Applied Linear Models

Term

Fall 2026

Updated

September 14, 2026

Linear models permeate statistics. They provide a foundation for applications ranging from modeling observational data to inference in designed experiments to spatial statistics and time series analysis to predictive modeling and more. This course is an introduction to linear models covering standard topics in model specification, estimation, inference, diagnostics, transformations, and several important extensions.

Instructor: Trevor Ruiz (he/him) [email]

Class meetings: TR 12:00pm–1:50pm in 180-272

Office hours: TR 2:30pm–4:00pm in 25-236

Final project due: Thursday 12/17/26 3:30pm

A tentative schedule for the term and detailed course policies can be found in the [course syllabus]. Please note the syllabus is subject to change. Readings, assignments, and materials (notes, scripts, etc.) will be posted below on a rolling basis.

Week 1 (8/24)

Regression and linear algebra review; random variables and random vectors

  • Handout 1 [pdf]
  • Homework 1 [pdf], due Thursday 9/3
  • Homework 1 solutions [pdf]
  • Week 1 slides [html]
  • Scripts:
    • Getting started in R [script]

Week 2 (8/31)

Least squares estimates and their properties

  • Handout 2 [pdf]
  • Homework 2 [pdf], due Thursday 9/10
  • Week 2 slides [html]
  • Scripts:
    • Simulating sampling variability [script]
    • Centering the predictor [script]
    • The shape of the sampling distribution [script]

Week 3 (9/7)

Inference in regression and model diagnostics

  • Handout 3 [pdf]
  • Homework 3 [pdf], due Thursday 9/17
  • Week 3 slides [html]
  • Scripts:
    • Inference and diagnostics [script]

Week 4

Transformations; unusual observations

  • Handout 4 [pdf]
  • Scripts:
    • Troubleshooting on simulated data [script]