We propose regression networks for the problem of few-shot classification, where a classifier must generalize to new classes not seen in the training set, given only a small number of examples of each class. In high dimensional embedding spaces the direction of data generally contains richer information than magnitude. Next to this, state-of-the-art few-shot metric methods that compare distances with aggregated class representations, have shown superior performance. Combining these two insights, we propose to meta-learn classification of embedded points by regressing the closest approximation in every class subspace while using the regression error as a distance metric. Similarly to recent approaches for few-shot learning, regression networks reflect a simple inductive bias that is beneficial in this limited-data regime and they achieve excellent results, especially when more aggregate class representations can be formed with multiple shots.