Definition:Pearson Correlation Coefficient
Jump to navigation
Jump to search
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
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): correlation coefficient: 1.
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): covariance
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): correlation coefficient: 1.
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): covariance
- 2011: Morris H. DeGroot and Mark J. Schervish: Probability and Statistics (4th ed.): $4.6$: Covariance and Correlation: Definition $4.6.2$