Consider the model y b1 x2b2 x3b3 e and suppose that application of least squares to 20 observations on these variables

Consider the model y ¼ b1 þ x2b2 þ x3b3 þ e and suppose that application of least squares to 20 observations on these variables yields the following results

cov ( bb) denotes the estimated covariance matrix

:

b1 b2 b3 2

4 3

5 ¼

0:96587 0:69914 1:7769 2

4 3

5; bcovðbÞ ¼

0:21812 0:019195 0:050301 0:019195 0:048526 0:031223 0:050301 0:031223 0:037120 2

4 3

5 s^2 ¼ 2:5193 R2 ¼ 0:9466

(a) Find the total variation, unexplained variation, and explained variation for this model.

(b) Find 95% interval estimates for b2 and b3.

(c) Use a t-test to test the hypothesis H0 :b2 1 against the alternative H1 :b2 < 1.

(d) Use your answers in part

(a) to test the joint hypothesis H0 :b2 ¼ 0; b3 ¼ 0.

(e) Test the hypothesis H0 :2b2 ¼ b3.