On the relation between initial value and slope

Suppose measurements of a particular feature are collected at baseline and at a number of subsequent time points and that for each individual there is a roughly linear trend in time. This paper takes three approaches to testing whether there is a relation between the initial value and the slope. It also considers whether the initial value for an individual is a useful predictor of the slope for that individual. The problems are formulated in terms of regression models with random coefficients. The solutions are illustrated using data from an observational study of clinical correlates of disability and progression in Huntington's disease.