(Continues questions 12 and 13.) Suppose, however, that e = 0. Then Dick has a problem. To see the problem more clearly, assume that n is large. Let Q =

X W be the design matrix, i.e., the first column is the Xi and the second column is the Wi. Show that Q

Q/n .

=

 E(X2 i ) E (XiWi)

E(XiWi) E (W2 i )



, Q

Y/n .

=

 E(XiYi)

E(WiYi)



.

(a) Suppose a = c = d = e = 1. What will Dick estimate for the coefficient of Xi in his regression?

(b) Suppose a = c = d = 1 and e = −1. What will Dick estimate for the coefficient of Xi in his regression?

(c) A textbook on regression advises that, when in doubt, put more explanatory variables into the equation, rather than fewer. What do you think?