Question

The following data about the sales and advertisement expenditure of a firms is given below (in ₹ Crores)

	Sales	Adv. Exp.
Mean	40	6
S.D.	10	1.5

Coefficient of correlation between sales and advertisement expenditure is 0.9.

What should be the advertisement expenditure if the firm proposes a sales target ₹ 60 crores?

Answer 1

Let X = Sales,

Y = Advertisement expenditure

Given, ${\displaystyle \overline{x}=40,\overline{y}=6,{\sigma }_{\text{X}}=10,{\sigma }_{\text{Y}}=1.5}$, r = 0.9

${\displaystyle {\text{b}}_{\text{XY}}=\text{r}\frac{{\sigma }_{\text{X}}}{{\sigma }_{\text{Y}}}=0.9\times \frac{10}{1.5}=6}$

${\displaystyle {\text{b}}_{\text{YX}}=\text{r}\frac{{\sigma }_{\text{Y}}}{{\sigma }_{\text{X}}}=0.9\times \frac{1.5}{10}=0.135}$

The regression equation of Y on X is

${\displaystyle (\text{Y}-\overline{y})={\text{b}}_{\text{YX}}(\text{X}-\overline{x})}$

∴ (Y - 6) = 0.135(X - 40)

∴ Y - 6 = 0.135X - 5.4

∴ Y = 0.135X - 5.4 + 6

∴ Y = 0.135X + 0.6

For X = 60, 

Y = 0.135(60) + 0.6 = 8.1 + 0.6 = 8.7

∴ The advertisement expenditure should be ₹ 8.7 crores if the firm proposes a sales target ₹ 60 crores