A New Bootstrap Goodness-of-Fit Test for Normal Linear Regression Models

Abstract: In this work, the distributional properties of the goodness-of-fit term in likelihood-based information criteria are explored. These properties are then leveraged to construct a novel goodness-of-fit test for normal linear regression models that relies on a non-parametric bootstrap. Several simulation studies are performed to investigate the properties and efficacy of the developed procedure, with these studies demonstrating that the bootstrap test offers distinct advantages as compared to other methods of assessing the goodness-of-fit of a normal linear regression model.