From: "Paul Lutus" Subject: Re: best polynomial fit Date: Mon, 18 Sep 2000 09:36:06 -0700 Newsgroups: sci.math.num-analysis,sci.physics Summary: [missing] E. Robert Tisdale wrote in message news:39C62B40.259CA0CD@netwood.net... > > "E. Robert Tisdale" wrote: > > > > > Try to forget about all that "overfitting" nonsense. > > > If you haven't got enough independent data points > > > to determine a unique set of coefficients to the desired accuracy, > > > then you just need to get more data. > > > > Frequently, in realistic situations the number of datapoints > > is too low and there is no chance to get more. > > This is the problem many people have to deal with. > > Thus ovrefitting is a very important problem > > one has to deal with and one should not forget. > > You're not making sense Alex. > If you can't get any more data points, > you don't need to worry about what the function does > between the data points that you do have. You're not making sense, Robert. The entire point of data regression is to try to fit limited data to a mathematical model, and hopefully also to establish the degree to which that fit may have meaning. An example is fitting three observations of an orbiting body to an ellipse, an entirely sound method used to establish an orbit for a previously unknown object. It is quite mathematically sound, and three good observations are all that are required. As the examples increase in complexity, the degree of correlation between the fitted curve and the data becomes increasingly important (in the ellipse example above, there is always a fit to a single outcome). There is a vast literature on this subject, and the advice "go out and get more data" is a standard joke in the field, before getting down to the more realistic task of making the most of the data that are available. And contrary to your opinion, what the function does between the data points is very important, and can be used to evaluate whether the function is likely to represent the underlying process or not. Here is a good tutorial introduction that discusses these issues: http://www.ecs.fullerton.edu/~mathews/numerical/lp.htm -- Paul Lutus www.arachnoid.com