I am attempting to automate some processes at work. Im familiar with statisical methods such as GLM, ANOVAs, Basic OLS, etc. But I am unsure of methods which I can use for this.

problem statement: Optimal point from collected data should be minimized based off the model value from the fitted curve/captured data and should also minimize the variance at the point.

I have this model here. I haven't fitted anything but looks pretty clear its a rational function curve. What I want to do is pick the point on the curve the minimizes, simultaneously, the actual value and the spread at the point. Visually this is easy for a 2, 3, 4 variable case but as models get larger it becomes more difficult. enter image description here

If someone could point me to a method that would be very helpful. further if someone could also point out some literature I can read to build improved models that can help me automate this process, that would be wonderful. It does not need to solely depending on the models produced, but if could help me attach a confidence level too it, that would be even better.



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