Covariance

Covariance is a statistical representation of the degree to which two variables vary together. Basically, covariance is a number that reflects the degree to which two variable vary together.

The covariance between two variables, Xi andYi, is defined as C(Xi,Yi)=x E[(Xi-E[Xi])(Yi-E[Yi])]

• The covariance of a variable with itself is its variance.

• If the expectation of either Xi or Yi is 0, the covariance between them is the expectatin of their product

-The covariance between linear function of variables Xi and Yi_WRITTEN Wi= a+bXi and Zi = c+dYi for constants a,b,c,d is given by C(Wi,Zi)=bdC(Xi,Yi)

Is the intimate connection between regrerssion and covariance. Which is a regression with one regresssor, Xi, plus an intercept

If the greater values of one variable correspond with the greater values of the other variable, or for the smaller values, then the variables shows similar behavior, the covariance is a positive.

If the greater values of one variable correspond to the smaller values of the other, the variables tend to show opposite behavior, the covariance is negative

If one variable is greater and paired equally often with both greater and lesser values on the other, the covariance will be near to zero.