My rule of thumb is that if the relative standard error of the residuals of the fit, what I call
SsubF, is 10% or greater that is a poor fit; 3-5% probably acceptable and meaningful; and 2% or less good. Values of 1% or less are excellent. One must also look at the estimates of the values all the free-to-vary parameters of a fit and if the relative standard
error of a given estimate is large, 15% or more, it is poorly determined. The RMS value of the these errors for all the free parameters should be less than 5% for a meaningful and significant fit.
Ross Macdonald
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Dr. J. Ross Macdonald is William R. Kenan Jr. Professor of Physics, Emeritus; Department of Physics and Astronomy of the University of North Carolina at Chapel Hill, and a member of NAS and NAE. Website:
http://jross macdonald.com