STAT 5374 -- Theory of Linear Statistical Models -- Fall 2017

Basic Information

Course instructor: Dr. Alex Trindade, 228 Mathematics & Statistics Building.
E-mail: alex.trindade"at"
Course Meets: 11:00 - 12:20 TR in MATH 115.
Office Hours (in 201): Tue/Thurs 9:00-11:00, 13:00-15:00, or by appointment.

Required Book

  • Linear Models in Statistics, by Rencher & Schaalje, 2nd edition, 2008, Wiley. ISBN-13: 978-0471754985.

    Other Books

    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: 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: The test schedule is as follows:

    Homework Assignments

    There will be weekly Assignment Sets. All work handed in must be stapled together. No late submissions will be accepted.



    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".


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