Fit review for multiple systems

[Migras]

Hello everyone

Im new here so I hope I dont get anything wrong. But heres my question:

I am writing my Bacherlors Thesis one chapter of said thesis revolves around finding a better fit to my data than the Van-Deemter equation H(u)=B/u + C*u
So after looking through some Data I found about 6 different alternatives (which mostly extend the equation by one term), which I would like to try and compare to each other. The problem is, that I have 9*4*5=180, of these systems (each consisting of 8-9 points) and I have no idea how to do that without making 180*7 and looking at them.
So I come here in the hopes of someone being able to recommend me some software or function or something like that, that would allow me to analyse my data more time efficient. My deadline is at the end of ferbruary I could really use some help.

Thanks for your attention

 

[staassis]

In general, you can perform estimation in a loop using R, Matlab or Stata. And then, you can aggregate residuals over systems for each configuration and compare the 6 configurations using a measure like BIC (Bayesian Information Criterion).

However, in your situation 8-9 data points are not sufficient for estimating 3 or more parameters in a system. They are not sufficient for estimating even 2 parameters in H(u)=B/u + C*u. See if you can introduce regularization by postulating that parameter sets (B,C,...) in different systems are somehow close to each other, for each configuration.