Correlation

Definition

It is a statistical measure that quantifies how linear the relationship between two variables is.

Coefficient of Correlation

$$\rho [X,Y]=\frac{\mathrm{cov}[X,Y]}{\sqrt{\mathbb{V}[X]\mathbb{V}[Y]}}$$

Note: $\rho [X,Y]\in [-1,1]$

• $\rho =-1$: Negative Linear relationship
• $\rho =0$: non linear relationship
• $\rho =+1$: Positive linear relationship

At $-1$ and $+1$, the Correlation is perfectly linear.