Measuring the Importance of Variables in Multiple Regression (3 of 3)
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