Following are two weekly forecasts made by two different methods for the number
ID: 410364 • 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 Week Method 1 Actual Demand 0.70 0.98 1.07 1.00 Forecast Method 2 0.82 1.21 0.90 1.15 Actual Demand 0.70 0.98 1.07 1.00 Week 0.90 1.08 0.97 1.17 4 The MAD for Method 1 thousand gallons (round your response to three decimal places) The mean squared error (MSE) for Method 1thousand gallons (round your response to three decimal places) The MAD for Method 2 thousand 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