Question

which of the following procedures will yield the same estimate of $\beta$ 1 as in multiple regression

Y=$\beta$0 + $\beta$ 1$\chi$1$+\beta$2$\chi$2+U ?

A. Run Y on $\chi$ 1, predict residual 1; run Y on 2, predict residual e2; run e1 on e2

B. Run X2 on X1 predict residual e; run e on Y

C.Run Y on X1 predict residual e1; run X2 on X predict residual e2; run e1 on e2

E. none of the above

Answer 1

It shall be noted that estimate of b1 as in multiple regression model Y=b0+b1X1+b2X2+u is estimated using normal equations.

The procedures as describe din option A, B and C does not yield the same estimate of b1.

Hence, the correct answer is E.