Formally, a correlation coefficient is defined between the two random variables (x and y, here). Let sx and xy denote the standard devations of x and y. Let sxy denote the covariance of x and y. The correlation coefficent between x and y, denoted sometimes rxy, is defined by:
rxy = sxy / sxsy
Correlation coefficients are between -1 and 1, inclusive, by definition. They are greater than zero for positive correlation and less than zero for negative correlations.
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