The following data about the sales and advertisement expenditure of a firms is given below (in ₹ Crores) What should be the advertisement expenditure if the firm proposes a sales target ₹ 60 crores? - Mathematics and Statistics

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Sum

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?

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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

Concept: Properties of Regression Coefficients
  Is there an error in this question or solution?
Chapter 3: Linear Regression - Exercise 3.2 [Page 48]

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