Data rate selection algorithms for Wi-Fi devices are an important area of research because they directly impact performance. Most of the proposals are based on measuring the transmission success probability for a given data rate. In dense scenarios, however, this probing approach will fail because frame collisions are misinterpreted as erroneous data rate selection. We propose FTMRate which uses the fine timing measurement (FTM) feature, recently introduced in IEEE 802.11. FTM allows stations to measure their distance from the AP. We argue that knowledge of the distance from the receiver can be useful in determining which data rate to use. We apply statistical learning (a form of machine learning) to estimate the distance based on measurements, estimate channel quality from the distance, and select data rates based on channel quality. We evaluate three distinct estimation approaches: exponential smoothing, Kalman filter, and particle filter. We present a performance evaluation of the three variants of FTMRate and show, in several dense and mobile (though line-of-sight only) scenarios, that it can outperform two benchmarks and provide close to optimal results in IEEE 802.11ax networks.