Regression Analysis by Example
by Chatterjee, Samprit; Hadi, Ali S.Edition: 5th
Format: Hardcover
Pub. Date: 2012-09-11
Publisher(s): Wiley
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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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