What is "covariance"

covariance \covariance\ n. a statistical measure of the relationship of two variables, formed by multiplying the difference of each variable from its mean, both variables being measured at the same time, and averaging all such products.

1878, from covariant (1853), from co- + variant.

n. 1 (context statistics English) A statistical measure defined as $scriptstyleoperatorname\{Cov\}(X,\; Y)\; =\; operatorname\{E\}((X\; -\; mu)\; (Y\; -\; nu))$ given two real number-valued random variables ''X'' and ''Y'', with expected values $scriptstyle\; E(X),=,mu$ and $scriptstyle\; E(Y),=,nu$. 2 (context computing programming English) The conversion of data types from wider to narrower in certain situations.

n. statistical measure of the variance of two random variables measured in the same mean time period

In probability theory and statistics, covariance is a measure of how much two random variables change together. If the greater values of one variable mainly correspond with the greater values of the other variable, and the same holds for the lesser values, i.e., the variables tend to show similar behavior, the covariance is positive. For example, as a balloon is blown up it gets larger in all dimensions. In the opposite case, when the greater values of one variable mainly correspond to the lesser values of the other, i.e., the variables tend to show opposite behavior, the covariance is negative. If a sealed balloon is squashed in one dimension then it will expand in the other two. The sign of the covariance therefore shows the tendency in the linear relationship between the variables. The magnitude of the covariance is not easy to interpret. The normalized version of the covariance, the correlation coefficient, however, shows by its magnitude the strength of the linear relation.

A distinction must be made between (1) the covariance of two random variables, which is a population parameter that can be seen as a property of the joint probability distribution, and (2) the sample covariance, which serves as an estimated value of the parameter.

In mathematics and physics, covariance is a measure of how much two variables change together, and may refer to: