Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

So I have got 2 variables, $A$ and $B$. I know for a fact that $E(A)$ = 0.

I don't know if they are independent.

$$Cov(A, B) = E(A B) - E(B) E(A)$$

I know that $E(A) = 0$.

Does that mean $E(A B) = 0$, too?

(I'm doing this question where I have to show the covariance between estimated residuals and each of the regressors must always be zero, ).

share|improve this question
add comment

1 Answer 1

up vote 1 down vote accepted

No, you still have to compute $E(AB)$. To show that the covariance of regression residuals and regressors is zero, write the sum of the squares and differentiate it with respect to the coefficients. Each derivative must be zero for the regression solution. If you look at the derivative you'll see that it is exactly $E(AB)$ (here $A$ is the residuals, $B$ is the regressor), so it must be zero. Hence since $E(A)=0$ you get that the covariance is zero too.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.