Could anyone help with the following question:
The fixed values in the problem are Xsubcript1=1, Xsubscript2=2, Xsubsrcipt3=3,Xsubscript4=4,Xsubscript5=5,Xsubscri pt6=6
Relationship btw X & Y given Yi=Bsubo+Bsub1Xi+ui
Estimate the slope Bsub1 of linear relation btw Y & X by: Bsub1tilde=1/8(Ysubscript6+Ysubscript5-Ysubscript2-Ysubscript1)
Three part question:
a. Show that this estimator is unbiased
b. Deduce its sampling variance. Compare this sampling variance with the OLS estimator of Bsub1
c. Compute the relative efficiency of the OLS estimator, defined as the ratio of the OLS estimator's variance to the variance of the estimator.