Question

"The MAD for the forecast developed using a weighted​ 2-year moving average with weights of 0.45 and 0.55 = __ miles ​(round your response to one decimal​ place).  ​(Hint: You will have only 3 years of matched​ data.)"

Score: 0 of 1 pt 3 of 5 (1 complete) HW Score: 0%, 0 of 5 pts Problem 4.5 Question Help The Carbondale Hospital is considering the purchase of a new ambulance. The decision will rest partly on the anticipated mileage to be driven next year. The miles driven during the past 5 years are as follows: Year Mileage 1 3,100 2 3,950 3 3 ,500 4 3,850 5 3,700 a) Using a 2-year moving average, the forecast for year 6 = 3775 miles (round your response to the nearest whole number). b) If a 2-year moving average is used to make the forecast, the MAD based on this = 58.3 miles (round your response to one decimal place). (Hint: You will have only 3 years of matched data.) c) The forecast for year 6 using a weighted 2-year moving average with weights of 0.45 and 0.55 (the weight of 0.55 is for the most recent period) = 3768 miles (round your response to the nearest whole number). The MAD for the forecast developed using a weighted 2-year moving average with weights of 0.45 and 0.55 = ||| miles (round your response to one decimal place). (Hint: You will have only 3 years of matched data.)

Answer 1

In weighted moving average, we determine the forecast as the sum of product of weights and the previous actual mileage. As we have to calculate the MAD, we will have 3 years of matched data or data where both forecast and actual will be available. These would be year 3, 4 and 5.

Forecast for year 3 = 0.55*3950+0.45*3100 = 3567.5.

As actual mileage for year 3 is 3500, absolute error is |3500-3567.5| = 67.5

Forecast for year 4 = 0.55*3500+0.45*3950 = 3702.5

As actual mileage for year 4 is 3850, absolute error is |3850-3702.5| = 147.5

Forecast for year 5 = 0.55*3850+0.45*3500 = 3692.5

As actual mileage for year 5 is 3700, absolute error is |3700-3692.5| = 7.5

Sum of all absolute errors = 67.5+147.5+7.5 = 222.5

Hence MAD = 222.5/3 = 74.2