The instability of ordinary least squares estimates of linear regression coefficients is demonstrated for mortality rates regressed around various socioeconomic, weather and pollution variables. A ridge regression technique presented by Hoer1 and Kennard (Technometrics 12 (1970) 69–82) is employed to arrive at “stable” regression coefficients which, in some instances, differ considerably from the ordinary least squares estimates. In addition, two methods of variable elimination are compared—one based on total squared error and the other on a ridge trace analysis.