1. 1 Curve-Fitting Regression – Examples

2. 2 Example 1 x23478955 y9651091123 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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4. 4 x23478955 y9651091123

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6. 6 x23478955 y9651091123

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8. 8 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?)

9. 9 Example 2 x2.53.5567.51012.51517.520 y75.53.93.63.12.82.62.42.3 Fit a power equation to the data.

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11. 11 x2.53.5567.51012.51517.520 y75.53.93.63.12.82.62.42.3 log x0.39794 0.54406 8 0.69897 0.77815 1 0.87506 1 11.09691 1.17609 1 1.24303 8 1.30103 log y 0.84509 8 0.74036 3 0.59106 5 0.55630 3 0.49136 2 0.44715 8 0.41497 3 0.38021 1 0.36172 8

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