The MAD for Method 1 = (thousand gallons) The mean squared error (MSE) for Metho

Question

The MAD for Method 1 = (thousand gallons)

The mean squared error (MSE) for Method 1 = (thousand gallons squared)

The MAD for Method 2 = (thousand gallons)

The mean squared error (MSE) for Method 2 = (thousand gallons squared)

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 1.00 1.07 1.04 Actual Demand 0.70 1.00 1.07 1.04 Forecast Week Method 1 Forecast Method 2 0.80 1.20 0.92 1.15 Week 0.90 1.05 0.95 1.17 4 4

Explanation / Answer

Solution:

Mean Absolute Deviation (MAD) is computed using the formula;

MAD = Absolute difference of Actual and Forecasted demands / Total number of periods

Mean Squared Error (MSE) is computed using the formula;

MSE = Sum of [A(t) - F(t)]^2 / N

where,

A(t) = Actual demand for period t

F(t) = Forecasted demand for period t

N = Number of periods

1) MAD for Method 1

MAD for Method 1 = Absolute difference [(0.90 - 0.70) + (1.05 - 1.00) + (0.95 - 1.07) + (1.17 - 1.04)] / 4

MAD for Method 1 = (0.20 + 0.05 + 0.12 + 0.13) / 4

MAD for Method 1 = 0.125 thousand gallons

2) MSE for Method 1

MSE for Method 1 = [(0.90 - 0.70)^2 + (1.05 - 1.00)^2 + (0.95 - 1.07)^2 + (1.17 - 1.04)^2] / 4

MSE for Method 1 = (0.04 + 0.0025 + 0.0144 + 0.0169) / 4

MSE for Method 1 = 0.0185 thousand gallons squared

3) MAD for Method 2

MAD for Method 2 = Absolute difference [(0.80 - 0.70) + (1.20 - 1.00) + (0.92 - 1.07) + (1.15 - 1.04)] / 4

MAD for Method 2 = (0.10 + 0.20 + 0.15 + 0.11) / 4

MAD for Method 2 = 0.140 thousand gallons

4) MSE for Method 2

MSE for Method 2 = [(0.80 - 0.70)^2 + (1.20 - 1.00)^2 + (0.92 - 1.07)^2 + (1.15 - 1.04)^2] / 4

MSE for Method 2 = (0.01 + 0.04 + 0.0225 + 0.0121) / 4

MSE for Method 2 = 0.0212 thousand gallons squared

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