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

Question

Todd 2024-5-14

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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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Torsten 2024-5-14

编辑：Torsten 2024-5-14

Coefficients and confidence bounds are listed in the lower right box.

https://uk.mathworks.com/products/curvefitting.html

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Answer 1

the cyclist 2024-5-14

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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 2024-5-14

在 MATLAB Online 中打开

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