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Improving the robustness of neural nets in regression tasks is key to their application in multiple domains. Deep learning-based approaches aim to achieve this goal either by improving their prediction of specific values (i.e., point prediction), or by producing prediction intervals (PIs) that quantify uncertainty. We present PIVEN, a deep neural network for producing both a PI and a value prediction. Our loss function expresses the value prediction as a function of the upper and lower bounds, thus ensuring that it falls within the interval without increasing model complexity. Moreover, our approach makes no assumptions regarding data distribution within the PI, making its value prediction more effective for various real-world problems. Experiments and ablation tests on known benchmarks show that our approach produces tighter uncertainty bounds than the current state-of-the-art approaches for producing PIs, while maintaining comparable performance to the state-of-the-art approach for value-prediction. Additionally, we go beyond previous work and include large image datasets in our evaluation, where PIVEN is combined with modern neural nets.