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 rAB and rBC and then estimate a range for the third correlation rAC. In the case of three records (n = 3), the third correlation rAC can only attain two possible values. Crossing borders between mathematical disciplines, such as statistics and geometry, can assist students in deepening their conceptual knowledge.
Pauline Vos has written an article called Pearson’s correlation between three variables; using students’ basic knowledge of geometry for an exercise in mathematical statistics. The article was recently published in International Journal of Mathematical Education in Science and Technology. Here is a copy of the article abstract: