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MathGroup Archive 2007

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Re: Re: Curve-fitting/data analysis question...

  • To: mathgroup at smc.vnet.net
  • Subject: [mg73416] Re: [mg73403] Re: Curve-fitting/data analysis question...
  • From: "Chris Chiasson" <chris at chiasson.name>
  • Date: Fri, 16 Feb 2007 00:53:17 -0500 (EST)
  • References: <200702110615.BAA11578@smc.vnet.net> <equnhn$ife$1@smc.vnet.net>

If the regression has this much "play" in it, I wonder if the model
correctly describes the system from which you captured the data. Then
again, I don't know much about statistics.

On 2/15/07, sherifffruitfly <sherifffruitfly at gmail.com> wrote:
> On Feb 14, 2:16 am, "Robert Dodier" <robert.dod... at gmail.com> wrote:
> > sherifffruitfly wrote:
> > > For each point p in my interval, I constructed two models - a linear
> > > one using the points to the LEFT of p, and an exponential one using
> > > the points to the RIGHT of p. I ran chi-squared to see which model p
> > > belongs to. At the beginning, LEFT wins pretty much every time. When
> > > RIGHT started winning is where I called the cut-off.
> >
> > Better still would be to choose the cut-off point to minimize the sum
> > of the goodness of fit (i.e., chi-square) on both sides.
> > (It's not a question of which side fits better, but rather how to get
> > better fit overall.) Maybe you're already doing that; I can't tell for
> > sure.
>
> Good idea. At best, I was doing a very ghetto version of your idea.
>
> > I would be interested to hear whether the total chi-square is
> > sensitive
> > to the placement of the cut-off point. Do you find that there is one
> > point which is much better than the rest, or is there a range of
> > points which are all more or less OK?
>
> I haven't noticed that - but that doesn't imply that it isn't there to
> be noticed.
>
> I *have* however noticed the following. For decreasing x, it's
> difficult to distinguish an exponential from a constant function. So
> really the bulk of the goodness-of-fit work is being done for
> increasing x of the linear models - linear models fail dramatically
> when the data becomes "exponential-ish".
>
> Is it reasonable to apply the above thought to your suggestion of
> minimizing the total goodness of fit by way of somehow weighting the
> linear part more heavily than the exponential, and then minimizing? If
> that is reasonable, are there any guiding heuristics? (I've never had
> to answer this sort of problem before - or even seen one.)
>
> > HTH
> > Robert Dodier
>
> Thanks!
>
> cdj
>
>
>


-- 
http://chris.chiasson.name/


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