36-401 Modern Regression

Personal study notes and worked derivations for Carnegie Mellon's 36-401 Modern Regression course (Fall 2025), written and knitted in R Markdown.

Overview

This repository follows the CMU 36-401 Modern Regression syllabus and works through the theory of linear regression from first principles. Each chapter pairs the mathematics (estimation, inference, prediction) with R code that fits and checks the models on real data sets, so the notes double as both a derivation reference and a runnable worked example.

The aim is to genuinely understand how linear models are learned and interpreted rather than just to apply them: where the estimators come from, why the assumptions matter, and how to read the output.

Topics covered

• Review of random variables, expectation, variance and covariance as the groundwork for regression.
• The simple linear regression model and the least squares estimators of the slope and intercept.
• Properties and inference for the estimated coefficients (the $\beta$), including estimating the error variance.
• Prediction and prediction intervals in simple linear regression.
• A short companion note on partial derivatives and "partial integrals" to support the derivations.

What's inside

Path	What it holds
notebook/	The source R Markdown notes, one .Rmd per chapter plus the partial-derivatives explainer.
Chapter-1---Review-of-Random_files/ … Chapter-4---Prediction_files/	Knitted GitHub-flavoured Markdown output of each chapter, with rendered figures under figure-gfm/. Browse these to read the notes directly on GitHub.
formula.Rmd	A complete formula reference for the simple linear regression model: assumptions, estimators and key results in one place.
handout/	Course handouts, homework briefs and the syllabus (third party course material, see note below).

Highlights

• Notes are written to be read on GitHub: each chapter's knitted README.md renders the maths and the figures inline.
• Every result is tied back to its derivation, so the estimators and intervals are explained, not just stated.
• R code is embedded throughout, so the same files serve as a reproducible analysis when re-knitted.

Getting started

These are R Markdown documents. To re-render a chapter from source:

# from R, in the repository root
install.packages("rmarkdown")   # if not already installed
rmarkdown::render("notebook/Chapter 1 - Review of Random.Rmd")

Or open any .Rmd in RStudio and click Knit. The knitted Markdown and figures are also committed under the *_files/ folders, so you can read everything without running R.

A note on course material

The PDFs under handout/ (syllabus, lecture handouts and homework briefs) are official 36-401 course material and remain the copyright of Carnegie Mellon University and the course staff. They are kept here only as a personal study reference and are not for redistribution. The notes themselves are my own working through of the material.