The multiple correlation coefficient (R) is the Pearson correlation between the predicted scores and the observed scores (Y' and Y). Just as r² is the proportion of the sum of squares explained in one-variable regression, R² is the proportion of the sum of squares explained in multiple regression. These concepts can be understood more concretely in terms of an example.

The dataset "Multiple regression example" contains hypothetical data for the college admissions problem discussed on the previous page. The regression equation for these data is:

where Y' is predicted college GPA, XY' = 0.3764 X

_{1}+0.0012 X_{2}+0.0227X_{3}-0.1533

Correlations with College GPAHigh School GPA 0.55 SAT 0.52 Quality of letters 0.35