STATS 100C - Linear Models
Spring 2026
Theory of linear models, with emphasis on matrix approach to linear regression and connections to multivariate normal distribution. Topics include simple and multiple linear regression, model fitting, inference about parameters, testing general linear hypotheses, specification issues, model checking, and model selection.
General info
- Lectures:
- LEC 3: TR 11am-12:15pm @ MS 5200
- LEC 4: TR 5pm-6:15pm @ MS 4000A
- Instructor: Arash A. Amini
- Office Hours: Tuesday 6:30pm-7:30pm.
- TAs: Keshav Singh and Yidong Ouyang.
- Midterm: Thursday, April 23, 2026, in class (each lecture during its own class time).
- Final Exam:
- LEC 3: Wednesday, June 10, 2026, 11:30 AM - 2:30 PM
- LEC 4: Wednesday, June 10, 2026, 3:00 PM - 6:00 PM
- Announcements: Campuswire (Use code 2738).
- Homework Submission: Gradescope (Lecture 3 code: KNJ8EG; Lecture 4 code: G6X7YJ).
- Attendance: iClicker (Lecture 3; Lecture 4).
- Grading: Attendance 5%, Homework 20%, Midterm 25%, Final 50%.
- Prerequisites: STATS 100B and linear algebra such as Math 33A.
Please read!
- Please do not email me your late homework. Instead, post a note on Campuswire (it can have attachments) and set the visibility to TAs and Instructors only. We will address the issue there. Only requests through Campuswire are considered.
Resources
- Homework, slides, and notes will be posted in the course Box folder.
- Lecture videos: Spring 2026 YouTube playlist.
Past lectures are available here:
- Previously recorded lectures – Spring 2023
- Previously recorded lectures – Winter 2022
- Previously recorded lectures – Spring 2021
- Previously recorded lectures – Winter 2021
- Previously recorded lectures – Spring 2020
Textbook
- B. Abraham and J. Ledolter, Introduction to Regression Modeling, 2006. ISBN: 978-0534420758
- Corrections, courtesy of Prof. Ledolter.
Data
Supplementary texts
- J. J. Faraway, Practical Regression and Anova using R: Introduction to doing regression in R.
- G. Strang, The Four Fundamental Subspaces: 4 Lines: Short overview of linear algebra.
Tentative syllabus
| Lec | Date | Topic |
|---|---|---|
| 1 | Mar 31 | Lin alg: independence, span, basis, dimension |
| 2 | Apr 2 | Lin alg: image, column space, rank, kernel, inner product, orthogonal complement |
| 3 | Apr 7 | Lin alg: projection, spectral decomposition, PSD |
| 4 | Apr 9 | Random vectors: expectation, $E(Ay) = AE(y)$, $E(BAC)$ |
| 5 | Apr 14 | Covariance matrix, properties, decorrelation |
| 6 | Apr 16 | Multivariate normal distribution |
| 7 | Apr 21 | Linear model, assumptions, MLE/OLS, geometric interpretation |
| MT | Apr 23 | Midterm (L1-L7), in class for each lecture during its own class time |
| 8 | Apr 28 | Geometric interpretation contd., variance estimation, hat matrix |
| 9 | Apr 30 | Properties of estimators ($\hat\beta$, $e$, $s^2$), sampling distributions |
| 10 | May 5 | Inference: CI and HT for $\beta_i$ (weave in pivot/t-distribution review) |
| 11 | May 7 | CI for regression function, prediction intervals |
| 12 | May 12 | General linear hypothesis, geometric interpretation |
| 13 | May 14 | F-test, additional sum of squares |
| 14 | May 19 | ANOVA, $R^2$, comparing models |
| 15 | May 21 | Quadratic forms, Cochran’s theorem (streamlined), proof of F-test |
| 16 | May 26 | Gauss-Markov; GLS/WLS |
| 17 | May 28 | Multicollinearity, VIF; diagnostics |
| 18 | Jun 2 | Leverage, influence, Cook’s D, residual analysis |
| 19 | Jun 4 | Model selection (AIC, Cp, PRESS) + brief modern topics (ridge, bias-variance) |
| Jun 10 | Final exam: LEC 3, 11:30 AM - 2:30 PM; LEC 4, 3:00 PM - 6:00 PM |
Miscellaneous
- For statistical computation, R is recommended.
p-value controversies: