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

Understanding and Interpreting Regression Parameter Estimates in Given Contexts: A Monte Carlo Study of Characteristics of Regression and Structural Coefficients, Effect Size R Squared and Significance Level of Predictors. - Download this document for free, or read online. Document in PDF available to download.

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)

Descriptors: Effect Size, Estimation (Mathematics), Mathematical Models, Monte Carlo Methods, Predictor Variables, Regression (Statistics), Sample Size

Author: Jiang, Ying Hong; Smith, Philip L.

Source: https://eric.ed.gov/?q=a&ft=on&ff1=dtySince_1992&pg=9066&id=ED470301