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I have a dataset which has a lot of vectors that are not equal to each other. I would like to confirm that they are all independent and uncorrelated. Just in the interest of making this task easier?

Is it safe to assume that if $Cor(X,Y) = 0$ and $Cor(X,Z) = 0$ then $Cor(Y,Z) = 0$?

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No, the assumption is not correct.

A counterexample is when $Y=kZ$ where $k \ne 0$ and hence $cor(X,Y)=cor(X,Z)$ but $Cor(Y,Z) \ne 0$.

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  • $\begingroup$ Since user specifically says vectors are unequal you might want to complicate the counter example slightly and let $Z=AY$ with $A$ some deterministic transform. $\endgroup$
    – Jesper for President
    Feb 9, 2020 at 11:09
  • $\begingroup$ oops, i missing the unequal part. thanks. $\endgroup$
    – Siong Thye Goh
    Feb 9, 2020 at 11:15
  • $\begingroup$ Thank you Siong for helping me with this. $\endgroup$
    – Electromagnet
    Feb 14, 2020 at 4:58

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