Statistical relationship between two sets of values can be visualized by looking at scatter-plots. However, for the purpose of further statistical analysis, numerical indices are needed that can describe both the magnitude and directionality of the statistical relation. Such a measure is covariance, Cxy, or cov(X,Y), which indicates the strength and trend of linear relationship between the two variables, X and Y.
Mathematically, covariance is
Covariance is a measure of how much the two variables vary together. For uncorrelated variables, Cxy = 0. If Cxy > 0, then Y tends to increase as X increases (and the converse). If Cxy < 0, then Y tends to decrease as X increases (and the converse).
The units of measurement of covariance(X,Y) are the units of X times the units of Y. The magnitude of covariance thus depends on the units of measurement. This reduces the usefulness of this measure. Another metric, correlation, is a dimensionless measure of linear relationship.
Frank, H. and Althoen, S.C. "The covariance Cxy" žB.1 in Statistics: Concepts and Applications Cambridge, Great Britain: Cambridge University Press, pp. 107-109, 1995.
Cite This As:
Dogra, Shaillay K., "Covariance." From QSARWorld--A Strand Life Sciences Web Resource.