Introduction to Linear Regression Analysis, 5th Edition

CONTENTS

PREFACE

1. INTRODUCTION

1.1 Regression and Model Building

1.2 Data Collection

1.3 Uses of Regression

1.4 Role of the Computer

2. SIMPLE LINEAR REGRESSION

2.1 Simple Linear Regression Model

2.2 Least-Squares Estimation of the Parameters

2.2.1 Estimation of β₀ and β₁

2.2.2 Properties of the Least-Squares Estimators and the Fitted Regression Model

2.2.3 Estimation of σ²

2.2.4 Alternate Form of the Model

2.3 Hypothesis Testing on the Slope and Intercept

2.3.1 Use of t Tests

2.3.2 Testing Significance of Regression

2.3.3 Analysis of Variance

2.4 Interval Estimation in Simple Linear Regression

2.4.1 Confidence Intervals on β₀, β₁ and σ²

2.4.2 Interval Estimation of the Mean Response

2.5 Prediction of New Observations

2.6 Coefficient of Determination

2.7 A Service Industry Application of Regression

2.8 Using SAS® and R for Simple Linear Regression

2.9 Some Considerations in the Use of Regression

2.10 Regression Through the Origin

2.11 Estimation by Maximum Likelihood

2.12 Case Where the Regressor x is Random

2.12.1 x and y Jointly Distributed

2.12.2 x and y Jointly Normally Distributed: Correlation Model

Problems

3. MULTIPLE LINEAR REGRESSION

3.1 Multiple Regression Models

3.2 Estimation of the Model Parameters

3.2.1 Least-Squares Estimation of the Regression Coefficients

3.2.2 Geometrical Interpretation of Least Squares

3.2.3 Properties of the Least-Squares Estimators

3.2.4 Estimation of σ²

3.2.5 Inadequacy of Scatter Diagrams in Multiple Regression

3.2.6 Maximum-Likelihood ...