Homework SourseAn analyst must decide between two different forecasting tec
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 = 125 + 2.2t, 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 | Units Sold |
| 11 | 144 |
| 12 | 148 |
| 13 | 151 |
| 14 | 147 |
| 15 | 154 |
| 16 | 149 |
| 17 | 154 |
| 18 | 156 |
| 19 | 158 |
| 20 | 163 |
Solution
As per forecasting method under Naïve approach :
Ft = At-1
Where,
Ft = Forecast value for period t
At-1 = Actual number of units sold
As per forecasting method using linear trend equation :
Ft = 125 + 2.2.t
Please find below table which highlights values of Absolute deviation and Squared error.
Following to be noted:
Absolute deviation for any item = Absolute value of difference between Forecast value – Units sold
Squared error = Absolute deviation^2
t
Units sold
Forecast-Naïve approach
Absolute deviation
Squared error
Forecast - Linear trend equation
Absolute deviation
Squared error
11
144
149.2
12
148
144
4
16
151.4
3.4
11.56
13
151
148
3
9
153.6
2.6
6.76
14
147
151
4
16
155.8
8.8
77.44
15
154
147
7
49
158
4
16
16
149
154
5
25
160.2
11.2
125.44
17
154
149
5
25
162.4
8.4
70.56
18
156
154
2
4
164.6
8.6
73.96
19
158
156
2
4
166.8
8.8
77.44
20
163
158
5
25
169
6
36
TOTAL =
37
173
61.8
495.16
Thus,
Mean Absolute deviation ( MAD ) for Forecast values using Naïve approach = 37/ 9 = 4.11 ( Remarks : Denominator i9 since there are 9 sets of data)
Mean Squared Error ( MSE) FOR FORECAST VALUES USING Naïve approach = 173 / 9 = 19.22
Mean absolute deviation ( MAD ) for forecast value using Linear Trend equation = 61.8 / 9 = 6.87
Mean squared error 9 MSE ) for forecast value using linear trend equation = 495.16/9 = 55.02
A forecast will have more accuracy with lesser values of MAD and MSE. Since, Forecast using Naïve approach has lesser values of MAD and MSE compared to that of Forecast using linear trend equation, Naïve method has more accuracy
MAD Naïve = 37
MAD Linear = 61.8
MSE Naïve = 173
MSE Linear = 495.16
| t | Units sold | Forecast-Naïve approach | Absolute deviation | Squared error | Forecast - Linear trend equation | Absolute deviation | Squared error |
| 11 | 144 | 149.2 | |||||
| 12 | 148 | 144 | 4 | 16 | 151.4 | 3.4 | 11.56 |
| 13 | 151 | 148 | 3 | 9 | 153.6 | 2.6 | 6.76 |
| 14 | 147 | 151 | 4 | 16 | 155.8 | 8.8 | 77.44 |
| 15 | 154 | 147 | 7 | 49 | 158 | 4 | 16 |
| 16 | 149 | 154 | 5 | 25 | 160.2 | 11.2 | 125.44 |
| 17 | 154 | 149 | 5 | 25 | 162.4 | 8.4 | 70.56 |
| 18 | 156 | 154 | 2 | 4 | 164.6 | 8.6 | 73.96 |
| 19 | 158 | 156 | 2 | 4 | 166.8 | 8.8 | 77.44 |
| 20 | 163 | 158 | 5 | 25 | 169 | 6 | 36 |
| TOTAL = | 37 | 173 | 61.8 | 495.16 |
