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Definition of Correlation

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Definition: Two random variables are positively correlated if high values of one are likely to be associated with high values of the other. They are negatively correlated if high values of one are likely to be associated with low values of the other.

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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