Introduction to Multiple Regression (2 of 3)
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
" 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
where Y' is predicted college GPA, X1
is high school
is SAT (verbal + math), and X3
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
Quality of letters 0.35