# How do I evaluate the error for a fitted non-linear curve

3 views (last 30 days)
yuval steinberg on 25 Aug 2022
Commented: yuval steinberg on 25 Aug 2022
Hi,
I have an experimental data spectrum which contains 3 overlapping peaks. I deconvoluted this spectrum with 3 Lorentianz using 'fit', as seen in the code. I'm quite happy with the fit, but I don't understand how I can estimate how good the fit is. Using the 'fit' function I can get R^2 goodness of fit but I found that its only good for linear regression type of fitting, not for a spectrum like mine.
More over, after I fit the data I integrate using 'trapz' over the 3 lorentianz in order to get their area. I need to estimate the error of these integrations. assuming I can get some form of goodness of fit for my fitted spectrum, how will I correlate it to an error of the integration?
I hope I managed to explain my problem.
Here is the fittype function I use in my code:
ft = fittype(@(A1,A2,A3,s1,s2,s3,x) A1*s1^2./(s1^2+(x-pos1).^2) + ...
A2*s2^2./(s2^2+(x-pos2).^2) + A3*s3^2./(s3^2+(x-pos3).^2), 'independent', 'x', 'dependent', 'y' );

Mathieu NOE on 25 Aug 2022
hello
using both experimental and fitted data you can compute R2 this way :
function Rsquared = my_Rsquared_coeff(data,data_fit)
% R2 correlation coefficient computation
% The total sum of squares
sum_of_squares = sum((data-mean(data)).^2);
% The sum of squares of residuals, also called the residual sum of squares:
sum_of_squares_of_residuals = sum((data-data_fit).^2);
% definition of the coefficient of correlation is
Rsquared = 1 - sum_of_squares_of_residuals/sum_of_squares;
end
yuval steinberg on 25 Aug 2022
thank you very much

Ben Mercer on 25 Aug 2022
Hi yuval, I'm not sure if I'm entirely clear on what you're asking. But to my understanding R^2 is not specific to linear regression, the criteria for using it is that the model must be a least-squares solution - otherwise you end up with meaningless (sometimes negative) R^2 values.
If an R^2 value is not output from whatever fitting function you are using, you can calculate it by calculating the value of your fitted model at your input data points, then calculate R^2 using the following definition:
The R^2 tells you how much variation in the data is captured by your model, as a fraction of the total variation. You can also calculate the RMS error between the data and model, but this will output a result in the physical units of whatever you are measuring, and this is not a very specific measure of how well your model captures patterns in te data.
yuval steinberg on 25 Aug 2022
thank you very much. I'll look in to this

### Categories

Find more on Linear and Nonlinear Regression in Help Center and File Exchange

R2020a

### Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!