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Commonality analysis is a procedure for decomposing the coefficient of determination (R superscript 2) in multiple regression analyses into the percent of variance in the dependent variable associated with each independent variable uniquely, and the proportion of explained variance associated with the common effects of predictors in various combinations. Commonality analysis is an attempt to understand the relative predictive power of regressor variables, both individually and in combination. Despite their utility, these methods have not been used with great frequency, perhaps because these methods are not fully automated in commonly used statistical packages. This paper explores the applications of commonality analyses by reanalyzing data from a study of the relationships among anger and stress in predicting depression among 247 undergraduate students. This data set is employed as a heuristic to make the discussion more accessible. In addition, a Statistical Analysis System (SAS) computer program procedure for obtaining all possible R superscript 2 values is discussed as an efficient method of implementing the required analyses. Two tables and one chart are appended. (Contains 13 references.) (Author/SLD)

The Pearson product-moment correlation, r, is commonly applied in educational research. Almost all researchers realize that r ranges between -1.00 and +1.00, and that negative coefficients indicate that the bivariate relationship is inverse. Researchers also recognize that the Pearson r only evaluates linear relationship, and is not sensitive to curvilinear relationship. However, few researchers, if pressed, could explain exactly what makes r negative or positive, from a mathematical point of view, even though most researchers know what such results mean. The present paper explores the factors that affect r, including those that impact its sign. The reasons for preferring r over the covariance are explored. Small data sets and graphs are employed to make the discussion concrete. Four figures, four tables. (Contains 8 references.) (Author)