I have been working on a personal project involving data fitting in JavaScript. The algorithm that I am using, fminsearch, seems to work well; my application consistently achieves r^2 values above .90 for accurate data. However, I feel that my analysis of the error is not complete without both confidence intervals and standard errors. I have viewed the following questions, but since they do not use JavaScript and I cannot find similar libraries in JavaScript, I am unsure how to continue:
I also looked at this JavaScript tensorflow question, yet I do not know how to use it for functions other than the ones solved for in the question:
Standard error of estimated parameters with tensorflow.js
If there is no robust algorithm that allows for standard errors and confidence intervals for any inputted nonlinear function, it would be nice to at least have an algorithm for the function Log[y] = Log[c] + a Log[x] + b (Log[x])^2. I am not fitting this function by converting to a quadratic as I have found that the fits are much more accurate when starting and ending in the same form.
If it helps, here is an example of the ideal analysis I want using Mathematica.
Any help would be greatly appreciated, and have a wonderful day (: