I3

A) 2.13 The normal error model for simple linear regression through the origin is Y = BX, +e for i = 1, ...,n where en, ..., en are iid NV(0, o?) random variables. a) Show that the least squares estimator for B is EL X? b) Find E(). c) Find VAR(B). (Hint: Note that = >_, KY, where k, - X,/ E. , X?. Hence E(B) = EL KE(Y.) = EL KiBX,. The X, which are treated as constants. Similarly, VAR(3) = V(CL_, k,Y) = EM, KV(Y ) by independence, and V(Y,) = 02. )