Applied Regression
Second Edition
Applied Regression
An Introduction
Second Edition
Colin Lewis-Beck
Iowa State University
Michael S. Lewis-Beck
University of Iowa
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Library of Congress Cataloging-in-Publication Data
Lewis-Beck, Michael S.
Applied regression : an introduction. — Second edition / Colin Lewis-Beck, Michael S. Lewis-Beck.
pages cm
Includes bibliographical references and index.
ISBN 978-1-4833-8147-3 (pbk. : alk. paper)
1. Regression analysis. I. Title.
HA31.3.L48 2016
519.5′36—dc23 2015011813
This book is printed on acid-free paper.
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Series Editor’s Introduction
Invented more than 200 years ago, apparently independently by the German mathematician Carl Friedrich Gauss and the French mathematician Adrien-Marie Legendre, the method of least squares occupies a central place in statistical methods. Linear least squares regression not only is very widely employed in research but also furnishes a basis for much of applied statistics. Many statistical models — generalized linear models, linear and generalized linear mixed-effects models, survival regression models, and linear structural equation models, to name a few of the more prominent — represent direct generalizations of linear regression; and computation for statistical models often involves least squares fitting — for example, the use of iterated weighted least squares to compute maximum likelihood estimates for generalized linear models. Both for its direct application and for its many generalizations, a sound background in linear least squares regression is fundamental to the study of statistics.
In Applied Regression, Colin and Michael Lewis-Beck provide a thorough primer in linear least squares regression, introducing the method from first principles. They attend to practical details of regression analysis; to the statistical model underlying inference in linear regression and to violations of the assumptions of the model; and — most important – to the interpretation of results and the interplay between statistical modeling and the substance of social research.
There is clearly a need for a brief, accessible, and nontechnical treatment of regression analysis, and the first edition of this monograph was one of the most widely read in the QASS series. I expect that this new, expanded, and extensively revised edition will be similarly well received.
On a personal note, I am particularly pleased to be able to assist in the publication of this monograph because I have known Michael Lewis-Beck since we were both graduate students at the University of Michigan many years ago, and I have subsequently had the pleasure of becoming acquainted with his son, Colin.
—John Fox
Series Editor
Preface
In this second edition of Applied Regression: An Introduction, we maintain our firm commitment to the method of ordinary least squares (OLS). We are not alone in our defense of OLS. Peter Kennedy (2008), author of a leading econometrics text, observed the following: “The central role of the OLS estimator in the econometrician’s catalog is that of a standard against which all other estimators are compared. The reason for this is that the OLS estimator is extraordinarily popular” (p. 43). This popularity was recently affirmed in a methodological content analysis of the articles in the three leading general political science journals, with the finding that “OLS is by far the most popular method” (Krueger & Lewis-Beck, 2008, p. 3). This is not surprising, since OLS is the analytic tool of the classical linear regression model.
As Jan Kmenta (1997), author of our favorite econometrics book, reminds us, “The need for familiarity with the basic principles of statistical inference and with the fundamentals of econometrics has not diminished. . . . Most econometric problems can be characterized as situations in which some of the basic assumptions of the classical regression model are violated” (pp. v–vi). In our monograph, we pay special attention to these basic regression assumptions. Also, in the writing, we are inspired again by Kmenta (1997) and his “philosophy of making everything as simple and clear as possible” (p. vii). It is our hope that readers agree that we have realized this goal. Indeed, if readers are interested in further analyzing or replicating the results presented in this monograph, the datasets are available for download through the SAGE website.
Acknowledgments
There are many people to thank for help on this project. At SAGE, we would especially like to thank Helen Salmon (Acquisitions Editor) and John Fox (Series Editor). Their general enthusiasm for this second edition, coupled with specific useful suggestions for improvement, are greatly appreciated. Also, we wish to take note of the insightful comments made by the many reviewers of our proposal. In addition, we acknowledge particular teachers, including Frank M. Andrews, John DiNardo, Lawrence B. Mohr, and Jan Kmenta, whose wisdom has abided. Furthermore, we are grateful to the Inter-University Consortium for Political and Social Research (ICPSR) Summer Program