Let be the (k + 1) 1 vector of OLS estimates. (i) Show that for any (k + 1) 1 vector b,

Let β̂ be the (k + 1) × 1 vector of OLS estimates.

(i) Show that for any (k + 1) × 1 vector b, we can write the sum of squared residuals as

(ii) Explain how the expression for SSR(b) in part (i) proves that β̂ uniquely minimizes SSR(b) over all possible values of b, assuming X has rank k + 1.

SSR(b) = ' + (B - b)'X'X(B - b).