Equations for deriving effect sizes for individual predictors and sets of predictors under specified conditions in multiple regression analysis: A technical report

Abstract

This technical report provides equations for deriving effect sizes for individual predictors and sets of predictors under specified conditions in multiple regression (MR) analyses. The effect size metric being obtained in each instance is either Pearson r or else proportion of variance explained, expressed as R-squared or semi-partial r-squared. For example, when individual predictors’ unstandardized regression weights (bi) are given along with the overall R-squared of the MR equation, their effect sizes are obtainable as semi-partial r-squared values by use of equation (5). Although the equations are not original (with their sources properly cited), having collected them and transformed them (algebraically) in this report may be helpful to readers of existing research who want to derive effect sizes from MR analysis components however they have been reported.