Question

Following are given information about advertising expenditure and sales.

	Advertisement expenditure (₹ in lakh) (X)	Sales (₹ in lakh) (Y)
Arithmetic mean	10	90
Standard deviation	3	12

Correlation coefficient between X and Y is 0.8.

1. Obtain the regression of Y on X
2. What is the likely sales when the advertising budget is ₹ 15 lakh?

Answer 1

Given: `bar x = 10, bar y = 90, sigma_x = 3, sigma_y = 12`, r = 0.8

(a) The regression equation of y on x is

y = `a + b_"YX"*x`

`"b"_"YX" = "r" sigma_y/sigma_x`

= `0.8 xx 12/3`

= 0.8 × 4 

= 3.2

a = `bar"y" -"b"_"YX" (bar x)`

a = 90 – 3.2 (10) 

a = 90 – 32

a = 58

Now, y = `a + b_"YX"*x`

y = 58 + 3.2x

y = 3.2x + 58  

(b) Sales when the advertising budget is ₹ 15 lakh

For X = 15,

Y = 58 + 3.2 (15)

= 58 + 48

= 106

∴ Likely sales is ₹ 106 lakh when advertising budget is ₹ 15 lakh.