It depends somewhat on the purpose of the curve. Is it just going to be used as the best guess within the range of points? Or is it going to be used to estimate a parameter that will be used in further predictions? And what is a "good fit" depends on what it represents. If it's a fairly sharply defined relation then a lot of scatter means there's noise and the measurement is poor. But if it's just exploratory and you don't even know whether there's a relation, then a lot of scatter may mean there just isn't any relation. You know you have a good fit when you have a relation based on a causal theory and the theory includes estimates of the uncertainty and your data is consistent with both. Note that this means the data can have /*too little scatter*/ to be consistent with the theory. A familiar occurence in freshman physics lab. Brent On 9/23/2018 7:32 AM, Henry Baker wrote:
The following xkcd comic (#2048) is funny, but it brings up a good point: are there any good methods for deciding when a particular curve fits a particular set of data points?
Should statistics & spreadsheet programs utilize such a method to warn users that the fit they've chosen isn't very good?
I've thought of somehow using color along the curve to indicate where the fit is good (perhaps "green") and portions along the curve where the fit isn't so good (perhaps "red"). A *spline* curve could also indicate its tension by means of color, for example. (Of course, none of this is going to help those who are color blind!)
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