Understanding and Interpreting Regression Parameter Estimates in Given Contexts: A Monte Carlo Study of Characteristics of Regression and Structual Coefficients, Effect Size R Squared and Significance Level of Predictors

This Monte Carlo study explored relationships among standard and unstandardized regression coefficients, structural coefficients, multiple R_ squared, and significance level of predictors for a variety of linear regression scenarios. Ten regression models with three predictors were included, and four conditions were varied that were expected to have influences on the relationship under investigation: (1) magnitude of direct effect from predictors to the outcome variable; (2) colinearity; (3) sample sizes; and (4) model misspecification. Results show that regression parameter estimates behave differently under influences of strength of direct effect of predictors, sample size, and collinearity conditions. Although all the parameter estimates are sensitive to variations of strengths of predictors' effects, some parameter estimates are vulnerable to variations of sample size and collinearity conditions. Standard regression coefficients Beta exhibit the best performance under these specific conditions. Structural coefficients, on the other hand, show relatively less sensitivity to variations of strength of direct effect of predictors, and are very vulnerable to collinearity conditions. R_Squared issensitive to strength of direct effect of predictors; it is vulnerable somewhat to collinearity conditions. Significance level of predictors is most sensitive to variations of strength of direct effect of predictors than structural coefficients; meanwhile,'it is largely vulnerable to sample size and somewhat vulnerable to collinearity conditions. One appendix contains 10 models, and the other contains the study tables. (Contains 10 figures (models), 17 tables, and 6 references.) (Author/SLD) Reproductions supplied by EDRS are the best that can be made from the original document. PERMISSION TO REPRODUCE AND DISSEMINATE THIS MATERIAL HAS BEEN GRANTED BY TO THE EDUCATIONAL RESOURCES INFORMATION CENTER (ERIC) U.S. DEPARTMENT OF EDUCATION Office of Educational Research and Improvement EDUCATIONAL RESOURCES INFORMATION CENTER (ERIC) This document has been reproduced as received from the person or organization originating it. 1:1 Minor changes have been made to improve reproduction quality. e Points of view or opinions stated in this document do not necessarily represent official OERI position or policy. Understanding and Interpreting Regression Parameter Estimates in Given Contexts: A Monte Carlo Study of Characteristics of Regression and Structual Coefficients, Effect Size R Squared and Significance Level of Predictors Ying Hong Jiang, Azusa Pacific University Philip L. Smith, University of Wisconsin-Milwaukee Paper Presented at American Educational Research Association Annual Meeting, 2002, New Orleans 2 3337 COPY AVAIILA 1