Correlations and Covariances

The two most widely used measures of how two variables move together (or do not) are the correlation and the covariance. For two data series, X (Xx, X2,.) and Y(Y,Y... ), the covariance provides a non-standardized measure of the degree to which they move together, and is estimated by taking the product of the deviations from the mean for each variable in each period.

The sign on the covariance indicates the type of relationship that the two variables have. A positive sign indicates that they move together and a negative that they move in opposite directions. While the covariance increases with the strength of the relationship, it is still relatively difficult to draw judgments on the strength of the relationship between two variables by looking at the covariance, since it is not standardized.

The correlation is the standardized measure of the relationship between two variables. It can be computed from the covariance -

Correlation = pXY = oXY loXoY--

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