Definition:Pearson Correlation Coefficient

Definition

Let $X$ and $Y$ be random variables.

Let the variances of $X$ and $Y$ exist and be finite.

Then the Pearson correlation coefficient of $X$ and $Y$, typically denoted $\map \rho {X, Y}$, is defined by:

$\map \rho {X, Y} = \dfrac {\cov {X, Y} } {\sqrt {\var X \, \var Y} }$

where $\cov {X, Y}$ is the covariance of $X$ and $Y$.

Source of Name

This entry was named for Karl Pearson.

Sources

• 2011: Morris H. DeGroot and Mark J. Schervish: Probability and Statistics (4th ed.): $4.6$: Covariance and Correlation: Definition $4.6.2$