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I am working with some data in which two component scores X and Y are added together to make a total score X + Y. Is there any known relationship between the correlation R for X vs. X + Y and the R for Y vs. X + Y?

I've played around a little bit, but I am not seeing anything except in the case where X and Y themselves are uncorrelated. (In that case, the R2 values sum to 1.)

ETA: With all due respect, this question is NOT a duplicate of the one already cited. I made abundantly clear that I am not talking about cases in which the variables have no correlation, which is a key feature of the other question. I am asking a much broader question.

denn333
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    The correlation between $X$ and $X + Y$ will depend on their variances and their covariance. That's evident from the formula, but it also follows that there is no general effect. The point about the correlation between $X$ and $X + Y$ when $X, Y$ are uncorrelated is that it provides a benchmark for the inbuilt correlation even where there is no "real" relationship. I don't see how you can get further without either special assumptions or simulations for plausible cases. It is evident from the case $Y = a + bX, b > 0,$ that the correlation could be as high as $+1$. – Nick Cox Mar 29 '14 at 16:28
  • Because questions about correlations are equivalent to questions about covariances, http://stats.stackexchange.com/questions/38721 ("Covariance of a variable and a linear combination of other variables") documents the relationship sought in this question. – whuber Mar 29 '14 at 20:39
  • No, it really doesn't. Read the question more carefully along with the answer I will post momentarily. – denn333 May 19 '14 at 22:41
  • Here is an ACTUAL answer to my question. [link](http://www.gymter.net/CorrelationsOfSums.pdf) I'll add that I don't appreciate that @ttnphns marked this question "answered" when the answer they cited addressed only a very narrow case. Of course, I had already read the answer, and I find it offensive that these two people would not only mark a question answered that was not answered but also do such a thing without even ASKING whether I had seen that previous question. – denn333 May 19 '14 at 22:51
  • Above comment is directed to @Peter-Flom as well. – denn333 May 19 '14 at 22:52
  • Please do not be offended with people who are trying to help you. I agree that the question marked as a duplicate isn't really one. But the one I pointed to earlier, as well as others such as http://stats.stackexchange.com/questions/31177, clearly address the relationships among the covariances, which *a fortiori* tell you that there are indeed "known relationships", and the original comment by @Nick Cox provides the perspective needed to appreciate both the breadth of this information as well as its (unavoidable) limitations. – whuber Aug 09 '14 at 19:57
  • That's incorrect, @whuber. Contrary to what Nick Cox said, and what you seem to be backing up, I indeed was able to go quite a bit further; see the link I posted in May. This question needs to be unmarked a duplicate, as the answer is not at any of those locations — not even close. – denn333 Aug 10 '14 at 00:00

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