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Math Help - Correlation Coefficient Question

  1. #1
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    Joined
    Aug 2009
    Posts
    1

    Correlation Coefficient Question

    Hi Everyone

    Need a bit of help on a correlation coefficient question I came across during revision:


    Shares A and B have the following Variance-Covaraince matrix.

    <br />
\left[<br />
\begin{array}{cc}<br />
\sigma_{a^2} & \sigma_{ab} \\<br />
\sigma_{ba} &  \sigma_{b^2} <br />
\end{array}<br />
\right] = \left[\begin{array}{cc}<br />
0.02 & -0.005 \\<br />
-0.005 & 0.01 <br />
\end{array}<br />
\right]

    What is the correlation coefficient between A and B?

    (a) .35
    (b) .125
    (c) -.35
    (d) -25

    If anyone could enlighten me with the answer and the method for getting the answer it would be much appreciated!
    Last edited by mr fantastic; August 11th 2009 at 04:29 AM.
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  2. #2
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    Joined
    Aug 2009
    Posts
    9

    Correct answer

    c. is correct. Denote X=sigma_ab - non-diagonal component of covariance matrix and Y=sigma^2_a*sigma^2_b - product of two diagonal components of cov matrix. Then Pearson correlation coeff is the ratio of X and square root of Y.
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