I apologize in advance if I overstep my (relatively minimal) statistical knowledge.
I am looking at two random variables X and Y, and am unhappy with the correlation between the two. On a whim, I looked at Corr(X, Y / X). Surprisingly (to me), this provided much better results. This is quite interesting, as this allows me to recover information about Y with much higher accuracy (in this case) if X is known.
I attempted to expand Corr(X, Y / X) and see if I could discover why this might be, but am a bit beyond my capability.
Is there anything to be said about this?