Understanding Regression Analysis,9780306484339

Understanding Regression Analysis

by
ISBN13: 9780306484339
ISBN10: 0306484331
Format: Paperback
Pub. Date: 2004-05-30
Publisher(s): Kluwer Academic Pub
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Summary

By assuming it is possible to understand regression analysis without fully comprehending all its underlying proofs and theories, this introduction to the widely used statistical technique is accessible to readers who may have only a rudimentary knowledge of mathematics. Chapters discuss: -descriptive statistics using vector notation and the components of a simple regression model; -the logic of sampling distributions and simple hypothesis testing; -the basic operations of matrix algebra and the properties of the multiple regression model; -testing compound hypotheses and the application of the regression model to the analyses of variance and covariance, and -structural equation models and influence statistics.

Table of Contents

1 The Origins and Uses of Regression Analysis
1(5)
2 Basic Matrix Algebra: Manipulating Vectors
6(5)
3 The Mean and Variance of a Variable
11(5)
4 Regression Models and Linear Functions
16(5)
5 Errors of Prediction and Least-Squares Estimation
21(5)
6 Least-Squares Regression and Covariance
26(5)
7 Covariance and Linear Independence
31(5)
8 Separating Explained and Error Variance
36(5)
9 Transforming Variables to Standard Form
41(5)
10 Regression Analysis with Standardized Variables 46(5)
11 Populations, Samples, and Sampling Distributions 51(5)
12 Sampling Distributions and Test Statistics 56(5)
13 Testing Hypotheses Using the t Test 61(5)
14 The t Test for the Simple Regression Coefficient 66(5)
15 More Matrix Algebra: Manipulating Matrices 71(5)
16 The Multiple Regression Model 76(5)
17 Normal Equations and Partial Regression Coefficients 81(5)
18 Partial Regression and Residualized Variables 86(5)
19 The Coefficient of Determination in Multiple Regression 91(5)
20 Standard Errors of Partial Regression Coefficients 96(5)
21 The Incremental Contributions of Variables 101(5)
22 Testing Simple Hypotheses Using the F Test 106(3)
23 Testing Compound Hypotheses Using the F Test 109(4)
24 Testing Hypotheses in Nested Regression Models 113(5)
25 Testing for Interaction in Multiple Regression 118(5)
26 Nonlinear Relationships and Variable Transformations 123(5)
27 Regression Analysis with Dummy Variables 128(5)
28 One-Way Analysis of Variance Using the Regression Model 133(5)
29 Two-Way Analysis of Variance Using the Regression Model 138(5)
30 Testing for Interaction in Analysis of Variance 143(4)
31 Analysis of Covariance Using the Regression Model 147(5)
32 Interpreting Interaction in Analysis of Covariance 152(4)
33 Structural Equation Models and Path Analysis 156(5)
34 Computing Direct and Total Effects of Variables 161(5)
35 Model Specification in Regression Analysis 166(5)
36 Influential Cases in Regression Analysis 171(5)
37 The Problem of Multicollinearity 176(5)
38 Assumptions of Ordinary Least-Squares Estimation 181(5)
39 Beyond Ordinary Regression Analysis 186(5)
Appendix A: Derivation of the Mean and Variance of a Linear Function 191(4)
Appendix B: Derivation of the Least-Squares Regression Coefficient 195(3)
Appendix C: Derivation of the Standard Error of the Simple Regression Coefficient 198(4)
Appendix D: Derivation of the Normal Equations 202(3)
Appendix E: Statistical Tables 205(5)
Suggested Readings 210(3)
Index 213

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