Fitting Straight Lines—The Linear Functional Relationship with Replicated Observations

Summary A medical example suggests the fitting of a linear functional model with replicated observations and inhomogeneous error variances. For a particular error structure relevant to the example being discussed, the paper considers the maximum‐likelihood estimation of the parameters in the model (slope, intercept and error variances). The estimators have no simple explicit form and need to be evaluated by iterative methods. In spite of this, simple closed‐form expressions are obtained for the asymptotic standard errors of the estimators. Some comments are made on alternative error structures which might be relevant in other biological and medical problems similar to the one considered in the paper.