Pearson Correlation Coefficient

Synonyms

Linear correlation coefficient; Pearson’s product-moment coefficient

Definition

Pearson correlation coefficient (PCC) is the one of the most popular coefficients to measure the dependence of two variables. Given two random variables $X$ and $Y$, PCC is defined as the normalization form of their covariance:

$$ PCC\left( {X,Y} \right) = \frac{{{\rm cov} (X,Y)}}{{{\sigma_X}{\sigma_Y}}} = \frac{{E\left[ {\left( {X - \bar{X}} \right)\left( {Y - \bar{Y}} \right)} \right]}}{{{\sigma_X}{\sigma_Y}}} $$

where $\bar{X}$ and $\bar{Y}$ are the average values of $X$ and $Y$, respectively; ${\sigma_X}$ and ${\sigma_Y}$ are the standard deviations.