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4. We have n statistical units. For unit i, we have (x; yi), for i 1,2,...,n. We used the least squares line to obtain the es(b) In the suggested exercises, we showed that e,-0 and where e is the ith residual, that is e -y (bo bi i). Show that 7n e0

4. We have n statistical units. For unit i, we have (x; yi), for i 1,2,...,n. We used the least squares line to obtain the estimated regression line bobi . (a) Show that the centroid (z, y) is a point on the least squares line, where x-(1/n) Σ-Χί and у-(1/ n) Σ|-1 yi. (Hint: Evaluate the line at x x.)
(b) In the suggested exercises, we showed that e,-0 and where e is the ith residual, that is e -y (bo bi i). Show that 7n e0 where ýi is the ith ajusted value, that isbo +bi xi. In other words, you will show that the vector of adjusted values y and the vector of residuals e which are an are orthogonal vectors in R'"
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imeAssume o ete 및2- 2x1 and o to nsx.di-とx; 왱iNou, we have bo ,bSo Can aluo àSS mean O -tclaim I. e に! に(

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4. We have n statistical units. For unit i, we have (x; yi), for i 1,2,...,n. We used the least squares line to obtain the estimated regression line bobi . (a) Show that the centroid (z, y) is a poin...
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