STAT8561 - Linear Statistical Analysis I

2026 Fall Lecture Notes

Author

Chi-Kuang Yeh

Published

November 1, 2026

Preface

The topic of this course includes statistical inference, Multivariate normal distribution, distribution of quadratic forms, linear models, regression models and experimental design models.

The course moves from Gaussian linear-model theory to regression, experimental comparisons, and model checking. Chapter 6 distinguishes outliers, leverage, and influence. Chapter 7 develops transformations and variable selection, including ridge and lasso. Later units develop experimental design, broader model checks, prediction assessment, and logistic regression. Poisson regression and fuller GLM theory remain supplementary reading. Advanced extensions are collected under Optional topic.

Prerequisites

Math 4751/6751 Mathematical Statistics I and Math 4752/6752 Mathematics and Statistics II.

Instructor

Chi-Kuang Yeh, Assistant Professor in the Department of Mathematics and Statistics, Georgia State University.

Office Hours

Wednesdays, 9:00 a.m. to 12:00 p.m., or by appointment.

Grade Distribution

  • Homework – 40%
  • Exam 1 – 20%
  • Exam 2 – 20%
  • Final Project – 20%
  • Attendance – *7%

Assignment

Exam

Project

Final assessment decision: The final assessment will be a Final Project, selected by a class vote of 20 to 5.

See Instruction for the project description, requirements, and grading criteria.

Topics and Corresponding Lectures

Those chapters are based on the lecture notes. This part will be updated frequently.

Progress after Lecture 21: Chapter 5 is complete. Chapter 6 has reached Section 6.3: Outliers.

Status Chapter Topic Lecture
✅ Welcome and Overview 1
✅ Ch. 1 Math Notation 2–3
✅ Ch. 2 Least Squares Estimation 3–6
✅ Ch. 3 Inference on Least Square Estimation 7–10
✅ Ch. 4 Model Comparison, Partial F Tests, and ANOVA 11–17
✅ Exam 1 15
✅ Ch. 5 Multiple Regression and Categorical Predictors 18–21
⏳ Ch. 6 Outliers, Leverage, and Influence 21–
⏳ Ch. 7 Transformations and Variable Selection TBA
📝 Exam 2 23

Optional topic

Students interested in extensions can read Quantile Regression, Mixed-Effects Models, and Contrasts and Estimable Comparisons. These readings include explanations, graphical examples, R code, and further reading; they are supplementary to the scheduled chapters.

Side Readings

  • Montgomery, Douglas C. (2017). Design and Analysis of Experiments. John Wiley & Sons. (Montgomery 2017)