1Yi , X1i , X2i2 satisfy the assumptions in Key Concept 6.4; in addition, var1ui X1i , X2i2 = 4 and var1X1i2 = 6. A rand

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1Yi , X1i , X2i2 satisfy the assumptions in Key Concept 6.4; in
addition, var1ui X1i , X2i2 = 4 and var1X1i2 = 6. A random sample
of size n = 400 is drawn from the population.
a. 1. Assume that X n 1 and X2 are uncorrelated. Compute the
variance of b [Hint: Look at Equation (6.20) in Appendix 6.2.]
b. Assume that corr n 1X1, X22 = 0.5. Compute the variance of
b1.
c. Comment on the following statements: “When X1 and X2 are
correlated, n the variance of b1 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.”