Why must the correlation coefficient for a straight line be $\displaystyle -1 \leq r \leq 1$
This has nothing to do with lines.
Correlation by the Cauchy-Schwarz inequality is between -1 and 1.
http://www.aiaccess.net/English/Glos...hy_schwarz.htm
http://www.aiaccess.net/English/Glos...oefficient.htm