# Correlation

From AMS Glossary

## correlation

- In general, a mutual relationship between variables or other entities.

In statistical terminology, it is a form of statistical dependence.

- When used without further qualification, the statistical term correlation usually refers to simple, linear correlation between two variables
*x*,*y*and is measured by the product-moment coefficient of correlation ρ or its sample estimate*r*defined as follows, where the respective population mean values of*x*and*y*are denoted by ξ and ζ, the respective standard deviations by σ(*x*) and σ(*y*), and where*E*is the expected value:The product moment*E*[(*x*- ξ) (*y*- ζ)] is usually called the covariance of*x*and*y*. In connection with correlation, the word "simple" is used in contradistinction to other qualifiers such as "multiple" or "partial." The word "linear" refers to a linear relationship between the two variables, or more precisely, to a linear approximation of the regression function of either variate with respect to the other.*See*autocorrelation, multiple correlation, partial correlation.