Linear Models

Shayle R. Searle, Marvin H. J. Gruber

• Publisher: Wiley
• Year: 2016
• Print ISBN: 9781118952832
• eBook ISBN: 9781118952856
• Edition: 2
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

Provides an easy-to-understand guide to statistical linear models and its uses in data analysis

This book defines a broad spectrum of statistical linear models that is useful in the analysis of data. Considerable rewriting was done to make the book more reader friendly than the first edition. Linear Models, Second Edition is written in such a way as to be self-contained for a person with a background in basic statistics, calculus and linear algebra. The text includes numerous applied illustrations, numerical examples, and exercises, now augmented with computer outputs in SAS and R. Also new to this edition is:

• A greatly improved internal design and format

• A short introductory chapter to ease understanding of the order in which topics are taken up

• Discussion of additional topics including multiple comparisons and shrinkage estimators

• Enhanced discussions of generalized inverses, the MINQUE, Bayes and Maximum Likelihood estimators for estimating variance components

Furthermore, in this edition, the second author adds many pedagogical elements throughout the book. These include numbered examples, end-of-example and end-of-proof symbols, selected hints and solutions to exercises available on the book's website, and references to "big data" in everyday life. Featuring a thorough update, Linear Models, Second Edition includes:

• A new internal format, additional instructional pedagogy, selected hints and solutions to exercises, and several more real-life applications

• Many examples using SAS and R with timely data sets

• Over 400 examples and exercises throughout the book to reinforce understanding

Linear Models, Second Edition is a textbook and a reference for upper-level undergraduate and beginning graduate-level courses on linear models, statisticians, engineers, and scientists who use multiple regression or analysis of variance in their work.

SHAYLE R. SEARLE, PhD, was Professor Emeritus of Biometry at Cornell University. He was the author of the first edition of Linear Models, Linear Models for Unbalanced Data, and Generalized, Linear, and Mixed Models (with Charles E. McCulloch), all from Wiley. The first edition of Linear Models appears in the Wiley Classics Library.

MARVIN H. J. GRUBER, PhD, is Professor Emeritus at Rochester Institute of Technology, School of Mathematical Sciences. Dr. Gruber has written a number of papers and has given numerous presentations at professional meetings during his tenure as a professor at RIT. His fields of interest include regression estimators and the improvement of their efficiency using shrinkage estimators. He has written and published two books on this topic. Another of his books, Matrix Algebra for Linear Models, also published by Wiley, provides good preparation for studying Linear Models. He is a member of the American Mathematical Society, the Institute of Mathematical Statistics and the American Statistical Association.

Table of contents

• Cover
• Series
• TitlePage
• Copyright
• PREFACE
• PREFACE TO FIRST EDITION
• ABOUT THE COMPANION WEBSITE
• INTRODUCTION AND OVERVIEW
• 1 GENERALIZED INVERSE MATRICES
• 2 DISTRIBUTIONS AND QUADRATIC FORMS
• 3 REGRESSION FOR THE FULL-RANK MODEL
• 4 INTRODUCING LINEAR MODELS: REGRESSION ON DUMMY VARIABLES
• 5 MODELS NOT OF FULL RANK
• 6 TWO ELEMENTARY MODELS
• 7 THE TWO-WAY CROSSED CLASSIFICATION
• 8 SOME OTHER ANALYSES
• 9 INTRODUCTION TO VARIANCE COMPONENTS
• 10 METHODS OF ESTIMATING VARIANCE COMPONENTS FROM UNBALANCED DATA
• REFERENCES
• AUTHOR INDEX
• SUBJECT INDEX
• EULA