[SciPy-User] a routine for fitting a straight line to data

Ralf Gommers ralf.gommers@gmail....
Sun Mar 31 06:08:03 CDT 2013


On Mon, Mar 25, 2013 at 2:27 AM, David Pine <djpine@gmail.com> wrote:

> scipy.stats.linregress does not do the job.  First, it does not allow for
> weighting of the data, relative, absolute, or otherwise.


Weighting could be easily added to linregress, that would be useful.


> It does not return the covariance matrix, which provides estimates of the
> uncertainties in the fitting parameters, nor does it return chi-squared,
> which is the standard measure of the quality of the fit in the physical
> sciences.


These are a little trickier to add, would require adding a
full_output=False input because just adding a return value would break
backwards compatibility. But it's also possible. Would you like to have a
go at adding your suggestions to linregress?

There's still the issue that if you enhance stats.linregress it will be
hard to find. Fitting tools are scattered all over, and it's not clear what
the best solution is. A doc section giving an overview of all fit
functionality would be a good start. See
https://github.com/scipy/scipy/pull/448 for a recent discussion on that
topic.

Ralf



> David
>
>
> On Mar 24, 2013, at 8:19 PM, josef.pktd@gmail.com wrote:
>
> > On Sun, Mar 24, 2013 at 7:53 PM, David Pine <djpine@gmail.com> wrote:
> >> I would like to submit a routine to scipy for performing least squares
> fitting of a straight line f(x) = ax + b to an (x,y) data set.  There are a
> number of ways of doing this currently using scipy or numpy but all have
> serious drawbacks.  Here is what is currently available, as far as I can
> tell, and what seem to me to be their drawbacks.
> >>
> >> 1. numpy.polyfit :
> >>    a.  It is slower than it needs to be.  polyfit uses matrix methods
> that are needed to find best fits to general polynomials (quadratic, cubic,
> quartic, and higher orders), but matrix methods are overkill when you just
> want to fit a straight line f(x)= ax + b to data set.  A direct approach
> can yield fits significantly faster.
> >>    b.  polyfit currently does not allow using absolute error estimates
> for weighting the data; only relative error estimates are currently
> possible.  This can be fixed, but for the moment it's a problem.
> >>    c.  New or inexperienced uses are unlikely to look for a routine to
> fit straight lines in a routine that is advertised as being for
> polynomials.  This is a more important point than it may seem.  Fitting
> data to a straight line is probably the most common curve fitting task
> performed, and the only one that many users will ever use.  It makes sense
> to cater to such users by providing them with a routine that does what they
> want in as clear and straightforward a manner as possible.  I am a physics
> professor and have seen the confusion first hand with a wide spectrum of
> students who are new to Python.  It should not be this hard for them.
> >>
> >> 2. scipy.linalg.lstsq
> >>    a.  Using linalg.lstsq to fit a straight line is clunky and very
> slow (on the order of 10 times slower than polyfit, which is already slower
> than it needs to be).
> >>    b.  While linalg.lstsq can be used to fit data with error estimates
> (i.e. using weighting), how to do this is far from obvious.  It's unlikely
> that anyone but an expert would figure out how to do it.
> >>    c.  linalg.lstsq requires the use of matrices, which will be
> unfamiliar to some users.  Moreover, it should not be necessary to use
> matrices when the task at hand only involves one-dimensional arrays.
> >>
> >> 3. scipy.curve_fit
> >>    a.  This is a nonlinear fitting routine.  As such, it searches for
> the global minimum in the objective function (chi-squared) rather than just
> calculating where the global minimum is using the analytical expressions
> for the best fits.  It's the wrong method for the problem, although it will
> work.
> >>
> >> Questions:  What do others in the scientific Python community think
> about the need for such a routine?   Where should routine to fit data to a
> straight line go?  It would seem to me that it should go in the
> scipy.optimize package, but I wonder what others think.
> >
> > scipy.stats.linregress if there is only one x
> >
> > Josef
> >
> >
> >> David Pine
> >> _______________________________________________
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