I am working with some data on which I used the poly() function to get 4th degree polynomials. I had one model that only had significance for the first degree, so I tried to simplify it and get different coefficients and other info under "Coefficients:" from the summary() function, by using lm1=lm(data1~data2) versus lm2=lm(data1~poly(data2, degree=1)).

My biggest question is should I use the lm2 instead of the lm1 in order to stay consistent with other models with higher degree polynomials?

  • $\begingroup$ Are you aware that poly(data2, degree=1) is simply a version of data2 that has been centered to 0 and standardized to a Euclidean length of 1? $\endgroup$
    – whuber
    Jul 5, 2019 at 17:05
  • 1
    $\begingroup$ I was not aware of the standardization, thank you, that helps tremendously. $\endgroup$ Jul 5, 2019 at 17:11
  • $\begingroup$ For the details of this, see the section headed "Orthogonal polynomials in one variable" in my post at stats.stackexchange.com/a/408855/919. The degree-one term is obtained by first "regressing against (a constant)," which centers it (takes out it mean) and then normalizing it. $\endgroup$
    – whuber
    Jul 5, 2019 at 17:53


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.