# Properties of Coefficient of Correlation

• The correlation coefficient is symmetrical with respect to $X$ and $Y$ i.e. ${r_{XY}} = {r_{YX}}$
• The correlation coefficient is the geometric mean of the two regression coefficients. $r = \sqrt {{b_{YX}} \times {b_{XY}}}$   or   $r = \sqrt {b \times d}$.
• The correlation coefficient is independent of origin and unit of measurement i.e. ${r_{XY}} = {r_{UV}}$.
• The correlation coefficient lies between $- 1$ and $+ 1$. i.e. $- 1 \leqslant r \leqslant + 1$.