covariance

Etymology

co- + variance

noun

1. (statistics) A statistical measure defined as scriptstyle operatorname Cov(X,Y)= operatorname E((X-μ)(Y-ν)) given two real-valued random variables X and Y, with expected values scriptstyle E(X),=,μ and scriptstyle E(Y),=,ν.
   The elements of such a correlation matrix do not have asymptotic variances and covariances of the form (1.2), even if S has a Wishart distribution. 2002, Karl G. Jöreskog, Dag Sörbom, PRELIS 2 User's Reference Guide, Scientific Software International, page 28
   Consequently, it can be shown that a covariance of two binary variables measures the extent to which the observed joint distribution of these variables differs from their expected joint distribution under the assumption that they are statistically independent. 1997, Michael Patrick Allen, Understanding Regression Analysis, Plenum Press, page 31
   The covariance of X and Y is the expected value of the product of two random variables, X − E(X) and Y − E(Y).[…]If two random variables tend to act like opposites, one is high when the other is low and vice versa, then the covariance will be negative. If two random variables tend to be high and low at the same time, then the covariance will be positive. In fact, the covariance measures the extent of a linear relationship between the two random variables. 2005, Steven J. Janke, Frederick Tinsley, Introduction to Linear Models and Statistical Inference, Wiley, page 133
2. (object-oriented programming) The conversion of data types from wider to narrower in certain situations.
   Coordinate term: contravariance
   As we will see in Chapter 8, we see both covariance and contravariance throughout the Java Collections. They largely exist to ensure that the generics just “do the right thing” and behave in a manner that should not surprise the developer. 2014, Benjamin J. Evans, David Flanagan, Java in a Nutshell, O'Reilly, page 149