Coral cover has been declining in recent decades due to increased temperatures and environmental stressors. However, the extent to which different stressors contribute both individually and in concert to bleaching and mortality is still very uncertain. We develop and use a novel regression approach, using non-linear parametric models that control for unobserved time invariant effects to estimate the effects on coral bleaching and mortality due to temperature, solar radiation, depth, hurricanes and anthropogenic stressors using historical data from a large bleaching event in 2005 across the Caribbean. Two separate models are created, one to predict coral bleaching, and the other to predict near-term mortality. A large ensemble of supporting data is assembled to control for omitted variable bias and improve fit, and a significant improvement in fit is observed from univariate linear regression based on temperature alone. The results suggest that climate stressors (temperature and radiation) far outweighed direct anthropogenic stressors (using distance from shore and nearby human population density as a proxy for such stressors) in driving coral health outcomes during the 2005 event. Indeed, temperature was found to play a role ~4 times greater in both the bleaching and mortality response than population density across their observed ranges. The empirical models tested in this study have large advantages over ordinary-least squares-they offer unbiased estimates for censored data, correct for spatial correlation, and are capable of handling more complex relationships between dependent and independent variables. The models offer a framework for preparing for future warming events and climate change; guiding monitoring and attribution of other bleaching and mortality events regionally and around the globe; and informing adaptive management and conservation efforts.