# Polynomial in linear regression

I am new to Regression and R. I know that polynomial functions are used when a regression model does not fit data (underfitting), but I want to know which degree of polynomial should be used? I also want to know that if a regression model uses multiple variables (e.g., y ~ x1+x2+x3+x4) then do I need a polynomial function in this model?

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That depends on the problem under consideration. A polynomial regression always yields a better fit than an affine regression but it could make no sense from the interpretation perspective. –  Stéphane Laurent Sep 4 '12 at 13:27
By presupposing a polynomial solution, this question implicitly rules out procedures that might be simpler or more effective. I would like to suggest that you begin your research by reviewing any appealing threads related to model selection. You may find many of these informative and stimulating. Then consider returning with a more specific question motivated by that information. –  whuber Sep 4 '12 at 15:46
Did you checked for linearity!? check for other models for non linear data. or you can always plot the data and try to build a polynomial model that as the same look...then just shape it (fit it)... –  user13840 Sep 4 '12 at 16:55