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If X and Y are correlated and Y and Z are correlated, then X and Z...

If X and Y are correlated and Y and Z are correlated, then X and Z are correlated.

prove or disprove?

Math   Statistics-And-Probability   
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Answer #1

Disprove

Correlation is not Transitive:

If X and Y are correlated and Y and Z are correlated, then it will not always be the case that X and Z are correlated. We have to check the corrleation between variables , their strenght and direction.

The single number (the correlation coefficient) does not encapsulate enough information to guarantee transitivity of the property of being positively correlated. However, if we know the correlation coefficient rXY and rYZ then we can find upper and lower bounds for rXZ .

THANKS

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