Mathematical Sciences: Statistical Graphics: Foundations of Regression Graphics

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Real-time, computationally intensive, graphical methods for regression are the focus of this research. In particular, it will emphasize the theoretical statistical foundations and the implications of standard displays such as the family of plots based on residuals for a broad class of peri-parametric models including generalized linear models. One goal of this research is to develop a purely graphical analysis with model assessment methods that do not originate in residuals. These developments will be available as extensions of the LISP-based computing environment XLISP-STAT. Graphical displays of quantitative data are a central tool of scientific inquiry. Although these have historically been limited to whatever could be presented on a two-dimensional sheet of paper, computing technology now routinely allows three- dimensional graphical displays. How to make effective and technically valid scientific use of this technology needs careful thought and a logical treatment. In turn, this should result in both a better understanding of standard displays and the construction of still more effective ones.