... natural gas. The size of the covariance, however, is difficult to interpret because the covariance has units. The units of the covariance are those of the x-variable times those of the y-variable. In this case, the covariance is 56,308.9 HDD × MCF. That’s a large number, but that does not imply a lot of association. Changes in the scales of the data make the covariance larger or smaller. For example, the covariance would be 10 times larger if gas were measured in hundreds rather than thousands of cubic feet.
Correlation is an easily interpreted measure of linear association derived from the covariance. The correlation is the covariance divided by the product of the standard deviations.