About

The covariance between two random variables $X$ and $Y$ is a measure of the degree of linear association between them. The covariance is defined as

$${\rm cov}(X,Y) = {\rm E} \left\[ \left( X - {\rm E}(X) \right) \left( Y - {\rm E}(Y) \right) \right\] = {\rm E} (XY) - {\rm E} (X) {\rm E} (Y) .$$

If $X$ and $Y$ are independent, we have ${\rm cov}(X,Y) = 0$. But the converse is in general not true.

The magnitude of the covariance depends on the variance of both $X$ and $Y$, and it is not easy to interpret. The correlation is often used instead to measure the degree of linear association between $X$ and $Y$ on a scale free basis.

history | show excerpt | excerpt history