Example 6.  Why is the RMS error for    essentially zero ?

Solution 6.

If you fit six points with a fifth degree polynomial, then it should be "an exact fit" provided that the abscissas are all distinct.

If the data is of a "polynomial type" then often times the RMS error will decrease with increasing degree of the polynomial fit.

Caveat.  Curve fitting is nice for data interpolation.  

Warning.  You are on your own if you use curve fitting for data extrapolation.  Things might "blow up" outside the interval where the data is located.  Too often this is the case.

(c) John H. Mathews 2004