Following are two weekly forecasts made by two different methods for the number
ID: 352366 • 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 Method 2 0.82 1.19 0.88 1.11 Actual Demand 0.72 1.00 1.00 0.97 Week Method 1 Demand Week 0.90 1.05 0.97 1.22 0.72 1.00 1.00 0.97 The MAD for Method 1 . 126 thousand gallons (round your response to three decima, places). The mean squared error (MSE) for Method 1 thousand round your response to three decimal places).Explanation / Answer
To calculate the MAD and MSE we have to calculate the error, absolute errors, and squared errors for all the weeks
Where,
Error = Actual demand - forecasted demand
Absolute error = absolute value of error
Squared error = square of error
Calculation of MAD and MSE for method 1 :
The errors, absolute errors and squared errors for all the weeks are
MAD = Sum of the absolute errors for all the periods / number of periods
= (0.18+0.05+0.03+0.25)/4
= 0.51/4
= 0.128
MSE = Sum of the squared errors for all the periods / number of periods
= (0.032+0.003+0.001+0.063)/4
= 0.099/4
= 0.025
Calculation of MAD and MSE for method 2 :
The error, abaolute error and squared errors for all the periods are
MAD = Sum of the absolute errors for all the periods / number of periods
= (0.1+0.19+0.12+0.14)/4
= 0.55/4
= 0.138
MSE = Sum of the squared errors for all the periods / number of periods
= (0.01+0.036+0.014+0.020)/4
= 0.080/4
= 0.020