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):	37.10	45.00	49.80	51.00	54.60	57.60	63.40	68.80	74.90

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

b. Compute +/- 2s control limits for the control chart for forecast errors using just data from the original nine periods. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

Control limits are 0 ±             

c. Suppose actual sales for the next five years turn out as follows:
       

Year	10	11	12	13	14
Sales (000):	78.60	82.40	88.90	92.00	96.90

Is the forecast performing adequately?

Yes

No

Answer 1

A.

n=	9
X	Y	X^2	XY
Year	Sales (000):
1	37.1	1	37.1
2	45	4	90
3	49.8	9	149.4
4	51	16	204
5	54.6	25	273
6	57.6	36	345.6
7	63.4	49	443.8
8	68.8	64	550.4
9	74.9	81	674.1
45	502	285	2767.4
	a =	34.4333
	b =	4.2733
	Y = a+ bX
	r=	0.968527

so,

using this :

n=	9
X	Y	X^2	XY
Year	Sales (000):			Forecast
1	37.1	1	37.1
2	45	4	90
3	49.8	9	149.4
4	51	16	204
5	54.6	25	273
6	57.6	36	345.6
7	63.4	49	443.8
8	68.8	64	550.4
9	74.9	81	674.1
45	502	285	2767.4
	a =	34.4333
	b =	4.2733
	Y = a+ bX
	r=	0.968527
10				77.17
11				81.44
12				85.71
13				89.99
14				94.26

B.

So using 2S:

	Year	1	2	3	4	5	6	7	8	9	10	11	12	13	14
	Sales (000):	37.1	45	49.8	51	54.6	57.6	63.4	68.8	74.9
	Forecast										77.17	81.44	85.71	89.99	94.26
M	Mean	55.8000										Not in Control
S	Std Dev	11.8407
UCL		79.48143
LCL		32.11857

C.

Year	10	11	12	13	14
Sales (000):	78.6	82.4	88.9	92	96.9
Forecast	77.17	81.44	85.71	89.99	94.26
APE	2%	1%	4%	2%	3%
MAPE	2%
Is the forecast performing adequately?
	Yes
	As MAPE is not very high