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/
- References:
- Curve-fitting/data analysis question...
- From: "sherifffruitfly" <sherifffruitfly@gmail.com>
- Curve-fitting/data analysis question...