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?
Solution
Let X = Sales,
Y = Advertisement expenditure
Given, `bar x = 40, bar y = 6, sigma_"X" = 10, sigma_"Y" = 1.5`, r = 0.9
`"b"_"XY" = "r" sigma_"X"/sigma_"Y" = 0.9 xx 10/1.5 = 6`
`"b"_"YX" = "r" sigma_"Y"/sigma_"X" = 0.9 xx 1.5/10 = 0.135`
The regression equation of Y on X is
`("Y" - bar y) = "b"_"YX" ("X" - bar 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