Linear Statistical Models

An introduction to the theory and application of linear statistical models, covering least squares estimation, hypothesis testing, and ANOVA/ANCOVA using R.

This course provided a rigorous introduction to the theory and application of linear statistical models, a cornerstone of modern data analysis. After a review of statistical inference and the R programming language, we delved into the core of linear models. I learned the principles of least squares estimation, the properties of Best Linear Unbiased Estimates (BLUEs), and the significance of the Gauss-Markov Theorem. The course balanced this strong theoretical foundation with practical applications, teaching me how to perform hypothesis testing and build one-way and two-way classification models, including ANOVA and ANCOVA, using R.

Instructor

Prof. Siva Athreya, International Centre for Theoretical Sciences- TIFR and Indian Statistical Institute, Bangalore Centre

Course Schedule & Topics

The course is structured over 12 weeks, blending theory, application, and practical implementation in R.

Week Primary Focus Key Topics Covered
1 Review of Statistical Inference Foundational concepts of estimation and hypothesis testing.
2 R Programming Review A refresher on working with the R statistical package for data analysis.
3 Least Squares Estimation Introduction to least squares estimation and estimable linear functions.
4 Normal Equations Deriving and solving the normal equations for linear models.
5 Properties of Estimators Understanding Best Linear Unbiased Estimates (BLUEs).
6 Gauss-Markov Theorem In-depth study of the Gauss-Markov Theorem and its implications.
7 Fundamental Theorems Degrees of freedom and the Fundamental Theorems of Least Squares.
8 Hypothesis Testing in Models Framework and application of testing linear hypotheses.
9 Classification Models Building and interpreting one-way and two-way classification models.
10 Analysis of Variance Performing Analysis of Variance (ANOVA) and Analysis of Covariance (ANCOVA).
11 Q&A and Clarifications A dedicated session for questions, answers, and clarifying complex topics.
12 Introduction to Random Effects An introduction to random effect and mixed-effect models.

Material used