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A wireless network can use the variance of measured received signal strength (RSS) on the links in a network to infer the locations of people or objects moving in the network deployment area. This paper provides a statistical model for the RSS variance as a function of a person's position with respect to the transmitter (TX) and receiver (RX) locations. We show that the ensemble mean of the RSS variance has an approximately linear relationship with the expected value of total affected power (ETAP), for a range of ETAP. We derive approximate expressions for the ETAP as a function of the person's position, for scattering and reflection, which are tested via simulation. Counterintuitively, we show that reflection, not scattering, causes the RSS variance contours to be shaped similar to Cassini ovals. Results reported in past literature and from a new experiment reported in this paper are shown to be as predicted by the analysis.