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.

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