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Predicting the performance of cloud services is intrinsically hard. In this work, we pursue an approach based upon statistical learning, whereby the behaviour of a system is learned from observations. Specifically, our testbed implementation collects device statistics from a server cluster and uses a regression method that accurately predicts, in real-time, client-side service metrics for a video streaming service running on the cluster. The method is service-agnostic in the sense that it takes as input operating-systems statistics instead of service-level metrics. We show that feature set reduction significantly improves prediction accuracy in our case, while simultaneously reducing model computation time. We also discuss design and implementation of a real-time analytics engine, which processes streams of device statistics and service metrics from testbed sensors and produces model predictions through online learning.