Chapter 7:

Question 1

Variance of Beta1hat:

Answer 1

Var(Beta1hat|xi)=Sigma^2/SSTx

Question 2

Variance of Beta0hat:

Answer 2

Var(Beta0hat|xi)=Sigma^2/n+xbar^2*Sigma^2/SSTx

Var(Beta0hat|xi)=Sigma^2(Summation of xi^2)/(nSSTx)

Question 3

Sigma^2:

Answer 3

Error Variance.

Generally unknown,because we do not observe error term u - we only observe residuals uhat.

Question 4

Estimate of the error variance:

Answer 4

Sigmahat^2=SSR/(n-2)=(Summation of (uihat^2))/(n-2)

n-2 degrees of freedom because of the two moment restrictions.

Question 5

Estimated Variance of Beta1hat:

Answer 5

Var(Beta1hat)hat=(Sigmahat^2)/SSTx

Question 6

Estimated Variance of Beta0hat:

Answer 6

Var(Beta0hat)hat=(Sigmahat^2Summation of xi^2)/(nSSTx)

Question 7

Standard Error of Beta1hat:

Answer 7

Square root of Estimated Variance of Beta1hat

Question 8

Standard Error of Beta0hat:

Answer 8

Square root of Estimated Variance of Beta0hat