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Statistics
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Correlation Coefficient
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Pearson Correlation Coefficient
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For random variables X and Y (For a population), the Pearson correlation coefficient can be calculated
by following formular.

.. math::

    r = \frac{cov(X,Y)}{\sigma_X * \sigma_Y} = \frac{E[(X - E[X]) * 
        (Y - E[Y])]}{\sqrt{E[(X - E[X])^2]} * \sqrt{E[(Y - E[Y])^2]}}


For a sample, the Pearson correlation coefficient is defined as,

.. math::

    r_{xy} = \frac{\sum_{i=1}^{n}(x_i - \overline{x})(y_i - \overline{y})}
        {\sqrt{\sum_{i=1}^{n}(x_i - \overline{x})^2} 
        * \sqrt{\sum_{i=1}^{n}(y_i - \overline{y})^2}}



Reference
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https://en.wikipedia.org/wiki/Pearson_correlation_coefficient



Spearman Rank Correlation Coefficient
+++++++++++++++++++++++++++++++++++++++


Reference
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https://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient