Simple proof that the correlation coefficient cannot exceed abs(1)

Load packages library(tidyverse) library(MASS) Motivation It is well-known that the notorious (Pearson’s) correlation cannot exceed an absolute value greater than 1, that is [ -1 \le r \le +1 ] or [ |r| \le 1 ] However, proofing this fact is less straightforward. A classical way of proofing the above inequality is by using the Cauchy-Schwarz inequality. From a teacher’s perspective, the CS inequality may not be ideal, because the students may lack some knowledge necessary for appreciating this …