Does the curvefit toolbox return the equation for the best fit line (or curve)?

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Todd
Todd 2024-5-14
编辑： Todd 2024-5-14
For example, let's say that a 5th order polynomial fits the data nicely. Does the curvefit results include the equation, or at least the coefficients, of the 5th order polynomial fit?
Perhaps a silly question, but you might be surprized at how many so-called curve fitting programs are out there that only care about displaying the fit.
Thank you for considering my question.
Todd

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the cyclist
the cyclist 2024-5-14
Yes, you can get the coefficients of the best-fit equation. @Torsten's comment illustrates where you can see them in the UI, and you can also get them programatically using the fit function.
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Steven Lord
Steven Lord 2024-5-14
Ran in:
And if you export the fit from the app using the last button on the toolstrip, you'll get a cfit or sfit object. You can use a number of different functions to post-process them.
load census
format longg
f = fit(cdate, pop, 'poly2')
f =
Linear model Poly2: f(x) = p1*x^2 + p2*x + p3 Coefficients (with 95% confidence bounds): p1 = 0.006541 (0.006124, 0.006958) p2 = -23.51 (-25.09, -21.93) p3 = 2.113e+04 (1.964e+04, 2.262e+04)
formula(f)
ans = 'p1*x^2 + p2*x + p3'
coeffnames(f)
ans = 3x1 cell array
{'p1'} {'p2'} {'p3'}
coeffvalues(f)
ans = 1x3
1.0e+00 * 0.00654113049421954 -23.5097459954225 21129.5921192301
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Note that not all types of fit give formulas you can use to evaluate the fit.
f2 = fit(cdate, pop, 'spline')
f2 =
Cubic spline interpolant: f2(x) = piecewise polynomial computed from p with cubic extrapolation Coefficients: p = coefficient structure
formula(f2)
ans = 'piecewise polynomial'
But then again you don't need to use the formula to evaluate it if you have the object.
populationFromQuadratic = f(1849)
populationFromQuadratic =
22.8952484620604
populationFromSpline = f2(1849)
populationFromSpline =
22.3548286873149

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