14. Multiple Regression

Introduction: Answering Questions with Multiple Regression368
 Multiple Regression versus ANOVA369
 Multiple Regression and Naturally Occurring Variables370
 “Proving” Cause and Effect Relationships372
Background: Predicting a Criterion Variable from Multiple Predictors373
 A Simple Predictive Equation373
 An Equation with Weighted Predictors377
 The Multiple Regression Equation377
The Results of a Multiple Regression Analysis381
 The Multiple Correlation Coefficient381
 Variance Accounted for by Predictor Variables: The Simplest Models381
 Variance Accounted for by Intercorrelated Predictor Variables385
 Testing the Significance of the Difference between Two R2 Values393
 Multiple Regression Coefficients397
Example: A Test of the Investment Model400
Overview of the Analysis401
Gathering and Entering Data402
 The Questionnaire402
 Entering the Data403
Computing Bivariate Correlations with PROC CORR406
 Writing the Program406
 Interpreting the Results of PROC CORR407
Estimating the Full Multiple Regression Equation with PROC REG409
 Writing the Program409
 Interpreting the Results of PROC REG411
Computing Uniqueness Indices with PROC REG415
 Writing the Program415
 Interpreting the Results of PROC REG with SELECTION=RSQUARE417
Summarizing the Results in Tables423
 The Results of PROC CORR423
 The Results of PROC REG424
Getting the Big Picture424
Formal Description of Results for a Paper425
Conclusion: Learning More about Multiple Regression426
Assumptions Underlying Multiple Regression427
References428

Overview

This chapter shows how to perform multiple regression analysis to investigate the relationship between a continuous criterion variable and multiple continuous predictor variables. It describes the different components of the multiple regression equation, and discusses the meaning of R2 and other results from a multiple regression analysis. It shows how bivariate correlations, multiple regression coefficients, and uniqueness indices can be reviewed to assess the relative importance of predictor variables. Fictitious data are examined using PROC CORR and PROC REG to show how the analysis can be conducted and to illustrate how the results can be summarized in tables and in text.


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