Correlation ratio
A characteristic of dependence between random variables. The correlation ratio of a random variable relative to a random variable
is the expression
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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).
Correlation ratio. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Correlation_ratio&oldid=46528