6.10 (Yi, X1i, X2i) satisfy the assumptions in Key Concept 6.4; in addition, var(ui X1i, X2i) = 4 and var(X1i) = 6. A random sample of size n = 400 is drawn from the population.

a. Assume that X1 and X2 are uncorrelated. Compute the variance of b n

1.

[Hint: Look at Equation (6.17) in Appendix 6.2.]

b. Assume that corr(X1, X2) = 0.5. Compute the variance of b n

1.

c. Comment on the following statements: “When X1 and X2 are correlated, the variance of b n

1 is larger than it would be if X1 and X2 were uncorrelated. Thus, if you are interested in b1, it is best to leave X2 out of the regression if it is correlated with X1.”