Regression Analysis by Example

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  • Edition: 5th
  • Format: Hardcover
  • Copyright: 2012-09-11
  • Publisher: Wiley

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Supplemental Materials

What is included with this book?


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

Prefacep. xiv
Introductionp. 1
What Is Regression Analysis?p. 1
Publicly Available Data Setsp. 2
Selected Applications of Regression Analysisp. 3
Steps in Regression Analysisp. 13
Scope and Organization of the Bookp. 21
Exercisesp. 23
Simple Linear Regressionp. 25
Introductionp. 25
Covariance and Correlation Coefficientp. 25
Example: Computer Repair Datap. 30
The Simple Linear Regression Modelp. 32
Parameter Estimationp. 33
Tests of Hypothesesp. 36
Confidence Intervalsp. 41
Predictionsp. 41
Measuring the Quality of Fitp. 43
Regression Line Through the Originp. 46
Trivial Regression Modelsp. 48
Bibliographic Notesp. 49
Exercisesp. 49
Multiple Linear Regressionp. 57
Introductionp. 57
Description of the Data and Modelp. 57
Example: Supervisor Performance Datap. 58
Parameter Estimationp. 61
Interpretations of Regression Coefficientsp. 62
Centering and Scalingp. 64
Properties of the Least Squares Estimatorsp. 67
Multiple Correlation Coefficientp. 68
Inference for Individual Regression Coefficientsp. 69
Tests of Hypotheses in a Linear Modelp. 71
Predictionsp. 81
Summaryp. 82
Exercisesp. 82
Appendix: Multiple Regression in Matrix Notationp. 89
Regression Diagnostics: Detection of Model Violationsp. 93
Introductionp. 93
The Standard Regression Assumptionsp. 94
Various Types of Residualsp. 96
Graphical Methodsp. 98
Graphs Before Fitting a Modelp. 101
Graphs After Fitting a Modelp. 105
Checking Linearity and Normality Assumptionsp. 105
Leverage, Influence, and Outliersp. 106
Measures of Influencep. 111
The Potential-Residual Plotp. 115
What to Do with the Outliers?p. 116
Role of Variables in a Regression Equationp. 117
Effects of an Additional Predictorp. 122
Robust Regressionp. 123
Exercisesp. 123
Qualitative Variables as Predictorsp. 129
Introductionp. 129
Salary Survey Datap. 130
Interaction Variablesp. 133
Systems of Regression Equationsp. 136
Other Applications of Indicator Variablesp. 147
Seasonalityp. 148
Stability of Regression Parameters Over Timep. 149
Exercisesp. 151
Transformation of Variablesp. 163
Introductionp. 163
Transformations to Achieve Linearityp. 165
Bacteria Deaths Due to XRay Radiationp. 167
Transformations to Stabilize Variancep. 171
Detection of Heteroscedastic Errorsp. 176
Removal of Heteroscedasticityp. 178
Weighted Least Squaresp. 179
Logarithmic Transformation of Datap. 180
Power Transformationp. 181
Summaryp. 185
Exercisesp. 186
Weighted Least Squaresp. 191
Introductionp. 191
Heteroscedastic Modelsp. 192
Two-Stage Estimationp. 195
Education Expenditure Datap. 197
Fitting a Dose-Response Relationship Curvep. 206
Exercisesp. 208
The Problem of Correlated Errorsp. 209
Introduction: Autocorrelationp. 209
Consumer Expenditure and Money Stockp. 210
Durbin-Watson Statisticp. 212
Removal of Autocorrelation by Transformationp. 214
Iterative Estimation With Autocorrelated Errorsp. 216
Autocorrelation and Missing Variablesp. 217
Analysis of Housing Startsp. 218
Limitations of Durbin-Watson Statisticp. 222
Indicator Variables to Remove Seasonalityp. 223
Regressing Two Time Seriesp. 226
Exercisesp. 228
Analysis of Collinear Datap. 233
Introductionp. 233
Effects of Collinearity on Inferencep. 234
Effects of Collinearity on Forecastingp. 240
Detection of Collinearityp. 245
Exercisesp. 254
Working With Collinear Datap. 259
Introductionp. 259
Principal Componentsp. 259
Computations Using Principal Componentsp. 263
Imposing Constraintsp. 263
Searching for Linear Functions of the βsp. 267
Biased Estimation of Regression Coefficientsp. 272
Principal Components Regressionp. 272
Reduction of Collinearity in the Estimation Datap. 274
Constraints on the Regression Coefficientsp. 276
Principal Components Regression: A Cautionp. 277
Ridge Regressionp. 280
Estimation by the Ridge Methodp. 281
Ridge Regression: Some Remarksp. 285
Summaryp. 287
Bibliographic Notesp. 288
Exercisesp. 288
Principal Componentsp. 291
Ridge Regressionp. 294
Surrogate Ridge Regressionp. 297
Variable Selection Proceduresp. 299
Introductionp. 299
Formulation of the Problemp. 300
Consequences of Variables Deletionp. 300
Uses of Regression Equationsp. 302
Criteria for Evaluating Equationsp. 303
Collinearity and Variable Selectionp. 306
Evaluating All Possible Equationsp. 306
Variable Selection Proceduresp. 307
General Remarks on Variable Selection Methodsp. 309
A Study of Supervisor Performancep. 310
Variable Selection With Collinear Datap. 314
The Homicide Datap. 314
Variable Selection Using Ridge Regressionp. 317
Selection of Variables in an Air Pollution Studyp. 318
A Possible Strategy for Fitting Regression Modelsp. 326
Bibliographic Notesp. 327
Exercisesp. 328
Appendix: Effects of Incorrect Model Specificationsp. 332
Logistic Regressionp. 335
Introductionp. 335
Modeling Qualitative Datap. 336
The Logit Modelp. 336
Example: Estimating Probability of Bankruptciesp. 338
Logistic Regression Diagnosticsp. 341
Determination of Variables to Retainp. 342
Judging the Fit of a Logistic Regressionp. 345
The Multinomial Logit Modelp. 347
Multinomial Logistic Regressionp. 347
Classification Problem: Another Approachp. 354
Exercisesp. 355
Further Topicsp. 359
Introductionp. 359
Generalized Linear Modelp. 359
Poisson Regression Modelp. 360
Introduction of New Drugsp. 361
Robust Regressionp. 363
Fitting a Quadratic Modelp. 364
Distribution of PCB in U.S. Baysp. 366
Exercisesp. 370
Statistical Tablesp. 371
Referencesp. 381
Indexp. 389
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