Ajit C. Tamhane

Predictive Analytics

Parametric Models for Regression and Classification Using R

• Gebundenes Buch

Produktbeschreibung

Provides a foundation in classical parametric methods of regression and classification essential for pursuing advanced topics in predictive analytics and statistical learning

This book covers a broad range of topics in parametric regression and classification including multiple regression, logistic regression (binary and multinomial), discriminant analysis, Bayesian classification, generalized linear models and Cox regression for survival data. The book also gives brief introductions to some modern computer-intensive methods such as classification and regression trees (CART), neural networks and support vector machines.

The book is organized so that it can be used by both advanced undergraduate or masters students with applied interests and by doctoral students who also want to learn the underlying theory. This is done by devoting the main body of the text of each chapter with basic statistical methodology illustrated by real data examples. Derivations, proofs andextensions are relegated to the Technical Notes section of each chapter, Exercises are also divided into theoretical and applied. Answers to selected exercises are provided. A solution manual is available to instructors who adopt the text.

Data sets of moderate to large sizes are used in examples and exercises. They come from a variety of disciplines including business (finance, marketing and sales), economics, education, engineering and sciences (biological, health, physical and social). All data sets are available at the book's web site. Open source software R is used for all data analyses. R codes and outputs are provided for most examples. R codes are also available at the book's web site.

Predictive Analytics: Parametric Models for Regression and Classification Using R is ideal for a one-semester upper-level undergraduate and/or beginning level graduate course in regression for students in business, economics, finance, marketing, engineering, and computer science. It is also an excellent resource for practitioners in these fields.

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Produktdetails

• Wiley Series in Probability and Statistics
• Verlag: Wiley / Wiley & Sons
• Artikelnr. des Verlages: 1W118948890
• 1. Auflage
• Seitenzahl: 384
• Erscheinungstermin: 13. Oktober 2020
• Englisch
• Abmessung: 260mm x 179mm x 27mm
• Gewicht: 832g
• ISBN-13: 9781118948897
• ISBN-10: 1118948890
• Artikelnr.: 56974310

Autorenporträt

Ajit C. Tamhane, PhD, is Professor of Industrial Engineering & Management Sciences with a courtesy appointment in Statistics at Northwestern University. He is a fellow of the American Statistical Association, Institute of Mathematical Statistics, American Association for Advancement of Science and an elected member of the International Statistical Institute.

Inhaltsangabe

Preface xiii

Acknowledgments xv

Abbreviations xvii

About the companion website xxi

1 Introduction 1

1.1 Supervised versus unsupervised learning 2

1.2 Parametric versus nonparametric models 3

1.3 Types of data 4

1.4 Overview of parametric predictive analytics 5

2 Simple linear regression and correlation 7

2.1 Fitting a straight line 9

2.1.1 Least squares (LS) method 9

2.1.2 Linearizing transformations 11

2.1.3 Fitted values and residuals 13

2.1.4 Assessing goodness of fit 14

2.2 Statistical inferences for simple linear regression 17

2.2.1 Simple linear regression model 17

2.2.2 Inferences on ß0 and ß1 18

2.2.3 Analysis of variance for simple linear regression 19

2.2.4 Pure error versus model error 20

2.2.5 Prediction of future observations 21

2.3 Correlation analysis 24

2.3.1 Bivariate normal distribution 26

2.3.2 Inferences on correlation coefficient 27

2.4 Modern extensions 28

2.5 Technical notes 29

2.5.1 Derivation of the LS estimators 29

2.5.2 Sums of squares 30

2.5.3 Distribution of the LS estimators 30

2.5.4 Prediction interval 32

Exercises 32

3 Multiple linear regression: basics 37

3.1 Multiple linear regression model 39

3.1.1 Model in scalar notation 39

3.1.2 Model in matrix notation 40

3.2 Fitting a multiple regression model 41

3.2.1 Least squares (LS) method 41

3.2.2 Interpretation of regression coefficients 45

3.2.3 Fitted values and residuals 45

3.2.4 Measures of goodness of fit 47

3.2.5 Linearizing transformations 48

3.3 Statistical inferences for multiple regression 49

3.3.1 Analysis of variance for multiple regression 49

3.3.2 Inferences on regression coefficients 51

3.3.3 Confidence ellipsoid for the ß vector 52

3.3.4 Extra sum of squares method 54

3.3.5 Prediction of future observations 59

3.4 Weighted and generalized least squares 60

3.4.1 Weighted least squares 60

3.4.2 Generalized least squares 62

3.4.3 Statistical inference on GLS estimator 63

3.5 Partial correlation coefficients 63

3.5.1 Test of significance of partial correlation coefficient 65

3.6 Special topics 66

3.6.1 Dummy variables 66

3.6.2 Interactions 69

3.6.3 Standardized regression 74

3.7 Modern extensions 75

3.7.1 Regression trees 76

3.7.2 Neural nets 78

3.8 Technical notes 81

3.8.1 Derivation of the LS estimators 81

3.8.2 Distribution of the LS estimators 81

3.8.3 Gauss-Markov theorem 82

3.8.4 Properties of fitted values and residuals 83

3.8.5 Geometric interpretation of least squares 83

3.8.6 Confidence ellipsoid for ß 85

3.8.7 Population partial correlation coefficient 85

Exercises 86

4 Multiple linear regression: model diagnostics 95

4.1 Model assumptions and distribution of residuals 95

4.2 Checking normality 96

4.3 Checking homoscedasticity 98

4.3.1 Variance stabilizing transformations 99

4.3.2 Box-Cox transformation 100

4.4 Detecting outliers 103

4.5 Checking model misspecification 106

4.6 Checking independence 108

4.6.1 Runs test 109

4.6.2 Durbin-Watson test 109

4.7 Checking influential observations 110