Homework SoursePLEASE SHOW ALL WORK ROUND 2 DECIMALS An analyst must decid
PLEASE SHOW ALL WORK & ROUND 2 DECIMALS!
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 + 1.9t, 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 answers to 2 decimal places.)
1. MAD (Naive) = ?
2. MAD (Linear) = ?
3. MSE (Naive) = ?
4. MSE (Linear) = ?
| t | Units Sold |
| 11 | 148 |
| 12 | 145 |
| 13 | 148 |
| 14 | 145 |
| 15 | 152 |
| 16 | 150 |
| 17 | 154 |
| 18 | 156 |
| 19 | 160 |
| 20 | 167 |
Solution
To calculate the MAD and MSE, we require the data to formulate Ft = 125 + 1.9t which is absolutely available in the form of Time data (t) and Units sold.
The t represents the time period during which each data point was collected – i.e., the first time period is 11, the second is 12 and so on. Hence, if someone wants to know the fitted value for value 11, it is 125 +1.9*(11) = 145.9.
MAD:
MAD stands for mean absolute deviation, which is the average of the absolute deviations. An absolute deviation is the absolute value of the actual data minus the fitted value
The best fitted line should have zero MAD; the larger the MAD, the worse the model. For instance, instead of using linear regression to generate a forecast, a practitioner might base the forecast on last month’s volume. This generates a different MAD value
The MAD value allows the practitioner to conclude that the model generated by linear regression is better than the model generated by last month’s volume.
MSD:
The linear trend plot also uses the accuracy measure MSD, which stands for mean square deviation. It is very similar to MAD, but instead of summing the absolute deviations, this measure sums up the squared deviations
So what is the difference? MSD weights large deviations more heavily because it takes the square of the deviations. In general, MSD is preferred over MAD because there seems to be more theoretical support for it.
Thank you.
