A multiple-regression methodology was used to help answer questions concerning model reliability, and to calibrate a time-dependent variable-density ground-water flow model of the gulf coast aquifer systems in the south-central United States. More than 40 regression models with 2 to 31 regressions parameters are used and detailed results are presented for 12 of the models. More than 3,000 values for grid-element volume-averaged head and hydraulic conductivity are used for the regression model observations. Calculated prediction interval half widths, though perhaps inaccurate due to a lack of normality of the residuals, are the smallest for models with only four regression parameters. In addition, the root-mean weighted residual decreases very little with an increase in the number of regression parameters. The various models showed considerable overlap between the prediction inter- vals for shallow head and hydraulic conductivity. Approximate 95-percent prediction interval half widths for volume-averaged freshwater head exceed 108 feet; for volume-averaged base 10 logarithm hydraulic conductivity, they exceed 0.89. All of the models are unreliable for the prediction of head and ground-water flow in the deeper parts of the aquifer systems, including the amount of flow coming from the underlying geopressured zone. Truncating the domain of solution of one model to exclude that part of the system having a ground-water density greater than 1.005 grams per cubic centimeter or to exclude that part of the systems below a depth of 3,000 feet, and setting the density to that of freshwater does not appreciably change the results for head and ground-water flow, except for locations close to the truncation surface.