These are all big topics, but any "parametric curve fitting" like this tool uses
is parameter estimation (the parameters of the various curves). That
already makes strong modeling assumptions (usually including IID, Gaussian noise, etc.,) to get the parameter estimates in the first place. I agree it would be even better to have ways to input measurement errors (in
both x- & y- !) per your example and have non-bootstrap options (I only said "probably"), residual diagnostics, etc.
Maybe a residuals plot and IID tests of residuals (i.e. tests of some of the strong assumptions!) would be a better next step for the author than error estimates, but I stand by my original feedback. Right now even the simplest case of a straight line fit is reported with only exact slope & intercept (well, not exact, but to an almost surely meaningless 16 decimals!), though I guess he thought to truncate the goodness of fit measures at ~4 digits.
Maybe a residuals plot and IID tests of residuals (i.e. tests of some of the strong assumptions!) would be a better next step for the author than error estimates, but I stand by my original feedback. Right now even the simplest case of a straight line fit is reported with only exact slope & intercept (well, not exact, but to an almost surely meaningless 16 decimals!), though I guess he thought to truncate the goodness of fit measures at ~4 digits.