Question

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	67	64
2	75	70	60
3	70	75	70
4	74	71	72
5	69	71	73
6	72	65	76
7	80	71	75
8	78	77	85

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)  F2  F1  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)  F2  F1  None  appears to be more accurate.



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)  F2  F1  None  appears to be more accurate.

Answer 1

FORECAST ERROR	F1	F2	BETTER?
MAD	4.13	5.13	F1
MSE	45.13	15.13	F2
MAPE	5.5	7	F1

EXPLANATION

FORECAST 1

PERIOD	ACTUAL DEMAND	FORECAST	DEVIATIONS	ABSOLUTE DEVIATION	ABS DEV / DEMAND
1	68	67	1	1	0.014706
2	75	70	5	5	0.066667
3	70	75	-5	5	0.071429
4	74	71	3	3	0.040541
5	69	71	-2	2	0.028986
6	72	65	7	7	0.097222
7	80	71	9	9	0.1125
8	78	77	1	1	0.012821

MAD = SIGMA(SUM OF ABSOLUTE DEVIATIONS) / N

MSE = SIGMA(SUM OF DEVIATIONS) ^ 2 / N

MAPE = (SIGMA(ABS DEV / DEMAND) / N) * 100

Where N represents the number of observations.

We know that N = 8

Sum of absolute deviations = 1 + 5 + 5 + 3 + 2 + 7 + 9 + 1 = 33

MAD = 33 / 8 = 4.13

Sum of deviations = 1 + 5 + -5 + 3 + -2 + 7 + 9 + 1 = 19

MSE = 19 ^2 / 8 = 45.13

Sum of abs dev / demand = 0.01 + 0.07 + 0.07 + 0.04 + 0.03 + 0.1 + 0.11 + 0.01 = 0.44

MAPE = (0.44 / 8) * 100 = 5.50

FORECAST 2

PERIOD	ACTUAL DEMAND	FORECAST	DEVIATIONS	ABSOLUTE DEVIATION	ABS DEV / DEMAND
1	68	64	4	4	0.058824
2	75	60	15	15	0.2
3	70	70	0	0	0
4	74	72	2	2	0.027027
5	69	73	-4	4	0.057971
6	72	76	-4	4	0.055556
7	80	75	5	5	0.0625
8	78	85	-7	7	0.089744

We know that N = 8

Sum of absolute deviations = 4 + 15 + 0 + 2 + 4 + 4 + 5 + 7 = 41

MAD = 41 / 8 = 5.13

Sum of deviations = 4 + 15 + 0 + 2 + -4 + -4 + 5 + -7 = 11

MSE = 11 ^2 / 8 = 15.13

Sum of abs dev/ demand = 0.06 + 0.2 + 0 + 0.03 + 0.06 + 0.06 + 0.06 + 0.09 = 0.56

MAPE = (0.56 / 8) * 100 = 7.00

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