# How to determine significance of polynomial?

I'm running a model where both a 2nd or 3rd order polynomial would seem to fit the data. I'm trying to decide which one to use. In the quadratic model (panel fixed effects) the first and second order of the variable are significant but less so compared to a model with a cubic included (y=x+x^2+x^3+e). On the other hand, in my case the quadratic specification would be more intuitive. And more generally, how should the significance of the polynomials be interpreted? If I've understood correctly, the significance of the highest polynomial determines whether the model specification is reasonable but all the lower order polynomials should be included irrespective of their significance.

• Check out this question. – Stat Dec 17 '14 at 21:34
• If you seriously consider quadratic vs cubic models, I urge you to consider using orthogonal polynomials; it can aid substantially in understanding and interpreting the effect of the additional term. But if you don't have a theoretical justification for polynomials and are just trying to fit a curvilinear relationship, you may be better off with some general smooth function via regression splines or smoothing splines or local-linear (or local-polynomial) models ("GAM"-type models). – Glen_b -Reinstate Monica Dec 17 '14 at 22:36