Sometimes R 2 > r 2 yx 1 + r 2 yx 2 : Correlated Variables are Not Always Redundant

An extreme example of regression on two variables is presented in which there is almost no correlation between y and x 1 and y and x 2, yet the coefficient of determination is 1.This example illustrates the often counter-intuitive nature of multivariate relationships and is also relevant to discussions on multicollinearity and variable selection techniques.