A 6 12 a here as in problem 6 t is just the dot

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Unformatted text preview: ith a a ￿ b￿ ￿ ·￿ aa ￿ √ ￿ . The shortest distance is (−9)2 + (−1)2 + (−1)2 + 112 = 204. a 6) 12) (a) Here, as in problem 6, ￿ T ￿ is just the dot product of ￿ with itself. This is m. aa a ￿ ￿ 1 Similarly ￿ T￿ = m bi so x = m m bi . ab ˆ i=1 i=1 ￿ − x￿ and ||e||2 = ￿m (bi − x)2 and the standard deviation is the square root of (b) ￿ = b ˆb e ˆ i=1 this last quantity. (c) ￿ = ￿ − x￿ = (1, 2, 6) − 3(1, 1, 1) = ( 2, −1, 3). This dots to 0 with (3, 3, 3). The e b ˆa − 111 ￿￿ T aa 1 projection matrix P = T = 1 1 1 . ￿￿ aa 3 111 22) We need to consider E (C, D) = (C − 2D − 4)2 + (C − D − 2)2 + (C − −1)2 + (C + D − 0)2 + (C + 2D)2 so ∂...
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