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Math Help - Correlation coefficient

  1. #1
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    Correlation coefficient

    Suppose i have 50 pairs that are independent X,Y. The observations are paired. I have the following estimator for the correlation coefficient.


    r = \frac{\sum ^n _{i=1}(X_i - \bar{X})(Y_i - \bar{Y})}{\sqrt{\sum ^n _{i=1}(X_i - \bar{X})^2} \sqrt{\sum ^n _{i=1}(Y_i - \bar{Y})^2}}.


    How can I estimate the distribution of this estimator without knowing anything about the bivariate distriubution?
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  2. #2
    Senior Member Sambit's Avatar
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    r\sqrt{\frac{n-2}{1-r^2}} follows a t distribution with n-2 df.
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  3. #3
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    Thanks for answer. How can I show that? Is it possible to derive it?
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