Suppose we wish to predict a criterion variable Y from a number of predictor variables X1, X2, . . . Xp. For example, we may wish to predict a measure of success in graduate school on the basis of undergraduate grades and verbal and quantitative Graduate Record Exam scores. Using the procedures of multiple regression, we can find the equation of the form
Y = b0 + b1X1 + b2 X2 + + bpXp that optimally predicts Y. The multiple correlation coefficient, Ry 12 , is simply the Pearson product-moment correlation coefficient between the predicted and actual Y scores.
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