To mitigate the burden of data labeling, we aim at improving data efficiency for both classification and regression setups in deep learning. However, the current focus is on classification problems while rare attention has been paid to deep regression, which usually requires more human effort to labeling. Further, due to the intrinsic difference between categorical and continuous label space, the common intuitions for classification, \textit{e.g.} cluster assumptions or pseudo labeling strategies, cannot be naturally adapted into deep regression. To this end, we first delved into the existing data-efficient methods in deep learning and found that they either encourage invariance to \textit{data stochasticity} (\textit{e.g.}, consistency regularization under different augmentations) or \textit{model stochasticity} (\textit{e.g.}, difference penalty for predictions of models with different dropout). To take the power of both worlds, we propose a novel \Chi-model by simultaneously encouraging the invariance to {data stochasticity} and {model stochasticity}. Further, the \Chi-model plays a minimax game between the feature extractor and task-specific heads to further enhance the invariance to model stochasticity. Extensive experiments verify the superiority of the \Chi-model among various tasks, from a single-value prediction task of age estimation to a dense-value prediction task of keypoint localization, a 2D synthetic and a 3D realistic dataset, as well as a multi-category object recognition task.