Fitting polynomial model to data in R

Question

I ve read the answers to this question and they are quite helpful  but I need help particularly in R    I have an example data set in R as follows   x  lt - c 32 64 96 118 126 144 152 5 158    y  lt - c 99 5 104 8 108 5 100 86 64 35 3 15    I want to fit a model to these data so that y   f x   I want it to be a 3rd order polynomial model   How can I do that in R    Additionally  can R help me to find the best fitting model

User · Answer

Which model is the  best fitting model  depends on what you mean by  best    R has tools to help  but you need to provide the definition for  best  to choose between them   Consider the following example data and code   x  lt - 1 10 y  lt - x   c -0 5 0 5   plot x y  xlim c 0 11   ylim c -1 12    fit1  lt - lm  y offset x  -1   fit2  lt - lm  y x   fit3  lt - lm  y poly x 3    fit4  lt - lm  y poly x 9    library splines  fit5  lt - lm  y ns x  3    fit6  lt - lm  y ns x  9     fit7  lt - lm  y   x   cos x pi     xx  lt - seq 0 11  length out 250  lines xx  predict fit1  data frame x xx    col  blue   lines xx  predict fit2  data frame x xx    col  green   lines xx  predict fit3  data frame x xx    col  red   lines xx  predict fit4  data frame x xx    col  purple   lines xx  predict fit5  data frame x xx    col  orange   lines xx  predict fit6  data frame x xx    col  grey   lines xx  predict fit7  data frame x xx    col  black     Which of those models is the best   arguments could be made for any of them  but I for one would not want to use the purple one for interpolation

User · Answer

To get a third order polynomial in x  x 3   you can do  lm y   x   I x 2    I x 3     or  lm y   poly x  3  raw TRUE     You could fit a 10th order polynomial and get a near-perfect fit  but should you   EDIT  poly x  3  is probably a better choice  see  hadley below

User · Answer

The easiest way to find the best fit in R is to code the model as   lm 1  lt - lm y   x   I x 2    I x 3    I x 4           After using step down AIC regression  lm s  lt - step lm 1

User · Answer

Regarding the question  can R help me find the best fitting model   there is probably a function to do this  assuming you can state the set of models to test  but this would be a good first approach for the set of n-1 degree polynomials   polyfit  lt - function i  x  lt - AIC lm y poly x i    as integer optimize polyfit interval   c 1 length x -1   minimum    Notes    The validity of this approach will depend on your objectives  the assumptions of optimize   and AIC   and if AIC is the criterion that you want to use   polyfit   may not have a single minimum  check this with something like   for  i in 2 length x -1  print polyfit i    I used the as integer   function because it is not clear to me how I would interpret a non-integer polynomial  for testing an arbitrary set of mathematical equations  consider the  Eureqa  program reviewed by Andrew Gelman here   Update  Also see the stepAIC function  in the MASS package  to automate model selection

[r] Fitting polynomial model to data in R

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