The sample Pearson product-moment correlation coefficient (r) is a measure of the linear association between two independent continuous variables, namely X and Y, measured on the same individuals or units. The values of the Pearson correlation coefficient measures the strength of the linear relationship between X and Y, while the sign of the correlation coefficient indicates the direction of the relationship between X and Y.

Given two continuous variables, X and Y, the Pearson correlation coefficient, rXY, is obtained as the ratio of the covariance between the two variables over the product of the respective standard deviations.

where x and y are the sample means for the variables X and Y, respectively.

The correlation coefficient is defined only if both the standard deviations are finite and both of ...