Question

 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?

Answer 1

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.