ABSTRACT

This innovative, intermediate-level statistics text presents the theory of linear statistical models at a level appropriate for senior undergraduate or first-year graduate students. It systematically presents the basic theory behind linear statistical models with motivation from an algebraic as well as a geometric perspective. Through the concepts and tools of matrix and linear algebra and distribution theory, it provides a framework for understanding classical and contemporary linear model theory. It does not, however, merely introduce formulas, but develops in students the art of statistical thinking and inspires learning at an intuitive level by emphasizing conceptual understanding.

chapter Chapter 1|31 pages

A Review of Vector and Matrix Algebra

chapter Chapter 2|40 pages

Properties of Special Matrices

chapter Chapter 3|18 pages

Generalized Inverses and Solutions to Linear Systems

chapter Chapter 4|46 pages

The General Linear Model

chapter Chapter 5|58 pages

Multivariate Normal and Related Distributions

chapter Chapter 6|19 pages

Sampling from the Multivariate Normal Distribution

chapter Chapter 7|66 pages

Inference for the General Linear Model

chapter Chapter 8|75 pages

Multiple Regression Models

chapter Chapter 9|27 pages

Fixed Effects Linear Models

chapter Chapter 10|21 pages

Random-Effects and Mixed-Effects Models

chapter Chapter 11|26 pages

Special Topics

chapter |7 pages

A Review of Probability Distributions

chapter |8 pages

Solutions to Selected Exercises