This paper introduces a novel framework for regression with deferral, where a learner can defer predictions to multiple experts. The framework addresses the unique challenges of regression due to the infinite and continuous nature of the label space. The authors analyze two scenarios: a single-stage scenario where both the predictor and deferral functions are learned simultaneously, and a two-stage scenario where a pre-trained predictor is used with a learned deferral function. They introduce new surrogate loss functions for both scenarios and prove that they are supported by H-consistency bounds, which provide stronger consistency guarantees than Bayes consistency. These bounds are non-asymptotic and hypothesis set-specific. The framework is versatile, applicable to multiple experts, accommodating any bounded regression losses, and addressing both instance-dependent and label-dependent costs. The single-stage formulation includes the recent regression with abstention framework as a special case. The authors report extensive experiments showing the effectiveness of their proposed algorithms.This paper introduces a novel framework for regression with deferral, where a learner can defer predictions to multiple experts. The framework addresses the unique challenges of regression due to the infinite and continuous nature of the label space. The authors analyze two scenarios: a single-stage scenario where both the predictor and deferral functions are learned simultaneously, and a two-stage scenario where a pre-trained predictor is used with a learned deferral function. They introduce new surrogate loss functions for both scenarios and prove that they are supported by H-consistency bounds, which provide stronger consistency guarantees than Bayes consistency. These bounds are non-asymptotic and hypothesis set-specific. The framework is versatile, applicable to multiple experts, accommodating any bounded regression losses, and addressing both instance-dependent and label-dependent costs. The single-stage formulation includes the recent regression with abstention framework as a special case. The authors report extensive experiments showing the effectiveness of their proposed algorithms.