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.