Properties of the 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. $$ – 1 \leqslant r \leqslant + 1$$.