Question

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

Series	$x$	$y$
A.M	$18$	$100$
Standard Deviation	$14$	$20$

• A. $145.32$
• B. $44.23$
• C. $159.43$
• D. $561.12$

Answer 1

The correct option is C $159.43$

$\overline{x}=18$, $\overline{y}=100$, ${\sigma }_x=14$, ${\sigma }_y=20$ and $r=0.8$
Regression line of y on x will be $y-\overline{y}=r\frac{{\sigma }_y}{{\sigma }_x}(x-\overline{x})$
Subsitute all the abpve value in an equation of regression line, we get
$y-100=\frac{0.8\times 20}{14}(x-18)$
$y-100=1.143(x-18)$
$y=1.143x+79.43$
Now, Subsitute the value of x=70, we get
$y=1.143\times 70+79.43=159.43$