Introduction to Econometrics 3rd Edition by James Stock, Mark Watson

تمرين 8

Suppose that (Y i X i ) satisfy the assumptions in Key Concept 4.3. A random sample of size n = 250 is drawn and yields

a. Test H 0 : 1 = 0 vs. H 1. 1 0 at the 5% level.
b. Construct a 95% confidence interval for 1.
c. Suppose you learned that Y i and X i were independent. Would you be surprised Explain.
d. Suppose that Y i and X i are independent and many samples of size n = 250 are drawn, regressions estimated, and (a) and (b) answered. In what fraction of the samples would H 0 from (a) be rejected In what fraction of samples would the value 1 = 0 be included in the confidence interval from (b)