  This article describes a multivariate polynomial regression method where the
uncertainty of the input parameters are approximated with Gaussian
distributions, derived from the central limit theorem for large weighted sums,
directly from the training sample. The estimated uncertainties can be
propagated into the optimal fit function, as an alternative to the statistical
bootstrap method. This uncertainty can be propagated further into a loss
function like quantity, with which it is possible to calculate the expected
loss function, and allows to select the optimal polynomial degree with
statistical significance. Combined with simple phase space splitting methods,
it is possible to model most features of the training data even with low degree
polynomials or constants.
