Applied Regression Modeling

by Pardoe, Iain

• ISBN13: 9781118097281
• ISBN10: 1118097289
• Edition: 2nd
• Format: Hardcover
• Copyright: 2012-07-23
• Publisher: Wiley

Summary

This book offers a practical, concise introduction to regression analysis for upper-level undergraduate students of diverse disciplines including, but not limited to statistics, the social and behavioral sciences, MBA, and vocational studies. The book's overall approach is strongly based on an abundant use of illustrations, examples, case studies, and graphics. It emphasizes major statistical software packages, including SPSS®, Minitab®, SAS®, R, and R/S-PLUS®. Detailed instructions for use of these packages, as well as for Microsoft Office Excel®, are provided on a specially prepared and maintained author web site. Select software output appears throughout the text. To help readers understand, analyze, and interpret data and make informed decisions in uncertain settings, many of the examples and problems use real-life situations and settings. The book introduces modeling extensions that illustrate more advanced regression techniques, including logistic regression, Poisson regression, discrete choice models, multilevel models, Bayesian modeling, and time series and forecasting. New to this edition are more exercises, simplification of tedious topics (such as checking regression assumptions and model building), elimination of repetition, and inclusion of additional topics (such as variable selection methods, further regression diagnostic tests, and autocorrelation tests).

Author Biography

Iain Pardoe, PhD, is an independent consultant and also serves on the faculty of mathematics and statistics at Thompson Rivers University, Canada. He has published extensively in his areas of research interest, which include Bayesian analysis, multilevel modeling, graphical methods, and statistics education.

Table of Contents

Preface	p. xi
Acknowledgments	p. xv
Introduction	p. xvii
Statistics in practice	p. xvii
Learning statistics	p. xix
Foundations	p. 1
Identifying and summarizing data	p. 1
Population distributions	p. 5
Selecting individuals at random-probability	p. 9
Random sampling	p. 11
Central limit theorem-normal version	p. 12
Central limit theorem-t-version	p. 14
Interval estimation	p. 15
Hypothesis testing	p. 19
The rejection region method	p. 19
The p-value method	p. 21
Hypothesis test errors	p. 24
Random errors and prediction	p. 25
Chapter Summary	p. 28
Problems	p. 29
Simple linear regression	p. 35
Probability model for X and Y	p. 35
Least Squares criterion	p. 40
Model evaluation	p. 45
Regression standard error	p. 46
Coefficient of determination-R2	p. 48
Slope parameter	p. 52
Model assumptions	p. 59
Checking the model assumptions	p. 61
Testing the model assumptions	p. 66
Model interpretation	p. 66
Estimation and prediction	p. 68
Confidence interval for the population mean, E(Y)	p. 68
Prediction interval for an individual Y-value	p. 69
Chapter summary	p. 72
Review example	p. 74
Problems	p. 78
Multiple linear regression	p. 83
Probability model for (X1, X2,...) and Y	p. 83
Least squares criterion	p. 87
Model evaluation	p. 92
Regression standard error	p. 92
Coefficient of determination-R2	p. 94
Regression parameters-global usefulness test	p. 101
Regression parameters-nested model test	p. 104
Regression parameters-individuals tests	p. 109
Model assumptions	p. 118
Checking the model assumptions	p. 119
Testing the model assumptions	p. 123
Model interpretation	p. 124
Estimation and prediction	p. 126
Confidence interval for the population mean, E(Y)	p. 126
Prediction interval for an individual Y-value	p. 127
Chapter summary	p. 130
Problems	p. 132
Regression model building I	p. 137
Transformations	p. 138
Natural logarithm transformation for predictors	p. 138
Polynomial transformation for predictors	p. 144
Reciprocal transformation for predictors	p. 147
Natural logarithm transformation for the response	p. 151
Transformations for the response and predictors	p. 155
Interactions	p. 159
Qualitative predictors	p. 166
Qualitative predictors with two levels	p. 167
Qualitative predictors with three or more levels	p. 174
Chapter summary	p. 182
Problems	p. 184
Regression model building II	p. 189
Influential points	p. 189
Outliers	p. 189
Leverage	p. 194
Cook's distance	p. 196
Regression pitfalls	p. 199
Nonconstant variance	p. 199
Autocorrelation	p. 202
Multicollinearity	p. 206
Excluding important predictor varibales	p. 209
Overfitting	p. 212
Extrapolations	p. 213
Missing data	p. 215
Power and sample size	p. 217
Model building guidelines	p. 218
Model selection	p. 221
Model interpretation using graphics	p. 224
Chapter summary	p. 231
Problems	p. 234
Case studies	p. 243
Home prices	p. 243
Data description	p. 243
Exploratory data analysis	p. 245
Regression model building	p. 246
Results and conclusions	p. 247
Further questions	p. 252
Vehicle fuel efficiency	p. 253
Data description	p. 253
Exploratory data analysis	p. 253
Regression model building	p. 255
Results and conclusions	p. 256
Further questions	p. 261
Pharmaceutical patches	p. 261
Data description	p. 261
Exploratory data analysis	p. 261
Regression model building	p. 263
Model diagnostics	p. 263
Results and conclusions	p. 264
Further questions	p. 266
Extensions	p. 267
Generalized linear models	p. 268
Logistic regression	p. 268
Poisson regression	p. 273
Discrete choice models	p. 275
Multilevel models	p. 278
Bayesian modeling	p. 281
Frequentist inference	p. 281
Bayesian inference	p. 281
Computer software help	p. 285
Problems	p. 287
Critical values for t-distributions	p. 289
Notation and formulas	p. 293
Univariate data	p. 293
Simple linear regression	p. 294
Multiple linear regression	p. 295
Mathematics refresher	p. 297
The natural logarithm and exponential functions	p. 297
Rounding and accuracy	p. 298
Answers for selected problems	p. 299
References	p. 309
Glossary	p. 315
Index	p. 321
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