# Measuring the Importance of Variables in Multiple Regression (2 of 3)

Only when it can be assumed that all variables that are correlated with any of the predictor variables and the criterion are included in the analysis can one begin to consider making causal inferences. It is doubtful that this can ever can be assumed validly except in the case of controlled experiments.

One measure of the importance of a variable in prediction is called the "usefulness" of the variable. Usefulness is defined as the drop in the R² that would result if the variable were not included in the regression analysis. For example, consider the problem of predicting college GPA. The multiple R² when College GPA is predicted by High School GPA, SAT, and Letters of recommendation is 0.3997. In a regression analysis conducted predicting College GPA from just High School GPA and SAT, R² = 0.3985. Therefore the usefulness of Letters of Recommendation is only: 0.3997 - 0.3985 = 0.0012.

On the other hand, leaving out SAT and predicting College GPA from High School GPA and Letters of Recommendation yields an R² = 0.3319. Therefore, the usefulness of SAT is 0.3997 - 0.3319 = 0.068.