Parameter estimation using nonlinear regression in Matlab

Dear Matlab experts,

I got coefficient values using nonlinear regression in Matlab. If someone ask me where the retailed results can be found, I would like to know how to explain this verbally.

My coding in Matlab is:

Time = [0,1,2,3,4,5,6,7]; Energy = [598,594,612,637,675,692,716,753]; Capital = [0,0,0,0,0,0,0,0]; Emission = [1467,1452,1580,1667,1815,1967,2069,2210]; ds = table(Time',Energy',Capital',Emission'); modelfun = @(b,x) b(1).*exp(-b(2)*x(:,1)).*x(:,2)-b(3)*x(:,3).^b(4).*x(:,2); pguess = [1,0.2,0.01,0.02]; mdl = fitnlm(ds,modelfun,pguess)

The coefficients parameters of the emissions function are estimated using the nonlinear regression models in Matlab. Coefficients are estimated using an interactive procedure starting from the initial values of the coefficients.

I would like to know if this explanation is correct or not.

If you have any better idea to explain this, then please let me know.

Thank you very much in advance.

Sincerely yours,

J1

Answer 1

[John D'Errico]

I would change the wording some.

The parameters of the emissions function are estimated using the nonlinear regression methods in Matlab. Coefficients are estimated using an iterative procedure starting from the initial values of the coefficients, minimizing the sum of the squares of the residuals.

The changes I made were relatively minor, but appropriate I think.

1. "nonlinear regression methods" instead of "nonlinear regression models". You could also say "nonlinear regression algorithms". A model is what you have provided, that is fit to the data, whereas an algorithm or method would be the scheme used to fit that model.

2. "iterative" replaces "interactive". To me that seems self evident. Simply the wrong choice of word.

3. I added the clause "minimizing the sum of the squares of the residuals". This was done because iterative methods might also be employed to minimize measures like the sum of absolute values, or other norms applied to the residuals.