Usually people do not ask for adequateness but whether the fit is "good" or, worse, "bad". But "good" or "bad" are not properties of the fit or the data. The data allow for a certain residual value (R value) depending on the amount of noise contained in the data. The simplest way to answer the question is therefore to calculate a theoretical R value that gives the R value approximately attainable with the given dataset including the standard uncertainties. When the R value from the least squares fit is much smaller than this theoretical R value, overfitting has occurred. When the R value from the least squares refinement is much larger than the theoretical R value, systematic errors apply. More about this topic is found in the November 2013 issue of Acta Crystallographica Section A (Volume 69, Part 6), doi:10.1107/S0108767313022514.
I cannot access the paper: could you handle me a private copy?
Your question does not look to me fully clear. If you make a fit, the residuals can show a dispersion that is not randomly distributed because the fitting function is not 'adequate', so it is not only depending on 'noise', as you state.
Usually the residual value should indicate that the closer to 1 the better the result
@ Hatem Maraqah: In this context I am referring to the crystallographic residual values (sometimes these are also called agreement factors), which are defined such that they are positive and approach zero for perfect agreement between observed intensities (or observed structure factor amplitudes = observed F-values) and calculated intensities (or calculated F-values).
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