Question

The data are received from a firm for advertisement and sale as given below:

	Sales (in crores)	Advertisement (in crores)
Mean	$40$	$6$
Standard Deviation	$10$	$1.5$
Coefficient of correlation $r=0.9$

If the firm fixed the target for sale as $60$ crores rupees, then calculate the amount for advertisement.

Answer 1

Here, $\overline{x}=40,y=6,\sigma x=10,\sigma y=1.5$
Therefore, the line of regression of $y$ on $x$ is
$y-\overline{y}=p\frac{{\sigma }_x}{{\sigma }_y}(x-\overline{x})$
$y-6=0.9\times \frac{1.5}{10}(x-40)$
$y=0.135(x-40)+6$
At $x=60$
$y=(0.135\times 20)+c$
$=2.7+6$
$y=8.7$
Therefore, the amount for advertisement is $8.7$ crore