Covariance

See: correlation

Covariance is a normalized ([[normalmeasure of how two variables ([[variable]]) \(X\) and \(Y\) change together linearly.

Given a population of size \(n\), it is calculated as follows:

$$ COV[X, Y] = E[(X - E[X])(Y - E[Y])] = \frac{\Sigma^n_{i=1} (X_i-\overline{X})(Y_i-\overline{Y})}{n} $$ The sign of the covariance indicates the direction of the relationship between variables: - when \(COV[X, Y] > 0\), \(X\) and \(Y\) increase and decrease together. - when \(COV[X, Y] < 0\), \(X\) tends to decrease while \(Y\) tends to increase and vice versa. - when \(COV[X, Y] = 0\), \(X\) and \(Y\) do not display any of the above two tendencies. No linear relationship between \(X\) and \(Y\).

Note: *Covariance can only measure the directional relationship, not the magnitude. *