Curve-Fitting Regression

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Curve-FittingRegression Examples
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Example 1
x 2 3 4 7 8 9 5 5
y 9 6 5 10 9 11 2 3

• Using least-square regression
• Fit a line to the data
• Fit a parabola to the data
• Which curve describes the relationship of the
  data better?

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x 2 3 4 7 8 9 5 5
y 9 6 5 10 9 11 2 3
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x 2 3 4 7 8 9 5 5
y 9 6 5 10 9 11 2 3
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• The best line only explains 21 of the
  uncertainty in the data whereas the best parabola
  explains 78 of the uncertainty.
• Note Polynomials of higher degree cannot fit
  worse than a polynomial of lower degree. (Why?)

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Example 2
x 2.5 3.5 5 6 7.5 10 12.5 15 17.5 20
y 7 5.5 3.9 3.6 3.1 2.8 2.6 2.4 2.3 2.3

• Fit a power equation to the data.

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x 2.5 3.5 5 6 7.5 10 12.5 15 17.5 20
y 7 5.5 3.9 3.6 3.1 2.8 2.6 2.4 2.3 2.3
log x 0.39794 0.544068 0.69897 0.778151 0.875061 1 1.09691 1.176091 1.243038 1.30103
log y 0.845098 0.740363 0.591065 0.556303 0.491362 0.447158 0.414973 0.380211 0.361728 0.361728
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