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What is a covariance?

What is a covariance? Here are some definitions.

Noun
  1. (statistics) A statistical measure defined as
  2. (object-oriented programming) The conversion of data types from wider to narrower in certain situations.
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Examples
Contour plots of genetic covariance functions fitted by the character process model.
The residual covariance matrix of the share equations will be singular, and thus one equation must be omitted when estimating the system.
An analysis of covariance was used to test whether differences between the slopes of regression lines were significant.
The matrix formulation of the model produces an estimate that can be easily transformed into genetic covariance and correlations.
The confidence interval of fit parameters was either determined from the covariance matrix or by F-test analysis.
If this occurs frequently, then MA experiments will be practically useless for studying any properties of mutational covariance.

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