Re: confidence region and leasqr()

[Olaf Till]

On Wed, Apr 10, 2013 at 12:53:24PM +0400, Dmitry Shkirmanov wrote:
> I just found how to do this with matlab(see 
> http://www.mathworks.com/help/stats/examples/weighted-nonlinear-regression.html
> ), needed value is  "ypredci".  Is it possible to do the same with
> octave?
> 
> 
> >Hello, list. I am new in octave.
> >I need to fit function to data points and plot the resulting
> >function and a prediction interval.
> >I found how to plot data points and resulting function by using leasqr().
> >But i can not find how to plot the prediction interval.
> >On the http://www.mathworks.com/help/curvefit/predint.html there
> >are examples of  graphs with prediction region. In these example
> >the prediction region is marked by the dashed line.
> >So, is it possible to plot the prediction region with octave?
> >
> >P.S.
> >on http://octave.sourceforge.net/optim/function/leasqr.html i found that
> >"Z = matrix that defines confidence region". But i have no idea
> >how "Z" defines this region and how to use it for plotting.

I know no Octave function to do such plots automatically.

You can obtain matrices (e.g. Z from leasqr) to define ellyptical
approximated confidence regions for the _parameters_. But to use these
to get confidence regions for the _data_ modelled by arbitrary
non-linear functions seems problematic to me. The only way I'd see is
complicated (eigendecomposition of Z or similar matrix, compute
confidence intervals along each principal component, compute the
corresponding intervals at each data point, determine sign of
dependence of each data point on each principal component, and add up
the data intervals at each data point for each principal component
(considering the sign)) and would only lead to rough approximations in
whom I'd have not much trust.  But maybe there is some standard way to
make such approximations which I don't know.

If you could tell (e.g. from some documentation) how Matlab computes
these confidence intervals for the data, we could probably tell you
how to do the same with Octave.

Olaf

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