Pearson Correlation Coefficient

statistics

Definition

Pearson Correlation Coefficient

Pearson’s correlation coefficient, often denoted as $r$ or $\rho$, is a statistic that measures the linear correlation between two variables $x$ and $y$.

$$r=\frac{{\sum }_{i=1}^n({\vec{x}}_i-\overline{\stackrel{⃗}{x}})\cdot ({\vec{y}}_i-\overline{\stackrel{⃗}{y}})}{\sqrt{{\sum }_{i=1}^n({\vec{x}}_i-{\overline{\stackrel{⃗}{x}}}_i{)}^2\cdot {\sum }_{i=1}^n({\vec{y}}_i-\overline{\stackrel{⃗}{y}}{)}^2}}$$

It value ranges from $-1$ to $+1$:

• $+1$ indicates a perfect positive linear relationship
• $-1$ indicates a perfect negative linear relationship
• $0$ indicates no linear relationship