Consider the line y = 0 + 1 x. (i) Let (x 1 , y

Consider the line

y = β₀ + β₁x.

(i) Let (x₁, y₁) and (x₂, y₂) be two points on the line. Show that (x̅, y̅) is also on the line, where x̅ = (x₁ + x₂)/2 is the average of the two values and y̅ = (y₁ + y₂) / 2.

(ii) Extend the result of part (i) to n points on the line, {(x_i, y_i): i = 1, . . . , n}.