Lagrange's Identity Reveals Correlation Coefficient and Straight-Line Connection

In this department The American Statistician publishes articles, reviews, and notes of interest to teachers of the first mathematical statistics course and of applied statistics courses.The department includes the Accent on Teaching Materials section; suitable contents for the section are described under the section heading.Articles and notes for the department, but not intended specifically for the section, should be useful to a substantial number of teachers of the indicated types of courses or should have the potential for fundamentally affecting the way in which a course is taught.Using an elementary but important identity, this article presents a simple proof that Pearson's correlation coefficient r is always between . 1 and 1 and that all points (x i , y i ) for i = 1, ., n fall on a straight line iff r 2 = 1. The presentation is suitable for a wide audience with minimal background.