Question

Consider the following time series:

Period 1, 2, 3, 4, 5, 6, 7, 8

Demand 15, 17, 14, 7, 10, 12, 7, 5

A. using a trend projection, forecast the demand for period 9

b. calculate the MAD for this forecast

SHOW ALL WORK! DO NOT USE EXCEL OR PHSTAT!

Answer 1

X	Y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
1	15	12.25	17.0	-14.4
2	17	6.25	37.5	-15.3
3	14	2.25	9.8	-4.7
4	7	0.25	15.0	1.9
5	10	0.25	0.8	-0.4
6	12	2.25	1.3	1.7
7	7	6.3	15.0	-9.7
8	5	12.25	34.5	-20.6

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	36	87	42.000	130.9	-61.5
mean	4.50	10.88	SSxx	SSyy	SSxy

sample size ,   n =   8          
here, x̅ =   4.50   ,   ȳ =   10.875  
                  
SSxx =    Σ(x-x̅)² =    42.00          
SSxy=   Σ(x-x̅)(y-ȳ) =   -61.5          
                  
slope ,    ß1 = SSxy/SSxx =   -1.4643          
                  
intercept,   ß0 = y̅-ß1* x̄ =   17.4643          
                  
so, trend equation is   Ŷ =   17.46   +   -1.46   *x

a)

period =9

Ŷ = 17.46 + -1.46 *9=4.3

b)

period, X	demand				forcast	absolute error, demad-forcast
1	15				16.00	1.0000
2	17				14.54	2.4643
3	14				13.07	0.9286
4	7				11.61	4.6071
5	10				10.14	0.1429
6	12				8.68	3.321
7	7				7.21	0.214
8	5				5.75	0.750

MAD = Σ|demand -forecast|/n= 13.429/8 = 1.679