Two Regression Lines Suffice to Determine r2 and r

Abstract

The Pearson correlation coefficient can be recovered from the two least-squares regression lines ŷ = b0 + b1x and x = a0 + a1y without any data. This can be done both algebraically and geometrically. This can be done without data even when the scales of the variables are different. The authors conclude with ways to use such information during instruction to help scaffold student understanding, number sense and problem-solving skills.