STAT 100C: Linear Models
Spring 2023
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
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Lectures: TR 9:30am-10:45am @ WGYOUNG 2200
- Instructor: Arash A. Amini
- Office Hours: No office hours.
- TA: Ian McGovern
- TA Office hours: TR 2PM @ Boelter 9406
- TA Discussion Section: M 4pm-4:50pm (DIS 2A) & M 5pm-5:50pm (DIS 2B) @ MS 5128
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Grader: Yasi Zhang
- Midterm: The midterm will be available on May 12 at 12:00 PM and should be completed no later than May 13 at 6:00 PM. Once you start the exam, you will have 180 minutes to finish it. The exam will be posted on Gradescope, and you will need to submit your completed exam on the platform.
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Final Exam: Monday, June 12, 2023, 11:30 AM - 2:30 PM.
- Announcements: Will be posted on Campuswire (Sign-up code: 9007)
- Homework Submission: Gradescope. (Sign-up code: BBWB8V)
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Attendance: iClicker. Sign-up by following this link.
- Grading: Attendance 5%, Homework 20%, Midterm 30%, Final 45%.
- 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 are in the Box folder.
- Lecture videos are posted in this Youtube playlist.
Past lectures are available here:
- Previously recorded lectures – Winter 2022
- Previously recorded lectures – Spring 2021. (Youtube playlist)
- Previously recorded lectures – Winter 2021 (Youtube playlist)
- Previously recorded lectures – Spring 2020 (Youtube playlist)
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.
Syllabus
| Lecture | Date | Topic |
|---|---|---|
| 1 | 04/04 | Review of linear algebra: linear independence; span; basis; |
| 2 | 04/06 | Review of linear algebra: image and column space; rank; inner product; orthogonal complement; projection |
| 3 | 04/11 | Review of linear algebra: spectral decomposition; PSD matrices; Expectation of random vectors |
| 4 | 04/13 | Covariance matrix |
| 5 | 04/18 | Multivariate normal distribution |
| 6 | 04/20 | Linear model; matrix-vector repr.; assumptions of the model; MLE of params. |
| 7 | 04/25 | MLE of params; geometric intepretation; variance estimation |
| 8 | 04/27 | Statistical properties of estimators; hat matrix; projection matrices |
| 9 | 05/02 | Inference I: Review of hypothesis testing (HT) and confidence intervals (CI) |
| 10 | 05/04 | Inference II: HT and CI for scalar parameters in linear models |
| 11 | 05/09 | Inference III: CI for regression function; prediction intervals |
| 12 | 05/11 | Inference IV: General linear hypothesis; geometrice intepretation |
| 13 | 05/16 | Inference V: Additional sum of squares and the F-test |
| 14 | 05/18 | Inference VI: Comparing models; ANOVA; R^2 and overfitting |
| 15 | 05/23 | Comparison of treatments (breif); qudratic forms and their distributions |
| 16 | 05/25 | Cochran's theorem; proof of F-test theorem; Gauss-Markov theorem |
| 17 | 05/30 | Generalized least-squares (GLS); Multicoliearity; variance inflation factor (VIF) |
| 18 | 06/01 | Diagnostics; Oultier detection: leverage and influence |
| 19 | 06/06 | Model selection |
| 20 | 06/08 | Modern approaches; advanced topics |
Miscellaneous
- For statistical computation, R is recommended.
p-value controversies: