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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?

Mihai Chelaru
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CashCab1221
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  • 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? – whuber Jul 05 '19 at 17:05
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    I was not aware of the standardization, thank you, that helps tremendously. – CashCab1221 Jul 05 '19 at 17:11
  • For the details of this, see the section headed "Orthogonal polynomials in one variable" in my post at https://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. – whuber Jul 05 '19 at 17:53

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