Date of Award

9-1991

Document Type

Thesis

Degree Name

Master of Science

Department

Department of Mathematics and Statistics

First Advisor

Daniel Reynolds, PhD

Abstract

This research created a learning environment, known as the Pearce Projection Modeling Environment (PPME) which is used as a tool by a teacher and student. The PPME was developed in an effort to create a new approach to the study of the General Linear Model through a constructive and projective, geometric approach. While the geometric approach to the GLM was developed over the past century, it has not been used extensively because of the inherent complexities associated with visualizing vector spaces. With the PPME, visualization is accomplished effortlessly. The PPME is a computer program that allows the student to enter response vectors and other vectors and data associated with the GLM and observe the relationships of those vectors interactively and in three-dimensions. The PPME encourages learning through constructive development by allowing the student to modify the vectors and observe the results of his actions. To validate the PPME as a learning tool, several data sets were generated and used to study three scenarios: The Sample Mean and Variance, A General Linear Test of the Population Mean, and An Ordinary Least Squares Simple Linear Regression.

AFIT Designator

AFIT-GSM-ENC-91S-22

DTIC Accession Number

ADA246668

Comments

The author's Vita page is omitted

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