Predictive Analytics - Ajit C Tamhane

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Résumé :
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Biographie:
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Sommaire:

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 ?0 and ?1 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 ? 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 ? 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

4.7.1 Leverage 111

4.7.2 Cook's distance 111

4.8 Checking multicollinearity 114

4.8.1 Multicollinearity: causes and consequences 114

4.8.2 Multicollinearity diagnostics 115

Exercises 119