This is in continuation with the earlier article:
Let us fit a Quartic (fourth degree) polynomial to the given data points:
(0, -1), (1, 0), (2, 5), (3, 14) and (4, 27).
The Vandermonde matrix for the above data points will be:
Solving this we get
Hence, the governing polynomial function for the experiment is given by
When we try to overfit a higher degree polynomial to the given data points, the coefficients of higher degrees of x will turn out to be 0.
Image provided by the author.