answer that MSE for Method 1 and Method 2 MSE and MAD Following are two weekly f
ID: 389933 • Letter: A
Question
answer that MSE for Method 1 and Method 2 MSE and MAD
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 Actual Week Method 1Demand Woek Method 2 Demand 0.85 1.05 0.95 1.17 0.70 1.00 1.00 0.97 0.80 1.19 0.92 1.15 0.70 1.00 1.00 0.97 The MAD for Method 1 0.113 thousand gallons (round your response to three decimel places) The mean squared error (MSE) for Method1thousand gallons fround your response to three decimal places).Explanation / Answer
To calculate the Mean absolute deviation and Mean squared error we have to first calculate the error,absolute errors and squared errors for all the periods.
Where,
Error = Actual value - forecasted value
Absolute error = Absolute value of error
Squared error = Square of error
Method 1:
So using the above formula thr errors absolute errors and squared errors for each week in method 1 are
a) Mean absolute deviation = Sum of the absolute errors for all the periods/number of periods
= (0.15+0.05+0.05+0.2) / 4
= 0.45/4
= 0.113 thousand gallons
b) Mean squared error = Sum of the squared errors for all the periods / number of periods
= (0.023+0.003+0.003+0.04) / 4
= 0.069/4
= 0.017 thousand gallons
Method 2:
So using the above formula thr errors absolute errors and squared errors for each week in method 1 are
a) Mean absolute deviation = Sum of the absolute errors for all the periods/number of periods
= (0.1+0.19+0.08+0.18) / 4
= 0.55/4
= 0.138 thousand gallons
b) Mean squared error = Sum of the squared errors for all the periods / number of periods
= (0.01+0.036+0.006+0.032) / 4
= 0.084/4
= 0.021 thousand gallons
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