# Relationship between Pearson correlation values [duplicate]

If I know the Pearson correlation between A and B and also know the Pearson correlation between A and C, can I infer anything about the correlation between B and C?

Assume that I no longer have access to the raw values for A, B, and C.

• This is becoming a FAQ: some version of this question is asked every few months. If you're really good at searching (I found a near duplicate at stats.stackexchange.com/questions/72790 by including "correlation" and "three" in the search terms, but that didn't quite work out and I had to look much harder) you ought to be able to find quite a few good and interesting answers. – whuber Aug 10 '15 at 19:31
• Thanks for the link. I wasn't quite sure how to formulate a good search on this topic. – Mike A. Aug 10 '15 at 20:03
• @MikeA. When you're wondering whether such a general statement is true a good strategy is often to look for a single counterexample. Here it's not difficult. Take $A$, $B$ and $C$ to have common pairwise correlation $\rho$. Now take $A^\prime$, $B^\prime$ and $C^\prime$ to be such that $A^\prime$ and $B^\prime$ have correlation $\rho$, but $A^\prime = C^\prime$ so that $B^\prime$ and $C^\prime$ also have correlation $\rho$. You clearly can't infer the correlation between the first and third based on the other two correlations. – dsaxton Aug 10 '15 at 20:44