STAT 8260 Spring 2026
Theory of Linear Models
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eLearning Commons #
UGA’s eLearning Commons (eLC) is the university’s learning management system. All class communications, announcements, homework assignments, and other materials will be posted exclusively on eLC. Students are responsible to check eLC regularly for updates on course requirements and deadlines. This website is intended only as a supplementary resource.
Lecture time and location #
- Wednesday and Friday 1:15 PM - 2:35 PM
- Brooks Hall, Room 520
Teaching team and office hours #
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Instructor: Xiaotian Zheng
Office Hour: Friday 3:00 – 4:00 PM (or by appointment) at Brooks Hall 452
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Teaching Assistant: Fei Wen
Office Hours: Wednesday 4:00 - 5:00 PM at Brooks Hall 515
Lecture schedule #
PACQ = Plane Answers to Complex Questions (4th ed.)
[link]
LRA = Linear Regression Analysis (2nd ed.)
[link]
| Week | Date | Topic | Optional readings | |
|---|---|---|---|---|
| Lecture 1 | Week 1 | Jan. 14 | The ordinary least squares (OLS) formula | - |
| Lecture 2 | Week 1 | Jan. 16 | Vector space, rank, column space, and null space | PACQ App. A, B |
| Lecture 3 | Week 2 | Jan. 21 | The geometry of OLS and orthogonal projection | - |
| Lecture 4 | Week 2 | Jan. 23 | The geometry of OLS and orthogonal projection | - |
| Lecture 5 | Week 3 | Jan. 28 | Consistency of the Normal Equations and generalized inverse | - |
| Lecture 6 | Week 3 | Jan. 30 | Gram-Schmidt orthogonalization, QR decomposition, and computation of OLS | LRA Ch. 11.2, 11.3, 11.9 |
| Lecture 7 | Week 4 | Feb. 4 | Gauss-Markov models and Gauss-Markov Theorem | - |
| Lecture 8 | Week 4 | Feb. 6 | Gaussian linear models I (multivariate Gaussian distributions and maximum likelihood estimation) | PACQ Ch. 1.2, 2.4 |
| Lecture 9 | Week 5 | Feb. 11 | Gaussian linear models II (complete sufficient statistics, best unbiased estimators, and sampling distributions of estimators) | PACQ Ch. 2.5, 2.6 |
| Lecture 10 | Week 5 | Feb. 13 | Bayesian estimation | |
| Lecture 11 | Week 6 | Feb. 18 | Bayesian estimation | LRA Ch. 3.12 |
| Lecture 12 | Week 6 | Feb. 20 | Finite sample inference (chi-squared and related distributions) | |
| Lecture 13 | Week 7 | Feb. 25 | Finite sample inference (distribution of quadratic forms) | PACQ Ch. 1.3 |
| Lecture 14 | Week 7 | Feb. 27 | Finite sample inference (testing the general linear hypothesis) | LRA Ch. 4.3 |
| Lecture 15 | Week 8 | Mar. 4 | Finite sample inference (likelihood ratio test) | LRA Ch. 4.2 |
| Lecture 16 | Week 8 | Mar. 6 | Finite sample inference (testing for a general subset, the geometric interpretation, and Cochran’s Theorem) | |
| Lecture 17 | Week 9 | Mar. 18 | Finite sample inference (Bayesian testing and Bayes factor); review | |
| - | Week 9 | Mar. 20 | Exam 1 (Lectures 1 - 11) | |
| Lecture 18 | Week 10 | Mar. 25 | Review of testing | - |
| Lecture 19 | Week 10 | Mar. 27 | Finite sample inference (confidence intervals and regions; prediction intervals) | LRA Ch. 5.1.3, 5.1.4, 5.2.1, 5.3.1 |
| Lecture 20 | Week 11 | Apr. 1 | Identifiability and estimability I (observational equivalence, identifiable functions) | PACQ Ch. 2.1 |
| Lecture 21 | Week 11 | Apr. 3 | Identifiability and estimability I (estimable functions) | PACQ Ch. 2.1, LRA Ch. 3.9 |
| Lecture 22 | Week 12 | Apr. 8 | Identifiability and estimability II (reparameterization) | - |
| Lecture 23 | Week 12 | Apr. 10 | Identifiability and estimability II (imposing constraints for unique solutions; a summary of inference under rank-deficient models) | - |
| Lecture 24 | Week 13 | Apr. 15 | Generalized least squares; review | - |
| - | Week 13 | Apr. 17 | Exam 2 (Lectures 12 - 22) | - |
| Lecture 25 | Week 14 | Apr. 22 | Linear mixed models | - |
| Lecture 26 | Week 14 | Apr. 24 | Linear mixed models | - |
Acknowledgements #
Course materials are based on Christensen (2011), Ding (2025), Gelman et al. (2013), Monahan (2008), Rencher and Schaalje (2008), Seber and Lee (2003), and Zimmerman (2020).
References #
Christensen, R. (2011). Plane Answers to Complex Questions: The Theory of Linear Models (4th ed.). New York, NY: Springer.
Ding, P. (2025). Linear Model and Extensions. Chapman & Hall.
Gelman, A., Stern, H. S., Carlin, J. B., Dunson, D. B., Vehtari, A., and Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed). New York, NY: Chapman and Hall/CRC.
Monahan, J. F. (2008). A Primer on Linear Models. Boca Raton, FL: Chapman & Hall/CRC
Rencher, A. C. and Schaalje, G. B. (2008). Linear Models in Statistics. Hoboken, NJ: John Wiley & Sons.
Seber, G. A., and Lee, A. J. (2003). Linear Regression Analysis. Hoboken, NJ: John Wiley & Sons.
Zimmerman, D. L. (2020). Linear Model Theory with Examples and Exercises. Cham, Switzerland: Springer.