Introduction to Multiple Regression (2 of 3)

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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:

Y' = 0.3764 X1+0.0012 X2 +0.0227X3 -0.1533

where Y' is predicted college GPA, X1 is high school GPA, X2 is SAT (verbal + math), and X3 is a rating of the quality of the letters of recommendation. The Y' scores from this analysis correlate 0.63 with College GPA. Therefore, the multiple correlation (R) is .63. As shown below, the R of 0.63 is higher than the simple correlation between college GPA and any of the other variables. 
Correlations with College GPA
High School GPA           0.55
SAT                       0.52
Quality of letters        0.35

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