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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?

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  • $\begingroup$ This question does not belong here and I voted to close, but I think it does not hurt to give you an idea of what might happen: you have to recall that correlation only measures the affine dependency between variables, not other kind of dependency. Imagine for example that $Y=X^2$: then $Y$ is entirely determined by the value of $X$, but their correlation can be very weak (it is zero when $X$ has a law symmetric with respect to the origin). On the other hand, $X$ and $Y/X$ are the same variable. $\endgroup$ Aug 7, 2014 at 19:58
  • $\begingroup$ I apologize. Thank you for the insight. $\endgroup$
    – bbush
    Aug 7, 2014 at 20:06

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