Approximation error is the difference between an interpolation estimate, ŷ = β₀ + β₁x + β₂x², and the measured response y. In response-surface optimization, it records how closely a surrogate function estimates measured profit at a threshold. section 4.1.3
The error behaves differently depending on the amount of data used to fit the model:
- With three measurements and three parabola parameters, the model fits the data exactly, so ε = 0. section 4.1.3
- With more measurements than fitted parameters, ε is generally nonzero and exposes the gap between the surrogate and measured responses. section 4.1.3
Interpolating profit measurements
A quadratic surrogate is fit to threshold values and aggregate profit measurements using linear regression. NumPy then evaluates the fitted parabola across a fine threshold grid; the interpolated response can be compared with measured values through ε.
