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Regression ensembles consisting of a collection of base regression models are often used to improve the estimation/prediction performance of a single regression model. It has been shown that the individual accuracy of the base models and the ensemble diversity are the two key factors affecting the performance of an ensemble. In this paper, we derive a theory for regression ensembles that illustrates the subtle trade-off between individual accuracy and ensemble diversity from the perspective of statistical correlations. Then, inspired by our derived theory, we further propose a novel loss function and a training algorithm for deep learning regression ensembles. We then demonstrate the advantage of our training approach over standard regression ensemble methods including random forest and gradient boosting regressors with both benchmark regression problems and chemical sensor problems involving analysis of Raman spectroscopy. Our key contribution is that our loss function and training algorithm is able to manage diversity explicitly in an ensemble, rather than merely allowing diversity to occur by happenstance.