# Correlation ratio

A characteristic of dependence between random variables. The correlation ratio of a random variable relative to a random variable is the expression

where is the variance of , is the conditional variance of given , which characterizes the spread of about its conditional mathematical expectation for a given value of . Invariably, . The equality corresponds to non-correlated random variables; if and only if there is an exact functional relationship between and ; if is linearly dependent on , the correlation ratio coincides with the squared correlation coefficient. The correlation ratio is non-symmetric in and , and so, together with , one considers (the correlation ratio of relative to , defined analogously). There is no simple relationship between and . See also Correlation (in statistics).

**How to Cite This Entry:**

Correlation ratio. A.V. Prokhorov (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Correlation_ratio&oldid=13666