Handbook of Regression Analysis

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 Kazakhstan and Mongolia. He is the coauthor of Regression Analysis by Example, Sensitivity Analysis in Linear Regression, and A Casebook for a First Course in Statistics and Data Analysis, all published by Wiley.Jeffrey S. Simonoff, PhD, is Professor of Statistics at the Leonard N. Stern School of Business of New York University. He is a Fellow of the American Statistical Association, a Fellow of the Institute of Mathematical Statistics, and an Elected Member of the International Statistical Institute. He has authored or coauthored more than ninety articles and five books on the theory and applications of statistics.

“I would be happy to recommend this nice handy book as a reference to my students. The clarity of the writing and proper choices of examples allows the presentations of many statistical methods shine.” (The American Statistician, 1 February 2015)“Overall, a valuable user-friendly resource. Summing Up: Highly recommended. Upper-division undergraduates through professionals.”  (Choice, 1 October 2013)“All in all, I also very much like the Handbook and if I were not to retire this year, I would be happy to tell my students that it is a very nice and handy book.”  (International Statistical Review, 15 February 2013)

• Preface xi Part I The Multiple Linear Regression Model1 Multiple Linear Regression 31.1 Introduction 31.2 Concepts and Background Material 41.2.1 The Linear Regression Model 41.2.2 Estimation Using Least Squares 51.2.3 Assumptions 81.3 Methodology 91.3.1 Interpreting Regression Coefficients 91.3.2 Measuring the Strength of the Regression Relationship 101.3.3 Hypothesis Tests and Confidence Intervals for _ 121.3.4 Fitted Values and Predictions 131.3.5 Checking Assumptions Using Residual Plots 141.4 Example — Estimating Home Prices 161.5 Summary 192 Model Building 232.1 Introduction 232.2 Concepts and Background Material 242.2.1 Using hypothesis tests to compare models 242.2.2 Collinearity 262.3 Methodology 292.3.1 Model Selection 292.3.2 Example—Estimating Home Prices (continued) 312.4 Indicator Variables and Modeling Interactions 382.4.1 Example—Electronic Voting and the 2004 Presidential Election 402.5 Summary 46Part II Addressing Violations of Assumptions3 Diagnostics for Unusual Observations 533.1 Introduction 533.2 Concepts and Background Material 543.3 Methodology 563.3.1 Residuals and Outliers 563.3.2 Leverage Points 573.3.3 Influential Points and Cook’s Distance 583.4 Example — Estimating Home Prices (continued) 603.5 Summary 644 Transformations and Linearizable Models 674.1 Introduction 674.2 Concepts and Background Material: the Log-Log Model 694.3 Concepts and Background Material: Semilog models 694.3.1 Logged response variable 704.3.2 Logged predictor variable 704.4 Example — Predicting Movie Grosses After One Week 714.5 Summary 785 Time Series Data and Autocorrelation 815.1 Introduction 815.2 Concepts and Background Material 835.3 Methodology: Identifying Autocorrelation 855.3.1 The Durbin-Watson Statistic 865.3.2 The Autocorrelation Function (ACF) 875.3.3 Residual Plots and the Runs Test 875.4 Methodology: Addressing Autocorrelation 885.4.1 Detrending and Deseasonalizing 885.4.2 Example — e-Commerce Retail Sales 895.4.3 Lagging and Differencing 965.4.4 Example — Stock Indexes 965.4.5 Generalized Least Squares (GLS): the Cochrane-Orcutt Procedure 1015.4.6 Example — Time Intervals Between Old Faithful Eruptions 1045.5 Summary 107Part III Categorical Predictors6 Analysis of Variance 1136.1 Introduction 1136.2 Concepts and Background Material 1146.2.1 One-way ANOVA 1146.2.2 Two-way ANOVA 1156.3 Methodology 1176.3.1 Codings for categorical predictors 1176.3.2 Multiple comparisons 1226.3.3 Levene’s test and weighted least squares 1246.3.4 Membership in multiple groups 1276.4 Example — DVD Sales of Movies 1296.5 Higher-Way ANOVA 1346.6 Summary 1367 Analysis of Covariance 1397.1 Introduction 1397.2 Methodology 1397.2.1 Constant shift models 1397.2.2 Varying slope models 1417.3 Example — International Grosses of Movies 1417.4 Summary 145Part IV Other Regression Models8 Logistic Regression 1498.1 Introduction 1498.2 Concepts and Background Material 1518.2.1 The logit response function 1518.2.2 Bernoulli and binomial random variables 1528.2.3 Prospective and retrospective designs 1538.3 Methodology 1568.3.1 Maximum likelihood estimation 1568.3.2 Inference, model comparison, and model selection 1578.3.3 Goodness-of-Fit 1598.3.4 Measures of association and classification accuracy 1618.3.5 Diagnostics 1638.4 Example — Smoking and Mortality 1638.5 Example — Modeling Bankruptcy 1678.6 Summary 1739 Multinomial Regression 1779.1 Introduction 1779.2 Concepts and Background Material 1789.2.1 Nominal Response Variable 1789.2.2 Ordinal Response Variable 1809.3 Methodology 1829.3.1 Estimation 1829.3.2 Inference, model comparisons, and strength of fit 1839.3.3 Lack of fit and violations of assumptions 1849.4 Example — City Bond Ratings 1859.5 Summary 18910 Count Regression 19110.1 Introduction 19110.2 Concepts and Background Material 19210.2.1 The Poisson random variable 19210.2.2 Generalized linear models 19310.3 Methodology 19410.3.1 Estimation and inference 19410.3.2 Offsets 19510.4 Overdispersion and Negative Binomial Regression 19610.4.1 Quasi-likelihood 19610.4.2 Negative Binomial Regression 19710.5 Example — Unprovoked Shark Attacks in Florida 19810.6 Other Count Regression Models 20610.7 Poisson Regression and Weighted Least Squares 20810.7.1 Example – International Grosses of Movies (continued) 20910.8 Summary 21111 Nonlinear Regression 21511.1 Introduction 21511.2 Concepts and Background Material 21611.3 Methodology 21811.3.1 Nonlinear least squares estimation 21811.3.2 Inference for nonlinear regression models 21911.4 Example — Michaelis-Menten Enzyme Kinetics 22011.5 Summary 225Bibliography 227Index 231