Applied Regression Modeling

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  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 2012-07-31
  • Publisher: Wiley

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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

Prefacep. xi
Acknowledgmentsp. xv
Introductionp. xvii
Statistics in practicep. xvii
Learning statisticsp. xix
Foundationsp. 1
Identifying and summarizing datap. 1
Population distributionsp. 5
Selecting individuals at random-probabilityp. 9
Random samplingp. 11
Central limit theorem-normal versionp. 12
Central limit theorem-t-versionp. 14
Interval estimationp. 15
Hypothesis testingp. 19
The rejection region methodp. 19
The p-value methodp. 21
Hypothesis test errorsp. 24
Random errors and predictionp. 25
Chapter Summaryp. 28
Problemsp. 29
Simple linear regressionp. 35
Probability model for X and Yp. 35
Least Squares criterionp. 40
Model evaluationp. 45
Regression standard errorp. 46
Coefficient of determination-R2p. 48
Slope parameterp. 52
Model assumptionsp. 59
Checking the model assumptionsp. 61
Testing the model assumptionsp. 66
Model interpretationp. 66
Estimation and predictionp. 68
Confidence interval for the population mean, E(Y)p. 68
Prediction interval for an individual Y-valuep. 69
Chapter summaryp. 72
Review examplep. 74
Problemsp. 78
Multiple linear regressionp. 83
Probability model for (X1, X2,...) and Yp. 83
Least squares criterionp. 87
Model evaluationp. 92
Regression standard errorp. 92
Coefficient of determination-R2p. 94
Regression parameters-global usefulness testp. 101
Regression parameters-nested model testp. 104
Regression parameters-individuals testsp. 109
Model assumptionsp. 118
Checking the model assumptionsp. 119
Testing the model assumptionsp. 123
Model interpretationp. 124
Estimation and predictionp. 126
Confidence interval for the population mean, E(Y)p. 126
Prediction interval for an individual Y-valuep. 127
Chapter summaryp. 130
Problemsp. 132
Regression model building Ip. 137
Transformationsp. 138
Natural logarithm transformation for predictorsp. 138
Polynomial transformation for predictorsp. 144
Reciprocal transformation for predictorsp. 147
Natural logarithm transformation for the responsep. 151
Transformations for the response and predictorsp. 155
Interactionsp. 159
Qualitative predictorsp. 166
Qualitative predictors with two levelsp. 167
Qualitative predictors with three or more levelsp. 174
Chapter summaryp. 182
Problemsp. 184
Regression model building IIp. 189
Influential pointsp. 189
Outliersp. 189
Leveragep. 194
Cook's distancep. 196
Regression pitfallsp. 199
Nonconstant variancep. 199
Autocorrelationp. 202
Multicollinearityp. 206
Excluding important predictor varibalesp. 209
Overfittingp. 212
Extrapolationsp. 213
Missing datap. 215
Power and sample sizep. 217
Model building guidelinesp. 218
Model selectionp. 221
Model interpretation using graphicsp. 224
Chapter summaryp. 231
Problemsp. 234
Case studiesp. 243
Home pricesp. 243
Data descriptionp. 243
Exploratory data analysisp. 245
Regression model buildingp. 246
Results and conclusionsp. 247
Further questionsp. 252
Vehicle fuel efficiencyp. 253
Data descriptionp. 253
Exploratory data analysisp. 253
Regression model buildingp. 255
Results and conclusionsp. 256
Further questionsp. 261
Pharmaceutical patchesp. 261
Data descriptionp. 261
Exploratory data analysisp. 261
Regression model buildingp. 263
Model diagnosticsp. 263
Results and conclusionsp. 264
Further questionsp. 266
Extensionsp. 267
Generalized linear modelsp. 268
Logistic regressionp. 268
Poisson regressionp. 273
Discrete choice modelsp. 275
Multilevel modelsp. 278
Bayesian modelingp. 281
Frequentist inferencep. 281
Bayesian inferencep. 281
Computer software helpp. 285
Problemsp. 287
Critical values for t-distributionsp. 289
Notation and formulasp. 293
Univariate datap. 293
Simple linear regressionp. 294
Multiple linear regressionp. 295
Mathematics refresherp. 297
The natural logarithm and exponential functionsp. 297
Rounding and accuracyp. 298
Answers for selected problemsp. 299
Referencesp. 309
Glossaryp. 315
Indexp. 321
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