Regression and metric space

#1
Hi,

I have two independent variables X and Y and one dependent variable Z. X alone explains 45 percent of the variation in Z (Rsquare) and Y explains 25 percent of Z. From multiple regression it follows that together X and Y explain 46 percent of the variation in Z.

Now if I consider X-Y samples to be points in a twodimensional space and regress Z on the Mahalanobis of distance of each sample I get an Rsquare which is approximately equal to half of the Rsquare of X (45/2). This is the case with various data sets I have tried.

Am I measuring a new process when I regress Z on Mahalanobis distance date, or am I doing the same as regressing Z on X and Y but with some rescaling?

Thanks in advance,
Senbet