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Math Help - Correlation & linear regression

  1. #1
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    Correlation & linear regression

    Y and Z are two random variables with Correlation of YZ of 0.5
    IF X=2Z-1, then correlation of XZ is equal to;

    Can anyone help? Thanks in advance
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  2. #2
    Senior Member Sambit's Avatar
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    Correlation coefficient between X and Z = \frac{Cov(X,Z)}{\sqrt{Var(X)}\sqrt{Var(Z)}} where
    Cov(X,Z) = Cov(2Z-1,Z) = 2Var(Z)
    and
    Var(X) = Var(2Z-1) = 4Var(Z)

    Now put these values in the first expression.

    For further reasons behind this simplification, see Properties of Covariance and Properties of Variance


    Note- By the way, your question is either incomplete or partially wrong since the answer has nothing to do with Correlation between Y and Z. Also, you need to know Var(Z).
    Last edited by Sambit; March 7th 2011 at 07:09 AM. Reason: Note added
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