Question

The following data relate to advertisement expenditure (in lakh of rupees) and their corresponding sales (in crores of rupees)

Advertisement expenditure	40	50	38	60	65	50	35
Sales	38	60	55	70	60	48	30

Estimate the sales corresponding to advertising expenditure of ₹ 30 lakh.

Answer 1

X	Y	X2	Y2	XY
40	38	1600	1444	1520
50	60	2500	3600	3000
38	55	1444	3025	2090
60	70	3600	4900	4200
65	60	4225	3600	3900
50	48	2500	2304	2400
35	32	1225	900	1050
338	361	17094	19773	18160

N = 7, ΣX = 338, ΣY = 361, ΣX² = 17094, ΣY² = 19773, ΣXY = 18160.

`bar"X" = (sum"X")/"N" = 338/7` = 48.29

`bar"Y" = (sum"Y")/"N" = 361/7` = 51.57

b_yx = `("N"sum"XY" - (sum"X")(sum"Y"))/("N"sum"X"^2 - (sum"X")^2)`

= `(7(18160) - (388)(361))/(7(17094) - (338)^2)`

= `(127120 - 122018)/(119658 - 114244)`

= `5102/5414`

= 0.942

Regression equation of Y on X

`"Y" - bar"Y" = "b"_"yx"("X" - bar"X")`

Y – 51.57 = 0.942(X – 48.29)

Y – 51.57 = 0.942X – 0.942 × 48.29

Y – 51.57 = 0.942X – 45.48918

Y = 0.942X + 51.57 – 48.29

Y = 0.942X + 6.081

To find the sales, when the advertising is X = ₹ 30 lakh in the above equation we get,

Y = 0.942(30) + 6.081

= 28.26 + 6.081

= 34.341

= ₹ 34.34 crores