I frequently solve similar problems in an Excel spreadsheet by creating an objective function (a calculated value in a cell I want minimized or maximized) and then use the Solver() AddIn to find the optimal, which can even be supplied with constraints (upper and lower limits, x+y

I found the ideal curve on Wikipedia, then I found an actual data set with a Google search of images. I digitized the data points and pasted them into an Excel spreadsheet, then I set up the regression in a double loop using the LINEST function, which returns both R² and F-value. The grouping of points yielding the highest F-value is the best choice. This is the same result you would get by multiplying the standard deviation times Student's-T and finding the minimum uncertainty. Fewer points yields lower sigma and higher T, while more points yields larger sigma and smaller T. The group yielding the smallest product of sigma*T (uncertainty) should also yield the largest F-value. This gives you a statistical measure to guide your selection of which points to include in the linear regression. The button runs through all of the reasonable combinations. I highlighted the best one in green. There are easier ways of doing this and I can send you a little C source code to implement the procedure, but having it in a spreadsheet also illustrates the process. You can paste your own data and solve the problem.

Dear Mr. Benton,

your method would help me a lot to find statistically validated results with the method of linearisation.

Thank you very much!

and I would also like to thank you for working so much on my question!

I don't know if you still need an answer, but this software I wrote, might do it well.

www.lerenisplezant.be/fitting.htm