A commonly used approximation method is polynomial regression, where the model response is generally approximated by a polynomial basis function of linear or quadratic order with or without coupling terms. The model output y_i for a given set x _i of the input parameters X can be formulated as the sum of the approximated value and an error term .

(2–6)

where p(x) is the polynomial basis,

(2–7)

and β is a vector containing the unknown regression coefficients. These coefficients are generally estimated from a given set of sampled support points by assuming independent errors with equal variance at each point. By using a matrix notation the resulting least squares solution reads

(2–8)

where P is a matrix containing the basis polynomials of the support point samples and y is the vector of support point values.