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matlabcurve-fitting

Fatorial Fit in Matlab

I have been using Curve Fitting app but can´t find a way to make a fatorial fit in it. Any ideias of how to perform a fatorial fit in my data?

x = [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30];

y = [20, 30, 42, 56, 512, 729, 1000, 1331, 1728, 2197, 2744, 3375, 28800, 36992, 46818, 58482, 72200, 88200, 106722, 128018, 1068672, 1322500, 1622400, 1974375, 2384928, 2861082, 3410400];
Solution

  • I will not help you about "fatorial fit" as you probably wrote it incorrectly.

    I suggest to start from graphical inspection..

    The plot of y(x) isn't encouraging. The plot of ln(y) as a function of x shows some regularly spaced steps.

    enter image description here

    This draw to introduce a periodic steps function into the equation model, for example the floor function.

    We plot z(x)=ln(y)- a.floor(x/8)

    With a=1.89 the curve becomes roughly continuous and smooth but not linear. To make it roughly linear one have to plot it in log-log scales.

    enter image description here

    A linear regression leads to the parameters of the related power function roughly z=c.x**p. Thus we get :

    enter image description here

    NOTE : The criteria of fitting was LMSRE (with LMSE the numerical result would be different : Slightly better for high values of y and much worse for small y ).