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Financial Statistics: Coefficient of Correlation

COEFFICIENT OF CORRELATION

The coefficient of correlation indicates an association between two variables.

The formula is:

where

r_xy is the correlation between X and Y

COV(X,Y) the covariance between X and Y

std_x is the standard deviation of X

The value of r_xy is always between -1 and 1.

The value -1 represents a perfect negative correlation (when one increases, the other decreases in exactly the same proportion.

The value +1 represents a perfect correlation (when one increases, the other increases in exactly the same proportion.

The value 0 represents a lack of correlation.

You can find an illustration of the correlation in the above graphs.

The above describe indicator is the most widely used type of correlation known as Pearson r. The value of correlation does not depend on the specific measurement units used. This line is called the regression line or least squares line, because it is determined such that the sum of the squared distances of all the data points from the line is the lowest possible.

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