What does a correlation coefficient mean?
(2) What does a coefficient of determination mean? And, (3) how does the coefficient of determination help put the interpretation of correlation coefficients into perspective? (1) What does a correlation coefficient mean? Correlation was once defined for me by one of my professors at UCLA as the “go-togetherness” of two sets of numbers. That definition has always made sense to me. The degree to which two sets of numbers go together can be calculated statistically as a correlation coefficient1. Correlation coefficients (often symbolized by r, or rxy) can turn out to be as high in a positive direction as +1.00 if the relationship between the two sets of numbers is perfect and in the same direction (as is the case in Table 1 below for Tests A and B). A correlation coefficient can also turn out to be as high in a negative direction as -1.00 if the relationship is perfect and in opposite directions (as is the case in Table 1 for Tests A and C, or B and C). A correlation coefficient can also
