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Second-order statistical regression models are developed for the rates of demand for different types of emergency medical services (EMS) as they relate to various socioeconomic, demographic, and other characteristics of a service area. The model parameters are estimated by the recent technique of ridge regression, which is shown to provide superior estimates to those of the ordinary least squares regression method, because of the presence of substantial multicollinearity (nonorthogonality) in the exogenous data set. The ridge results are also compared with those derived from a related Bayesian approach. The resulting models provide substantial fits to the empirical data for the EMS system of the city of Atlanta, GA.