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Handbook and reference guide for students and practitioners of statistical regression-based analyses in R


Handbook of Regression Analysis with Applications in R, Second Edition is a comprehensive and up-to-date guide to conducting complex regressions in the R statistical programming language. The authors' thorough treatment of "classical" regression analysis in the first edition is complemented here by their discussion of more advanced topics including time-to-event survival data and longitudinal and clustered data.


The book further pays particular attention to methods that have become prominent in the last few decades as increasingly large data sets have made new techniques and applications possible. These include:





Regularization methods

Smoothing methods

Tree-based methods



In the new edition of the Handbook, the data analyst's toolkit is explored and expanded. Examples are drawn from a wide variety of real-life applications and data sets. All the utilized R code and data are available via an author-maintained website.


Of interest to undergraduate and graduate students taking courses in statistics and regression, the Handbook of Regression Analysis will also be invaluable to practicing data scientists and statisticians.

Handbook of Regression Analysis With Applications in R

Preface to the Second Edition xv





Preface to the First Edition xix





Part I The Multiple Linear Regression Model





1 Multiple Linear Regression 3





1.1 Introduction 3





1.2 Concepts and Background Material 4





1.2.1 The Linear Regression Model 4





1.2.2 Estimation Using Least Squares 5





1.2.3 Assumptions 8





1.3 Methodology 9





1.3.1 Interpreting Regression Coefficients 9





1.3.2 Measuring the Strength of the Regression Relationship 10





1.3.3 Hypothesis Tests and Confidence Intervals for 12





1.3.4 Fitted Values and Predictions 13





1.3.5 Checking Assumptions Using Residual Plots 14





1.4 Example -Estimating Home Prices 15





1.5 Summary 19





2 Model Building 23





2.1 Introduction 23





2.2 Concepts and Background Material 24





2.2.1 Using Hypothesis Tests to Compare Models 24





2.2.2 Collinearity 26





2.3 Methodology 29





2.3.1 Model Selection 29





2.3.2 Example-Estimating Home Prices (continued) 31





2.4 Indicator Variables and Modeling Interactions 38





2.4.1 Example-Electronic Voting and the 2004 Presidential Election 40





2.5 Summary 46





Part II Addressing Violations of Assumptions





3 Diagnostics for Unusual Observations 53





3.1 Introduction 53





3.2 Concepts and Background Material 54





3.3 Methodology 56





3.3.1 Residuals and Outliers 56





3.3.2 Leverage Points 57





3.3.3 Influential Points and Cook's Distance 58





3.4 Example- Estimating Home Prices (continued) 60





3.5 Summary 63





4 Transformations and Linearizable Models 67





4.1 Introduction 67





4.2 Concepts and Background Material: The Log-Log Model 69





4.3 Concepts and Background Material: Semilog Models 69





4.3.1 Logged Response Variable 70





4.3.2 Logged Predictor Variable 70





4.4 Example- Predicting Movie Grosses After One Week 71





4.5 Summary 77





5 Time Series Data and Autocorrelation 79





5.1 Introduction 79





5.2 Concepts and Background Material 81





5.3 Methodology: Identifying Autocorrelation 83





5.3.1 The Durbin-Watson Statistic 83





5.3.2 The Autocorrelation Function (ACF) 84





5.3.3 Residual Plots and the Runs Test 85





5.4 Methodology: Addressing Autocorrelation 86





5.4.1 Detrending and Deseasonalizing 86





5.4.2 Example- e-Commerce Retail Sales 87





5.4.3 Lagging and Differencing 93





5.4.4 Example- Stock Indexes 94





5.4.5 Generalized Least Squares (GLS): The Cochrane-Orcutt Procedure 99





5.4.6 Example- Time Intervals Between Old Faithful Geyser Eruptions 100





5.5 Summary 104





Part III Categorical Predictors





6 Analysis of Variance 109





6.1 Introduction 109





6.2 Concepts and Background Material 110





6.2.1 One-Way ANOVA 110





6.2.2 Two-Way ANOVA 111





6.3 Methodology 113





6.3.1 Codings for Categorical Predictors 113





6.3.2 Multiple Comparisons 118





6.3.3 Levene's Test and Weighted Least Squares 120





6.3.4 Membership in Multiple Groups 123





6.4 Example-DVD Sales of Movies 125





6.5 Higher-Way ANOVA 130





6.6 Summary 132





7 Analysis of Covariance 135





7.1 Introduction 135





7.2 Methodology 136





7.2.1 Constant Shift Models 136





7.2.2 Varying Slope Models 137





7.3 Example -International Grosses of Movies 137





7.4 Summary 142





Part IV Non-Gaussian Regression Models





8 Logistic Regression 145





8.1 Introduction 145





8.2 Concepts and Background Material 147





8.2.1 The Logit Response Function 148





8.2.2 Bernoulli and Binomial Random Variables 149





8.2.3 Prospective and Retrospective Designs 149





8.3 Methodology 152





8.3.1 Maximum Likelihood Estimation 152





8.3.2 Inference, Model Comparison, and Model Selection 153





8.3.3 Goodness-of-Fit 155





8.3.4 Measures of Association and Classification Accuracy 157





8.3.5 Diagnostics 159





8.4 Example- Smoking and Mortality 159





8.5 Example- Modeling Bankruptcy 163





8.6 Summary 168





9 Multinomial Regression 173





9.1 Introduction 173





9.2 Concepts and Background Material 174





9.2.1 Nominal Response Variable 174





9.2.2 Ordinal Response Variable 176





9.3 Methodology 178





9.3.1 Estimation 178





9.3.2 Inference, Model Comparisons, and Strength of Fit 178





9.3.3 Lack of Fit and Violations of Assumptions 180





9.4 Example- City Bond Ratings 180





9.5 Summary 184





10 Count Regression 187





10.1 Introduction 187





10.2 Concepts and Background Material 188





10.2.1 The Poisson Random Variable 188





10.2.2 Generalized Linear Models 189





10.3 Methodology 190





10.3.1 Estimation and Inference 190





10.3.2 Offsets 191





10.4 Overdispersion and Negative Binomial Regression 192





10.4.1 Quasi-likelihood 192





10.4.2 Negative Binomial Regression 193





10.5 Example- Unprovoked Shark Attacks in Florida 194





10.6 Other Count Regression Models 201





10.7 Poisson Regression and Weighted Least Squares 203





10.7.1 Example- International Grosses of Movies (continued) 204





10.8 Summary 206





11 Models for Time-to-Event (Survival) Data 209





11.1 Introduction 210





11.2 Concepts and Background Material 211





11.2.1 The Nature of Survival Data 211





11.2.2 Accelerated Failure Time Models 212





11.2.3 The Proportional Hazards Model 214





11.3 Methodology 214





11.3.1 The Kaplan-Meier Estimator and the Log-Rank Test 214





11.3.2 Parametric (Likelihood) Estimation 219





11.3.3 Semiparametric (Partial Likelihood) Estimation 221





11.3.4 The Buckley-James Estimator 223





11.4 Example-The Survival of Broadway Shows (continued) 223





11.5 Left-Truncated/Right-Censored Data and Time-Varying Covariates 230





11.5.1 Left-Truncated/Right-Censored Data 230





11.5.2 Example-The Survival of Broadway Shows (continued) 233





11.5.3 Time-Varying Covariates 233





11.5.4 Example-Female Heads of Government 235





11.6 Summary 238





Part V Other Regression Models





12 Nonlinear Regression 243





12.1 Introduction 243





12.2 Concepts and Background Material 244





12.3 Methodology 246





12.3.1 Nonlinear Least Squares Estimation 246





12.3.2 Inference for Nonlinear Regression Models 247





12.4 Example -Michaelis-Menten Enzyme Kinetics 248





12.5 Summary 252





13 Models for Longitudinal and Nested Data 255





13.1 Introduction 255





13.2 Concepts and Background Material 257





13.2.1 Nested Data and ANOVA 257





13.2.2 Longitudinal Data and Time Series 258





13.2.3 Fixed Effects Versus Random Effects 259





13.3 Methodology 260





13.3.1 The Linear Mixed Effects Model 260





13.3.2 The Generalized Linear Mixed Effects Model 262





13.3.3 Generalized Estimating Equations 262





13.3.4 Nonlinear Mixed Effects Models 263





13.4 Example -Tumor Growth in a Cancer Study 264





13.5 Example -Unprovoked Shark Attacks in the United States 269





13.6 Summary 275





14 Regularization Methods and Sparse Models 277





14.1 Introduction 277





14.2 Concepts and Background Material 278





14.2.1 The Bias-Variance Tradeoff 278





14.2.2 Large Numbers of Predictors and Sparsity 279





14.3 Methodology 280





14.3.1 Forward Stepwise Regression 280





14.3.2 Ridge Regression 281





14.3.3 The Lasso 281





14.3.4 Other Regularization Methods 283





14.3.5 Choosing the Regularization Parameter(s) 284





14.3.6 More Structured Regression Problems 285





14.3.7 Cautions About Regularization Methods 286





14.4 Example- Human Development Index 287





14.5 Summary 289





Part VI Nonparametric and Semiparametric Models





15 Smoothing and Additive Models 295





15.1 Introduction 296





15.2 Concepts and Background Material 296





15.2.1 The Bias-Variance Tradeoff 296





15.2.2 Smoothing and Local Regression 297





15.3 Methodology 298





15.3.1 Local Polynomial Regression 298





15.3.2 Choosing the Bandwidth 298





15.3.3 Smoothing Splines 299





15.3.4 Multiple Predictors, the Curse of Dimensionality, and Additive Models 300





15.4 Example- Prices of German Used Automobiles 301





15.5 Local and Penalized Likelihood Regression 304





15.5.1 Example- The Bechdel Rule and Hollywood Movies 305





15.6 Using Smoothing to Identify Interactions 307





15.6.1 Example- Estimating Home Prices (continued) 308





15.7 Summary 310





16 Tree-Based Models 313





16.1 Introduction 314





16.2 Concepts and Background Material 314





16.2.1 Recursive Partitioning 314





16.2.2 Types of Trees 317





16.3 Methodology 318





16.3.1 CART 318





16.3.2 Conditional Inference Trees 319





16.3.3 Ensemble Methods 320





16.4 Examples 321





16.4.1 Estimating Home Prices (continued) 321





16.4.2 Example-Courtesy in Airplane Travel 322





16.5 Trees for Other Types of Data 327





16.5.1 Trees for Nested and Longitudinal Data 327





16.5.2 Survival Trees 328





16.6 Summary 332





Bibliography 337





Index 343