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This paper introduces a statistical classifier that quickly locates line outages in a power system utilizing only time series phasor measurement data sampled during the system's transient response to the outage. The presented classifier is a linear multinomial regression model that is trained by solving a maximum likelihood optimization problem using synthetic data. The synthetic data is produced through dynamic simulations which are initialized by random samples of a forecast load/generation distribution. Real time computation of the proposed classifier is minimal and therefore the classifier is capable of locating a line outage before steady state is reached, allowing for quick corrective action in response to an outage. In addition, the output of the classifier fits into a statistical framework that is easily accessible. Specific line outages are identified as being difficult to localize and future improvements to the classifier are proposed. [ABSTRACT FROM PUBLISHER]