Question

The following data represent a company's yearly sales volume and its advertising expenditure over a period of 8 years.

Advertising (x)	Sales (y)
400,000	6,000,000
500,000	7,200,000
500,000	8,000,000
660,000	7,500,000
790,000	8,900.000
540,000	8,100,000
420,000	5,900.000
380,000	4,000,000

1. If the company's advertising expenditure is $315,000, what are the predicted sales?
2. If the company wanted $9,500,000 in sales, what should the advertising budget be?

Answer 1

X	Y	XY	X^2	Y^2
400,000	6,000,000	2.4E+12	1.6E+11	3.6E+13
500,000	7,200,000	3.6E+12	2.5E+11	5.184E+13
500,000	8,000,000	4E+12	2.5E+11	6.4E+13
660,000	7,500,000	4.95E+12	4.36E+11	5.625E+13
790,000	8,900.00	7.03E+09	6.24E+11	79210000
540,000	8,100,000	4.37E+12	2.92E+11	6.561E+13
420,000	5,900.00	2.48E+09	1.76E+11	34810000
380,000	4,000,000	1.52E+12	1.44E+11	1.6E+13

From the above table and formula we get the value are as;

n	8
sum(XY)	20853509000000
sum(X)	4190000.00
sum(Y)	40814800.00
sum(X^2)	2332100000000.00
sum(Y^2)	289700114020000

b	-3.802980
a	7093660.7341

ycap = a + bx

ycap = 7093660.7341 - 3.802980x

when x = 315000

The best predicted sales =

7093660.7341 - 3.802980 * 315000
= 5895722.0

ycap = 7093660.7341 - 3.802980 * 315000

when ycap = 9500000

9500000 = 7093660.7341 - 3.802980 * x

3.802980 * x = 7093660.7341 - 9500000

x = -632751