Using transfer learning where we can use our knowledge about one task to do another. First set of layers of a neural network are usually feature extraction layers and will be useful for all tasks with the same input distribution. So, we should replace the last fully connected layer and Softmax responsible for classification with one neuron for regression-or fully connected-layer for correction then one neuron for regression.
We can optionally freeze the first set of layers if we have few data or to converge fast. Then we can train the network with the data we have and using the suitable loss for the regression problem, making use of the robust feature extraction -first set of layers- of a pre-trained model on huge data.
