APA Dictionary of Psychology

(symbol: R²) a numerical index that reflects the degree to which variation in a response or outcome variable (e.g., workers’ incomes) is accounted for by its relationship with two or more predictor variables (e.g., age, gender, years of education). More specifically, it is a measure of the percentage of variance in a dependent variable that is accounted for by its relationship with a weighted linear combination of a set of independent variables. Obtained by multiplying the value of the multiple correlation coefficient (R) by itself, the coefficient of multiple determination ranges in value from 0 to 1. Low values indicate that the outcome is relatively unrelated to the predictors, whereas values closer to 1 indicate that the outcome and the predictors are highly related. For example, if R = .40, then the coefficient of multiple determination is .40² = .16 and interpreted to mean 16% of the variance in outcome is explainable by the set of predictors. Also called multiple correlation coefficient squared; squared multiple correlation coefficient.