Curve fitting with loglog data

2021 8 6
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更新时间：2021 8 9
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I am having some issues fitting a curve using polyfit to log data. I think I am making a silly mistake during the fit plotting as the fitting is really bad during the beggining but can't seem to figure it out. Any help would be greatly appreciated! I have attached the data as: msd_help
load('msd_help')
figure()
loglog(s,m)
hold on
linearCoefficients = polyfit((s),(m), 1);
yFit = polyval(linearCoefficients, s);
loglog(s, yFit, 'r-', 'LineWidth', 2)

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Yazan
Yazan 2021-8-6
编辑：Yazan 2021-8-6
You are not doing anything wrong, and the fitting is working. However, you are plotting the results using a base 10 logarithmic scale. See below the same result plotted using a linear scale.

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 采纳的回答

Star Strider
Star Strider 2021-8-6

0 个投票

Fit it to a power function:
LD = load('msd_help.mat');
m = LD.m;
s = LD.s;
fcn = @(b,x) x.^b(1).*exp(b(2));
B = fminsearch(@(b) norm(m - fcn(b,s)), rand(2,1))
yFit = fcn(B,s);
figure
loglog(s,m,'.')
hold on
plot(s, yFit,'-r')
hold off
grid
producing:
B =
0.867368600071621
-27.933653082691194
and:
.

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Yazan
Yazan 2021-8-6
A 5th order polynomial also gives reasonable results.
Alex Sha
Alex Sha 2021-8-7
If the fitting function types are free, the follow is good enough:
y = p1*x/(1+p2*x^2)^p3+p4
Root of Mean Square Error (RMSE): 5.64364594544832E-13
Sum of Squared Residual: 1.91104437345451E-21
Correlation Coef. (R): 0.999945510161687
R-Square: 0.999891023292516
Parameter Best Estimate
---------- -------------
p1 3.82443123959562E-13
p2 2.48820059997632E-6
p3 0.334013945130774
p4 -8.79374499358471E-13
Manny Kins
Manny Kins 2021-8-9
编辑：Manny Kins 2021-8-9
Thanks all for your help. In reference to Star Strider's answer, it is good for me because I wanted to fit to a straight line (apologies for not mentioning this in the initial question). Is there a reason why the straight line fit on the log plot only passes the later stages of the data (after s=100) and misses the rest?
Star Strider
Star Strider 2021-8-9
‘Is there a reason why the straight line fit on the log plot only passes the later stages of the data (after s=100) and misses the rest?’
Yes.
The first-order unweighted power fit may not be the ideal model. (However the actual error is exceedingly small, and close to the limit of IEEE 754 floating-point representation.)
The best model is a mathematical expression of the process that created those data.
.
Manny Kins
Manny Kins 2021-8-9
Thanks for your help and insight
Star Strider
Star Strider 2021-8-9
As always, my pleasure!
.

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