An analyst must decide between two different forecasting techniques for weekly s
ID: 467237 • 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 = 123 + 1.8t, 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.)
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 = 123 + 1.8t, 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.)
Explanation / Answer
The Linear Regression line for given data is given as Ft = 123 + 1.8t. By using this fitting line forecast values for next periods are calculated as follows:
Linear Regression method of Forecasting
t
Units Sold
Forecast Value (Ft =123+1.8t)
Forecast Error (Et = At - Ft)
Absolute Deviation (|Et|)
Squared Error (Et2)
11
143
142.8
0.2
0.2
0.04
12
146
144.6
1.4
1.4
1.96
13
152
146.4
5.6
5.6
31.36
14
142
148.2
-6.2
6.2
38.44
15
154
150
4
4
16
16
152
151.8
0.2
0.2
0.04
17
155
153.6
1.4
1.4
1.96
18
155
155.4
-0.4
0.4
0.16
19
159
157.2
1.8
1.8
3.24
20
165
159
6
6
36
Total
14
27.2
129.2
Mean Absolute Deviation (MAD) = average of the absolute value of forecast deviation
MAD (Linear) = 27.2/10 = 2.72
Mean Square Error (MSE) = average of the squared value of forecast deviation
MSE (Linear) = 129.2/10 = 12.92
Simple Naive method
According to naïve method forecast value of required period is equal to demand in most recent period. Thus, according to naïve method forecast for time period 12 will be equal to actual demand occurred in most recent previous period, 11.
Naive method of Forecasting
t
Units Sold
Forecast Value (Ft =123+1.8t)
Forecast Error (Et = At - Ft)
Absolute Deviation (|Et|)
Squared Error (Et2)
11
143
12
146
143
3
3
9
13
152
146
6
6
36
14
142
152
-10
10
100
15
154
142
12
12
144
16
152
154
-2
2
4
17
155
152
3
3
9
18
155
155
0
0
0
19
159
155
4
4
16
20
165
159
6
6
36
Total
22
46
354
Mean Absolute Deviation (MAD) = average of the absolute value of forecast deviation
MAD (Naïve) = 46/9 = 5.11
Mean Square Error (MSE) = average of the squared value of forecast deviation
MSE (Linear) = 354/9 = 39.33
MAD (Naive)
2.72
MAD (Linear)
12.92
MSE (Naive)
5.11
MSE (Linear)
39.33
The MAD and MSE of linear regression method is less than that of Naïve method, thus, linear regression method has higher accuracy than Naïve method.
Linear Regression method of Forecasting
t
Units Sold
Forecast Value (Ft =123+1.8t)
Forecast Error (Et = At - Ft)
Absolute Deviation (|Et|)
Squared Error (Et2)
11
143
142.8
0.2
0.2
0.04
12
146
144.6
1.4
1.4
1.96
13
152
146.4
5.6
5.6
31.36
14
142
148.2
-6.2
6.2
38.44
15
154
150
4
4
16
16
152
151.8
0.2
0.2
0.04
17
155
153.6
1.4
1.4
1.96
18
155
155.4
-0.4
0.4
0.16
19
159
157.2
1.8
1.8
3.24
20
165
159
6
6
36
Total
14
27.2
129.2
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