Convolutional neural networks (CNNs) have shown exceptional performance for a range of medical imaging tasks. However, conventional CNNs are not able to explain their reasoning process, therefore limiting their adoption in clinical practice. In this work, we propose an inherently interpretable CNN for regression using similarity-based comparisons (INSightR-Net) and demonstrate our methods on the task of diabetic retinopathy grading. A prototype layer incorporated into the architecture enables visualization of the areas in the image that are most similar to learned prototypes. The final prediction is then intuitively modeled as a mean of prototype labels, weighted by the similarities. We achieved competitive prediction performance with our INSightR-Net compared to a ResNet baseline, showing that it is not necessary to compromise performance for interpretability. Furthermore, we quantified the quality of our explanations using sparsity and diversity, two concepts considered important for a good explanation, and demonstrated the effect of several parameters on the latent space embeddings.