The Use of Marginal Likelihood for a Diagnostic Test for the Goodness of Fit of the Simple Linear Regression Model

Abstract

A novel test procedure is proposed to diagnose the goodness of fit of a simple regression model by applying a marginal likelihood under the assumption of smoothness of the alternative regression curve. No specific form for the alternative regression function is assumed. An advantage of the proposed test procedure is that it simultaneously provides an estimated regression curve (spline). Some existing diagnostic procedures are explored in relation to the one proposed. The procedure is applied to data of a spectrophotometric analysis of mixtures of two types of flour, cornstarch and casein (soybean).