correlation coefficient

The correlation coefficient scales the covariance of two random variables by their respective standard deviations such that it is agnostic to units of measurement.

Formally,
the correlation coefficient ${\rho }_{X,Y}$ of random variables $X,Y$ is given by

where $\mathrm{Cov}(X,Y)$ is the covariance of $X$ with $Y$, and ${\sigma }_Z$ is the standard deviation of $Z$.

For any two random variables, $-1\le \rho \le 1$, and the variables are said to be uncorrelated when $\rho =0$.

If two random variables are independent, then $\rho =0$, but n.b. $\rho =0$ does not imply independence.