Final answer:
To forecast mileage for an ambulance, a 2-year moving average, weighted moving average, and exponential smoothing are used. The 2-year moving average and weighted averages both predict 3,800 miles for year 6. The MAD is 0 miles because the forecasts equal the actual mileage. Exponential smoothing requires iterative calculations with an alpha of 0.50.
Step-by-step explanation:
The question relates to forecasting future mileage for an ambulance based on historical data using different statistical techniques, such as moving averages, weighted moving averages, and exponential smoothing. Here is how each part of the question can be addressed:
- a) To forecast year 6 using a 2-year moving average, we take the average mileage of the last two years (years 4 and 5). (3,800 + 3,800) / 2 = 3,800 miles (no calculation necessary as both years are the same).
- b) To find the MAD (Mean Absolute Deviation), we would compare each two-year average forecast against the actual mileage for the following year. However, since the forecast is always equal to the actual mileage, the MAD is 0 miles.
- c) For a weighted 2-year moving average with weights of 0.40 and 0.60 for the 5th and 4th year respectively: (0.40 * 3,800) + (0.60 * 3,800) = 3,800 miles. Again, as both years have the same mileage, weighting does not change the forecast.
- d) Using exponential smoothing with α (alpha) = 0.50 and a starting forecast of 3,000 miles for year 1, the forecast for each year is calculated using the formula Ft+1 = α * At + (1 - α) * Ft, where Ft+1 is the forecast for the next period, At is the actual value of the current period, and Ft is the forecast for the current period. Applying this formula iteratively for each year, the forecast for year 6 can be calculated (this requires step-by-step calculation).
These calculations require an understanding of time series analysis and forecasting methods.