On the Degree of Inflation of Measures of Fit Induced by Empirical Model Building

摘要

This dissertation explores the distributional properties of commonly used statistics developed in the course of empirical model building. A review of some of the more noteworthy efforts to investigate the distribution of the coefficient of determination of determination, R-squared, in the best subset regression is given. To overcome the shortcomings of these results, a permutation test based on Fisher's randomization test is developed to provide a practical basis for assessing the statistical significance of a regression in such situations. An investigation is made into the distributional properties of the multiple correlation coefficient in the choice of a transformation of the dependent variable. The study investigates the possibility that pedestrian use of transformations, such as y* = (y+c) to the p, may lead to an inflationary effect on the sample correlation. A practical management science application of the statistical procedures developed in this study is explored in the area of parametric cost estimation. (Author)