Multiple Correlations
A multiple correlation coefficient (R) evaluates the degree of relatedness between a cluster of variables and a single outcome variable. This is a valuable tool for the social science researcher because something as complex as human behavior can rarely be attributed to a single cause. Multiple correlations allow us to examine relationships that are more complex than simple bivariate correlations.
Squaring the multiple correlation coefficient yields the coefficient of determination, symbolized 
. The interpretation of is identical to 
, except that is talking about the set of variables rather than just one.
As a practical matter, the multiple R can be interpreted in the same way as Person’s r except that we must keep in mind that R tells us about how a cluster of variables relates to a criterion variable rather than a single variable. It is important to know that R is more complex than merely the sum of separate r-values. This is so because the formula subtracts out the variance shared between the predictor variables. This means that the greater the correlation between the predictor variables, the less increase you have in R when they are added. The only time that R is the sum of the individual r-values is when the predictor variables are completely unrelated.
Key Terms
Covariance, correlation, Correlation Coefficient, Pearson’s r, Scattergram, Scatterplot, x-axis, y-axis, linear relationship, positive relationship, negative relationship, Inverse Relationship, Direct Relationship, Regression Line, Trendline, Bivariate, Multiple Correlation, Coefficient of Determination
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