Federated distillation (FD) paradigm has been recently proposed as a promising alternative to federated learning (FL) especially in wireless sensor networks with limited communication resources. However, all state-of-the art FD algorithms are designed for only classification tasks and less attention has been given to regression tasks. In this work, we propose an FD framework that properly operates on regression learning problems. Afterwards, we present a use-case implementation by proposing an indoor localization system that shows a good trade-off communication load vs. accuracy compared to federated learning (FL) based indoor localization. With our proposed framework, we reduce the number of transmitted bits by up to 98%. Moreover, we show that the proposed framework is much more scalable than FL, thus more likely to cope with the expansion of wireless networks.