Definition:Pearson Correlation Coefficient

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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 $Y$.


Also known as

The Pearson correlation coefficient is also known as the product-moment correlation coefficient.

Some sources do not hyphenate (or are inconsistent in their presentation): product moment correlation coefficient.

Some sources refer to it in its full form as the Pearson product-moment correlation coefficient.


Also see

  • Results about the Pearson correlation coefficient can be found here.


Source of Name

This entry was named for Karl Pearson.


Historical Note

The Pearson correlation coefficient was explored in considerable depth by Karl Pearson, who discovered many of its properties.


Sources