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

Exercise 22

Consider the problem described at the end of Section 2.6: running a regression and only estimating an intercept.

(i) Given a sample {y_i : i = 1, 2, . . . , n}, let be the solution to

Show that inside the squared residual and then doing a little algebra.)

(ii) Define residuals Argue that these residuals always sum to zero.

Step 1 of 2

a.

Consider a sample of data given below

Let the sample average be .

Hence

Since,

The second term is minimum when,

Hence the term is minimized when