Predicting the performance of an underwater acoustic network (UAN) is a challenging task due to the spatiotemporal variability of the links and its complicated dependence on multiple factors. We present a machine-learning model based on logistic regression (LogR) to capture the spatio-temporal variation in the performance of a UAN. The model captures the effect of environmental factors such as wind speed, tide, current velocity etc., and modem-specific factors, on the performance of the UAN, which can be quantified by the packet success rate (PSR). As the PSR is a complicated non-linear function of environmental/modem-specific factors, developing a forward model in this regard is a difficult task, motivating our data-driven model. Our results indicate that LogR can quantify UAN performance with fair accuracy.