Synopses & Reviews
A Primer on Linear Models presents a concise yet complete foundation for understanding basic linear models. Designed for a one-semester graduate course, this textbook begins with a practical discussion of basic algebraic and geometric concepts as they apply to the linear model. The book??'s two distinguishing features are the constant use of non-full-rank design matrices to seamlessly incorporate regression, analysis of variance (ANOVA), and various mixed models and attention to the exact, finite sample theory supporting common statistical methods.
A Primer on Linear Models provides a brief, yet complete foundation for the understanding of basic linear models. It focuses on the theory behind the methodology students learn in other courses. As a result, the style follows the route of theorem/proof/corollary/example/exercise with discussions of the motivations for the assumptions from theory and practice. The coverage progresses steadily in both difficulty and sophistication of the proofs, discussion, and exercises, paralleling the growth of students as they master the subject.
Avoiding leaps in the development and proofs, or referring to other sources for the details of the proofs, the author demonstrates the complete development of the material. This gives students learning the material for the first time enough information to understand complex concepts with confidence. Pedagocial Features
?? Proofs and discussion from both algebraic and geometric viewpoints
?? Exercises at the end of each chapter escalate in degrees of difficulty
?? Multipart exercises taken from past quizzes and final exams
?? 196 equations
?? Summaries, discussions, notes, and exercises at theend of each chapter
Synopsis
Since the linear model forms the groundwork for most applied statistics, a course on the theory of the linear model is often required in most graduate statistics programs. A Primer on Linear Models presents a concise yet complete foundation for understanding basic linear models. Designed for a one-semester graduate course, this textbook begins with a practical discussion of basic algebra and geometry concepts as they apply to the linear model. The book then proceeds to an in-depth treatment of more advanced topics such as the Gauss-Markov model. The text also includes exercises of various levels of difficulty and features the constant use of non full-rank design matrices.
Synopsis
A Primer on Linear Models presents a unified, thorough, and rigorous development of the theory behind the statistical methodology of regression and analysis of variance (ANOVA). It seamlessly incorporates these concepts using non-full-rank design matrices and emphasizes the exact, finite sample theory supporting common statistical methods.
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.