Lec6 Curve Fitting

Lec6 Curve Fitting - Admin Items Physics 257 Lecture 6:...

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Physics 257 Lecture 6: Curve Fitting Prof. Matt Dobbs Physics Department, McGill U. Prof. M. Dobbs, Physics 257 October 25, 2007 2 Admin Items ± November 8– Last “regular” lecture. ± November 15 – Last lecture (democratic) z We will do 2/3 of the following: ¾ Review and open floor for questions. ¾ Fun-stuff with matlab (image processing, etc.) – not on exam. ¾ Cosmology lecture. ± Nov 22 – Study break for final quiz, no lecture. ± November 29, 1-2:30pm – Final Quiz (in class, 90 min). Worth 15%. Lots of challenge questions . Prof. M. Dobbs, Physics 257 October 25, 2007 3 Curve Fitting ± Regression analysis – statistical term for determining the best fit curve. ± Curve fitting amounts to comparing data to a theoretical function z Function might be motivated by a theory z … or it might be ad hoc. ± Curve fitting can be used to: z Test a theory. z Interpolate z Extrapolate Prof. M. Dobbs, Physics 257 October 25, 2007 4 Interpolation ± Some data can be interpolated by simply connecting the dots. ± This doesn’t always work well: z Some intuition is required to determine what sort of interpolation is reasonable. z Curve fitting: what sort of curve is reasonable? Plots from: http://users.ce.ufl.edu/~kg url/Classes/Lect3421/NM5_curve_s02.pdf
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Prof. M. Dobbs, Physics 257 October 25, 2007 5 Curve Fitting Finding the best fit parameters for any curve is as simple as minimizing the χ 2 . (errr… not always that easy). ± We derived the equations for this explicitly for a straight line fit. ± Similar equations exist for a polynomial of any order, y= ax n + bx n-1 + cx n-2 + dx n-3 + ex n-4 + … + z ± For linear functions, this is calculable analytically. ± For functions that are non-linear in the fit parameters, it is more complicated. Sometimes the functions can be linearized, but often we need to resort to numerical minimization. = i i i x f a y ) ( () Δ = i i i i i y a x f y 2 2 2 ) ; ( χ Prof. M. Dobbs, Physics 257 October 25, 2007 6 Curve Fitting ± Where does the χ 2 come from?
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Lec6 Curve Fitting - Admin Items Physics 257 Lecture 6:...

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