Preface

1 Introduction

1.1 What Is Regression Analysis?
1.2 Publicly Available Data Sets
1.3 Selected Applications of Regression Analysis 1.4 Steps in Regression Analysis 1.5 Scope and Organization of the Book
Exercises

2 Simple Linear Regression

2.1 Introduction
2.2 Covariance and Correlation Coefficient
2.3 Example: Computer Repair Data
2.4 The Simple Linear Regression Model
2.5 Parameter Estimation
2.6 Tests of Hypotheses
2.7 Confidence Intervals
2.8 Predictions
2.9 Measuring the Quality of Fit
2.10 Regression Line Through the Origin
2.11 Trivial Regression Models
2.12 Bibliographic Notes
Exercises

3 Multiple Linear Regression

3.1 Introduction
3.2 Description of the Data and Model
3.3 Example: Supervisor Performance Data
3.4 Parameter Estimation
3.5 Interpretations of Regression Coefficients
3.6 Properties of the Least Squares Estimators
3.7 Multiple Correlation Coefficient
3.8 Inference for Individual Regression Coefficients
3.9 Tests of Hypotheses in a Linear Model 3.10 Predictions
3.11 Summary
Exercises
Appendix: Multiple Regression in Matrix Notation

4 Regression Diagnostics: Detection of Model Violations

4.1 Introduction
4.2 The Standard Regression Assumptions
4.3 Various Types of Residuals
4.4 Graphical Methods
4.5 Graphs Before Fitting a Model 4.6 Graphs After Fitting a Model
4.7 Checking Linearity and Normality Assumptions
4.8 Leverage, Influence, and Outliers 4.9 Measures of Influence 4.10 The Potential-Residual Plot
4.11 What to Do with the Outliers?
4.12 Role of Variables in a Regression Equation 4.13 Effects of an Additional Predictor
4.14 Robust Regression
Exercises

5 Qualitative Variables as Predictors

5.1 Introduction
5.2 Salary Survey Data
5.3 Interaction Variables
5.4 Systems of Regression Equations 5.5 Other Applications of Indicator Variables
5.6 Seasonality
5.7 Stability of Regression Parameters Over Time
Exercises

6 Transformation of Variables

6.1 Introduction
6.2 Transformations to Achieve Linearity
6.3 Bacteria Deaths Due to X-Ray Radiation
6.4 Transformations to Stabilize Variance
6.5 Detection of Heteroscedastic Errors
6.6 Removal of Heteroscedasticity
6.7 Weighted Least Squares
6.8 Logarithmic Transformation of Data
6.9 Power Transformation
6.10 Summary
Exercises

7 Weighted Least Squares

7.1 Introduction
7.2 Heteroscedastic Models 7.3 Two-Stage Estimation
7.4 Education Expenditure Data
7.5 Fitting a Dose-Response Relationship Curve
Exercises

8 The Problem of Correlated Errors

8.1 Introduction: Autocorrelation
8.2 Consumer Expenditure and Money Stock
8.3 Durbin–Watson Statistic
8.4 Removal of Autocorrelation by Transformation
8.5 Iterative Estimation With Autocorrelated Errors
8.6 Autocorrelation and Missing Variables
8.7 Analysis of Housing Starts
8.8 Limitations of Durbin–Watson Statistic
8.9 Indicator Variables to Remove Seasonality
8.10 Regressing Two Time Series
Exercises

9 Analysis of Collinear Data

9.1 Introduction
9.2 Effects on Inference
9.3 Effects on Forecasting
9.4 Detection of Multicollinearity
9.5 Centering and Scaling 9.6 Principal Components Approach
9.7 Imposing Constraints
9.8 Searching for Linear Functions of the β's
9.9 Computations Using Principal Components
9.10 Bibliographic Notes
Exercises
Appendix: Principal Components

10 Biased Estimation of Regression Coefficients

10.1 Introduction
10.2 Principal Components Regression
10.3 Removing Dependence Among the Predictors
10.4 Constraints on the Regression Coefficients
10.5 Principal Components Regression: A Caution
10.6 Ridge Regression
10.7 Estimation by the Ridge Method
10.8 Ridge Regression: Some Remarks
10.9 Summary
Exercises
Appendix: Ridge Regression

11 Variable Selection Procedures

11.1 Introduction
11.2 Formulation of the Problem
11.3 Consequences of Variables Deletion
11.4 Uses of Regression Equations 11.5 Criteria for Evaluating Equations 11.6 Multicollinearity and Variable Selection
11.7 Evaluating All Possible Equations
11.8 Variable Selection Procedures 11.9 General Remarks on Variable Selection Methods
11.10 A Study of Supervisor Performance
11.11 Variable Selection With Collinear Data
11.12 The Homicide Data
11.13 Variable Selection Using Ridge Regression
11.14 Selection of Variables in an Air Pollution Study
11.15 A Possible Strategy for Fitting Regression Models
11.16 Bibliographic Notes
Exercises
Appendix: Effects of Incorrect Model Specifications

12 Logistic Regression

12.1 Introduction
12.2 Modeling Qualitative Data
12.3 The Logit Model
12.4 Example: Estimating Probability of Bankruptcies
12.5 Logistic Regression Diagnostics
12.6 Determination of Variables to Retain
12.7 Judging the Fit of a Logistic Regression
12.8 Classification Problem: Another Approach
Exercises

Appendix A: Statistical Tables

References

Index