Question

What would be the estimated sale on the advertisement expenditure of Rs $15$ lakhs,on the basis of following data obtained from the company?.The coefficient of correlation is $0.8$.

	Advertising expenditure(in Rs.lakhs) $x$	Sale (in Rs lakhs) $y$
Mean	$20$	$90$
standard Deviation	$5$	$12$

• A. Rs $105$ lakhs
• B. Rs$106$ lakhs
• C. Rs $110$ lakhs
• D. Rs $120$ lakhs

Answer 1

The correct option is B Rs$106$ lakhs

$\overline{x}=20$, $\overline{y}=90$, ${\sigma }_x=5$, ${\sigma }_y=12$ 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
$y-90=\frac{0.8\times 12}{5}(x-20)$
$y-90=1.92(x-20)$
$y=1.92x+90-38.4$
Now, Subsitute the value of x=15, we get
$y=1.92\times 15+51.6=80.4$