Question

If byx = -0.9 and bxy = -0.4, What is the value of r?​

Answer 1

x and y are negative so negatively correlated with r

Answer 2

Concept:

To determine the strength of a relationship between data, correlation coefficient (r) formulas are applied.

Given:

$b_{xy} =-0.4$

$b_{yx} =-0.9$

Find:

What is the value of the correlation coefficient(r)?

Solution:

The two regression coefficients $b_{xy}$ and $b_{xy}$ have the same sign as the coefficient of correlation(r).

The geometric mean of the regression coefficients is the coefficient of correlation.

$r^{2} =b_{xy} *b_{yx}$

$r=\sqrt{b_{xy} *b_{yy} }$

$r=\sqrt{-0.4 *-0.9 }$

$r=\sqrt{0.36 }$

$r=0.6$

∴ $r=-0.6$ (same sign as  $b_{xy}$ and $b_{xy}$, negatively correlated.)

Hence the value of the correlation coefficient(r) is $-0.6$.