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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.
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 Î²âÇÖs | 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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