I don't know that there's an "algorithm" for making that sort of
judgement. A few things that probably should be considered:

1) Am I looking for an interpolating scheme (splines and Bezier
curves) where each data point is considered to be exact and I'm using
those algorithms to estimate values between the exact data points.
2) Am I curve fitting where each data point isn't necessarily exact
but is considered to be representative of the process/phenomenon I am
observing.
3) When selecting the form of equation to use in curve fitting, what
do I know about the underlying process to which the data pertain?
Should it be linear? Quadratic? Exponential growth/decay? Is there an
asymptote?

A statistics text should discuss some of these issues as they relate to
generic curve fitting. Any information you can gather relative to a
specific problem can help answer specific questions. A numerical
methods text should discuss the mechanics of curve fitting.


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MrShorty
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