[SciPy-user] Polyfit may be poorly conditioned

[Ryan May]

massimo sandal wrote:
> Gnata Xavier ha scritto:
>> Quoting :
>>
>> "Well think about it one second : A  fit with a 12 order polynomial 
>> will always have a smaller least mean square error the a fit using a 
>> <12 order polynomial. Your must figure out we before using a polyfit.
>>
>>  >>Well, this is reasonable but it is not what I see happening. Often 
>> the algorithm takes the highest-degree polynomial, but not always."
>>
>> This simply cannot be. Polyfit is just fine. The goal of my trivial 
>> example is to show that polyfit is fine.
>> My goal is only to tell to Massimo what there must be a pb somewhere 
>> in its code.
> 
> Pardon my utter ignorance, but imagine my data are just a straight line. 
> How can a parable, or a 3rd order polynomial, fit them better than a 
> straight line itself?
> 

Just as it takes 2 points to define a line, it takes 3 points to define 
a parabola, and n+1 points to define an nth order polynomial.  Thus, you 
can define a polynomial that passes through all of your data points. 
This will produce an RMS error of 0.  However, if you know the points 
lie along a line, this is clearly not optimal and you are simply fitting 
the curve to noise in the data.

Ryan

-- 
Ryan May
Graduate Research Assistant
School of Meteorology
University of Oklahoma