How Prism reports nonlinear regression results when the fit is perfect
The whole point of nonlinear regression is to fit a model to your data, to obtain the best-fit values of the parameters. It does this by minimizing the sum-of-squares. What happens when the data are perfect, so the curve goes right through every point and the sum-of-squares is zero?
Prism handles this situation sensibly when you choose least-squares nonlinear regression fit. Prism reports 'perfect fit' and states the best-fit values of the parameters. It correctly reports that the sum-of-squares is 0.0 and R2 is 1.000. It does not report values for the standard errors of the parameters or for their confidence intervals.
In contrast, Prism can get confused by perfect data if you choose a robust fit, or if you checked the option to count or exclude outliers (which requires a robust fit first). In these cases, Prism can report that the fit was "interrupted" and can report "value too large" instead of parameter values.
It is easy to work around this problem. If your data are perfect, there is no point in choosing a robust fit and there won't be any outliers to find. Turn off these options, and Prism will fit the curve just fine. This has been fixed in 5.03 and 5.0c.