HW-11 - Problem L11-1: Work problem #5 (Ch. 8 Burden &...

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1. a-c By hand. Clearly show all work. 2. a-f using regression program in Excel. . Solution: x y 4 102.56 4.2 113.18 4.5 130.11 4.7 142.05 5.1 167.53 5.5 195.14 5.9 224.87 6.3 256.73 6.8 299.5 7.1 326.72 a) Construct the Least Squares polynomial of degree one and compute the error. Where f(x i ) = ax i + b 1... 1... 1... 2 2 1... 1... i i i i i m i m i m i i i m i m m x y x y a m x x = = = = =    -       =   -     2 1... 1... 1... 1... 2 2 1... 1... i i i i i i m i m i m i m i i i m i m x y x y x b m x x = = = = = =     -         =   -     2 1... min [ ( )] i i i m y f x = - 2 (a,b) 1... min [ ( )] i i i m y ax b = - +
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X Y X 2 X*Y 4 102.56 16 410.24 4.2 113.18 17.64 475.356 4.5 130.11 20.25 585.495 4.7 142.05 22.09 667.635 5.1 167.53 26.01 854.403 5.5 195.14 30.25 1073.27 5.9 224.87 34.81 1326.733 6.3 256.73 39.69 1617.399 6.8 299.5 46.24 2036.6 7.1 326.72 50.41 2319.712 Sum 54.1 1958.39 303.39 11366.84 10 * (11366.84) – (11366.84)*(54.1) a= ---------------------------------------------- = 72.08452 10 * (303.39) – (54.1) 2 (303.39) * (1958.39) – (11366.84) * (54.1) b= ------------------------------------------------- = -194.138 10 * (303.39) – (54.1) 2 X Y X 2 X*Y F(x) (Y-F(x)) 2 4 102.56 16 410.24 94.19983 69.89244 4.2 113.18 17.64 475.356 108.6167 20.8234 4.5 130.11 20.25 585.495 130.2421 0.017447 4.7 142.05 22.09 667.635 144.659 6.806842 5.1 167.53 26.01 854.403 173.4928 35.55498 5.5 195.14 30.25 1073.27 202.3266 51.64731 5.9 224.87 34.81 1326.733 231.1604 39.5693 6.3 256.73 39.69 1617.399 259.9942 10.65514 6.8 299.5 46.24 2036.6 296.0365 11.99597 7.1 326.72 50.41 2319.712 317.6618 82.05035 Sum 54.1 1958.39 303.39 11366.84 1958.39 329.0132 Least square error = 329.0132
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b) Construct the Least Squares polynomial of degree two and compute the error. X Y X 2 X*Y x 3 x 4 x 5 x 6 x 2 *y x 3 *y x 4 *y 2 1 ( ) n i i i i y a bx cx = - + + 4 102.56 16 410.24 64 256 1024 4096 1640.96 6563.84 26255.36 0.014 4.2 113.18 17.64 475.356 74.088 311.1696 1306.912 5489.032 1996.495 8385.28 35218.18 0.005912 4.5 130.11 20.25 585.495 91.125 410.0625 1845.281 8303.766 2634.728 11856.27 53353.23 0.0018 4.7 142.05 22.09 667.635 103.823 487.9681 2293.45 10779.22 3137.885 14748.06 69315.87 -0.00893 5.1 167.53 26.01 854.403 132.651 676.5201 3450.253 17596.29 4357.455 22223.02 113337.4 -0.01755 5.5 195.14 30.25 1073.27 166.375 915.0625 5032.844 27680.64 5902.985 32466.42 178565.3 -0.0124 5.9 224.87 34.81 1326.733 205.379 1211.736 7149.243 42180.53 7827.725 46183.58 272483.1 -0.00347 6.3 256.73 39.69 1617.399 250.047 1575.296 9924.365 62523.5 10189.61 64194.57 404425.8
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This note was uploaded on 08/25/2011 for the course CPE 404 taught by Professor Merz during the Fall '09 term at Missouri S&T.

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HW-11 - Problem L11-1: Work problem #5 (Ch. 8 Burden &...

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