Introduction to Regression Modeling (with CD-ROM)

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ISBN: 9780534420758 | 0534420753
Cover: Hardcover
Copyright: 1/20/2005

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Using a data-driven approach, this book is an exciting blend of theory and interesting regression applications. Students learn the theory behindregression while actively applying it. Working with many case studies, projects, and exercises from areas such as engineering, business, social sciences, and the physical sciences, students discover the purpose of regression and learn how, when, and where regression models work. The book covers the analysis of observational data as well as of data that arise from designed experiments. Special emphasis is given to the difficulties when working with observational data, such as problems arising from multicollinearity and "messy" data situations that violate some of the usual regression assumptions. Throughout the text, students learn regression modeling by solving exercises that emphasize theoretical concepts, by analyzing realdata sets, and by working on projects that require them to identify a problem of interest and collect data that are relevant to the problem'ssolution. The book goes beyond linear regression by covering nonlinear models, regression models with time series errors, and logistic andPoisson regression models.

Introduction to Regression Models

(25)

Introduction

(1)

Examples

(13)

Payout of an Investment

(1)

Period of Oscillation of a Pendulum

(1)

Salary of College Teachers

(2)

Hardness Data

(2)

Urea Formaldehyde Foam Insulation

(2)

Oral Contraceptive Data

(2)

Gas Consumption Data

(4)

A General Model

(1)

Important Reasons for Modeling

(1)

Data Plots and Empirical Modeling

(4)

An Iterative Model Building Approach

(1)

Some Comments on Data

(4)

Exercises

(3)

Simple Linear Regression

(41)

The Model

(1)

Important Assumptions

(1)

Objectives of the Analysis

(1)

Estimation of Parameters

(2)

Maximum Likelihood Estimation

(1)

Least Squares Estimation

(1)

Fitted Values, Residuals, and the Estimate of σ2

(2)

Consequences of the Least Squares Fit

(1)

Estimation of σ2

(1)

Least Squares Calculations for the Hardness Example

(1)

Properties of Least Squares Estimates

(2)

Expected Values of Least Squares Estimates

(1)

Variances of Least Squares Estimates

(1)

Inferences about the Regression Parameters

(5)

Inference about β1

(3)

Inference about μ0 = β0 + β1x0

(1)

Hardness Example Continued

(1)

Prediction

(3)

Hardness Example Continued

(1)

Analysis of Variance Approach to Regression

(5)

Coefficient of Determination: R2

(1)

Hardness Example Continued

(1)

Another Example

(5)

Related Models

(16)

Regression through the Origin

(1)

The Case of Random x's

(1)

Appendix: Univariate Distributions

(3)

Exercises

(11)

A Review of Matrix Algebra and Important Results on Random Vectors

(20)

Review of Matrix Algebra

(7)

Matrix Approach to Simple Linear Regression

(2)

Least Squares

(2)

Hardness Example

(1)

Vectors of Random Variables

(4)

The Multivariate Normal Distribution

(2)

Important Results on Quadratic Forms

(5)

Exercises

(4)

Multiple Linear Regression Model

(57)

Introduction

(3)

Two Examples

(2)

The General Linear Model

(1)

Estimation of the Model

(12)

A Geometric Interpretation of Least Squares

(4)

Useful Properties of Estimates and Other Related Vectors

(4)

Preliminary Discussion of Residuals

(3)

Statistical Inference

102

(10)

Confidence Intervals and Tests of Hypotheses for a Single Parameter

102

(6)

Prediction of a New Observation

108

(4)

The Additional Sum of Squares Principle

112

(9)

Introduction

112

(2)

Test of a Set of Linear Hypotheses

114

(6)

Joint Confidence Regions for Several Parameters

120

(1)

The Analysis of Variance and the Coefficient of Determination, R2

121

(4)

Coefficient of Determination, R2

124

(1)

Generalized Least Squares

125

(19)

Introduction

125

(3)

Generalized Least Squares Estimation

128

(1)

Weighted Least Squares

129

(1)

Appendix: Proofs of Results

130

(4)

Exercises

134

(10)

Specification Issues in Regression Models

144

(25)

Elementary Special Cases

144

(3)

One-Sample Problem

144

(1)

Two-Sample Problem

145

(1)

Polynomial Models

146

(1)

Systems of Straight Lines

147

(4)

Comparison of Several ``Treatments''

151

(3)

X Matrices with Nearly Linear-Dependent Columns

154

(6)

Detection of Multicollinearity

158

(1)

Guarding against Multicollinearity

159

(1)

X Matrices with Orthogonal Columns

160

(9)

Exercises

163

(6)

Model Checking

169

(53)

Introduction

169

(1)

Residual Analysis

170

(12)

Residuals and Residual Plots

170

(3)

Added Variable Plots

173

(4)

Checking the Normality Assumption

177

(1)

Serial Correlation among the Errors

177

(5)

Example: Residual Plots for the UFFI Data

182

(1)

The Effect of Individual Cases

182

(17)

Outliers

182

(4)

Leverage and Influence Measures

186

(6)

Example: Forestry Data

192

(7)

Assessing the Adequacy of the Functional Form: Testing for Lack of Fit

199

(6)

Lack-of-Fit Test with More Than One Independent Variable

204

(1)

Variance-Stabilizing Transformations

205

(17)

Box--Cox Transformations

206

(1)

Several Useful Results for Logarithmic Transformations

207

(1)

Appendix

208

(2)

Exercises

210

(12)

Model Selection

222

(23)

Introduction

222

(5)

All Possible Regressions

227

(7)

R2, Radj, S2, and Akaike's Information Criterion

227

(4)

Cp Statistic

231

(2)

Press Statistic

233

(1)

Automatic Methods

234

(11)

Forward Selection

234

(2)

Backward Elimination

236

(1)

Stepwise Regression

237

(1)

Exercises

238

(7)

Case Studies in Linear Regression

245

(43)

Educational Achievement of Iowa Students

245

(8)

Analysis of Achievement Scores

246

(3)

Analysis of Teacher Salaries

249

(3)

Concluding Comments

252

(1)

Predicting the Price of Bordeaux Wine

253

(5)

Factors Influencing the Auction Price of Iowa Cows

258

(8)

Predicting U.S. Presidential Elections

266

(14)

A Purely Economics-Based Model Proposed by Ray Fair

266

(8)

Prediction Models Proposed by Political Scientists

274

(4)

Concluding Comments

278

(2)

Student Projects Leading to Additional Case Studies

280

(8)

Exercises

283

(5)

Nonlinear Regression Models

288

(19)

Introduction

288

(1)

Overview of Useful Deterministic Models, With Emphasis on Nonlinear Growth Curve Models

289

(4)

Nonlinear Regression Models

293

(1)

Inference in the Nonlinear Regression Model

294

(5)

The Newton-Raphson Method of Determining the Minimum of a Function

294

(2)

Application to Nonlinear Regression: Newton--Raphson and Gauss-Newton Methods

296

(1)

Standard Errors of the Maximum Likelihood Estimates

297

(2)

Implementation Issues

299

(1)

Examples

299

(8)

Example 1: Loss in Chlorine Concentration

299

(3)

Example 2: Shoot Length of Plants Exposed to Gamma Irradiation

302

(3)

Exercises

305

(2)

Regression Models for Time Series Situations

307

(36)

A Brief Introduction to Time Series Models

307

(6)

First-Order Autoregressive Model

307

(3)

Random Walk Model

310

(1)

Second-Order Autoregressive Model

311

(1)

Noisy Random Walk Model

311

(1)

Summary of Time Series Models

312

(1)

Remark

313

(1)

The Effects of Ignoring the Autocorrelation in the Errors

313

(3)

Inefficiency of Least Squares Estimation

313

(2)

Spurious Regression Results When Nonstationary Errors Are Involved

315

(1)

The Estimation of Combined Regression Time Series Models

316

(4)

A Regression Model with First-Order Autoregressive Errors

316

(3)

Regression Model with Noisy Random Walk Errors

319

(1)

Forecasting With Combined Regression Time Series Models

320

(4)

Forecasts from the Regression Model with First-Order Autoregressive Errors

321

(1)

Forecasts from the Regression Model with Errors Following a Noisy Random Walk

322

(1)

Forecasts When the Explanatory Variable Must Be Forecast

323

(1)

Model-Building Strategy and Example

324

(3)

Cointegration and Regression with Time Series Data: An Example

327

(16)

Exercises

334

(9)

Logistic Regression

343

(39)

The Model

343

(3)

Interpretation of the Parameters

346

(4)

Relationship between Logistic Regression and the Analysis of 2 x 2 Contingency Tables

347

(2)

Another Advantage of Modeling Odds Ratios by Logistic Regression

349

(1)

Estimation of the Parameters

350

(3)

Inference

353

(3)

Likelihood Ratio Tests

353

(1)

Deviance

354

(1)

Standard Errors of the Maximum Likelihood Estimates

355

(1)

Model-Building Approach in the Context of Logistic Regression Models

356

(4)

Preliminary Model Specification

356

(1)

Assessing Model Fit

357

(2)

Model Diagnostics

359

(1)

Examples

360

(12)

Example 1: Death Penalty and Race of the Victim

360

(4)

Example 2: Hand Washing in Bathrooms at the University of Iowa

364

(2)

Example 3: Survival of the Donner Party

366

(6)

Overdispersion

372

(1)

Other Models for Binary Responses

373

(1)

Modeling Responses with More Than Two Categorical Outcomes

374

(8)

Exercises

377

(5)

Generalized Linear Models and Poisson Regression

382

(21)

The Model

382

(1)

Estimation of the Parameters in the Poisson Regression Model

383

(2)

Inference in the Poison Regression Model

385

(2)

Likelihood Ratio Tests

385

(1)

Standard Errors of the Maximum Likelihood Estimates the Wald Tests

386

(1)

Overdispersion

387

(2)

Examples

389

(14)

Example 1: Mating Success of African Elephants

389

(6)

Example 2: Reproduction of Ceriodaphnia Organisms

395

(4)

Exercises

399

(4)

Answers to Selected Exercises

403

(11)

Statistical Tables

414

(7)

References

421

(4)

List of Data Files

425

(2)

Index

427

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Introduction to Regression Modeling (with CD-ROM)

Summary

Table of Contents

Supplemental Materials