solutions5bd

solutions5bd - ± 1 1 1 1 0 1 2 3 ² 1 0 1 1 1 2 1 3 ± c c...

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Math 33a/2, Quiz 5bd, November 15, 2007 Name: UCLA ID: 1. Find the straight line y = c 0 + c 1 x that provides the best fit (in the least-squares sense) to the four points (0 , - 1) , (1 , 2) , (2 , 1) , (3 , 4). Solution. Plugging in the four points into the straight-line formula y = c 0 + c 1 x , we have - 1 = c 0 + 0 · c 1 , 2 = c 0 + 1 · c 1 , 1 = c 0 + 2 · c 1 , 4 = c 0 + 3 · c 1 , or 1 0 1 1 1 2 1 3 ± c 0 c 1 ² = - 1 2 1 4 . We wish to find the vector ± c 0 c 1 ² which provides the best least-squares approximation to a solution. To do this, we multiply both sides by the matrix ± 1 1 1 1 0 1 2 3 ² and solve the resulting system of equations:
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Unformatted text preview: ± 1 1 1 1 0 1 2 3 ² 1 0 1 1 1 2 1 3 ± c c 1 ² = ± 1 1 1 1 0 1 2 3 ² -1 2 1 4 ± 4 6 6 14 ²± c c 1 ² = ± 6 16 ² . The inverse of the matrix ± 4 6 6 14 ² is 1 4 · 14-6 · 6 ± 14-6-6 4 ² = 1 20 ± 14-6-6 4 ² . Hence ± c c 1 ² = 1 20 ± 14-6-6 4 ²± 6 16 ² = 1 20 ±-12 28 ² = 1 5 ±-3 7 ² . Hence the best-fit line to the four points is y =-3 5 + 7 5 x . 1...
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This note was uploaded on 04/02/2008 for the course MATH 33a taught by Professor Lee during the Fall '08 term at UCLA.

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