# Covariance

© Paul Cooijmans

## Explanation

Covariance is the variance that is shared between two paired variables, and therewith closely related to the correlation. The difference is that the covariance is still to be understood in terms of units on the measurement scales of the variables, while the correlation is a standardized unitless index between -1 and 1 (this standardization taking place through dividing by the two variables' standard deviations). The covariance is actual variance that is shared; the *proportion* of the total variance that is shared on the other hand is equal to the square of the correlation. The covariance between variables x and y over *N* pairs is computed by summing the cross-products of the variables' deviations, and dividing by the number of pairs:

Covariance_{xy} = Σ (X - mean_{x})(Y - mean_{y}) / *N*