What is Multiple Correlation?

Answer 1

Let me assume that you are familiar with the (Pearson) correlation coefficient. If you estimate how one variable might be a linear function of another (using least-squares) then the measure of how strong the association is is known as that with which you are correlation coefficient. If you generalise by estimating what linear function one variable is of two or more other variables then the measure of how strong the relationship is is the multiple correlation.

For mathematical reasons which may or may not interest you, and which I won't go into here, if we now go backwards we find that the multiple correlation for the situation where one variable is regressed against one other variable is just the square of the Pearson correlation coefficient.

As you probably know, the Pearson ranges from -1 to +1. Because the multiple correlation is the squared value it ranges only from 0 to 1 and can indicate only degree of association, not the sense of direction.