Polynomial Representations for Response Surface Modeling 1

In response surface models the expected response is usually taken to be a low degree polynomial in the design variables that are coded from the factor settings. We argue that an overparameterized polynomial representation of the expected response ooers great economy and transparency. As an illustration, we exhibit a constructive path of design improvement relative to the Kiefer design ordering, for polynomial regression up to degree three when the experimental domain is a ball.