Regression Analysis

This is my solution to Homework 3 (Tarea 3) of my regression analysis course. It has three problems, and each one lives in its own folder with the data, the Quarto notebook, the final PDF report and a plain R script.

All the code is written in R. The reports were built with Quarto inside Positron.

What's inside

12 - Regression Analysis/
├── 01 - First Regression Analysis/    Multiple linear regression
├── 02 - Second Regression Analysis/   Logistic regression
├── 03 - Third Regression Analysis/    Poisson regression
├── LICENSE
└── README.md

Every folder has the same files:

File	What it is
notebook.qmd	The Quarto notebook with the code, the results and my comments
notebook.pdf	The report I hand in
notebook.html	The same report as a web page
regression_analysis_N.R	Only the code, so it can be run without Quarto
data/	The Excel file used in that problem (folders 02 and 03)

1. Prostate cancer (multiple linear regression)

Uses the prostate dataset from the genridge package to predict the level of prostate specific antigen (lpsa) from eight clinical variables.

What I did:

• Described every variable with summary statistics, histograms and Shapiro-Wilk tests.
• Made a correlation plot of all the variables.
• Split the data into 70% for training and 30% for testing, with set.seed(123).
• Fitted a full linear model and checked multicollinearity with the VIF.
• Selected variables with forward, backward and stepwise selection, plus Lasso, Ridge and Elastic Net.
• Compared all the models on the test set with RMSE and MAE.
• Took the best method (backward selection) and checked its ANOVA table, its F statistic, and the normality, homoscedasticity and independence of its residuals.

2. Seed germination (logistic regression)

Uses germ.xlsx, where 831 seeds of two types (OA73 and OA75) were planted on two rootstocks (bean and cucumber). The question is whether the rootstock and the seed type decide if a plant germinates.

I compared a model with only the main effects against one with an interaction. The interaction turned out to be significant, so I interpreted that model using odds ratios. The best combination was cucumber with OA75, with about a 68% chance of germinating.

3. Cervical cancer deaths (Poisson regression)

Uses cervical.xlsx, with the number of deaths from cervical cancer between 1969 and 1973 in four countries (Belgium, England and Wales, France and Italy), split into four age groups.

I fitted a Poisson model with age and country as explanatory variables and read the coefficients as rate ratios. Deaths go up sharply with age in every country. The model showed overdispersion, so I also fitted a quasi-Poisson model to make sure the conclusions still held, and they did. One thing to keep in mind: the data doesn't include the population of each country, so the differences between countries mostly reflect how big each country is, not how risky it is.

How to run it

You'll need R (I used version 4.6.1). Positron or RStudio make it easier, but they're optional.

Just the R scripts. Open the folder of the problem you want, set it as your working directory and run the script:

setwd("path/to/02 - Second Regression Analysis")
source("regression_analysis_2.R", echo = TRUE)

Each script installs any package it's missing the first time you run it, so you don't need to install anything by hand.

The full reports. Open notebook.qmd in Positron and press Preview, or run this from a terminal inside the folder:

quarto render notebook.qmd

This rebuilds both the HTML and the PDF. Positron already comes with Quarto, so there's nothing else to set up.

Packages used

tidyverse, readxl, knitr, genridge, skimr, psych, corrplot, car, lmtest, glmnet, MASS, performance, see and gt.

License

This project is under the MIT License. See LICENSE for the details.