Following are two weekly forecasts made by two different met

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)

Solution

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