Using Geometry to Visualize Abstract Aspects of Statistical Formulae Relevant to Correlation and Regression

• Activity Number: 143
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Education
• Author(s): Kyle Nickodem* and Qinjun Wang and Ernest Davenport and Steven A. Culpepper
• Companies: University of Minnesota College of Education & Human Development and University of Minnesota College of Education & Human Development and University of Minnesota College of Education & Human Development and University of Illinois at Urbana-Champaign
• Keywords: geometry ; statistics pedagogy ; visual representation ; regression ; correlation

Abstract

In undergraduate and graduate statistics courses, concepts are often taught using algebraic or computational explanations. These may not, however, be optimal teaching methods for all students. Thus, the use of geometry can provide an alternative pedagogy that satisfies different learning styles without a loss of accuracy and rigor. This paper demonstrates an approach using geometric diagrams to introduce students to the concepts of bivariate, partial, and part correlations, multiple regression, R2, and R2 change in a concrete manner. In addition to supplementing current teaching methods, a geometric approach provides a visual representation of concepts that enables students to see statistics while requiring only a high school level of geometrical background knowledge.