20. 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 = 124 + 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? Units Sold t 11 12 13 14 15 16 17 18 19 20 147 148 151 145 155 152 155 157 160 165
C3Q20
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Naïve Method:
| Period | Sales |
| 11 | 147 |
| 12 | 148 |
| 13 | 151 |
| 14 | 145 |
| 15 | 155 |
| 16 | 152 |
| 17 | 155 |
| 18 | 157 |
| 19 | 160 |
| 20 | 165 |
The Naïve approach assumes that things will continue to happen as they did in the past.
| Period | Sales | Naïve |
| 11 | 147 | |
| 12 | 148 | 147 |
| 13 | 151 | 148 |
| 14 | 145 | 151 |
| 15 | 155 | 145 |
| 16 | 152 | 155 |
| 17 | 155 | 152 |
| 18 | 157 | 155 |
| 19 | 160 | 157 |
| 20 | 165 | 160 |
Now Returns the absolute value of a number:
ABS for Period 12 = Sales - Naïve = 148 - 147 = 1
ABS for Period 13 = Sales - Naïve = 151 - 148 = 3
ABS for Period 14 = Sales - Naïve = 145 - 151 = 6
ABS for Period 15 = Sales - Naïve = 155 - 145 = 10
ABS for Period 16 = Sales - Naïve = 152 - 155 = 3
ABS for Period 17 = Sales - Naïve = 155 - 152 = 3
ABS for Period 18 = Sales - Naïve = 157 - 155 = 2
ABS for Period 19 = Sales - Naïve = 160 - 157 = 3
ABS for Period 20 = Sales - Naïve = 165 - 160 = 5
MAD = Average of ABS = (1+3+6+10+3+3+2+3+5)/9 = 4.00
Now doing Square of ABS.
ABS for Period 12 = (1)^2 = 1
ABS for Period 13 = (3)^2 = 9
ABS for Period 14 = (6)^2 = 36
ABS for Period 15 = (10)^2 = 100
ABS for Period 16 = (3)^2 = 9
ABS for Period 17 = (3)^2 = 9
ABS for Period 18 = (2)^2 = 4
ABS for Period 19 = (3)^2 = 9
ABS for Period 20 = (5)^2 = 25
MSE =Total of Squared ABS / (No of Items - 1)
MSE = Total of (1+9+36+100+9+9+4+9+25) / (9-1) = 25.25
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