Question

Find the value of $y$ from the following data when $x=70$ and coefficient of correlation is $0.8$.

	$x$	$y$
Mean	$18$	$100$
S.D.	$14$	$20$

Answer 1

$\overline{x}=18$	$\overline{y}=100$
${\sigma }_x=14$	${\sigma }_y=20$

Regression line $y$ on $x$
$(y-\overline{y})=r\frac{{\sigma }_y}{{\sigma }_x}(x-\overline{x})$
$(y-100)=0.8\left(\frac{20}{14}\right)(x-18)$
$(y-100)=\frac{8}{10}\times \frac{20}{14}(x-18)$
$y-100=\frac{8}{7}(x-18)$
Putting the value of $x=70$
$y-100=\frac{8}{7}[70-18]$
$y-100=\frac{8}{7}\times 52$
$y=100+\frac{416}{7}$
$y=100+59.43$
$y=159.43$.