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 18
2 22
3 18
4 24
5 19
6 16
7 21
8 19
9 22
10 19
11 16
12 23
  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 18
    2 22
    3 18
    4 24
    5 19
    6 16
    7 21
    8 19
    9 22
    10 19
    11 16
    12 23
  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 10.42.

Solutions

Expert Solution

a) Four Week moving average:

Week Sales Four week moving Average Error Error²
1 18 - - - -
2 22 - - - -
3 18 - - - -
4 24 - - - -
5 19 (18+22+18+24)/4 = 20.500 -1.500 2.250
6 16 (22+18+24+19)/4 = 20.750 -4.750 22.563
7 21 (18+24+19+16)/4 = 19.250 1.750 3.063
8 19 (24+19+16+21)/4 = 20.000 -1.000 1.000
9 22 (19+16+21+19)/4 = 18.750 3.250 10.563
10 19 (16+21+19+22)/4 = 19.500 -0.500 0.250
11 16 (21+19+22+19)/4 = 20.250 -4.250 18.063
12 23 (19+22+19+16)/4 = 19.000 4.000 16.000
Total -3.000 73.750

Five Week moving Average :

Month Sales Five week moving Average Error Error²
1 18 - - - -
2 22 - - - -
3 18 - - - -
4 24 - - - -
5 19 - - - -
6 16 (18+22+18+24+19)/5 = 20.200 -4.200 17.640
7 21 (22+18+24+19+16)/5 = 19.800 1.200 1.440
8 19 (18+24+19+16+21)/5 = 19.600 -0.600 0.360
9 22 (24+19+16+21+19)/5 = 19.800 2.200 4.840
10 19 (19+16+21+19+22)/5 = 19.400 -0.400 0.160
11 16 (16+21+19+22+19)/5 = 19.400 -3.400 11.560
12 23 (21+19+22+19+16)/5 = 19.400 3.600 12.960
Total -1.600 48.960

b)

MSE for four week moving average = ∑(A-F)²/n = 73.75/8 = 9.22

MSE for four week moving average = ∑(A-F)²/n = 48.96/7 = 6.99

c)

5 week moving average is the best.


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