Question

A textbook publishing company has compiled data on total annual sales of its business texts for the preceding nine years:

Year	1	2	3	4	5	6	7	8	9
Sales (000):	37.20	44.80	47.40	51.60	55.70	57.30	60.50	69.90	73.80

a. Using an appropriate model, forecast textbook sales for each of the next five years. (Round your intermediate calculations to 3 decimal places and final answers to 2 decimal places.)

Year	10	11	12	13	14
Forecast

Answer 1

a.

Using linear trend equation,

Year	10	11	12	13	14
Forecast	76.49	80.71	84.94	89.16	93.39

calculation

	Year (x)	Sales (000): (y)	xy	x2
	1	37.2	37.2	1
	2	44.8	89.6	4
	3	47.4	142.2	9
	4	51.6	206.4	16
	5	55.7	278.5	25
	6	57.3	343.8	36
	7	60.5	423.5	49
	8	69.9	559.2	64
	9	73.8	664.2	81
Total	45	498.2	2744.6	285

x-bar = Sum(x)/n = 45/9 = 5
y-bar = Sum(y)/n = 498.2/9 = 55.35555556 = 55.356 (Rounded to 3 decimal places)

b = (Sum(xy) – n*x-bar*y-bar)/(Sum(x2) – n*x-bar*x-bar) = (2744.6-9*5*55.356)/(285–9*5*5)
   = 253.58/60= 4.226333333 = 4.226(Rounded to 3 decimal places)

a = y-bar –b*x-bar
= 55.356-4.226*5 = 34.226

Regression equation is y = a + bx,
we get following regression equation by substituting values of a and b
Regression equation is y =34.226 + 4.226x

Formula