Question

An article cost Rs. $75$ at Gwalior. Find the corresponding most appropriate value at Bhopal using the following data:

	Gwalior	Bhopal
Mean value	$65$	$67$
Standard Deviation	$2.5$	$3.5$

The correlation coefficient between the values of the two cities is $0.8$

Answer 1

$\overline{x}=65,\overline{y}=67,{\sigma }_x=2.5,{\sigma }_y=2.5,\rho =0.8$
regression line of $y$ on $x$ is
$y-\overline{y}=\rho \frac{{\sigma }_y}{{\sigma }_x}(x-\overline{x})$
$y-67=\frac{0.8\times 3.5}{2.5}(x-65)$
$y-67=\frac{28}{25}(x-65)$
putting $x=75$
$y-67=\frac{28}{25}(75-65)$
$y-67=\frac{28}{25}\left(10\right)$
$y-67=\frac{56}{5}=11.5\Rightarrow y=78.2$
required value is Rs.$78.2$