Lectures

Stat 151A: Linear Models

Lectures marked with a \(*\) are still in progress.

These lecture notes are meant to supplement the reading indicated in the course schedule.

Course overview

These notes summarize the key topics in each unit.

Introduction

• Course philosophy
• Sample means
• Linear algebra review

Unit 1: Multlinear regression

• Simple linear regression
• Multilinear regression
• Paths to least squares
• Transforming the regressors
  • One-hot encodings
  • Interacting continuous regressors
  • Supplement: Linear transformations
• Transforming the response variable

Unit 2: Inference for linear regression

• Confidence intervals (review)
• Modeling of OLS
• OLS under normality
  • Supplement: The multivariate normal
  • Supplement: The distribution of the residual variance estimator
  • Variable selection and F-tests
• OLS under non-normality
  • Supplement: Asymptotics under misspecification
• Statistical versus practical significance

Unit 3: Machine learning and regularization

• OLS for prediction with expressive basis functions
• Bayesian methods and L2 regularization

Unit 4: How regression can go wrong

• The FWL theorem
• Regression to the mean
• Omitted variables
• Influence and outliers