Correlation

Correlation measures the linear association between two variables in a unitless scale.

$\rho =\text{Corr}(X,Y)\equiv \frac{\text{Cov}(X,Y)}{\sqrt{\text{Var}(X)\text{Var}(Y)}}=\frac{{\sigma }_{XY}}{{\sigma }_X{\sigma }_Y}$

• $|\rho |\le 1$
• If $X,Y$ are independent $⟹\rho =0$.