STAT8561 - Linear Statistical Analysis I

2026 Fall Lecture Notes

Author

Chi-Kuang Yeh

Published

September 29, 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. A short final unit extends the same design-matrix framework to logistic and Poisson regression. 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

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.

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–
📝 Exam 1 15
⏳ Ch. 5 Multiple Regression and Categorical Predictors TBA
📝 Exam 2 25

Optional topic

Students interested in extensions can read Quantile Regression and Mixed-Effects Models. 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)