Let b^ be the 1k 1 12 3 1 vector of OLS estimates.

(i) Show that for any 1k 1 12 3 1 vector

b, we can write the sum of squared residuals as SSR1b2 5 u^ ru^ 1 1b^ 2 b2 rXrX1b^ 2 b2.

{Hint: Write 1y 2 Xb2 r 1y 2 Xb2 5 3u^ 1 X1b^ 2 b2 4 r 3u^ 1 X1b^ 2 b2 4 and use the fact that Xru^ 5 0.}