Maryam -

In https://www.stata.com/features/overview/nonlinear-regression/

they start by saying "Stata’s nl fits an arbitrary function by least squares."

If you want to change a parameter, then the model will not be a proper fit to your sample.

You can research the term "graphical residual analysis" so you can see the fit of your model for your sample. "Cross-validation" is used to try to avoid so closely fitting to your particular sample that other data you thought would be modeled well are not. You could try dividing your sample and using a graphical residual analysis for each resulting nonlinear regression, as found by Stata nl.

You might want to try another function.

I hope I addressed your question.

Cheers - Jim

Using this program, it should be easy. Let me know if you need assistance.

www.lerenisplezant.be/fitting.htm

Remember Koen Van de Moortel, statisticians will tell you, and have told you, that there is a difference between a response variable (which is a random variable), and a predictor variable (which is not a random variable).

A regression model is not a deterministic model.

James R Knaub Of course I know that a regression model is not "deterministic". It is a kind of glasses through which we look at our data, a template. It can only tell us "if you assume this or that kind of relationship in your data, these are te best fitting parameters." I'm only questioning what is to be considered as "the best".