[SciPy-User] How to estimate error in polynomial coefficients from scipy.polyfit?
Charles R Harris
Thu Mar 25 23:14:25 CDT 2010
On Thu, Mar 25, 2010 at 9:40 PM, David Goldsmith <email@example.com>wrote:
> On Thu, Mar 25, 2010 at 3:40 PM, Jeremy Conlin <firstname.lastname@example.org> 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.
Oh, there are lots of things. Detector responses, platinum resistance
thermometers, optical aberrations, so on and so forth. Polynomials aren't
always appropriate and they are usually useless for extrapolation, but they
are often invaluable for getting a compact representation of the data.
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