# correlation question

• Sep 4th 2011, 04:43 AM
vacony
correlation question
Hi everybody,

Can enybody help me out:

Considering three random variables X, Y and Z
if cor(X,Y)=90 and cor(Y,Z)=80
Can we deduce from this cor(X,Z)? if yes, how?

thank you
• Sep 5th 2011, 12:02 AM
CaptainBlack
Re: correlation question
Quote:

Originally Posted by vacony
Hi everybody,

Can enybody help me out:

Considering three random variables X, Y and Z
if cor(X,Y)=90 and cor(Y,Z)=80
Can we deduce from this cor(X,Z)? if yes, how?

thank you

Please clarify your question, the correlation of two RVs is restricted to the interval [-1,1]

CB
• Sep 5th 2011, 12:13 AM
vacony
Re: correlation question
sorry:
cor(X,Y)=90% and cor(Y,Z)=80%.
• Sep 5th 2011, 02:05 AM
CaptainBlack
Re: correlation question
Quote:

Originally Posted by vacony
Hi everybody,

Can enybody help me out:

Considering three random variables X, Y and Z
if cor(X,Y)=90 and cor(Y,Z)=80
Can we deduce from this cor(X,Z)? if yes, how?

thank you

No.

The easiest way to show this is with a counter example (or rather a pair of examples both of which have the given correlations but the remaining unspecified correlations differ) where each of X, Y and Z is ~N(0,1)

CB