Federated Echo State Networks represent an efficient methodology for learning in pervasive environments with private temporal data due to the low computational cost required by the learning phase. In this paper, we propose Partial Federated Ridge Regression (pFedRR), an approximate, communication-efficient version of the **exact** method for learning the readout in a federated setting. Each client compresses the local statistics to be exchanged with the server via an importance-based method, which selects the most relevant neurons with respect to the local distribution. We evaluate the methodology on two Human State Monitoring benchmarks, and results show that the importance-based selection of the information significantly reduces the communication cost, while acting as a regularization method to improve the generalization capabilities.