LSE stock-price regression and variable selection (R)

A multiple-linear-regression study that builds an explanatory model for Vodafone's share price (VOD) using a basket of other LSE-listed stocks as predictors. The focus is on the variable-selection workflow: screening for multicollinearity, applying leaps/stepwise/forward/backward selection, Box-Cox response transforms, and residual diagnostics.

Despite the repo name, this is not a time-series forecasting project — it is an explanatory regression study. The original 2023 coursework used an LSE basket supplied with the assignment; that file is no longer available, so the analysis now runs on a clearly-labelled synthetic dataset with the same schema.

What's here

.
├── report/
│   └── stock-regression-analysis.Rmd   # main write-up (renders to PDF)
├── R/
│   └── stock-regression-analysis.R     # same analysis as a sourced script
├── data/
│   ├── generate_demo_data.R            # generate the synthetic lse dataset
│   └── README.md                       # synthetic-data notes + schema
└── output/
    ├── stock-regression-analysis.pdf   # rendered report
    └── figures/                        # key charts exported as PNG

Quick start

# R 4.x with: install.packages(c("car","leaps","MASS","corrplot","GGally","ggpubr","broom","tidyverse","rmarkdown"))
Rscript data/generate_demo_data.R                                    # one-off data generation
Rscript -e 'rmarkdown::render("report/stock-regression-analysis.Rmd")'
open output/stock-regression-analysis.pdf

What the analysis covers

1. Multicollinearity screening — correlation matrix, scatterplot inspection, pruning of redundant predictors (EXPN, SVT, SMT, Year).
2. Transformations — log transforms on SSE, LLOY, ABF to linearise their relationship with VOD.
3. Variable selection — leaps-and-bounds, stepwise (both), forward, and backward selection compared head-to-head.
4. Response transforms — Box-Cox identifies $\lambda \approx 2.6$–$2.8$ on VOD; the selection process is re-run on the transformed response.
5. Residual diagnostics — the standard lm plot panel, residual ACF, and PRESS statistic.

Headline figures

A key caveat

The residuals are strongly autocorrelated, which is the expected consequence of fitting OLS to price levels. The in-sample fit numbers look impressive (adj-$R^2 \approx 0.91$) but the standard errors are underestimated. A proper analysis would model returns (or log-returns) directly, or use an ARIMAX / dynamic regression. This project documents the workflow rather than claiming a real forecasting result.

Bug fixes vs. the original draft

#	Original	Fixed
1	Backward fit referenced data = lsenew4 inside the subset() call that defined lsenew4 (lazy-eval quirk)	Build the data frame first, then fit
2	for (i in x){ x <- c(...) } reassigned the loop variable inside its own body	Plain for (v in candidate_vars) loop
3	Hard-coded column indices lsenew[,-c(2,8,13,15)] left undocumented	Annotated in comments

Disclaimer

This is a learning exercise. Nothing here is investment advice.