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Covariance

Alternate name

cov

Basic definition

The covariance of a set of variables is a measure of the strength of their correlation.

Detailed definition

Covariance provides a measure of the strength of the correlation between two or more sets of random variates. The covariance for two random variates X and Y, each with sample size N, is defined by the expectation value cov(X, Y) | = | ⟨(X - μ_X)(Y - μ_Y)⟩ | = | ⟨X Y⟩ - μ_X μ_y where μ_x = ⟨X⟩ and μ_y = ⟨Y⟩ are the respective means, which can be written out explicitly as cov(X, Y) = sum_(i = 1)^N ((x_i - x^_)(y_i - y^_))/N.

Related terms

bivariate normal distribution | correlation coefficient | covariance matrix | statistical correlation | variance

Related Wolfram Language symbol

Covariance

Educational grade level

college level

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