Definitions for Covariancekoʊˈvɛər i əns
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(statistics) the mean value of the product of the deviations of two variates from their respective means
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.
A statistical measure defined as given two real-valued random variables X and Y, with expected values and .
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 smaller values, i.e., the variables tend to show similar behavior, the covariance is positive. In the opposite case, when the greater values of one variable mainly correspond to the smaller values of the other, i.e., the variables tend to show opposite behavior, the covariance is negative. 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 the covariance of two random variables, which is a population parameter that can be seen as a property of the joint probability distribution, and the sample covariance, which serves as an estimated value of the parameter.
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