Following are two weekly forecasts made by two different methods for the number
ID: 410365 • Letter: F
Question
Following are two weekly forecasts made by two different methods for the number of gallons of gasoline, in thousands, demanded at a local gasoline station. Also shown are actual demand levels, in thousands of gallons Forecast Actual Forecast Method2 0.82 1.21 0.90 1.15 Actual Demand 0.70 0.98 1.07 1.00 Week Method 1 Demand Week 0.90 1.08 0.97 1.17 0.70 0.98 1.07 1.00 4 The MAD for Method 1thousand gallons (round your response to three decimal places) The mean squared error (MSE) for Method 1 = | thousand gallons2 (round your fuponse to three decimal places) The MAD for Method 2thousand gallons (round your response to three decimal places) The mean squared error (MSE) for Method 2thousand gallons (round your response to three decimal places)Explanation / Answer
Following table calculates and presents values of absolute deviations and Squared error under both Forecast method
Following are to be noted :
Absolute deviation = Absolute difference in values of Actual demand and corresponding forecast value
Squared error = Absolute deviation^2
MAD = Sum of values of Absolute deviation / 4 ( i.e. number of observations)
Mean Squared error ( MSE ) = Sum of values of Squared error / 4
Week
Actual demand
Forecast method 1
Absolute Deviation
Squared error
Forecast method 2
Absolute Deviation
Squared error
1
0.7
0.9
0.2
0.04
0.82
0.12
0.0144
2
0.98
1.08
0.1
0.01
1.21
0.23
0.0529
3
1.07
0.97
0.1
0.01
0.9
0.17
0.0289
4
1
1.17
0.17
0.0289
1.15
0.15
0.0225
SUM:
0.57
0.0889
0.67
0.1187
Therefore,
MAD for Method 1 = 0.57 / 4 = 0.142 Thousand Gallons
Mean Squared error ( MSE) for Method 1 = 0.0889 / 4 = 0.022 Thousand Gallon Square
MAD for method 2 = 0.67/4 = 0.167 Thousand Gallons
Mean squared error ( MSE ) for Method 2 = 0.1187 / 4 = 0.29 thousand Gallon Square
Week
Actual demand
Forecast method 1
Absolute Deviation
Squared error
Forecast method 2
Absolute Deviation
Squared error
1
0.7
0.9
0.2
0.04
0.82
0.12
0.0144
2
0.98
1.08
0.1
0.01
1.21
0.23
0.0529
3
1.07
0.97
0.1
0.01
0.9
0.17
0.0289
4
1
1.17
0.17
0.0289
1.15
0.15
0.0225
SUM:
0.57
0.0889
0.67
0.1187