value for a hypothesis test that the population slope is zero. (The p-value is going to be extremely small and not be on any t-table. Figure out how you can use Excel to calculateit. (Look up the t.dist functionality in the help menus.)

2)(20 points) The last lessons have spent a lot of time describing the slope and intercept terms (and their variances) of the one-variable sample regression function. We also know that for any particular value of the independent variable (call it X0), that the predicted value of Y0is0010ˆˆˆYX. (This is sometimes called a “point prediction.”) a)(10) Prove that 0ˆYis an unbiased estimator of E[Y0|X0].b)(10) Derive the formula for the variance of 0ˆY. Show at least two steps in this derivation.a.Hint 1: You are looking for 010()()Var YVarX. This is the variance of a sum of two random variables. What is the general formula for such a sum? (Go back to week 2 lectures, if you need a reminder.) Use that formula now.b.Hint 2: If you did hint 1 correctly, you will see you need the formula for01ˆˆcov(,). Take it on faith that this can be found to be011ˆˆˆcov(,)var()X . (You might find it interesting that the two estimators 0ˆˆˆ