# About

Tag Info

Covariance is a quantity used to measure the strength and direction of the linear relationship between two variables. The covariance is unscaled, & thus often difficult to interpret; when scaled by the variables' SDs, it becomes Pearson's correlation coefficient.

Covariance is a quantity used to measure the strength and direction of the linear relationship between two variables. The covariance between $X$ and $Y$ is defined as $${\rm cov}(X,Y) = E \left[ \left( X-E(X) \right) \left( Y-E(Y) \right) \right] = E(XY) - E(X)E(Y)$$ Since the magnitude is difficult to interpret in isolation, the covariance is often scaled by the standard deviations of $X$ and $Y$ to produce the Pearson product-moment correlation coefficient.