The Relationship among Sums of Squares, Correlation Coefficients, and Suppression

We examine the relationship between the extra sum of squares SSR(x 2 |x 1 ), the regression sum of squares SSR(x 2 ), and the correlation coefficients r y1 , r y2 , and r 12 . From this we develop a necessary and sufficient condition for suppression in terms of the correlation coefficients. We use this to investigate the conditions under which suppression can occur algebraically and graphically. We believe that expressing suppression in terms of correlation coefficients may help students and applied researchers to identify cases of suppression and to understand when suppression can occur.