+Demonstrate the unbias of the least-squares estimators A and B of and in simple regression:...

+Demonstrate the unbias of the least-squares estimators A and B of α and β in simple regression:

(a) Expressing the least-squares slope B as a linear function of the observations, B ¼ PmiYi (as in the text), and using the assumption of linearity, EðYiÞ ¼ α þ βxi, show that EðBÞ ¼ β. [Hint: EðBÞ ¼ PmiEðYiÞ.]

(b) Show that A can also be written as a linear function of the Yis. Then, show that EðAÞ ¼ α.