Question

4. We have n statistical units. For unit i, we have (xi; yi), for i-1,2,... ,n. We used the least squares line to obtain the estimated regression line у = bo +biz. (a) Show that the centroid (x, y) is a point on the least squares line, where x = (1/n) and у = (1/n) Σ¡ı yi. (Hint: E ) i-1 valuate the line at x = x. (b) In the suggested exercises, we showed that e,-0 and e-0, where ei is the ith residual, that is ei = yǐー(0+51 Xi). Show that where f is the ith ajusted value, that is bo b . In other words, you will show that the vector of adjusted values y and the vector of residuals e which are ji e1 e2 y2 and e- en yn are orthogonal vectors in R"

Answer 1

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