We use statistical learning to estimate end-to-end QoS metrics from device statistics, collected from a server cluster and an OpenFlow network. The results from our testbed, which runs a video-on-demand service and a key-value store, demonstrate that the learned models can estimate QoS metrics like frame rate or response time with errors bellow 10% for a given client. Interestingly, we find that service-level QoS metrics seem "encoded" in network statistics and it suffices to collect OpenFlow per port statistics to achieve accurate estimation at small overhead for data collection and model computation.