How to optimize a curve fit to data in terms of amount of x-data included based on the R^2 values?

I have a curve fit to data, but I want to find out where along the curve the fit is the most successful in terms of a parameter such as the R^2 value. Therefore, if ages are along the x-axis, I want to know at what age I should cut off the curve in order for the fit to be the most successful. I would greatly appreciate any suggestions.

[dpb]

Use N+1 points for a polynomial of degree N and R^2 is identically one with zero residuals.

Need a better criterion for "most successful" -- a sample dataset to see the issue and why one would want to censor it arbitrarily also might add some context that could strongly influence choices.