How to find the best constant coefficients for any formula for the given set of data?

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What are the tools, and the methods of finding the constant coefficients(with conditions(c > 0)) of any formula that you may come up with? For ex: Let’s say you have a set of data that has upward curvy looking when you scatter plot it with respect to time. But the data itself is not supposed to go to infinity by its nature so you assume that it should follow S curve(S sigmoid curve). So you wanna create a function with custom coefficients. How do you find the best coefficients? I used excel and tried to minimize the SSE(Sum Squared Errors) by using the solver tool but it doesn’t work well. It is very inconsistant. I have also got sas guide but I couldn’t find a way of doing it with a custom formula(not inbuild ones).

I can’t put an example formula right now since I am on my phone. But I can do it later when I get back home if necessary.

Thanks for the answers in advance.