This paper presents first- and second-order statistical models of the total emergency medical service (EMS) demand rate using socio-economic, demographic and other characteristics of an area as the exogenous variables. Due to the multicollinear or non-orthogonal nature of the exogenous data, parameter estimates result are compared with those derived from the ordinary least squares method and a related Bayesian approach. These models are shown to provide highly significant fits to the empirical data. It is suggested that such models possess considerable utility as quantitative tool for evaluating and planning EMS systems.