Given three points A,B,C, the objective is to determine the line that minimizes the sum of squares of the residuals or the sum of the absolute values of the residuals.
a. For the former, the best line passes through the means of the x and y.
b. For the latter, the best line passes through points A and C.
If there are more than three points, statement (a) remains valid but (b) weakens since the best line still passes through (at least) two points but not necessarily the endpoints.
