Introductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge

Exercise 2

Let 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 uniquely minimizes SSR(b) over all possible values of b, assuming X has rank k + 1.

Step 1 of 2

Consider be the vector of OLS estimates

Consider

Substitute in, the result is:

By first normal condition,

That means,

Thus,