Plane Answers to Complex Questions The Theory of Linear Models
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
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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 applications. In testing the generalized least squares models of Section 3.8, even though the data may not be independent or homoscedastic, there are conditions under which the standard F statistic (based on those assumptions) still has the standard F distribution under the reduced model. Section 3.8 contains a new subsection examining such conditions. The major change in the fourth edition has been a more extensive discussion of best prediction and associated ideas of R2 in Sections 6.3 and 6.4. It also includes a nice result that justifies traditional uses of residual plots. One portion of the new material is viewing best predictors (best linear predictors) as perpendicular projections of the dependent random variable y into the space of rando
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