Question

From the given data.

Variable	x	y
Mean	$6$	$8$
Standard Deviation	$4$	$6$

and correlation coefficient: $\frac{2}{3}$. Find Regression coefficients $b_{yx}$ and $b_{xy}$.

Answer 1

Given: correlation coefficient $:r=\frac{2}{3}$

standard deviation of $x$ $:S_x=4$,standard deviation of $y$ $:S_y=6$

$b_{yx}=\frac{r}{{S_x}^2}=\frac{\frac{2}{3}}{4^2}=\frac{1}{24}$

$b_{xy}=\frac{r}{{S_y}^2}=\frac{\frac{2}{3}}{6^2}=\frac{1}{54}$