Proving that data follows a polynomial function

[gsingh2011]

I can prove that data follows a curve of the form y=Ax^n and y=Ae^x by using log log and natural log transformations. I have some data that I believe is more complex, something of the form y=a_nx^n+a_n-1x^n-1+...+a₁x+a₀, in other words a polynomial function. Is there any way I can prove that it follows this form and what the order of the function would be?

 

[bpet]

For fixed n the constants a_n, ... can be found by multivariate linear regression. Two ways to select the "best" n (i.e. to fit but not overfit) are by visual inspection and by use of a model selection criterion such as Bayesian information criterion.

Also a comment on the wording; in working with real data it's never possible to "prove" the data is from a particular model, only to show the model is in good agreement with the data.

 

[gsingh2011]

Thanks for the reply. According to wikipedia, that model selection criterion you suggested only works if the data follows an exponential curve. Do you know anything for polynomials? I couldn't find anything just from googling, or I might have missed something since this is new to me.