An analyst must decide between two different forecasting techniques for weekly s
ID: 398276 • Letter: A
Question
An analyst must decide between two different forecasting techniques for weekly sales of roller blades: a linear trend equation and the naive approach. The linear trend equation is Ft 124+2.1t, and it was developed using data from periods 1 through 10. Based on data for periods 11 through 20 as shown in the table, which of these two methods has the greater accuracy if MAD and MSE are used? Round your intermediate calculations and final answers to 2 decimal places.) t 12 13 14 15 16 17 18 19 20 Units Sold 145 145 152 144 152 149 156 155 162 165Explanation / Answer
Please refer below table for ready reference :
T
Units sold
Forecast ( Naïve)
Absolute deviation ( AD)
Squared Error ( SE)
Forecast( Linear trend)
Absolute deviation ( AD)
Squared Error ( SE)
11
145
12
145
145
0
0
149.2
4.2
17.64
13
152
145
7
49
151.3
0.7
0.49
14
144
152
8
64
153.4
9.4
88.36
15
152
144
8
64
155.5
3.5
12.25
16
149
152
3
9
157.6
8.6
73.96
17
156
149
7
49
159.7
3.7
13.69
18
155
156
1
1
161.8
6.8
46.24
19
162
155
7
49
163.9
1.9
3.61
20
165
162
3
9
166
1
1
Sum =
44
294
39.8
257.24
Following may be noted :
= Absolute difference between forecast value and corresponding actual sales
= Sum of absolute deviation / 9 ( i.e. number of observations)
= Sum of squared error / 9 ( i.e. number of observations )
Based on above ,
For Naïve method :
MAD = 44/9 = 4.89 ( rounded to 2 decimal places )
MSE = 294 / 9 = 32.67 ( rounded to 2 decimal places )
For Linear trend method :
MAD = 39.8 / 9 = 4.42
MSE = 257.24 / 9 = 28.58
It is always desirable to have lower MAD and MSE since it yields lower forecast error.
The values of MAD and MSE derived basis linear trend method is lesser than that of as derived basis Naïve method. Therefore, Linear Trend method has the greater accuracy.
LINEAR TREND METHOD HAS GREATER ACCURACY
T
Units sold
Forecast ( Naïve)
Absolute deviation ( AD)
Squared Error ( SE)
Forecast( Linear trend)
Absolute deviation ( AD)
Squared Error ( SE)
11
145
12
145
145
0
0
149.2
4.2
17.64
13
152
145
7
49
151.3
0.7
0.49
14
144
152
8
64
153.4
9.4
88.36
15
152
144
8
64
155.5
3.5
12.25
16
149
152
3
9
157.6
8.6
73.96
17
156
149
7
49
159.7
3.7
13.69
18
155
156
1
1
161.8
6.8
46.24
19
162
155
7
49
163.9
1.9
3.61
20
165
162
3
9
166
1
1
Sum =
44
294
39.8
257.24