Finding a polynomial fit to a set of data

Question

I am trying to find a polynomial to fit the data listed as

data = {{0,6.67},{6,17.33},{10,42.67},{13,37.33},{17,30.10},{20,29.31},{28,28.74}}

I set this string equal to data and use the routine

LinearModelFit[data,{x,x^2,x^3,x^4,x^5,x^6},x]

The answer I get is

Fitted Model[6.67-42.6435x +16.1427x^2 -<<19>>x^3 +<<20>>x^4 -0.00367168x^5 +0.0000409458x^6.

I don't understand why i am not getting any factors for the x^3 x^4 terms. Is there some way I can rectify this situation?

You are getting all the terms. Use Normal to see the model. — MelaGo, Feb 25 '20 at 01:33
Perhaps InterpolatingPolynomial might help you, see e.g. Get polynomial interpolation formula. — Artes, Feb 25 '20 at 01:57
Fit[data, {1, x, x^2, x^3, x^4, x^5, x^6}, x] gives quite a good fit. If you want to exclude3 the x^3 and x^4 terms, simply exclude them from the fit. Such as this: Fit[data, {1, x, x^2, x^5, x^6}, x]. The result isn't nearly as good a fit to the original. — Mark R, Feb 25 '20 at 03:04

score 1 · Answer 1 · answered Feb 25 '20 at 02:27

1

As per @MelaGo...

Normal@LinearModelFit[data,{x,x^2,x^3,x^4,x^5,x^6},x]

6.67 - 42.6435 x + 16.1427 x^2 - 2.09464 x^3 + 0.126902 x^4 - 0.00367168 x^5 + 0.0000409458 x^6

answered Feb 25 '20 at 02:27

MikeY

1 Answers1