We present and evaluate a surrogate model, based on hardware performance counter measurements, to estimate computer system power consumption. Power and energy are especially important in the design and operation of large data centers and of clusters used for scientific computing. Tradeoffs are made between performance and power consumption, this needs to be dynamic because activity varies over time. While it is possible to instrument systems for fine-grain power monitoring, such instrumentation is costly and not commonly available. Furthermore, the latency and sampling periods of hardware power monitors can be large compared to time scales at which workloads can change and dynamic power controls can operate. Given these limitations, we argue that surrogate models of the kind we present here can provide low-cost and accurate estimates of power consumption to drive on-line dynamic control mechanisms and for use in off-line tuning. In this brief paper, we discuss a general approach to building system power estimation models based on hardware performance counters. Using this technique, we then present a model for an Intel Core i7 system that has an absolute estimation error of 5.32 percent (median) and acceptable data collection overheads on varying workloads, CPU power states (frequency and voltage), and number of active cores. Since this method is based on event sampling of hardware counters, one can make a tradeoff between estimation accuracy and data-collection overhead.