My Math Forum relation between order of polynomial fit and range of x data

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 January 12th, 2018, 05:53 AM #1 Newbie   Joined: Jan 2018 From: Germany Posts: 4 Thanks: 0 relation between order of polynomial fit and range of x data Hi everybody, I have y-data that span an x-data range of say 1:100. The data are nicely fitted with a polynomial fit of 3rd order (Matlab/python: polyfit(x,y,3)). I have a second set of y-data (say: yy), spanning only half of the data range, say x=51:100. Is there any reasonable rationale that we could use to argue why we should use a 2nd order polynomial fit for this subset of data, in order to do something comparable to the 3rd order polynomial fit on the larger set of data? Intuitively it looks nice... but is it the good way to do it? Kind regards, Chris
 January 12th, 2018, 07:44 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,931 Thanks: 2207 It's a good idea to develop some mathematical reasoning (or model) that tells you what sort of relationship should exist. It's also highly desirable to know how accurate your values for x and y are. Thanks from v8archie
January 12th, 2018, 08:09 AM   #3
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 Originally Posted by chr Hi everybody, I have y-data that span an x-data range of say 1:100. The data are nicely fitted with a polynomial fit of 3rd order (Matlab/python: polyfit(x,y,3)). I have a second set of y-data (say: yy), spanning only half of the data range, say x=51:100. Is there any reasonable rationale that we could use to argue why we should use a 2nd order polynomial fit for this subset of data, in order to do something comparable to the 3rd order polynomial fit on the larger set of data? Intuitively it looks nice... but is it the good way to do it? Kind regards, Chris
Do a formal hypothesis test to see whether the coefficient of x^3 is significant.

 January 12th, 2018, 09:28 AM #4 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,675 Thanks: 2655 Math Focus: Mainly analysis and algebra Following on from Skipjack's comment, the properties of cubic curves are vastly different to those of quadratic curves for values of $x$ with a large magnitude. For the polynomial fit to have any meaning at all you ought to have a clear idea which is more appropriate qualitatively. (or perhaps, given your cubic fit, a cuartic would be the better choice).
 January 14th, 2018, 09:32 AM #5 Newbie   Joined: Jan 2018 From: Germany Posts: 4 Thanks: 0 order of polynomial fit @Micrm@ss: Great idea. That is it. I would still have to figure out which test would be most appropriate. If I could bring the problem into the form of a maximum likelihood form, a likelihood ratio test would tell me which order is appropriate.

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