I have been working on a personal project trying to emulate the nonlinear regression functionality of Mathematica for three free parameters. I am able to accurately fit functions, yet I am unsure how to report the standard error and confidence intervals like Mathematica.
See here:
Whenever I apply the algorithms in the below tutorials for three free parameters, I get imaginary numbers as my answers:
https://www.youtube.com/watch?v=3IgIToOV2Wk
Is there a problem with using the above algorithms, which are demonstrated with two parameters, for three parameters? How would I compute the standard error and confidence intervals for three parameters?
If it is helpful, here is the function that has given me imaginary results: $$c * x^b * e^{(a * log10(x)^2)}. $$
May I recommend a Bayesian inversion for estimating confidence intervals on non-linear regression problems. See Data Analysis, A Bayesian Tutorial, D. S. Silva. Oxford Press (2006).