STAT 5374 -- Theory of Linear Statistical Models -- Spring 2026
Basic Information
Course instructor:
Dr. Alex
Trindade, 233 Mathematics & Statistics Building.
E-mail: alex.trindade"at"ttu.edu.
Course Meets: 12:30 - 1:50 TR in MATH 109.
Office Hours: TR 2:00-3:00, F 4:00-5:00, or by appointment.
Required Book
Linear Models in Statistics, by Rencher & Schaalje, 2nd edition, 2008, Wiley. ISBN-13: 978-0471754985.
Other Books
- Methodology
- Linear Model Methodology. Khuri, A. (2010). CRC Press.
- Plane Answers to Complex Questions: The Theory of Linear Models. Christensen, R. (1996). Second Edition. Springer.
- Linear Statistical Models. Stapleton, J.H. (2009). Second Edition. Wiley.
- Linear Models for Unbalanced Data. Searle, S.R. (1987). Wiley.
- Theory and Application of the Linear Model. Graybill, F.A. (1976). Duxbury Press.
- Linear Models. Searle, S.R. (1971). Wiley.
- Theory of matrices
- A Matrix Handbook for Statisticians, Seber, G.A.F. (2007). Wiley.
- Matrix Algebra From a Statistician's Perspective, Harville, D.A. (1997). Springer.
- Handbook of Matrices, Lutkepohl, H. (1996). Wiley.
- Matrices with Applications in Statistics. Graybill, F.A., 2nd ed., (1983). Wadsworth.
Course Objectives and Syllabus
Classical linear models are at the core of statistics, and are
the most commonly used set of statistical techniques in practice.
The two main subclasses of the classical linear model are
(1) linear regression models, and (2) analysis of variance (ANOVA) models.
A third subclass, (3) analysis of covariance models (ANCOVA) models,
combines elements of regression and ANOVA.
Because these models are such important practical tools for data analysis,
instruction in the practical aspects of their application is a crucial part of
a statistician's training. However, these methods are not a collection
of unrelated, specialized techniques. This course will cover the general theory of estimation and
inference in the linear model, which includes regression, ANOVA, and ANCOVA as special cases. This corresponds to chapters 1-9 and 12-14 of the book. Prerequisite
: STAT 5329 (Math-Stat). The list of topics is as follows:
- Concepts from linear algebra: matrices; vectors; matrix algebra; inner products; orthogonal projections; eigenvalues and eigenvectors; systems of equations; generalized inverses.
- Random vectors & matrices: quadratic forms; the multivariate normal and associated chi-square, t, and F distributions.
- The linear model (full rank case): regression; Gauss-Markov Theorem & best linear unbiased estimators (BLUEs); OLS & GLS; statistical inference.
- The linear model (non-full rank case): ANOVA models (one-way & two-way).
- The linear mixed model (time permitting).
This theory is worth studying because it unifies and yields insight into the
methods used in many important subcases of the linear model; and
because its ideas point the way and, in some cases, carry over directly to
more general (not-necessarily-linear) modeling of data.
In summary, this is a theory course, and as such it is not a complete course
in linear models. Very important practical aspects of these models will be
covered in other courses.
Expected Student Learning Outcomes
By the end of the course, students will be expected to become adept at solving problems that form part of the syllabus for the Applied Statistics Preliminary Examination. These include: linear algebra computations relating to vectors, matrices, projection operators, eigenvalues and eigenvectors, systems of equations, and generalized inverses. Calculations pertaining to random vectors & matrices, quadratic forms, and the multivariate normal and associated chi-square, t, and F distributions. The primary goal of the course is to cover the theory of statistical inference for the linear model in both the full rank and less than full rank cases (for the design matrix). Thus knowledge of the properties and theorems relating to inference for model coefficients under ordinary least squares, generalized least squares, and maximum likelihood estimation, will be at the heart of the expected learning outcomes.
Methods of Assessing the Expected Learning Outcomes
The expected learning outcomes for the course will be assessed through a mix of homework assignments (10%), two midterm tests (25% each), and a comprehensive final exam (40%). The traditional grading scale will be used:
- A: 90-100%.
- B: 80-89%.
- C: 70-79%.
- D: 60-69%.
- F: 0-59%.
The test schedule is as follows:
- Test 1: Thursday Feb 26.
- Test 2: Thursday Apr 9.
- Final Exam: Friday, May 8, 7:30 - 10:00 pm.
Homework Assignments
There will be weekly Assignment Sets. All work handed in must be stapled together. No late submissions will be accepted.
- Set 0 (due Friday Jan 16): Hwk 0.
Course Materials
Software
I will use R as the primary software tool. SAS is also recommended. Some assignments will require extensive use of a software package of your choice. For details on R see my statistical computing page, and especially the section on "Linear Models & GLMs".
Policies
- Required/Recommended Texas Tech Policies can be found on the
Canvas course page.
- Use of Generative AI Tools. The use of generative AI (GAI) for working assignments is not forbidden, but it should be used with discretion. I view GAI as another way to collaborate with peers on solving problems. This can used incorrectly, e.g. when you simply copy your smart friends work (or ask GAI to solve the problem directly), or can be used correctly, e.g., when you discuss with friends the results/steps needed to find a solution after you have put some thought into it (or use GAI more like a search engine to query side questions and digest literature). Remember: you do NOT want to surrender your thought process to the "tool" (friend or GAI); the "tool" will not be available during tests!
- Electronic Devices in Tests. In the spirit of keeping costs down, I will permit the usage of apps on smart devices (phones, tablets, laptops, etc.), but any kind of communication or accessing of the web via these devices is forbidden.
- Collaboration. My policies on this are as follows.
- Homeworks: Discussion with peers regarding material/concepts covered in the
course is permitted, and is encouraged since it usually leads to greater comprehension. However, each person must write up his/her own
solution to a particular problem, and not simply have someone else do it for them.
- Tests: Any form of collaboration on tests, including e-device communication or trying to see what the person next to you is writing, is strictly forbidden and will not be tolerated.
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