DMS 9703777 Foundations of Regression Graphics Dennis Cook University of Minnesota ABSTRACT This research centers on finding how real-time, computationally intensive, graphical methods can be used to investigate the statistical structure of regression problems. It is based on the premise that the full benefit of modern computer graphics cannot be realized in regression analyses without sound theoretical foundations. Emphasis is placed on the expansion and application of an emerging theory for regression graphics based on dimension-reduction subspaces, and on the implications of this theory for the interpretation of standard graphical constructions. Graphical foundations for regressions with a censored survival time as the response are given special attention. The ability to visualize statistical data plays an important role in analyzing complex relationships. For example, a measure of the marginal impact of mandatory testing in grade schools requires understanding how different socioeconomic settings influence performance. Recent advances in high performance computing, one of the Federal Strategic Areas, allow for the opportunity to develop new graphical techniques that go far beyond traditional graphics in both applicability and power. This research centers on finding how computer graphics can be used to investigate complex statistical relationships. It stems from the notion that, even in complex systems, it is possible to construct easily understood graphical displays that contain all or nearly all of the relevant information in the data. This ability to preserve information in easily understood displays requires new theoretical foundations that are an integral part of this study.
