Posted by Sarah on Tuesday, December 25, 2012 at 3:46pm.
It depends what you mean by best.
If you have n discrete points, you can always make a polynomial curve go though every single point by using order n-1.( Two points - straight line order 1, Three points - parabola order two, Four points - cubic, order three etc.) That is probably not what you want in a real world problem with many points because the higher the order the bumpier the curve (straight line - constant direction, parabola first up then down, cubic up- down - up etc). In other words you need to choose your model based on what is appropriate for the type of problem you are working.
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