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Regression analysis provides a conceptually simple method for investigating relationships among variables. Carrying out a successful application of regression analysis, however, requires a balance of theoretical results, empirical rules, and subjective judgement. Regression Analysis by Example, Third Edition explains the principles underlying exploratory data analysis, emphasizing data analysis rather than statistical theory. This is not just another edition of the book; it is a major rewriting and reorganization of the previous edition. The new edition is expanded and updated to reflect recent advances in the field, offering in-depth treatment of diagnostic plots, time series regression, multicollinearity, and logistic regression. Suitable for anyone with an understanding of elementary statistics, Regression Analysis by Example, Third Edition illustrates methods of regression analysis, with examples containing the types of irregularities commonly encountered in the real world. 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. Each of the methods described can be carried out with most currently available statistical software packages.

SAMPRIT CHATTERJEE, PhD, is Professor of Statistics at New York University. A well-known research scientist and Fulbright scholar, Dr. Chatterjee has coauthored Sensitivity Analysis in Linear Regression (with Dr. Hadi) and A Casebook for a First Course in Statistics and Data Analysis, both available from Wiley. ALI S. HADI, PhD, is the Stephen H. Weiss Presidential Fellow and Professor of Statistical and Computing Sciences at Cornell University. The author/coauthor of three other books, Dr. Hadi is a Fellow of the American Statistical Association and an elected member of the International Statistical Institute. BERTRAM PRICE, PhD, is President of Price Associates, a consulting firm in Washington D.C. Dr. Price's experience spans both academia and business, including work as a business scientist at IBM, and he has served as an associate editor of The American Statistician.

Preface

xiii

Introduction

1

(20)

What Is Regression Analysis?

1

(1)

Publicly Available Data Sets

2

(1)

Selected Applications of Regression Analysis

3

(4)

Steps in Regression Analysis

7

(10)

Scope and Organization of the Book

17

(4)

Exercises

18

(3)

Simple Linear Regression

21

(30)

Introduction

21

(1)

Covariance and Correlation Coefficient

21

(5)

Example: Computer Repair Data

26

(3)

The Simple Linear Regression Model

29

(1)

Parameter Estimation

30

(3)

Tests of Hypotheses

33

(4)

Confidence Intervals

37

(1)

Predictions

38

(2)

Measuring the Quality of Fit

40

(3)

Regression Line Through the Origin

43

(1)

Trivial Regression Models

44

(1)

Bibliographic Notes

45

(6)

Exercises

45

(6)

Multiple Linear Regression

51

(34)

Introduction

51

(1)

Description of the Data and Model

51

(1)

Example: Supervisor Performance Data

52

(3)

Parameter Estimation

55

(1)

Interpretations of Regression Coefficients

56

(3)

Properties of the Least Squares Estimators

59

(1)

Multiple Correlation Coefficient

60

(1)

Inference for Individual Regression Coefficients

61

(2)

Tests of Hypotheses in a Linear Model

63

(11)

Predictions

74

(1)

Summary

74

(11)

Exercises

75

(5)

Appendix

80

(5)

Regression Diagnostics: Detection of Model Violations

85

(38)

Introduction

85

(1)

The Standard Regression Assumptions

85

(3)

Various Types of Residuals

88

(2)

Graphical Methods

90

(3)

Graphs Before Fitting a Model

93

(4)

Graphs After Fitting a Model

97

(1)

Checking Linearity and Normality Assumptions

97

(1)

Leverage, Influence, and Outliers

98

(5)

Measures of Influence

103

(4)

The Potential-Residual Plot

107

(1)

What to Do with the Outliers?

108

(1)

Role of Variables in a Regression Equation

109

(4)

Effects of an Additional Predictor

113

(3)

Robust Regression

116

(7)

Exercises

116

(7)

Qualitative Variables as Predictors

123

(30)

Introduction

123

(1)

Salary Survey Data

124

(3)

Interaction Variables

127

(4)

Systems of Regression Equations

131

(9)

Other Applications of Indicator Variables

140

(1)

Seasonality

141

(1)

Stability of Regression Parameters Over Time

142

(11)

Exercises

144

(9)

Transformation of Variables

153

(28)

Introduction

153

(2)

Transformations to Achieve Linearity

155

(2)

Bacteria Deaths Due to X-Ray Radiation

157

(4)

Transformations to Stabilize Variance

161

(5)

Detection of Heteroscedastic Errors

166

(2)

Removal of Heteroscedasticity

168

(2)

Weighted Least Squares

170

(1)

Logarithmic Transformation of Data

170

(4)

Power Transformation

174

(2)

Summary

176

(5)

Exercises

176

(5)

Weighted Least Squares

181

(20)

Introduction

181

(1)

Heteroscedastic Models

182

(3)

Two-Stage Estimation

185

(2)

Education Expenditure Data

187

(10)

Fitting a Dose-Response Relationship Curve

197

(4)

Exercises

199

(2)

The Problem of Correlated Errors

201

(24)

Introduction: Autocorrelation

201

(1)

Consumer Expenditure and Money Stock

202

(2)

Durbin-Watson Statistic

204

(2)

Removal of Autocorrelation by Transformation

206

(2)

Iterative Estimation With Autocorrelated Errors

208

(1)

Autocorrelation and Missing Variables

209

(1)

Analysis of Housing Starts

210

(4)

Limitations of Durbin-Watson Statistic

214

(2)

Indicator Variables to Remove Seasonality

216

(3)

Regressing Two Time Series

219

(6)

Exercises

220

(5)

Analysis of Collinear Data

225

(38)

Introduction

225

(1)

Effects on Inference

226

(6)

Effects on Forecasting

232

(4)

Detection of Multicollinearity

236

(6)

Centering and Scaling

242

(3)

Principal Components Approach

245

(4)

Imposing Constraints

249

(3)

Searching for Linear Functions of the β's

252

(3)

Computations Using Principal Components

255

(3)

Bibliographic Notes

258

(5)

Exercises

258

(2)

Appendix: Principal Components

260

(3)

Biased Estimation of Regression Coefficients

263

(22)

Introduction

263

(1)

Principal Components Regression

264

(2)

Removing Dependence Among the Predictors

266

(2)

Constraints on the Regression Coefficients

268

(1)

Principal Components Regression: A Caution

269

(2)

Ridge Regression

271

(2)

Estimation by the Ridge Method

273

(3)

Ridge Regression: Some Remarks

276

(3)

Summary

279

(6)

Exercises

279

(2)

Appendix: Ridge Regression

281

(4)

Variable Selection Procedures

285

(34)

Introduction

285

(1)

Formulation of the Problem

286

(1)

Consequences of Variables Deletion

286

(2)

Uses of Regression Equations

288

(1)

Criteria for Evaluating Equations

289

(2)

Multicollinearity and Variable Selection

291

(1)

Evaluating All Possible Equations

291

(1)

Variable Selection Procedures

292

(2)

General Remarks on Variable Selection Methods

294

(1)

A Study of Supervisor Performance

295

(4)

Variable Selection With Collinear Data

299

(1)

The Homicide Data

300

(3)

Variable Selection Using Ridge Regression

303

(1)

Selection of Variables in an Air Pollution Study

303

(7)

A Possible Strategy for Fitting Regression Models

310

(2)

Bibliographic Notes

312

(7)

Exercises

312

(4)

Appendix: Effects of Incorrect Model Specifications

316

(3)

Logistic Regression

319

(16)

Introduction

319

(1)

Modeling Qualitative Data

320

(1)

The Logit Model

320

(2)

Example: Estimating Probability of Bankruptcies

322

(3)

Logistic Regression Diagnostics

325

(2)

Determination of Variables to Retain

327

(1)

Judging the Fit of a Logistic Regression

328

(2)

Classification Problem: Another Approach

330

(5)

Exercises

331

(4)

Appendix: Statistical Tables

335

(12)

References

347

(8)

Index

355

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