Introduction to Regression Modeling

Cover
Contents
Preface
Chapter 1: Introduction to Regression Models
	1.1 Introduction
	1.2 Examples
	1.3 A General Model
	1.4 Important Reasons for Modeling
	1.5 Data Plots and Empirical Modeling
	1.6 An Iterative Model Building Approach
	1.7 Some Comments on Data
	Exercises
Chapter 2: Simple Linear Regression
	2.1 The Model
	2.2 Estimation of Parameters
	2.3 Fitted Values, Residuals, and the Estimate of o2
	2.4 Properties of Least Squares Estimates
	2.5 Inferences about the Regression Parameters
	2.6 Prediction
	2.7 Analysis of Variance Approach to Regression
	2.8 Another Example
	2.9 Related Models
	Appendix: Univariate Distributions
	Exercises
Chapter 3: A Review of Matrix Algebra and Important Results on Random Vectors
	3.1 Review of Matrix Algebra
	3.2 Matrix Approach to Simple Linear Regression
	3.3 Vectors of Random Variables
	3.4 The Multivariate Normal Distribution
	3.5 Important Results on Quadratic Forms
	Exercises
Chapter 4: Multiple Linear Regression Model
	4.1 Introduction
	4.2 Estimation of the Model
	4.3 Statistical Inference
	4.4 The Additional Sum of Squares Principle
	4.5 The Analysis of Variance and the Coefficient of Determination, R2
	4.6 Generalized Least Squares
	Appendix: Proofs of Results
	Exercises
Chapter 5: Specification Issues in Regression Models
	5.1 Elementary Special Cases
	5.2 Systems of Straight Lines
	5.3 Comparison of Several \"Treatments\"
	5.4 X Matrices with Nearly Linear-Dependent Columns
	5.5 X Matrices with Orthogonal Columns
	Exercises
Chapter 6: Model Checking
	6.1 Introduction
	6.2 Residual Analysis
	6.3 The Effect of Individual Cases
	6.4 Assessing the Adequacy of the Functional Form: Testing for Lack of Fit
	6.5 Variance-Stabilizing Transformations
	Appendix
	Exercises
Chapter 7: Model Selection
	7.1 Introduction
	7.2 All Possible Regressions
	7.3 Automatic Methods
	Exercises
Chapter 8: Case Studies in Linear Regression
	8.1 Educational Achievement of Iowa Students
	8.2 Predicting the Price of Bordeaux Wine
	8.3 Factors Influencing the Auction Price of Iowa Cows
	8.4 Predicting U.S. Presidential Elections
	8.5 Student Projects Leading to Additional Case Studies
	Exercises
Chapter 9: Nonlinear Regression Models
	9.1 Introduction
	9.2 Overview of Useful Deterministic Models, With Emphasis on Nonlinear Growth Curve Models
	9.3 Nonlinear Regression Mode
	9.4 Inference in the Nonlinear Regression Model
	9.5 Examples
	Exercises
Chapter 10: Regression Models for Time Series Situations
	10.1 A Brief Introduction to Time Series Models
	10.2 The Effects of Ignoring the Autocorrelation in the Errors
	10.3 The Estimation of Combined Regression Time Series Models
	10.4 Forecasting with Combined Regression Time Series Models
	10.5 Model-Building Strategy and Example
	10.6 Cointegration and Regression with Time Series Data: An Example
	Exercises
Chapter 11: Logistic Regression
	11.1 The Model
	11.2 Interpretation of the Parameters
	11.3 Estimation of the Parameters
	11.4 Inference
	11.5 Model-Building Approach in the Context of Logistic Regression Models
	11.6 Examples
	11.7 Overdispersion
	11.8 Other Models for Binary Responses
	11.9 Modeling Responses with More Than Two Categorical Outcomes
	Exercises
Chapter 12: Generalized Linear Models and Poisson Regression
	12.1 The Model
	12.2 Estimation of the Parameters in the Poisson Regression Model
	12.3 Inference in the Poisson Regression Model
	12.4 Overdispersion
	12.5 Examples
	Exercises
Brief Answers to Selected Exercises
Statistical Tables
References
List of Data Files
Index