A cross term multiplies two distinct predictors, β5x1x2, to model how their joint effect changes the response. In a two-parameter response-surface model, it complements the constant, linear, and separate quadratic terms. section 4.2.2
For threshold x1 and order_size x2, the cross term helps interpolate behavior between the center and corner measurements along the diagonals of a central-composite design. With d parameters, one pairwise term is required for every parameter pair, yielding d(d − 1)/2 terms. section 4.2.2
Fitting and using the term
A NumPy design matrix includes ones, x0, x1, x0², x1², and x0x1. Linear regression estimates the coefficients; interpolation evaluates the fitted surface over a grid, and optimization selects its highest predicted response.
