Curve Fitting Analysis.docx

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  • Words: 328
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Solution:

Sum

x 1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 28.0000

y 0.5000 2.5000 2.0000 4.0000 3.5000 6.0000 5.5000 24.0000

x2 1.0000 4.0000 9.0000 16.0000 25.0000 36.0000 49.0000 140.0000

7.0000a0 + 28.0000a1 = 24.0000 28.0000a0 + 140.0000a1 = 119.5000 a0 = 0.0714 a1 = 0.8393 y = 0.0714 + 0.8393x

xy 0.5000 5.0000 6.0000 16.0000 17.5000 36.0000 38.5000 119.5000

Solution: X 1.00 2.00 3.00 4.00 5.00 6.00 7.00 28.00

y 0.50 2.50 2.00 4.00 3.50 6.00 5.50 24.00

x2 1.00 4.00 9.00 16.00 25.00 36.00 49.00 140.00

7a0 +

x3 1.00 8.00 27.00 64.00 125.00 216.00 343.00 784.00

28a1 +

x4 1.00 16.00 81.00 256.00 625.00 1296.00 2401.00 4676.00

140a2 =

xy 0.50 5.00 6.00 16.00 17.50 36.00 38.50 119.50

24.0

x2y 0.50 10.00 18.00 64.00 87.50 216.00 269.50 665.50

28a0 + 140a1 + 784a2 = 119.5 140a0 + 784a1 + 4676a2 = 665.5 a0 = -0.2857 a1 = 1.0774 a2 = -0.0298 y = -0.2857 + 1.0774x – 0.0298x2

Using the same example x 1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 28.0000

y 0.5000 2.5000 2.0000 4.0000 3.5000 6.0000 5.5000 0

ln(y) -0.6931 0.9163 0.6931 1.3863 1.2528 1.7918 1.7047 7.0519

x2 1.0000 4.0000 9.0000 16.0000 25.0000 36.0000 49.0000 140.0000

xy -0.6931 1.8326 2.0794 5.5452 6.2638 10.7506 11.9332 37.7117

7.0000a0 + 28.0000a1 = 7.0519 28.0000a0 + 140.0000a1 = 37.7117 a0 = -0.3503 a = 𝑒 𝑎𝑜 =0.7044

a1 = 0.3394 b = a1 = 0.3394 thus, y = 0.7044e0.3394x

Using the same example x 1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 -

y x1 = log(x) y = log(y) 0.5000 0.0000 -0.3010 2.5000 0.3010 0.3979 2.0000 0.4771 0.3010 4.0000 0.6021 0.6021 3.5000 0.6990 0.5441 6.0000 0.7782 0.7782 5.5000 0.8451 0.7404 3.7024 3.0626

7.0000a0 + 3.7024a1 = 3.0626 3.7024a0 + 2.4890a1 = 2.2374 a0 =-0.1779 a1 = 1.1636 a = 10a0 = 0.6639 b = a1 = 1.1636

y = 0.6639x1.1636

x12 0.0000 0.0906 0.2276 0.3625 0.4886 0.6055 0.7142 2.4890

x1y1 0.0000 0.1198 0.1436 0.3625 0.3803 0.6055 0.6257 2.2374

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