(YOU MUST SHOW ALL OF YOUR WORK) Sam Houston is considering the purchase of new

Question

(YOU MUST SHOW ALL OF YOUR WORK)

Sam Houston is considering the purchase of new utility vehicles. The decision will rest partly on the anticipated mileage to be driven by each vehicle next year. The miles driven during the past five years are as follows:

Year

Mileage

1

4,500

2

5,000

3

5,500

4

5,800

5

5,700

6

5,300

7

5,900

                       

Forecast the mileage for the 8th year using a 2-year moving average

Find the MAD and MAPE based on the 2 year moving average (Hint: You will have only 5 years of matched data).

Compute the forecast for years 2 through 8 using exponential smoothing, an initial forecast for year one of 4000 miles, and alpha = .1 and alpha of .5    Which alpha predicts the best forecast?

Year

Mileage

1

4,500

2

5,000

3

5,500

4

5,800

5

5,700

6

5,300

7

5,900

Explanation / Answer

MAD = absolute deviation / no of years assessed

APE = Absolute error value / Actual value x100

MAPE = mean of all APEs

Part II

In exponential smoothening

Ft+1 = Ft + alpha (At -Ft)

With alpha = 0.1 we get

F2 = 4000+0.1 x( 500) = 4050

F3 = 4050 + 0.1( 950) = 4145

F4 = 4145 + 0.1( 1355) = 4280.5

F5  = 4280 + 0.1 ( 1520) = 4432

F6 = 4432+0.1 (1268) = 4459

F7 = 4459+0.1 ( 741.2) = 4533

F8 = 4533+ 0.1 ( 1367) = 4669

With alpha = 0.5

F2 = 4000+0.5x500 = 4250

F3 = 4250 + 0.5 x750 = 4625

F4 = 4625+ 0.5 x( 875) =5062.5

f5 = 5062.5 + 0.5 x737.5 = 5431

F6 = 5431 + 0.5x 269 = 5565.5

F7 = 5565.5 -0.5 x265 = 5432.75

F8 = 5432.75 + 0.5 x467 = 5666

The alpha value of 0.5 has better predictions.

Year Mileage MA Abs. Error MAD APE MAPE 1 4500 2 5000 3 5500 4750 750 13.63 4 5800 5250 550 9.48 5 5700 5650 50 440 0.877 7.84 6 5300 5750 450 8.49 7 5900 5500 400 6.77 8 5600

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.