Multiple discriminant analysis (MDA) is frequently used to develop statistical credit-scoring models for loan evaluation purposes. Current legislative efforts to insure that credit is being granted in a nondiscriminatory manner have focused considerable attention on the reliability of such models. This article examines the theoretical requirements of the MDA model in the context of a realistic lending situation and illustrates the extent of bias when these theoretical assumptions are not fully met. The article concludes that failure to rigorously meet all the theoretical assumptions of the statistical model may not be as critical as insuring that credit managers fully understand the limitations of these types of decision tools. Furthermore, the evidence indicates that statistical models other than multiple discriminant analysis are possibly more relevant to the credit-granting decision.

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A regional model is developed to consider the trade-off between economies of scale inherent in waste water treatment plants and added pipe network collection costs. The resulting mixed integer programing model relies on piecewise linear approximations of concave cost curves and incorporates capacity limits dictated by maximum tolerable environmental impact at potential treatment plant sites. Cost savings possible for a region consisting of the central portion of Dane County, Wisconsin, are demonstrated. The ever increasing emphasis on and costs of water pollution control have focused attention on potential cost savings in alternative institutional arrangements and regional approaches toward that end. One of the vory fundamental tradeoffs, that of cost savings due to economies of scale inherent in waste water treatment plants versus the added collection cost of the extended interceptor system, has been identified in a number of recent investigations [Deininger, 1966, 1972; Meier, I971; Wanielista and Bauer, 1972; Joeres et al., 1973]. This paper focuses on the development of a computer model to select an optimal regional waste water treatment system, given prior definition of all reasonable interceptor routes conneeting individual communities, local treatment plant sites, and associated maximum discharge potentials. The latter are based on a determination of tolerable local environmental impact, given prevalent treatment efficiencies. The model is applied to an example region consisting of the expected 1990 service requirements of the central portion of Dane County, Wisconsin [Bauer, Sheaffer and McCall, Inc., 1970; Wisconsin Department of Health and Social Services, 1970]; its solution is subsequently compared to a politically likely alternative regional waste water management scheme to evaluate potential cost savings. BACKGROUND One of the early and clear descriptions of a regional approach was presented by Deininger [1966]. The simplified model chosen relied on a formulation known as the 'transportation problem' and assumed different linear expansion costs for both individual treatment plants and interceptors (Figure. la). The resulting formulation thus did not include economies of scale for either plants or pipes but instead •lected the optimal regional plan based on geographic site advantages and waste water piping differences. Different combinations of plants and waste water 'shipments' satisfying the demand are evaluated by the algorithm to select a least cost allocation. A later effort by Deininger [1972] incorporated the realistic assumption that in order to construct any facility an initial fixed cost must be reckoned with that is independent of capacity (Figure lb). Although mathematical complexity is markedly increased by this assumption, the focus is still that of a regional system looking only on spatial cost advantages and their exploitation without addressing the equally important question of cost savings possible solely as a function of Copyright ¸ 1974 by the American Geophysical Union, 643 scale...

The use of multiple regression analysis as a tool of real estate valuation has received considerable attention in recent years. The primary objectives of this study are to investigate the multicollinearity among the property characteristics (regressor variables) and examine the stability of the estimated regression coefficients over time. Ridge regression techniques are used to partially adjust for the presence of collinearity. The results indicate that the ridge regression model provides a consistent set of properly signed, statistically significant regression coefficients throughout the sample period. Furthermore, ridge regression techniques are shown to have certain advantages over those of ordinary least squares for establishing logical and consistent values for specific property characteristics. Copyright American Real Estate and Urban Economics Association.