From the library, this work sheet compares the Mathcad calculated coefficients vs NIST. They both meet, and fit equally. The point is not there.
The NIST and it's corollary Mathcad offer an approximation [ 7 coefficients ], the attached work sheet proposes an appropriate model [ 4 coefficients ]. In term of numerical approximation, the preference is the SGompertz model.
You have a bit of a problem with the data set. It is missing one of the data points, and some of the data values have been rounded. The result is that one cannot reproduce the validated coefficients from that data.
Interestingly enough with the correct data genfit does not reproduce the coefficients exactly (although it is quite close) while genfitX does.
I'm not sure about the data set from the library "Thurber". The one in the work sheet is the original from Leslie, at the time we were doing the Data Analysis Pack (this summer). Sometimes things don't go the way it's supposed. We had very intensive exchange, and many surprises. In some examples, the genfit, ratint ... would do nothing but red. But, my magic Thiele was OK. So, I insisted so much for Thiele, that it has been included. Well, it finalizes to a rational fit. But, the way coefficients are calculated is very simple and robust. In other words, Thiele is a rescue tool. It does not like noisy data sets at all.
You must have discovered something in Thurber. I'm an unconditional lover of the rational fit, but a model equation is a preferable alternative.
I checked the data against the data posted by NIST at their web site. I discovered that the data in the work sheet is missing one of the 37 data points, and that other data points have rounded data.
The reason I checked is that the coefficients in the worksheet are not accurate. When I calculated the actual coefficients, they were noticeably different and the SS was noticeably lower. The coefficients in the work sheet are slightly rounded versions of the true coefficients, as posted by NIST. Thus they are inaccurate with respect to the incorrect data in the worksheet.