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Preface xiii
1 Scatterplots and Regression 1
1.1 Scatterplots, 1
1.2 Mean Functions, 9
1.3 Variance Functions, 11
1.4 Summary Graph, 11
1.5 Tools for Looking at Scatterplots, 12
1.5.1 Size, 13
1.5.2 Transformations, 14
1.5.3 Smoothers for the Mean Function, 14
1.6 Scatterplot Matrices, 15
Problems, 17
2 Simple Linear Regression 19
2.1 Ordinary Least Squares Estimation, 21
2.2 Least Squares Criterion, 23
2.3 Estimating σ 2, 25
2.4 Properties of Least Squares Estimates, 26
2.5 Estimated Variances, 27
2.6 Comparing Models: The Analysis of Variance, 28
2.6.1 The F-Test for Regression, 30
2.6.2 Interpreting p-values, 31
2.6.3 Power of Tests, 31
2.7 The Coefficient of Determination, R2, 31
2.8 Confidence Intervals and Tests, 32
2.8.1 The Intercept, 32
2.8.2 Slope, 33
2.8.3 Prediction, 34
2.8.4 Fitted Values, 35
2.9 The Residuals, 36
Problems, 38
3 Multiple Regression 47
3.1 Adding a Term to a Simple Linear Regression Model, 47
3.1.1 Explaining Variability, 49
3.1.2 Added-Variable Plots, 49
3.2 The Multiple Linear Regression Model, 50
3.3 Terms and Predictors, 51
3.4 Ordinary Least Squares, 54
3.4.1 Data and Matrix Notation, 54
3.4.2 Variance-Covariance Matrix of e, 56
3.4.3 Ordinary Least Squares Estimators, 56
3.4.4 Properties of the Estimates, 57
3.4.5 Simple Regression in Matrix Terms, 58
3.5 The Analysis of Variance, 61
3.5.1 The Coefficient of Determination, 62
3.5.2 Hypotheses Concerning One of the Terms, 62
3.5.3 Relationship to the t -Statistic, 63
3.5.4 t-Tests and Added-Variable Plots, 63
3.5.5 Other Tests of Hypotheses, 64
3.5.6 Sequential Analysis of Variance Tables, 64
3.6 Predictions and Fitted Values, 65
Problems, 65
4 Drawing Conclusions 69
4.1 Understanding Parameter Estimates, 69
4.1.1 Rate of Change, 69
4.1.2 Signs of Estimates, 70
4.1.3 Interpretation Depends on Other Terms in the Mean
Function, 70
4.1.4 Rank Deficient and Over-Parameterized Mean
Functions, 73
4.1.5 Tests, 74
4.1.6 Dropping Terms, 74
4.1.7 Logarithms, 76
4.2 Experimentation Versus Observation, 77
4.3 Sampling from a Normal Population, 80
4.4 More on R2, 81
4.4.1 Simple Linear Regression and R2, 83
4.4.2 Multiple Linear Regression, 84
4.4.3 Regression through the Origin, 84
4.5 Missing Data, 84
4.5.1 Missing at Random, 84
4.5.2 Alternatives, 85
4.6 Computationally Intensive Methods, 87
4.6.1 Regression Inference without Normality, 87
4.6.2 Nonlinear Functions of Parameters, 89
4.6.3 Predictors Measured with Error, 90
Problems, 92
5 Weights, Lack of Fit, and More 96
5.1 Weighted Least Squares, 96
5.1.1 Applications of Weighted Least Squares, 98
5.1.2 Additional Comments, 99
5.2 Testing for Lack of Fit, Variance Known, 100
5.3 Testing for Lack of Fit, Variance Unknown, 102
5.4 General F Testing, 105
5.4.1 Non-null Distributions, 107
5.4.2 Additional Comments, 108
5.5 Joint Confidence Regions, 108
Problems, 110
6 Polynomials and Factors 115
6.1 Polynomial Regression, 115
6.1.1 Polynomials with Several Predictors, 117
6.1.2 Using the Delta Method to Estimate a Minimum or a
Maximum, 120
6.1.3 Fractional Polynomials, 122
6.2 Factors, 122
6.2.1 No Other Predictors, 123
6.2.2 Adding a Predictor: Comparing Regression Lines, 126
6.2.3 Additional Comments, 129
6.3 Many Factors, 130
6.4 Partial One-Dimensional Mean Functions, 131
6.5 Random Coefficient Models, 134
Problems, 137
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