# You are given the following information about advertising expenditure and sales - Mathematics and Statistics

Sum

You are given the following information about advertising expenditure and sales:

 Advertisement Expenditure (Rs. in lakh)             (X) Sales (Rs. in lakh)            (Y) Arithmetic mean 10 90 Standard deviation 3 12

Correlation coefficient between X and Y = 0.8.

(a) Obtain the two regression equations.

(b) What is the likely sales when the advertising budget is ? 15 lakh?

(c) What should be the advertising budget if the company wants to attain sales target of ₹ 120 lakh?

#### Solution

Given : barx = 10, bary = 90, sigma_x = 3, sigma_y = 12,

(a) Line of regression of y on x is given by:

y - bary = b_(yx) (x - barx)

b_yx = (rsigmay)/(sigmax)
= 0.8 x 12/3 = 3.2

y - 90 = 3.2 (x - 10)

i.e y = 3.2x + 58

And line of regression of x on y is

x - barx = b_xy (y - bary)

Here, b_xy = (rsigmax)/(sigmay)

= 0.8 x 3/12 = 0.2
x - 10 = 0.2 ( y - 90)
x = 0.2y - 8

(b) y when x = 15 lakh
y = 3.2x + 58
y = 3.2 x 15 + 58
y = 58 + 48
y = 106

when the advertising budget is Rs 15 lakhs likely sales is Rs 106 lakhs

(c) x when y = 120 lakhs
x = 0.2y - 8
x = 0.2 x 120 - 8
x = 24 - 8
x = 16

If the company wants to attain sales target of Rs 120 lakhs advertising budget should be Rs 16 lakhs.

Concept: Lines of Regression of X on Y and Y on X Or Equation of Line of Regression
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