I am assuming that we are defining the new variable as a linear combination of 2 "old" ones.

So let's say we have , and we define

whereA,Bare constants, anda,bare the indexes of two of theX's that you are going to combine.

So the correlation coef of this new one versus any old one is:

Let's reduce this to a function of the known variables.

Finally we know

And so we get:

Now you said you have estimates of all these parameters. I can't say how good your corr corf will be, if you stick yourestimatesinto the formula. And looking back at this, maybe I should have started with thesamplecorrelation coefficient formula, rather than with the population. So maybe you might want to rederive what I did using the same version. Ithinkjust trying to do the arithmetic in my head that you will get the same formula except that the population parameters will be replaced with the sample ones (the sample corr coeff just has an (n-1) instead of annin the denominator which will cancel out ).