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  <title>Chapter 14 View best lambda value | Introduction to R for Crime Analysts</title>
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<li class="chapter" data-level="" data-path="index.html"><a href="index.html"><i class="fa fa-check"></i>Preface</a>
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<li class="chapter" data-level="2.1" data-path="getting-started-with-r.html"><a href="getting-started-with-r.html#the-r-environment"><i class="fa fa-check"></i><b>2.1</b> The R Environment</a>
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<li class="chapter" data-level="2.4" data-path="getting-started-with-r.html"><a href="getting-started-with-r.html#basic-operations-and-functions-in-r"><i class="fa fa-check"></i><b>2.4</b> Basic Operations and Functions in R</a>
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<li class="chapter" data-level="2.4.2" data-path="getting-started-with-r.html"><a href="getting-started-with-r.html#logical-operations"><i class="fa fa-check"></i><b>2.4.2</b> Logical Operations</a></li>
<li class="chapter" data-level="2.4.3" data-path="getting-started-with-r.html"><a href="getting-started-with-r.html#basic-functions"><i class="fa fa-check"></i><b>2.4.3</b> Basic Functions</a></li>
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<li class="chapter" data-level="2.5" data-path="getting-started-with-r.html"><a href="getting-started-with-r.html#conclusion-1"><i class="fa fa-check"></i><b>2.5</b> Conclusion</a></li>
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<li class="chapter" data-level="3" data-path="data-management-in-r.html"><a href="data-management-in-r.html"><i class="fa fa-check"></i><b>3</b> Data Management in R</a>
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<li class="chapter" data-level="3.1" data-path="data-management-in-r.html"><a href="data-management-in-r.html#data-import-and-export"><i class="fa fa-check"></i><b>3.1</b> Data Import and Export</a>
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<li class="chapter" data-level="3.1.1" data-path="data-management-in-r.html"><a href="data-management-in-r.html#importing-data"><i class="fa fa-check"></i><b>3.1.1</b> Importing Data</a></li>
<li class="chapter" data-level="3.1.2" data-path="data-management-in-r.html"><a href="data-management-in-r.html#exporting-data"><i class="fa fa-check"></i><b>3.1.2</b> Exporting Data</a></li>
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<li class="chapter" data-level="3.2" data-path="data-management-in-r.html"><a href="data-management-in-r.html#data-cleaning-and-preparation"><i class="fa fa-check"></i><b>3.2</b> Data Cleaning and Preparation</a>
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<li class="chapter" data-level="3.2.1" data-path="data-management-in-r.html"><a href="data-management-in-r.html#handling-missing-data"><i class="fa fa-check"></i><b>3.2.1</b> Handling Missing Data</a></li>
<li class="chapter" data-level="3.2.2" data-path="data-management-in-r.html"><a href="data-management-in-r.html#filtering-and-subsetting-data"><i class="fa fa-check"></i><b>3.2.2</b> Filtering and Subsetting Data</a></li>
<li class="chapter" data-level="3.2.3" data-path="data-management-in-r.html"><a href="data-management-in-r.html#data-transformations"><i class="fa fa-check"></i><b>3.2.3</b> Data Transformations</a></li>
<li class="chapter" data-level="3.2.4" data-path="data-management-in-r.html"><a href="data-management-in-r.html#the-dplyr-pipeline"><i class="fa fa-check"></i><b>3.2.4</b> The dplyr Pipeline</a></li>
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<li class="chapter" data-level="3.3" data-path="data-management-in-r.html"><a href="data-management-in-r.html#working-with-categorical-data"><i class="fa fa-check"></i><b>3.3</b> Working with Categorical Data</a>
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<li class="chapter" data-level="3.3.1" data-path="data-management-in-r.html"><a href="data-management-in-r.html#creating-and-manipulating-factors"><i class="fa fa-check"></i><b>3.3.1</b> Creating and Manipulating Factors</a></li>
<li class="chapter" data-level="3.3.2" data-path="data-management-in-r.html"><a href="data-management-in-r.html#recoding-variables"><i class="fa fa-check"></i><b>3.3.2</b> Recoding Variables</a></li>
<li class="chapter" data-level="3.3.3" data-path="data-management-in-r.html"><a href="data-management-in-r.html#frequency-tables-and-cross-tabulations"><i class="fa fa-check"></i><b>3.3.3</b> Frequency Tables and Cross-Tabulations</a></li>
</ul></li>
<li class="chapter" data-level="3.4" data-path="data-management-in-r.html"><a href="data-management-in-r.html#conclusion-2"><i class="fa fa-check"></i><b>3.4</b> Conclusion</a></li>
</ul></li>
<li class="chapter" data-level="4" data-path="connecting-to-and-accessing-a-postgresql-database.html"><a href="connecting-to-and-accessing-a-postgresql-database.html"><i class="fa fa-check"></i><b>4</b> Connecting to and Accessing a PostgreSQL Database</a>
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<li class="chapter" data-level="4.1" data-path="connecting-to-and-accessing-a-postgresql-database.html"><a href="connecting-to-and-accessing-a-postgresql-database.html#introduction-1"><i class="fa fa-check"></i><b>4.1</b> Introduction</a></li>
<li class="chapter" data-level="4.2" data-path="connecting-to-and-accessing-a-postgresql-database.html"><a href="connecting-to-and-accessing-a-postgresql-database.html#setting-up-the-environment"><i class="fa fa-check"></i><b>4.2</b> Setting Up the Environment</a>
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<li class="chapter" data-level="4.2.1" data-path="connecting-to-and-accessing-a-postgresql-database.html"><a href="connecting-to-and-accessing-a-postgresql-database.html#installing-necessary-packages"><i class="fa fa-check"></i><b>4.2.1</b> Installing Necessary Packages</a></li>
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<li class="chapter" data-level="4.3" data-path="connecting-to-and-accessing-a-postgresql-database.html"><a href="connecting-to-and-accessing-a-postgresql-database.html#connecting-to-postgresql-using-rpostgres"><i class="fa fa-check"></i><b>4.3</b> Connecting to PostgreSQL (Using RPostgres)</a></li>
<li class="chapter" data-level="4.4" data-path="connecting-to-and-accessing-a-postgresql-database.html"><a href="connecting-to-and-accessing-a-postgresql-database.html#querying-data-from-postgresql"><i class="fa fa-check"></i><b>4.4</b> Querying Data from PostgreSQL</a>
<ul>
<li class="chapter" data-level="4.4.1" data-path="connecting-to-and-accessing-a-postgresql-database.html"><a href="connecting-to-and-accessing-a-postgresql-database.html#executing-a-query"><i class="fa fa-check"></i><b>4.4.1</b> Executing a Query</a></li>
</ul></li>
<li class="chapter" data-level="4.5" data-path="connecting-to-and-accessing-a-postgresql-database.html"><a href="connecting-to-and-accessing-a-postgresql-database.html#handling-errors-and-troubleshooting"><i class="fa fa-check"></i><b>4.5</b> Handling Errors and Troubleshooting</a></li>
<li class="chapter" data-level="4.6" data-path="connecting-to-and-accessing-a-postgresql-database.html"><a href="connecting-to-and-accessing-a-postgresql-database.html#conclusion-3"><i class="fa fa-check"></i><b>4.6</b> Conclusion</a></li>
</ul></li>
<li class="chapter" data-level="5" data-path="descriptive-statistics-and-visualisations.html"><a href="descriptive-statistics-and-visualisations.html"><i class="fa fa-check"></i><b>5</b> Descriptive Statistics and Visualisations</a>
<ul>
<li class="chapter" data-level="5.1" data-path="descriptive-statistics-and-visualisations.html"><a href="descriptive-statistics-and-visualisations.html#introduction-to-descriptive-statistics"><i class="fa fa-check"></i><b>5.1</b> Introduction to Descriptive Statistics</a>
<ul>
<li class="chapter" data-level="5.1.1" data-path="descriptive-statistics-and-visualisations.html"><a href="descriptive-statistics-and-visualisations.html#understanding-descriptive-statistics"><i class="fa fa-check"></i><b>5.1.1</b> Understanding Descriptive Statistics</a></li>
<li class="chapter" data-level="5.1.2" data-path="descriptive-statistics-and-visualisations.html"><a href="descriptive-statistics-and-visualisations.html#basic-descriptive-statistics-in-r"><i class="fa fa-check"></i><b>5.1.2</b> Basic Descriptive Statistics in R</a></li>
</ul></li>
<li class="chapter" data-level="5.2" data-path="descriptive-statistics-and-visualisations.html"><a href="descriptive-statistics-and-visualisations.html#creating-visualisations-with-ggplot2"><i class="fa fa-check"></i><b>5.2</b> Creating Visualisations with ggplot2</a>
<ul>
<li class="chapter" data-level="5.2.1" data-path="descriptive-statistics-and-visualisations.html"><a href="descriptive-statistics-and-visualisations.html#introduction-to-ggplot2"><i class="fa fa-check"></i><b>5.2.1</b> Introduction to ggplot2</a></li>
<li class="chapter" data-level="5.2.2" data-path="descriptive-statistics-and-visualisations.html"><a href="descriptive-statistics-and-visualisations.html#creating-basic-plots"><i class="fa fa-check"></i><b>5.2.2</b> Creating Basic Plots</a></li>
<li class="chapter" data-level="5.2.3" data-path="descriptive-statistics-and-visualisations.html"><a href="descriptive-statistics-and-visualisations.html#customising-your-plots"><i class="fa fa-check"></i><b>5.2.3</b> Customising Your Plots</a></li>
</ul></li>
<li class="chapter" data-level="5.3" data-path="descriptive-statistics-and-visualisations.html"><a href="descriptive-statistics-and-visualisations.html#descriptive-statistics-with-dplyr"><i class="fa fa-check"></i><b>5.3</b> Descriptive Statistics with dplyr</a>
<ul>
<li class="chapter" data-level="5.3.1" data-path="descriptive-statistics-and-visualisations.html"><a href="descriptive-statistics-and-visualisations.html#using-dplyr-to-summarise-data"><i class="fa fa-check"></i><b>5.3.1</b> Using dplyr to Summarise Data</a></li>
<li class="chapter" data-level="5.3.2" data-path="descriptive-statistics-and-visualisations.html"><a href="descriptive-statistics-and-visualisations.html#combining-dplyr-with-ggplot2"><i class="fa fa-check"></i><b>5.3.2</b> Combining dplyr with ggplot2</a></li>
</ul></li>
<li class="chapter" data-level="5.4" data-path="descriptive-statistics-and-visualisations.html"><a href="descriptive-statistics-and-visualisations.html#advanced-visualisation-techniques"><i class="fa fa-check"></i><b>5.4</b> Advanced Visualisation Techniques</a>
<ul>
<li class="chapter" data-level="5.4.1" data-path="descriptive-statistics-and-visualisations.html"><a href="descriptive-statistics-and-visualisations.html#faceting"><i class="fa fa-check"></i><b>5.4.1</b> Faceting</a></li>
<li class="chapter" data-level="5.4.2" data-path="descriptive-statistics-and-visualisations.html"><a href="descriptive-statistics-and-visualisations.html#combining-multiple-geoms"><i class="fa fa-check"></i><b>5.4.2</b> Combining Multiple Geoms</a></li>
<li class="chapter" data-level="5.4.3" data-path="descriptive-statistics-and-visualisations.html"><a href="descriptive-statistics-and-visualisations.html#saving-your-plots"><i class="fa fa-check"></i><b>5.4.3</b> Saving Your Plots</a></li>
</ul></li>
<li class="chapter" data-level="5.5" data-path="descriptive-statistics-and-visualisations.html"><a href="descriptive-statistics-and-visualisations.html#conclusion-4"><i class="fa fa-check"></i><b>5.5</b> Conclusion</a></li>
</ul></li>
<li class="chapter" data-level="6" data-path="survey-analysis-in-r.html"><a href="survey-analysis-in-r.html"><i class="fa fa-check"></i><b>6</b> Survey Analysis in R</a>
<ul>
<li class="chapter" data-level="6.1" data-path="survey-analysis-in-r.html"><a href="survey-analysis-in-r.html#introduction-to-survey-data"><i class="fa fa-check"></i><b>6.1</b> Introduction to Survey Data</a>
<ul>
<li class="chapter" data-level="6.1.1" data-path="survey-analysis-in-r.html"><a href="survey-analysis-in-r.html#key-concepts-in-survey-analysis"><i class="fa fa-check"></i><b>6.1.1</b> Key Concepts in Survey Analysis</a></li>
<li class="chapter" data-level="6.1.2" data-path="survey-analysis-in-r.html"><a href="survey-analysis-in-r.html#required-packages"><i class="fa fa-check"></i><b>6.1.2</b> Required Packages</a></li>
</ul></li>
<li class="chapter" data-level="6.2" data-path="survey-analysis-in-r.html"><a href="survey-analysis-in-r.html#importing-and-preparing-survey-data"><i class="fa fa-check"></i><b>6.2</b> Importing and Preparing Survey Data</a>
<ul>
<li class="chapter" data-level="6.2.1" data-path="survey-analysis-in-r.html"><a href="survey-analysis-in-r.html#importing-spss-data"><i class="fa fa-check"></i><b>6.2.1</b> Importing SPSS Data</a></li>
<li class="chapter" data-level="6.2.2" data-path="survey-analysis-in-r.html"><a href="survey-analysis-in-r.html#converting-data-for-survey-analysis"><i class="fa fa-check"></i><b>6.2.2</b> Converting Data for Survey Analysis</a></li>
</ul></li>
<li class="chapter" data-level="6.3" data-path="survey-analysis-in-r.html"><a href="survey-analysis-in-r.html#descriptive-analysis-of-survey-data"><i class="fa fa-check"></i><b>6.3</b> Descriptive Analysis of Survey Data</a>
<ul>
<li class="chapter" data-level="6.3.1" data-path="survey-analysis-in-r.html"><a href="survey-analysis-in-r.html#calculating-weighted-means-and-totals"><i class="fa fa-check"></i><b>6.3.1</b> Calculating Weighted Means and Totals</a></li>
<li class="chapter" data-level="6.3.2" data-path="survey-analysis-in-r.html"><a href="survey-analysis-in-r.html#frequencies-and-cross-tabulations"><i class="fa fa-check"></i><b>6.3.2</b> Frequencies and Cross-tabulations</a></li>
</ul></li>
<li class="chapter" data-level="6.4" data-path="survey-analysis-in-r.html"><a href="survey-analysis-in-r.html#working-with-the-srvyr-package"><i class="fa fa-check"></i><b>6.4</b> Working with the srvyr Package</a>
<ul>
<li class="chapter" data-level="6.4.1" data-path="survey-analysis-in-r.html"><a href="survey-analysis-in-r.html#creating-a-survey-design-object-with-srvyr"><i class="fa fa-check"></i><b>6.4.1</b> Creating a Survey Design Object with srvyr</a></li>
<li class="chapter" data-level="6.4.2" data-path="survey-analysis-in-r.html"><a href="survey-analysis-in-r.html#using-srvyr-for-descriptive-statistics"><i class="fa fa-check"></i><b>6.4.2</b> Using srvyr for Descriptive Statistics</a></li>
</ul></li>
<li class="chapter" data-level="6.5" data-path="survey-analysis-in-r.html"><a href="survey-analysis-in-r.html#weighting-survey-data"><i class="fa fa-check"></i><b>6.5</b> Weighting Survey Data</a>
<ul>
<li class="chapter" data-level="6.5.1" data-path="survey-analysis-in-r.html"><a href="survey-analysis-in-r.html#applying-weights"><i class="fa fa-check"></i><b>6.5.1</b> Applying Weights</a></li>
<li class="chapter" data-level="6.5.2" data-path="survey-analysis-in-r.html"><a href="survey-analysis-in-r.html#analysing-weighted-data"><i class="fa fa-check"></i><b>6.5.2</b> Analysing Weighted Data</a></li>
</ul></li>
<li class="chapter" data-level="6.6" data-path="survey-analysis-in-r.html"><a href="survey-analysis-in-r.html#practical-example-survey-data-analysis-workflow"><i class="fa fa-check"></i><b>6.6</b> Practical Example: Survey Data Analysis Workflow</a>
<ul>
<li class="chapter" data-level="6.6.1" data-path="survey-analysis-in-r.html"><a href="survey-analysis-in-r.html#step-1-import-data"><i class="fa fa-check"></i><b>6.6.1</b> Step 1: Import Data</a></li>
<li class="chapter" data-level="6.6.2" data-path="survey-analysis-in-r.html"><a href="survey-analysis-in-r.html#step-2-define-survey-design"><i class="fa fa-check"></i><b>6.6.2</b> Step 2: Define Survey Design</a></li>
<li class="chapter" data-level="6.6.3" data-path="survey-analysis-in-r.html"><a href="survey-analysis-in-r.html#step-3-descriptive-analysis"><i class="fa fa-check"></i><b>6.6.3</b> Step 3: Descriptive Analysis</a></li>
<li class="chapter" data-level="6.6.4" data-path="survey-analysis-in-r.html"><a href="survey-analysis-in-r.html#step-4-advanced-analysis-regression"><i class="fa fa-check"></i><b>6.6.4</b> Step 4: Advanced Analysis (Regression)</a></li>
</ul></li>
<li class="chapter" data-level="6.7" data-path="survey-analysis-in-r.html"><a href="survey-analysis-in-r.html#conclusion-5"><i class="fa fa-check"></i><b>6.7</b> Conclusion</a></li>
</ul></li>
<li class="chapter" data-level="7" data-path="inferential-statistics.html"><a href="inferential-statistics.html"><i class="fa fa-check"></i><b>7</b> Inferential Statistics</a>
<ul>
<li class="chapter" data-level="7.1" data-path="inferential-statistics.html"><a href="inferential-statistics.html#hypothesis-testing"><i class="fa fa-check"></i><b>7.1</b> Hypothesis Testing</a>
<ul>
<li class="chapter" data-level="7.1.1" data-path="inferential-statistics.html"><a href="inferential-statistics.html#t-tests"><i class="fa fa-check"></i><b>7.1.1</b> T-tests</a></li>
<li class="chapter" data-level="7.1.2" data-path="inferential-statistics.html"><a href="inferential-statistics.html#chi-square-tests"><i class="fa fa-check"></i><b>7.1.2</b> Chi-square Tests</a></li>
<li class="chapter" data-level="7.1.3" data-path="inferential-statistics.html"><a href="inferential-statistics.html#anova-analysis-of-variance"><i class="fa fa-check"></i><b>7.1.3</b> ANOVA (Analysis of Variance)</a></li>
</ul></li>
<li class="chapter" data-level="7.2" data-path="inferential-statistics.html"><a href="inferential-statistics.html#correlation-analysis"><i class="fa fa-check"></i><b>7.2</b> Correlation Analysis</a>
<ul>
<li class="chapter" data-level="7.2.1" data-path="inferential-statistics.html"><a href="inferential-statistics.html#pearson-correlation"><i class="fa fa-check"></i><b>7.2.1</b> Pearson Correlation</a></li>
<li class="chapter" data-level="7.2.2" data-path="inferential-statistics.html"><a href="inferential-statistics.html#spearman-correlation"><i class="fa fa-check"></i><b>7.2.2</b> Spearman Correlation</a></li>
<li class="chapter" data-level="7.2.3" data-path="inferential-statistics.html"><a href="inferential-statistics.html#pearson-vs-spearman"><i class="fa fa-check"></i><b>7.2.3</b> Pearson vs Spearman?</a></li>
<li class="chapter" data-level="7.2.4" data-path="inferential-statistics.html"><a href="inferential-statistics.html#visualising-correlations"><i class="fa fa-check"></i><b>7.2.4</b> Visualising Correlations</a></li>
</ul></li>
<li class="chapter" data-level="7.3" data-path="inferential-statistics.html"><a href="inferential-statistics.html#conclusion-6"><i class="fa fa-check"></i><b>7.3</b> Conclusion</a></li>
</ul></li>
<li class="chapter" data-level="" data-path="references.html"><a href="references.html"><i class="fa fa-check"></i>References</a></li>
<li class="chapter" data-level="8" data-path="regression-analysis-1.html"><a href="regression-analysis-1.html"><i class="fa fa-check"></i><b>8</b> Regression Analysis</a>
<ul>
<li class="chapter" data-level="8.1" data-path="regression-analysis-1.html"><a href="regression-analysis-1.html#introduction-to-regression-analysis"><i class="fa fa-check"></i><b>8.1</b> Introduction to Regression Analysis</a>
<ul>
<li class="chapter" data-level="8.1.1" data-path="regression-analysis-1.html"><a href="regression-analysis-1.html#what-is-linear-regression"><i class="fa fa-check"></i><b>8.1.1</b> What is Linear Regression?</a></li>
</ul></li>
<li class="chapter" data-level="8.2" data-path="regression-analysis-1.html"><a href="regression-analysis-1.html#simple-linear-regression-in-r"><i class="fa fa-check"></i><b>8.2</b> Simple Linear Regression in R</a>
<ul>
<li class="chapter" data-level="8.2.1" data-path="regression-analysis-1.html"><a href="regression-analysis-1.html#performing-simple-linear-regression"><i class="fa fa-check"></i><b>8.2.1</b> Performing Simple Linear Regression</a></li>
<li class="chapter" data-level="8.2.2" data-path="regression-analysis-1.html"><a href="regression-analysis-1.html#interpreting-the-output"><i class="fa fa-check"></i><b>8.2.2</b> Interpreting the Output</a></li>
</ul></li>
<li class="chapter" data-level="8.3" data-path="regression-analysis-1.html"><a href="regression-analysis-1.html#multiple-linear-regression"><i class="fa fa-check"></i><b>8.3</b> Multiple Linear Regression</a>
<ul>
<li class="chapter" data-level="8.3.1" data-path="regression-analysis-1.html"><a href="regression-analysis-1.html#performing-multiple-linear-regression"><i class="fa fa-check"></i><b>8.3.1</b> Performing Multiple Linear Regression</a></li>
<li class="chapter" data-level="8.3.2" data-path="regression-analysis-1.html"><a href="regression-analysis-1.html#detailed-interpretation-of-the-output"><i class="fa fa-check"></i><b>8.3.2</b> Detailed Interpretation of the Output</a></li>
</ul></li>
<li class="chapter" data-level="8.4" data-path="regression-analysis-1.html"><a href="regression-analysis-1.html#checking-model-assumptions"><i class="fa fa-check"></i><b>8.4</b> Checking Model Assumptions</a>
<ul>
<li class="chapter" data-level="8.4.1" data-path="regression-analysis-1.html"><a href="regression-analysis-1.html#assumption-1-linearity"><i class="fa fa-check"></i><b>8.4.1</b> Assumption 1: Linearity</a></li>
<li class="chapter" data-level="8.4.2" data-path="regression-analysis-1.html"><a href="regression-analysis-1.html#assumption-2-normality-of-residuals"><i class="fa fa-check"></i><b>8.4.2</b> Assumption 2: Normality of Residuals</a></li>
<li class="chapter" data-level="8.4.3" data-path="regression-analysis-1.html"><a href="regression-analysis-1.html#assumption-3-homoscedasticity"><i class="fa fa-check"></i><b>8.4.3</b> Assumption 3: Homoscedasticity</a></li>
<li class="chapter" data-level="8.4.4" data-path="regression-analysis-1.html"><a href="regression-analysis-1.html#assumption-4-independence-of-errors"><i class="fa fa-check"></i><b>8.4.4</b> Assumption 4: Independence of Errors</a></li>
<li class="chapter" data-level="8.4.5" data-path="regression-analysis-1.html"><a href="regression-analysis-1.html#assumption-5-multicollinearity"><i class="fa fa-check"></i><b>8.4.5</b> Assumption 5: Multicollinearity</a></li>
</ul></li>
<li class="chapter" data-level="8.5" data-path="regression-analysis-1.html"><a href="regression-analysis-1.html#transformations-and-interaction-terms"><i class="fa fa-check"></i><b>8.5</b> Transformations and Interaction Terms</a>
<ul>
<li class="chapter" data-level="8.5.1" data-path="regression-analysis-1.html"><a href="regression-analysis-1.html#when-and-how-to-apply-transformations"><i class="fa fa-check"></i><b>8.5.1</b> When and How to Apply Transformations</a></li>
<li class="chapter" data-level="8.5.2" data-path="regression-analysis-1.html"><a href="regression-analysis-1.html#using-interaction-terms"><i class="fa fa-check"></i><b>8.5.2</b> Using Interaction Terms</a></li>
</ul></li>
<li class="chapter" data-level="8.6" data-path="regression-analysis-1.html"><a href="regression-analysis-1.html#logistic-regression"><i class="fa fa-check"></i><b>8.6</b> Logistic Regression</a>
<ul>
<li class="chapter" data-level="8.6.1" data-path="regression-analysis-1.html"><a href="regression-analysis-1.html#performing-logistic-regression-in-r"><i class="fa fa-check"></i><b>8.6.1</b> Performing Logistic Regression in R</a></li>
<li class="chapter" data-level="8.6.2" data-path="regression-analysis-1.html"><a href="regression-analysis-1.html#interpreting-logistic-regression-output"><i class="fa fa-check"></i><b>8.6.2</b> Interpreting Logistic Regression Output</a></li>
</ul></li>
<li class="chapter" data-level="8.7" data-path="regression-analysis-1.html"><a href="regression-analysis-1.html#checking-model-assumptions-for-logistic-regression"><i class="fa fa-check"></i><b>8.7</b> Checking Model Assumptions for Logistic Regression</a>
<ul>
<li class="chapter" data-level="8.7.1" data-path="regression-analysis-1.html"><a href="regression-analysis-1.html#assumption-1-linearity-of-the-logit"><i class="fa fa-check"></i><b>8.7.1</b> Assumption 1: Linearity of the Logit</a></li>
<li class="chapter" data-level="8.7.2" data-path="regression-analysis-1.html"><a href="regression-analysis-1.html#assumption-2-independence-of-observations"><i class="fa fa-check"></i><b>8.7.2</b> Assumption 2: Independence of Observations</a></li>
<li class="chapter" data-level="8.7.3" data-path="regression-analysis-1.html"><a href="regression-analysis-1.html#assumption-3-absence-of-multicollinearity"><i class="fa fa-check"></i><b>8.7.3</b> Assumption 3: Absence of Multicollinearity</a></li>
<li class="chapter" data-level="8.7.4" data-path="regression-analysis-1.html"><a href="regression-analysis-1.html#assumption-4-sufficient-sample-size"><i class="fa fa-check"></i><b>8.7.4</b> Assumption 4: Sufficient Sample Size</a></li>
</ul></li>
<li class="chapter" data-level="8.8" data-path="regression-analysis-1.html"><a href="regression-analysis-1.html#model-validation-and-diagnostics"><i class="fa fa-check"></i><b>8.8</b> Model Validation and Diagnostics</a>
<ul>
<li class="chapter" data-level="8.8.1" data-path="regression-analysis-1.html"><a href="regression-analysis-1.html#cross-validation"><i class="fa fa-check"></i><b>8.8.1</b> Cross-Validation</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="9" data-path="define-cross-validation-parameters.html"><a href="define-cross-validation-parameters.html"><i class="fa fa-check"></i><b>9</b> Define cross-validation parameters</a></li>
<li class="chapter" data-level="10" data-path="train-the-model-using-cross-validation.html"><a href="train-the-model-using-cross-validation.html"><i class="fa fa-check"></i><b>10</b> Train the model using cross-validation</a></li>
<li class="chapter" data-level="11" data-path="view-results.html"><a href="view-results.html"><i class="fa fa-check"></i><b>11</b> View results</a>
<ul>
<li class="chapter" data-level="11.0.1" data-path="view-results.html"><a href="view-results.html#dealing-with-overfitting"><i class="fa fa-check"></i><b>11.0.1</b> Dealing with Overfitting</a></li>
</ul></li>
<li class="chapter" data-level="12" data-path="prepare-data-for-glmnet.html"><a href="prepare-data-for-glmnet.html"><i class="fa fa-check"></i><b>12</b> Prepare data for glmnet</a></li>
<li class="chapter" data-level="13" data-path="fit-lasso-model.html"><a href="fit-lasso-model.html"><i class="fa fa-check"></i><b>13</b> Fit Lasso model</a></li>
<li class="chapter" data-level="14" data-path="view-best-lambda-value.html"><a href="view-best-lambda-value.html"><i class="fa fa-check"></i><b>14</b> View best lambda value</a>
<ul>
<li class="chapter" data-level="14.1" data-path="view-best-lambda-value.html"><a href="view-best-lambda-value.html#conclusion-7"><i class="fa fa-check"></i><b>14.1</b> Conclusion</a></li>
</ul></li>
<li class="chapter" data-level="15" data-path="geographic-mapping-and-spatial-analysis.html"><a href="geographic-mapping-and-spatial-analysis.html"><i class="fa fa-check"></i><b>15</b> Geographic Mapping and Spatial Analysis</a></li>
<li class="chapter" data-level="" data-path="exercise-answers.html"><a href="exercise-answers.html"><i class="fa fa-check"></i>Exercise Answers</a>
<ul>
<li class="chapter" data-level="" data-path="exercise-answers.html"><a href="exercise-answers.html#chapter-2"><i class="fa fa-check"></i>Chapter 2</a></li>
<li class="chapter" data-level="" data-path="exercise-answers.html"><a href="exercise-answers.html#chapter-3"><i class="fa fa-check"></i>Chapter 3</a></li>
<li class="chapter" data-level="" data-path="exercise-answers.html"><a href="exercise-answers.html#chapter-5"><i class="fa fa-check"></i>Chapter 5</a></li>
<li class="chapter" data-level="" data-path="exercise-answers.html"><a href="exercise-answers.html#chapter-6"><i class="fa fa-check"></i>Chapter 6</a></li>
<li class="chapter" data-level="" data-path="exercise-answers.html"><a href="exercise-answers.html#chapter-7"><i class="fa fa-check"></i>Chapter 7</a></li>
<li class="chapter" data-level="" data-path="exercise-answers.html"><a href="exercise-answers.html#chapter-8"><i class="fa fa-check"></i>Chapter 8</a></li>
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<h1><span class="header-section-number">Chapter 14</span> View best lambda value<a href="view-best-lambda-value.html#view-best-lambda-value" class="anchor-section" aria-label="Anchor link to header"></a></h1>
<p>print(lasso_model$lambda.min)
Regularization methods add a penalty to the coefficients, shrinking less important ones towards zero, which helps to prevent overfitting.</p>
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<h2><span class="header-section-number">14.1</span> Conclusion<a href="view-best-lambda-value.html#conclusion-7" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p>In this chapter, you have learned how to perform and interpret linear, multiple linear, and logistic regression in R, as well as how to validate your models and check their assumptions. Regression is a powerful tool, but its effectiveness depends on understanding and ensuring the assumptions are met.</p>
<p>Key Points:
Linear and Logistic Regression: Both types of regression help model relationships, with linear regression suited for continuous outcomes and logistic regression for binary outcomes.
Model Assumptions: Checking assumptions is crucial for ensuring your model’s validity.
Validation: Techniques like cross-validation help assess model performance and prevent overfitting.
Comparison with SPSS: R offers more flexibility and control over the modeling process, though the core principles remain consistent.
In the next chapter, we will explore another critical aspect of data analysis: Geographic Mapping and Spatial Analysis. You’ll learn how to work with geographic data, create maps, and perform spatial analysis in R, building on the skills you’ve developed in regression analysis.</p>

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