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 |
- Compute four-week and five-week moving averages for the time
series. Round your answers to two decimal places.
Week
Sales4-Week
Moving Average5-Week
Moving Average1 18 2 22 3 18 4 24 5 19 6 16 7 21 8 19 9 22 10 19 11 16 12 23 - 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 = - 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.
orchestra answered 3 years agoRelated Solutions
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
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...
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
19
6
15
7
21
8
19
9
21
10
19
11
15
12
23
Compute four-week and five-week moving averages for the time
series. If required, round your answers to two decimal
places.
Week
Sales
4 Period
Moving Average
5 Period
Moving Average
1
17
2
20
3
18
4
22
5
19...
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
22
3
19
4
23
5
19
6
16
7
21
8
18
9
22
10
21
11
14
12
22
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
22
3
19
4
23
5
19
6
16
7
21...
Refer to the gasoline sales time series data in the given table. Week Sales (1,000s of...
Refer to the gasoline sales time series data in the given
table.
Week
Sales (1,000s of gallons)
1
18
2
22
3
15
4
24
5
18
6
15
7
21
8
19
9
21
10
20
11
16
12
22
Compute four-week and five-week moving averages for the time
series.
If required, round your answers to two decimal places.
Week
Sales
4 Period
Moving Average
5 period
Moving Average
1
18
2
22
3
15
4
24
5
18...
Refer to the gasoline sales time series data in the given table. Week Sales (1,000s of...
Refer to the gasoline sales time series data in the given
table.
Week
Sales (1,000s of gallons)
1
18
2
22
3
15
4
24
5
18
6
15
7
21
8
19
9
21
10
20
11
16
12
22
(a)
Compute four-week and five-week moving averages for the time
series.
If required, round your answers to two decimal places.
Week
Sales
4 Period
Moving Average
5 period
Moving Average
1
18
2
22
3
15
4
24
5...
Refer to the gasoline sales time series data in the given table. Week Sales (1,000s of...
Refer to the gasoline sales time series data in the given
table.
Week
Sales (1,000s of gallons)
1
17
2
21
3
19
4
23
5
18
6
16
7
20
8
18
9
22
10
20
11
15
12
22
(a)
Compute four-week and five-week moving averages for the time
series.
If required, round your answers to two decimal places.
Week
Sales
4 Period
Moving Average
5 period
Moving Average
1
17
2
21
3
19
4
23
5...
Refer to the gasoline sales time series data in the given table. Week Sales (1,000s of...
Refer to the gasoline sales time series data in the given
table.
Week
Sales (1,000s of gallons)
1
17
2
23
3
14
4
25
5
17
6
16
7
22
8
19
9
21
10
19
11
17
12
23
(a)
Compute four-week and five-week moving averages for the time
series.
If required, round your answers to two decimal places.
Week
Sales
4 Period
Moving Average
5 period
Moving Average
1
17
2
23
3
14
4
25
5...
Refer to the gasoline sales time series data in the given table. Week Sales (1,000s of...
Refer to the gasoline sales time series data in the given
table.
Week
Sales (1,000s of gallons)
1
17
2
21
3
16
4
24
5
17
6
18
7
22
8
20
9
21
10
19
11
16
12
25
(a)
Compute four-week and five-week moving averages for the time
series.
If required, round your answers to two decimal places.
Week
Sales
4 Period
Moving Average
5 period
Moving Average
1
17
2
21
3
16
4
24
5...
Refer to the gasoline sales time series data in the given table. Week Sales (1,000s of...
Refer to the gasoline sales time series data in the given
table.
Week
Sales (1,000s of gallons)
1
16
2
22
3
17
4
23
5
15
6
17
7
21
8
19
9
20
10
18
11
15
12
23
(a)
Compute four-week and five-week moving averages for the time
series.
If required, round your answers to two decimal places.
Week
Sales
4 Period
Moving Average
5 period
Moving Average
1
16
2
22
3
17
4
23
5...
Refer to the gasoline sales time series data in the given table. Week Sales (1,000s of...
Refer to the gasoline sales time series data in the given
table.
Week
Sales (1,000s of gallons)
1
17
2
21
3
19
4
23
5
18
6
16
7
20
8
18
9
22
10
20
11
15
12
22
(a)
Compute four-week and five-week moving averages for the time
series.
If required, round your answers to two decimal places.
Week
Sales
4 Period
Moving Average
5 period
Moving Average
1
17
2
21
3
19
4
23
5...
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