Question

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 1 2 3 4 5 Mileage 3 comma 100 4 comma 050 3 comma 450 3 comma 750 3 comma 800 ​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​ = 108.3 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 0.40 and 0.60 ​(the weight of 0.60 is for the most recent​ period) = nothing miles ​(round your response to the nearest whole​ number).

Answer 1

Answer:

a. Year 6 Forecast = 3,775

b. Mean Absolute Deviation (MAD) = 108.3

c. Year 6 Forecast = 3,780

Explanation:

Given

The miles driven during the past 5 years are as​ follows

Year 1 -- 3,100

Year 2 --- 4,050

Year 3 --- 3,450

Year 4 ---- 3,750

Year 5 --- 3,800

a. The forecast for year 6 is calculated as follows;

Using a 2 year moving average

Forecast = ½(Year 4 + Year 5)

Forecast = ½(3750 + 3800)

Forecast = ½ * 7550

Forecast = 3,775

b. Calculating the Mean Absolute Deviation (MAD), if two years moving average is used.

------------------------------2 year difference ----- Difference

Year 1 -- 3,100 ------------------------------------------

Year 2 --- 4,050 -----------------------------------------

Year 3 --- 3,450 ---- 3,575 -------- 125

Year 4 ---- 3,750 ---- 3,750 ------ 0

Year 5 --- 3,800 ----- 3,600 ------ 200

The 2-year difference column is calculated using.

Summation of previous 2 years forecast * ½

Year 1 and 2 are empty because they don't have previous 2 years.

For year 3;

2 year difference = ½ (year 1 + year 2)

= ½(3,100 + 4,050)

= ½ (7,150)

= 3,575

For year 4

2 year difference = ½ (year 2 + year 3)

= ½(4,050 + 3,750)

= ½ (7,500)

= 3,750

For year 5:

2 year difference = ½ (year 3 + year 4)

= ½(3,750 + 3,450)

= ½ (7,200)

= 3,600

Mean Absolute Deviation (MAD) = (Summation of Difference)/3

Mean Absolute Deviation (MAD) = (125 + 0 + 200)

Mean Absolute Deviation (MAD) = 325/3

Mean Absolute Deviation (MAD) = 108.3

c. for year 6 using a weighted​ 2-year moving average with weights of 0.40 and 0.60

For year 5:

Forecast = 0.4 * year 4 + 0.6 * year 5

= 0.4(3,750) + 0.6(3,800)

= 3,780