Multiple correlation coefficient in R

Question

I am looking for a way to calculate the multiple correlation coefficient in R http://en.wikipedia.org/wiki/Multiple_correlation, is there a built-in function to calculate it ? I have one dependent variable and three independent ones. I am not able to find it online, any idea ?

Answer 1

The easiest way to calculate what you seem to be asking for when you refer to 'the multiple correlation coefficient' (i.e. the correlation between two or more independent variables on the one hand, and one dependent variable on the other) is to create a multiple linear regression (predicting the values of one variable treated as dependent from the values of two or more variables treated as independent) and then calculate the coefficient of correlation between the predicted and observed values of the dependent variable.

Here, for example, we create a linear model called mpg.model, with mpg as the dependent variable and wt and cyl as the independent variables, using the built-in mtcars dataset:

> mpg.model <- lm(mpg ~ wt + cyl, data = mtcars)

Having created the above model, we correlate the observed values of mpg (which are embedded in the object, within the model data frame) with the predicted values for the same variable (also embedded):

> cor(mpg.model$model$mpg, mpg.model$fitted.values)
[1] 0.9111681

R will in fact do this calculation for you, but without telling you so, when you ask it to create the summary of a model (as in Brian's answer): the summary of an lm object contains R-squared, which is the square of the coefficient of correlation between the predicted and observed values of the dependent variable. So an alternative way to get the same result is to extract R-squared from the summary.lm object and take the square root of it, thus:

> sqrt(summary(mpg.model)$r.squared)
[1] 0.9111681

I feel that I should point out, however, that the term 'multiple correlation coefficient' is ambiguous.