Statistics Toolbox

Overfitting

If the cubic polynomial is a good fit, it is tempting to try a higher order polynomial to see if even more precise predictions are possible.

Since the true function is cubic, this amounts to overfitting the data. Use the data entry box for degree and type 5 for a quintic model.

As measured by the confidence bounds, the fit is precise near the data points. But, in the region between the data groups, the uncertainty of prediction rises dramatically.

This bulge in the confidence bounds happens because the data really does not contain enough information to estimate the higher order polynomial terms precisely, so even interpolation using polynomials can be risky in some cases.

Confidence Bounds

The aoctool Demo