Two different forecasting techniques (F1 and F2) were used to
forecast demand for cases of bottled water. Actual demand and the
two sets of forecasts are as follows:
PREDICTED DEMAND | |||
Period | Demand | F1 | F2 |
1 | 68 | 63 | 62 |
2 | 75 | 66 | 61 |
3 | 70 | 73 | 70 |
4 | 74 | 65 | 71 |
5 | 69 | 71 | 73 |
6 | 72 | 69 | 73 |
7 | 80 | 70 | 76 |
8 | 78 | 72 | 80 |
a. Compute MAD for each set of forecasts. Given
your results, which forecast appears to be more accurate?
(Round your answers to 2 decimal place.)
MAD F1 | |
MAD F2 | |
(Click to
select) F1 F2 None appears
to be more accurate.
b. Compute the MSE for each set of forecasts.
Given your results, which forecast appears to be more accurate?
(Round your answers to 2 decimal
places.)
MSE F1 | |
MSE F2 | |
(Click to
select) F1 F2 None appears
to be more accurate.
c. In practice, either MAD or
MSE would be employed to compute forecast errors. What factors
might lead a manager to choose one rather than the other?
Either one might already be in use, familiar to users, and have
past values for comparison. If (Click to
select) control charts tracking
signals are used, MSE would be natural;
if (Click to select) control
charts tracking signals are used, MAD would
be more natural.
d. Compute MAPE for each data set. Which forecast
appears to be more accurate? (Round your intermediate
calculations to 2 decimal places and and final answers to 2 decimal
places.)
MAPE F1 | |
MAPE F2 | |
(Click to select) F1 F2 None appears to be more accurate.
a. Mean Absolute Deviation (MAD) calculation:
PREDICTED DEMAND | |||||
Period | Demand (D) | F1 | F2 | Absolute Error |(D-F1)| | Absolute Error |(D-F2)| |
1 | 68 | 63 | 62 | 5 | 6 |
2 | 75 | 66 | 61 | 9 | 14 |
3 | 70 | 73 | 70 | 3 | 0 |
4 | 74 | 65 | 71 | 9 | 3 |
5 | 69 | 71 | 73 | 2 | 4 |
6 | 72 | 69 | 73 | 3 | 1 |
7 | 80 | 70 | 76 | 10 | 4 |
8 | 78 | 72 | 80 | 6 | 2 |
Mean Absolute Deviation (MAD) (Average) | 5.88 | 4.25 | |||
MAD F1 | 5.88 | ||||
MAD F2 | 4.25 |
F2 is more accurate as value of MAD F2 is lower.
b. Mean Squared Error (MSE) Calculation:
PREDICTED DEMAND | |||||||
Period | Demand (D) | F1 | F2 | Absolute Error (D-F1) | Absolute Error (D-F2) | squared error = (D-F1)^2 | squared error = (D-F2)^2 |
1 | 68 | 63 | 62 | 5 | 6 | 25 | 36 |
2 | 75 | 66 | 61 | 9 | 14 | 81 | 196 |
3 | 70 | 73 | 70 | 3 | 0 | 9 | 0 |
4 | 74 | 65 | 71 | 9 | 3 | 81 | 9 |
5 | 69 | 71 | 73 | 2 | 4 | 4 | 16 |
6 | 72 | 69 | 73 | 3 | 1 | 9 | 1 |
7 | 80 | 70 | 76 | 10 | 4 | 100 | 16 |
8 | 78 | 72 | 80 | 6 | 2 | 36 | 4 |
Mean Squared Error (MSE)= {Sum of squared error/(n-1)} | 5.88 | 4.25 | 49.29 | 39.71 | |||
MSE F1 | 49.29 | ||||||
MSE F2 | 39.71 |
Where n is number of errors = 8
F2 is more accurate as value of MSE F2 is lower.
c. Either one might already be in use, familiar to users, and have past values for comparison. If control charts are used, MSE would be natural; if tracking signals are used, MAD would be more natural
d. Mean Absolute Percentage Error (MAPE) Calculation:
PREDICTED DEMAND | |||||||
Period | Demand (D) | F1 | F2 | Absolute Error (D-F1) | Absolute Error (D-F2) | Absolute Percentage Error {(D-F1)/D} *100 | Absolute Percentage Error {(D-F2)/D} *100 |
1 | 68 | 63 | 62 | 5 | 6 | 7.35% | 8.82% |
2 | 75 | 66 | 61 | 9 | 14 | 12.00% | 18.67% |
3 | 70 | 73 | 70 | 3 | 0 | 4.29% | 0.00% |
4 | 74 | 65 | 71 | 9 | 3 | 12.16% | 4.05% |
5 | 69 | 71 | 73 | 2 | 4 | 2.90% | 5.80% |
6 | 72 | 69 | 73 | 3 | 1 | 4.17% | 1.39% |
7 | 80 | 70 | 76 | 10 | 4 | 12.50% | 5.00% |
8 | 78 | 72 | 80 | 6 | 2 | 7.69% | 2.56% |
Mean Absolute Percentage Error (MAPE) (Avearge) | 5.88 | 4.25 | 7.88% | 5.79% | |||
MAPE F1 | 7.88% | ||||||
MAPE F2 | 5.79% |
F2 is more accurate as value of MAPE F2 is lower.
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