Foundations of Multiple Regression and Analysis of Variance

This book provides a rigorous development of the foundations of linear models for multiple regression and Analysis of Variance (ANOVA), based on orthogonal projections and relations among linear subspaces. It is appropriate for the linear models course required in most statistics Ph.D. programs.

Autorentext

Lynn Roy LaMotte is Professor Emeritus in the Biostatistics Program, School of Public Health, LSU Health-New Orleans. Elected Fellow of the American Statistical Association, 1985, for "important, innovative, seminal, and diverse contributions to the theory and application of linear statistical models," he is author of about 100 articles in diverse academic journals, cited more than 2,000 times, nearly 500 since 2020.

Inhalt

1 Introduction 2 MLR & ANOVA Illustrations I Basics 3 Matrices and Vectors 4 Linear Subspaces 5 Orthogonal Projection 6 The Gram-Schmidt Construction 7 Further Results as Exercises II Inference 8 LMs, LS, and the GM Theorem 9 Estimability 10 Inference on the Mean 11 Restricted Linear Models 12 Special Hypotheses 13 On Methods of Model-Building III ANOVA Models: Linear Models for Effects of Categorical Factors 14 Introduction 15 ANOVA Effects 16 Models with ANOVA Effects 17 Type III 18 ANOVA Exercises and Projects 19 Yates's MWSM 20 Proportional Subclass Numbers 21 ANOVA Comments Appendices Appendix A Proofs and Solutions to Selected Exercises Appendix B Sampling Distributions Bibliography Index