question archive Consider the following time series Period 1 2 3 4 5 6 7 8 Demand 16 17 15 9 12 13 8 5 a) Using a trend projection, forecast the demand for Period 9
Subject:StatisticsPrice:2.87 Bought7
Consider the following time series
Period 1 2 3 4 5 6 7 8
Demand 16 17 15 9 12 13 8 5
a) Using a trend projection, forecast the demand for Period 9.
b) Calculate the MAD for this forecast.
a) The forecasted demand for Period 9 is
Round to one decimal place as needed.)
Answer
Period(t) |
Demand(D) |
t*D |
t-square |
|
1 |
16 |
16 |
1 |
|
2 |
17 |
34 |
4 |
|
3 |
15 |
45 |
9 |
|
4 |
9 |
36 |
16 |
|
5 |
12 |
60 |
25 |
|
6 |
13 |
78 |
36 |
|
7 |
8 |
56 |
49 |
|
8 |
5 |
40 |
64 |
|
Total |
36 |
95 |
365 |
204 |
A.a) For trend projection, we have below formulae
Dt=b0+b1*t
b1={n*∑t*D-∑t*∑D}/{n*∑t^2-(∑t)^2}
b0=(Y-bar)-(b1*t-bar)
Y-bar=∑D/n
t-bar=∑t/n
First calculate b1
b1=(8*365-36*95)/(8*204-36*36)
upon solving, we get
b1=-500/336=-1.49
b1=-1.49
now, to calculate b0
Y-bar=∑D/n
Y-bar =95/8=11.875
t-bar=∑t/n
t-bar =36/8=4.5
b0=(Y-bar)-(b1*t-bar)
b0=11.875-(-1.49)*4.5
b0=18.58
now to forecast demand for period 9
Dt=b0+b1*t
D9=18.58+(-1.49)*9
D9=5.19
Hence forecast for period 9 demand is 5.19
A.b) calculate MAD
MAD formula is given as
MAD=∑Dt-Ft/n
From the given table, we need to calculate forecasted demand and deviation for each period
Period(t) |
Actual Demand(D) |
Forecasted Demand(F=b0+b1*t) |
Deviation(D-F) |
Absolute Deviation|D-F| |
1 |
16 |
17.09 |
-1.09 |
1.09 |
2 |
17 |
15.6 |
1.4 |
1.4 |
3 |
15 |
14.11 |
0.89 |
0.89 |
4 |
9 |
12.62 |
-3.62 |
3.62 |
5 |
12 |
11.13 |
0.87 |
0.87 |
6 |
13 |
9.64 |
3.36 |
3.36 |
7 |
8 |
8.15 |
-0.15 |
0.15 |
8 |
5 |
6.66 |
-1.66 |
1.66 |
∑|Dt-Ft|=13.04
MAD=∑Dt-Ft/n
MAD=13.04/8
MAD=1.63