Applied Regression Modeling

Transcription

1 Applied Regression Modeling A Business Approach Iain Pardoe University of Oregon Charles H. Lundquist College of Business Eugene, Oregon WILEY- INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION

2 CONTENTS Preface Acknowledgments xiii xv Introduction xvii 1.1 Statistics in business xvii 1.2 Learning statistics xix 1 Foundations Identifying and summarizing data Population distributions Selecting individuals at random probability Random sampling Central limit theorem normal version Student's t-distribution Central limit theorem t version Interval estimation Hypothesis testing The rejection region method The p-value method Hypothesis test errors Random errors and prediction 23 vii

3 VIII CONTENTS 1.8 Chapter summary 26 Problems 27 2 Simple linear regression Probability model for X and Y Least Squares criterion Model evaluation Regression Standard error Coefficient of determination R Slope parameter Model assumptions Checking the model assumptions Model Interpretation Estimation and prediction Confidence interval for the population mean, E(y) Prediction interval for an individual F-value Chapter summary Review example 66 Problems 70 3 Multiple linear regression Probability model for (Xx, X 2,...) and Y Least Squares criterion 77 3J Model evaluation Regression Standard error Coefficient of determination R Regression parameters global usefulness test Regression parameters nested model test Regression parameters individual tests Model assumptions Checking the model assumptions Model interpretation Estimation and prediction Confidence interval for the population mean, E(7) Prediction interval for an individual F-value Chapter summary 114 Problems Regression model building I Transformations Natural logarithm transformation for predictors 122

4 CONTENTS IX Polynomial transformation for predictors Reciprocal transformation for predictors Natural logarithm transformation for the response Transformations for the response and predictors Interactions Qualitative predictors Qualitative predictors with two levels Qualitative predictors with three or more levels Chapter summary 158 Problems Regression model buifding II Influential points Outliers Leverage Cook's distance Regression pitfalls Autocorrelation Multicollinearity Excluding important predictor variables Overfitting Extrapolation Missing Data Model building guidelines Model Interpretation using graphics Chapter summary 194 Problems Case studies Homeprices Data description Exploratory data analysis Regression model building Results and conclusions Further questions Vehicle fuel efficiency Data description Exploratory data analysis Regression model building Results and conclusions Further questions 219

5 X CONTENTS 7 Extensions Generalized linear modeis Logistic regression Poisson regression Discrete choice modeis Multilevel modeis Bayesian modeling Frequentist inference Bayesian inference 235 Appendix A: Computer Software help 237 A.l SPSS 238 A. 1.1 Getting started and summarizing univariate data 238 A. 1.2 Simple linear regression 241 A. 1.3 Multiple linear regression 243 A.2 Minitab 245 A.2.1 Getting started and summarizing univariate data 245 A.2.2 Simple linear regression 248 A.2.3 Multiple linear regression 249 A.3 SAS 251 A.3.1 Getting started and summarizing univariate data 252 A.3.2 Simple linear regression 254 A.3.3 Multiple linear regression 255 A.4 R and S-PLUS 257 A.4.1 Getting started and summarizing univariate data 258 A.4.2 Simple linear regression 260 A.4.3 Multiple linear regression 261 A.5 Excel 263 A.5.1 Getting started and summarizing univariate data 263 A.5.2 Simple linear regression 265 A.5.3 Multiple linear regression 265 Problems 267 Appendix B: Critical values for t-distributions 269 Appendix C: Notation and formulas 273 C.l Univariate data 273 C.2 Simple linear regression 274 C.3 Multiple linear regression 275 Appendix D: Mathematics refresher 277

6 CONTENTS XI D. 1 The natural logarithm and exponential functions 277 D.2 Rounding and accuracy 278 Appendix E: Brief answers to selected problems 279 References 287 Glossary 291 Index 297