Consider observations on three variables X1;X2 and X3: Suppose that X1 is regressed on X2: When the residual of the above regression is regressed on X3; the regression coefficient of X3 is b3: When X1 is regressed on X2 and X3 simultaneously, the regression coefficient of X3 is b3* : (a) Show that |b3|<=|b3*|.
(b) When does the equality hold in (a)?
So I get that X1=a1+b2X2+e; e=a2+b3X3+e1; therefore, X1=a1+a2+b2X2+b3X3+e1; again, X1=a3+b2*X2+b3*X3+e2
Now how to proceed?