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This situation may arise when model evaluations are expensive; when privacy, security and bandwidth constraints are imposed; or when there is a need for real-time, on-device explanations. Our algorithm uses a bootstrapping approach to quantify the uncertainty that inevitably arises when generating explanations from a finite sample of model queries. Through a simulation study, we show that the uncertainty intervals generated by our algorithm exhibit a favorable trade-off between interval width and coverage probability compared to the naive confidence intervals from classical regression analysis as well as current Bayesian approaches for quantifying explanation uncertainty. 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