| 释义 |
Correlation (Statistical)For two variables  and  ,
 | (1) |
 denotes Standard Deviation and  is the Covariance of these two variables. Forthe general case of variables  and  , where  , 2, ...,  ,
 | (2) |
 are elements of the Covariance Matrix. In general, a correlation gives the strength of therelationship between variables. The variance of any quantity is alway Nonnegative bydefinition, so
 | (3) |
 | (4) |
 | (5) |
 | (6) |
 | (7) |
 | (8) |
 | (9) |
 | (10) |
 | (11) |
 | (12) |
 . For a linear combination of two variables,
Examine the cases where  ,
 | (14) |
 | (15) |
 , which requires that the argument of theVariance is a constant. Therefore,  , so  . If , is either perfectlycorrelated ( ) or perfectly anticorrelated ( ) with .See also Covariance, Covariance Matrix, Variance |
