Problem One

1. Show that   1 xi(xi − ) =    1 (xi − ) 2 (Note that the same holds even if we were to show 1 xi(gi − g¯) =   1 (xi − ) (gi − g¯))

Problem Two

2a) Suppose you are interested in a simple regression, gi  = βˆ0＋βˆ1xi ＋ui, from a sample data-set. Use your proof in ≈estion 1 to show the analytic formulae for βˆ0 and βˆ1 .

2b) Suppose you are interested in a multiple regression, gi  = βˆ0＋βˆ1x1i＋βˆ2x2i＋ui, from a sample data-set. Use your proof in question 1 to show the analytic formulae for βˆ0 , βˆ1 , βˆ2 . [Note: What

I want you to learn from ≈estion 2b) is that as you continue adding explanatory variables, you can keep on deriving the analytic formula for the coefcients.]

Problem Tree

3. “Given the the frst four Gauss-Markov assumptions, OLS estimator is unbiased but it is not BLUE. With the f尤h assumption, homoskedasticity, the OLS estimation is BLUE.”Brieay discuss the reasoning behind statement.

Problem Four

4. Wooldridge Chapter 1, computer exercise C5. Use the data in FERTIL2 to answer the question. Use the data in FERTIL2 to answer the question.

Problem Five

5.  Wooldridge Chapter 1, computer exercise C7.  Use the data in“ALCOHOL” to answer the question.

Use the data in“ALCOHOL” to answer the questions.