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