In a bivariate data set, the regression coefficient of $Y$ on $X$ is $b_{yx} = 0.8$ and the regression coefficient of $X$ on $Y$ is $b_{xy} = 0.45$. The Pearson correlation coefficient $r$ between $X$ and $Y$ is ________ (round off to 1 decimal place).
Answer Key:
0.6
Step-by-Step Solution & Explanation
The relationship between the regression coefficients and the correlation coefficient is:
$r = \pm \sqrt{b_{yx} \cdot b_{xy}}$
Since both $b_{yx}$ and $b_{xy}$ are positive, $r$ must also be positive:
$r = \sqrt{0.8 \times 0.45} = \sqrt{0.36} = 0.6$