We propose a capsule based regression network (CaReNet), a framework that is based on capsule networks (CapsNet), rather than on the conventional convolutional neural networks (CNNs) to determine estimates of continuous variables. The core principles of CaReNet remain that of routing-by-agreement and translation equivariance proposed in the CapsNet architecture for classification problems. However, unlike the CapsNet architecture, the final layer capsules in CaReNet architecture capture the number of values to regress in their dimensionality. An output vector returned by each of these capsules contains all the regressed values while the corresponding activity vector, determined by squashing an output vector, captures the likelihood of the regressed values being present in the corresponding capsule. We show that our novel CaReNet architecture achieves state-of-the-art performance on regressing facial keypoints from images, an important problem that plays a significant role in face recognition systems. The performance of CaReNet has been evaluated on the dataset from Kaggle Facial Keypoints Detection competition. Further, the flexibility in CaReNet architecture allows it to be easily extendable to any other regression problem such as 3D reconstruction of facial models from 2D images.