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Assume I have some data to which I am fitting a curve. The curve is nonlinear, so I am using NonlinearModelFit. Let's assume I want to see the process of how a curve fits. Is there a good way to do that?

Would something along the lines of setting MaxIterations to 100 and then looking at the fit and then starting the fit again (initializing the values with the results from the first 100 iterations) work? Or are there intermediate values in the fitting process that will be lost?

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You could use StepMonitor

data = {{0, 1}, {1, 0}, {3, 2}, {5, 4}, {6, 4}, {7, 5}};
nlm = NonlinearModelFit[data, Log[a + b x^2], {a, b}, x, 
  StepMonitor :> 
   Print["R^2 = ",
     1 - Total[(data[[All,  2]] - (Log[a + b x^2] 
     /. {x -> data[[All, 1]]}))^2]/ Total[(data[[All, 2]] - Mean[data[[All, 2]]])^2]]]
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