the Pearson correlation coefficient, also known as Pearson’s r, is a correlation coefficient that measures linear correlation between two sets of data. 1

linear-correlation-coefficient.png

Definition

Given two random variables and , the Pearson correlation coefficient is often denoted as and is defined as

\rho_{XY} = \frac{\text{Cov}[X, Y]}{\text{stdev}[X]\text{stdev}[Y]}

Note that the above ratio is only well-defined when and are both greater than zero. However, it is often assumed that the correlation is 0 when one of the standard deviations is 0 (in which case will also be zero).

Footnotes

  1. Linear correlation | Definition, examples, explanations