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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.
Estimate the likely sales for a proposed advertisement expenditure of ₹ 10 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 X on Y is
`("X" - bar x) = "b"_"XY" ("Y" - bar y)`
∴ (X - 40) = 6(Y - 6)
∴ X - 40 = 6Y - 36
∴ X = 6Y - 36 + 40
∴ X = 6Y + 4
For Y = 10, we get
X = 6(10) + 4 = 60 + 4 = 64
∴ The likely sale is ₹ crores for a proposed advertisement expenditure of ₹ 10 crores.
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