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I want to know if

corr({a,b},c) = 0

is the same as saying that

corr(a,c) = 0

corr(b,c) = 0

But that the first is just a short-hand way of writing it.

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  • $\begingroup$ I haven't seen it being used this way but if you explicitly define it I think it can make sense in certain contexts. But I don't think it is a standard notation. $\endgroup$ – flawr Apr 16 at 7:22
  • $\begingroup$ I too think it looks weird. What is done is two regressions Y1 = B1*X1 + G1*X2 + a (error term) and then this Y2 = B2*X1 + G2*X2 + b (error term) these two error terms have to be uncorrelated with another error term, a. Don't know if that helps interpreting my question $\endgroup$ – Emil Krabbe Apr 16 at 7:46
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What is common is applying function to sets.
So if we have sets $M,N$, then $$corr(M,N) = \{ corr(m,n) \mid m \in M, n \in N\},$$

meaning that we apply the function to all elements. You would still need to define this term before using it, but no one should be surprised by it.

Now for your special case, you want $M = \{a,b\}$, $N = \{c\}$ and $corr(M,N) = \{0\}$. You could even define that $corr(M,N) = 0$ means that every element in $corr(M,N)$ is zero, this is also a common occurrence to save parentheses (e.g. when discussing vector spaces).

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  • $\begingroup$ So am I correct in my question that these two statements are correct? Is it right to just write the two equations instead of the one complicating one $\endgroup$ – Emil Krabbe Apr 17 at 8:36
  • $\begingroup$ It is always ok to write the two equations. If you want to write just a single one, define and explain it at some point. Because, as you noticed yourself, it might be complicated for a reader to understand. $\endgroup$ – Dirk Apr 18 at 7:14
  • $\begingroup$ I think for my own sake I just keep it as two separate ones. $\endgroup$ – Emil Krabbe Apr 18 at 7:54

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