bk x k b2 x 2 bk x k 0 thus we obtain the mean

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Unformatted text preview: bk X ki ∑ e = ∑Y i i − nb1 − b2 ∑ X 2 i − ... − bk ∑ X ki b 1 1 b ei = ∑ Yi − b1 − 2 ∑ X 2 i − ... − k ∑ X ki ∑n n n n e = Y − b1 − b2 X 2 − ... − bk X k = Y − (Y − b2 X 2 − ... − bk X k ) − b2 X 2 − ... − bk X k = 0 Thus we obtain the mean value of the residuals in terms of the means of Y and the X variables. 6 EXERCISE 3.9 Yi = β 1 + β 2 X 2 i + ... + β k X ki + ui ˆ Yi = b1 + b2 X 2 i + ... + bk X ki ˆ ei = Yi − Yi = Yi − b1 − b2 X 2 i − ... − bk X ki ∑ e = ∑Y i i − nb1 − b2 ∑ X 2 i − ... − bk ∑ X ki b 1 1 b ei = ∑ Yi − b1 − 2 ∑ X 2 i − ... − k ∑ X ki ∑n n n n...
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This note was uploaded on 03/27/2014 for the course ECONOMICS 106 taught by Professor Johnsmith during the Spring '14 term at Aalto University.

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