General question about correlations: If A is correlated w/ B, and B is correlated w/

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I was wondering, if A is correlated with B, and B is correlated with C, does that always mean A is correlated with C? For the sake of argument let's say the correlation is a Pearson's r coefficient.
In addition, if A and B is 0.4, and B and C is 0.15, is there a way of calculating A and C without using all of the individual observations again, only from the rs of A and B and B and C?
 
I was wondering, if A is correlated with B, and B is correlated with C, does that always mean A is correlated with C? For the sake of argument let's say the correlation is a Pearson's r coefficient.
In addition, if A and B is 0.4, and B and C is 0.15, is there a way of calculating A and C without using all of the individual observations again, only from the rs of A and B and B and C?

The quick answer is that the Pearson correlation coefficient is not transitive.

Here is a discussion of your question: Sotos paper.
 
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