Applied Regression Modeling

by Pardoe, Iain

• ISBN13: 9781119615866
• ISBN10: 1119615860
• Edition: 3rd
• Format: Hardcover
• Copyright: 2020-12-03
• Publisher: Wiley

Summary

Master the fundamentals of regression without learning calculus with this one-stop resource

The newly and thoroughly revised 3rd Edition of Applied Regression Modeling delivers a concise but comprehensive treatment of the application of statistical regression analysis for those with little or no background in calculus. Accomplished instructor and author Dr. Iain Pardoe has reworked many of the more challenging topics, included learning outcomes and additional end-of-chapter exercises, and added coverage of several brand-new topics including multiple linear regression using matrices.

The methods described in the text are clearly illustrated with multi-format datasets available on the book's supplementary website. In addition to a fulsome explanation of foundational regression techniques, the book introduces modeling extensions that illustrate advanced regression strategies, including model building, logistic regression, Poisson regression, discrete choice models, multilevel models, Bayesian modeling, and time series forecasting. Illustrations, graphs, and computer software output appear throughout the book to assist readers in understanding and retaining the more complex content. Applied Regression Modeling covers a wide variety of topics, like:

• Simple linear regression models, including the least squares criterion, how to evaluate model fit, and estimation/prediction
• Multiple linear regression, including testing regression parameters, checking model assumptions graphically, and testing model assumptions numerically
• Regression model building, including predictor and response variable transformations, qualitative predictors, and regression pitfalls
• Three fully described case studies, including one each on home prices, vehicle fuel efficiency, and pharmaceutical patches

Perfect for students of any undergraduate statistics course in which regression analysis is a main focus, Applied Regression Modeling also belongs on the bookshelves of non-statistics graduate students, including MBAs, and for students of vocational, professional, and applied courses like data science and machine learning.

Author Biography

Iain Pardoe, PhD, received his PhD in Statistics from the University of Minnesota. He is an Online Instructor of the "Regression Methods" graduate course at Pennsylvania State University. He also teaches "Biostatistics," "Mathematics for Computing Science," and "Mathematics for Teachers" at Thompson Rivers University and was previously an Associate Professor at the University of Oregon.

Table of Contents

Preface xv

Acknowledgments xix

Glossary xxi

Introduction xxxi

I.1 Statistics in practice xxxi

I.2 Learning statistics xxxv

1 Foundations 1

1.1 Identifying and summarizing data 2

1.2 Population distributions 8

1.3 Selecting individuals at random—probability 17

1.4 Random sampling 20

1.4.1 Central limit theorem—normal version 22

1.4.2 Central limit theorem—t-version 25

1.5 Interval estimation 29

1.6 Hypothesis testing 36

1.6.1 The rejection region method 37

1.6.2 The p-value method 42

1.6.3 Hypothesis test errors 49

1.7 Random errors and prediction 50

1.8 Chapter summary 57

Problems 59

2 Simple linear regression 71

2.1 Probability model for ; and ; 72

2.2 Least squares criterion 83

2.3 Model evaluation 92

2.3.1 Regression standard error 94

2.3.2 Coefficient of determination—R2 . 98

2.3.3 Slope parameter 107

2.4 Model assumptions 122

2.4.1 Checking the model assumptions 124

2.4.2 Testing the model assumptions 134

2.5 Model interpretation 135

2.6 Estimation and prediction 136

2.6.1 Confidence interval for the population mean, E(;) 137

2.6.2 Prediction interval for an individual ;-value 141

2.7 Chapter summary 147

2.7.1 Review example 149

Problems 156

3 Multiple linear regression 175

3.1 Probability model for (;1, ;2, ) and ; 177

3.2 Least squares criterion 184

 

3.3 Model evaluation 195

3.3.1 Regression standard error 196

3.3.2 Coefficient of determination—R2

. 199

3.3.3 Regression parameters—global usefulness test 214

3.3.4 Regression parameters—nested model test 223

3.3.5 Regression parameters—individual tests 236

3.4 Model assumptions 255

3.4.1 Checking the model assumptions 256

3.4.2 Testing the model assumptions 265

3.5 Model interpretation 270

3.6 Estimation and prediction 273

3.6.1 Confidence interval for the population mean, E(;) 274

3.6.2 Prediction interval for an individual ;-value 277

3.7 Chapter summary 283

Problems 286

4 Regression model building I 299

4.1 Transformations 302

4.1.1 Natural logarithm transformation for predictors 302

4.1.2 Polynomial transformation for predictors 312

4.1.3 Reciprocal transformation for predictors 321

4.1.4 Natural logarithm transformation for the response 328

4.1.5 Transformations for the response and predictors 336

4.2 Interactions 343

4.3 Qualitative predictors 357

4.3.1 Qualitative predictors with two levels 358

4.3.2 Qualitative predictors with three or more levels 374

4.4 Chapter summary 392

Problems 395

5 Regression model building II 413

5.1 Influential points 416

5.1.1 Outliers 416

5.1.2 Leverage 424

5.1.3 Cook’s distance 429

5.2 Regression pitfalls 435

5.2.1 Nonconstant variance 435

5.2.2 Autocorrelation 442

5.2.3 Multicollinearity 450

5.2.4 Excluding important predictor variables 458

5.2.5 Overfitting 463

5.2.6 Extrapolation 465

5.2.7 Missing data 469

5.2.8 Power and sample size 475

5.3 Model building guidelines 478

5.4 Model selection 484

5.5 Model interpretation using graphics 491

5.6 Chapter summary 504

Problems 508

C Notation and formulas 635

C.1 Univariate data 635

C.2 Simple linear regression 637

C.3 Multiple linear regression 639