>, <span class="fl">2.069</span>, <span class="fl">1.631</span>, <span class="fl">1.536</span>, <span class="fl">2.56</span>, <span class="fl">1.962</span>, <span class="fl">2.531</span>, <span class="fl">2.715</span>, <span class="fl">2.457</span>, <span class="fl">2.09</span>, <span class="fl">1.789</span>, <span class="fl">1.858</span>, <span class="fl">1.452</span>, <span class="fl">3.842</span>, <span class="fl">1.719</span>, <span class="fl">2.111</span>, <span class="fl">1.695</span>, <span class="fl">2.211</span>, <span class="fl">1.794</span>, <span class="fl">1.917</span>, <span class="fl">2.144</span>, <span class="fl">1.253</span>, <span class="fl">2.659</span>, <span class="fl">1.58</span>, <span class="fl">2.126</span>, <span class="fl">3.029</span>, <span class="fl">2.964</span>, <span class="fl">1.611</span>, <span class="fl">2.215</span>, <span class="fl">2.388</span>, <span class="fl">2.196</span>, <span class="fl">1.751</span>, <span class="fl">2.165</span>, <span class="fl">1.682</span>, <span class="fl">1.523</span>, <span class="fl">1.292</span>, <span class="fl">1.649</span>, <span class="fl">2.588</span>, <span class="fl">0.796</span>, <span class="fl">2.574</span>, <span class="fl">1.979</span>, <span class="fl">2.354</span>, <span class="fl">1.718</span>, <span class="fl">1.742</span>, <span class="fl">1.603</span>, <span class="fl">2.639</span>, <span class="fl">1.829</span>, <span class="fl">2.084</span>, <span class="fl">2.22</span>, <span class="fl">1.473</span>, <span class="fl">2.341</span>, <span class="fl">1.698</span>, <span class="fl">1.196</span>, <span class="fl">1.872</span>, <span class="fl">2.219</span>, <span class="fl">2.42</span>, <span class="fl">1.827</span>, <span class="fl">1.461</span>, <span class="fl">1.338</span>, <span class="fl">2.09</span>, <span class="fl">1.697</span>, <span class="fl">1.562</span>, <span class="fl">2.04</span>, <span class="fl">1.609</span>, <span class="fl">2.458</span>, <span class="fl">2.65</span>, <span class="fl">1.429</span>, <span class="fl">1.675</span>, <span class="fl">1.947</span>, <span class="fl">2.069</span>, <span class="fl">1.572</span>, <span class="fl">1.348</span>, <span class="fl">2.288</span>, <span class="fl">1.773</span>, <span class="fl">0.791</span>,<span class="fl">1.905</span>, <span class="fl">2.463</span>, <span class="fl">1.431</span>, <span class="fl">2.631</span>, <span class="fl">3.114</span>, <span class="fl">2.135</span>, <span class="fl">1.527</span>, <span class="fl">2.293</span>, <span class="fl">3.042</span>, <span class="fl">2.927</span>, <span class="fl">2.665</span>, <span class="fl">2.301</span>, <span class="fl">2.46</span>, <span class="fl">2.592</span>, <span class="fl">1.75</span>, <span class="fl">1.759</span>, <span class="fl">1.536</span>, <span class="fl">2.259</span>, <span class="fl">2.048</span>, <span class="fl">2.571</span>, <span class="fl">2.046</span>, <span class="fl">1.78</span>, <span class="fl">1.552</span>, <span class="fl">1.953</span>, <span class="fl">2.893</span>, <span class="fl">1.713</span>, <span class="fl">2.851</span>, <span class="fl">1.624</span>, <span class="fl">2.631</span>, <span class="fl">1.819</span>, <span class="fl">1.658</span>, <span class="fl">2.158</span>, <span class="fl">1.789</span>, <span class="fl">3.004</span>, <span class="fl">2.503</span>, <span class="fl">1.933</span>, <span class="fl">2.091</span>, <span class="fl">2.316</span>, <span class="fl">1.704</span>, <span class="fl">1.606</span>, <span class="fl">1.165</span>, <span class="fl">2.102</span>, <span class="fl">2.32</span>, <span class="fl">2.23</span>, <span class="fl">1.716</span>, <span class="fl">1.79</span>, <span class="fl">1.146</span>, <span class="fl">2.187</span>, <span class="fl">2.717</span>, <span class="fl">1.796</span>, <span class="fl">1.953</span>, <span class="fl">1.335</span>, <span class="fl">2.119</span>, <span class="fl">1.666</span>, <span class="fl">1.826</span>, <span class="fl">2.709</span>, <span class="fl">2.871</span>, <span class="fl">1.092</span>, <span class="fl">2.262</span>, <span class="fl">2.104</span>, <span class="fl">2.166</span>,<span class="fl">1.69</span>, <span class="fl">2.973</span>, <span class="fl">2.145</span>, <span class="fl">1.971</span>, <span class="fl">2.095</span>, <span class="fl">1.697</span>, <span class="fl">2.455</span>, <span class="fl">1.92</span>, <span class="fl">2.164</span>, <span class="fl">2.13</span>, <span class="fl">2.993</span>, <span class="fl">2.529</span>, <span class="fl">1.726</span>, <span class="fl">2.442</span>, <span class="fl">1.102</span>, <span class="fl">2.056</span>, <span class="fl">1.808</span>, <span class="fl">2.305</span>, <span class="fl">1.969</span>, <span class="fl">1.556</span>, <span class="fl">1.072</span>, <span class="fl">2.042</span>, <span class="fl">1.512</span>, <span class="fl">1.423</span>, <span class="fl">3.681</span>, <span class="fl">1.991</span>, <span class="fl">1.897</span>, <span class="fl">1.37</span>, <span class="fl">1.338</span>, <span class="fl">2.016</span>, <span class="fl">2.639</span>, <span class="fl">1.389</span>, <span class="fl">1.612</span>, <span class="fl">2.135</span>, <span class="fl">2.681</span>, <span class="fl">3.223</span>, <span class="fl">1.796</span>, <span class="fl">2.01</span>, <span class="fl">1.523</span>, <span class="fl">1.744</span>, <span class="fl">2.485</span>, <span class="fl">2.335</span>, <span class="fl">1.415</span>, <span class="fl">2.076</span>, <span class="fl">2.435</span>, <span class="fl">1.728</span>, <span class="fl">2.85</span>, <span class="fl">1.844</span>, <span class="fl">1.754</span>, <span class="fl">1.343</span>, <span class="fl">2.303</span>, <span class="fl">2.246</span>, <span class="fl">2.476</span>, <span class="fl">3.239</span>, <span class="fl">2.457</span>, <span class="fl">2.382</span>, <span class="fl">1.64</span>, <span class="fl">1.589</span>, <span class="fl">2.056</span>, <span class="fl">2.226</span>, <span class="fl">1.886</span>, <span class="fl">2.833</span>, <span class="fl">1.715</span>, <span class="fl">2.631</span>, <span class="fl">2.55</span>, <span class="fl">1.912</span>, <span class="fl">1.877</span>, <span class="fl">1.935</span>, <span class="fl">1.539</span>, <span class="fl">2.803</span>, <span class="fl">2.923</span>, <span class="fl">2.358</span>, <span class="fl">2.094</span>, <span class="fl">1.855</span>, <span class="fl">1.535</span>, <span class="fl">2.135</span>, <span class="fl">1.93</span>, <span class="fl">2.182</span>, <span class="fl">1.359</span>, <span class="fl">2.002</span>, <span class="fl">1.699</span>, <span class="fl">2.5</span>, <span class="fl">2.366</span>, <span class="fl">2.069</span>, <span class="fl">1.418</span>, <span class="fl">2.333</span>, <span class="fl">1.514</span>, <span class="fl">1.758</span>, <span class="fl">2.535</span>, <span class="fl">2.564</span>, <span class="fl">2.487</span>, <span class="fl">1.591</span>, <span class="fl">1.624</span>, <span class="fl">2.798</span>, <span class="fl">1.691</span>, <span class="fl">1.999</span>, <span class="fl">1.869</span>, <span class="fl">1.004</span>, <span class="fl">1.427</span>, <span class="fl">1.826</span>, <span class="fl">2.688</span>, <span class="fl">1.657</span>, <span class="fl">1.672</span>, <span class="fl">2.015</span>, <span class="fl">2.371</span>, <span class="fl">2.115</span>, <span class="fl">2.328</span>, <span class="fl">1.495</span>, <span class="fl">2.884</span>, <span class="fl">2.328</span>, <span class="fl">3.381</span>, <span class="fl">2.17</span>, <span class="fl">3.47</span>, <span class="fl">3.058</span>, <span class="fl">1.811</span>, <span class="fl">2.524</span>, <span class="fl">2.642</span>, <span class="fl">3.741</span>, <span class="fl">4.336</span>, <span class="fl">4.842</span>, <span class="fl">4.55</span>, <span class="fl">2.841</span>, <span class="fl">3.166</span>, <span class="fl">3.816</span>, <span class="fl">2.561</span>, <span class="fl">3.654</span>, <span class="fl">2.481</span>, <span class="fl">2.665</span>, <span class="fl">3.203</span>, <span class="fl">3.549</span>, <span class="fl">2.236</span>, <span class="fl">3.222</span>, <span class="fl">3.111</span>, <span class="fl">3.49</span>, <span class="fl">3.147</span>, <span class="fl">2.52</span>, <span class="fl">2.292</span>, <span class="fl">2.889</span>, <span class="fl">2.246</span>, <span class="fl">1.937</span>, <span class="fl">2.646</span>, <span class="fl">2.957</span>, <span class="fl">4.007</span>, <span class="fl">2.386</span>, <span class="fl">3.251</span>, <span class="fl">2.762</span>, <span class="fl">3.011</span>, <span class="fl">4.305</span>, <span class="fl">3.906</span>, <span class="fl">3.583</span>, <span class="fl">3.236</span>, <span class="fl">3.436</span>, <span class="fl">3.058</span>, <span class="fl">3.007</span>, <span class="fl">3.489</span>, <span class="fl">2.864</span>, <span class="fl">3.428</span>, <span class="fl">2.819</span>, <span class="fl">2.25</span>, <span class="fl">4.683</span>, <span class="fl">2.352</span>, <span class="fl">3.108</span>, <span class="fl">3.994</span>, <span class="fl">4.393</span>, <span class="fl">3.208</span>, <span class="fl">2.592</span>, <span class="fl">3.193</span>, <span class="fl">1.694</span>, <span class="fl">3.957</span>, <span class="fl">2.346</span>, <span class="fl">4.789</span>, <span class="fl">3.515</span>, <span class="fl">2.754</span>, <span class="fl">2.72</span>, <span class="fl">2.463</span>, <span class="fl">2.633</span>, <span class="fl">3.048</span>, <span class="fl">3.111</span>, <span class="fl">3.745</span>, <span class="fl">2.384</span>, <span class="fl">2.094</span>, <span class="fl">3.183</span>, <span class="fl">3.074</span>, <span class="fl">3.977</span>, <span class="fl">3.354</span>, <span class="fl">3.411</span>, <span class="fl">2.387</span>, <span class="fl">3.171</span>, <span class="fl">3.887</span>, <span class="fl">2.646</span>, <span class="fl">2.504</span>, <span class="fl">3.587</span>, <span class="fl">3.845</span>, <span class="fl">2.971</span>, <span class="fl">2.891</span>, <span class="fl">1.823</span>, <span class="fl">2.417</span>, <span class="fl">2.175</span>, <span class="fl">2.735</span>, <span class="fl">4.273</span>, <span class="fl">2.976</span>, <span class="fl">3.835</span>, <span class="fl">4.065</span>, <span class="fl">2.318</span>, <span class="fl">3.596</span>, <span class="fl">3.395</span>, <span class="fl">2.751</span>, <span class="fl">2.673</span>, <span class="fl">2.556</span>, <span class="fl">2.542</span>, <span class="fl">2.608</span>, <span class="fl">2.354</span>, <span class="fl">2.599</span>, <span class="fl">1.458</span>, <span class="fl">3.795</span>, <span class="fl">2.491</span>, <span class="fl">3.06</span>, <span class="fl">2.545</span>, <span class="fl">2.993</span>, <span class="fl">3.305</span>, <span class="fl">4.756</span>, <span class="fl">3.774</span>, <span class="fl">2.855</span>, <span class="fl">2.988</span>, <span class="fl">2.498</span>, <span class="fl">3.169</span>, <span class="fl">2.887</span>, <span class="fl">2.704</span>, <span class="fl">3.515</span>, <span class="fl">3.425</span>, <span class="fl">2.287</span>, <span class="fl">2.434</span>, <span class="fl">2.365</span>, <span class="fl">3.086</span>, <span class="fl">2.696</span>, <span class="fl">2.868</span>, <span class="fl">2.813</span>, <span class="fl">4.309</span>, <span class="fl">3.255</span>, <span class="fl">3.413</span>, <span class="fl">4.593</span>, <span class="fl">4.111</span>, <span class="fl">1.916</span>, <span class="fl">1.858</span>, <span class="fl">2.975</span>, <span class="fl">3.35</span>, <span class="fl">2.901</span>, <span class="fl">2.241</span>, <span class="fl">4.225</span>, <span class="fl">3.223</span>, <span class="fl">5.224</span>, <span class="fl">4.073</span>, <span class="fl">4.08</span>, <span class="fl">2.606</span>, <span class="fl">3.169</span>, <span class="fl">4.411</span>, <span class="fl">3.791</span>, <span class="fl">3.089</span>, <span class="fl">2.465</span>, <span class="fl">3.343</span>, <span class="fl">3.2</span>, <span class="fl">2.913</span>, <span class="fl">4.877</span>, <span class="fl">2.358</span>, <span class="fl">3.279</span>, <span class="fl">2.581</span>, <span class="fl">2.347</span>, <span class="fl">2.691</span>, <span class="fl">2.827</span>, <span class="fl">1.873</span>, <span class="fl">3.751</span>, <span class="fl">2.538</span>, <span class="fl">2.758</span>, <span class="fl">3.05</span>, <span class="fl">3.079</span>, <span class="fl">2.201</span>, <span class="fl">1.858</span>, <span class="fl">2.216</span>, <span class="fl">3.403</span>, <span class="fl">3.501</span>, <span class="fl">2.578</span>, <span class="fl">3.078</span>, <span class="fl">3.186</span>, <span class="fl">1.665</span>, <span class="fl">2.081</span>, <span class="fl">2.974</span>, <span class="fl">3.297</span>, <span class="fl">4.073</span>, <span class="fl">4.448</span>, <span class="fl">3.984</span>, <span class="fl">2.25</span>, <span class="fl">2.752</span>, <span class="fl">2.304</span>, <span class="fl">3.68</span>, <span class="fl">3.102</span>, <span class="fl">2.862</span>, <span class="fl">2.677</span>, <span class="fl">3.023</span>, <span class="fl">3.681</span>, <span class="fl">3.255</span>, <span class="fl">3.692</span>, <span class="fl">2.356</span>, <span class="fl">4.591</span>, <span class="fl">3.082</span>, <span class="fl">3.297</span>, <span class="fl">3.258</span>, <span class="fl">2.216</span>, <span class="fl">3.247</span>, <span class="fl">4.324</span>, <span class="fl">2.362</span>, <span class="fl">2.563</span>, <span class="fl">3.206</span>, <span class="fl">3.585</span>, <span class="fl">4.72</span>, <span class="fl">3.331</span>, <span class="fl">5.083</span>, <span class="fl">3.498</span>, <span class="fl">2.417</span>, <span class="fl">2.364</span>, <span class="fl">2.341</span>, <span class="fl">2.759</span>, <span class="fl">2.953</span>, <span class="fl">3.231</span>, <span class="fl">3.078</span>, <span class="fl">3.369</span>, <span class="fl">3.529</span>, <span class="fl">2.866</span>, <span class="fl">2.891</span>, <span class="fl">3.022</span>, <span class="fl">3.127</span>, <span class="fl">2.866</span>, <span class="fl">2.605</span>, <span class="fl">3.056</span>, <span class="fl">2.569</span>, <span class="fl">2.501</span>, <span class="fl">3.32</span>, <span class="fl">2.123</span>, <span class="fl">3.78</span>, <span class="fl">3.847</span>, <span class="fl">3.785</span>, <span class="fl">3.924</span>, <span class="fl">2.132</span>, <span class="fl">2.752</span>, <span class="fl">2.449</span>, <span class="fl">3.456</span>, <span class="fl">3.073</span>, <span class="fl">2.688</span>, <span class="fl">3.329</span>, <span class="fl">4.271</span>, <span class="fl">3.53</span>, <span class="fl">2.928</span>, <span class="fl">2.689</span>, <span class="fl">2.332</span>, <span class="fl">2.934</span>, <span class="fl">2.276</span>, <span class="fl">3.11</span>, <span class="fl">2.894</span>, <span class="fl">4.637</span>, <span class="fl">2.435</span>, <span class="fl">2.838</span>, <span class="fl">3.035</span>, <span class="fl">4.831</span>, <span class="fl">2.812</span>, <span class="fl">2.714</span>, <span class="fl">3.086</span>, <span class="fl">3.519</span>, <span class="fl">4.232</span>, <span class="fl">2.77</span>, <span class="fl">3.341</span>, <span class="fl">3.09</span>, <span class="fl">2.531</span>, <span class="fl">2.822</span>, <span class="fl">3.038</span>, <span class="fl">2.935</span>, <span class="fl">2.568</span>, <span class="fl">2.387</span>, <span class="fl">2.499</span>, <span class="fl">4.13</span>, <span class="fl">3.001</span>, <span class="fl">3.132</span>, <span class="fl">3.577</span>, <span class="fl">3.222</span>, <span class="fl">3.28</span>, <span class="fl">2.659</span>, <span class="fl">2.822</span>, <span class="fl">2.14</span>, <span class="fl">4.203</span>, <span class="fl">2.997</span>, <span class="fl">3.12</span>, <span class="fl">2.562</span>, <span class="fl">3.082</span>, <span class="fl">3.806</span>, <span class="fl">3.339</span>, <span class="fl">3.152</span>, <span class="fl">2.458</span>, <span class="fl">2.391</span>, <span class="fl">3.141</span>, <span class="fl">2.579</span>, <span class="fl">3.104</span>, <span class="fl">4.045</span>, <span class="fl">4.763</span>, <span class="fl">2.1</span>, <span class="fl">3.069</span>, <span class="fl">2.785</span>, <span class="fl">4.284</span>, <span class="fl">4.506</span>, <span class="fl">2.906</span>, <span class="fl">5.102</span>, <span class="fl">3.519</span>, <span class="fl">3.688</span>, <span class="fl">4.429</span>, <span class="fl">4.279</span>, <span class="fl">4.5</span>, <span class="fl">2.635</span>, <span class="fl">2.679</span>, <span class="fl">2.198</span>, <span class="fl">3.345</span>, <span class="fl">3.082</span>, <span class="fl">3.387</span>, <span class="fl">3.082</span>, <span class="fl">2.903</span>, <span class="fl">3.004</span>, <span class="fl">5.793</span>, <span class="fl">3.985</span>, <span class="fl">4.22</span>, <span class="fl">4.724</span>, <span class="fl">3.731</span>, <span class="fl">3.406</span>, <span class="fl">3.5</span>, <span class="fl">3.674</span>, <span class="fl">5.633</span>, <span class="fl">3.122</span>, <span class="fl">3.33</span>, <span class="fl">2.608</span>, <span class="fl">3.645</span>, <span class="fl">3.799</span>, <span class="fl">4.086</span>, <span class="fl">2.887</span>, <span class="fl">4.07</span>, <span class="fl">3.96</span>, <span class="fl">4.299</span>, <span class="fl">2.981</span>, <span class="fl">2.264</span>, <span class="fl">4.404</span>, <span class="fl">2.278</span>, <span class="fl">4.504</span>, <span class="fl">5.638</span>, <span class="fl">4.872</span>, <span class="fl">4.27</span>, <span class="fl">3.727</span>, <span class="fl">2.853</span>, <span class="fl">2.795</span>, <span class="fl">3.211</span>)</span>
<span id="cb315-2"><a href="kvantitativa-variabler.html#cb315-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb315-3"><a href="kvantitativa-variabler.html#cb315-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb315-4"><a href="kvantitativa-variabler.html#cb315-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb315-5"><a href="kvantitativa-variabler.html#cb315-5" aria-hidden="true" tabindex="-1"></a>age <span class="ot"><-</span> <span class="fu">c</span>(<span class="dv">9</span>, <span class="dv">8</span>, <span class="dv">7</span>, <span class="dv">9</span>, <span class="dv">9</span>, <span class="dv">8</span>, <span class="dv">6</span>, <span class="dv">6</span>, <span class="dv">8</span>, <span class="dv">9</span>, <span class="dv">6</span>, <span class="dv">8</span>, <span class="dv">8</span>, <span class="dv">8</span>, <span class="dv">8</span>, <span class="dv">7</span>, <span class="dv">5</span>, <span class="dv">6</span>, <span class="dv">9</span>, <span class="dv">9</span>, <span class="dv">5</span>, <span class="dv">5</span>, <span class="dv">4</span>, <span class="dv">7</span>, <span class="dv">9</span>, <span class="dv">3</span>, <span class="dv">9</span>, <span class="dv">5</span>, <span class="dv">8</span>, <span class="dv">9</span>, <span class="dv">5</span>, <span class="dv">9</span>, <span class="dv">8</span>, <span class="dv">7</span>, <span class="dv">5</span>, <span class="dv">8</span>, <span class="dv">9</span>, <span class="dv">8</span>, <span class="dv">8</span>, <span class="dv">8</span>, <span class="dv">9</span>, <span class="dv">8</span>, <span class="dv">5</span>, <span class="dv">8</span>, <span class="dv">5</span>, <span class="dv">9</span>, <span class="dv">7</span>, <span class="dv">8</span>, <span class="dv">6</span>, <span class="dv">8</span>, <span class="dv">5</span>, <span class="dv">9</span>, <span class="dv">9</span>, <span class="dv">8</span>, <span class="dv">6</span>, <span class="dv">9</span>, <span class="dv">9</span>, <span class="dv">7</span>, <span class="dv">4</span>, <span class="dv">8</span>, <span class="dv">8</span>, <span class="dv">8</span>, <span class="dv">6</span>, <span class="dv">4</span>, <span class="dv">8</span>, <span class="dv">6</span>, <span class="dv">9</span>, <span class="dv">7</span>, <span class="dv">5</span>, <span class="dv">9</span>, <span class="dv">8</span>, <span class="dv">8</span>, <span class="dv">9</span>, <span class="dv">9</span>, <span class="dv">9</span>, <span class="dv">7</span>, <span class="dv">5</span>, <span class="dv">5</span>, <span class="dv">9</span>, <span class="dv">6</span>, <span class="dv">7</span>, <span class="dv">6</span>, <span class="dv">8</span>, <span class="dv">8</span>, <span class="dv">7</span>, <span class="dv">8</span>, <span class="dv">7</span>, <span class="dv">9</span>, <span class="dv">5</span>, <span class="dv">9</span>, <span class="dv">9</span>, <span class="dv">9</span>, <span class="dv">7</span>, <span class="dv">8</span>, <span class="dv">8</span>, <span class="dv">9</span>, <span class="dv">9</span>, <span class="dv">9</span>, <span class="dv">7</span>, <span class="dv">8</span>, <span class="dv">8</span>, <span class="dv">7</span>, <span class="dv">9</span>, <span class="dv">4</span>, <span class="dv">9</span>, <span class="dv">6</span>, <span class="dv">8</span>, <span class="dv">6</span>, <span class="dv">7</span>, <span class="dv">7</span>, <span class="dv">8</span>, <span class="dv">7</span>, <span class="dv">7</span>, <span class="dv">7</span>, <span class="dv">7</span>, <span class="dv">8</span>, <span class="dv">7</span>, <span class="dv">5</span>, <span class="dv">8</span>, <span class="dv">7</span>, <span class="dv">9</span>, <span class="dv">7</span>, <span class="dv">7</span>, <span class="dv">6</span>, <span class="dv">8</span>, <span class="dv">8</span>, <span class="dv">8</span>, <span class="dv">9</span>, <span class="dv">7</span>, <span class="dv">8</span>, <span class="dv">9</span>, <span class="dv">8</span>, <span class="dv">8</span>, <span class="dv">9</span>, <span class="dv">8</span>, <span class="dv">6</span>, <span class="dv">6</span>, <span class="dv">8</span>, <span class="dv">9</span>, <span class="dv">5</span>, <span class="dv">7</span>, <span class="dv">9</span>, <span class="dv">6</span>, <span class="dv">9</span>, <span class="dv">9</span>, <span class="dv">9</span>, <span class="dv">6</span>, <span class="dv">8</span>, <span class="dv">9</span>, <span class="dv">8</span>, <span class="dv">8</span>, <span class="dv">9</span>, <span class="dv">9</span>, <span class="dv">9</span>, <span class="dv">7</span>, <span class="dv">8</span>, <span class="dv">6</span>, <span class="dv">9</span>, <span class="dv">9</span>, <span class="dv">9</span>, <span class="dv">7</span>, <span class="dv">8</span>, <span class="dv">5</span>, <span class="dv">8</span>, <span class="dv">9</span>, <span class="dv">6</span>, <span class="dv">9</span>, <span class="dv">6</span>, <span class="dv">8</span>, <span class="dv">5</span>, <span class="dv">7</span>, <span class="dv">7</span>, <span class="dv">4</span>, <span class="dv">9</span>, <span class="dv">8</span>, <span class="dv">9</span>, <span class="dv">9</span>, <span class="dv">9</span>, <span class="dv">5</span>, <span class="dv">9</span>, <span class="dv">7</span>, <span class="dv">6</span>, <span class="dv">9</span>, <span class="dv">9</span>, <span class="dv">9</span>, <span class="dv">7</span>, <span class="dv">5</span>, <span class="dv">8</span>, <span class="dv">9</span>, <span class="dv">7</span>, <span class="dv">9</span>, <span class="dv">8</span>, <span class="dv">9</span>, <span class="dv">6</span>, <span class="dv">6</span>, <span class="dv">8</span>, <span class="dv">9</span>, <span class="dv">5</span>, <span class="dv">6</span>, <span class="dv">6</span>, <span class="dv">9</span>, <span class="dv">7</span>, <span class="dv">9</span>, <span class="dv">8</span>, <span class="dv">5</span>, <span class="dv">7</span>, <span class="dv">6</span>, <span class="dv">9</span>, <span class="dv">7</span>, <span class="dv">9</span>, <span class="dv">9</span>, <span class="dv">8</span>, <span class="dv">9</span>, <span class="dv">7</span>, <span class="dv">9</span>, <span class="dv">4</span>, <span class="dv">9</span>, <span class="dv">5</span>, <span class="dv">8</span>, <span class="dv">9</span>, <span class="dv">8</span>, <span class="dv">3</span>, <span class="dv">9</span>, <span class="dv">8</span>, <span class="dv">6</span>, <span class="dv">9</span>, <span class="dv">8</span>, <span class="dv">8</span>, <span class="dv">7</span>, <span class="dv">6</span>, <span class="dv">8</span>, <span class="dv">9</span>, <span class="dv">4</span>, <span class="dv">7</span>, <span class="dv">8</span>, <span class="dv">8</span>, <span class="dv">9</span>, <span class="dv">6</span>, <span class="dv">8</span>, <span class="dv">6</span>, <span class="dv">8</span>, <span class="dv">9</span>, <span class="dv">8</span>, <span class="dv">7</span>, <span class="dv">9</span>, <span class="dv">8</span>, <span class="dv">7</span>, <span class="dv">9</span>, <span class="dv">8</span>, <span class="dv">9</span>, <span class="dv">6</span>, <span class="dv">8</span>, <span class="dv">9</span>, <span class="dv">8</span>, <span class="dv">9</span>, <span class="dv">9</span>, <span class="dv">8</span>, <span class="dv">7</span>, <span class="dv">5</span>, <span class="dv">7</span>, <span class="dv">8</span>, <span class="dv">9</span>, <span class="dv">9</span>, <span class="dv">6</span>, <span class="dv">8</span>, <span class="dv">7</span>, <span class="dv">9</span>, <span class="dv">7</span>, <span class="dv">7</span>, <span class="dv">5</span>, <span class="dv">9</span>, <span class="dv">9</span>, <span class="dv">8</span>, <span class="dv">8</span>, <span class="dv">9</span>, <span class="dv">6</span>, <span class="dv">7</span>, <span class="dv">5</span>, <span class="dv">9</span>, <span class="dv">5</span>, <span class="dv">7</span>, <span class="dv">6</span>, <span class="dv">8</span>, <span class="dv">7</span>, <span class="dv">8</span>, <span class="dv">4</span>, <span class="dv">8</span>, <span class="dv">5</span>, <span class="dv">8</span>, <span class="dv">7</span>, <span class="dv">7</span>, <span class="dv">9</span>, <span class="dv">9</span>, <span class="dv">8</span>, <span class="dv">9</span>, <span class="dv">6</span>, <span class="dv">8</span>, <span class="dv">9</span>, <span class="dv">4</span>, <span class="dv">6</span>, <span class="dv">7</span>, <span class="dv">9</span>, <span class="dv">8</span>, <span class="dv">6</span>, <span class="dv">8</span>, <span class="dv">7</span>, <span class="dv">5</span>, <span class="dv">8</span>, <span class="dv">7</span>, <span class="dv">11</span>, <span class="dv">10</span>, <span class="dv">14</span>, <span class="dv">11</span>, <span class="dv">11</span>, <span class="dv">12</span>, <span class="dv">10</span>, <span class="dv">11</span>, <span class="dv">10</span>, <span class="dv">14</span>, <span class="dv">13</span>, <span class="dv">14</span>, <span class="dv">12</span>, <span class="dv">12</span>, <span class="dv">10</span>, <span class="dv">13</span>, <span class="dv">10</span>, <span class="dv">11</span>, <span class="dv">10</span>, <span class="dv">11</span>, <span class="dv">10</span>, <span class="dv">13</span>, <span class="dv">14</span>, <span class="dv">11</span>, <span class="dv">10</span>, <span class="dv">11</span>, <span class="dv">13</span>, <span class="dv">10</span>, <span class="dv">10</span>, <span class="dv">12</span>, <span class="dv">10</span>, <span class="dv">10</span>, <span class="dv">10</span>, <span class="dv">11</span>, <span class="dv">11</span>, <span class="dv">11</span>, <span class="dv">10</span>, <span class="dv">11</span>, <span class="dv">11</span>, <span class="dv">13</span>, <span class="dv">13</span>, <span class="dv">11</span>, <span class="dv">11</span>, <span class="dv">14</span>, <span class="dv">11</span>, <span class="dv">10</span>, <span class="dv">10</span>, <span class="dv">10</span>, <span class="dv">14</span>, <span class="dv">13</span>, <span class="dv">10</span>, <span class="dv">14</span>, <span class="dv">10</span>, <span class="dv">11</span>, <span class="dv">13</span>, <span class="dv">12</span>, <span class="dv">13</span>, <span class="dv">10</span>, <span class="dv">13</span>, <span class="dv">11</span>, <span class="dv">14</span>, <span class="dv">11</span>, <span class="dv">13</span>, <span class="dv">11</span>, <span class="dv">11</span>, <span class="dv">10</span>, <span class="dv">11</span>, <span class="dv">11</span>, <span class="dv">10</span>, <span class="dv">11</span>, <span class="dv">13</span>, <span class="dv">12</span>, <span class="dv">10</span>, <span class="dv">10</span>, <span class="dv">14</span>, <span class="dv">11</span>, <span class="dv">10</span>, <span class="dv">11</span>, <span class="dv">10</span>, <span class="dv">11</span>, <span class="dv">13</span>, <span class="dv">13</span>, <span class="dv">10</span>, <span class="dv">11</span>, <span class="dv">11</span>, <span class="dv">12</span>, <span class="dv">10</span>, <span class="dv">10</span>, <span class="dv">11</span>, <span class="dv">10</span>, <span class="dv">11</span>, <span class="dv">14</span>, <span class="dv">13</span>, <span class="dv">12</span>, <span class="dv">11</span>, <span class="dv">11</span>, <span class="dv">11</span>, <span class="dv">14</span>, <span class="dv">12</span>, <span class="dv">10</span>, <span class="dv">12</span>, <span class="dv">11</span>, <span class="dv">10</span>, <span class="dv">11</span>, <span class="dv">13</span>, <span class="dv">10</span>, <span class="dv">10</span>, <span class="dv">11</span>, <span class="dv">13</span>, <span class="dv">10</span>, <span class="dv">11</span>, <span class="dv">10</span>, <span class="dv">13</span>, <span class="dv">11</span>, <span class="dv">10</span>, <span class="dv">11</span>, <span class="dv">11</span>, <span class="dv">14</span>, <span class="dv">11</span>, <span class="dv">13</span>, <span class="dv">11</span>, <span class="dv">11</span>, <span class="dv">10</span>, <span class="dv">13</span>, <span class="dv">10</span>, <span class="dv">13</span>, <span class="dv">10</span>, <span class="dv">12</span>, <span class="dv">10</span>, <span class="dv">14</span>, <span class="dv">12</span>, <span class="dv">10</span>, <span class="dv">11</span>, <span class="dv">14</span>, <span class="dv">12</span>, <span class="dv">10</span>, <span class="dv">10</span>, <span class="dv">10</span>, <span class="dv">10</span>, <span class="dv">12</span>, <span class="dv">13</span>, <span class="dv">11</span>, <span class="dv">12</span>, <span class="dv">11</span>, <span class="dv">12</span>, <span class="dv">11</span>, <span class="dv">11</span>, <span class="dv">12</span>, <span class="dv">12</span>, <span class="dv">13</span>, <span class="dv">11</span>, <span class="dv">12</span>, <span class="dv">10</span>, <span class="dv">12</span>, <span class="dv">13</span>, <span class="dv">10</span>, <span class="dv">12</span>, <span class="dv">10</span>,<span class="dv">12</span>, <span class="dv">10</span>, <span class="dv">11</span>, <span class="dv">10</span>, <span class="dv">12</span>, <span class="dv">14</span>, <span class="dv">10</span>, <span class="dv">10</span>, <span class="dv">12</span>, <span class="dv">10</span>, <span class="dv">10</span>, <span class="dv">13</span>, <span class="dv">12</span>, <span class="dv">12</span>, <span class="dv">11</span>, <span class="dv">13</span>, <span class="dv">12</span>, <span class="dv">10</span>, <span class="dv">11</span>, <span class="dv">11</span>, <span class="dv">13</span>, <span class="dv">12</span>, <span class="dv">13</span>, <span class="dv">13</span>, <span class="dv">10</span>, <span class="dv">12</span>, <span class="dv">12</span>, <span class="dv">14</span>, <span class="dv">11</span>, <span class="dv">10</span>, <span class="dv">13</span>, <span class="dv">11</span>, <span class="dv">11</span>, <span class="dv">13</span>, <span class="dv">12</span>, <span class="dv">10</span>, <span class="dv">10</span>, <span class="dv">12</span>, <span class="dv">13</span>, <span class="dv">11</span>, <span class="dv">10</span>, <span class="dv">11</span>, <span class="dv">11</span>, <span class="dv">11</span>, <span class="dv">11</span>, <span class="dv">11</span>, <span class="dv">14</span>, <span class="dv">12</span>, <span class="dv">13</span>, <span class="dv">13</span>, <span class="dv">10</span>, <span class="dv">12</span>, <span class="dv">10</span>, <span class="dv">10</span>, <span class="dv">12</span>, <span class="dv">11</span>, <span class="dv">12</span>, <span class="dv">11</span>, <span class="dv">11</span>, <span class="dv">12</span>, <span class="dv">12</span>, <span class="dv">14</span>, <span class="dv">11</span>, <span class="dv">10</span>, <span class="dv">11</span>, <span class="dv">12</span>, <span class="dv">13</span>, <span class="dv">12</span>, <span class="dv">11</span>, <span class="dv">11</span>, <span class="dv">11</span>, <span class="dv">14</span>, <span class="dv">11</span>, <span class="dv">13</span>, <span class="dv">12</span>, <span class="dv">10</span>, <span class="dv">12</span>, <span class="dv">13</span>, <span class="dv">10</span>, <span class="dv">10</span>, <span class="dv">10</span>, <span class="dv">10</span>, <span class="dv">14</span>, <span class="dv">12</span>, <span class="dv">11</span>, <span class="dv">11</span>, <span class="dv">12</span>, <span class="dv">14</span>, <span class="dv">14</span>, <span class="dv">10</span>, <span class="dv">11</span>, <span class="dv">11</span>, <span class="dv">10</span>, <span class="dv">10</span>, <span class="dv">12</span>, <span class="dv">12</span>, <span class="dv">11</span>, <span class="dv">12</span>, <span class="dv">10</span>, <span class="dv">12</span>, <span class="dv">13</span>, <span class="dv">10</span>, <span class="dv">12</span>, <span class="dv">10</span>, <span class="dv">13</span>, <span class="dv">12</span>, <span class="dv">10</span>, <span class="dv">12</span>, <span class="dv">10</span>, <span class="dv">11</span>, <span class="dv">12</span>, <span class="dv">11</span>, <span class="dv">12</span>, <span class="dv">10</span>, <span class="dv">13</span>, <span class="dv">12</span>, <span class="dv">11</span>, <span class="dv">11</span>, <span class="dv">11</span>, <span class="dv">11</span>, <span class="dv">12</span>, <span class="dv">14</span>, <span class="dv">11</span>, <span class="dv">11</span>, <span class="dv">12</span>, <span class="dv">14</span>, <span class="dv">11</span>, <span class="dv">13</span>, <span class="dv">11</span>, <span class="dv">10</span>, <span class="dv">13</span>, <span class="dv">12</span>, <span class="dv">11</span>, <span class="dv">13</span>, <span class="dv">14</span>, <span class="dv">10</span>, <span class="dv">11</span>, <span class="dv">11</span>, <span class="dv">15</span>, <span class="dv">15</span>, <span class="dv">18</span>, <span class="dv">19</span>, <span class="dv">19</span>, <span class="dv">16</span>, <span class="dv">17</span>, <span class="dv">15</span>, <span class="dv">15</span>, <span class="dv">15</span>, <span class="dv">15</span>, <span class="dv">15</span>, <span class="dv">19</span>, <span class="dv">18</span>, <span class="dv">16</span>, <span class="dv">17</span>, <span class="dv">16</span>, <span class="dv">15</span>, <span class="dv">15</span>, <span class="dv">15</span>, <span class="dv">18</span>, <span class="dv">17</span>, <span class="dv">15</span>, <span class="dv">17</span>, <span class="dv">17</span>, <span class="dv">16</span>, <span class="dv">17</span>, <span class="dv">15</span>, <span class="dv">15</span>, <span class="dv">16</span>, <span class="dv">16</span>, <span class="dv">15</span>, <span class="dv">18</span>, <span class="dv">15</span>, <span class="dv">16</span>, <span class="dv">17</span>, <span class="dv">16</span>, <span class="dv">16</span>, <span class="dv">15</span>, <span class="dv">18</span>, <span class="dv">15</span>, <span class="dv">16</span>, <span class="dv">17</span>, <span class="dv">16</span>, <span class="dv">16</span>, <span class="dv">15</span>, <span class="dv">18</span>, <span class="dv">16</span>, <span class="dv">15</span>)</span>
<span id="cb315-6"><a href="kvantitativa-variabler.html#cb315-6" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb315-7"><a href="kvantitativa-variabler.html#cb315-7" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb315-8"><a href="kvantitativa-variabler.html#cb315-8" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb315-9"><a href="kvantitativa-variabler.html#cb315-9" aria-hidden="true" tabindex="-1"></a>height <span class="ot"><-</span> <span class="fu">c</span>(<span class="dv">57</span>, <span class="fl">67.5</span>, <span class="fl">54.5</span>, <span class="dv">53</span>, <span class="dv">57</span>, <span class="dv">61</span>, <span class="dv">58</span>, <span class="dv">56</span>, <span class="fl">58.5</span>, <span class="dv">60</span>, <span class="dv">53</span>, <span class="dv">54</span>, <span class="fl">58.5</span>, <span class="fl">60.5</span>, <span class="dv">58</span>, <span class="dv">53</span>, <span class="dv">50</span>, <span class="dv">53</span>, <span class="dv">59</span>, <span class="fl">61.5</span>, <span class="dv">49</span>, <span class="fl">52.5</span>, <span class="dv">48</span>, <span class="fl">62.5</span>, <span class="dv">65</span>, <span class="fl">51.5</span>, <span class="dv">60</span>, <span class="dv">52</span>, <span class="dv">60</span>, <span class="dv">60</span>, <span class="dv">49</span>, <span class="fl">65.5</span>, <span class="dv">60</span>, <span class="fl">57.5</span>, <span class="dv">52</span>, <span class="dv">59</span>, <span class="dv">59</span>, <span class="dv">55</span>, <span class="dv">57</span>, <span class="dv">57</span>, <span class="dv">60</span>, <span class="dv">59</span>, <span class="dv">51</span>, <span class="dv">57</span>, <span class="dv">50</span>, <span class="dv">57</span>, <span class="dv">54</span>, <span class="fl">52.5</span>, <span class="dv">55</span>, <span class="fl">60.5</span>, <span class="fl">54.5</span>, <span class="fl">61.5</span>, <span class="dv">62</span>, <span class="fl">54.5</span>, <span class="dv">54</span>, <span class="dv">57</span>, <span class="fl">62.5</span>, <span class="dv">60</span>, <span class="dv">50</span>, <span class="fl">57.5</span>, <span class="dv">60</span>, <span class="dv">60</span>, <span class="dv">51</span>, <span class="dv">49</span>, <span class="dv">59</span>, <span class="fl">57.5</span>, <span class="dv">58</span>, <span class="fl">55.5</span>, <span class="dv">52</span>, <span class="fl">60.5</span>, <span class="dv">57</span>, <span class="dv">58</span>, <span class="dv">60</span>, <span class="dv">59</span>, <span class="fl">59.5</span>, <span class="dv">56</span>, <span class="dv">53</span>, <span class="dv">51</span>, <span class="dv">69</span>, <span class="dv">53</span>, <span class="dv">57</span>, <span class="dv">53</span>, <span class="dv">63</span>, <span class="fl">54.5</span>, <span class="dv">58</span>, <span class="dv">63</span>, <span class="dv">52</span>, <span class="fl">61.5</span>, <span class="fl">52.5</span>, <span class="dv">62</span>, <span class="fl">61.5</span>, <span class="fl">64.5</span>, <span class="fl">57.5</span>, <span class="dv">60</span>, <span class="dv">60</span>, <span class="dv">61</span>, <span class="dv">58</span>, <span class="fl">61.5</span>, <span class="dv">55</span>, <span class="dv">55</span>, <span class="dv">52</span>, <span class="dv">54</span>, <span class="dv">63</span>, <span class="dv">47</span>, <span class="fl">60.5</span>, <span class="dv">56</span>, <span class="fl">58.5</span>, <span class="dv">55</span>, <span class="fl">58.5</span>, <span class="dv">51</span>, <span class="fl">59.5</span>, <span class="dv">54</span>, <span class="dv">58</span>, <span class="dv">58</span>, <span class="fl">52.5</span>, <span class="fl">60.5</span>, <span class="fl">54.5</span>, <span class="fl">46.5</span>, <span class="fl">56.5</span>, <span class="dv">55</span>, <span class="dv">57</span>, <span class="fl">54.5</span>, <span class="dv">54</span>, <span class="dv">53</span>, <span class="dv">57</span>, <span class="dv">59</span>, <span class="dv">55</span>, <span class="fl">55.5</span>, <span class="fl">51.5</span>, <span class="dv">61</span>, <span class="fl">63.5</span>, <span class="fl">57.5</span>, <span class="dv">53</span>, <span class="fl">56.5</span>, <span class="dv">54</span>, <span class="dv">52</span>, <span class="dv">53</span>, <span class="fl">61.5</span>, <span class="fl">58.5</span>, <span class="dv">52</span>, <span class="dv">58</span>, <span class="dv">61</span>, <span class="dv">51</span>, <span class="dv">62</span>, <span class="fl">64.5</span>, <span class="fl">58.5</span>, <span class="fl">52.5</span>, <span class="dv">58</span>, <span class="dv">66</span>, <span class="fl">63.5</span>, <span class="dv">64</span>, <span class="fl">58.5</span>, <span class="dv">64</span>, <span class="fl">60.5</span>, <span class="dv">55</span>, <span class="dv">53</span>, <span class="dv">48</span>, <span class="fl">58.5</span>, <span class="fl">64.5</span>, <span class="fl">60.5</span>, <span class="dv">56</span>, <span class="fl">58.5</span>, <span class="dv">54</span>, <span class="dv">58</span>, <span class="fl">64.5</span>, <span class="fl">50.5</span>, <span class="dv">60</span>, <span class="fl">51.5</span>, <span class="dv">59</span>, <span class="dv">53</span>, <span class="dv">53</span>, <span class="fl">53.5</span>, <span class="dv">52</span>, <span class="dv">64</span>, <span class="dv">63</span>, <span class="dv">58</span>, <span class="fl">58.5</span>, <span class="fl">59.5</span>, <span class="dv">51</span>, <span class="fl">57.5</span>, <span class="dv">47</span>, <span class="fl">55.5</span>, <span class="dv">57</span>, <span class="dv">61</span>, <span class="fl">55.5</span>, <span class="fl">53.5</span>, <span class="dv">50</span>, <span class="fl">61.5</span>, <span class="fl">61.5</span>, <span class="dv">55</span>, <span class="dv">58</span>, <span class="fl">56.5</span>, <span class="dv">57</span>, <span class="dv">52</span>, <span class="fl">52.5</span>, <span class="fl">62.5</span>, <span class="dv">65</span>, <span class="dv">50</span>, <span class="fl">57.5</span>, <span class="fl">56.5</span>, <span class="fl">57.5</span>, <span class="dv">54</span>, <span class="fl">59.5</span>, <span class="fl">59.5</span>, <span class="dv">58</span>, <span class="dv">57</span>, <span class="dv">55</span>, <span class="dv">60</span>, <span class="fl">56.5</span>, <span class="dv">60</span>, <span class="dv">59</span>, <span class="dv">63</span>, <span class="dv">59</span>, <span class="dv">53</span>, <span class="fl">61.5</span>, <span class="dv">48</span>, <span class="dv">63</span>, <span class="fl">55.5</span>, <span class="fl">64.5</span>, <span class="dv">59</span>, <span class="fl">58.5</span>, <span class="dv">46</span>, <span class="dv">62</span>, <span class="dv">53</span>, <span class="fl">49.5</span>, <span class="dv">68</span>, <span class="fl">59.5</span>, <span class="fl">55.5</span>, <span class="dv">55</span>, <span class="fl">51.5</span>, <span class="dv">56</span>, <span class="dv">63</span>, <span class="dv">48</span>, <span class="fl">56.5</span>, <span class="dv">59</span>, <span class="fl">60.5</span>, <span class="dv">65</span>, <span class="dv">55</span>, <span class="dv">55</span>, <span class="dv">51</span>, <span class="fl">52.5</span>, <span class="dv">64</span>, <span class="dv">59</span>, <span class="fl">53.5</span>, <span class="fl">60.5</span>, <span class="fl">59.5</span>, <span class="fl">56.5</span>, <span class="dv">63</span>, <span class="fl">56.5</span>, <span class="fl">61.5</span>, <span class="dv">52</span>, <span class="dv">57</span>, <span class="fl">63.5</span>, <span class="dv">63</span>, <span class="dv">65</span>, <span class="fl">61.5</span>, <span class="dv">62</span>, <span class="dv">55</span>, <span class="dv">51</span>, <span class="dv">54</span>, <span class="dv">57</span>, <span class="dv">56</span>, <span class="fl">61.5</span>, <span class="dv">53</span>, <span class="dv">59</span>, <span class="dv">56</span>, <span class="dv">59</span>, <span class="fl">52.5</span>, <span class="fl">52.5</span>, <span class="dv">50</span>, <span class="fl">59.5</span>, <span class="dv">64</span>, <span class="dv">61</span>, <span class="fl">57.5</span>, <span class="dv">60</span>, <span class="dv">55</span>, <span class="dv">56</span>, <span class="dv">51</span>, <span class="fl">59.5</span>, <span class="fl">50.5</span>, <span class="fl">57.5</span>, <span class="dv">54</span>, <span class="dv">57</span>, <span class="dv">58</span>, <span class="dv">60</span>, <span class="dv">49</span>, <span class="dv">57</span>, <span class="dv">52</span>, <span class="dv">52</span>, <span class="fl">59.5</span>, <span class="dv">58</span>, <span class="dv">64</span>, <span class="dv">57</span>, <span class="dv">53</span>, <span class="dv">62</span>, <span class="dv">53</span>, <span class="fl">56.5</span>, <span class="dv">57</span>, <span class="dv">48</span>, <span class="fl">49.5</span>, <span class="dv">51</span>, <span class="fl">59.5</span>, <span class="dv">56</span>, <span class="dv">54</span>, <span class="fl">57.5</span>, <span class="fl">55.5</span>, <span class="dv">50</span>, <span class="dv">60</span>, <span class="dv">57</span>, <span class="dv">69</span>, <span class="dv">64</span>, <span class="dv">63</span>, <span class="dv">58</span>, <span class="fl">66.5</span>, <span class="fl">60.5</span>, <span class="dv">57</span>, <span class="dv">64</span>, <span class="dv">61</span>, <span class="fl">68.5</span>, <span class="fl">69.5</span>, <span class="dv">72</span>, <span class="dv">71</span>, <span class="dv">63</span>, <span class="fl">61.5</span>, <span class="fl">63.5</span>, <span class="dv">62</span>, <span class="dv">65</span>, <span class="dv">61</span>, <span class="dv">63</span>, <span class="dv">66</span>, <span class="dv">68</span>, <span class="dv">66</span>, <span class="dv">72</span>, <span class="dv">66</span>, <span class="dv">67</span>, <span class="dv">64</span>, <span class="fl">60.5</span>, <span class="dv">63</span>, <span class="dv">64</span>, <span class="fl">60.5</span>, <span class="dv">62</span>, <span class="dv">60</span>, <span class="fl">64.5</span>, <span class="dv">67</span>, <span class="fl">61.5</span>, <span class="dv">66</span>, <span class="dv">60</span>, <span class="dv">64</span>, <span class="fl">68.5</span>, <span class="dv">67</span>, <span class="dv">67</span>, <span class="dv">66</span>, <span class="fl">62.5</span>, <span class="dv">61</span>, <span class="dv">62</span>, <span class="fl">66.5</span>, <span class="dv">60</span>, <span class="dv">64</span>, <span class="dv">62</span>, <span class="dv">58</span>, <span class="fl">68.5</span>, <span class="fl">61.5</span>, <span class="fl">64.5</span>, <span class="dv">67</span>, <span class="fl">68.5</span>, <span class="dv">61</span>, <span class="dv">65</span>, <span class="dv">70</span>, <span class="dv">60</span>, <span class="dv">72</span>, <span class="dv">59</span>, <span class="dv">69</span>, <span class="fl">67.5</span>, <span class="fl">65.5</span>, <span class="fl">65.5</span>, <span class="fl">64.5</span>, <span class="dv">62</span>, <span class="fl">65.5</span>, <span class="fl">67.5</span>, <span class="dv">68</span>, <span class="fl">63.5</span>, <span class="fl">58.5</span>, <span class="fl">65.5</span>, <span class="dv">65</span>, <span class="fl">70.5</span>, <span class="dv">63</span>, <span class="fl">63.5</span>, <span class="dv">66</span>, <span class="dv">63</span>, <span class="fl">67.5</span>, <span class="fl">61.5</span>, <span class="dv">60</span>, <span class="fl">64.5</span>, <span class="fl">68.5</span>, <span class="fl">64.5</span>, <span class="dv">61</span>, <span class="dv">57</span>, <span class="fl">62.5</span>, <span class="dv">58</span>, <span class="fl">62.5</span>, <span class="fl">72.5</span>, <span class="fl">65.5</span>, <span class="fl">69.5</span>, <span class="fl">66.5</span>, <span class="dv">59</span>, <span class="dv">68</span>, <span class="dv">67</span>, <span class="dv">63</span>, <span class="fl">64.5</span>, <span class="dv">62</span>, <span class="dv">62</span>, <span class="dv">66</span>, <span class="dv">62</span>, <span class="fl">62.5</span>, <span class="dv">57</span>, <span class="fl">68.5</span>, <span class="dv">59</span>, <span class="fl">61.5</span>, <span class="dv">65</span>, <span class="fl">66.5</span>, <span class="dv">65</span>, <span class="dv">68</span>, <span class="dv">67</span>, <span class="fl">64.5</span>, <span class="dv">70</span>, <span class="dv">60</span>, <span class="dv">64</span>, <span class="fl">62.5</span>, <span class="dv">61</span>, <span class="dv">64</span>, <span class="fl">65.5</span>, <span class="dv">61</span>, <span class="fl">65.4</span>, <span class="fl">63.5</span>, <span class="fl">67.5</span>, <span class="dv">66</span>, <span class="dv">62</span>, <span class="fl">61.5</span>, <span class="dv">69</span>, <span class="dv">66</span>, <span class="dv">66</span>, <span class="dv">69</span>, <span class="dv">71</span>, <span class="fl">60.5</span>, <span class="dv">58</span>, <span class="dv">63</span>, <span class="dv">69</span>, <span class="fl">59.5</span>, <span class="dv">64</span>, <span class="dv">74</span>, <span class="fl">64.5</span>, <span class="dv">70</span>, <span class="dv">67</span>, <span class="fl">64.5</span>, <span class="dv">65</span>, <span class="fl">62.5</span>, <span class="dv">68</span>, <span class="fl">68.5</span>, <span class="fl">67.5</span>, <span class="dv">60</span>, <span class="dv">68</span>, <span class="dv">65</span>, <span class="dv">64</span>, <span class="dv">73</span>, <span class="dv">59</span>, <span class="fl">70.5</span>, <span class="dv">66</span>, <span class="fl">61.5</span>, <span class="dv">67</span>, <span class="fl">62.5</span>, <span class="fl">52.5</span>, <span class="dv">72</span>, <span class="dv">71</span>, <span class="fl">65.5</span>, <span class="dv">60</span>, <span class="dv">60</span>, <span class="fl">60.5</span>, <span class="dv">59</span>, <span class="dv">68</span>, <span class="dv">62</span>, <span class="fl">64.5</span>, <span class="dv">63</span>, <span class="dv">66</span>, <span class="dv">67</span>, <span class="dv">57</span>, <span class="dv">63</span>, <span class="dv">62</span>, <span class="dv">65</span>, <span class="fl">68.5</span>, <span class="dv">69</span>, <span class="dv">71</span>, <span class="dv">58</span>, <span class="fl">63.5</span>, <span class="fl">66.5</span>, <span class="dv">67</span>, <span class="dv">64</span>, <span class="dv">61</span>, <span class="dv">67</span>, <span class="fl">67.5</span>, <span class="dv">68</span>, <span class="fl">66.5</span>, <span class="dv">67</span>, <span class="fl">60.5</span>, <span class="dv">70</span>, <span class="fl">63.5</span>, <span class="dv">65</span>, <span class="dv">63</span>, <span class="dv">61</span>, <span class="fl">65.5</span>, <span class="fl">67.5</span>, <span class="dv">61</span>, <span class="dv">63</span>, <span class="fl">63.5</span>, <span class="dv">70</span>, <span class="fl">71.5</span>, <span class="fl">65.5</span>, <span class="dv">74</span>, <span class="dv">68</span>, <span class="dv">61</span>, <span class="dv">61</span>, <span class="dv">61</span>, <span class="fl">61.5</span>, <span class="dv">67</span>, <span class="dv">63</span>, <span class="fl">67.5</span>, <span class="fl">70.5</span>, <span class="fl">70.5</span>, <span class="dv">62</span>, <span class="dv">62</span>, <span class="fl">61.5</span>, <span class="dv">62</span>, <span class="fl">60.5</span>, <span class="fl">62.5</span>, <span class="dv">63</span>, <span class="dv">63</span>, <span class="dv">62</span>, <span class="fl">65.5</span>, <span class="dv">65</span>, <span class="dv">70</span>, <span class="dv">66</span>, <span class="dv">63</span>, <span class="dv">68</span>, <span class="dv">59</span>, <span class="fl">68.5</span>, <span class="dv">63</span>, <span class="dv">63</span>, <span class="dv">66</span>, <span class="dv">62</span>, <span class="dv">68</span>, <span class="fl">72.5</span>, <span class="dv">64</span>, <span class="fl">65.5</span>, <span class="fl">61.5</span>, <span class="dv">57</span>, <span class="dv">64</span>, <span class="dv">66</span>, <span class="fl">64.5</span>, <span class="dv">67</span>, <span class="dv">72</span>, <span class="dv">65</span>, <span class="dv">63</span>, <span class="dv">62</span>, <span class="dv">71</span>, <span class="dv">61</span>, <span class="fl">65.5</span>, <span class="dv">62</span>, <span class="fl">65.5</span>, <span class="fl">70.5</span>, <span class="dv">62</span>, <span class="fl">65.5</span>, <span class="dv">65</span>, <span class="dv">61</span>, <span class="fl">69.5</span>, <span class="dv">65</span>, <span class="fl">65.5</span>, <span class="fl">63.5</span>, <span class="fl">60.5</span>, <span class="dv">65</span>, <span class="dv">67</span>, <span class="fl">63.5</span>, <span class="fl">59.5</span>, <span class="fl">63.5</span>, <span class="dv">61</span>, <span class="dv">66</span>, <span class="dv">64</span>, <span class="dv">62</span>, <span class="fl">60.5</span>, <span class="dv">71</span>, <span class="fl">64.5</span>, <span class="dv">61</span>, <span class="fl">62.5</span>, <span class="fl">64.5</span>, <span class="dv">68</span>, <span class="fl">68.5</span>, <span class="dv">62</span>, <span class="dv">60</span>, <span class="fl">59.5</span>, <span class="dv">61</span>, <span class="dv">63</span>, <span class="fl">67.5</span>, <span class="dv">69</span>, <span class="dv">68</span>, <span class="dv">58</span>, <span class="dv">65</span>, <span class="dv">69</span>, <span class="dv">70</span>, <span class="dv">71</span>, <span class="dv">66</span>, <span class="dv">72</span>, <span class="dv">66</span>, <span class="dv">68</span>, <span class="dv">70</span>, <span class="fl">67.5</span>, <span class="dv">70</span>, <span class="dv">64</span>, <span class="dv">66</span>, <span class="dv">62</span>, <span class="fl">65.5</span>, <span class="fl">64.5</span>, <span class="fl">66.5</span>, <span class="dv">67</span>, <span class="dv">63</span>, <span class="dv">64</span>, <span class="dv">69</span>, <span class="dv">71</span>, <span class="dv">68</span>, <span class="fl">70.5</span>, <span class="dv">67</span>, <span class="dv">69</span>, <span class="dv">62</span>, <span class="fl">67.5</span>, <span class="dv">73</span>, <span class="dv">64</span>, <span class="fl">68.5</span>, <span class="dv">62</span>, <span class="fl">73.5</span>, <span class="fl">66.5</span>, <span class="dv">67</span>, <span class="dv">63</span>, <span class="fl">69.5</span>, <span class="dv">70</span>, <span class="dv">66</span>, <span class="dv">66</span>, <span class="dv">63</span>, <span class="fl">70.5</span>, <span class="dv">60</span>, <span class="dv">72</span>, <span class="dv">70</span>, <span class="dv">72</span>, <span class="dv">67</span>, <span class="dv">68</span>, <span class="dv">60</span>, <span class="dv">63</span>, <span class="fl">66.5</span>)</span></code></pre></div>
</div>
</div>
<p></br></p>
<div id="analys-av-en-kvantitativ-variabel" class="section level2 hasAnchor" number="6.1">
<h2><span class="header-section-number">6.1</span> Analys av en kvantitativ variabel<a href="kvantitativa-variabler.html#analys-av-en-kvantitativ-variabel" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<div id="enklare-deskriptiva-mått" class="section level3 hasAnchor" number="6.1.1">
<h3><span class="header-section-number">6.1.1</span> Enklare deskriptiva mått<a href="kvantitativa-variabler.html#enklare-deskriptiva-mått" class="anchor-section" aria-label="Anchor link to header"></a></h3>
<p>Det första steget i en dataanalys, oavsett vilken, är nästan alltid en beskrivning av datamaterialet. Såväl analytikern som mottagaren tjänar mycket på att få en helhetsbild av datamaterialet. För att initiera en sådan analys är det vanligt att beräkna sedan tidigare kända stickprovsmedelvärden och stickprovsstandardavvikelser. Utöver dessa är det också bra att beräkna medianer och kvartilavstånd (på engelska: inter-quartile range, IQR) för att få en mer robust bild av variablernas läge och spridning. Dessa värden beräknas med koden nedan.</p>
<div class="sourceCode" id="cb316"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb316-1"><a href="kvantitativa-variabler.html#cb316-1" aria-hidden="true" tabindex="-1"></a><span class="do">#### Värden för fev ####</span></span>
<span id="cb316-2"><a href="kvantitativa-variabler.html#cb316-2" aria-hidden="true" tabindex="-1"></a>fev_bar <span class="ot"><-</span> <span class="fu">mean</span>(fev) <span class="co"># Medelvärde</span></span>
<span id="cb316-3"><a href="kvantitativa-variabler.html#cb316-3" aria-hidden="true" tabindex="-1"></a>fev_sd <span class="ot"><-</span> <span class="fu">sd</span>(fev) <span class="co"># Standardavvikelse</span></span>
<span id="cb316-4"><a href="kvantitativa-variabler.html#cb316-4" aria-hidden="true" tabindex="-1"></a>fev_md <span class="ot"><-</span> <span class="fu">median</span>(fev) <span class="co"># Median</span></span>
<span id="cb316-5"><a href="kvantitativa-variabler.html#cb316-5" aria-hidden="true" tabindex="-1"></a>fev_iqr <span class="ot"><-</span> <span class="fu">IQR</span>(fev) <span class="co"># Kvartilavstånd</span></span>
<span id="cb316-6"><a href="kvantitativa-variabler.html#cb316-6" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb316-7"><a href="kvantitativa-variabler.html#cb316-7" aria-hidden="true" tabindex="-1"></a>fev_bar</span>
<span id="cb316-8"><a href="kvantitativa-variabler.html#cb316-8" aria-hidden="true" tabindex="-1"></a>[<span class="dv">1</span>] <span class="fl">2.63678</span></span>
<span id="cb316-9"><a href="kvantitativa-variabler.html#cb316-9" aria-hidden="true" tabindex="-1"></a>fev_sd</span>
<span id="cb316-10"><a href="kvantitativa-variabler.html#cb316-10" aria-hidden="true" tabindex="-1"></a>[<span class="dv">1</span>] <span class="fl">0.8670591</span></span>
<span id="cb316-11"><a href="kvantitativa-variabler.html#cb316-11" aria-hidden="true" tabindex="-1"></a>fev_md</span>
<span id="cb316-12"><a href="kvantitativa-variabler.html#cb316-12" aria-hidden="true" tabindex="-1"></a>[<span class="dv">1</span>] <span class="fl">2.5475</span></span>
<span id="cb316-13"><a href="kvantitativa-variabler.html#cb316-13" aria-hidden="true" tabindex="-1"></a>fev_iqr</span>
<span id="cb316-14"><a href="kvantitativa-variabler.html#cb316-14" aria-hidden="true" tabindex="-1"></a>[<span class="dv">1</span>] <span class="fl">1.1375</span></span>
<span id="cb316-15"><a href="kvantitativa-variabler.html#cb316-15" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb316-16"><a href="kvantitativa-variabler.html#cb316-16" aria-hidden="true" tabindex="-1"></a><span class="do">#### Värden för age ####</span></span>
<span id="cb316-17"><a href="kvantitativa-variabler.html#cb316-17" aria-hidden="true" tabindex="-1"></a>age_bar <span class="ot"><-</span> <span class="fu">mean</span>(age) <span class="co"># Medelvärde</span></span>
<span id="cb316-18"><a href="kvantitativa-variabler.html#cb316-18" aria-hidden="true" tabindex="-1"></a>age_sd <span class="ot"><-</span> <span class="fu">sd</span>(age) <span class="co"># Standardavvikelse</span></span>
<span id="cb316-19"><a href="kvantitativa-variabler.html#cb316-19" aria-hidden="true" tabindex="-1"></a>age_md <span class="ot"><-</span> <span class="fu">median</span>(age) <span class="co"># Median</span></span>
<span id="cb316-20"><a href="kvantitativa-variabler.html#cb316-20" aria-hidden="true" tabindex="-1"></a>age_iqr <span class="ot"><-</span> <span class="fu">IQR</span>(age) <span class="co"># Kvartilavstånd</span></span>
<span id="cb316-21"><a href="kvantitativa-variabler.html#cb316-21" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb316-22"><a href="kvantitativa-variabler.html#cb316-22" aria-hidden="true" tabindex="-1"></a>age_bar</span>
<span id="cb316-23"><a href="kvantitativa-variabler.html#cb316-23" aria-hidden="true" tabindex="-1"></a>[<span class="dv">1</span>] <span class="fl">9.931193</span></span>
<span id="cb316-24"><a href="kvantitativa-variabler.html#cb316-24" aria-hidden="true" tabindex="-1"></a>age_sd</span>
<span id="cb316-25"><a href="kvantitativa-variabler.html#cb316-25" aria-hidden="true" tabindex="-1"></a>[<span class="dv">1</span>] <span class="fl">2.953935</span></span>
<span id="cb316-26"><a href="kvantitativa-variabler.html#cb316-26" aria-hidden="true" tabindex="-1"></a>age_md</span>
<span id="cb316-27"><a href="kvantitativa-variabler.html#cb316-27" aria-hidden="true" tabindex="-1"></a>[<span class="dv">1</span>] <span class="dv">10</span></span>
<span id="cb316-28"><a href="kvantitativa-variabler.html#cb316-28" aria-hidden="true" tabindex="-1"></a>age_iqr</span>
<span id="cb316-29"><a href="kvantitativa-variabler.html#cb316-29" aria-hidden="true" tabindex="-1"></a>[<span class="dv">1</span>] <span class="dv">4</span></span></code></pre></div>
<p>Ett smidigt sätt att ta fram deskriptiv statistik för en variabel är att använda funktionen <strong><code>summary()</code></strong>. Den används enkelt som nedan.</p>
<div class="sourceCode" id="cb317"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb317-1"><a href="kvantitativa-variabler.html#cb317-1" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(fev) <span class="co"># Beskrivande statistiv för fev</span></span>
<span id="cb317-2"><a href="kvantitativa-variabler.html#cb317-2" aria-hidden="true" tabindex="-1"></a> Min. 1st Qu. Median Mean 3rd Qu. Max. </span>
<span id="cb317-3"><a href="kvantitativa-variabler.html#cb317-3" aria-hidden="true" tabindex="-1"></a> <span class="fl">0.791</span> <span class="fl">1.981</span> <span class="fl">2.547</span> <span class="fl">2.637</span> <span class="fl">3.119</span> <span class="fl">5.793</span> </span>
<span id="cb317-4"><a href="kvantitativa-variabler.html#cb317-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb317-5"><a href="kvantitativa-variabler.html#cb317-5" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(age) <span class="co"># Beskrivande statistiv för age</span></span>
<span id="cb317-6"><a href="kvantitativa-variabler.html#cb317-6" aria-hidden="true" tabindex="-1"></a> Min. 1st Qu. Median Mean 3rd Qu. Max. </span>
<span id="cb317-7"><a href="kvantitativa-variabler.html#cb317-7" aria-hidden="true" tabindex="-1"></a> <span class="fl">3.000</span> <span class="fl">8.000</span> <span class="fl">10.000</span> <span class="fl">9.931</span> <span class="fl">12.000</span> <span class="fl">19.000</span> </span></code></pre></div>
<p>Som synes beräknar funktionen variablernas största respektiva minsta värde, deras medelvärde och median, samt deras första respektive tredje kvartiler.</p>
<p>I situationer då andra percentiler är av intresse kan funktionen <strong><code>quantile()</code></strong> användas. Som argument i funktionen anges dels vilken variabel beräkningen ska utföras på, dels vilka percentiler som önskas. För att plocka fram den 10:e och 90:e percentilen för <code>fev</code> används koden nedan.</p>
<div class="sourceCode" id="cb318"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb318-1"><a href="kvantitativa-variabler.html#cb318-1" aria-hidden="true" tabindex="-1"></a><span class="fu">quantile</span>(fev, <span class="at">probs =</span> <span class="fu">c</span>(<span class="fl">0.1</span>, <span class="fl">0.9</span>)) <span class="co"># Percentiler för fev</span></span>
<span id="cb318-2"><a href="kvantitativa-variabler.html#cb318-2" aria-hidden="true" tabindex="-1"></a> <span class="dv">10</span><span class="sc">% 90%</span> </span>
<span id="cb318-3"><a href="kvantitativa-variabler.html#cb318-3" aria-hidden="true" tabindex="-1"></a><span class="fl">1.612</span> <span class="fl">3.813</span> </span></code></pre></div>
<p>I detta fall tolkas den 90:e percentilen som att 90% av individenerna har ett lägre värde än <span class="math inline">\(3.813\)</span>. Percentilerna beräknas på olika sätt beroende på om variabeln har ett jämnt eller udda antal observationer (precis som medianen beräknades på olika sätt under första halvan av grundkursen i statistik). <code>R</code> känner av detta automatiskt, och kan så räkna ut percentilerna på rätt sätt. För framtida referens är det dock bra att komma ihåg att percentiler kan ligga mellan två observationer.</p>
<p>Notera att tolkingen av percentilen ovan inte är helt olik de tolkningar av kvartiler som redogjorts för i tidigare kurser i statistik. Försök använda <strong><code>quantile()</code></strong> för att ta fram de tre kvartilerna, och jämför med värdena ovan. Den korrekta koden finns i fliken här nedan.</p>
<button title="kod_percentiler" type="button" onclick="if(document.getElementById('kod_percentiler') .style.display=='none')
{document.getElementById('kod_percentiler') .style.display=''}
else{document.getElementById('kod_percentiler') .style.display='none'}">
Visa kod för percentiler
</button>
<div id="kod_percentiler" style="display:none">
<div class="alert alert-info">
<p>Argumentet <code>probs = c(0.25, 0.5, 0.75)</code> får funktionen att returnera första kvartilen, medianen, och tredje kvartilen. Fundera gärna på hur kvartiler bör tolkas, och övertyga dig själv om att koden ger rätt resultat.</p>
<div class="sourceCode" id="cb319"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb319-1"><a href="kvantitativa-variabler.html#cb319-1" aria-hidden="true" tabindex="-1"></a><span class="fu">quantile</span>(fev, <span class="at">probs =</span> <span class="fu">c</span>(<span class="fl">0.25</span>, <span class="fl">0.5</span>, <span class="fl">0.75</span>)) <span class="co"># Kvartiler för fev</span></span>
<span id="cb319-2"><a href="kvantitativa-variabler.html#cb319-2" aria-hidden="true" tabindex="-1"></a> <span class="dv">25</span><span class="sc">% 50%</span> <span class="dv">75</span>% </span>
<span id="cb319-3"><a href="kvantitativa-variabler.html#cb319-3" aria-hidden="true" tabindex="-1"></a><span class="fl">1.9810</span> <span class="fl">2.5475</span> <span class="fl">3.1185</span> </span></code></pre></div>
</div>
</div>
<p></br></p>
</div>
<div id="frekvenstabeller" class="section level3 hasAnchor" number="6.1.2">
<h3><span class="header-section-number">6.1.2</span> Frekvenstabeller<a href="kvantitativa-variabler.html#frekvenstabeller" class="anchor-section" aria-label="Anchor link to header"></a></h3>
<p>Frekvenstabeller kan användas för att ge en mer detaljerad bild av en specifik variabel, och de kan även agera som stöd vid framtida analyser. I <code>R</code> skapas frekvenstabeller med hjälp av funktionen <strong><code>table()</code></strong>, vilken skriver ut en tabell i konsollen. För att frekvenstabeller ska vara användbara är det bra om variabeln som ska beskrivas inte antar för många olika värden. I sådana fall blir frekvenstabellen inte särskillt sammanfattande, utan bara ett sätt att återge alla värden som finns i datamaterialet. Frekvenstabeller lämpar sig därför till att beskriva diskreta variabler (som inte tar alltför många variabelvärden) som till exempel <code>age</code>, precis som här nedan.</p>
<div class="sourceCode" id="cb320"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb320-1"><a href="kvantitativa-variabler.html#cb320-1" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(age) <span class="co"># Frekvenstabell för age</span></span>
<span id="cb320-2"><a href="kvantitativa-variabler.html#cb320-2" aria-hidden="true" tabindex="-1"></a>age</span>
<span id="cb320-3"><a href="kvantitativa-variabler.html#cb320-3" aria-hidden="true" tabindex="-1"></a> <span class="dv">3</span> <span class="dv">4</span> <span class="dv">5</span> <span class="dv">6</span> <span class="dv">7</span> <span class="dv">8</span> <span class="dv">9</span> <span class="dv">10</span> <span class="dv">11</span> <span class="dv">12</span> <span class="dv">13</span> <span class="dv">14</span> <span class="dv">15</span> <span class="dv">16</span> <span class="dv">17</span> <span class="dv">18</span> <span class="dv">19</span> </span>
<span id="cb320-4"><a href="kvantitativa-variabler.html#cb320-4" aria-hidden="true" tabindex="-1"></a> <span class="dv">2</span> <span class="dv">9</span> <span class="dv">28</span> <span class="dv">37</span> <span class="dv">54</span> <span class="dv">85</span> <span class="dv">94</span> <span class="dv">81</span> <span class="dv">90</span> <span class="dv">57</span> <span class="dv">43</span> <span class="dv">25</span> <span class="dv">19</span> <span class="dv">13</span> <span class="dv">8</span> <span class="dv">6</span> <span class="dv">3</span> </span></code></pre></div>
<p>Utskriften är i detta fall uppdelad i två rader. Den övre raden visar de olika åldrarna som finns angivna i variabeln, och den undre raden anger hur många personer som angivit varje ålder. Det var alltså två treåringar, nio fyraåringar, och 28 femåringar som undersöktes i studien, till exempel.</p>
<p>I fallet med <code>age</code> gav <strong><code>table()</code></strong> en värdefull sammanfattning av hur åldersspridningen ser ut i datamaterialet. Eftersom det bara finns 17 olika åldrar i datamaterialet är tabellen relativt liten, och den skulle utan några större problem få plats på ett A4 (t.ex. i en rapport). I fallet <code>fev</code>, däremot, finns väldigt många olika variabelvärden, och en frekvenstabell för variabeln blir därför en enda stor röra (resultatet av att köra <code>table(fev)</code> finns gömt under fliken här nedan). Därför är det, som sagt, bäst att använda frekvenstabeller när antalet olika variabelvärden är relativt litet. Vad <em>litet</em> betyder i detta fallet är en smaksak, och det finns inga specifika regler eller bestämmelser för detta.</p>
<button title="tab_fev" type="button" onclick="if(document.getElementById('tab_fev') .style.display=='none')
{document.getElementById('tab_fev') .style.display=''}
else{document.getElementById('tab_fev') .style.display='none'}">
Visa tabell
</button>
<div id="tab_fev" style="display:none">
<div class="alert alert-info">
<p>Inte särskilt tilltalande att ha med i en rapport:</p>
<div class="sourceCode" id="cb321"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb321-1"><a href="kvantitativa-variabler.html#cb321-1" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(fev) <span class="co"># Stökig frekvenstabell för fev</span></span>
<span id="cb321-2"><a href="kvantitativa-variabler.html#cb321-2" aria-hidden="true" tabindex="-1"></a>fev</span>
<span id="cb321-3"><a href="kvantitativa-variabler.html#cb321-3" aria-hidden="true" tabindex="-1"></a><span class="fl">0.791</span> <span class="fl">0.796</span> <span class="fl">0.839</span> <span class="fl">1.004</span> <span class="fl">1.072</span> <span class="fl">1.092</span> <span class="fl">1.102</span> <span class="fl">1.146</span> <span class="fl">1.165</span> <span class="fl">1.196</span> <span class="fl">1.253</span> <span class="fl">1.256</span> <span class="fl">1.282</span> </span>
<span id="cb321-4"><a href="kvantitativa-variabler.html#cb321-4" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-5"><a href="kvantitativa-variabler.html#cb321-5" aria-hidden="true" tabindex="-1"></a><span class="fl">1.292</span> <span class="fl">1.335</span> <span class="fl">1.338</span> <span class="fl">1.343</span> <span class="fl">1.344</span> <span class="fl">1.348</span> <span class="fl">1.359</span> <span class="fl">1.37</span> <span class="fl">1.389</span> <span class="fl">1.4</span> <span class="fl">1.404</span> <span class="fl">1.415</span> <span class="fl">1.418</span> </span>
<span id="cb321-6"><a href="kvantitativa-variabler.html#cb321-6" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> </span>
<span id="cb321-7"><a href="kvantitativa-variabler.html#cb321-7" aria-hidden="true" tabindex="-1"></a><span class="fl">1.423</span> <span class="fl">1.427</span> <span class="fl">1.429</span> <span class="fl">1.431</span> <span class="fl">1.452</span> <span class="fl">1.458</span> <span class="fl">1.461</span> <span class="fl">1.472</span> <span class="fl">1.473</span> <span class="fl">1.481</span> <span class="fl">1.495</span> <span class="fl">1.512</span> <span class="fl">1.514</span> </span>
<span id="cb321-8"><a href="kvantitativa-variabler.html#cb321-8" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-9"><a href="kvantitativa-variabler.html#cb321-9" aria-hidden="true" tabindex="-1"></a><span class="fl">1.523</span> <span class="fl">1.527</span> <span class="fl">1.535</span> <span class="fl">1.536</span> <span class="fl">1.539</span> <span class="fl">1.547</span> <span class="fl">1.552</span> <span class="fl">1.556</span> <span class="fl">1.558</span> <span class="fl">1.562</span> <span class="fl">1.569</span> <span class="fl">1.572</span> <span class="fl">1.577</span> </span>
<span id="cb321-10"><a href="kvantitativa-variabler.html#cb321-10" aria-hidden="true" tabindex="-1"></a> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-11"><a href="kvantitativa-variabler.html#cb321-11" aria-hidden="true" tabindex="-1"></a> <span class="fl">1.58</span> <span class="fl">1.589</span> <span class="fl">1.591</span> <span class="fl">1.602</span> <span class="fl">1.603</span> <span class="fl">1.606</span> <span class="fl">1.609</span> <span class="fl">1.611</span> <span class="fl">1.612</span> <span class="fl">1.624</span> <span class="fl">1.631</span> <span class="fl">1.634</span> <span class="fl">1.64</span> </span>
<span id="cb321-12"><a href="kvantitativa-variabler.html#cb321-12" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">3</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-13"><a href="kvantitativa-variabler.html#cb321-13" aria-hidden="true" tabindex="-1"></a><span class="fl">1.649</span> <span class="fl">1.65</span> <span class="fl">1.657</span> <span class="fl">1.658</span> <span class="fl">1.665</span> <span class="fl">1.666</span> <span class="fl">1.672</span> <span class="fl">1.675</span> <span class="fl">1.682</span> <span class="fl">1.69</span> <span class="fl">1.691</span> <span class="fl">1.694</span> <span class="fl">1.695</span> </span>
<span id="cb321-14"><a href="kvantitativa-variabler.html#cb321-14" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-15"><a href="kvantitativa-variabler.html#cb321-15" aria-hidden="true" tabindex="-1"></a><span class="fl">1.697</span> <span class="fl">1.698</span> <span class="fl">1.699</span> <span class="fl">1.703</span> <span class="fl">1.704</span> <span class="fl">1.708</span> <span class="fl">1.713</span> <span class="fl">1.715</span> <span class="fl">1.716</span> <span class="fl">1.718</span> <span class="fl">1.719</span> <span class="fl">1.72</span> <span class="fl">1.724</span> </span>
<span id="cb321-16"><a href="kvantitativa-variabler.html#cb321-16" aria-hidden="true" tabindex="-1"></a> <span class="dv">2</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-17"><a href="kvantitativa-variabler.html#cb321-17" aria-hidden="true" tabindex="-1"></a><span class="fl">1.726</span> <span class="fl">1.728</span> <span class="fl">1.735</span> <span class="fl">1.742</span> <span class="fl">1.744</span> <span class="fl">1.747</span> <span class="fl">1.75</span> <span class="fl">1.751</span> <span class="fl">1.754</span> <span class="fl">1.755</span> <span class="fl">1.758</span> <span class="fl">1.759</span> <span class="fl">1.773</span> </span>
<span id="cb321-18"><a href="kvantitativa-variabler.html#cb321-18" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-19"><a href="kvantitativa-variabler.html#cb321-19" aria-hidden="true" tabindex="-1"></a><span class="fl">1.776</span> <span class="fl">1.78</span> <span class="fl">1.789</span> <span class="fl">1.79</span> <span class="fl">1.794</span> <span class="fl">1.796</span> <span class="fl">1.808</span> <span class="fl">1.811</span> <span class="fl">1.819</span> <span class="fl">1.823</span> <span class="fl">1.826</span> <span class="fl">1.827</span> <span class="fl">1.829</span> </span>
<span id="cb321-20"><a href="kvantitativa-variabler.html#cb321-20" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-21"><a href="kvantitativa-variabler.html#cb321-21" aria-hidden="true" tabindex="-1"></a><span class="fl">1.844</span> <span class="fl">1.855</span> <span class="fl">1.858</span> <span class="fl">1.869</span> <span class="fl">1.872</span> <span class="fl">1.873</span> <span class="fl">1.877</span> <span class="fl">1.878</span> <span class="fl">1.886</span> <span class="fl">1.895</span> <span class="fl">1.897</span> <span class="fl">1.905</span> <span class="fl">1.912</span> </span>
<span id="cb321-22"><a href="kvantitativa-variabler.html#cb321-22" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">3</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-23"><a href="kvantitativa-variabler.html#cb321-23" aria-hidden="true" tabindex="-1"></a><span class="fl">1.916</span> <span class="fl">1.917</span> <span class="fl">1.919</span> <span class="fl">1.92</span> <span class="fl">1.93</span> <span class="fl">1.931</span> <span class="fl">1.932</span> <span class="fl">1.933</span> <span class="fl">1.935</span> <span class="fl">1.937</span> <span class="fl">1.94</span> <span class="fl">1.942</span> <span class="fl">1.947</span> </span>
<span id="cb321-24"><a href="kvantitativa-variabler.html#cb321-24" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-25"><a href="kvantitativa-variabler.html#cb321-25" aria-hidden="true" tabindex="-1"></a><span class="fl">1.953</span> <span class="fl">1.962</span> <span class="fl">1.969</span> <span class="fl">1.971</span> <span class="fl">1.979</span> <span class="fl">1.987</span> <span class="fl">1.991</span> <span class="fl">1.999</span> <span class="fl">2.002</span> <span class="fl">2.004</span> <span class="fl">2.01</span> <span class="fl">2.015</span> <span class="fl">2.016</span> </span>
<span id="cb321-26"><a href="kvantitativa-variabler.html#cb321-26" aria-hidden="true" tabindex="-1"></a> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-27"><a href="kvantitativa-variabler.html#cb321-27" aria-hidden="true" tabindex="-1"></a><span class="fl">2.017</span> <span class="fl">2.04</span> <span class="fl">2.042</span> <span class="fl">2.046</span> <span class="fl">2.048</span> <span class="fl">2.056</span> <span class="fl">2.069</span> <span class="fl">2.071</span> <span class="fl">2.076</span> <span class="fl">2.081</span> <span class="fl">2.084</span> <span class="fl">2.09</span> <span class="fl">2.091</span> </span>
<span id="cb321-28"><a href="kvantitativa-variabler.html#cb321-28" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">3</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> </span>
<span id="cb321-29"><a href="kvantitativa-variabler.html#cb321-29" aria-hidden="true" tabindex="-1"></a><span class="fl">2.093</span> <span class="fl">2.094</span> <span class="fl">2.095</span> <span class="fl">2.1</span> <span class="fl">2.102</span> <span class="fl">2.104</span> <span class="fl">2.111</span> <span class="fl">2.115</span> <span class="fl">2.118</span> <span class="fl">2.119</span> <span class="fl">2.123</span> <span class="fl">2.126</span> <span class="fl">2.13</span> </span>
<span id="cb321-30"><a href="kvantitativa-variabler.html#cb321-30" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-31"><a href="kvantitativa-variabler.html#cb321-31" aria-hidden="true" tabindex="-1"></a><span class="fl">2.132</span> <span class="fl">2.135</span> <span class="fl">2.14</span> <span class="fl">2.144</span> <span class="fl">2.145</span> <span class="fl">2.158</span> <span class="fl">2.164</span> <span class="fl">2.165</span> <span class="fl">2.166</span> <span class="fl">2.17</span> <span class="fl">2.175</span> <span class="fl">2.182</span> <span class="fl">2.187</span> </span>
<span id="cb321-32"><a href="kvantitativa-variabler.html#cb321-32" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">3</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-33"><a href="kvantitativa-variabler.html#cb321-33" aria-hidden="true" tabindex="-1"></a><span class="fl">2.193</span> <span class="fl">2.196</span> <span class="fl">2.198</span> <span class="fl">2.201</span> <span class="fl">2.211</span> <span class="fl">2.215</span> <span class="fl">2.216</span> <span class="fl">2.219</span> <span class="fl">2.22</span> <span class="fl">2.226</span> <span class="fl">2.23</span> <span class="fl">2.236</span> <span class="fl">2.241</span> </span>
<span id="cb321-34"><a href="kvantitativa-variabler.html#cb321-34" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-35"><a href="kvantitativa-variabler.html#cb321-35" aria-hidden="true" tabindex="-1"></a><span class="fl">2.246</span> <span class="fl">2.25</span> <span class="fl">2.258</span> <span class="fl">2.259</span> <span class="fl">2.262</span> <span class="fl">2.264</span> <span class="fl">2.276</span> <span class="fl">2.278</span> <span class="fl">2.287</span> <span class="fl">2.288</span> <span class="fl">2.292</span> <span class="fl">2.293</span> <span class="fl">2.301</span> </span>
<span id="cb321-36"><a href="kvantitativa-variabler.html#cb321-36" aria-hidden="true" tabindex="-1"></a> <span class="dv">2</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-37"><a href="kvantitativa-variabler.html#cb321-37" aria-hidden="true" tabindex="-1"></a><span class="fl">2.303</span> <span class="fl">2.304</span> <span class="fl">2.305</span> <span class="fl">2.316</span> <span class="fl">2.318</span> <span class="fl">2.32</span> <span class="fl">2.328</span> <span class="fl">2.332</span> <span class="fl">2.333</span> <span class="fl">2.335</span> <span class="fl">2.336</span> <span class="fl">2.341</span> <span class="fl">2.346</span> </span>
<span id="cb321-38"><a href="kvantitativa-variabler.html#cb321-38" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> </span>
<span id="cb321-39"><a href="kvantitativa-variabler.html#cb321-39" aria-hidden="true" tabindex="-1"></a><span class="fl">2.347</span> <span class="fl">2.348</span> <span class="fl">2.352</span> <span class="fl">2.354</span> <span class="fl">2.356</span> <span class="fl">2.358</span> <span class="fl">2.362</span> <span class="fl">2.364</span> <span class="fl">2.365</span> <span class="fl">2.366</span> <span class="fl">2.371</span> <span class="fl">2.382</span> <span class="fl">2.384</span> </span>
<span id="cb321-40"><a href="kvantitativa-variabler.html#cb321-40" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-41"><a href="kvantitativa-variabler.html#cb321-41" aria-hidden="true" tabindex="-1"></a><span class="fl">2.386</span> <span class="fl">2.387</span> <span class="fl">2.388</span> <span class="fl">2.391</span> <span class="fl">2.417</span> <span class="fl">2.419</span> <span class="fl">2.42</span> <span class="fl">2.434</span> <span class="fl">2.435</span> <span class="fl">2.442</span> <span class="fl">2.449</span> <span class="fl">2.455</span> <span class="fl">2.457</span> </span>
<span id="cb321-42"><a href="kvantitativa-variabler.html#cb321-42" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> </span>
<span id="cb321-43"><a href="kvantitativa-variabler.html#cb321-43" aria-hidden="true" tabindex="-1"></a><span class="fl">2.458</span> <span class="fl">2.46</span> <span class="fl">2.463</span> <span class="fl">2.465</span> <span class="fl">2.476</span> <span class="fl">2.481</span> <span class="fl">2.485</span> <span class="fl">2.487</span> <span class="fl">2.491</span> <span class="fl">2.498</span> <span class="fl">2.499</span> <span class="fl">2.5</span> <span class="fl">2.501</span> </span>
<span id="cb321-44"><a href="kvantitativa-variabler.html#cb321-44" aria-hidden="true" tabindex="-1"></a> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-45"><a href="kvantitativa-variabler.html#cb321-45" aria-hidden="true" tabindex="-1"></a><span class="fl">2.503</span> <span class="fl">2.504</span> <span class="fl">2.52</span> <span class="fl">2.524</span> <span class="fl">2.529</span> <span class="fl">2.531</span> <span class="fl">2.535</span> <span class="fl">2.538</span> <span class="fl">2.542</span> <span class="fl">2.545</span> <span class="fl">2.55</span> <span class="fl">2.556</span> <span class="fl">2.56</span> </span>
<span id="cb321-46"><a href="kvantitativa-variabler.html#cb321-46" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-47"><a href="kvantitativa-variabler.html#cb321-47" aria-hidden="true" tabindex="-1"></a><span class="fl">2.561</span> <span class="fl">2.562</span> <span class="fl">2.563</span> <span class="fl">2.564</span> <span class="fl">2.568</span> <span class="fl">2.569</span> <span class="fl">2.57</span> <span class="fl">2.571</span> <span class="fl">2.574</span> <span class="fl">2.578</span> <span class="fl">2.579</span> <span class="fl">2.581</span> <span class="fl">2.588</span> </span>
<span id="cb321-48"><a href="kvantitativa-variabler.html#cb321-48" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-49"><a href="kvantitativa-variabler.html#cb321-49" aria-hidden="true" tabindex="-1"></a><span class="fl">2.592</span> <span class="fl">2.599</span> <span class="fl">2.604</span> <span class="fl">2.605</span> <span class="fl">2.606</span> <span class="fl">2.608</span> <span class="fl">2.631</span> <span class="fl">2.633</span> <span class="fl">2.635</span> <span class="fl">2.639</span> <span class="fl">2.642</span> <span class="fl">2.646</span> <span class="fl">2.65</span> </span>
<span id="cb321-50"><a href="kvantitativa-variabler.html#cb321-50" aria-hidden="true" tabindex="-1"></a> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">3</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> </span>
<span id="cb321-51"><a href="kvantitativa-variabler.html#cb321-51" aria-hidden="true" tabindex="-1"></a><span class="fl">2.659</span> <span class="fl">2.665</span> <span class="fl">2.673</span> <span class="fl">2.677</span> <span class="fl">2.679</span> <span class="fl">2.681</span> <span class="fl">2.688</span> <span class="fl">2.689</span> <span class="fl">2.691</span> <span class="fl">2.696</span> <span class="fl">2.704</span> <span class="fl">2.709</span> <span class="fl">2.714</span> </span>
<span id="cb321-52"><a href="kvantitativa-variabler.html#cb321-52" aria-hidden="true" tabindex="-1"></a> <span class="dv">2</span> <span class="dv">2</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-53"><a href="kvantitativa-variabler.html#cb321-53" aria-hidden="true" tabindex="-1"></a><span class="fl">2.715</span> <span class="fl">2.717</span> <span class="fl">2.72</span> <span class="fl">2.725</span> <span class="fl">2.732</span> <span class="fl">2.735</span> <span class="fl">2.751</span> <span class="fl">2.752</span> <span class="fl">2.754</span> <span class="fl">2.758</span> <span class="fl">2.759</span> <span class="fl">2.762</span> <span class="fl">2.77</span> </span>
<span id="cb321-54"><a href="kvantitativa-variabler.html#cb321-54" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-55"><a href="kvantitativa-variabler.html#cb321-55" aria-hidden="true" tabindex="-1"></a><span class="fl">2.785</span> <span class="fl">2.795</span> <span class="fl">2.797</span> <span class="fl">2.798</span> <span class="fl">2.803</span> <span class="fl">2.812</span> <span class="fl">2.813</span> <span class="fl">2.819</span> <span class="fl">2.822</span> <span class="fl">2.827</span> <span class="fl">2.833</span> <span class="fl">2.838</span> <span class="fl">2.841</span> </span>
<span id="cb321-56"><a href="kvantitativa-variabler.html#cb321-56" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-57"><a href="kvantitativa-variabler.html#cb321-57" aria-hidden="true" tabindex="-1"></a> <span class="fl">2.85</span> <span class="fl">2.851</span> <span class="fl">2.853</span> <span class="fl">2.855</span> <span class="fl">2.862</span> <span class="fl">2.864</span> <span class="fl">2.866</span> <span class="fl">2.868</span> <span class="fl">2.871</span> <span class="fl">2.884</span> <span class="fl">2.887</span> <span class="fl">2.889</span> <span class="fl">2.891</span> </span>
<span id="cb321-58"><a href="kvantitativa-variabler.html#cb321-58" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">2</span> </span>
<span id="cb321-59"><a href="kvantitativa-variabler.html#cb321-59" aria-hidden="true" tabindex="-1"></a><span class="fl">2.893</span> <span class="fl">2.894</span> <span class="fl">2.901</span> <span class="fl">2.903</span> <span class="fl">2.906</span> <span class="fl">2.913</span> <span class="fl">2.923</span> <span class="fl">2.927</span> <span class="fl">2.928</span> <span class="fl">2.934</span> <span class="fl">2.935</span> <span class="fl">2.953</span> <span class="fl">2.957</span> </span>
<span id="cb321-60"><a href="kvantitativa-variabler.html#cb321-60" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-61"><a href="kvantitativa-variabler.html#cb321-61" aria-hidden="true" tabindex="-1"></a><span class="fl">2.964</span> <span class="fl">2.971</span> <span class="fl">2.973</span> <span class="fl">2.974</span> <span class="fl">2.975</span> <span class="fl">2.976</span> <span class="fl">2.98</span> <span class="fl">2.981</span> <span class="fl">2.988</span> <span class="fl">2.993</span> <span class="fl">2.997</span> <span class="dv">3</span> <span class="fl">3.001</span> </span>
<span id="cb321-62"><a href="kvantitativa-variabler.html#cb321-62" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-63"><a href="kvantitativa-variabler.html#cb321-63" aria-hidden="true" tabindex="-1"></a><span class="fl">3.004</span> <span class="fl">3.007</span> <span class="fl">3.011</span> <span class="fl">3.016</span> <span class="fl">3.022</span> <span class="fl">3.023</span> <span class="fl">3.029</span> <span class="fl">3.035</span> <span class="fl">3.038</span> <span class="fl">3.042</span> <span class="fl">3.048</span> <span class="fl">3.05</span> <span class="fl">3.056</span> </span>
<span id="cb321-64"><a href="kvantitativa-variabler.html#cb321-64" aria-hidden="true" tabindex="-1"></a> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-65"><a href="kvantitativa-variabler.html#cb321-65" aria-hidden="true" tabindex="-1"></a><span class="fl">3.058</span> <span class="fl">3.06</span> <span class="fl">3.069</span> <span class="fl">3.073</span> <span class="fl">3.074</span> <span class="fl">3.078</span> <span class="fl">3.079</span> <span class="fl">3.082</span> <span class="fl">3.086</span> <span class="fl">3.089</span> <span class="fl">3.09</span> <span class="fl">3.102</span> <span class="fl">3.104</span> </span>
<span id="cb321-66"><a href="kvantitativa-variabler.html#cb321-66" aria-hidden="true" tabindex="-1"></a> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">4</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-67"><a href="kvantitativa-variabler.html#cb321-67" aria-hidden="true" tabindex="-1"></a><span class="fl">3.108</span> <span class="fl">3.11</span> <span class="fl">3.111</span> <span class="fl">3.114</span> <span class="fl">3.12</span> <span class="fl">3.122</span> <span class="fl">3.127</span> <span class="fl">3.132</span> <span class="fl">3.135</span> <span class="fl">3.141</span> <span class="fl">3.147</span> <span class="fl">3.152</span> <span class="fl">3.166</span> </span>
<span id="cb321-68"><a href="kvantitativa-variabler.html#cb321-68" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-69"><a href="kvantitativa-variabler.html#cb321-69" aria-hidden="true" tabindex="-1"></a><span class="fl">3.169</span> <span class="fl">3.171</span> <span class="fl">3.183</span> <span class="fl">3.186</span> <span class="fl">3.193</span> <span class="fl">3.2</span> <span class="fl">3.203</span> <span class="fl">3.206</span> <span class="fl">3.208</span> <span class="fl">3.211</span> <span class="fl">3.222</span> <span class="fl">3.223</span> <span class="fl">3.231</span> </span>
<span id="cb321-70"><a href="kvantitativa-variabler.html#cb321-70" aria-hidden="true" tabindex="-1"></a> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">2</span> <span class="dv">1</span> </span>
<span id="cb321-71"><a href="kvantitativa-variabler.html#cb321-71" aria-hidden="true" tabindex="-1"></a><span class="fl">3.236</span> <span class="fl">3.239</span> <span class="fl">3.247</span> <span class="fl">3.251</span> <span class="fl">3.255</span> <span class="fl">3.258</span> <span class="fl">3.279</span> <span class="fl">3.28</span> <span class="fl">3.297</span> <span class="fl">3.305</span> <span class="fl">3.32</span> <span class="fl">3.329</span> <span class="fl">3.33</span> </span>
<span id="cb321-72"><a href="kvantitativa-variabler.html#cb321-72" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-73"><a href="kvantitativa-variabler.html#cb321-73" aria-hidden="true" tabindex="-1"></a><span class="fl">3.331</span> <span class="fl">3.339</span> <span class="fl">3.341</span> <span class="fl">3.343</span> <span class="fl">3.345</span> <span class="fl">3.35</span> <span class="fl">3.354</span> <span class="fl">3.369</span> <span class="fl">3.381</span> <span class="fl">3.387</span> <span class="fl">3.395</span> <span class="fl">3.403</span> <span class="fl">3.406</span> </span>
<span id="cb321-74"><a href="kvantitativa-variabler.html#cb321-74" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-75"><a href="kvantitativa-variabler.html#cb321-75" aria-hidden="true" tabindex="-1"></a><span class="fl">3.411</span> <span class="fl">3.413</span> <span class="fl">3.425</span> <span class="fl">3.428</span> <span class="fl">3.436</span> <span class="fl">3.456</span> <span class="fl">3.47</span> <span class="fl">3.489</span> <span class="fl">3.49</span> <span class="fl">3.498</span> <span class="fl">3.5</span> <span class="fl">3.501</span> <span class="fl">3.515</span> </span>
<span id="cb321-76"><a href="kvantitativa-variabler.html#cb321-76" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> </span>
<span id="cb321-77"><a href="kvantitativa-variabler.html#cb321-77" aria-hidden="true" tabindex="-1"></a><span class="fl">3.519</span> <span class="fl">3.529</span> <span class="fl">3.53</span> <span class="fl">3.549</span> <span class="fl">3.556</span> <span class="fl">3.577</span> <span class="fl">3.583</span> <span class="fl">3.585</span> <span class="fl">3.587</span> <span class="fl">3.596</span> <span class="fl">3.645</span> <span class="fl">3.654</span> <span class="fl">3.674</span> </span>
<span id="cb321-78"><a href="kvantitativa-variabler.html#cb321-78" aria-hidden="true" tabindex="-1"></a> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-79"><a href="kvantitativa-variabler.html#cb321-79" aria-hidden="true" tabindex="-1"></a> <span class="fl">3.68</span> <span class="fl">3.681</span> <span class="fl">3.688</span> <span class="fl">3.692</span> <span class="fl">3.727</span> <span class="fl">3.731</span> <span class="fl">3.741</span> <span class="fl">3.745</span> <span class="fl">3.751</span> <span class="fl">3.774</span> <span class="fl">3.78</span> <span class="fl">3.785</span> <span class="fl">3.791</span> </span>
<span id="cb321-80"><a href="kvantitativa-variabler.html#cb321-80" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-81"><a href="kvantitativa-variabler.html#cb321-81" aria-hidden="true" tabindex="-1"></a><span class="fl">3.795</span> <span class="fl">3.799</span> <span class="fl">3.806</span> <span class="fl">3.816</span> <span class="fl">3.835</span> <span class="fl">3.842</span> <span class="fl">3.845</span> <span class="fl">3.847</span> <span class="fl">3.887</span> <span class="fl">3.906</span> <span class="fl">3.924</span> <span class="fl">3.957</span> <span class="fl">3.96</span> </span>
<span id="cb321-82"><a href="kvantitativa-variabler.html#cb321-82" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-83"><a href="kvantitativa-variabler.html#cb321-83" aria-hidden="true" tabindex="-1"></a><span class="fl">3.977</span> <span class="fl">3.984</span> <span class="fl">3.985</span> <span class="fl">3.994</span> <span class="fl">4.007</span> <span class="fl">4.045</span> <span class="fl">4.065</span> <span class="fl">4.07</span> <span class="fl">4.073</span> <span class="fl">4.08</span> <span class="fl">4.086</span> <span class="fl">4.111</span> <span class="fl">4.13</span> </span>
<span id="cb321-84"><a href="kvantitativa-variabler.html#cb321-84" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-85"><a href="kvantitativa-variabler.html#cb321-85" aria-hidden="true" tabindex="-1"></a><span class="fl">4.203</span> <span class="fl">4.22</span> <span class="fl">4.225</span> <span class="fl">4.232</span> <span class="fl">4.27</span> <span class="fl">4.271</span> <span class="fl">4.273</span> <span class="fl">4.279</span> <span class="fl">4.284</span> <span class="fl">4.299</span> <span class="fl">4.305</span> <span class="fl">4.309</span> <span class="fl">4.324</span> </span>
<span id="cb321-86"><a href="kvantitativa-variabler.html#cb321-86" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-87"><a href="kvantitativa-variabler.html#cb321-87" aria-hidden="true" tabindex="-1"></a><span class="fl">4.336</span> <span class="fl">4.393</span> <span class="fl">4.404</span> <span class="fl">4.411</span> <span class="fl">4.429</span> <span class="fl">4.448</span> <span class="fl">4.5</span> <span class="fl">4.504</span> <span class="fl">4.506</span> <span class="fl">4.55</span> <span class="fl">4.591</span> <span class="fl">4.593</span> <span class="fl">4.637</span> </span>
<span id="cb321-88"><a href="kvantitativa-variabler.html#cb321-88" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-89"><a href="kvantitativa-variabler.html#cb321-89" aria-hidden="true" tabindex="-1"></a><span class="fl">4.683</span> <span class="fl">4.72</span> <span class="fl">4.724</span> <span class="fl">4.756</span> <span class="fl">4.763</span> <span class="fl">4.789</span> <span class="fl">4.831</span> <span class="fl">4.842</span> <span class="fl">4.872</span> <span class="fl">4.877</span> <span class="fl">5.083</span> <span class="fl">5.102</span> <span class="fl">5.224</span> </span>
<span id="cb321-90"><a href="kvantitativa-variabler.html#cb321-90" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span>
<span id="cb321-91"><a href="kvantitativa-variabler.html#cb321-91" aria-hidden="true" tabindex="-1"></a><span class="fl">5.633</span> <span class="fl">5.638</span> <span class="fl">5.793</span> </span>
<span id="cb321-92"><a href="kvantitativa-variabler.html#cb321-92" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">1</span> </span></code></pre></div>
</div>
</div>
<p></br></p>
<p><img src="docs/images/note.png" width="5%" style="display: block; margin: auto;" /></p>
<style>
div.yellow{ background-color:#FFFA94; border-radius: 5px; padding: 20px;}
</style>
<div class="yellow">
<p><font size="4"> Saknade värden i frekvenstabeller </font></p>
<p>Funktionen <strong><code>table()</code></strong> hanterar saknade värden, <code>NA</code>, på olika sätt, beroende på hur kommandot <code>useNA</code> specificeras. För att illustrera detta används vektorn</p>
<div class="sourceCode" id="cb322"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb322-1"><a href="kvantitativa-variabler.html#cb322-1" aria-hidden="true" tabindex="-1"></a>mis_vec <span class="ot"><-</span> <span class="fu">c</span>(<span class="dv">1</span>, <span class="dv">2</span>, <span class="dv">3</span>, <span class="cn">NA</span>, <span class="dv">1</span>, <span class="dv">2</span>, <span class="dv">3</span>)</span></code></pre></div>
<p>När <strong><code>table()</code></strong> används som vanligt renderas tabellen som visas nedan.</p>
<div class="sourceCode" id="cb323"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb323-1"><a href="kvantitativa-variabler.html#cb323-1" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(mis_vec)</span>
<span id="cb323-2"><a href="kvantitativa-variabler.html#cb323-2" aria-hidden="true" tabindex="-1"></a>mis_vec</span>
<span id="cb323-3"><a href="kvantitativa-variabler.html#cb323-3" aria-hidden="true" tabindex="-1"></a><span class="dv">1</span> <span class="dv">2</span> <span class="dv">3</span> </span>
<span id="cb323-4"><a href="kvantitativa-variabler.html#cb323-4" aria-hidden="true" tabindex="-1"></a><span class="dv">2</span> <span class="dv">2</span> <span class="dv">2</span> </span></code></pre></div>
<p>När inget anges kommer <code>R</code> automatiskt anta att antalet <code>NA</code> i datamaterialet inte är av intresse, och därför exkludera det ur tabellen. Ibland kan det dock vara så att bortfallet faktiskt spelar roll, och i transparenta studier är det bra att rapportera hur stort borfallet är (om det finns något sådant, det vill säga). För att <code>R</code> ska räkna antalet saknade värden och skriva med det i tabellen används argumentet <code>useNA = "ifany"</code>, då renderas istället tabellen här nedan.</p>
<div class="sourceCode" id="cb324"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb324-1"><a href="kvantitativa-variabler.html#cb324-1" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(mis_vec, <span class="at">useNA =</span> <span class="st">"ifany"</span>)</span>
<span id="cb324-2"><a href="kvantitativa-variabler.html#cb324-2" aria-hidden="true" tabindex="-1"></a>mis_vec</span>
<span id="cb324-3"><a href="kvantitativa-variabler.html#cb324-3" aria-hidden="true" tabindex="-1"></a> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">3</span> <span class="sc"><</span><span class="cn">NA</span><span class="sc">></span> </span>
<span id="cb324-4"><a href="kvantitativa-variabler.html#cb324-4" aria-hidden="true" tabindex="-1"></a> <span class="dv">2</span> <span class="dv">2</span> <span class="dv">2</span> <span class="dv">1</span> </span></code></pre></div>
<p>Det är alltså bra att fundera över huruvida eventuellt bortfall bör räknas med när en frekvenstabell ska skapas, och om sådant är fallet, använda <code>useNA = "ifany"</code>.</p>
</div>
<p></br></p>
</div>
<div id="histogram" class="section level3 hasAnchor" number="6.1.3">
<h3><span class="header-section-number">6.1.3</span> Histogram<a href="kvantitativa-variabler.html#histogram" class="anchor-section" aria-label="Anchor link to header"></a></h3>
<p>I fall där frekvenstabeller blir stökiga på grund av ett stort antal olika variabelvärden kan <strong>histogram</strong> användas som ett mer kompakt alternativ. Histogram används huvudsakligen för att ge en bild av hur kontinuerliga variabler är fördelade, men de kan också användas för diskreta variabler med väldigt många olika variabelvärden.</p>
<p>I <code>R</code> skapas histogram med funktionen <strong><code>hist()</code></strong>. Ett enkelt histogram över variabeln <code>fev</code> skapas med koden nedan.</p>
<div class="sourceCode" id="cb325"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb325-1"><a href="kvantitativa-variabler.html#cb325-1" aria-hidden="true" tabindex="-1"></a><span class="fu">hist</span>(fev) <span class="co"># Histogram över fev</span></span></code></pre></div>
<p><img src="docs/images/unnamed-chunk-300-1.png" width="672" style="display: block; margin: auto;" /></p>
<div id="etiketter" class="section level5 hasAnchor" number="6.1.3.0.1">
<h5><span class="header-section-number">6.1.3.0.1</span> Etiketter<a href="kvantitativa-variabler.html#etiketter" class="anchor-section" aria-label="Anchor link to header"></a></h5>
<p>Funktionen <strong><code>hist()</code></strong> har väldigt många olika argument som kan användas för att justera diagrammet som skapas. Tre alternativ som är bra att känna till är <code>main</code>, <code>xlab</code>, och <code>ylab</code>. Med hjälp av dessa justeras diagrammets titel, samt texten som hör till varje axel. Med koden nedan ändras dessa argument för att skapa ett mer informativt diagram.</p>
<div class="sourceCode" id="cb326"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb326-1"><a href="kvantitativa-variabler.html#cb326-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Histogram med titel och nya labels</span></span>
<span id="cb326-2"><a href="kvantitativa-variabler.html#cb326-2" aria-hidden="true" tabindex="-1"></a><span class="fu">hist</span>(fev,</span>
<span id="cb326-3"><a href="kvantitativa-variabler.html#cb326-3" aria-hidden="true" tabindex="-1"></a> <span class="at">main =</span> <span class="st">"Forcerad andingsvolym"</span>,</span>
<span id="cb326-4"><a href="kvantitativa-variabler.html#cb326-4" aria-hidden="true" tabindex="-1"></a> <span class="at">ylab =</span> <span class="st">"Frekvens"</span>,</span>
<span id="cb326-5"><a href="kvantitativa-variabler.html#cb326-5" aria-hidden="true" tabindex="-1"></a> <span class="at">xlab =</span> <span class="st">"FEV (liter per sekund)"</span>) </span></code></pre></div>
<p>Från och med nu kommer de olika diagrammen dölja sig i flikar under koden. Detta för att texten ska förbli relativt kort och lättnavigerad.</p>
<button title="hist_labs" type="button" onclick="if(document.getElementById('hist_labs') .style.display=='none')
{document.getElementById('hist_labs') .style.display=''}
else{document.getElementById('hist_labs') .style.display='none'}">
Visa figur
</button>
<div id="hist_labs" style="display:none">
<div class="alert alert-info">
<p><img src="docs/images/unnamed-chunk-302-1.png" width="672" style="display: block; margin: auto;" /></p>
</div>
</div>
<p></br></p>
<p>I det fall då en titel eller text inte önskas alls kan argumentet bara lämnas blankt. Testa till exempel att göra histogrammet ovan med argumenten <code>main = " "</code> eller <code>xlab = " "</code></p>
</div>
<div id="längd-på-axlarna" class="section level5 hasAnchor" number="6.1.3.0.2">
<h5><span class="header-section-number">6.1.3.0.2</span> Längd på axlarna<a href="kvantitativa-variabler.html#längd-på-axlarna" class="anchor-section" aria-label="Anchor link to header"></a></h5>
<p>I vissa fall behöver längden på diagrammets axlar justeras. I <code>R</code> görs detta med argumenten <code>ylim</code> och <code>xlim</code>. För att ändra argumenten anges en vektor med två element, det första anger det lägsta axelvärdet som ska tillåtas, och det andra elementet anger det högsta axelvärdet som ska tillåtas.</p>
<p>Antag att axlarna i histogrammet ovan av någon anledning ska förlängas så att att <span class="math inline">\(x\)</span>-axeln går från -5 till 10, och <span class="math inline">\(y\)</span>-axeln går från 0 till 200 (notera att ett negativt <span class="math inline">\(x\)</span>-värde inte nödvändigtvis är rimligt i just detta exempel, men det kan vara önskvärt i andra fall). En sådan figur skapas med hjälp av koden nedan.</p>
<div class="sourceCode" id="cb327"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb327-1"><a href="kvantitativa-variabler.html#cb327-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Histogram med nya axellängder</span></span>
<span id="cb327-2"><a href="kvantitativa-variabler.html#cb327-2" aria-hidden="true" tabindex="-1"></a><span class="fu">hist</span>(fev,</span>
<span id="cb327-3"><a href="kvantitativa-variabler.html#cb327-3" aria-hidden="true" tabindex="-1"></a> <span class="at">xlim =</span> <span class="fu">c</span>(<span class="sc">-</span><span class="dv">5</span>, <span class="dv">10</span>),</span>
<span id="cb327-4"><a href="kvantitativa-variabler.html#cb327-4" aria-hidden="true" tabindex="-1"></a> <span class="at">ylim =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="dv">200</span>)) </span></code></pre></div>
<button title="hist_lims" type="button" onclick="if(document.getElementById('hist_lims') .style.display=='none')
{document.getElementById('hist_lims') .style.display=''}
else{document.getElementById('hist_lims') .style.display='none'}">
Visa figur
</button>
<div id="hist_lims" style="display:none">
<div class="alert alert-info">
<p><img src="docs/images/unnamed-chunk-304-1.png" width="672" style="display: block; margin: auto;" /></p>
</div>
</div>
<p></br></p>
</div>
<div id="frekvenser-ovanför-varje-klass" class="section level5 hasAnchor" number="6.1.3.0.3">
<h5><span class="header-section-number">6.1.3.0.3</span> Frekvenser ovanför varje klass<a href="kvantitativa-variabler.html#frekvenser-ovanför-varje-klass" class="anchor-section" aria-label="Anchor link to header"></a></h5>
<p>När histogram sparas i ett eget objekt, till exempel vid namn <code>h</code>, sparas även information så som frekvenser och klassmitter i objektet. För åtkomst till denna information används <code>$</code>, på ett liknande sätt som det används för åtkomst till variabler i en data frame.</p>
<div class="sourceCode" id="cb328"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb328-1"><a href="kvantitativa-variabler.html#cb328-1" aria-hidden="true" tabindex="-1"></a>h <span class="ot"><-</span> <span class="fu">hist</span>(fev, <span class="at">ylim =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="dv">170</span>)) <span class="co"># Sparar histogram i h</span></span>
<span id="cb328-2"><a href="kvantitativa-variabler.html#cb328-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb328-3"><a href="kvantitativa-variabler.html#cb328-3" aria-hidden="true" tabindex="-1"></a>h<span class="sc">$</span>mids <span class="co"># Plockar ut klassmitter m.h.a. $mids</span></span>
<span id="cb328-4"><a href="kvantitativa-variabler.html#cb328-4" aria-hidden="true" tabindex="-1"></a> [<span class="dv">1</span>] <span class="fl">0.75</span> <span class="fl">1.25</span> <span class="fl">1.75</span> <span class="fl">2.25</span> <span class="fl">2.75</span> <span class="fl">3.25</span> <span class="fl">3.75</span> <span class="fl">4.25</span> <span class="fl">4.75</span> <span class="fl">5.25</span> <span class="fl">5.75</span></span>
<span id="cb328-5"><a href="kvantitativa-variabler.html#cb328-5" aria-hidden="true" tabindex="-1"></a>h<span class="sc">$</span>counts <span class="co"># Plockar ut frekvenser m.h.a. $counts</span></span>
<span id="cb328-6"><a href="kvantitativa-variabler.html#cb328-6" aria-hidden="true" tabindex="-1"></a> [<span class="dv">1</span>] <span class="dv">3</span> <span class="dv">37</span> <span class="dv">127</span> <span class="dv">148</span> <span class="dv">136</span> <span class="dv">103</span> <span class="dv">48</span> <span class="dv">30</span> <span class="dv">16</span> <span class="dv">3</span> <span class="dv">3</span></span></code></pre></div>
<p>Den sparade informationen kan nu användas för att ange frekvensen i varje klass i histogrammet. För att göra detta används tilläggsfunktionen <strong><code>text()</code></strong> som nedan. De två första argumenten i funktionen anger kordinater för texten i <span class="math inline">\(x\)</span>- och <span class="math inline">\(y\)</span>-led (de bestämmer var texten ska ligga i diagrammet). Argumentet <code>labels</code> anger vilken text som skrivas ut, och eftersom det är frekvenserna som önskas specificeras argumentet som <code>labels = h$counts</code>. Det sista argumentet, <code>adj</code>, ser till så att texten centreras ovanför varje klass, testa gärna att sätta in andra värden istället för <span class="math inline">\(0.5\)</span> och <span class="math inline">\(-0.5\)</span> för att se vad som händer.</p>
<div class="sourceCode" id="cb329"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb329-1"><a href="kvantitativa-variabler.html#cb329-1" aria-hidden="true" tabindex="-1"></a>h <span class="ot"><-</span> <span class="fu">hist</span>(fev, <span class="at">ylim =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="dv">170</span>)) </span>
<span id="cb329-2"><a href="kvantitativa-variabler.html#cb329-2" aria-hidden="true" tabindex="-1"></a><span class="fu">text</span>(h<span class="sc">$</span>mids, h<span class="sc">$</span>counts, <span class="at">labels =</span> h<span class="sc">$</span>counts, <span class="at">adj =</span> <span class="fu">c</span>(<span class="fl">0.5</span>, <span class="sc">-</span><span class="fl">0.5</span>))</span></code></pre></div>
<button title="hist_counts" type="button" onclick="if(document.getElementById('hist_counts') .style.display=='none')
{document.getElementById('hist_counts') .style.display=''}
else{document.getElementById('hist_counts') .style.display='none'}">
Visa figur
</button>
<div id="hist_counts" style="display:none">
<div class="alert alert-info">
<p><img src="docs/images/unnamed-chunk-307-1.png" width="672" style="display: block; margin: auto;" /></p>
</div>
</div>
<p></br></p>
</div>
<div id="klassgränser-och-antal-klasser" class="section level5 hasAnchor" number="6.1.3.0.4">
<h5><span class="header-section-number">6.1.3.0.4</span> Klassgränser och antal klasser<a href="kvantitativa-variabler.html#klassgränser-och-antal-klasser" class="anchor-section" aria-label="Anchor link to header"></a></h5>
<p>Argumentet <code>breaks</code> kan användas på två olika sätt. Antingen kan en vektor med önskade klassgränser anges, eller så kan argumentet anges för att justera antalet klasser i ett histogra. Jämför till exempel de två histogrammen som genereras nedan, och fundera på hur de hänger ihop med koden.</p>
<div class="sourceCode" id="cb330"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb330-1"><a href="kvantitativa-variabler.html#cb330-1" aria-hidden="true" tabindex="-1"></a><span class="fu">hist</span>(fev, <span class="at">breaks =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="dv">1</span>, <span class="dv">3</span>, <span class="dv">6</span>))</span></code></pre></div>
<button title="hist_breaks" type="button" onclick="if(document.getElementById('hist_breaks') .style.display=='none')
{document.getElementById('hist_breaks') .style.display=''}
else{document.getElementById('hist_breaks') .style.display='none'}">
Visa figur
</button>
<div id="hist_breaks" style="display:none">
<div class="alert alert-info">
<p><img src="docs/images/unnamed-chunk-309-1.png" width="672" style="display: block; margin: auto;" /></p>
</div>
</div>
<p></br></p>
<div class="sourceCode" id="cb331"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb331-1"><a href="kvantitativa-variabler.html#cb331-1" aria-hidden="true" tabindex="-1"></a><span class="fu">hist</span>(fev, <span class="at">breaks =</span> <span class="dv">20</span>) </span></code></pre></div>
<button title="hist_breaks1" type="button" onclick="if(document.getElementById('hist_breaks1') .style.display=='none')
{document.getElementById('hist_breaks1') .style.display=''}
else{document.getElementById('hist_breaks1') .style.display='none'}">
Visa figur
</button>
<div id="hist_breaks1" style="display:none">
<div class="alert alert-info">
<p><img src="docs/images/unnamed-chunk-311-1.png" width="672" style="display: block; margin: auto;" /></p>
</div>
</div>
<p></br></p>
<p>Notera att argumentet <code>breaks</code> kan vara lite tjurigt i det senare fallet. Ibland blir det så att <code>R</code> (av helt oförståeliga själ) delvis ignorerar argummentet och väljer klassgränser som programmet själv ser som lämpliga. Det är bra för användaren att ha detta i sitt medvetande, då det inte alltid behöver vara så att koden i sig är fel, utan det kan bara vara <code>R</code> som spökar.</p>
<p>I de fall där klassbredderna är olika är det bra att använda argumentet <code>freq = FALSE</code>. <code>R</code> använder då frekvenstätheter, istället för frekvenser, i histogrammet, och diagrammets <span class="math inline">\(y\)</span>-axel blir mycket lättare att tolka.</p>
</div>
<div id="ytterligare-specifikationer" class="section level5 hasAnchor" number="6.1.3.0.5">
<h5><span class="header-section-number">6.1.3.0.5</span> Ytterligare specifikationer<a href="kvantitativa-variabler.html#ytterligare-specifikationer" class="anchor-section" aria-label="Anchor link to header"></a></h5>
<p>Av rent estetiska själ kan det vara önskvärt att ta bort kantlinjerna runt de olika staplarna. I <code>R</code> ordnas detta med argumentet <code>border = FALSE</code>. Dessutom kan staplarnas färg ändras till något lite roligare än grått, detta ändras med hjälp av argumentet <code>col</code> (en samling av hur olika färger kodas i <code>R</code> finns <a href="http://www.stat.columbia.edu/~tzheng/files/Rcolor.pdf?utm_source=twitterfeed&utm_medium=twitter">här</a>
).</p>
<p>Ett lite snyggare histogram skulle till exempel kunna skapas som nedan.</p>
<div class="sourceCode" id="cb332"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb332-1"><a href="kvantitativa-variabler.html#cb332-1" aria-hidden="true" tabindex="-1"></a><span class="fu">hist</span>(fev, </span>
<span id="cb332-2"><a href="kvantitativa-variabler.html#cb332-2" aria-hidden="true" tabindex="-1"></a> <span class="at">main =</span> <span class="st">""</span>, <span class="co"># Tar bort histogrammets titel</span></span>
<span id="cb332-3"><a href="kvantitativa-variabler.html#cb332-3" aria-hidden="true" tabindex="-1"></a> <span class="at">xlab =</span> <span class="st">"FEV (liter/sek)"</span>, <span class="co"># Etikett på x-axel</span></span>
<span id="cb332-4"><a href="kvantitativa-variabler.html#cb332-4" aria-hidden="true" tabindex="-1"></a> <span class="at">ylab =</span> <span class="st">"Frekvens"</span>, <span class="co"># Etikett på x-axel</span></span>
<span id="cb332-5"><a href="kvantitativa-variabler.html#cb332-5" aria-hidden="true" tabindex="-1"></a> <span class="at">breaks =</span> <span class="dv">20</span>, <span class="co"># Antal klasser</span></span>
<span id="cb332-6"><a href="kvantitativa-variabler.html#cb332-6" aria-hidden="true" tabindex="-1"></a> <span class="at">border =</span> <span class="cn">FALSE</span>, <span class="co"># Tar bort kant runt staplar</span></span>
<span id="cb332-7"><a href="kvantitativa-variabler.html#cb332-7" aria-hidden="true" tabindex="-1"></a> <span class="at">col =</span> <span class="st">"plum"</span>) <span class="co"># Ändrar färg på staplarna</span></span></code></pre></div>
<p><img src="docs/images/unnamed-chunk-312-1.png" width="672" style="display: block; margin: auto;" /></p>
<p><img src="docs/images/note.png" width="5%" style="display: block; margin: auto;" /></p>
<style>
div.yellow{ background-color:#FFFA94; border-radius: 5px; padding: 20px;}
</style>
<div class="yellow">
<p><font size="4"> Klassgränser och antalet klasser </font></p>
<p>Valen som görs ovan är naturligtvis subjektiva, och det finns inget som säger vad som är snyggt eller inte. Det är dock bra att tänka lite extra på hur klassgränser och antalet klasser specificeras i ett histogram, eftersom detta kan påverka hur väl diagrammet faktiskt speglar datamaterialet.</p>
<p>Här nedan illustreras samma datamaterial i fyra histogram med olika klassgränser och antal klasser. Datamaterialet som illustreras är normalfördelat, vilket tydligt kan ses i figurerna längst upp till vänster och längst ner till höger. I de övriga diagrammen är det svårt att säga något som helst om huruvida datamaterialet är normalfördelat eller ej.</p>
<p><img src="docs/images/unnamed-chunk-315-1.png" width="672" style="display: block; margin: auto;" /></p>
<p>Det är därför värt att testa ett par olika alternativ innan ett slutligt diagram väljs, för att hitta den inställning som illustrerar datamaterialet så bra som möjligt.</p>
</div>
<p></br></p>
</div>
</div>
</div>
<div id="analys-av-två-kvantitativa-variabler" class="section level2 hasAnchor" number="6.2">
<h2><span class="header-section-number">6.2</span> Analys av två kvantitativa variabler<a href="kvantitativa-variabler.html#analys-av-två-kvantitativa-variabler" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p>Detta avsnitt handlar om hur två kvantitativa variabler kan illustreras i samma figur. Avsnittet är uppdelat i två delar, där distinktionen grundar sig i vilka variabeltyper det är som ska illustreras. Baserat på denna distinktion bestäms vilken typ av diagram som är mest lämpligt (precis som i statistik A4/A8), och det är därför väldigt bra att tänka på vilken typ av variabler som ska beskrivas innan den deskriptiva analysen påbörjas.</p>
<div id="två-kontinuerliga-variabler" class="section level3 hasAnchor" number="6.2.1">
<h3><span class="header-section-number">6.2.1</span> Två kontinuerliga variabler<a href="kvantitativa-variabler.html#två-kontinuerliga-variabler" class="anchor-section" aria-label="Anchor link to header"></a></h3>
<p>De två vanligaste sätten att beskriva två kontinuerliga variabler är <em>spridningsdiagram</em> och <em>Pearsons korrelationskoefficient</em>. Det förra är ett bra sätt att illustrera samvariation mellan variabler, och den senare mäter huruvida det finns något linjärt samband mellan de båda variablerna.</p>
<div id="spridningsdiagram" class="section level4 hasAnchor" number="6.2.1.1">
<h4><span class="header-section-number">6.2.1.1</span> Spridningsdiagram<a href="kvantitativa-variabler.html#spridningsdiagram" class="anchor-section" aria-label="Anchor link to header"></a></h4>
<p>Många gånger kan det vara av intresse att skapa en figur för att se om två kontinuerliga variabler samvarierar på något sätt, och då är spridningsdiagram (scatter plot) ett bra alternativ. Spridningsdiagram skapas med det generiska kommandot <code>plot()</code> i <code>R</code>, och kan till stor del justeras på samma sätt som histogrammen ovan.</p>
<p>För att skapa ett vanligt spridningsdiagram där <code>height</code> finns <span class="math inline">\(x\)</span>-axeln och <code>fev</code> finns på <span class="math inline">\(y\)</span>-axeln används koden nedan.</p>
<div class="sourceCode" id="cb333"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb333-1"><a href="kvantitativa-variabler.html#cb333-1" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(<span class="at">x =</span> height, <span class="at">y =</span> fev)</span></code></pre></div>
<p><img src="docs/images/unnamed-chunk-316-1.png" width="672" style="display: block; margin: auto;" /></p>
<p>I figuren kan cirklarna som representerar varje observation bytas ut till andra symboler, detta görs genom att ändra argumentet <code>pch</code> till ett siffervärde mellan 0 och 25. Till exempel kan cirklarna bytas ut till kvadrater med hjälp av koden nedan (en sida som sammanfattar vilket siffervärde som ger vilken symbol finns <a href="http://www.sthda.com/english/wiki/r-plot-pch-symbols-the-different-point-shapes-available-in-r">här</a>.</p>
<div class="sourceCode" id="cb334"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb334-1"><a href="kvantitativa-variabler.html#cb334-1" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(<span class="at">x =</span> height, <span class="at">y =</span> fev, <span class="at">pch =</span> <span class="dv">0</span>)</span></code></pre></div>
<button title="scat_square" type="button" onclick="if(document.getElementById('scat_square') .style.display=='none')
{document.getElementById('scat_square') .style.display=''}
else{document.getElementById('scat_square') .style.display='none'}">
Visa figur
</button>
<div id="scat_square" style="display:none">
<div class="alert alert-info">
<p><img src="docs/images/unnamed-chunk-318-1.png" width="672" style="display: block; margin: auto;" /></p>
</div>
</div>
<p></br></p>
<p>Det finns en del argument som fyller samma funktion i <code>plot()</code> som i <code>hist()</code>, dessa är</p>
<ul>
<li><code>main</code>, <code>xlab</code> och <code>ylab</code> för titlar och etiketter</li>
<li><code>ylim</code> och <code>xlim</code> för axellängder</li>
<li><code>col</code> för färger på punkterna.</li>
</ul>
<p>Ett lite snyggare spridningsdiagram kan skapas som</p>
<div class="sourceCode" id="cb335"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb335-1"><a href="kvantitativa-variabler.html#cb335-1" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(<span class="at">x =</span> height, <span class="co"># x-variabel</span></span>
<span id="cb335-2"><a href="kvantitativa-variabler.html#cb335-2" aria-hidden="true" tabindex="-1"></a> <span class="at">y =</span> fev, <span class="co"># y-variabel</span></span>
<span id="cb335-3"><a href="kvantitativa-variabler.html#cb335-3" aria-hidden="true" tabindex="-1"></a> <span class="at">ylab =</span> <span class="st">"FEV (liter/sek)"</span>, <span class="co"># Etikett till y-axel</span></span>
<span id="cb335-4"><a href="kvantitativa-variabler.html#cb335-4" aria-hidden="true" tabindex="-1"></a> <span class="at">xlab =</span> <span class="st">"Längd"</span>, <span class="co"># Etikett till x-axel</span></span>
<span id="cb335-5"><a href="kvantitativa-variabler.html#cb335-5" aria-hidden="true" tabindex="-1"></a> <span class="at">pch =</span> <span class="dv">16</span>, <span class="co"># Ifylld punkt som markör</span></span>
<span id="cb335-6"><a href="kvantitativa-variabler.html#cb335-6" aria-hidden="true" tabindex="-1"></a> <span class="at">col =</span> <span class="st">"blue"</span>) <span class="co"># Ändrar färg på punkterna</span></span></code></pre></div>
<p><img src="docs/images/unnamed-chunk-319-1.png" width="672" style="display: block; margin: auto;" /></p>
</div>
<div id="pearsons-korrelationskoefficient" class="section level4 hasAnchor" number="6.2.1.2">
<h4><span class="header-section-number">6.2.1.2</span> Pearsons korrelationskoefficient<a href="kvantitativa-variabler.html#pearsons-korrelationskoefficient" class="anchor-section" aria-label="Anchor link to header"></a></h4>
<p>Pearsons korrelationskoefficient är ofta ett bra komplement till ett spridningsdiagram. Korrelationskoefficienten kan ta värden mellan -1 och 1, och mäter hur pass linjär samvariationen mellan två <strong>kontinuerliga</strong> variabler är, alltså hur väl punkterna i spridningsdiagrammet är samlade runt en rät linje.</p>
<p>En korrelationskoefficient som ligger nära 1 tyder på stark, positiv samvariation. Om den ena variabeln har ett högt värde, är det högst troligt att även den andra har det (se den översta figuren här nedan). Motsvarande gäller för obseravtioner med låga värden. En korrelationskoefficient på -1 tyder på det motsatta, om den ena variabeln har ett högt värde förväntas den andra variabeln ha ett lågt värde (se den mellersta figuren här nedan). Slutligen tyder en korrelationskoefficient nära 0 på att ingen linjär smavariation finns, punkterna bör alltså vara spridda slumpmässigt i diagrammet (se den nedre figuren här nedan).</p>
<p><img src="docs/images/unnamed-chunk-321-1.png" width="672" style="display: block; margin: auto;" /><img src="docs/images/unnamed-chunk-321-2.png" width="672" style="display: block; margin: auto;" /><img src="docs/images/unnamed-chunk-321-3.png" width="672" style="display: block; margin: auto;" /></p>
<p>I <code>R</code> beräknas stickproveskorrelationen mellan två variabler med hjälp av funktionen <code>cor()</code>. Stickprovskorrelationen mellan <code>height</code> och <code>fev</code> beräknas
som</p>
<div class="sourceCode" id="cb336"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb336-1"><a href="kvantitativa-variabler.html#cb336-1" aria-hidden="true" tabindex="-1"></a><span class="fu">cor</span>(<span class="at">x =</span> height, <span class="at">y =</span> fev) </span>
<span id="cb336-2"><a href="kvantitativa-variabler.html#cb336-2" aria-hidden="true" tabindex="-1"></a>[<span class="dv">1</span>] <span class="fl">0.868135</span></span></code></pre></div>
<p>Vilket ser ut att stämma relativt väl överens med spridningsdiagrammet i det förra avsnittet.</p>
<p><img src="docs/images/note.png" width="5%" style="display: block; margin: auto;" /></p>
<style>
div.yellow{ background-color:#FFFA94; border-radius: 5px; padding: 20px;}
</style>
<div class="yellow">
<p><font size="4"> Korrelation och icke-linjära samband </font></p>
<p>En sak som är viktig att komma ihåg är att Pearsons korrelations-koefficient bara mäter hur stark den <strong>linjära</strong> samvariationen mellan två variabler är. Det finns naturligtvis flera typer av samvariation som <strong>inte</strong> är linjära, och i deskriptiva analyser är det därför viktigt att använda korrelations-koefficienten med viss försiktigthet, och gärna tillsammans med spridningsdiagram. Här nedan följer ett exempel som visar på varför en viss grad av försiktighet är nödvändig.</p>
<p>I fliken finns två variabler <code>x_cor</code> och <code>y_cor</code> som används för att illustrera en situation då korrelationskoefficienten, när tolkas felaktigt, kan ge en skev bild av datamaterialet.</p>
<button title="sin_plot" type="button" onclick="if(document.getElementById('sin_plot') .style.display=='none')
{document.getElementById('sin_plot') .style.display=''}
else{document.getElementById('sin_plot') .style.display='none'}">
Visa datamaterial
</button>
<div id="sin_plot" style="display:none">
<div class="alert alert-info">
<div class="sourceCode" id="cb337"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb337-1"><a href="kvantitativa-variabler.html#cb337-1" aria-hidden="true" tabindex="-1"></a>x_cor <span class="ot"><-</span> <span class="fu">c</span>(<span class="sc">-</span><span class="fl">5.86439253855497</span>, <span class="sc">-</span><span class="fl">1.43597680237144</span>, <span class="sc">-</span><span class="fl">0.557658380828798</span>, <span class="fl">0.553684489801526</span>, <span class="sc">-</span><span class="fl">1.48444498702884</span>, <span class="sc">-</span><span class="fl">4.54311690945178</span>, <span class="sc">-</span><span class="fl">4.70674677751958</span>, <span class="fl">4.60378906968981</span>, <span class="sc">-</span><span class="fl">1.43077093642205</span>, <span class="sc">-</span><span class="fl">2.44445485342294</span>, <span class="sc">-</span><span class="fl">4.48213258478791</span>, <span class="fl">1.71518361009657</span>, <span class="sc">-</span><span class="fl">4.26403472386301</span>, <span class="sc">-</span><span class="fl">0.208796096965671</span>, <span class="sc">-</span><span class="fl">3.69642441999167</span>, <span class="sc">-</span><span class="fl">0.304030154831707</span>, <span class="fl">2.30663920473307</span>, <span class="fl">4.72523551527411</span>, <span class="fl">2.10758776031435</span>, <span class="fl">5.78801127243787</span>, <span class="fl">4.59385838359594</span>, <span class="sc">-</span><span class="fl">3.53894815407693</span>, <span class="sc">-</span><span class="fl">4.06569141335785</span>, <span class="sc">-</span><span class="fl">0.933496956713498</span>, <span class="fl">5.01003466453403</span>, <span class="sc">-</span><span class="fl">2.92779209185392</span>, <span class="fl">0.383819226175547</span>, <span class="fl">1.69766232836992</span>, <span class="sc">-</span><span class="fl">0.0605317857116461</span>, <span class="fl">2.15893999580294</span>, <span class="sc">-</span><span class="fl">0.937316212803125</span>, <span class="sc">-</span><span class="fl">1.26719969697297</span>, <span class="sc">-</span><span class="fl">1.06448861863464</span>, <span class="sc">-</span><span class="fl">0.70016285777092</span>, <span class="fl">3.85658694896847</span>, <span class="sc">-</span><span class="fl">4.302495572716</span>, <span class="sc">-</span><span class="fl">4.40025229286402</span>, <span class="sc">-</span><span class="fl">1.75088406633586</span>, <span class="fl">4.64191750902683</span>, <span class="sc">-</span><span class="fl">5.45604836661369</span>, <span class="fl">2.1750651570037</span>, <span class="sc">-</span><span class="fl">2.65939560346305</span>, <span class="sc">-</span><span class="fl">2.80156862642616</span>, <span class="sc">-</span><span class="fl">0.296186163090169</span>, <span class="sc">-</span><span class="fl">5.6524095358327</span>, <span class="fl">2.24203268252313</span>, <span class="sc">-</span><span class="fl">4.34353812318295</span>, <span class="fl">5.11039749998599</span>, <span class="sc">-</span><span class="fl">1.71673354133964</span>, <span class="sc">-</span><span class="fl">0.19572323653847</span>, <span class="fl">0.433533512055874</span>, <span class="fl">2.86123791430146</span>, <span class="fl">3.56698769889772</span>, <span class="fl">5.12141733337194</span>, <span class="fl">5.66679778229445</span>, <span class="fl">1.42487081419677</span>, <span class="fl">1.02799868490547</span>, <span class="fl">3.07261069491506</span>, <span class="sc">-</span><span class="fl">0.523379808291793</span>, <span class="sc">-</span><span class="fl">3.97485722322017</span>, <span class="fl">2.47302148025483</span>, <span class="sc">-</span><span class="fl">0.959513308480382</span>, <span class="fl">0.435494952835143</span>, <span class="fl">2.56544065196067</span>, <span class="sc">-</span><span class="fl">4.23642921354622</span>, <span class="fl">2.51910498552024</span>, <span class="sc">-</span><span class="fl">3.43450129777193</span>, <span class="fl">4.40523060131818</span>, <span class="fl">4.14423972554505</span>, <span class="fl">2.7713297791779</span>, <span class="sc">-</span><span class="fl">0.659573706798255</span>, <span class="sc">-</span><span class="fl">0.316247899085283</span>, <span class="sc">-</span><span class="fl">4.37690794095397</span>, <span class="fl">0.701152271591127</span>, <span class="fl">5.01649497449398</span>, <span class="sc">-</span><span class="fl">2.51752826850861</span>, <span class="sc">-</span><span class="fl">5.19016728177667</span>, <span class="fl">0.846395524218678</span>, <span class="sc">-</span><span class="fl">3.74603203497827</span>, <span class="fl">2.9088171645999</span>, <span class="sc">-</span><span class="fl">5.34782209899276</span>, <span class="fl">4.68921250384301</span>, <span class="fl">3.54415418487042</span>, <span class="sc">-</span><span class="fl">0.661200986243784</span>, <span class="fl">3.53289462905377</span>, <span class="fl">4.25234192423522</span>, <span class="fl">4.19615561608225</span>, <span class="fl">2.602389623411</span>, <span class="sc">-</span><span class="fl">1.57098864857107</span>, <span class="fl">2.30702747404575</span>, <span class="sc">-</span><span class="fl">4.52308602724224</span>, <span class="fl">5.23059280961752</span>, <span class="sc">-</span><span class="fl">5.76080022845417</span>, <span class="sc">-</span><span class="fl">0.810422932729125</span>, <span class="fl">0.611223335377872</span>, <span class="fl">3.11755008157343</span>, <span class="fl">1.94819243531674</span>, <span class="sc">-</span><span class="fl">2.98065088782459</span>, <span class="fl">5.24784311838448</span>, <span class="fl">2.04372919443995</span>, <span class="sc">-</span><span class="fl">2.52907108515501</span>, <span class="fl">2.27760804723948</span>, <span class="sc">-</span><span class="fl">1.01213886961341</span>, <span class="fl">1.89285836555064</span>, <span class="fl">1.48235849384218</span>, <span class="sc">-</span><span class="fl">0.756356027908623</span>, <span class="sc">-</span><span class="fl">2.67695398908108</span>, <span class="sc">-</span><span class="fl">2.8729636548087</span>, <span class="sc">-</span><span class="fl">1.13260476384312</span>, <span class="fl">5.53976978547871</span>, <span class="sc">-</span><span class="fl">4.86333254165947</span>, <span class="fl">3.73086743988097</span>, <span class="fl">3.51884004659951</span>, <span class="fl">2.53500320389867</span>, <span class="sc">-</span><span class="fl">4.02673621941358</span>, <span class="fl">4.72284496296197</span>, <span class="sc">-</span><span class="fl">5.26503092329949</span>, <span class="fl">2.81897336896509</span>, <span class="fl">3.97550426702946</span>, <span class="sc">-</span><span class="fl">1.89988576434553</span>, <span class="fl">2.14803829137236</span>, <span class="sc">-</span><span class="fl">1.21428278367966</span>, <span class="fl">1.86381844617426</span>, <span class="sc">-</span><span class="fl">3.91419969219714</span>, <span class="sc">-</span><span class="fl">5.26569446269423</span>, <span class="sc">-</span><span class="fl">5.33130717650056</span>, <span class="sc">-</span><span class="fl">0.940515568479896</span>, <span class="sc">-</span><span class="fl">0.887071288190782</span>, <span class="fl">1.18806012813002</span>, <span class="sc">-</span><span class="fl">5.16970119997859</span>, <span class="sc">-</span><span class="fl">0.87442019674927</span>, <span class="fl">0.449586038477719</span>, <span class="sc">-</span><span class="fl">3.53376394417137</span>, <span class="sc">-</span><span class="fl">3.34293064288795</span>, <span class="sc">-</span><span class="fl">2.21858079917729</span>, <span class="fl">3.05507892742753</span>, <span class="fl">2.79804273694754</span>, <span class="fl">2.70105247199535</span>, <span class="fl">2.82882257737219</span>, <span class="sc">-</span><span class="fl">0.00406247656792402</span>, <span class="sc">-</span><span class="fl">3.01224234234542</span>, <span class="sc">-</span><span class="fl">5.17500651441514</span>, <span class="sc">-</span><span class="fl">4.46285936515778</span>, <span class="sc">-</span><span class="fl">5.56699248589575</span>, <span class="fl">0.391616527922451</span>, <span class="sc">-</span><span class="fl">3.77570909075439</span>, <span class="sc">-</span><span class="fl">0.801314611919224</span>, <span class="sc">-</span><span class="fl">0.834749462082982</span>, <span class="sc">-</span><span class="fl">5.10326085425913</span>, <span class="sc">-</span><span class="fl">4.49976385105401</span>, <span class="fl">4.30535251367837</span>, <span class="fl">1.95064429007471</span>, <span class="sc">-</span><span class="fl">4.27386486344039</span>, <span class="sc">-</span><span class="fl">1.22882923856378</span>, <span class="sc">-</span><span class="fl">4.94328713882715</span>, <span class="fl">1.95183547865599</span>, <span class="sc">-</span><span class="fl">1.91666411329061</span>, <span class="sc">-</span><span class="fl">1.86356966011226</span>, <span class="fl">5.11462553031743</span>, <span class="sc">-</span><span class="fl">3.20687001664191</span>, <span class="sc">-</span><span class="fl">3.38617214374244</span>, <span class="sc">-</span><span class="fl">1.3609501440078</span>, <span class="fl">5.20629471447319</span>, <span class="fl">4.32619164604694</span>, <span class="fl">1.36014333274215</span>, <span class="sc">-</span><span class="fl">1.66064143180847</span>, <span class="fl">0.160328395664692</span>, <span class="sc">-</span><span class="fl">3.09523442387581</span>, <span class="sc">-</span><span class="fl">2.80701953172684</span>, <span class="fl">3.52882725466043</span>, <span class="fl">1.92389569245279</span>, <span class="sc">-</span><span class="fl">3.34456553310156</span>, <span class="sc">-</span><span class="fl">1.08310336433351</span>, <span class="sc">-</span><span class="fl">4.21733734756708</span>, <span class="fl">2.41087722312659</span>, <span class="fl">1.32709406409413</span>, <span class="fl">2.75043877400458</span>, <span class="sc">-</span><span class="fl">4.4830230306834</span>, <span class="sc">-</span><span class="fl">1.22587357275188</span>, <span class="sc">-</span><span class="fl">1.48652502615005</span>, <span class="sc">-</span><span class="fl">0.891042815521359</span>, <span class="fl">4.15688028931618</span>, <span class="sc">-</span><span class="fl">2.4806948332116</span>, <span class="sc">-</span><span class="fl">3.21958520170301</span>, <span class="fl">1.8265458997339</span>, <span class="sc">-</span><span class="fl">5.35168910678476</span>, <span class="fl">5.40245028678328</span>, <span class="sc">-</span><span class="fl">5.22069438826293</span>, <span class="sc">-</span><span class="fl">0.696254429407418</span>, <span class="fl">3.07486899476498</span>, <span class="sc">-</span><span class="fl">2.64368547219783</span>, <span class="fl">0.313281577080488</span>, <span class="fl">4.13077652547508</span>, <span class="fl">0.59310564212501</span>, <span class="sc">-</span><span class="fl">4.45451829582453</span>, <span class="sc">-</span><span class="fl">3.89451640751213</span>, <span class="sc">-</span><span class="fl">1.54594003781676</span>, <span class="sc">-</span><span class="fl">3.08049134351313</span>, <span class="fl">0.177653674967587</span>, <span class="fl">3.50173227488995</span>, <span class="sc">-</span><span class="fl">2.01388649828732</span>, <span class="fl">3.16356065869331</span>, <span class="sc">-</span><span class="fl">4.8224638486281</span>, <span class="sc">-</span><span class="fl">4.89060790836811</span>, <span class="fl">1.16010802611709</span>, <span class="sc">-</span><span class="fl">4.60733616258949</span>, <span class="fl">3.94017753470689</span>, <span class="sc">-</span><span class="fl">2.344950302504</span>, <span class="sc">-</span><span class="fl">3.18453837186098</span>, <span class="sc">-</span><span class="fl">4.00804762355983</span>, <span class="sc">-</span><span class="fl">2.76524977572262</span>, <span class="sc">-</span><span class="fl">4.77857188414782</span>, <span class="fl">1.92331372294575</span>, <span class="fl">2.0959399882704</span>, <span class="fl">1.89606608077884</span>, <span class="fl">4.46141163725406</span>, <span class="sc">-</span><span class="fl">4.31323133502156</span>, <span class="fl">2.20478624850512</span>, <span class="sc">-</span><span class="fl">0.232552042230964</span>, <span class="fl">4.8380277575925</span>, <span class="fl">3.11489412467927</span>, <span class="fl">3.46245760470629</span>, <span class="fl">1.87206973694265</span>, <span class="fl">2.80687589105219</span>, <span class="fl">1.83384580537677</span>, <span class="fl">2.63242583256215</span>, <span class="fl">0.495583872310817</span>, <span class="sc">-</span><span class="fl">5.15827745106071</span>, <span class="sc">-</span><span class="fl">4.84405103512108</span>, <span class="sc">-</span><span class="fl">5.21479791775346</span>, <span class="fl">3.35555247310549</span>, <span class="sc">-</span><span class="fl">1.44319519400597</span>, <span class="fl">1.4710839567706</span>, <span class="fl">2.24455487541854</span>, <span class="fl">1.27918676845729</span>, <span class="sc">-</span><span class="fl">1.61587416194379</span>, <span class="sc">-</span><span class="fl">0.146192556247115</span>, <span class="sc">-</span><span class="fl">1.50593885779381</span>, <span class="sc">-</span><span class="fl">2.21367011871189</span>, <span class="fl">3.85590899270028</span>, <span class="fl">2.31367619521916</span>, <span class="fl">0.817260009236634</span>, <span class="fl">3.81954930536449</span>, <span class="fl">1.78521729446948</span>, <span class="sc">-</span><span class="fl">0.931415791623294</span>, <span class="sc">-</span><span class="fl">4.05018984898925</span>, <span class="fl">2.88604778051376</span>, <span class="sc">-</span><span class="fl">3.54378416575491</span>, <span class="fl">0.934073282405734</span>, <span class="fl">1.91026193741709</span>, <span class="fl">3.90620255470276</span>, <span class="sc">-</span><span class="fl">3.09297367371619</span>, <span class="sc">-</span><span class="fl">0.781432407908142</span>, <span class="sc">-</span><span class="fl">3.37139746919274</span>, <span class="sc">-</span><span class="fl">3.48574412427843</span>, <span class="sc">-</span><span class="fl">0.201942172832787</span>, <span class="sc">-</span><span class="fl">1.03117333631963</span>, <span class="sc">-</span><span class="fl">2.29081455152482</span>, <span class="fl">4.9195710606873</span>, <span class="fl">5.59172852151096</span>, <span class="sc">-</span><span class="fl">3.06280124746263</span>, <span class="sc">-</span><span class="fl">5.04959790408611</span>, <span class="sc">-</span><span class="fl">1.67600579280406</span>, <span class="sc">-</span><span class="fl">5.62163967546076</span>, <span class="fl">0.00048559159040451</span>, <span class="fl">2.44796640146524</span>, <span class="sc">-</span><span class="fl">4.40249607246369</span>, <span class="sc">-</span><span class="fl">3.12038963846862</span>, <span class="sc">-</span><span class="fl">5.90665160212666</span>, <span class="sc">-</span><span class="fl">3.07803991343826</span>, <span class="sc">-</span><span class="fl">2.705247589387</span>, <span class="sc">-</span><span class="fl">1.41524924430996</span>, <span class="sc">-</span><span class="fl">5.66812112554908</span>, <span class="sc">-</span><span class="fl">5.52824538107961</span>, <span class="fl">4.69527727738023</span>, <span class="sc">-</span><span class="fl">0.0249824076890945</span>, <span class="sc">-</span><span class="fl">4.41420126333833</span>, <span class="fl">0.268953206017613</span>, <span class="fl">1.70019644312561</span>, <span class="fl">3.85920576564968</span>, <span class="fl">0.982753903605044</span>, <span class="sc">-</span><span class="fl">2.0266708675772</span>, <span class="sc">-</span><span class="fl">2.07221507281065</span>, <span class="sc">-</span><span class="fl">3.13442851323634</span>, <span class="fl">0.901587945409119</span>, <span class="sc">-</span><span class="fl">3.32639229577035</span>, <span class="sc">-</span><span class="fl">2.64481509849429</span>, <span class="sc">-</span><span class="fl">1.4289373839274</span>, <span class="sc">-</span><span class="fl">1.01676025986671</span>, <span class="sc">-</span><span class="fl">0.260985455475748</span>, <span class="sc">-</span><span class="fl">2.20148284826428</span>, <span class="fl">0.471208141185343</span>, <span class="fl">3.62979944888502</span>, <span class="sc">-</span><span class="fl">1.63145815953612</span>, <span class="fl">5.50091175176203</span>, <span class="fl">4.04855551756918</span>, <span class="sc">-</span><span class="fl">0.204747154377401</span>, <span class="sc">-</span><span class="fl">1.6134633757174</span>, <span class="fl">4.006162667647</span>, <span class="sc">-</span><span class="fl">5.78578860964626</span>, <span class="sc">-</span><span class="fl">4.4473615558818</span>, <span class="sc">-</span><span class="fl">0.51764655020088</span>, <span class="fl">1.77362532075495</span>, <span class="sc">-</span><span class="fl">4.23136412724853</span>, <span class="fl">3.21683595143259</span>, <span class="fl">4.25683191139251</span>, <span class="fl">5.71499114949256</span>, <span class="sc">-</span><span class="fl">5.90049939695746</span>, <span class="sc">-</span><span class="fl">4.94474141299725</span>, <span class="sc">-</span><span class="fl">0.461656811647117</span>, <span class="fl">0.22233750578016</span>, <span class="sc">-</span><span class="fl">0.368306050077081</span>, <span class="sc">-</span><span class="fl">0.631843621842563</span>, <span class="sc">-</span><span class="fl">2.71005070768297</span>, <span class="sc">-</span><span class="fl">5.55788201931864</span>, <span class="sc">-</span><span class="fl">5.35080788377672</span>, <span class="sc">-</span><span class="fl">5.84003126062453</span>, <span class="fl">2.66926260385662</span>, <span class="sc">-</span><span class="fl">3.76998704764992</span>, <span class="sc">-</span><span class="fl">0.425729823298752</span>, <span class="sc">-</span><span class="fl">2.05537411943078</span>, <span class="fl">0.216768493875861</span>, <span class="sc">-</span><span class="fl">3.48466119077057</span>, <span class="fl">3.64808512665331</span>, <span class="fl">2.10386463347822</span>, <span class="fl">4.14911777805537</span>, <span class="fl">2.46440581697971</span>, <span class="sc">-</span><span class="fl">3.05821720417589</span>, <span class="sc">-</span><span class="fl">0.770339076407254</span>, <span class="sc">-</span><span class="fl">4.01560948323458</span>, <span class="fl">1.64552938565612</span>, <span class="sc">-</span><span class="fl">4.31913993693888</span>, <span class="sc">-</span><span class="fl">2.94404711388052</span>, <span class="fl">2.63366373907775</span>, <span class="sc">-</span><span class="fl">0.509436529129744</span>, <span class="sc">-</span><span class="fl">2.43900655489415</span>, <span class="fl">3.90388449747115</span>, <span class="fl">4.94141294248402</span>, <span class="sc">-</span><span class="fl">2.8335997145623</span>, <span class="sc">-</span><span class="fl">0.750269285403192</span>, <span class="sc">-</span><span class="fl">3.51249697431922</span>, <span class="fl">3.06972266547382</span>, <span class="fl">5.7715987348929</span>, <span class="fl">3.49607700482011</span>, <span class="sc">-</span><span class="fl">5.46911952272058</span>, <span class="fl">1.49682352971286</span>, <span class="fl">0.185940451920033</span>, <span class="fl">2.61120565887541</span>, <span class="sc">-</span><span class="fl">2.07450593076646</span>, <span class="fl">1.94110536295921</span>, <span class="fl">4.13435281813145</span>, <span class="fl">0.668913943693042</span>, <span class="fl">0.533427002839744</span>, <span class="fl">1.13682076055557</span>, <span class="sc">-</span><span class="fl">3.3515594098717</span>, <span class="fl">2.10873214714229</span>, <span class="fl">4.52574804984033</span>, <span class="fl">2.65504027716815</span>, <span class="fl">5.93163960892707</span>, <span class="fl">4.58176778163761</span>, <span class="sc">-</span><span class="fl">2.80901133175939</span>, <span class="sc">-</span><span class="fl">3.70125117525458</span>, <span class="fl">4.5074990959838</span>, <span class="sc">-</span><span class="fl">2.17553016263992</span>, <span class="sc">-</span><span class="fl">0.41508043371141</span>, <span class="sc">-</span><span class="fl">1.84128791559488</span>, <span class="sc">-</span><span class="fl">2.52211849205196</span>, <span class="sc">-</span><span class="fl">2.9997620433569</span>, <span class="fl">3.17430431395769</span>, <span class="sc">-</span><span class="fl">2.54884536657482</span>, <span class="sc">-</span><span class="fl">0.108684950508177</span>, <span class="sc">-</span><span class="fl">3.15567467641085</span>, <span class="sc">-</span><span class="fl">5.37086521089077</span>, <span class="sc">-</span><span class="fl">2.30455892533064</span>, <span class="fl">5.67356565501541</span>, <span class="sc">-</span><span class="fl">5.33359614573419</span>, <span class="sc">-</span><span class="fl">3.17525636963546</span>, <span class="sc">-</span><span class="fl">3.78735836036503</span>, <span class="sc">-</span><span class="fl">0.00814633537083864</span>, <span class="sc">-</span><span class="fl">1.17351124249399</span>, <span class="sc">-</span><span class="fl">1.76926239486784</span>, <span class="sc">-</span><span class="fl">0.631798535585403</span>, <span class="sc">-</span><span class="fl">5.41753455530852</span>, <span class="fl">4.33960485365242</span>, <span class="sc">-</span><span class="fl">4.70884873252362</span>, <span class="sc">-</span><span class="fl">2.85036724805832</span>, <span class="sc">-</span><span class="fl">2.89936948008835</span>, <span class="fl">4.22600639238954</span>, <span class="sc">-</span><span class="fl">1.10508747305721</span>, <span class="fl">1.77784910704941</span>, <span class="fl">0.364222071133554</span>, <span class="sc">-</span><span class="fl">5.72863668389618</span>, <span class="sc">-</span><span class="fl">4.27188852801919</span>, <span class="sc">-</span><span class="fl">5.86537114251405</span>, <span class="fl">1.52154471259564</span>, <span class="sc">-</span><span class="fl">2.15860872622579</span>, <span class="fl">1.88831554446369</span>, <span class="fl">4.67907990887761</span>, <span class="fl">4.60909154545516</span>, <span class="sc">-</span><span class="fl">5.56265650782734</span>, <span class="sc">-</span><span class="fl">0.851920531131327</span>, <span class="sc">-</span><span class="fl">1.72764524258673</span>, <span class="fl">3.68325364496559</span>, <span class="fl">1.29211596306413</span>, <span class="fl">4.76557127572596</span>, <span class="sc">-</span><span class="fl">4.73709072265774</span>, <span class="sc">-</span><span class="fl">5.0276418523863</span>, <span class="sc">-</span><span class="fl">5.31207323726267</span>, <span class="fl">5.46919869817793</span>, <span class="fl">0.556542861275375</span>, <span class="sc">-</span><span class="fl">3.09453079663217</span>, <span class="fl">0.398685554042459</span>, <span class="sc">-</span><span class="fl">0.384768535383046</span>, <span class="sc">-</span><span class="fl">0.531101575121284</span>, <span class="sc">-</span><span class="fl">0.0766403647139668</span>, <span class="sc">-</span><span class="fl">5.65018736477941</span>, <span class="sc">-</span><span class="fl">2.89195249322802</span>, <span class="fl">1.10902743134648</span>, <span class="sc">-</span><span class="fl">5.56165512744337</span>, <span class="sc">-</span><span class="fl">4.23958828020841</span>, <span class="sc">-</span><span class="fl">5.01453134045005</span>, <span class="sc">-</span><span class="fl">0.189870553091168</span>, <span class="sc">-</span><span class="fl">2.83492263313383</span>, <span class="fl">2.41574100404978</span>, <span class="sc">-</span><span class="fl">2.05251438729465</span>, <span class="sc">-</span><span class="fl">5.96921091992408</span>, <span class="fl">4.23230962269008</span>, <span class="sc">-</span><span class="fl">2.39341560378671</span>, <span class="fl">3.69120146613568</span>, <span class="fl">3.35365698114038</span>, <span class="fl">4.95318208169192</span>, <span class="fl">2.78710991330445</span>, <span class="fl">3.91960581298918</span>, <span class="sc">-</span><span class="fl">3.40767204668373</span>, <span class="sc">-</span><span class="fl">2.59056472219527</span>, <span class="fl">4.46527017373592</span>, <span class="sc">-</span><span class="fl">0.534307681024075</span>, <span class="fl">5.52204624004662</span>, <span class="fl">5.36765942070633</span>, <span class="fl">0.336890671402216</span>, <span class="fl">1.15953898429871</span>, <span class="fl">0.351983623579144</span>, <span class="fl">0.0615966478362679</span>, <span class="fl">5.42799248266965</span>, <span class="sc">-</span><span class="fl">4.37932213023305</span>, <span class="fl">3.13442898541689</span>, <span class="sc">-</span><span class="fl">3.14388785976917</span>, <span class="fl">5.89572857413441</span>, <span class="fl">5.56920766364783</span>, <span class="sc">-</span><span class="fl">0.842380355112255</span>, <span class="sc">-</span><span class="fl">5.95428342372179</span>, <span class="fl">0.466116718947887</span>, <span class="fl">3.39090068824589</span>, <span class="sc">-</span><span class="fl">3.98534075729549</span>, <span class="sc">-</span><span class="fl">5.00015527568758</span>, <span class="fl">2.99162599258125</span>, <span class="sc">-</span><span class="fl">2.87129613943398</span>, <span class="sc">-</span><span class="fl">4.36781460978091</span>, <span class="fl">4.76908676885068</span>, <span class="sc">-</span><span class="fl">5.67027823068202</span>, <span class="sc">-</span><span class="fl">4.05202140379697</span>, <span class="sc">-</span><span class="fl">2.03874458279461</span>, <span class="fl">5.96935374476016</span>, <span class="fl">3.04529627133161</span>, <span class="fl">1.46130614262074</span>, <span class="sc">-</span><span class="fl">4.8296627746895</span>, <span class="fl">5.18354105204344</span>, <span class="fl">2.60001885239035</span>, <span class="fl">4.74056925158948</span>, <span class="fl">3.47412625607103</span>, <span class="sc">-</span><span class="fl">3.83562496025115</span>, <span class="fl">1.47017023991793</span>, <span class="fl">0.20291362144053</span>, <span class="fl">3.64169818349183</span>, <span class="sc">-</span><span class="fl">1.36433559469879</span>, <span class="fl">5.50361108779907</span>, <span class="sc">-</span><span class="fl">0.567957239225507</span>, <span class="sc">-</span><span class="fl">1.23456984199584</span>, <span class="fl">1.33138702344149</span>, <span class="fl">5.14894889015704</span>, <span class="sc">-</span><span class="fl">2.75500717945397</span>, <span class="fl">5.42817679233849</span>, <span class="sc">-</span><span class="fl">0.385761078447104</span>, <span class="fl">2.53641148936003</span>, <span class="fl">1.07004427537322</span>, <span class="fl">5.20073131285608</span>, <span class="fl">3.42966685909778</span>, <span class="sc">-</span><span class="fl">2.25469410605729</span>, <span class="fl">4.43185863643885</span>, <span class="fl">3.94910727906972</span>, <span class="fl">2.33184932917356</span>, <span class="sc">-</span><span class="fl">3.19552502408624</span>, <span class="sc">-</span><span class="fl">5.40801217965782</span>, <span class="sc">-</span><span class="fl">3.02428950089961</span>, <span class="sc">-</span><span class="fl">2.64520167466253</span>, <span class="sc">-</span><span class="fl">0.800308775156736</span>, <span class="fl">3.50004907697439</span>, <span class="fl">0.120768285356462</span>, <span class="sc">-</span><span class="fl">2.46703495178372</span>, <span class="fl">5.66788987442851</span>)</span>
<span id="cb337-2"><a href="kvantitativa-variabler.html#cb337-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb337-3"><a href="kvantitativa-variabler.html#cb337-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb337-4"><a href="kvantitativa-variabler.html#cb337-4" aria-hidden="true" tabindex="-1"></a>y_cor <span class="ot"><-</span> <span class="fu">c</span>(<span class="fl">0.692116077725195</span>, <span class="sc">-</span><span class="fl">0.833820835658524</span>, <span class="fl">0.551094316233229</span>, <span class="fl">0.478165553350035</span>, <span class="sc">-</span><span class="fl">0.996419884224274</span>, <span class="sc">-</span><span class="fl">0.992730153952847</span>, <span class="sc">-</span><span class="fl">0.787317798367764</span>, <span class="sc">-</span><span class="fl">0.885604533948131</span>, <span class="sc">-</span><span class="fl">1.06152101350711</span>, <span class="fl">0.457057894147183</span>, <span class="sc">-</span><span class="fl">0.729896585604075</span>, <span class="sc">-</span><span class="fl">0.978794513790041</span>, <span class="sc">-</span><span class="fl">0.60522686417355</span>, <span class="fl">0.797339815551349</span>, <span class="fl">0.390540098705696</span>, <span class="fl">0.791056199476351</span>, <span class="sc">-</span><span class="fl">0.0658394160600363</span>, <span class="sc">-</span><span class="fl">1.07956091031993</span>, <span class="sc">-</span><span class="fl">0.377898994096769</span>, <span class="fl">0.676724127351636</span>, <span class="sc">-</span><span class="fl">0.92271062688403</span>, <span class="fl">0.68211062246375</span>, <span class="sc">-</span><span class="fl">0.265586770375202</span>, <span class="sc">-</span><span class="fl">0.281990646259145</span>, <span class="sc">-</span><span class="fl">0.933569187989352</span>, <span class="fl">0.970442057904559</span>, <span class="fl">0.855239683269214</span>, <span class="sc">-</span><span class="fl">0.913340432870525</span>, <span class="fl">1.05755126441053</span>, <span class="sc">-</span><span class="fl">0.557728609466566</span>, <span class="sc">-</span><span class="fl">0.413071062494649</span>, <span class="sc">-</span><span class="fl">0.750623331324987</span>, <span class="sc">-</span><span class="fl">0.496536315071716</span>, <span class="sc">-</span><span class="fl">0.00276258290690587</span>, <span class="fl">0.0894836188515442</span>, <span class="sc">-</span><span class="fl">0.68468900083751</span>, <span class="sc">-</span><span class="fl">0.769706234509263</span>, <span class="sc">-</span><span class="fl">1.12258289596224</span>, <span class="sc">-</span><span class="fl">0.862053797212771</span>, <span class="sc">-</span><span class="fl">0.136507484911278</span>, <span class="sc">-</span><span class="fl">0.231558312720629</span>, <span class="fl">0.512022766999122</span>, <span class="fl">0.670063652650559</span>, <span class="fl">0.734333679199448</span>, <span class="fl">0.11875944371307</span>, <span class="sc">-</span><span class="fl">0.26798051360053</span>, <span class="sc">-</span><span class="fl">0.600224989852732</span>, <span class="sc">-</span><span class="fl">0.589775882767548</span>, <span class="sc">-</span><span class="fl">0.92930591562741</span>, <span class="fl">0.922846118851976</span>, <span class="fl">0.578995361790117</span>, <span class="fl">0.97066756897238</span>, <span class="fl">0.68790797465233</span>, <span class="sc">-</span><span class="fl">0.536706968725068</span>, <span class="fl">0.441770394137291</span>, <span class="sc">-</span><span class="fl">0.881256478813447</span>, <span class="sc">-</span><span class="fl">0.361936174831535</span>, <span class="fl">1.05982364925898</span>, <span class="fl">0.548092220946772</span>, <span class="sc">-</span><span class="fl">0.240150837343345</span>, <span class="fl">0.359091389633033</span>, <span class="sc">-</span><span class="fl">0.36895423258766</span>, <span class="fl">0.613186081882422</span>, <span class="fl">0.623229100015448</span>, <span class="sc">-</span><span class="fl">0.486751410585548</span>, <span class="fl">0.46160923108823</span>, <span class="fl">0.903730917053862</span>, <span class="sc">-</span><span class="fl">0.659747459903884</span>, <span class="sc">-</span><span class="fl">0.449591389386599</span>, <span class="fl">0.705197272782706</span>, <span class="fl">0.174335085452261</span>, <span class="fl">0.843079786347905</span>, <span class="sc">-</span><span class="fl">0.640998796648546</span>, <span class="fl">0.249470157541554</span>, <span class="sc">-</span><span class="fl">1.02428382665794</span>, <span class="fl">0.274645055014929</span>, <span class="sc">-</span><span class="fl">0.569701349870323</span>, <span class="sc">-</span><span class="fl">0.227953728783033</span>, <span class="fl">0.21991606361946</span>, <span class="fl">0.862578816245065</span>, <span class="sc">-</span><span class="fl">0.454157706556781</span>, <span class="sc">-</span><span class="fl">0.992151900718503</span>, <span class="fl">0.726538430118473</span>, <span class="fl">0.366356885419869</span>, <span class="fl">0.698431515406227</span>, <span class="sc">-</span><span class="fl">0.589898304479426</span>, <span class="sc">-</span><span class="fl">0.42313463129314</span>, <span class="fl">0.351647363269612</span>, <span class="sc">-</span><span class="fl">0.915081710580083</span>, <span class="sc">-</span><span class="fl">0.203387000470344</span>, <span class="sc">-</span><span class="fl">0.945642100191838</span>, <span class="sc">-</span><span class="fl">0.42970695945602</span>, <span class="fl">0.437503680874048</span>, <span class="sc">-</span><span class="fl">0.143954453092994</span>, <span class="fl">0.213954707871942</span>, <span class="fl">0.965641966991328</span>, <span class="sc">-</span><span class="fl">0.842223666863874</span>, <span class="fl">0.965819897883947</span>, <span class="sc">-</span><span class="fl">0.628395164741264</span>, <span class="sc">-</span><span class="fl">0.561860829959186</span>, <span class="fl">0.318873605579769</span>, <span class="sc">-</span><span class="fl">0.319851707066493</span>, <span class="sc">-</span><span class="fl">0.324045829438118</span>, <span class="sc">-</span><span class="fl">0.952772340775089</span>, <span class="sc">-</span><span class="fl">0.924445349040963</span>, <span class="fl">0.0753221581027099</span>, <span class="fl">0.500514167001168</span>, <span class="fl">0.876576303959421</span>, <span class="sc">-</span><span class="fl">0.570347773359213</span>, <span class="fl">0.019722702177426</span>, <span class="sc">-</span><span class="fl">0.89257920086998</span>, <span class="fl">0.258685868429658</span>, <span class="fl">0.759805312436448</span>, <span class="fl">0.262874143005627</span>, <span class="sc">-</span><span class="fl">0.322119082028071</span>, <span class="sc">-</span><span class="fl">1.02183036134721</span>, <span class="sc">-</span><span class="fl">0.598527601774096</span>, <span class="fl">0.696783591016198</span>, <span class="fl">0.0570775881532332</span>, <span class="sc">-</span><span class="fl">0.888576552095211</span>, <span class="sc">-</span><span class="fl">0.359856562825605</span>, <span class="sc">-</span><span class="fl">0.65347558048046</span>, <span class="sc">-</span><span class="fl">0.961958430946146</span>, <span class="fl">0.0979345855190165</span>, <span class="sc">-</span><span class="fl">0.492788566103075</span>, <span class="sc">-</span><span class="fl">0.33472866844283</span>, <span class="sc">-</span><span class="fl">0.413830595911876</span>, <span class="sc">-</span><span class="fl">0.150506615673904</span>, <span class="sc">-</span><span class="fl">0.749560511121892</span>, <span class="sc">-</span><span class="fl">0.577635086304876</span>, <span class="sc">-</span><span class="fl">0.113693313572898</span>, <span class="fl">0.557698126284979</span>, <span class="fl">0.650887752184128</span>, <span class="fl">1.09609841455634</span>, <span class="sc">-</span><span class="fl">0.239600812541057</span>, <span class="fl">0.925275829714373</span>, <span class="fl">0.988146976419745</span>, <span class="fl">0.667171239978437</span>, <span class="fl">0.787995243735866</span>, <span class="fl">0.928322239709289</span>, <span class="fl">0.956953986603638</span>, <span class="sc">-</span><span class="fl">0.630923702091154</span>, <span class="sc">-</span><span class="fl">0.770594811693208</span>, <span class="fl">0.0361742629265017</span>, <span class="fl">0.614372251426405</span>, <span class="fl">0.339422414729519</span>, <span class="fl">0.105203804090473</span>, <span class="sc">-</span><span class="fl">0.0811484394321826</span>, <span class="sc">-</span><span class="fl">0.644019143260316</span>, <span class="sc">-</span><span class="fl">0.957072615434561</span>, <span class="sc">-</span><span class="fl">0.657568606516498</span>, <span class="sc">-</span><span class="fl">0.657184692154678</span>, <span class="sc">-</span><span class="fl">0.715883475657522</span>, <span class="sc">-</span><span class="fl">0.983216106811242</span>, <span class="sc">-</span><span class="fl">0.701445457809133</span>, <span class="sc">-</span><span class="fl">0.746729244754527</span>, <span class="sc">-</span><span class="fl">0.721298971546328</span>, <span class="sc">-</span><span class="fl">0.917333397952104</span>, <span class="sc">-</span><span class="fl">0.7440246871844</span>, <span class="fl">0.942722246720506</span>, <span class="fl">0.742486110862305</span>, <span class="sc">-</span><span class="fl">0.87643277604441</span>, <span class="sc">-</span><span class="fl">0.397882897374624</span>, <span class="sc">-</span><span class="fl">0.609278544430292</span>, <span class="sc">-</span><span class="fl">0.788774517324603</span>, <span class="sc">-</span><span class="fl">1.03008786999627</span>, <span class="fl">0.900174883722106</span>, <span class="fl">0.876550985507823</span>, <span class="fl">0.772520611319698</span>, <span class="fl">0.714399684849063</span>, <span class="sc">-</span><span class="fl">0.734153776138897</span>, <span class="fl">0.843446606937203</span>, <span class="sc">-</span><span class="fl">0.520221715898307</span>, <span class="sc">-</span><span class="fl">0.873207573363112</span>, <span class="fl">0.183251446777576</span>, <span class="sc">-</span><span class="fl">0.786414826767054</span>, <span class="fl">0.764042479408094</span>, <span class="sc">-</span><span class="fl">0.849391737954901</span>, <span class="sc">-</span><span class="fl">0.744589245253425</span>, <span class="sc">-</span><span class="fl">1.01871713617985</span>, <span class="fl">0.00793431716737572</span>, <span class="sc">-</span><span class="fl">0.315083596059678</span>, <span class="fl">0.336162131415597</span>, <span class="fl">1.10719386364714</span>, <span class="sc">-</span><span class="fl">0.920051555908693</span>, <span class="sc">-</span><span class="fl">0.332402980346329</span>, <span class="sc">-</span><span class="fl">0.387380886383534</span>, <span class="sc">-</span><span class="fl">0.744629579313388</span>, <span class="fl">0.249807585560943</span>, <span class="fl">0.85315614501589</span>, <span class="fl">0.564613607101056</span>, <span class="fl">0.860703086960768</span>, <span class="sc">-</span><span class="fl">0.41180534727551</span>, <span class="fl">0.155062583456708</span>, <span class="sc">-</span><span class="fl">0.84944302770448</span>, <span class="sc">-</span><span class="fl">0.0232354897945976</span>, <span class="sc">-</span><span class="fl">1.21581192855228</span>, <span class="fl">0.942392667564932</span>, <span class="fl">0.968358502729973</span>, <span class="fl">0.843350560478223</span>, <span class="sc">-</span><span class="fl">0.633419379891784</span>, <span class="fl">0.973409076411311</span>, <span class="sc">-</span><span class="fl">0.965002020381659</span>, <span class="sc">-</span><span class="fl">0.723426638130645</span>, <span class="sc">-</span><span class="fl">0.635624656346435</span>, <span class="sc">-</span><span class="fl">0.907780517197421</span>, <span class="sc">-</span><span class="fl">0.0659472296454691</span>, <span class="fl">0.0290512372461689</span>, <span class="fl">0.943477419282174</span>, <span class="sc">-</span><span class="fl">0.115736535875326</span>, <span class="fl">0.662690666046125</span>, <span class="sc">-</span><span class="fl">0.9681085235679</span>, <span class="sc">-</span><span class="fl">0.769870076469868</span>, <span class="sc">-</span><span class="fl">0.43319885747632</span>, <span class="sc">-</span><span class="fl">0.953036650100475</span>, <span class="sc">-</span><span class="fl">0.934255632582831</span>, <span class="sc">-</span><span class="fl">0.712949266901575</span>, <span class="sc">-</span><span class="fl">0.371267882159617</span>, <span class="fl">0.770395281297423</span>, <span class="sc">-</span><span class="fl">0.915116089169343</span>, <span class="fl">0.990521822374141</span>, <span class="fl">0.807322690010507</span>, <span class="sc">-</span><span class="fl">0.848620205350821</span>, <span class="fl">0.845720759505633</span>, <span class="sc">-</span><span class="fl">0.992056768890273</span>, <span class="fl">0.48865106070475</span>, <span class="fl">0.447179115401043</span>, <span class="sc">-</span><span class="fl">0.78738628578981</span>, <span class="sc">-</span><span class="fl">0.882652853235678</span>, <span class="sc">-</span><span class="fl">0.580708608540424</span>, <span class="fl">1.12462815136212</span>, <span class="sc">-</span><span class="fl">0.886842239561658</span>, <span class="sc">-</span><span class="fl">0.876510666038672</span>, <span class="sc">-</span><span class="fl">0.0528351480259851</span>, <span class="sc">-</span><span class="fl">1.07946627084427</span>, <span class="sc">-</span><span class="fl">0.926451976564244</span>, <span class="fl">1.04189351967588</span>, <span class="sc">-</span><span class="fl">0.873138160446389</span>, <span class="sc">-</span><span class="fl">0.323302547342293</span>, <span class="sc">-</span><span class="fl">0.0398336883927105</span>, <span class="sc">-</span><span class="fl">0.0723876475197</span>, <span class="fl">0.0299203623621222</span>, <span class="fl">0.26771157331388</span>, <span class="sc">-</span><span class="fl">0.799702005811923</span>, <span class="sc">-</span><span class="fl">0.0927464925429201</span>, <span class="sc">-</span><span class="fl">0.140132425501586</span>, <span class="fl">0.791514174457469</span>, <span class="fl">0.661362629969618</span>, <span class="sc">-</span><span class="fl">0.194673394925077</span>, <span class="sc">-</span><span class="fl">0.826110437080204</span>, <span class="fl">0.0521029906218902</span>, <span class="fl">0.993778152017857</span>, <span class="sc">-</span><span class="fl">0.135797400885025</span>, <span class="fl">0.861960227188668</span>, <span class="fl">0.702640664956012</span>, <span class="fl">0.734991552394919</span>, <span class="sc">-</span><span class="fl">0.482055266374795</span>, <span class="sc">-</span><span class="fl">0.15321908581954</span>, <span class="sc">-</span><span class="fl">0.941768627602878</span>, <span class="fl">0.172938151698188</span>, <span class="fl">1.0452041992147</span>, <span class="sc">-</span><span class="fl">0.909228336253595</span>, <span class="sc">-</span><span class="fl">0.966156394921463</span>, <span class="fl">0.272876182068588</span>, <span class="fl">0.922914912684233</span>, <span class="fl">0.274903818453297</span>, <span class="sc">-</span><span class="fl">0.685046983835134</span>, <span class="fl">1.01215693839823</span>, <span class="fl">0.819070409348976</span>, <span class="fl">0.856227674956861</span>, <span class="fl">0.789428305518576</span>, <span class="sc">-</span><span class="fl">1.08349033649955</span>, <span class="fl">0.251286664934293</span>, <span class="fl">0.111426160383657</span>, <span class="sc">-</span><span class="fl">0.861936599935431</span>, <span class="fl">0.887230833488581</span>, <span class="sc">-</span><span class="fl">1.04773500244942</span>, <span class="fl">0.951517615425827</span>, <span class="sc">-</span><span class="fl">0.936397263489121</span>, <span class="fl">0.171010205107887</span>, <span class="sc">-</span><span class="fl">0.464208296441551</span>, <span class="sc">-</span><span class="fl">0.609430728927302</span>, <span class="sc">-</span><span class="fl">0.575950432922157</span>, <span class="fl">1.06164100137271</span>, <span class="sc">-</span><span class="fl">0.122266753685931</span>, <span class="fl">0.966287429868908</span>, <span class="fl">0.581564671231955</span>, <span class="sc">-</span><span class="fl">1.08817933125627</span>, <span class="sc">-</span><span class="fl">0.580379324594687</span>, <span class="fl">1.03281086814407</span>, <span class="sc">-</span><span class="fl">0.348869193069082</span>, <span class="fl">0.745142774179912</span>, <span class="fl">0.567237298372281</span>, <span class="sc">-</span><span class="fl">1.07948998560629</span>, <span class="fl">0.0517884494519469</span>, <span class="sc">-</span><span class="fl">0.181908987477246</span>, <span class="fl">0.959735673555604</span>, <span class="sc">-</span><span class="fl">0.890529355141261</span>, <span class="sc">-</span><span class="fl">0.286825361441517</span>, <span class="fl">0.5194807972762</span>, <span class="sc">-</span><span class="fl">0.821528526196263</span>, <span class="fl">0.451678946467058</span>, <span class="sc">-</span><span class="fl">1.13755433623201</span>, <span class="sc">-</span><span class="fl">0.647394918459111</span>, <span class="fl">1.11755054614341</span>, <span class="sc">-</span><span class="fl">0.572189434431056</span>, <span class="fl">0.537328007215023</span>, <span class="fl">0.80585733992751</span>, <span class="sc">-</span><span class="fl">0.903018870834392</span>, <span class="fl">0.609266424849447</span>, <span class="fl">0.9168705239366</span>, <span class="fl">0.612378460576535</span>, <span class="fl">0.51330690518088</span>, <span class="fl">0.619295145555417</span>, <span class="fl">0.0739018077311075</span>, <span class="sc">-</span><span class="fl">0.360211626817118</span>, <span class="fl">0.928834828811469</span>, <span class="fl">0.548861930170216</span>, <span class="fl">0.27891033502873</span>, <span class="fl">0.629701339579054</span>, <span class="sc">-</span><span class="fl">0.545770238682216</span>, <span class="fl">1.02493997465363</span>, <span class="fl">0.677732512511985</span>, <span class="fl">0.512342385480205</span>, <span class="sc">-</span><span class="fl">0.563566564867947</span>, <span class="sc">-</span><span class="fl">0.499778393251972</span>, <span class="fl">0.135866115302711</span>, <span class="fl">0.94627533975966</span>, <span class="fl">0.0524937887958016</span>, <span class="sc">-</span><span class="fl">0.244888692869009</span>, <span class="sc">-</span><span class="fl">1.12082462487432</span>, <span class="sc">-</span><span class="fl">0.719907209607575</span>, <span class="fl">1.00667181435325</span>, <span class="fl">0.587339268146245</span>, <span class="fl">0.525369587475545</span>, <span class="fl">0.116621365487128</span>, <span class="fl">0.0508602438018313</span>, <span class="sc">-</span><span class="fl">0.802706540742785</span>, <span class="fl">0.694343718370414</span>, <span class="fl">0.0346940197725392</span>, <span class="fl">0.784159600151842</span>, <span class="fl">0.838395539018007</span>, <span class="fl">0.459368890835023</span>, <span class="fl">0.866974611760156</span>, <span class="fl">0.0528053656688342</span>, <span class="sc">-</span><span class="fl">1.08648127648979</span>, <span class="fl">1.04313494380031</span>, <span class="fl">0.507105448819916</span>, <span class="sc">-</span><span class="fl">0.673336071921562</span>, <span class="sc">-</span><span class="fl">0.631624742395916</span>, <span class="sc">-</span><span class="fl">0.444355259541822</span>, <span class="fl">0.340284440437517</span>, <span class="fl">0.476499394293787</span>, <span class="sc">-</span><span class="fl">0.676650757568411</span>, <span class="fl">0.949218974919565</span>, <span class="sc">-</span><span class="fl">0.552239842328508</span>, <span class="sc">-</span><span class="fl">0.892022109030021</span>, <span class="fl">0.722671286426101</span>, <span class="fl">0.863173008060452</span>, <span class="sc">-</span><span class="fl">0.870035077996046</span>, <span class="fl">0.666044476900363</span>, <span class="fl">0.399800786701317</span>, <span class="sc">-</span><span class="fl">0.902105309464301</span>, <span class="sc">-</span><span class="fl">0.327330240437956</span>, <span class="fl">0.582333659618165</span>, <span class="sc">-</span><span class="fl">1.04118647337577</span>, <span class="fl">0.374628419458681</span>, <span class="fl">0.975500452347226</span>, <span class="fl">1.11807023884526</span>, <span class="fl">0.430445983928438</span>, <span class="fl">0.775979329187456</span>, <span class="fl">0.901168524943803</span>, <span class="sc">-</span><span class="fl">0.178248981348715</span>, <span class="sc">-</span><span class="fl">0.0324343500448203</span>, <span class="fl">0.496659607431612</span>, <span class="sc">-</span><span class="fl">0.455993445133844</span>, <span class="fl">1.08446294951181</span>, <span class="fl">0.31210075299887</span>, <span class="fl">0.979991122264016</span>, <span class="sc">-</span><span class="fl">0.627660741306241</span>, <span class="sc">-</span><span class="fl">0.893155340150051</span>, <span class="fl">0.331431540329934</span>, <span class="sc">-</span><span class="fl">0.0574182076128606</span>, <span class="sc">-</span><span class="fl">0.573875698051284</span>, <span class="sc">-</span><span class="fl">0.851669095478101</span>, <span class="fl">0.509540521704214</span>, <span class="fl">0.842563085161535</span>, <span class="sc">-</span><span class="fl">0.445790499937521</span>, <span class="sc">-</span><span class="fl">0.488148274278827</span>, <span class="sc">-</span><span class="fl">1.00000971308572</span>, <span class="fl">0.750717107650914</span>, <span class="fl">0.385189991815612</span>, <span class="sc">-</span><span class="fl">0.71432092292147</span>, <span class="fl">0.691388931950444</span>, <span class="sc">-</span><span class="fl">1.11184411614013</span>, <span class="sc">-</span><span class="fl">0.337024133112692</span>, <span class="sc">-</span><span class="fl">0.827471547601959</span>, <span class="sc">-</span><span class="fl">0.871687732023444</span>, <span class="sc">-</span><span class="fl">1.06905464378816</span>, <span class="fl">0.0944049479804341</span>, <span class="sc">-</span><span class="fl">0.0169893750874063</span>, <span class="sc">-</span><span class="fl">0.997835764718766</span>, <span class="fl">0.380411826809133</span>, <span class="sc">-</span><span class="fl">0.941900543925321</span>, <span class="sc">-</span><span class="fl">1.29054424821311</span>, <span class="sc">-</span><span class="fl">0.99249496058113</span>, <span class="sc">-</span><span class="fl">0.949842557020156</span>, <span class="sc">-</span><span class="fl">0.404215020038054</span>, <span class="fl">0.0647648419477043</span>, <span class="fl">0.492438306722134</span>, <span class="fl">0.887835951467139</span>, <span class="fl">0.87494312701596</span>, <span class="fl">0.575746537260541</span>, <span class="fl">0.338525111524258</span>, <span class="fl">1.00095143145309</span>, <span class="fl">0.241769246710808</span>, <span class="fl">0.899207125012576</span>, <span class="sc">-</span><span class="fl">0.678461931814348</span>, <span class="fl">0.189889832655481</span>, <span class="sc">-</span><span class="fl">0.581158606619191</span>, <span class="sc">-</span><span class="fl">0.727976273121182</span>, <span class="fl">0.930054847124453</span>, <span class="fl">0.653144522968482</span>, <span class="fl">0.176551055270141</span>, <span class="sc">-</span><span class="fl">0.533423432541824</span>, <span class="fl">0.865739420200622</span>, <span class="sc">-</span><span class="fl">0.474139877566841</span>, <span class="fl">0.293145174517555</span>, <span class="fl">0.354327758401527</span>, <span class="fl">0.815337022899501</span>, <span class="sc">-</span><span class="fl">1.08101701113977</span>, <span class="fl">0.82278581508067</span>, <span class="sc">-</span><span class="fl">0.0431081510758147</span>, <span class="fl">1.04132522096649</span>, <span class="fl">0.524951746682782</span>, <span class="sc">-</span><span class="fl">0.993426699521503</span>, <span class="fl">0.631744939827365</span>, <span class="fl">0.0709007298133944</span>, <span class="sc">-</span><span class="fl">0.271754635437279</span>, <span class="fl">0.832096335135455</span>, <span class="sc">-</span><span class="fl">0.68804061681554</span>, <span class="fl">0.742072601691465</span>, <span class="fl">0.943729735608386</span>, <span class="sc">-</span><span class="fl">0.130215855909967</span>, <span class="sc">-</span><span class="fl">0.581137545540033</span>, <span class="fl">0.995667609461697</span>, <span class="fl">1.00926658886954</span>, <span class="fl">0.609834597051648</span>, <span class="sc">-</span><span class="fl">0.0480545501906195</span>, <span class="sc">-</span><span class="fl">0.030081984508683</span>, <span class="fl">0.773978460184942</span>, <span class="fl">0.630026868098328</span>, <span class="fl">0.787489191743331</span>, <span class="sc">-</span><span class="fl">0.126706512812433</span>, <span class="sc">-</span><span class="fl">0.815946746752882</span>, <span class="fl">0.927014256322037</span>, <span class="fl">0.878520117718395</span>, <span class="sc">-</span><span class="fl">0.818300729363242</span>, <span class="sc">-</span><span class="fl">0.939861414262159</span>, <span class="fl">0.383374915016445</span>, <span class="sc">-</span><span class="fl">0.361952298070514</span>, <span class="sc">-</span><span class="fl">0.573478966354709</span>, <span class="fl">0.846810192777705</span>, <span class="fl">1.07876450582925</span>, <span class="sc">-</span><span class="fl">0.815416053273182</span>, <span class="sc">-</span><span class="fl">1.05012205676904</span>, <span class="sc">-</span><span class="fl">0.494305637011417</span>, <span class="fl">0.336976113298814</span>, <span class="sc">-</span><span class="fl">0.966394021248254</span>, <span class="fl">0.770021134498414</span>, <span class="fl">0.138068916310278</span>, <span class="sc">-</span><span class="fl">1.03810537426467</span>, <span class="fl">0.820994176723859</span>, <span class="fl">0.439047680723385</span>, <span class="sc">-</span><span class="fl">1.03761045203866</span>, <span class="sc">-</span><span class="fl">0.194799550931192</span>, <span class="fl">0.517542667931891</span>, <span class="sc">-</span><span class="fl">0.896932625734218</span>, <span class="sc">-</span><span class="fl">0.910902040542301</span>, <span class="sc">-</span><span class="fl">0.772447333215392</span>, <span class="fl">0.764862844103926</span>, <span class="sc">-</span><span class="fl">0.258852077275202</span>, <span class="fl">0.658500894604562</span>, <span class="fl">0.322701881663578</span>, <span class="sc">-</span><span class="fl">0.433746793503408</span>, <span class="sc">-</span><span class="fl">0.427160971046463</span>, <span class="fl">0.799620457272055</span>, <span class="sc">-</span><span class="fl">0.209058723465767</span>, <span class="sc">-</span><span class="fl">0.828836013742181</span>, <span class="sc">-</span><span class="fl">0.113169127607347</span>, <span class="sc">-</span><span class="fl">0.00575135876008619</span>, <span class="fl">1.18235488908229</span>, <span class="sc">-</span><span class="fl">0.164927025768732</span>, <span class="fl">1.11476710397186</span>, <span class="fl">0.409038999872967</span>, <span class="fl">0.044165125913567</span>, <span class="fl">0.63751883848208</span>, <span class="fl">1.02399771931605</span>, <span class="fl">0.0931674689632747</span>, <span class="fl">0.368893205056112</span>)</span></code></pre></div>
</div>
</div>
<p></br></p>
<p>Kopiera de två variablerna och klistra in dem i <code>R</code>. En snabb korrelationsanalys ger då en väldigt svag korrelation.</p>
<div class="sourceCode" id="cb338"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb338-1"><a href="kvantitativa-variabler.html#cb338-1" aria-hidden="true" tabindex="-1"></a><span class="fu">cor</span>(<span class="at">x =</span> x_cor, <span class="at">y =</span> y_cor) </span>
<span id="cb338-2"><a href="kvantitativa-variabler.html#cb338-2" aria-hidden="true" tabindex="-1"></a>[<span class="dv">1</span>] <span class="sc">-</span><span class="fl">0.0217337</span></span></code></pre></div>
<p>En förhastad slutsats skulle då kunna vara att de två variablerna är helt oberoende, och inte samvarierar på något sätt. Denna slutsats är dock felaktig, vilket framgår tydligt om sambandet illustreras i en figur.</p>
<div class="sourceCode" id="cb339"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb339-1"><a href="kvantitativa-variabler.html#cb339-1" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(<span class="at">x =</span> x_cor, <span class="co"># x-variabel</span></span>
<span id="cb339-2"><a href="kvantitativa-variabler.html#cb339-2" aria-hidden="true" tabindex="-1"></a> <span class="at">y =</span> y_cor, <span class="co"># y-variabel</span></span>
<span id="cb339-3"><a href="kvantitativa-variabler.html#cb339-3" aria-hidden="true" tabindex="-1"></a> <span class="at">ylab =</span> <span class="st">""</span>, <span class="co"># Etikett till y-axel</span></span>
<span id="cb339-4"><a href="kvantitativa-variabler.html#cb339-4" aria-hidden="true" tabindex="-1"></a> <span class="at">xlab =</span> <span class="st">""</span>, <span class="co"># Etikett till x-axel</span></span>
<span id="cb339-5"><a href="kvantitativa-variabler.html#cb339-5" aria-hidden="true" tabindex="-1"></a> <span class="at">pch =</span> <span class="dv">16</span>, <span class="co"># Ifylld punkt som markör</span></span>
<span id="cb339-6"><a href="kvantitativa-variabler.html#cb339-6" aria-hidden="true" tabindex="-1"></a> <span class="at">col =</span> <span class="st">"blue"</span>) <span class="co"># Ändrar färg på punkterna</span></span></code></pre></div>
<p><img src="docs/images/unnamed-chunk-326-1.png" width="672" style="display: block; margin: auto;" /></p>
<p>Som synes finns en tydlig, <strong>icke-linjär</strong>, samvariation variablerna emellan, vilket inte framgår av korrelationskoefficienten. Slutsatsen om brist på samvariation skulle därför vara fel.</p>
<p>Det är alltså viktigt att komma ihåg att <strong>korrelationskoefficienten bara mäter hur pass väl punkterna samlar sig runt en rät linje</strong>, och variablerna <strong>inte</strong> kan betraktas som helt oberoende bara för att korrelationskoefficienten är (när) 0. En analys som bygger på oberoende variabler skulle i detta fallet bli missvisande.</p>
</div>
<p></br></p>
</div>
</div>
<div id="en-kontinuerlig-och-en-diskret-variabel" class="section level3 hasAnchor" number="6.2.2">
<h3><span class="header-section-number">6.2.2</span> En kontinuerlig och en diskret variabel<a href="kvantitativa-variabler.html#en-kontinuerlig-och-en-diskret-variabel" class="anchor-section" aria-label="Anchor link to header"></a></h3>
<p>När en av de två variablerna är diskret finns en risk att spridningsdiagram blir svårtolkade, och det är därför bäst att använda en annan typ av figur för att illustrera de två variablerna tillsammans. I sådana fall är box plots (lådagram) det vanligaste alternativet. Om antalet variabelvärden i den diskreta variabeln är lågt kan det även vara lämpligt att skapa ett histogram per variabelvärde, och sedan placera histogrammen bredvid varandra.</p>
<div id="lådagram" class="section level4 hasAnchor" number="6.2.2.1">
<h4><span class="header-section-number">6.2.2.1</span> Lådagram<a href="kvantitativa-variabler.html#lådagram" class="anchor-section" aria-label="Anchor link to header"></a></h4>
<p>Lådagram kan ses och tolkas som motsvarigheten till ett spridningsdiagram, med skillnaden att det i detta fall illustrerar en kontinuerlig och en diskret variabel. På samma sätt som spridningsdiagramet ger lådagrammet en uppfattning om hur två variabler samvarierar, och ger även en bild av hur de båda variablernas spridning ser ut.</p>
<p>För att skapa lådagram används funktionen <code>boxplot()</code>, och argumentet som används är av formen <code>y ~ x</code>, där <code>y</code> är den kontinuerliga variabeln, och <code>x</code> är den diskreta. För att skapa ett lådagram som illustrerar samvariationen mellan <code>fev</code> och <code>age</code> kan ett lådagram skapas som nedan.</p>
<div class="sourceCode" id="cb340"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb340-1"><a href="kvantitativa-variabler.html#cb340-1" aria-hidden="true" tabindex="-1"></a><span class="fu">boxplot</span>(fev <span class="sc">~</span> age)</span></code></pre></div>
<p><img src="docs/images/unnamed-chunk-327-1.png" width="672" style="display: block; margin: auto;" /></p>
<p>För att göra ett diagram med liggande lådor används argumentet <code>horizontal = TRUE</code>, och precis som i tidigare diagram kan såväl <code>main</code> som <code>xlab</code>, <code>ylab</code>, och <code>col</code> för att justera histogrammets utseende. Ett modifierat lådagram kan skapas med hjälp av koden nedan.</p>
<div class="sourceCode" id="cb341"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb341-1"><a href="kvantitativa-variabler.html#cb341-1" aria-hidden="true" tabindex="-1"></a><span class="fu">boxplot</span>(fev <span class="sc">~</span> age, <span class="co"># Variabler som används</span></span>
<span id="cb341-2"><a href="kvantitativa-variabler.html#cb341-2" aria-hidden="true" tabindex="-1"></a> <span class="at">ylab =</span> <span class="st">"Ålder"</span>, <span class="co"># Etikett till y-axel</span></span>
<span id="cb341-3"><a href="kvantitativa-variabler.html#cb341-3" aria-hidden="true" tabindex="-1"></a> <span class="at">xlab =</span> <span class="st">"FEV (liter/sek)"</span>, <span class="co"># Etikett till x-axel</span></span>
<span id="cb341-4"><a href="kvantitativa-variabler.html#cb341-4" aria-hidden="true" tabindex="-1"></a> <span class="at">horizontal =</span> <span class="cn">TRUE</span>, <span class="co"># Ger liggande lådor</span></span>
<span id="cb341-5"><a href="kvantitativa-variabler.html#cb341-5" aria-hidden="true" tabindex="-1"></a> <span class="at">col =</span> <span class="st">"lightblue"</span>) <span class="co"># Ändrar färg på lådorna</span></span></code></pre></div>
<p><img src="docs/images/unnamed-chunk-328-1.png" width="672" style="display: block; margin: auto;" /></p>
</div>
<div id="uppdelade-histogram" class="section level4 hasAnchor" number="6.2.2.2">
<h4><span class="header-section-number">6.2.2.2</span> Uppdelade histogram<a href="kvantitativa-variabler.html#uppdelade-histogram" class="anchor-section" aria-label="Anchor link to header"></a></h4>
<p>Om den diskreta variabeln har få variabelvärden, eller om ett litet antal grupper ska studeras, kan det vara informativt att göra ett histogram per variabelvärde/grupp och vissa dessa vid sidan av varandra.</p>
<p>Genom att temporärt förändra <code>R</code>:s grundinställningar är det möjligt att få <code>R</code> att skriva ut flera diagram bredvid (eller ovanför) varandra. För att ändra grundinställningarna används kod i stil med <code>par(mfrow = c(rader, kolumner)</code>, där <code>rader</code> och <code>kolumner</code> ersätts med siffror som anger hur många bilder som ska läggas i vertikal respektive horisontell ledd. Grundinställningen i <code>R</code> är <code>par(mfrow = c(1, 1)</code>, vilket betyder att en figur i taget visas i panelen, och det är viktigt att återställa denna inställning när figuren är färdig. Dessa förändringar illustreras bäst med hjälp av exempel.</p>
<p>Antag att det är av intresse att jämföra <code>fev</code> för åldrarna 5 respektive 10 år. För att skapa två histogram och visa dem bredvid varandra ersätts <code>rader</code> med <code>1</code> och <code>kolumner</code> med <code>2</code>, och sedan skapas histogrammen som vanligt. Efter detta återställs <code>kolumner</code> till <code>1</code> för att sedan kunna skapa figurer som vanligt.</p>
<p>Och sedan skapas de båda histogrammen som</p>
<div class="sourceCode" id="cb342"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb342-1"><a href="kvantitativa-variabler.html#cb342-1" aria-hidden="true" tabindex="-1"></a><span class="fu">par</span>(<span class="at">mfrow =</span> <span class="fu">c</span>(<span class="dv">1</span>, <span class="dv">2</span>)) <span class="co"># Två figurer bredvid varandra</span></span>
<span id="cb342-2"><a href="kvantitativa-variabler.html#cb342-2" aria-hidden="true" tabindex="-1"></a><span class="fu">hist</span>(fev[age <span class="sc">==</span> <span class="dv">5</span>], <span class="at">col =</span> <span class="st">"red"</span>) <span class="co"># Histogram över femåringar</span></span>
<span id="cb342-3"><a href="kvantitativa-variabler.html#cb342-3" aria-hidden="true" tabindex="-1"></a><span class="fu">hist</span>(fev[age <span class="sc">==</span> <span class="dv">10</span>], <span class="at">col =</span> <span class="st">"blue"</span>) <span class="co"># Histogram över tioåringar</span></span></code></pre></div>
<p><img src="docs/images/unnamed-chunk-329-1.png" width="672" style="display: block; margin: auto;" /></p>
<div class="sourceCode" id="cb343"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb343-1"><a href="kvantitativa-variabler.html#cb343-1" aria-hidden="true" tabindex="-1"></a><span class="fu">par</span>(<span class="at">mfrow =</span> <span class="fu">c</span>(<span class="dv">1</span>, <span class="dv">1</span>)) <span class="co"># Återställer default</span></span></code></pre></div>
<p>Det går även att lägga till flera rader med figurer vid behov. För att skapa två figurer till under de som gjordes ovan ändras även <code>rader</code> till <code>2</code>. Detta ger resultatet nedan.</p>
<div class="sourceCode" id="cb344"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb344-1"><a href="kvantitativa-variabler.html#cb344-1" aria-hidden="true" tabindex="-1"></a><span class="fu">par</span>(<span class="at">mfrow =</span> <span class="fu">c</span>(<span class="dv">2</span>, <span class="dv">2</span>)) <span class="co"># Två figurer bredvid varandra</span></span>
<span id="cb344-2"><a href="kvantitativa-variabler.html#cb344-2" aria-hidden="true" tabindex="-1"></a><span class="fu">hist</span>(fev[age <span class="sc">==</span> <span class="dv">5</span>], <span class="at">col =</span> <span class="st">"red"</span>) <span class="co"># Histogram över femåringar</span></span>
<span id="cb344-3"><a href="kvantitativa-variabler.html#cb344-3" aria-hidden="true" tabindex="-1"></a><span class="fu">hist</span>(fev[age <span class="sc">==</span> <span class="dv">10</span>], <span class="at">col =</span> <span class="st">"blue"</span>) <span class="co"># Histogram över tioåringar</span></span>
<span id="cb344-4"><a href="kvantitativa-variabler.html#cb344-4" aria-hidden="true" tabindex="-1"></a><span class="fu">hist</span>(fev[age <span class="sc">==</span> <span class="dv">3</span>], <span class="at">col =</span> <span class="st">"green"</span>) <span class="co"># Histogram över ettåringar</span></span>
<span id="cb344-5"><a href="kvantitativa-variabler.html#cb344-5" aria-hidden="true" tabindex="-1"></a><span class="fu">hist</span>(fev[age <span class="sc">==</span> <span class="dv">15</span>], <span class="at">col =</span> <span class="st">"yellow"</span>) <span class="co"># Histogram över femtonåringar</span></span></code></pre></div>
<p><img src="docs/images/unnamed-chunk-330-1.png" width="672" style="display: block; margin: auto;" /></p>
<div class="sourceCode" id="cb345"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb345-1"><a href="kvantitativa-variabler.html#cb345-1" aria-hidden="true" tabindex="-1"></a><span class="fu">par</span>(<span class="at">mfrow =</span> <span class="fu">c</span>(<span class="dv">1</span>, <span class="dv">1</span>)) <span class="co"># Återställer default</span></span></code></pre></div>
<p>Notera att figureran blir ihoptryckta när det läggs bredvid/ovanpå varandra. Det är därför bra att inte rada upp/stapla för många diagram i samma figur, då detta kan påverka diagrammens tydlighet.</p>
</div>
</div>
</div>
<div id="övningsuppgifter" class="section level2 hasAnchor" number="6.3">
<h2><span class="header-section-number">6.3</span> Övningsuppgifter<a href="kvantitativa-variabler.html#övningsuppgifter" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<div id="uppgift-1-1" class="section level3 hasAnchor" number="6.3.1">
<h3><span class="header-section-number">6.3.1</span> Uppgift 1<a href="kvantitativa-variabler.html#uppgift-1-1" class="anchor-section" aria-label="Anchor link to header"></a></h3>
<p>I fliken nedan finns ett simulerat datamaterial med två variabler, <code>value1</code> och <code>value2</code>. Variablerna är helt fiktiva, och har ingen tolkning i termer av verkliga fenomen, men de kan kan utan problem användas i en övningsuppgift som denna.</p>
<button title="data_61" type="button" onclick="if(document.getElementById('data_61') .style.display=='none')
{document.getElementById('data_61') .style.display=''}
else{document.getElementById('data_61') .style.display='none'}">
Visa datamaterial
</button>
<div id="data_61" style="display:none">
<div class="alert alert-info">
<div class="sourceCode" id="cb346"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb346-1"><a href="kvantitativa-variabler.html#cb346-1" aria-hidden="true" tabindex="-1"></a>df <span class="ot"><-</span> <span class="fu">data.frame</span>(<span class="at">value1 =</span> <span class="fu">c</span>(<span class="fl">7.73</span>,<span class="fl">1.77</span>,<span class="fl">2.42</span>,<span class="fl">5.33</span>,<span class="fl">4.22</span>,<span class="fl">6.71</span>,<span class="sc">-</span><span class="fl">0.62</span>,<span class="fl">1.86</span>,<span class="sc">-</span><span class="fl">1.02</span>,<span class="fl">4.18</span>,<span class="fl">7.79</span>,<span class="fl">11.81</span>,<span class="fl">0.52</span>,<span class="fl">4.61</span>,<span class="fl">3.42</span>,<span class="sc">-</span><span class="fl">0.42</span>,<span class="fl">0.68</span>,<span class="fl">2.28</span>,<span class="sc">-</span><span class="fl">0.86</span>,<span class="fl">4.62</span>,<span class="fl">5.15</span>,<span class="fl">5.94</span>,<span class="fl">6.77</span>,<span class="fl">8.96</span>,<span class="fl">3.33</span>,<span class="fl">4.71</span>,<span class="fl">4.81</span>,<span class="fl">5.58</span>,<span class="fl">3.97</span>,<span class="fl">3.36</span>,<span class="fl">1.8</span>,<span class="fl">8.99</span>,<span class="fl">3.88</span>,<span class="fl">6.58</span>,<span class="fl">7.83</span>,<span class="fl">5.97</span>,<span class="sc">-</span><span class="fl">0.33</span>,<span class="fl">6.32</span>,<span class="fl">0.43</span>,<span class="fl">2.27</span>,<span class="fl">0.61</span>,<span class="fl">5.99</span>,<span class="fl">3.49</span>,<span class="fl">7.78</span>,<span class="sc">-</span><span class="fl">2.93</span>,<span class="fl">6.34</span>,<span class="sc">-</span><span class="fl">0.09</span>,<span class="fl">4.21</span>,<span class="fl">1.34</span>,<span class="fl">4.31</span>,<span class="fl">3.25</span>,<span class="fl">2.73</span>,<span class="fl">6.91</span>,<span class="fl">9.45</span>,<span class="fl">1.24</span>,<span class="sc">-</span><span class="fl">2.92</span>,<span class="fl">5.82</span>,<span class="fl">2.42</span>,<span class="fl">0.78</span>,<span class="fl">3.89</span>,<span class="fl">2.16</span>,<span class="fl">7.8</span>,<span class="fl">0.04</span>,<span class="fl">0.97</span>,<span class="fl">5.41</span>,<span class="fl">3.42</span>,<span class="fl">3.65</span>,<span class="fl">1.71</span>,<span class="fl">2.29</span>,<span class="fl">11.29</span>,<span class="fl">16.41</span>,<span class="fl">6.55</span>,<span class="sc">-</span><span class="fl">0.58</span>,<span class="fl">3.62</span>,<span class="fl">5.18</span>,<span class="fl">6.21</span>,<span class="fl">5.18</span>,<span class="fl">0.06</span>,<span class="fl">11.37</span>,<span class="fl">3.31</span>,<span class="fl">10.83</span>,<span class="fl">9.19</span>,<span class="sc">-</span><span class="fl">0.32</span>,<span class="fl">6.57</span>,<span class="fl">2.25</span>,<span class="fl">8.38</span>,<span class="sc">-</span><span class="fl">0.93</span>,<span class="sc">-</span><span class="fl">1.68</span>,<span class="fl">1.71</span>,<span class="fl">2.66</span>,<span class="fl">4.75</span>,<span class="fl">3.68</span>,<span class="fl">2.35</span>,<span class="fl">13.44</span>,<span class="fl">6.52</span>,<span class="sc">-</span><span class="fl">5.94</span>,<span class="fl">5.49</span>,<span class="fl">5.21</span>,<span class="fl">1.83</span>,<span class="sc">-</span><span class="fl">1.61</span>,<span class="fl">4.7</span>,<span class="fl">2.69</span>,<span class="fl">4.05</span>,<span class="fl">1.74</span>,<span class="fl">8.51</span>,<span class="fl">7.42</span>,<span class="fl">1.45</span>,<span class="sc">-</span><span class="fl">3.87</span>,<span class="fl">2.58</span>,<span class="fl">1.65</span>,<span class="fl">3.16</span>,<span class="fl">6.75</span>,<span class="fl">4.72</span>,<span class="fl">1.64</span>,<span class="fl">5.18</span>,<span class="fl">2.79</span>,<span class="fl">1.23</span>,<span class="fl">5.22</span>,<span class="fl">6.44</span>,<span class="fl">4.8</span>,<span class="fl">3.28</span>,<span class="fl">4.38</span>,<span class="fl">0.78</span>,<span class="fl">0.09</span>,<span class="fl">4.16</span>,<span class="fl">6.69</span>,<span class="sc">-</span><span class="fl">0.49</span>,<span class="fl">5.9</span>,<span class="fl">1.59</span>,<span class="fl">12.13</span>,<span class="fl">11.22</span>,<span class="fl">0.6</span>,<span class="fl">0.57</span>,<span class="fl">5.2</span>,<span class="sc">-</span><span class="fl">1.52</span>,<span class="fl">5.54</span>,<span class="fl">4.4</span>,<span class="sc">-</span><span class="fl">4.86</span>,<span class="fl">6.48</span>,<span class="fl">8.84</span>,<span class="fl">1.77</span>,<span class="fl">2.51</span>,<span class="fl">3.74</span>,<span class="fl">3.45</span>,<span class="fl">1.11</span>,<span class="fl">4.1</span>,<span class="sc">-</span><span class="fl">1.09</span>,<span class="fl">6.81</span>,<span class="fl">2.31</span>,<span class="fl">3.4</span>,<span class="fl">5.12</span>,<span class="fl">7.56</span>,<span class="fl">1.72</span>,<span class="fl">11.01</span>,<span class="sc">-</span><span class="fl">1.14</span>,<span class="fl">4.28</span>,<span class="sc">-</span><span class="fl">1.05</span>,<span class="fl">1.25</span>,<span class="fl">1.47</span>,<span class="fl">3.64</span>,<span class="fl">1.94</span>,<span class="sc">-</span><span class="fl">2.2</span>,<span class="sc">-</span><span class="fl">1.61</span>,<span class="fl">9.85</span>,<span class="fl">5.51</span>,<span class="fl">12.37</span>,<span class="fl">4.33</span>,<span class="fl">2.27</span>,<span class="fl">3.09</span>,<span class="fl">5.9</span>,<span class="fl">4.39</span>,<span class="fl">8.46</span>,<span class="fl">3.5</span>,<span class="fl">5.89</span>,<span class="fl">8.32</span>,<span class="sc">-</span><span class="fl">5.38</span>,<span class="fl">6.11</span>,<span class="fl">0.67</span>,<span class="fl">3.01</span>,<span class="fl">4.44</span>,<span class="fl">2.27</span>,<span class="fl">1.38</span>,<span class="fl">2.38</span>,<span class="fl">1.73</span>,<span class="fl">6.79</span>,<span class="fl">0.4</span>,<span class="fl">4.48</span>,<span class="fl">0.12</span>,<span class="fl">5.83</span>,<span class="fl">1.6</span>,<span class="fl">5.68</span>,<span class="fl">13.11</span>,<span class="fl">3.73</span>,<span class="fl">4.19</span>,<span class="fl">4.39</span>,<span class="fl">9.84</span>,<span class="sc">-</span><span class="fl">0.32</span>,<span class="fl">4.21</span>,<span class="fl">7.77</span>,<span class="fl">1.34</span>,<span class="fl">8.47</span>,<span class="dv">3</span>,<span class="fl">0.17</span>,<span class="fl">4.54</span>,<span class="fl">1.4</span>,<span class="sc">-</span><span class="fl">1.71</span>,<span class="fl">0.84</span>,<span class="fl">1.62</span>,<span class="fl">10.47</span>,<span class="fl">2.69</span>,<span class="fl">1.17</span>,<span class="fl">2.85</span>,<span class="dv">8</span>,<span class="fl">6.43</span>,<span class="fl">6.28</span>,<span class="fl">6.73</span>,<span class="fl">7.06</span>,<span class="fl">8.72</span>,<span class="fl">5.29</span>,<span class="fl">4.66</span>,<span class="sc">-</span><span class="fl">2.95</span>,<span class="fl">4.94</span>,<span class="fl">3.33</span>,<span class="sc">-</span><span class="fl">1.7</span>,<span class="sc">-</span><span class="fl">0.76</span>,<span class="fl">6.63</span>,<span class="sc">-</span><span class="dv">2</span>,<span class="fl">3.05</span>,<span class="fl">1.85</span>,<span class="fl">8.17</span>,<span class="fl">10.81</span>,<span class="fl">11.66</span>,<span class="fl">5.92</span>,<span class="fl">2.66</span>,<span class="fl">2.25</span>,<span class="fl">7.41</span>,<span class="sc">-</span><span class="dv">3</span>,<span class="fl">7.93</span>,<span class="fl">2.63</span>,<span class="fl">2.84</span>,<span class="fl">6.74</span>,<span class="fl">2.94</span>,<span class="fl">6.73</span>,<span class="fl">8.87</span>,<span class="fl">4.62</span>,<span class="fl">4.89</span>,<span class="sc">-</span><span class="fl">0.32</span>,<span class="fl">0.4</span>,<span class="fl">2.86</span>,<span class="sc">-</span><span class="fl">1.12</span>,<span class="fl">8.16</span>,<span class="fl">0.39</span>,<span class="fl">6.93</span>,<span class="fl">3.96</span>,<span class="fl">1.09</span>,<span class="dv">4</span>,<span class="sc">-</span><span class="fl">0.52</span>,<span class="fl">3.2</span>,<span class="fl">3.63</span>,<span class="fl">7.1</span>,<span class="fl">6.44</span>,<span class="fl">1.78</span>,<span class="sc">-</span><span class="fl">2.59</span>,<span class="fl">2.8</span>,<span class="sc">-</span><span class="fl">3.83</span>,<span class="sc">-</span><span class="fl">0.6</span>,<span class="fl">2.29</span>,<span class="fl">2.77</span>,<span class="fl">2.65</span>,<span class="fl">3.06</span>,<span class="fl">6.92</span>,<span class="fl">1.32</span>,<span class="fl">3.56</span>,<span class="fl">5.55</span>,<span class="fl">8.36</span>,<span class="dv">3</span>,<span class="fl">0.58</span>,<span class="fl">0.8</span>,<span class="fl">4.22</span>,<span class="fl">0.59</span>,<span class="fl">9.71</span>,<span class="sc">-</span><span class="fl">2.14</span>,<span class="fl">8.27</span>,<span class="fl">1.52</span>,<span class="fl">0.68</span>,<span class="fl">7.82</span>,<span class="fl">8.38</span>,<span class="fl">5.43</span>,<span class="fl">8.75</span>,<span class="fl">2.41</span>,<span class="fl">5.07</span>,<span class="fl">10.9</span>,<span class="fl">3.24</span>,<span class="fl">3.95</span>,<span class="dv">4</span>,<span class="fl">1.2</span>,<span class="sc">-</span><span class="fl">1.93</span>,<span class="sc">-</span><span class="fl">1.19</span>,<span class="fl">6.12</span>,<span class="fl">2.79</span>,<span class="fl">6.67</span>,<span class="fl">0.09</span>,<span class="fl">4.81</span>,<span class="fl">3.36</span>,<span class="fl">4.03</span>,<span class="sc">-</span><span class="fl">2.24</span>,<span class="fl">2.58</span>,<span class="sc">-</span><span class="fl">0.93</span>,<span class="sc">-</span><span class="dv">3</span>,<span class="fl">3.76</span>,<span class="sc">-</span><span class="fl">1.75</span>,<span class="fl">2.28</span>,<span class="dv">1</span>,<span class="fl">8.41</span>,<span class="fl">1.67</span>,<span class="fl">6.41</span>,<span class="fl">0.06</span>,<span class="fl">5.77</span>,<span class="fl">3.47</span>,<span class="fl">3.55</span>,<span class="fl">3.03</span>,<span class="fl">5.43</span>,<span class="fl">2.62</span>,<span class="fl">4.82</span>,<span class="fl">3.66</span>,<span class="fl">6.32</span>,<span class="fl">5.02</span>,<span class="fl">4.69</span>,<span class="sc">-</span><span class="fl">2.92</span>,<span class="sc">-</span><span class="fl">3.59</span>,<span class="sc">-</span><span class="fl">0.55</span>,<span class="fl">6.28</span>,<span class="fl">1.15</span>,<span class="fl">3.03</span>,<span class="fl">4.11</span>,<span class="fl">9.45</span>,<span class="fl">9.45</span>,<span class="fl">5.12</span>,<span class="fl">4.43</span>,<span class="fl">3.4</span>,<span class="fl">9.38</span>,<span class="fl">4.82</span>,<span class="fl">2.99</span>,<span class="fl">4.69</span>,<span class="fl">10.65</span>,<span class="fl">3.93</span>,<span class="fl">3.34</span>,<span class="fl">5.2</span>,<span class="fl">4.81</span>,<span class="fl">1.01</span>,<span class="fl">2.98</span>,<span class="fl">4.56</span>,<span class="fl">1.09</span>,<span class="fl">0.82</span>,<span class="fl">4.85</span>,<span class="fl">5.22</span>,<span class="sc">-</span><span class="fl">1.28</span>,<span class="fl">6.53</span>,<span class="fl">4.8</span>,<span class="fl">9.19</span>,<span class="fl">11.63</span>,<span class="fl">1.64</span>,<span class="fl">1.53</span>,<span class="fl">8.77</span>,<span class="fl">4.44</span>,<span class="fl">6.53</span>,<span class="fl">4.33</span>,<span class="fl">6.72</span>,<span class="fl">8.12</span>,<span class="fl">8.22</span>,<span class="sc">-</span><span class="fl">3.83</span>,<span class="fl">2.91</span>,<span class="sc">-</span><span class="fl">1.83</span>,<span class="fl">5.3</span>,<span class="fl">3.76</span>,<span class="fl">3.93</span>,<span class="sc">-</span><span class="fl">1.32</span>,<span class="fl">7.94</span>,<span class="sc">-</span><span class="fl">2.42</span>,<span class="fl">9.69</span>,<span class="sc">-</span><span class="fl">1.45</span>,<span class="fl">7.61</span>,<span class="fl">5.5</span>,<span class="fl">3.89</span>,<span class="fl">6.66</span>,<span class="fl">3.82</span>,<span class="fl">14.27</span>,<span class="fl">7.61</span>,<span class="fl">9.16</span>,<span class="fl">10.21</span>,<span class="fl">6.13</span>,<span class="fl">1.42</span>,<span class="fl">3.58</span>,<span class="fl">5.79</span>,<span class="fl">4.94</span>,<span class="fl">0.07</span>,<span class="sc">-</span><span class="fl">0.88</span>,<span class="fl">11.42</span>,<span class="fl">3.59</span>,<span class="fl">0.5</span>,<span class="fl">0.51</span>,<span class="fl">6.02</span>,<span class="fl">5.66</span>,<span class="fl">5.46</span>,<span class="fl">4.35</span>,<span class="fl">7.44</span>,<span class="fl">1.57</span>,<span class="fl">15.44</span>,<span class="fl">7.28</span>,<span class="fl">1.1</span>,<span class="fl">14.6</span>,<span class="sc">-</span><span class="fl">2.48</span>,<span class="sc">-</span><span class="fl">3.37</span>,<span class="sc">-</span><span class="fl">4.1</span>,<span class="fl">7.88</span>,<span class="fl">6.05</span>,<span class="fl">4.56</span>,<span class="fl">4.12</span>,<span class="fl">6.45</span>,<span class="fl">2.62</span>,<span class="fl">8.68</span>,<span class="fl">1.52</span>,<span class="fl">0.26</span>,<span class="fl">1.83</span>,<span class="fl">0.57</span>,<span class="fl">6.93</span>,<span class="fl">7.05</span>,<span class="sc">-</span><span class="fl">0.22</span>,<span class="fl">6.92</span>,<span class="fl">3.93</span>,<span class="fl">2.75</span>,<span class="sc">-</span><span class="fl">6.45</span>,<span class="fl">2.75</span>,<span class="fl">3.34</span>,<span class="fl">9.07</span>,<span class="fl">11.64</span>,<span class="fl">7.47</span>,<span class="fl">9.13</span>,<span class="fl">3.44</span>,<span class="sc">-</span><span class="fl">0.1</span>,<span class="fl">4.39</span>,<span class="fl">4.26</span>,<span class="fl">8.97</span>,<span class="dv">3</span>,<span class="sc">-</span><span class="fl">3.46</span>,<span class="sc">-</span><span class="fl">1.42</span>,<span class="fl">3.19</span>,<span class="fl">7.1</span>,<span class="fl">0.51</span>,<span class="fl">0.8</span>,<span class="fl">2.99</span>,<span class="fl">4.25</span>,<span class="fl">3.5</span>,<span class="fl">0.9</span>,<span class="fl">4.21</span>,<span class="fl">2.91</span>,<span class="fl">5.94</span>,<span class="fl">2.77</span>,<span class="fl">10.72</span>,<span class="sc">-</span><span class="fl">1.92</span>,<span class="fl">6.31</span>,<span class="fl">5.74</span>,<span class="fl">5.85</span>,<span class="fl">7.75</span>,<span class="fl">13.77</span>,<span class="fl">9.69</span>,<span class="fl">10.9</span>,<span class="fl">7.97</span>,<span class="fl">8.36</span>,<span class="fl">1.28</span>,<span class="sc">-</span><span class="fl">2.33</span>,<span class="fl">2.42</span>,<span class="fl">4.59</span>,<span class="fl">4.93</span>,<span class="sc">-</span><span class="fl">0.53</span>,<span class="fl">7.74</span>,<span class="fl">9.76</span>,<span class="fl">4.05</span>,<span class="fl">15.55</span>,<span class="fl">4.31</span>,<span class="fl">0.52</span>,<span class="sc">-</span><span class="fl">0.71</span>,<span class="fl">5.93</span>,<span class="fl">9.8</span>,<span class="fl">5.78</span>,<span class="fl">6.37</span>,<span class="fl">1.65</span>,<span class="fl">8.61</span>,<span class="fl">6.44</span>,<span class="sc">-</span><span class="fl">1.34</span>,<span class="fl">13.49</span>,<span class="fl">5.42</span>,<span class="fl">7.94</span>,<span class="sc">-</span><span class="dv">1</span>,<span class="fl">5.26</span>,<span class="fl">4.41</span>,<span class="fl">2.97</span>,<span class="fl">2.88</span>,<span class="sc">-</span><span class="fl">0.19</span>,<span class="fl">0.67</span>),</span>
<span id="cb346-2"><a href="kvantitativa-variabler.html#cb346-2" aria-hidden="true" tabindex="-1"></a> <span class="at">value2=</span> <span class="fu">c</span>(<span class="dv">4</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">2</span>,<span class="dv">4</span>,<span class="dv">2</span>,<span class="dv">2</span>,<span class="dv">2</span>,<span class="dv">2</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">2</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">2</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">4</span>,<span class="dv">2</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">2</span>,<span class="dv">2</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">2</span>,<span class="dv">4</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">2</span>,<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">2</span>,<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">2</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">4</span>,<span class="dv">4</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">2</span>,<span class="dv">2</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">4</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">2</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">4</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">4</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">2</span>,<span class="dv">2</span>,<span class="dv">4</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">4</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">4</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">4</span>,<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">2</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">4</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">2</span>,<span class="dv">2</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">4</span>,<span class="dv">4</span>,<span class="dv">2</span>,<span class="dv">4</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">2</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">2</span>,<span class="dv">4</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">4</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">2</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">4</span>,<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">4</span>,<span class="dv">4</span>,<span class="dv">2</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">2</span>,<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">2</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">4</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">4</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">4</span>,<span class="dv">4</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">4</span>,<span class="dv">2</span>,<span class="dv">4</span>,<span class="dv">2</span>,<span class="dv">2</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">2</span>,<span class="dv">1</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">2</span>))</span></code></pre></div>
</div>
</div>
<p></br></p>
<ol style="list-style-type: lower-alpha">
<li><p>Kopiera koden i fliken och kör den i <code>R</code>. Koden skapar en data frame vid namn <code>df</code> som innehåller de två variablerna.</p></li>
<li><p>Undersök vilken vektortyp de två variablerna lagras i. Bekriv sedan variablera, var och en för sig, på ett lämpligt sätt.</p></li>
</ol>
<button title="q_61_b" type="button" onclick="if(document.getElementById('q_61_b') .style.display=='none')
{document.getElementById('q_61_b') .style.display=''}
else{document.getElementById('q_61_b') .style.display='none'}">
Visa svar
</button>
<div id="q_61_b" style="display:none">
<div class="alert alert-info">
<p><strong><code>value1</code>:</strong></p>
<div class="sourceCode" id="cb347"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb347-1"><a href="kvantitativa-variabler.html#cb347-1" aria-hidden="true" tabindex="-1"></a><span class="fu">class</span>(df<span class="sc">$</span>value1) <span class="co"># Kollar vektortyp</span></span>
<span id="cb347-2"><a href="kvantitativa-variabler.html#cb347-2" aria-hidden="true" tabindex="-1"></a><span class="sc">></span> [<span class="dv">1</span>] <span class="st">"numeric"</span></span>
<span id="cb347-3"><a href="kvantitativa-variabler.html#cb347-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb347-4"><a href="kvantitativa-variabler.html#cb347-4" aria-hidden="true" tabindex="-1"></a><span class="fu">head</span>(df<span class="sc">$</span>value1) <span class="co"># Skriver ut de första värdena i value</span></span>
<span id="cb347-5"><a href="kvantitativa-variabler.html#cb347-5" aria-hidden="true" tabindex="-1"></a><span class="sc">></span> [<span class="dv">1</span>] <span class="fl">7.73</span> <span class="fl">1.77</span> <span class="fl">2.42</span> <span class="fl">5.33</span> <span class="fl">4.22</span> <span class="fl">6.71</span></span></code></pre></div>
<p>Som synes är <code>class</code> en kavantitativ variabel, och den verkar även vara kontinuerlig (dess värden är inte heltal), därför skulle variabeln lämpligen kunna beskrivas med hjälp av ett histogram.</p>
<div class="sourceCode" id="cb348"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb348-1"><a href="kvantitativa-variabler.html#cb348-1" aria-hidden="true" tabindex="-1"></a><span class="fu">hist</span>(df<span class="sc">$</span>value1, <span class="at">xlab =</span> <span class="st">"Value"</span>, <span class="at">main =</span> <span class="st">"Histogram över 'value'"</span>)</span></code></pre></div>
<p><img src="docs/images/unnamed-chunk-333-1.png" width="672" style="display: block; margin: auto;" /></p>
<hr />
<p><strong><code>value2</code></strong></p>
<div class="sourceCode" id="cb349"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb349-1"><a href="kvantitativa-variabler.html#cb349-1" aria-hidden="true" tabindex="-1"></a><span class="fu">class</span>(df<span class="sc">$</span>value2) <span class="co"># Kollar vektortyp</span></span>
<span id="cb349-2"><a href="kvantitativa-variabler.html#cb349-2" aria-hidden="true" tabindex="-1"></a><span class="sc">></span> [<span class="dv">1</span>] <span class="st">"numeric"</span></span>
<span id="cb349-3"><a href="kvantitativa-variabler.html#cb349-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb349-4"><a href="kvantitativa-variabler.html#cb349-4" aria-hidden="true" tabindex="-1"></a><span class="fu">head</span>(df<span class="sc">$</span>value2) <span class="co"># Skriver ut de första värdena i value</span></span>
<span id="cb349-5"><a href="kvantitativa-variabler.html#cb349-5" aria-hidden="true" tabindex="-1"></a><span class="sc">></span> [<span class="dv">1</span>] <span class="dv">4</span> <span class="dv">1</span> <span class="dv">1</span> <span class="dv">3</span> <span class="dv">1</span> <span class="dv">1</span></span></code></pre></div>
<p><code>value2</code> är kvantitativ men antar bara heltalsvärde, alltså är det en diskret variabel. Lämpligt är därför att beskriva den med en frekvenstabell</p>
<div class="sourceCode" id="cb350"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb350-1"><a href="kvantitativa-variabler.html#cb350-1" aria-hidden="true" tabindex="-1"></a>tab_v2 <span class="ot"><-</span> <span class="fu">table</span>(df<span class="sc">$</span>value2)</span>
<span id="cb350-2"><a href="kvantitativa-variabler.html#cb350-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb350-3"><a href="kvantitativa-variabler.html#cb350-3" aria-hidden="true" tabindex="-1"></a>tab_v2</span>
<span id="cb350-4"><a href="kvantitativa-variabler.html#cb350-4" aria-hidden="true" tabindex="-1"></a><span class="sc">></span> </span>
<span id="cb350-5"><a href="kvantitativa-variabler.html#cb350-5" aria-hidden="true" tabindex="-1"></a><span class="er">></span> <span class="dv">1</span> <span class="dv">2</span> <span class="dv">3</span> <span class="dv">4</span> </span>
<span id="cb350-6"><a href="kvantitativa-variabler.html#cb350-6" aria-hidden="true" tabindex="-1"></a><span class="sc">></span> <span class="dv">127</span> <span class="dv">112</span> <span class="dv">151</span> <span class="dv">110</span></span></code></pre></div>
<p>eller eventuellt ett stapeldiagram</p>
<div class="sourceCode" id="cb351"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb351-1"><a href="kvantitativa-variabler.html#cb351-1" aria-hidden="true" tabindex="-1"></a><span class="fu">barplot</span>(tab_v2, <span class="at">ylab =</span> <span class="st">"Frekvens"</span>)</span></code></pre></div>
<p><img src="docs/images/unnamed-chunk-336-1.png" width="672" style="display: block; margin: auto;" /></p>
</div>
</div>
<p></br></p>
<ol start="3" style="list-style-type: lower-alpha">
<li>Antag nu att du är intresserad av att studera sambandet mellan de två variablerna. Närmare bestämt vill du ha <code>value1</code> som beroende variabel och <code>value2</code> som oberoende. För att göra en första, deskriptiv, analys vill du illustrera sambandet mellan de två variablerna. Hur kan du göra det på ett lämpligt sätt? <em>Ledning: kom ihåg att tänka på variabeltyper!</em></li>
</ol>
<button title="q_61_c" type="button" onclick="if(document.getElementById('q_61_c') .style.display=='none')
{document.getElementById('q_61_c') .style.display=''}
else{document.getElementById('q_61_c') .style.display='none'}">
Visa svar
</button>
<div id="q_61_c" style="display:none">
<div class="alert alert-info">
<p>Eftersom <code>value1</code> är kontinuerlig och <code>value2</code> är diskret behövs ett diagram som klarar av att kombinera dessa två variabeltyper. Enligt kapiteltextens resonemang bör denna typ av variabelkomination illustreras med en box plot.</p>
<div class="sourceCode" id="cb352"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb352-1"><a href="kvantitativa-variabler.html#cb352-1" aria-hidden="true" tabindex="-1"></a><span class="fu">boxplot</span>(df<span class="sc">$</span>value1 <span class="sc">~</span> df<span class="sc">$</span>value2)</span></code></pre></div>
<p><img src="docs/images/unnamed-chunk-337-1.png" width="672" style="display: block; margin: auto;" /></p>
<p>Att döma av figuren ser det ut som att <code>value1</code> stiger när <code>value2</code> också gör det. Du kommer lära dig mer om hur sambandet kan kvantifieras/testas i senare delar av kursen.</p>
</div>
</div>
<p></br></p>
</div>
<div id="uppgift-2-1" class="section level3 hasAnchor" number="6.3.2">
<h3><span class="header-section-number">6.3.2</span> Uppgift 2<a href="kvantitativa-variabler.html#uppgift-2-1" class="anchor-section" aria-label="Anchor link to header"></a></h3>
<p>Kör koden</p>
<div class="sourceCode" id="cb353"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb353-1"><a href="kvantitativa-variabler.html#cb353-1" aria-hidden="true" tabindex="-1"></a><span class="fu">set.seed</span>(<span class="dv">211101</span>)</span>
<span id="cb353-2"><a href="kvantitativa-variabler.html#cb353-2" aria-hidden="true" tabindex="-1"></a>value3 <span class="ot"><-</span> <span class="fu">rnorm</span>(<span class="at">n =</span> <span class="dv">500</span>, <span class="at">mean =</span> (<span class="fl">9.89</span> <span class="sc">+</span> <span class="fl">2.059</span> <span class="sc">*</span> df<span class="sc">$</span>value1), <span class="at">sd =</span> <span class="dv">3</span>)</span>
<span id="cb353-3"><a href="kvantitativa-variabler.html#cb353-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb353-4"><a href="kvantitativa-variabler.html#cb353-4" aria-hidden="true" tabindex="-1"></a>df <span class="ot"><-</span> <span class="fu">cbind</span>(df, value3)</span></code></pre></div>
<p>för att lägga till ytterligare en variabel, <code>value3</code>, till <code>df</code> från Uppgift 1. <code>value3</code> är en kontinuerlig variabel, och av anledningar som vid denna tidpunkt är oförklarliga finns en misstanke om linjärt samband mellan <code>value3</code> och <code>value1</code>. Du önskar göra en regressionsanalys för att studera det linjära sambandet, men först behövs en kort deskriptiv studie. Regressionsanalysen är tänkt att ha <code>value3</code> som <span class="math inline">\(y\)</span>-variabel och <code>value1</code> som <span class="math inline">\(x\)</span>-variabel.</p>
<ol style="list-style-type: lower-alpha">
<li>Skapa en figur med två histogram sida vid sida. Det vänstra histogrammet ska visa föredlningen för <code>value1</code> och det högra fördelningen för <code>value3</code>. På så sätt kan du kontrollera grundantagandet att <span class="math inline">\(y\)</span>-variabeln i regressionsanalysen är normalfördelad. Ser antagandet ut att gälla i detta fall?</li>
</ol>
<button title="q_62_a" type="button" onclick="if(document.getElementById('q_62_a') .style.display=='none')
{document.getElementById('q_62_a') .style.display=''}
else{document.getElementById('q_62_a') .style.display='none'}">
Visa svar
</button>
<div id="q_62_a" style="display:none">
<div class="alert alert-info">
<p>För att skapa histogram används <code>hist()</code> som vanligt, och för att få två diagram bredvid varandra justeras <code>par(mfrow = c(rader, kolumner))</code> på lämpligt sätt.</p>
<div class="sourceCode" id="cb354"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb354-1"><a href="kvantitativa-variabler.html#cb354-1" aria-hidden="true" tabindex="-1"></a><span class="fu">par</span>(<span class="at">mfrow =</span> <span class="fu">c</span>(<span class="dv">1</span>, <span class="dv">2</span>)) <span class="co"># Två kolumner, en rad</span></span>
<span id="cb354-2"><a href="kvantitativa-variabler.html#cb354-2" aria-hidden="true" tabindex="-1"></a><span class="fu">hist</span>(df<span class="sc">$</span>value1, <span class="at">main =</span> <span class="st">"Value 1"</span>)</span>
<span id="cb354-3"><a href="kvantitativa-variabler.html#cb354-3" aria-hidden="true" tabindex="-1"></a><span class="fu">hist</span>(df<span class="sc">$</span>value3, <span class="at">main =</span> <span class="st">"Value 3"</span>)</span></code></pre></div>
<p><img src="docs/images/unnamed-chunk-339-1.png" width="672" style="display: block; margin: auto;" /></p>
<div class="sourceCode" id="cb355"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb355-1"><a href="kvantitativa-variabler.html#cb355-1" aria-hidden="true" tabindex="-1"></a><span class="fu">par</span>(<span class="at">mfrow =</span> <span class="fu">c</span>(<span class="dv">1</span>, <span class="dv">1</span>)) <span class="co"># Återställer grundinställning</span></span></code></pre></div>
</div>
</div>
<p></br></p>
<ol start="2" style="list-style-type: lower-alpha">
<li>Skapa ett spridningsdiagram med <code>value1</code> på den vågräta axeln och <code>value3</code> på den lodräta. Uppskatta även korrelationen mellan de två variablerna. Ser det ut som att variablerna är linjärt relaterade med varandra?</li>
</ol>
<button title="q_62_b" type="button" onclick="if(document.getElementById('q_62_b') .style.display=='none')
{document.getElementById('q_62_b') .style.display=''}
else{document.getElementById('q_62_b') .style.display='none'}">
Visa svar
</button>
<div id="q_62_b" style="display:none">
<div class="alert alert-info">
<p>Funktionen <code>plot()</code> används för att skapa ett spridningsdiagram, och <code>cor()</code> för att beräkna stickprovskorrelationen.</p>
<div class="sourceCode" id="cb356"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb356-1"><a href="kvantitativa-variabler.html#cb356-1" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(<span class="at">x =</span> df<span class="sc">$</span>value1, <span class="at">y =</span> df<span class="sc">$</span>value3, <span class="co"># Anger variabler</span></span>
<span id="cb356-2"><a href="kvantitativa-variabler.html#cb356-2" aria-hidden="true" tabindex="-1"></a> <span class="at">pch =</span> <span class="dv">20</span>, <span class="co"># Byter stil på punkterna</span></span>
<span id="cb356-3"><a href="kvantitativa-variabler.html#cb356-3" aria-hidden="true" tabindex="-1"></a> <span class="at">col =</span> <span class="st">"forestgreen"</span>) <span class="co"># Byter färg på punkterna</span></span></code></pre></div>
<p><img src="docs/images/unnamed-chunk-340-1.png" width="672" style="display: block; margin: auto;" /></p>
<div class="sourceCode" id="cb357"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb357-1"><a href="kvantitativa-variabler.html#cb357-1" aria-hidden="true" tabindex="-1"></a><span class="fu">cor</span>(df<span class="sc">$</span>value1, df<span class="sc">$</span>value3) </span>
<span id="cb357-2"><a href="kvantitativa-variabler.html#cb357-2" aria-hidden="true" tabindex="-1"></a><span class="sc">></span> [<span class="dv">1</span>] <span class="fl">0.9317125</span></span></code></pre></div>
<p>korrelationen är väldigt hög, och spridningsdiagrammet antyder att ett linjärt samband finns (dock är det omöjligt säga om det är ett orsakssamband eller ej).</p>
<hr />
<p>Den som är intresserad kan gå händelserna i förväg och skatta regressionsmodellen (detta kommer tas upp på Mattias del av kursen) och sedan rita in regressionslinjen i diagrammet ovan.</p>
<p>Regressionsmodellen skattas med <code>lm(yvariabel ~ xvariabel)</code> och regressionslinjen ritas in med <code>abline()</code></p>
<div class="sourceCode" id="cb358"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb358-1"><a href="kvantitativa-variabler.html#cb358-1" aria-hidden="true" tabindex="-1"></a>regressionsmodell <span class="ot"><-</span> <span class="fu">lm</span>(df<span class="sc">$</span>value3 <span class="sc">~</span> df<span class="sc">$</span>value1) <span class="co"># Skattar regressionsmodell</span></span>
<span id="cb358-2"><a href="kvantitativa-variabler.html#cb358-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb358-3"><a href="kvantitativa-variabler.html#cb358-3" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(<span class="at">x =</span> df<span class="sc">$</span>value1, <span class="at">y =</span> df<span class="sc">$</span>value3, <span class="co"># Anger variabler</span></span>
<span id="cb358-4"><a href="kvantitativa-variabler.html#cb358-4" aria-hidden="true" tabindex="-1"></a> <span class="at">pch =</span> <span class="dv">20</span>, <span class="co"># Byter stil på punkterna</span></span>
<span id="cb358-5"><a href="kvantitativa-variabler.html#cb358-5" aria-hidden="true" tabindex="-1"></a> <span class="at">col =</span> <span class="st">"forestgreen"</span>) <span class="co"># Byter färg på punkterna</span></span>
<span id="cb358-6"><a href="kvantitativa-variabler.html#cb358-6" aria-hidden="true" tabindex="-1"></a><span class="fu">abline</span>(regressionsmodell, <span class="at">col =</span> <span class="st">"red"</span>) <span class="co"># Ritar regressionslinje</span></span></code></pre></div>
<p><img src="docs/images/unnamed-chunk-341-1.png" width="672" style="display: block; margin: auto;" /></p>
<p><strong>Notera att detta inte är något du förväntas kunna ännu, utan det är bara för den intresserade.</strong></p>
</div>
</div>
<p></br></p>
</div>
<div id="uppgift-3-1" class="section level3 hasAnchor" number="6.3.3">
<h3><span class="header-section-number">6.3.3</span> Uppgift 3<a href="kvantitativa-variabler.html#uppgift-3-1" class="anchor-section" aria-label="Anchor link to header"></a></h3>
<p>Läs igenom sida 8 i föreläsningsanteckningarna till Kapitel 6 (<em>Programmering_KvantitativaVariabler.pdf</em>).</p>
<ol style="list-style-type: lower-alpha">
<li>Skapa en liknande vektor med deskrivptiva mått för <code>alder</code> (se sida 6 i samma anteckningar). Kopiera även koden krävs för att skapa objektet <code>desk_tab</code> som finns på sida 8.</li>
</ol>
<button title="q_63_a" type="button" onclick="if(document.getElementById('q_63_a') .style.display=='none')
{document.getElementById('q_63_a') .style.display=''}
else{document.getElementById('q_63_a') .style.display='none'}">
Visa svar
</button>
<div id="q_63_a" style="display:none">
<div class="alert alert-info">
<p>Vi börjar med att kopiera in all kod som krävs för att skapa <code>desk_tab</code> (det blir lättare att modifiera koden så att den använder <code>alder</code> efteråt).</p>
<div class="sourceCode" id="cb359"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb359-1"><a href="kvantitativa-variabler.html#cb359-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Vektorer från sida 6</span></span>
<span id="cb359-2"><a href="kvantitativa-variabler.html#cb359-2" aria-hidden="true" tabindex="-1"></a>langd <span class="ot"><-</span> <span class="fu">c</span>(<span class="fl">194.1</span>, <span class="fl">175.1</span>, <span class="fl">167.1</span>, <span class="fl">161.6</span>, <span class="fl">176.8</span>, <span class="fl">180.9</span>,</span>
<span id="cb359-3"><a href="kvantitativa-variabler.html#cb359-3" aria-hidden="true" tabindex="-1"></a> <span class="fl">180.6</span>, <span class="fl">174.8</span>, <span class="fl">172.4</span>, <span class="fl">187.3</span>, <span class="fl">186.8</span>, <span class="fl">194.6</span>,</span>
<span id="cb359-4"><a href="kvantitativa-variabler.html#cb359-4" aria-hidden="true" tabindex="-1"></a> <span class="fl">154.3</span>, <span class="fl">169.7</span>, <span class="fl">169.5</span>, <span class="fl">168.0</span>, <span class="fl">187.4</span>, <span class="fl">184.7</span>,</span>
<span id="cb359-5"><a href="kvantitativa-variabler.html#cb359-5" aria-hidden="true" tabindex="-1"></a> <span class="fl">195.2</span>, <span class="fl">184.4</span>)</span>
<span id="cb359-6"><a href="kvantitativa-variabler.html#cb359-6" aria-hidden="true" tabindex="-1"></a>alder <span class="ot"><-</span> <span class="fu">c</span>(<span class="dv">21</span>, <span class="dv">20</span>, <span class="dv">29</span>, <span class="dv">26</span>, <span class="dv">20</span>, <span class="dv">20</span>, <span class="dv">21</span>, <span class="dv">29</span>, <span class="dv">29</span>, <span class="dv">22</span>,</span>
<span id="cb359-7"><a href="kvantitativa-variabler.html#cb359-7" aria-hidden="true" tabindex="-1"></a> <span class="dv">21</span>, <span class="dv">22</span>, <span class="dv">23</span>, <span class="dv">26</span>, <span class="dv">23</span>, <span class="dv">25</span>, <span class="dv">21</span>, <span class="dv">24</span>, <span class="dv">24</span>, <span class="dv">23</span>)</span>
<span id="cb359-8"><a href="kvantitativa-variabler.html#cb359-8" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb359-9"><a href="kvantitativa-variabler.html#cb359-9" aria-hidden="true" tabindex="-1"></a><span class="co"># Deskriptiva mått för langd (från sida 7)</span></span>
<span id="cb359-10"><a href="kvantitativa-variabler.html#cb359-10" aria-hidden="true" tabindex="-1"></a>langd_bar <span class="ot"><-</span> <span class="fu">mean</span>(langd) <span class="co"># Medelvärde</span></span>
<span id="cb359-11"><a href="kvantitativa-variabler.html#cb359-11" aria-hidden="true" tabindex="-1"></a>langd_sd <span class="ot"><-</span> <span class="fu">sd</span>(langd) <span class="co"># Standardavvikelse</span></span>
<span id="cb359-12"><a href="kvantitativa-variabler.html#cb359-12" aria-hidden="true" tabindex="-1"></a>langd_md <span class="ot"><-</span> <span class="fu">median</span>(langd) <span class="co"># Median</span></span>
<span id="cb359-13"><a href="kvantitativa-variabler.html#cb359-13" aria-hidden="true" tabindex="-1"></a>langd_iqr <span class="ot"><-</span> <span class="fu">IQR</span>(langd) <span class="co"># Kvartilavstånd</span></span>
<span id="cb359-14"><a href="kvantitativa-variabler.html#cb359-14" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb359-15"><a href="kvantitativa-variabler.html#cb359-15" aria-hidden="true" tabindex="-1"></a><span class="co"># Kod som skapar desk_tab (från sida 8)</span></span>
<span id="cb359-16"><a href="kvantitativa-variabler.html#cb359-16" aria-hidden="true" tabindex="-1"></a>desk_tab <span class="ot"><-</span> <span class="fu">cbind</span>(langd_bar, langd_sd, langd_md,</span>
<span id="cb359-17"><a href="kvantitativa-variabler.html#cb359-17" aria-hidden="true" tabindex="-1"></a> langd_iqr)</span>
<span id="cb359-18"><a href="kvantitativa-variabler.html#cb359-18" aria-hidden="true" tabindex="-1"></a><span class="fu">colnames</span>(desk_tab) <span class="ot"><-</span> <span class="fu">c</span>(<span class="st">"Medelvärde"</span>, <span class="st">"Std. Av."</span>,</span>
<span id="cb359-19"><a href="kvantitativa-variabler.html#cb359-19" aria-hidden="true" tabindex="-1"></a> <span class="st">"Median"</span>, <span class="st">"Kvartilavst."</span>)</span>
<span id="cb359-20"><a href="kvantitativa-variabler.html#cb359-20" aria-hidden="true" tabindex="-1"></a><span class="fu">rownames</span>(desk_tab) <span class="ot"><-</span> <span class="fu">c</span>(<span class="st">"Langd"</span>)</span>
<span id="cb359-21"><a href="kvantitativa-variabler.html#cb359-21" aria-hidden="true" tabindex="-1"></a>desk_tab</span>
<span id="cb359-22"><a href="kvantitativa-variabler.html#cb359-22" aria-hidden="true" tabindex="-1"></a><span class="sc">></span> Medelvärde Std. Av. Median Kvartilavst.</span>
<span id="cb359-23"><a href="kvantitativa-variabler.html#cb359-23" aria-hidden="true" tabindex="-1"></a><span class="sc">></span> Langd <span class="fl">178.265</span> <span class="fl">11.2964</span> <span class="fl">178.7</span> <span class="fl">17.275</span></span></code></pre></div>
<p>För att skapa en vektor med deskriptiva mått över <code>alder</code> kan vi antingen skapa de fyra mellersta objekten ovan (från sida 7) en gång till för <code>alder</code>, eller så kan vi lägga in värdena i en vektor direkt, som i koden nedan</p>
<div class="sourceCode" id="cb360"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb360-1"><a href="kvantitativa-variabler.html#cb360-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Deskriptiv vektor för alder</span></span>
<span id="cb360-2"><a href="kvantitativa-variabler.html#cb360-2" aria-hidden="true" tabindex="-1"></a>desk_alder <span class="ot"><-</span> <span class="fu">c</span>(<span class="fu">mean</span>(alder), <span class="fu">sd</span>(alder), <span class="fu">median</span>(alder), <span class="fu">IQR</span>(alder))</span>
<span id="cb360-3"><a href="kvantitativa-variabler.html#cb360-3" aria-hidden="true" tabindex="-1"></a>desk_alder</span>
<span id="cb360-4"><a href="kvantitativa-variabler.html#cb360-4" aria-hidden="true" tabindex="-1"></a><span class="sc">></span> [<span class="dv">1</span>] <span class="fl">23.450000</span> <span class="fl">3.017057</span> <span class="fl">23.000000</span> <span class="fl">4.250000</span></span></code></pre></div>
</div>
</div>