Problem 15-08 (Algorithmic) Refer again to the gasoline sales time series data i
ID: 375258 • Letter: P
Question
Problem 15-08 (Algorithmic)
Refer again to the gasoline sales time series data in the following table.
23
Week Sales (1000s of gallons) 1 16 2 22 3 19 4 24 5 17 6 18 7 21 8 16 9 25 10 21 11 14 1223
a. Using a weight of 1/2 for the most recent observation, 1/3 for the second most recent, and 1/6 for third most recent, compute a three-week weighted moving average for the time series. Use rounded for two decimal places values for intermediate colculations Weighted Moving Average Forecast Forecast (Error)2 Week Sales Error 16 19 24 17 18 21 16 25 21 14 23 4 8 10 12 Total b. Compute the MSE for the weighted moving average in part a. Do you prefer this weighted moving average to the unweighted moving average? Remember that the MSE for the unweighted moving average is 10.22. Round your answer to two decimal places MSE =Explanation / Answer
Following table calculates Values of Forecast error and ( Error)^2
Forecast error = Sales – weighted moving average forecast
WEEK
SALES
Weighted moving average forecast
Forecast error
Error^2
1
16
2
22
3
19
4
24
18.50
5.50
30.25
5
17
21.33
-4.33
18.78
6
18
20.33
-2.33
5.44
7
21
20.67
0.33
0.11
8
16
18.00
-2.00
4.00
9
25
18.67
6.33
40.11
10
21
20.00
1.00
1.00
11
14
19.83
-5.83
34.03
12
23
21.83
1.17
1.36
TOTAL
135.08
MSE for weighted moving average = 135.08 / 9 ( i.e. number of observations) = 15.008 ( 15.01 rounded to 2 decimal places )
MSE = 15.01
Since MSE for unweighted moving average 10.22 < MSE for weighted moving average 15.01, MSE for unweighted moving average is preferable .
WEEK
SALES
Weighted moving average forecast
Forecast error
Error^2
1
16
2
22
3
19
4
24
18.50
5.50
30.25
5
17
21.33
-4.33
18.78
6
18
20.33
-2.33
5.44
7
21
20.67
0.33
0.11
8
16
18.00
-2.00
4.00
9
25
18.67
6.33
40.11
10
21
20.00
1.00
1.00
11
14
19.83
-5.83
34.03
12
23
21.83
1.17
1.36
TOTAL
135.08