Second Course in Statistics, A: Regression Analysis, 8th edition

1. 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 σ²
• 3.6 Assessing the Utility of the Model: Making Inferences About the Slope β₁
• 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)
• Case Study 1: Legal Advertising–Does It Pay?

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 σ², the Variance of ε
• 4.6 Testing Overall Model Utility: The Analysis of Variance F-Test
• 4.7 Inferences About the Individual β Parameters
• 4.8 Multiple Coefficients of Determination: R² and R²_adj
• 4.9 Using the Model for Estimation and Prediction
• 4.10 An Interaction Model with Quantitative Predictors
• 4.11 A Quadratic (Second-Order) Model with a Quantitative Predictor
• 4.12 More Complex Multiple Regression Models (Optional)
• 4.13 A Test for Comparing Nested Models
• 4.14 A Complete Example
• Case Study 2: Modeling the Sale Prices of Residential Properties in Four Neighborhoods

5. Principles of 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

6. Variable Screening Methods

• 6.1 Introduction: Why Use a Variable-Screening Method?
• 6.2 Stepwise Regression
• 6.3 All-Possible-Regressions-Selection Procedure
• 6.4 Caveats
• Case Study 3: Deregulation of the Intrastate Trucking Industry

7. Some Regression Pitfalls

• 7.1 Introduction
• 7.2 Observational Data Versus Designed Experiments
• 7.3 Parameter Estimability and Interpretation
• 7.4 Multicollinearity
• 7.5 Extrapolation: Predicting Outside the Experimental Region
• 7.6 Variable 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 Detection of Residual Correlation: The Durbin-Watson Test
• Case Study 4: An Analysis of Rain Levels in California
• Case Study 5: Factors Affecting the Sale Price of Condominium Units Sold at Public Auction

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 Variables
• 9.6 Logistic Regression
• 9.7 Poisson Regression
• 9.8 Ridge and Lasso Regression
• 9.9 Robust Regression
• 9.10 Nonparametric Regression Models

10. 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)
• Case Study 6: Modeling Daily Peak Electricity Demands

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 an 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
• Case Study 7: Voice Versus Face Recognition -- Does One Follow the Other?

Appendices

• A: Derivation of the Least Squares Estimates of β₀ and β₁ in Simple Linear Regression
• A.1 Introduction
• A.2 Matrices and Matrix Multiplication
• A.3 Identity Matrices and Matrix Inversion
• A.4 Solving Systems of Simultaneous Linear Equations
• A.5 The Least Squares Equations and Their Solution
• A.6 Calculating SSE and s²
• A.7 Standard Errors of Estimators, Test Statistics, and Confidence Intervals for β₀, β₁, ... , β_k
• A.8 A Confidence Interval for a Linear Function of the β Parameters and for E(y)
• A.9 A Prediction Interval for Some Value of y to be Observed in the Future
• B: The Mechanics of a Multiple Regression Analysis
• C: A Procedure for Inverting a Matrix
• D: Statistical Tables
• Table 1: Normal Curve Areas
• Table 2: Critical Values for Student's t
• Table 3: Critical Values for the F Statistic: F_.10
• Table 4: Critical Values for the F Statistic: F_.05
• Table 5: Critical Values for the F Statistic: F_.025
• Table 6: Critical Values for the F Statistic: F_.01
• Table 7: Critical Values for the Durbin-Watson d Statistic (α=.05)
• Table 8: Critical Values for the Durbin-Watson d Statistic (α=.01)
• Table 9: Critical Values for the X²-Statistic
• Table 10: Percentage Points of the Studentized Range, q(p,v), Upper 5%
• Table 11: Percentage Points of the Studentized Range, q(p,v), Upper 1%
• E: File Layouts for Case Study Data Sets

  Answers to Odd Numbered Exercises

  Index

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