Regression Models: Facts And Fallacies

The logic of regression analysis as an operations research tool is critically examined, and a formal basis for its application to mining problems is developed. The traditional view of regression analysis as a statistical discipline does not provide an adequate basis for evaluating a regression model in a specific area such as ore reserve calculation or process control. In particular, the validity of the residual-sum-of-squares criterion is questioned, and the need for a criterion based on interpolative features of the model is emphasized. Strictly speaking, a regression model is statistically supported only at points at which observations are available, yet inferences are drawn with regard to a continuum. When considered as a mathematical function, therefore, the model is observationally defined only on a domain consisting of a finite number of points. Extension of this domain to an interval of the real line must be based on physical rather than statistical argument. Vector space and function theory concepts useful as a logical framework for a physically oriented problem analysis are discussed and their usefulness demonstrated in a practical problem.