A Primer on Linear Models

Employing non-full-rank design matrices throughout, this text provides a concise yet solid foundation for understanding basic linear models. It introduces the basic algebra and geometry of the linear least squares problem, before delving into estimability and the Gauss-Markov model. After presenting the statistical tools of hypothesis tests and confidence intervals, the author analyzes mixed models, such as two-way mixed ANOVA, and the multivariate linear model. The text presents proofs and discussions from both algebraic and geometric viewpoints and includes exercises of varying levels of difficulty at the end of each chapter.

With coverage steadily progressing in complexity, the text first provides examples of the general linear model, including multiple regression models, one-way ANOVA, mixed-effects models, and time series models. It then introduces the basic algebra and geometry of the linear least squares problem, before delving into estimability and the Gauss-Markov model. After presenting the statistical tools of hypothesis tests and confidence intervals, the author analyzes mixed models, such as two-way mixed ANOVA, and the multivariate linear model. The appendices review linear algebra fundamentals and results as well as Lagrange multipliers.

This book enables complete comprehension of the material by taking a general, unifying approach to the theory, fundamentals, and exact results of linear models.