Statistics for Business: Decision Making and Analysis, 3rd Edition

... measure of dependence. Because the correlation is a parameter of the joint distribution of X and Y, it too is denoted by a Greek letter. The usual choice is the letter ρ (rho, pronounced “row”). The correlation between the stock values is

$$\rho =\text{Corr}\left(X,\hspace{0.17em}Y\right)=\frac{\text{Cov}\left(X,\hspace{0.17em}Y\right)}{{\sigma }_{X\hspace{0.17em}}{\sigma }_Y}\approx \frac{2.19}{\sqrt{4.99\times 5.27}}\approx 0.43$$

Because it removes the units from the covariance, the correlation does not change if we change the units of X or Y. Suppose we measured the random variables X and Y in cents rather than dollars. For example, X could be −500, 0, or 500 cents. This change in units increases the covariance by 100² to 21,900 ¢², but the correlation remains 0.43.

The correlation between random variables shares another property with the correlation in data: It ranges from − 1 to + 1.

$$-1\le \text{Corr}$$