Pearson's correlation between three variables; using students’ basic knowledge of geometry for an exercise in mathematical statistics

Abstract

When studying correlations, how do the three bivariate correlation coefficients between three variables relate? After transforming Pearson's correlation coefficient r into a Euclidean distance, undergraduate students can tackle this problem using their secondary school knowledge of geometry (Pythagoras’ theorem and similarity of triangles). Through a geometric interpretation, we start from two correlation coefficients r _AB and r _BC and then estimate a range for the third correlation r _AC. In the case of three records (n = 3), the third correlation r _AC can only attain two possible values. Crossing borders between mathematical disciplines, such as statistics and geometry, can assist students in deepening their conceptual knowledge.

Keywords:

• bivariate correlation
• range restrictions
• correlative distance
• person space
• trans-disciplinarity