Indeed. Computing the exact polynomial going through all noisy points also doesn’t make sense because adding or removing a data point wildly changes the polynom

Indeed. Computing the exact polynomial going through all noisy points also doesn’t make sense because adding or removing a data point wildly changes the polynomial. So, you can’t claim any of your polynomials really describes your problem. Even if your data isn’t noisy and the point added lies exactly on the previous polynomial (making the problem degenerate) chances are float rounding and numerical stability of your code can have that effect (https://arachnoid.com/polysolve/#x_limits https://arachnoid.com/polysolve/#x_limits)