A Dynamic Test for Misspecification of a Linear Model

Various linear models may be specified when attempting to estimate an apparent linear trend in real data sets, based on assumptions about the possibly unknown mechanism for generating the data. However, in many cases the best-fit line obtained from implementation of the specified model does not agree at all with the apparent trend in a scatterplot of the data, based on the evident geometric structure. We use both real and simulated data to illustrate the consequences of misspecifying a particular linear model for situations in which that model is inappropriate, and propose a dynamic test which may be used to determine when its specification is appropriate