3.14 Correlation

SW 2.3

It’s often hard to interpret covariances directly (the “units” are whatever the units of \(X\) are times the units of \(Y\)), so it is common to scale the covariance to get the correlation between two random variables:

\[ \mathrm{corr}(X,Y) := \frac{\mathrm{cov}(X,Y)}{\sqrt{\mathrm{var}(X)} \sqrt{\mathrm{var}(Y)}} \] The correlation has the property that it is always between \(-1\) and \(1\).

If \(\mathrm{corr}(X,Y) = 0\), then \(X\) and \(Y\) are said to be uncorrelated.