Following are two weekly forecasts made by two different methods for the number
ID: 390049 • 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 Actual Demand 0.70 0.98 1.07 1.00 Actual Demand 0.70 0.98 1.07 1.00 Forecast Forecast Method 2 0.82 1.20 0.90 1.11 Week Method 1 Week 0.95 1.02 0.95 1.17 4 The MAD for Method 1thousand 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 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
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
= (0.25+0.04+0.12+0.17) / 4
= 0.58/4
= 0.145 thousand gallons
b) Mean squared error = Sum of the squared errors for all the periods / number of periods
= (0.063+0.002+0.014+0.029) / 4
= 0.108/4
= 0.027 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
= (0.12+0.22+0.17+0.11) / 4
= 0.62/4
= 0.155 thousand gallons
b) Mean squared error = Sum of the squared errors for all the periods / number of periods
= (0.014+0.048+0.029+0.012) / 4
= 0.103/4
= 0.026 thousand gallons