# [SciPy-User] How to estimate error in polynomial coefficients from scipy.polyfit?

Jeremy Conlin jlconlin@gmail....
Mon Mar 29 10:08:48 CDT 2010

```On Thu, Mar 25, 2010 at 9:40 PM, David Goldsmith
<d.l.goldsmith@gmail.com> wrote:
> On Thu, Mar 25, 2010 at 3:40 PM, Jeremy Conlin <jlconlin@gmail.com> wrote:
>>
>> Yikes!  This sounds like it may be more trouble than it's worth.  I
>> have a few sets of statistical data that each need to have curves fit
>> to them.
>
> That's an awfully generic need - it may be obvious from examination of the
> data that a line is inappropriate, but besides polynomials there are many
> other non-linear models (which can be linearly fit to data by means of data
> transformation) which possess fewer parameters (and thus are simpler from a
> parameter analysis perspective).  So, the question is: why are you fitting
> to polynomials?  If it's just to get a good fit to the data, you might be
> getting "more fit" than your data warrants (and even if that isn't a
> problem, you probably want to use a polynomial form different from "standard
> form," e.g., Lagrange interpolators).  Are you sure something like an
> exponential growth/decay or power law model (both of which are "more
> natural," linearizable, two-parameter models) wouldn't be more appropriate -
> it would almost certainly be simpler to analyze (and perhaps easier to
> justify to a referee).
>
> On this note, perhaps some of our experts might care to comment: what
> "physics" (in a generalized sense) gives rise to a polynomial dependency of
> degree higher than two?  The only generic thing I can think of is something
> where third or higher order derivatives proportional to the independent
> variable are important, and those are pretty uncommon.

I will only be fitting data to a first or second degree polynomial.
Eventually I would like to fit my data to an exponential or a power
law, just to see how it compares to a low-order polynomial.  Choosing
these functions was based on qualitative analysis (i.e. "it looks