There are countless tests available to evaluate the goodness of fit for a model to a set of data, but like all things statistical they give you information that you must interpret rather than a FIT / NO FIT binary response.
While p-values may be of value in some circumstances, there are many cases where their use is more misleading than instructional, and you need to look at error terms, residuals or other measures. Understanding and implementing these is a topic for very very many shelves of books and hours of discussion with people who have spent a very long time studying the subject.
I think you need to find someone suitably qualified and start by telling them what your data are, how it was collected, what you want it to be used for and the audience for your analysis.
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