Regression Analysis by Example

by Chatterjee, Samprit; Hadi, Ali S.

• ISBN13: 9780470905845
• ISBN10: 0470905840
• Edition: 5th
• Format: Hardcover
• Copyright: 2012-09-11
• Publisher: Wiley

Summary

This Fifth Edition has been expanded and thoroughly updated to reflect recent advances in the field. The emphasis continues to be on exploratory data analysis rather than statistical theory. The coverage offers in-depth treatment of regression diagnostics, transformation, multicollinearity, logistic regression, and robust regression. Methods of regression analysis are clearly demonstrated, and examples containing the types of irregularities commonly encountered in the real world are provided. Each example isolates one or two techniques and features detailed discussions of the techniques themselves, the required assumptions, and the evaluated success of each technique.

Author Biography

SAMPRIT CHATTERJEE, PhD, is Professor Emeritus of Statistics at New York University. A Fellow of the American Statistical Association, Dr. Chatterjee has been a Fulbright scholar in both Kazhakstan and Mongolia. He is the coauthor of Sensitivity Analysis in Linear Regression and A Casebook for a First Course in Statistics and Data Analysis, both published by Wiley.

ALI S. HADI, PhD, is a Distinguished University Professor and former vice provost at the American University in Cairo (AUC). He is the founding Director of the Actuarial Science Program at AUC. He is also a Stephen H. Weiss Presidential Fellow and Professor Emeritus at Cornell University. Dr. Hadi is the author of four other books, a Fellow of the American Statistical Association, and an elected Member of the International Statistical Institute.

Table of Contents

Preface	p. xiv
Introduction	p. 1
What Is Regression Analysis?	p. 1
Publicly Available Data Sets	p. 2
Selected Applications of Regression Analysis	p. 3
Steps in Regression Analysis	p. 13
Scope and Organization of the Book	p. 21
Exercises	p. 23
Simple Linear Regression	p. 25
Introduction	p. 25
Covariance and Correlation Coefficient	p. 25
Example: Computer Repair Data	p. 30
The Simple Linear Regression Model	p. 32
Parameter Estimation	p. 33
Tests of Hypotheses	p. 36
Confidence Intervals	p. 41
Predictions	p. 41
Measuring the Quality of Fit	p. 43
Regression Line Through the Origin	p. 46
Trivial Regression Models	p. 48
Bibliographic Notes	p. 49
Exercises	p. 49
Multiple Linear Regression	p. 57
Introduction	p. 57
Description of the Data and Model	p. 57
Example: Supervisor Performance Data	p. 58
Parameter Estimation	p. 61
Interpretations of Regression Coefficients	p. 62
Centering and Scaling	p. 64
Properties of the Least Squares Estimators	p. 67
Multiple Correlation Coefficient	p. 68
Inference for Individual Regression Coefficients	p. 69
Tests of Hypotheses in a Linear Model	p. 71
Predictions	p. 81
Summary	p. 82
Exercises	p. 82
Appendix: Multiple Regression in Matrix Notation	p. 89
Regression Diagnostics: Detection of Model Violations	p. 93
Introduction	p. 93
The Standard Regression Assumptions	p. 94
Various Types of Residuals	p. 96
Graphical Methods	p. 98
Graphs Before Fitting a Model	p. 101
Graphs After Fitting a Model	p. 105
Checking Linearity and Normality Assumptions	p. 105
Leverage, Influence, and Outliers	p. 106
Measures of Influence	p. 111
The Potential-Residual Plot	p. 115
What to Do with the Outliers?	p. 116
Role of Variables in a Regression Equation	p. 117
Effects of an Additional Predictor	p. 122
Robust Regression	p. 123
Exercises	p. 123
Qualitative Variables as Predictors	p. 129
Introduction	p. 129
Salary Survey Data	p. 130
Interaction Variables	p. 133
Systems of Regression Equations	p. 136
Other Applications of Indicator Variables	p. 147
Seasonality	p. 148
Stability of Regression Parameters Over Time	p. 149
Exercises	p. 151
Transformation of Variables	p. 163
Introduction	p. 163
Transformations to Achieve Linearity	p. 165
Bacteria Deaths Due to XRay Radiation	p. 167
Transformations to Stabilize Variance	p. 171
Detection of Heteroscedastic Errors	p. 176
Removal of Heteroscedasticity	p. 178
Weighted Least Squares	p. 179
Logarithmic Transformation of Data	p. 180
Power Transformation	p. 181
Summary	p. 185
Exercises	p. 186
Weighted Least Squares	p. 191
Introduction	p. 191
Heteroscedastic Models	p. 192
Two-Stage Estimation	p. 195
Education Expenditure Data	p. 197
Fitting a Dose-Response Relationship Curve	p. 206
Exercises	p. 208
The Problem of Correlated Errors	p. 209
Introduction: Autocorrelation	p. 209
Consumer Expenditure and Money Stock	p. 210
Durbin-Watson Statistic	p. 212
Removal of Autocorrelation by Transformation	p. 214
Iterative Estimation With Autocorrelated Errors	p. 216
Autocorrelation and Missing Variables	p. 217
Analysis of Housing Starts	p. 218
Limitations of Durbin-Watson Statistic	p. 222
Indicator Variables to Remove Seasonality	p. 223
Regressing Two Time Series	p. 226
Exercises	p. 228
Analysis of Collinear Data	p. 233
Introduction	p. 233
Effects of Collinearity on Inference	p. 234
Effects of Collinearity on Forecasting	p. 240
Detection of Collinearity	p. 245
Exercises	p. 254
Working With Collinear Data	p. 259
Introduction	p. 259
Principal Components	p. 259
Computations Using Principal Components	p. 263
Imposing Constraints	p. 263
Searching for Linear Functions of the βâÇÖs	p. 267
Biased Estimation of Regression Coefficients	p. 272
Principal Components Regression	p. 272
Reduction of Collinearity in the Estimation Data	p. 274
Constraints on the Regression Coefficients	p. 276
Principal Components Regression: A Caution	p. 277
Ridge Regression	p. 280
Estimation by the Ridge Method	p. 281
Ridge Regression: Some Remarks	p. 285
Summary	p. 287
Bibliographic Notes	p. 288
Exercises	p. 288
Principal Components	p. 291
Ridge Regression	p. 294
Surrogate Ridge Regression	p. 297
Variable Selection Procedures	p. 299
Introduction	p. 299
Formulation of the Problem	p. 300
Consequences of Variables Deletion	p. 300
Uses of Regression Equations	p. 302
Criteria for Evaluating Equations	p. 303
Collinearity and Variable Selection	p. 306
Evaluating All Possible Equations	p. 306
Variable Selection Procedures	p. 307
General Remarks on Variable Selection Methods	p. 309
A Study of Supervisor Performance	p. 310
Variable Selection With Collinear Data	p. 314
The Homicide Data	p. 314
Variable Selection Using Ridge Regression	p. 317
Selection of Variables in an Air Pollution Study	p. 318
A Possible Strategy for Fitting Regression Models	p. 326
Bibliographic Notes	p. 327
Exercises	p. 328
Appendix: Effects of Incorrect Model Specifications	p. 332
Logistic Regression	p. 335
Introduction	p. 335
Modeling Qualitative Data	p. 336
The Logit Model	p. 336
Example: Estimating Probability of Bankruptcies	p. 338
Logistic Regression Diagnostics	p. 341
Determination of Variables to Retain	p. 342
Judging the Fit of a Logistic Regression	p. 345
The Multinomial Logit Model	p. 347
Multinomial Logistic Regression	p. 347
Classification Problem: Another Approach	p. 354
Exercises	p. 355
Further Topics	p. 359
Introduction	p. 359
Generalized Linear Model	p. 359
Poisson Regression Model	p. 360
Introduction of New Drugs	p. 361
Robust Regression	p. 363
Fitting a Quadratic Model	p. 364
Distribution of PCB in U.S. Bays	p. 366
Exercises	p. 370
Statistical Tables	p. 371
References	p. 381
Index	p. 389
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