ProfessorE.Z.Stuffhasdecidedthattheleastsquaresestimatoristoomuchtrouble. Noting that two points determine a line, Dr. Stuff chooses two points from a sample of sizeNand draws a line between them, calling the slope of this line the EZ estimator ofb2in the simple regression model. Algebraically, if the two points arex1;y1andx2;y2, the EZ estimation rule is

bEZ14y2y1x2x1

Assuming that all the assumptions of the simple regression model hold:

1. (a)Show thatbEZis a ''linear'' estimator.
2. (b)Show thatbEZis an unbiased estimator.
3. (c)Find the variance ofbEZ.
4. (d)Find the probability distribution ofbEZ.
5. (e)ConvinceProfessorStuffthattheEZestimatorisnotasgoodastheleastsquares
6. estimator. No proof is required here.