6. (Total 9 points) Suppose we estimate a linear regression equation Yi = Bo + BiXi tui by OLS. (a) (3 points) Show that _ _Zu; = 0, where the us's are the regression residuals. (b) (3 points) Suppose we regress Xi on ui by OLS, including a constant term in the regression. Show that the estimated coefficient on u; is equal to zero. (c) (3 points) Suppose we regress Yi on the predicted value Yi by OLS, including a constant term in the regression. Show that the estimated coefficient on Y is equal to one. Hint: the regression residual is defined by uj = Yi - Y; where the predicted value Yi = Bo + BIXi. Here, Bo and B1 are the OLS estimators.)