Question

In: Statistics and Probability

Refer to the gasoline sales time series data in the given table. Week Sales (1000s of...

Refer to the gasoline sales time series data in the given table.

Week Sales (1000s of gallons)
1 17
2 20
3 18
4 22
5 17
6 16
7 22
8 17
9 23
10 21
11 14
12 22
  1. Compute four-week and five-week moving averages for the time series. Round your answers to two decimal places.

    Week

    Sales
    4-Week
    Moving Average
    5-Week
    Moving Average
    1 17
    2 20
    3 18
    4 22
    5 17
    6 16
    7 22
    8 17
    9 23
    10 21
    11 14
    12 22
  2. Compute the MSE for the four-week and five-week moving average forecasts. Round your intermediate calculations and final answers to two decimal places.

    MSE for four-week moving average =

    MSE for five-week moving average =
  3. What appears to be the best number of weeks of past data (three, four, or five) to use in the moving average computation? Recall that MSE for the three-week moving average is 12.87.

Solutions

Expert Solution

a) Fromt the givend ata

Week Sales 4 Week Moving Aveages 5 Week Moving Averages
1 17
2 20
3 18
4 22
5 17 19.25
6 16 19.25 18.80
7 22 18.25 18.60
8 17 19.25 19.00
9 23 18.00 18.80
10 21 19.50 19.00
11 14 20.75 19.80
12 22 18.75 19.40

b) MSE for 4 Week moving averages:

Week Sales 4 Week Moving Aveages Absolute Error Error^2
1 17
2 20
3 18
4 22
5 17 19.25 2.25 5.0625
6 16 19.25 3.25 10.5625
7 22 18.25 3.75 14.0625
8 17 19.25 2.25 5.0625
9 23 18 5 25
10 21 19.5 1.5 2.25
11 14 20.75 6.75 45.5625
12 22 18.75 3.25 10.5625
Total: 28 118.125

MSE of 4 Week moving average is 118.125/8 = 14.7656

and

MSE for 5 Week moving averages:

Week Sales 5 Week Moving Aveages Absolute Error Error^2
1 17
2 20
3 18
4 22
5 17
6 16 18.80 2.8 7.84
7 22 18.60 3.4 11.56
8 17 19.00 2 4
9 23 18.80 4.2 17.64
10 21 19.00 2 4
11 14 19.80 5.8 33.64
12 22 19.40 2.6 6.76
Total: 22.8 85.44

MSE of 5 Week moving average is 85.44/7 = 12.2057

c) since MSE of 5 week moving average is smaller than that of 4 week moving average and also 3 week moving average (12.87)

Therefoore, 5 Week moving average is best method to predict the future value for this given data


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