Question

If the two regression cofficients are 0.8 and 0.6 the cofficient of correlation is -0.69

Answer 1

Answer on Question #67808 – Math – Statistics and Probability

Question

If the two regression coefficients are 0.8 and 0.6 the coefficient of correlation is -0.69

Solution

Since both regression coefficients must have the same sign and the sign is determined by $r$ (and vice versa), the coefficient of correlation is

$$r = \sqrt {b _ {x} b _ {y}} = \sqrt {0 . 8 * 0 6} \approx 0. 6 9, \mathrm {not} - 0. 6 9.$$

The regression coefficient as well as the coefficient of correlation shows if a correlation is positive or negative. So they must have the same sign.

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