Linear Models in Statistics, 2nd Edition

by Alvin C. Rencher (Brigham Young Univ., Provo, Utah); G. Bruce Schaalje (Brigham Young Univ., Provo, UT)

• ISBN13: 9780470192603
• ISBN10: 0470192607
• Format: eBook
• Copyright: 2008-01-01
• Publisher: Wiley-Interscience

Summary

Linear Models in Statistics, Second Edition includes full coverage of advanced topics, such as mixed and generalized linear models, Bayesian linear models, two-way models with empty cells, geometry of least squares, vector-matrix calculus, simultaneous inference, and logistic and nonlinear regression. Algebraic, geometrical, frequentist, and Bayesian approaches to both the inference of linear models and the analysis of variance are also illustrated. Through the expansion of relevant material and the inclusion of the latest technological developments in the field, this book provides readers with the theoretical foundation to correctly interpret computer software output as well as effectively use, customize, and understand linear models. The linear model remains the main tool of the applied statistician and is central to the training of any statistician regardless of whether the focus is applied or theoretical. This completely revised and updated new edition successfully develops the basic theory of linear models for regression, analysis of variance, analysis of covariance, and linear mixed models. Recent advances in the methodology related to linear mixed models, generalized linear models, and the Bayesian linear model are also addressed. This modern Second Edition features: * New chapters on Bayesian linear models as well as random and mixed linear models * Expanded discussion of two-way models with empty cells * Additional sections on the geometry of least squares * Updated coverage of simultaneous inference The book is complemented with easy-to-read proofs, real data sets, and an extensive bibliography. A thorough review of the requisite matrix algebra has been added for transitional purposes, and numerous theoretical and applied problems have been incorporated with selected answers provided at the end of the book. A related Web site includes additional data sets and SAS(r) code for all numerical examples. Linear Model in Statistics, Second Edition is a must-have book for courses in statistics, biostatistics, and mathematics at the upper-undergraduate and graduate levels. It is also an invaluable reference for researchers who need to gain a better understanding of regression and analysis of variance.

Table of Contents

Preface

Introduction

Matrix Algebra

Random Vectors and Matrices

Multivariate Normal Distribution

Distribution of Quadratic Forms in y

Simple Linear Regression

Multiple Regression: Estimation

Multiple Regression: tests of Hypotheses and Confidence Intervals

Multiple Regression: Model Validation and Diagnostics

Multiple Regression: random x's

Multiple Regression: Bayesian Inference

Analysis-of-Variance Models

One-Way Analysis-of-Variance: balanced Case

Two-Way Analysis-of Variance: Balanced Case

Analysis-of-Variance: The Cell Means Model for Unbalanced Data

Analysis-of-Covariance

Linear Mixed Models

Additional Models

Answers and Hits to the Problems

References

Index

Table of Contents provided by Publisher. All Rights Reserved.