Alternative Methods of Regression

248 Pages·1993·7.44 MB·English

by  David Birkes

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Alternative Methods of Regression
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Alternative Methods of Regression
DAVID BIRKES YADOLAH DODGE
Oregon State University University of Neuchätel
A Wiley-Interscience Publication
JOHN WILEY & SONS, INC.
New York · Chichester · Brisbane · Toronto · Singapore
To my parents.
—Dave
To Kay.
—Yadolah
This text is printed on acid-free paper.
Copyright © 1993 by John Wiley & Sons, Inc.
All rights reserved. Published simultaneously in Canada.
Reproduction or translation of any part of this work beyond
that permitted by Section 107 or 108 of the 1976 United
States Copyright Act without the permission of the copyright
owner is unlawful. Requests for permission or further
information should be addressed to the Permissions Department,
John Wiley & Sons, Inc., 605 Third Avenue, New York, NY
10158-0012.
Library of Congress Cataloging in Publication Data:
Birkes, David
Alternative methods of regression / David Birkes, Yadolah Dodge.
p. cm.
"A Wiley-Interscience publication."
' Includes index.
ISBN 0-471-56881-3
1. Regression analysis. I. Dodge, Yadolah, 1944- II. Title.
QA278.2.D64 1993
519.5'36—dc20 92-31165
10 9 8 7 6 5 43
Contents
Preface
Acknowledgments
1. Linear Regression Analysis
1.1 Introduction, 1
1.2 Example, 2
1.3 The Linear Regression Model, 3
1.4 Estimating the Regression Coefficients, 5
1.5 Testing the Significance of the Relationship, 6
1.6 The Need for Alternative Methods, 6
1.7 The Origin of the Word "Regression", 8
Notes, 10
References, 11
2. Constructing and Checking the Model
2.1 Introduction, 13
2.2 Checking the Model, 14
2.3 Modifying the Model, 15
2.4 Examples, 16
Notes, 24
References, 27
3. Least-Squares Regression
3.1 Introduction, 29
3.2 An Example of Simple Regression, 29
3.3 Estimating the Regression Line, 31
3.4 Testing ß = 0, 33
3.5 Checking Normality, 37
3.6 An Example of Multiple Regression, 38
3.7 Estimating the Regression Coefficients, 38
3.8 Testing the Regression Coefficients, 42
3.9 Testing ß = ··■ = ß = 0, 45
g + l p
3.10 Testing ß = 0, 45
3
3.11 The Coefficient of Determination, 47
3.12 Computation, 47
Notes, 49
References, 54
4. Least-Absolute-Deviations Regression
4.1 Introduction, 57
4.2 Estimating the Regression Line, 57
4.3 Nonuniqueness and Degeneracy, 61
4.4 Testing ß = 0, 62
4.5 An Example of Multiple Regression, 66
4.6 Estimating the Regression Coefficients, 68
4.7 Testing ß = ··· = ß = 0, 76
q+l p
4.8 Computation, 78
Notes, 78
References, 83
5. M-Regression
5.1 Introduction, 85
5.2 An Example of Simple Regression, 85
5.3 Estimating the Regression Line, 87
5.4 Testing ß = 0, 90
5.5 An Example of Multiple Regression, 91
5.6 Estimating the Regression Coefficients, 93
5.7 Testing ß = ··· = ß = 0, 95
Q+] p
5.8 Computation, 97
Notes, 99
References, 109
6. Nonparametric Regression
6.1 Introduction, 111
6.2 An Example of Simple Regression, 111
6.3 Estimating the Regression Line, 113
CONTENTS
6.4 Testing ß = 0, 118
6.5 An Example of Multiple Regression, 121
6.6 Estimating the Regression Coefficients, 122
6.7 Testing ß = ··■ = ß = 0, 126
q + x p
6.8 Computation, 130
Notes, 130
References, 140
7. Bayesian Regression
7.1 Introduction, 143
7.2 The Bayesian Approach, 143
7.3 An Example of Simple Regression, 144
7.4 Estimating the Regression Line, 145
7.5 Testing ß = 0, 149
7.6 An Example of Multiple Regression, 153
7.7 Estimating the Regression Coefficients, 154
7.8 Testing ß = ··· = ß = 0, 157
9 + l p
7.9 Computation, 160
Notes, 161
References, 170
8. Ridge Regression
8.1 Introduction, 173
8.2 An Example of Simple Regression, 173
8.3 Estimating the Regression Line, 173
8.4 An Example of Multiple Regression, 176
8.5 Standardization, 177
8.6 Estimating the Regression Coefficients, 178
8.7 Collinearity, 180
Notes, 183
References, 187
9. Comparisons
9.1 Introduction, 189
9.2 Comparison of Properties, 189
9.3 Comparisons on Three Data Sets, 196
Notes, 199
References, 203
viii CONTENTS
10. Other Methods 205
10.1 Introduction, 205
10.2 Other Methods of Linear Regression, 205
10.3 More General Methods of Regression, 209
References, 212
Appendix 215
Student's i-Distribution, 215
/"■-Distribution, 216
Chi-squared Distribution, 222
Index 223