Find the best model for my fitting

$f=b1*x1+b2*x2+b3$

$f=b1*x1^b2+b3*x2+b4$

$f=b1*x1^b2+b3*x2^b4+b5$

1. I use nlinfit to fit my data to these three model, and I ouput MSE, besides use MSE, is there any math method I could rely on to choose which model is the best? or what output from nlinfit can also be used?
2. I found BIC (https://en.wikipedia.org/wiki/Bayesian_information_criterion), sorry but I didn't understand, is there a way to find the likeyhood function for the three objective function? Then use BIC

Thank you.

[John D'Errico]

@Miraboreasu

Please don't keep on adding new questions. If you have a new question, then ask it in a separate question. Your second question is virtualy unrelated to the first.

[Miraboreasu]

@John D'Errico My bad, thank you for the note

[John D'Errico]

The problem is, if people keep appending new questions to the first, that turns one question into a long term consulting relationship. It make it difficult for others to follow and learn from the questions, because they can't search for anything. And it may well be that different people are better able to answer your next question. So just ask another question.

Answer 1

[Image Analyst]

"Best" is sometime subjective, unless you have some ground truth that you can compare your predictions again. If you do have some ground truth, even then it can be subjective because there are several metrics that you can use to compare your predicted data against the ground truth. If picking the model that gives the lowest MSE or MAE or R or R squared to the ground truth works for you and you're happy with it, then who's to say it's wrong? I'd just go with that.

You could use several metrics to compare your $f to the known ground truth values. If all metrics always suggest the same model, then that model is most likely the one to use.

[Miraboreasu]

Thanks, sorry I add another question instead of openning new thread.