Applied Regression Modeling

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.

Master the fundamentals of regression without learning calculus with this one-stop resourceThe 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 patchesPerfect 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.

Preface xiAcknowledgments xvIntroduction xviiI.1 Statistics in Practice xviiI.2 Learning Statistics xixAbout the Companion Website xxi1 Foundations 11.1 Identifying and Summarizing Data 21.2 Population Distributions 51.3 Selecting Individuals at Random--Probability 91.4 Random Sampling 111.4.1 Central limit theorem--normal version 121.4.2 Central limit theorem--t-version 141.5 Interval Estimation 161.6 Hypothesis Testing 201.6.1 The rejection region method 201.6.2 The p-value method 231.6.3 Hypothesis test errors 271.7 Random Errors and Prediction 281.8 Chapter Summary 31Problems 312 Simple Linear Regression 392.1 Probability Model for X and Y 402.2 Least Squares Criterion 452.3 Model Evaluation 502.3.1 Regression standard error 512.3.2 Coefficient of determination--R² 532.3.3 Slope parameter 572.4 Model Assumptions 652.4.1 Checking the model assumptions 662.4.2 Testing the model assumptions 722.5 Model Interpretation 722.6 Estimation and Prediction 742.6.1 Confidence interval for the population mean, E(Y) 742.6.2 Prediction interval for an individual Y -value 752.7 Chapter Summary 792.7.1 Review example 80Problems 833 Multiple Linear Regression 953.1 Probability Model for (X1, X2, . . .) and Y 963.2 Least Squares Criterion 1003.3 Model Evaluation 1063.3.1 Regression standard error 1063.3.2 Coefficient of determination--R² 1083.3.3 Regression parameters--global usefulness test 1153.3.4 Regression parameters--nested model test 1203.3.5 Regression parameters--individual tests 1273.4 Model Assumptions 1373.4.1 Checking the model assumptions 1373.4.2 Testing the model assumptions 1433.5 Model Interpretation 1453.6 Estimation and Prediction 1463.6.1 Confidence interval for the population mean, E(Y ) 1473.6.2 Prediction interval for an individual Y -value 1483.7 Chapter Summary 151Problems 1524 Regression Model Building I 1594.1 Transformations 1614.1.1 Natural logarithm transformation for predictors 1614.1.2 Polynomial transformation for predictors 1674.1.3 Reciprocal transformation for predictors 1714.1.4 Natural logarithm transformation for the response 1754.1.5 Transformations for the response and predictors 1794.2 Interactions 1844.3 Qualitative Predictors 1914.3.1 Qualitative predictors with two levels 1924.3.2 Qualitative predictors with three or more levels 2014.4 Chapter Summary 210Problems 2115 Regression Model Building II 2215.1 Influential Points 2235.1.1 Outliers 2235.1.2 Leverage 2285.1.3 Cook's distance 2305.2 Regression Pitfalls 2345.2.1 Nonconstant variance 2345.2.2 Autocorrelation 2375.2.3 Multicollinearity 2425.2.4 Excluding important predictor variables 2465.2.5 Overfitting 2495.2.6 Extrapolation 2505.2.7 Missing data 2525.2.8 Power and sample size 2555.3 Model Building Guidelines 2565.4 Model Selection 2595.5 Model Interpretation Using Graphics 2635.6 Chapter Summary 270Problems 272Notation and Formulas 287Univariate Data 287Simple Linear Regression 288Multiple Linear Regression 289Bibliography 293Glossary 299Index 305