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Very robust regression? 
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#1
Mar207, 09:37 AM

P: 3

Hi,
I want to model a set of a few dozen points on the xy plane where y can be anywhere from 0 to 100 and x increases by 1 for each point on the yaxis, ex: (1, 26) (2, 84) (3, 2) etc. . . Is it possible to accurately model such a random array of points with an equation? Someone once suggested using an 'interpolating polynomial in the Lagrange form', but that does not appear to work well with such a random array of points. If it can't be done with a known regression technique, here is my question: Given the points (1, 26) (2, 84) (3, 2) (4, 100) (5, 50), could a function exist  any function of any category  which will hit each point? Thanks. 


#2
Mar207, 10:34 AM

Mentor
P: 15,201

[tex]27x^4 + 323\frac1 3x^31335x^2+2204\frac2 3x1140[/tex] You generally don't want to do that, however. For example, this particular polynomial rapidly goes negative as x goes below 1 or above 5. In other words, it has very little extrapolative capability. You will quickly start to lose even interpolative capability with the exactfit polynomial as the number of points increases. You want to develop a fit to a less expressive model. There is no magic oneformfitsall method. People can still get advanced degrees in statistics, after all. 


#3
Mar207, 08:07 PM

P: 1,295

If you tell us what you expect from this "model", we can suggest various methods that are suited to the task.



#4
Mar207, 09:29 PM

Sci Advisor
P: 2,751

Very robust regression?
As Crosson says, obviuosly you must be expecting something from this model besides hitting all the points. You already have all the points so you must be expecting something additional, but what is it?



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