A Second Course in Statistics: Regression Analysis

A Review of Basic Concepts (Optional) 1.1 Statistics and Data 1.2 Populations, Samples and Random Sampling 1.3 Describing Qualitative Data 1.4 Describing Quantitative Data Graphically 1.5 Describing Quantitative Data Numerically 1.6 The Normal Probability Distribution 1.7 Sampling Distributions and the Central Limit Theorem 1.8 Estimating a Population Mean 1.9 Testing a Hypothesis about a Population mean 1.10 Inferences about the Difference Between Two Population Means 1.11 Comparing Two Population Variances 2. Introduction to Regression Analysis 2.1 Modeling a Response 2.2 overview of Regression Analysis 2.3 Regression Applications 2.4 Collecting the Data for Regression 3. Simple Linear Regression 3.1 Introduction 3.2 The Straight-Line Probabilistic Model 3.3 Fitting the Model: The Method of Least-Squares 3.4 Model Assumptions 3.5 An Estimator of s2 3.6 Assessing the Utility of the Model: Making Inferences About the Slope A A 1 3.7 The Coefficient of Correlation 3.8 The Coefficient of Determination 3.9 Using the Model for Estimation and Prediction 3.10 A Complete Example 3.11 Regression Through the Origin (Optional) 3.12 A Summary of the Steps to Follow in a Simple Linear Regression Analysis 4. Multiple Regression Models 4.1 General Form of a Multiple Regression Model 4.2 Model Assumptions 4.3 A First-Order Model with Quantitative Predictors 4.4 Fitting the Model: The Method of Least Squares 4.5 Estimation of s2 , the variance of e 4.6 Inferences about the A A parameters 4.7 The Multiple Coefficient of Determination, R2 4.8 Testing the Utility of a Model: The Analysis of Variance F test 4.9 An Interaction Model with Quantitative Predictors 4.10 A Quadratic (Second-Order) Model with a Quantitative Predictor 4.11 Using the model for Estimation and Prediction 4.12 More Complex Multiple Regression Models (Optional) 4.13 A Test for Comparing Nested Models 4.14 A Complete Example 4.15 A Summary of the Steps to Follow in a Multiple Regression Analysis 5. Model Building 5.1 Introduction: Why Model Building is Important 5.2 The Two Types of independent Variables: Quantitative and Qualitative 5.3 Models with a Single Quantitative Independent Variable 5.4 First-Order Models with Two or More Quantitative Independent Variables 5.5. Second-Order Models with Two or More Quantitative Independent Variables 5.6 Coding Quantitative Independent Variables (Optional) 5.7 Models with One Qualitative Independent Variable 5.8 Models with Two Qualitative Independent Variables 5.9 Models with Three or more Qualitative Independent Variables 5.10 Models with Both Quantitative and Qualitative Independent Variables 5.11 External Model Validation (Optional) 5.12 Model Building: An Example 6. Variable Screening Methods 6.1 Introduction: Why Use a Variable Screening Method? 6.2 Stepwise Regression 6.3 All-Posssible-Regressions Selection Procedure 6.4 Caveats 7. Some Regression Pitfalls 7.1 Introduction 7.2 Observational DataVersus Designed Experiments 7.3 Deviating from the Assumptions 7.4 Parameter Estimability and Interpretation 7.5 Multicollinearity 7.6 Extrapolation: Predicting Outside the Experimental Region 7.7 Data Transformations 8. Residual Analysis 8.1 Introduction 8.2 Plotting Residuals and Detecting Lack of Fit 8.3 Detecting Unequal Variances 8.4 Checking the Normality Assumption 8.5 Detecting Outliers and Identifying Influential Observations 8.6 Detecting Residual Correlation: The Durbin-Watson Test 9. Special Topics in Regression (Optional) 9.1 Introduction 9.2 Piecewise Linear Regression 9.3 Inverse Prediction 9.4 Weighted Least Squares 9.5 Modeling Qualitative Dependent Variable 9.6 Logistic Regression 9.7 Ridge Regression 9.8 Robust Regression 9.9 Nonparametric Regression Models 10. Introduction to Time Series Modeling and Forecasting 10.1 What is a Time Series? 10.2 Time Series Components 10.3 Forecasting using Smoothing Techniques (Optional) 10.4 Forecasting: The Regression Approach 10.5 Autocorrelation and Autoregressive Error Models 10.6 Other Models for Autocorrelated Errors (Optional) 10.7 Constructing Time Series Models 10.8 Fitting Time Series Models With Autoregressive Errors 10.9 Forecasting with Time Series Autoregressive Models 10.10 Seasonal Time Series Models: An Example 10.11 Forecasting Using Lagged Values of the Dependent Variable (Optional) 11. Principles of Experimental Design 11.1 Introduction 11.2 Experimental Design Terminology 11.3 Controlling the Information in an Experiment 11.4 Noise-Reducing Designs 11.5 Volume-Increasing Designs 11.6 Selecting the Sample Size 11.7 The Importance of Randomization 12. The Analysis of Variance for Designed Experiments 12.1 Introduction 12.2 The Logic Behind Analysis of Variance 12.3. One-Factor Completely Randomized Designs 12.4 Randomized Block Designs 12.5 Two-Factor Factorial Experiments 12.6 More Complex Factorial Designs (Optional) 12.7 Follow up Analysis: Tukey's Multiple Comparisons of Means 12.8 Other Multiple Comparisons Methods (Optional) 12.9 Checking ANOVA Assumptions 13. CASE STUDY: Modeling the Sale Prices of Residential Properties in Four Neighborhoods 13.1 The Problem 13.2 The Data 13.3 The Theoretical Model 13.4 The Hypothesized Regression Models 13.5 Model Comparisons 13.6 Interpreting the Prediction Equation 13.7 Predicting the Sale Price of a Property 13.8 Conclusions 14. CASE STUDY: An Analysis of Rain Levels in California 14.1 The Problem 14.2 The Data 14.3 A Model for Average Annual Precipitation 14.4 A Residual Analysis of the Model 14.5 Adjustments to the Model 14.6 Conclusions 15. CASE STUDY: Reluctance to Transmit Bad News: the MUM Effect 15.1 The Problem 15.2 The Design 15.3 Analysis of Variance Models and Results 15.4 Follow up Analysis 15.5 Conclusions 16. CASE STUDY: An Investigation of Factors Affecting the Sale Price of Condominium Units Sold at Public Auction 16.1 The Problem 16.2 The Data 16.3 The Models 16.4 The Regression Analyses 16.5 An Analysis of the Residuals form Model 3 16.6 What the Model 3 Regression Analysis Tells Us 16.7 Comparing the Mean Sale Price for Two Types of Units (Optional) 16.8 Conclusions 17. CASE STUDY: Modeling Daily Peak Electricity Demands 17.1 The Problem 17.2 The Data 17.3 The Models 17.4 The Regression and Autoregression Analyses 17.5 Forecasting Daily Peak Electricity Demand 17.6 Conclusions Appendix A: The Mechanics of a Multiple Regression Analysis. Appendix B: A Procedure for Inverting a Matrix. Appendix C: Statistical Tables. Appendix D: SAS for Windows Tutorial. Appendix E: SPSS for Windows Tutorial. Appendix F: MINITAB for Windows Tutorial. Appendix G: Sealed Bid Data for Fixed and Competitive Highway Construction Contracts. Appendix H: Real Estate Appraisals and Sales Data for Six Neighborhoods in Tampa, Florida. Appendix I: Condominium Sales Data. Answers to Odd-Numbered Exercises. Index.