To ensure the safe deployment of AI models, it is crucial to identify potential failure modes to prevent costly errors. While failure detection in classification problems has received significant attention, characterizing failure or risk in regression is more complex and less explored. In this paper, we propose a new framework to characterize risk regimes in regression models. Our framework leverages the principle of anchoring to estimate both uncertainties and non-conformity scores, that can be used to jointly categorize samples into distinct risk regimes, thus enabling a fine-grained analysis of model failure. Additionally, we introduce a suite of metrics for evaluating such failure detectors in regression settings. Our results on synthetic and real-world benchmarks demonstrate the effectiveness of our framework over existing methods that rely solely on predictive uncertainties or feature inconsistency to assess risk.