Fit parameter statistics using lsqcurvefit?

I'm looking for statistics on a fit to experimental data to ensure that the fit is good and is not overparameterized. Useful statistics would include t-test, F and p-values, covariance matrix, etc. Now, I'm aware that fitting with fitnlm from the statistics toolbox would accomplish this easily. However, after much trial and error, I've found that the routine in fitnlm does not fit my data very well. Using lsqcurvefit gives much better results and is much faster. Putting the final fit parameters from lsqcurvefit into fitnlm using the same model often results in errors and will not fit. At this point, I need to use lsqcurvefit to get accurate results.

Is there a good method for getting relevant fit statistics with lsqcurvefit? If it comes down to it, it it possible to calculate these t, p, and F manually from the outputs of lsqcurvefit?