  A local surrogate for an AI-model correcting a simpler 'base' model is
introduced representing an analytical method to yield explanations of
AI-predictions. The approach is studied here in the context of the base model
being linear regression. The AI-model approximates the residual error of the
linear model and the explanations are formulated in terms of the change of the
interpretable base model's parameters. Criteria are formulated for the precise
relation between lost accuracy of the surrogate, the accuracy of the AI-model,
and the surrogate fidelity. It is shown that, assuming a certain maximal amount
of noise in the observed data, these criteria induce neighborhoods of the
instances to be explained which have an ideal size in terms of maximal accuracy
and fidelity.
