Verify the results of Exercise 6.9 for the data in Example 6.5. Exercise 6.9 Consider the reparameterization of the model Y = Xβ + ϵ, where W = XC and C is nonsingular. (a) Show that W-space is the...

Verify the results of Exercise 6.9 for the data in Example 6.5.

Exercise 6.9

Consider the reparameterization

of the model Y = Xβ + ϵ, where W = XC and C is nonsingular.

(a) Show that W-space is the same as the X-space.

(b) Show that P W = P X.

(c) Express
 as a function of
.

Example 6.5

Consider the model

Then, the X-space consists of all points of the form (z_1,
z₂
0)’. In terms of the “room” analogy considered in Figure 6.3, the X-space consists of the floor. Suppose we observe the Y vector to be Y = (2 4 3)’. Then,

 Figure 6.3