Lack-of-fit Testing for Polynomial Regression Models Without Replications

Abstract

Parametric and non-parametric approaches are developed to test the adequacy of the polynomial model Y=β°+j=1pβjXj+ε  when there is no replication in the values of the independent variable. The proposed tests avoid partitioning of the sample space of the continuous covariate. This paper suggests three tests based on the following concept: if the model is appropriate for a selected application, then the error component ε1,ε2,…,εn is a random sample with zero mean and constant variance. Simulation results are provided to illustrate the power and size of the proposed tests. An example is used to illustrate the methodologies. These tests are also compared with the classical lack-of-fit test to demonstrate their advantage.