
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
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 ydata that span an xdata 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 ydata (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: 20,472 Thanks: 2039 
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.

January 12th, 2018, 08:09 AM  #3  
Senior Member Joined: Oct 2009 Posts: 771 Thanks: 278  Quote:
 
January 12th, 2018, 09:28 AM  #4 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,636 Thanks: 2621 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.


Tags 
data, data range, fit, order, polynomial, range, relation 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
How to find order of a recurrence relation? help  siri  Math  3  June 17th, 2017 12:03 PM 
Relation between two sets of data  aspn  Elementary Math  7  September 1st, 2015 09:44 AM 
What's the range of this relation?  mick7  PreCalculus  1  June 16th, 2015 09:19 AM 
Data conversion to a specified range  Dan  Linear Algebra  1  June 12th, 2013 04:01 PM 
Order relation  PrototypePHX  Applied Math  0  March 7th, 2013 09:01 AM 