Second Course in Statistics, A: Regression Analysis

<p>1. A Review of Basic Concepts (Optional)</p> <p>1.1 Statistics and Data</p> <p>1.2 Populations, Samples, and Random Sampling</p> <p>1.3 Describing Qualitative Data</p> <p>1.4 Describing Quantitative Data Graphically</p> <p>1.5 Describing Quantitative Data Numerically</p> <p>1.6 The Normal Probability Distribution</p> <p>1.7 Sampling Distributions and the Central Limit Theorem</p> <p>1.8 Estimating a Population Mean</p> <p>1.9 Testing a Hypothesis About a Population Mean</p> <p>1.10 Inferences About the Difference Between Two Population Means</p> <p>1.11 Comparing Two Population Variances</p> <p>&nbsp;</p> <p>2. Introduction to Regression Analysis</p> <p>2.1 Modeling a Response</p> <p>2.2 Overview of Regression Analysis</p> <p>2.3 Regression Applications</p> <p>2.4 Collecting the Data for Regression</p> <p>&nbsp;</p> <p>3. Simple Linear Regression</p> <p>3.1 Introduction</p> <p>3.2 The Straight-Line Probabilistic Model</p> <p>3.3 Fitting the Model: The Method of Least Squares</p> <p>3.4 Model Assumptions</p> <p>3.5 An Estimator of s2</p> <p>3.6 Assessing the Utility of the Model: Making Inferences About the Slope ß1</p> <p>3.7 The Coefficient of Correlation</p> <p>3.8 The Coefficient of Determination</p> <p>3.9 Using the Model for Estimation and Prediction</p> <p>3.10 A Complete Example</p> <p>3.11 Regression Through the Origin (Optional)</p> <p>&nbsp;</p> <p>Case Study 1: Legal Advertising--Does It Pay?</p> <p>&nbsp;</p> <p>4. Multiple Regression Models</p> <p>4.1 General Form of a Multiple Regression Model</p> <p>4.2 Model Assumptions</p> <p>4.3 A First-Order Model with Quantitative Predictors</p> <p>4.4 Fitting the Model: The Method of Least Squares</p> <p>4.5 Estimation of s2, the Variance of e</p> <p>4.6 Testing the Utility of a Model: The Analysis of Variance F-Test</p> <p>4.7 Inferences About the Individual ß Parameters</p> <p>4.8 Multiple Coefficients of Determination: R2 and R2adj</p> <p>4.9 Using the Model for Estimation and Prediction</p> <p>4.10 An Interaction Model with Quantitative Predictors</p> <p>4.11 A Quadratic (Second-Order) Model with a Quantitative Predictor</p> <p>4.12 More Complex Multiple Regression Models (Optional)</p> <p>4.13 A Test for Comparing Nested Models</p> <p>4.14 A Complete Example</p> <p>&nbsp;</p> <p>Case Study 2: Modeling the Sale Prices of Residential Properties in Four Neighborhoods</p> <p>&nbsp;</p> <p>5. Principles of Model Building</p> <p>5.1 Introduction: Why Model Building is Important</p> <p>5.2 The Two Types of Independent Variables: Quantitative and Qualitative</p> <p>5.3 Models with a Single Quantitative Independent Variable</p> <p>5.4 First-Order Models with Two or More Quantitative Independent Variables</p> <p>5.5 Second-Order Models with Two or More Quantitative Independent Variables</p> <p>5.6 Coding Quantitative Independent Variables (Optional)</p> <p>5.7 Models with One Qualitative Independent Variable</p> <p>5.8 Models with Two Qualitative Independent Variables</p> <p>5.9 Models with Three or More Qualitative Independent Variables</p> <p>5.10 Models with Both Quantitative and Qualitative Independent Variables</p> <p>5.11 External Model Validation</p> <p>&nbsp;</p> <p>6. Variable Screening Methods</p> <p>6.1 Introduction: Why Use a Variable-Screening Method?</p> <p>6.2 Stepwise Regression</p> <p>6.3 All-Possible-Regressions Selection Procedure</p> <p>6.4 Caveats</p> <p>&nbsp;</p> <p>Case Study 3: Deregulation of the Intrastate Trucking Industry</p> <p>&nbsp;</p> <p>7. Some Regression Pitfalls</p> <p>7.1 Introduction</p> <p>7.2 Observational Data Versus Designed Experiments</p> <p>7.3 Parameter Estimability and Interpretation</p> <p>7.4 Multicollinearity</p> <p>7.5 Extrapolation: Predicting Outside the Experimental Region</p> <p>7.6 Variable Transformations</p> <p>&nbsp;</p> <p>8. Residual Analysis</p> <p>8.1 Introduction</p> <p>8.2 Plotting Residuals</p> <p>8.3 Detecting Lack of Fit</p> <p>8.4 Detecting Unequal Variances</p> <p>8.5 Checking the Normality Assumption</p> <p>8.6 Detecting Out</p>