Correlation

See: covariance

Correlation measures the linear relationship between two variables (variable) \(X\) and \(Y\) using the Pearson correlation coefficient, the most commonly used measure of correlation for continuous variables.

\[ \rho_{X,Y} = \frac{cov(X,Y)}{\sigma_{X}\sigma_{Y}} $$ $$ \sigma_X=\sqrt{\frac{\sum_{i=1}^n\left(X_i-\bar{X}\right)^2}{n}} $$ $$ \sigma_Y=\sqrt{\frac{\sum_{i=1}^n\left(Y_i-\bar{Y}\right)^2}{n}} \]

Correlation measures the direction and magnitude of the linear relationship (linear regression).