Correlation among a paired multiple vairable for a special case

#1
Hi all,

I've run into a stats problem that I can't figure out. I have a pair of linked variables (x,y) that I want to correlate with a third variable (z). I don't want to do a multiple regression, because I'm not interested in how the the two variables explain the third independent of each other, or to get a regression equation, and I'm more interested in something like a pearson's correlation coefficient and statistical significance.

In this case, x and y represent two biological morphometrics describing one specific attribute, and vary together in a paired fashion with that attribute, while the third variable, z is an ecological factor.

Is there a way to treat x and y as a single unit and correlate it to z? I'm not interested on how x and y behave independently, only as a single linked unit. Unfortunately, I can't just take a ratio and do a simple linear correlation, because with the data I have it won't be accurate enough. I've searched online, and I can't find anything that sounds like this.

The data structure I suppose would look like this

(x1,y1)=z1
(x2,y2)=z2
.
.
.(xN,yN)=zN
 
#2
One way is to do the multiple regression and to ignore everything except the Rsq value. This is the square of the multiple correlation coefficient which will be positive or negative according to whether high z values tend to be associated with high or low xy pairs.