Prove that ŷ0 is an unbiased estimator of Y0.

Also: Derive the formula for the variance of ŷ0
a. Hint 1: You are looking for Var(Y^0)=Var(B^0+B^1X0). This is the variance of a sum of two random variables. What is the general formula for such a sum?
b. Hint 2: If you did hint 1 correctly, you will see you need the formula for cov(B^0,B^1) . Take it on faith that this can be found to be cov(B^0,B^1)= -x̄ var(B^1) . (You might find it interesting that the two estimators have a negative correlation. A steeper slope tends to imply a lower intercept, and vice versa.)

note: B^0 = Beta hat 0