Q.If $b_{yx}=0.8$ and $b_{xy}=0.45$, find the coefficient of correlation between $x$ and $y$.

Use the geometric-mean property linking $r$ to the two regression coefficients. …

The correlation coefficient is the (signed) geometric mean of the two regression coefficients:

Substituting,

Both $b_{yx}$ and $b_{xy}$ are positive, so by Property 1 the sign of $r$ is positive. …

Adding or averaging the coefficients (e.g. $\tfrac{0.8+0.45}{2}$) instead of taking the geometric mean. $r$ is $\sqr …