This textbook provides a wide-ranging introduction to the use and theory of linear models for analyzing data. The author's emphasis is on providing a unified treatment of linear models, including analysis of variance models and regression models, based on projections, orthogonality, and other vector space ideas. Every chapter comes with numerous exercises and examples that make it ideal for a graduate-level course. All of the standard topics are covered in depth: ANOVA, estimation including Bayesian estimation, hypothesis testing, multiple comparisons, regression analysis, and experimental design models. In addition, the book covers topics that are not usually treated at this level, but which are important in their own right: balanced incomplete block designs, testing for lack of fit, testing for independence, models with singular covariance matrices, variance component estimation, best linear and best linear unbiased prediction, collinearity, and variable selection. This new edition includes a more extensive discussion of best prediction and associated ideas of R2, as well as new sections on inner products and perpendicular projections for more general spaces and Milliken and Graybill’s generalization of Tukey’s one degree of freedom for nonadditivity test.
Springer Texts in Statistics Series Editors G. Casella S. Fienberg I. Olkin For other titles published in this series, go to www.springer.com/series/417 Ronald Christensen Plane Answers to Complex Questions The Theory of Linear Models Fourth edition Ronald Christensen Department of Mathematics and Statistics MSC01 1115 1 University of New Mexico Albuquerque, New Mexico, 87131-0001 USA
[email protected] Series Editors: George Casella Department of Statistics University of Florida Gainesville, FL 32611-8545 USA Stephen Fienberg Department of Statistics Carnegie Mellon University Pittsburgh, PA 15213-3890 USA Ingram Olkin Department of Statistics Stanford University Stanford, CA 94305 USA ISSN 1431-875X ISBN 978-1-4419-9815-6 e-ISBN 978-1-4419-9816-3 DOI 10.1007/978-1-4419-9816-3 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2011928555 © Springer Science+Business Media, LLC 2011 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) To Dad, Mom, Sharon, Fletch, and Don Preface Preface to the Fourth Edition “Critical assessment of data is the the essential task of the educated mind.” Professor Garrett G. Fagan, Pennsylvania State University. The last words in his audio course The Emperors of Rome, The Teaching Company. As with the prefaces to the second and third editions, this focuses on changes to the previous edition. The preface to the first edition discusses the core of the book. Two substantial changes have occurred in Chapter 3. Subsection 3.3.2 uses a simplified method of finding the reduced model and includes some additional discussion of a