Problem with fitting an experimental curve

Hello everyone,

I'm trying to fit an experimental curve, described by the attached 'Data001.mat', with an analytical expression of the form:

y=k*x^n

where 'x' is the vector of abscissae in Data001 (first column of the mat file; I'm attaching a graphical representation of the data contained in Data001, named as 'exp.png', so to be more clear). In the analytical expression, both k and n are the parameters that I want to determine, so that the analytically calculated vector 'y' matches to the best the second column of the .mat file Data001.

Hope to hear from you soon.

Best regards,

A

Answer 1

[Rik]

Your function doesn't fit the data well. You should probably consider using an offset term as well.

S=load(websave('data.mat','https://www.mathworks.com/matlabcentral/answers/uploaded_files/647220/Data001.mat'));
x=S.Data001(:,1);
y=S.Data001(:,2);

f=fit(x,y,@(k,n,x)k.*x.^n,'start',[-1,1])

f = 
     General model:
     f(x) = k.*x.^n
     Coefficients (with 95% confidence bounds):
       k =       7e+05  (-2.835e+04, 1.428e+06)
       n =     -0.4585  (-0.5573, -0.3598)

y_fit=f.k.*x.^f.n;
plot(x,y),hold on
plot(x,y_fit)