Effect of the Number of Fit Power Series Terms on the Predictions

  The quality of a fit depends more on the number of terms used than the number of data points used. The plots in the following projections are nearly identical for 101 and 100001 data points fitted between x=0 and x=1. As the maximum power of x increases from 7 to 9 the curve more closely approachs the original function. How far out one can go with the prediction depends on the limit that one wants to place on the errors.

  As one increases the number of terms a point is reached where the process breaks down as seen when one adds the term corresponding to x¹⁰ to the fit with 100001 data points.