Covariance as correlation

Correlation is one of the most widely used and a well-known measure of the assocation (linear association, that is) of two variables. Perhaps less well-known is that the correlation is in principle analoguous to the covariation. To see this, consider the a formula of the covariance of two empirical datasets, $X$ and $Y$: $$COV(X,Y) = \frac{1}{n} \cdot \big( \sum (X_i -\bar{X}) \cdot (Y_i - \bar{Y}) \big) $$ In other words, the covariance of $X$ and $Y$ $COV(X,Y)$ is the average of difference of some value to its …