| 释义 |
CovarianceGiven  sets of variates denoted  , ...,  , a quantity called the Covariance Matrix is defined by
where  and  are the Means of  and  , respectively.An individual element  of the Covariance Matrix is called the covariance of the two variates and, and provides a measure of how strongly correlated these variables are. In fact, the derived quantity
 | (4) |
 ,  are the Standard Deviations, is called the Correlation of and . Note that if and are taken from the same set ofvariates (say,  ), then
 | (5) |
 . The covariance is also symmetric since
 | (6) |
 | (7) |
For two independent variates  and  ,
 | (8) |
 , then  tends to increase as increases. If  , then tends to decrease as increases.
The covariance obeys the identity
By induction, it therefore follows that
See also Correlation (Statistical), Covariance Matrix, Variance |
