Next section: Regression toward the mean

It is important to bear in mind that the usefulness of a variable refers specifically to the usefulness of a variable when the other variables are included in the regression equation. For instance, although the Letters of Recommendation add practically nothing to the ability to predict College GPA once High School GPA and SAT are known, they are somewhat predictive of College GPA when taken alone: The Pearson correlation between Letters of Recommendation and College GPA is 0.35.

In sum, the usefulness of a variable refers how much it adds to the predictability of the criterion over and above the other predictor variables in the equation. If two predictor variables are highly correlated, then neither will contribute much to the prediction above and beyond the other.

Next section: Regression toward the mean