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| Preface | |
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| Introduction | |
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| Regression and Model Building | |
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| Data Collection | |
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| Uses of Regression | |
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| Role of the Computer | |
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| Simple Linear Regression | |
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| Simple Linear Regression Model | |
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| Least-Squares Estimation of the Parameters | |
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| Estimation of [beta subscript 0] and [beta subscript 1] | |
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| Properties of the Least-Squares Estimators and the Fitted Regression Model | |
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| Estimation of [sigma superscript 2] | |
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| An Alternate Form of the Model | |
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| Hypothesis Testing on the Slope and Intercept | |
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| Use of t-Tests | |
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| Testing Significance of Regression | |
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| The Analysis of Variance | |
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| Interval Estimation in Simple Linear Regression | |
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| Confidence Intervals on [beta subscript 0], [beta subscript 1], and [sigma superscript 2] | |
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| Interval Estimation of the Mean Response | |
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| Prediction of New Observations | |
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| Coefficient of Determination | |
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| Some Considerations in the Use of Regression | |
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| Regression Through the Origin | |
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| Estimation by Maximum Likelihood | |
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| Case Where the Regressor x is Random | |
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| x and y Jointly Distributed | |
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| x and y Jointly Normally Distributed: The Correlation Model | |
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| Problems | |
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| Multiple Linear Regression | |
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| Multiple Regression Models | |
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| Estimation of the Model Parameters | |
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| Least-Squares Estimation of the Regression Coefficients | |
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| A Geometrical Interpretation of Least Squares | |
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| Properties of the Least-Squares Estimators | |
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| Estimation of [sigma superscript 2] | |
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| Inadequacy of Scatter Diagrams in Multiple Regression | |
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| Maximum-Likelihood Estimation | |
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| Hypothesis Testing in Multiple Linear Regression | |
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| Test for Significance of Regression | |
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| Tests on Individual Regression Coefficients | |
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| Special Case of Orthogonal Columns in X | |
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| Testing the General Linear Hypothesis | |
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| Confidence Intervals in Multiple Regression | |
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| Confidence Intervals on the Regression Coefficients | |
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| Confidence Interval Estimation of the Mean Response | |
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| Simultaneous Confidence Intervals on Regression Coefficients | |
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| Prediction of New Observations | |
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| Hidden Extrapolation in Multiple Regression | |
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| Standardized Regression Coefficients | |
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| Multicollinearity | |
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| Why Do Regression Coefficients have the Wrong Sign? | |
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| Problems | |
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| Model Adequacy Checking | |
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| Introduction | |
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| Residual Analysis | |
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| Definition of Residuals | |
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| Methods for Scaling Residuals | |
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| Residual Plots | |
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| Partial Regression and Partial Residual Plots | |
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| Other Residual Plotting and Analysis Methods | |
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| The PRESS Statistic | |
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| Detection and Treatment of Outliers | |
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| Lack of Fit of the Regression Model | |
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| A Formal Test for Lack of Fit | |
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| Estimation of Pure Error from Near-Neighbors | |
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| Problems | |
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| Transformations and Weighting to Correct Model Inadequacies | |
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| Introduction | |
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| Variance-Stabilizing Transformations | |
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| Transformations to Linearize the Model | |
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| Analytical Methods for Selecting a Transformation | |
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| Transformations on y: The Box-Cox Method | |
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| Transformations on the Regressor Variables | |
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| Generalized and Weighted Least Squares | |
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| Generalized Least Squares | |
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| Weighted Least Squares | |
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| Some Practical Issues | |
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| Problems | |
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| Diagnostics for Leverage and Influence | |
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| Importance of Detecting Influential Observations | |
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| Leverage | |
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| Measures of Influence: Cook's D | |
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| Measures of Influence: DFFITS and DFBETAS | |
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| A Measure of Model Performance | |
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| Detecting Groups of Influential Observations | |
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| Treatment of Influential Observations | |
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| Problems | |
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| Polynomial Regression Models | |
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| Introduction | |
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| Polynomial Models in One Variable | |
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| Basic Principles | |
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| Piecewise Polynomial Fitting (Splines) | |
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| Polynomial and Trigonometric Terms | |
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| Nonparametric Regression | |
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| Kernel Regression | |
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| Locally Weighted Regression (Loess) | |
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| Final Cautions | |
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| Polynomial Models in Two or More Variables | |
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| Orthogonal Polynomials | |
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| Problems | |
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| Indicator Variables | |
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| The General Concept of Indicator Variables | |
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| Comments on the Use of Indicator Variables | |
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| Indicator Variables versus Regression on Allocated Codes | |
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| Indicator Variables as a Substitute for a Quantitative Regressor | |
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| Regression Approach to Analysis of Variance | |
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| Problems | |
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| Variable Selection and Model Building | |
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| Introduction | |
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| The Model-Building Problem | |
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| Consequences of Model Misspecification | |
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| Criteria for Evaluating Subset Regression Models | |
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| Computational Techniques for Variable Selection | |
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| All Possible Regressions | |
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| Stepwise Regression Methods | |
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| Some Final Recommendations for Practice | |
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| Problems | |
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| Multicollinearity | |
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| Introduction | |
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| Sources of Multicollinearity | |
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| Effects of Multicollinearity | |
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| Multicollinearity Diagnostics | |
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| Examination of the Correlation Matrix | |
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| Variance Inflation Factors | |
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| Eigensystem Analysis of X'X | |
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| Other Diagnostics | |
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| Methods for Dealing with Multicollinearity | |
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| Collecting Additional Data | |
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| Model Respecification | |
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| Ridge Regression | |
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| Other Methods | |
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| Comparison and Evaluation of Biased Estimators | |
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| Problems | |
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| Robust Regression | |
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| The Need for Robust Regression | |
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| M-Estimators | |
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| Properties of Robust Estimators | |
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| Breakdown Point | |
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| Efficiency | |
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| Survey of Other Robust Regression Estimators | |
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| High-Breakdown-Point Estimators | |
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| Bounded Influence Estimators | |
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| Other Procedures | |
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| Computing Robust Regression Estimators | |
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| Problems | |
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| Introduction to Nonlinear Regression | |
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| Linear and Nonlinear Regression Models | |
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| Linear Regression Models | |
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| Nonlinear Regression Models | |
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| Nonlinear Least Squares | |
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| Transformation to a Linear Model | |
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| Parameter Estimation in a Nonlinear System | |
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| Linearization | |
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| Other Parameter Estimation Methods | |
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| Starting Values | |
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| Computer Programs | |
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| Statistical Inference in Nonlinear Regression | |
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| Examples of Nonlinear Regression Models | |
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| Problems | |
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| Generalized Linear Models | |
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| Introduction | |
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| Logistic Regression Models | |
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| Models with a Binary Response Variable | |
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| Estimating the Parameters in a Logistic Regression Model | |
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| Interpretation of the Parameters in a Logistic Regression Model | |
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| Hypothesis Tests on Model Param6ters | |
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| Poisson Regression | |
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| The Generalized Linear Model | |
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| Link Functions and Linear Predictors | |
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| Parameter Estimation and Inference in the GLM | |
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| Prediction and Estimation with the GLM | |
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| Residual Analysis in the GLM | |
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| Overdispersion | |
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| Problems | |
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| Other Topics in the Use of Regression Analysis | |
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| Regression Models with Autocorrelation Errors | |
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| Source and Effects of Autocorrelation | |
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| Detecting the Presence of Autocorrelation | |
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| Parameter Estimation Methods | |
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| Effect of Measurement Errors in the Regressors | |
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| Simple Linear Regression | |
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| The Berkson Model | |
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| Inverse Estimation--The Calibration Problem | |
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| Bootstrapping in Regression | |
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| Bootstrap Sampling in Regression | |
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| Bootstrap Confidence Intervals | |
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| Classification and Regression Trees (CART) | |
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| Neural Networks | |
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| Designed Experiments for Regression | |
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| Problems | |
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| Validation of Regression Models | |
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| Introduction | |
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| Validation Techniques | |
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| Analysis of Model Coefficients and Predicted Values | |
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| Collecting Fresh Data--Confirmation Runs | |
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| Data Splitting | |
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| Data from Planned Experiments | |
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| Problems | |
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| Statistical Tables | |
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| Data Sets For Exercises | |
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| Supplemental Technical Material | |
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| Background on Basic Test Statistics | |
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| Background from the Theory of Linear Models | |
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| Important Results on SS[subscript R] and SS[subscript Res] | |
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| The Gauss-Markov Theorem, Var([varepsilon]) = [sigma superscript 2]I | |
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| Computational Aspects of Multiple Regression | |
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| A Result on the Inverse of a Matrix | |
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| Development of the PRESS Statistic | |
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| Development of S[superscript 2 subscript (i)] | |
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| An Outlier Test Based on R-Student | |
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| The Gauss-Markov Theorem, Var([varepsilon]) = V | |
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| The Bias in MS[subscript Res] When the Model is Underspecified | |
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| Computation of Influence Diagnostics | |
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| Generalized Linear Models | |
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| References | |
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| Index | |