re storé lll h, 20; April, th moving July forecast model compare w found in prob
ID: 354058 • Letter: R
Question
re storé lll h, 20; April, th moving July forecast model compare w found in problem 4? le Dest nverage mo ode 6.* A restaurant wants to forecast its weekl y sales Historical data (in dollars) for 15 weeks are sho below and can be found on worksheet OM6 Data Workbook at OM6 Online. (Not Vue copy the data from the worksheet to the appr Excel template.) a. Plot the data and provide insights about the ting C9P6 in the thing with oothing at Just Say series b. What is the forecast for week 16, using a two Sales c. What is the forecast for week 16, using a three. d. Compute MSE for the two- and three-period e. Find the best number of periods for the moving period moving average? period moving average? moving average models and compare your results average model based on MSE. Time Period Observation 1623 1533 1455 1386 1209 1348 ut the time ing a two- 4 ing a three- inExplanation / Answer
PLEASE FIND ANSWERS TO QUESTION 6 ( items b, c,d,e,)
Please find below table with calculated values for reference .
Following formula may be noted:
i)Basis 2 year moving average ,
Ft = ( at-1 + at-2 ) /2
Ft = Forecast for period t
at-1 = Observation for period t-1
at-2 = Observation for period t- 2
ii)Basis 3 year moving average ,
Ft = ( at-1 + at-2 + at-3 ) / 3
Ft = Forecast for period t
At-1, at-2, at-3 = Observations for period t-1, t-2 and t-3 respectively
iii)Squared error for period t ( SEt) = Square ( Ft – At)
Time period
Observation
Forecast ( 2 period moving average)
Squared error ( SE)
Forecast ( 3 period moving average)
Squared error ( SE)
1
1623
2
1533
3
1455
1578
15129
4
1386
1494
11664
1537
22801.00
5
1209
1420.5
44732.25
1458
62001.00
6
1348
1297.5
2550.25
1350
4.00
7
1581
1278.5
91506.25
1314.33
71111.11
8
1332
1464.5
17556.25
1379.33
2240.44
9
1245
1456.5
44732.25
1420.33
30741.78
10
1521
1288.5
54056.25
1386.00
18225.00
11
1421
1383
1444
1366.00
3025.00
12
1502
1471
961
1395.67
11306.78
13
1656
1461.5
37830.25
1481.33
30508.44
14
1614
1579
1225
1526.33
7685.44
15
1332
1635
91809
1590.67
66908.44
16
1473
1534.00
SUM =
415195.75
326558.44
Accordingly .
b)Forecast for week 16 using 2 period moving average = 1473
c)Forecast for week 16 using 3 period moving average = 1534
d)Sum of Squared errors basis 2 year moving average = 415195.75
Therefore, Mean square Error ( MSE ) basis 2 year moving average = 415195.75 / 13 i.e number of observations = 31938.13
Sum of squared error basis 3 year moving average = 326558.44
Therefore ,
Mean Square error ( MSE ) basis 3 year moving average = 326558.44 / 12i.e. number of observations = 27213.20
e)Since MSE basis 3 year moving average ( i.e. 27213.20 ) < MSE basis 2 year moving average ( i.e. 31938.13) , the best number of periods for the moving average model is 3 years
Time period
Observation
Forecast ( 2 period moving average)
Squared error ( SE)
Forecast ( 3 period moving average)
Squared error ( SE)
1
1623
2
1533
3
1455
1578
15129
4
1386
1494
11664
1537
22801.00
5
1209
1420.5
44732.25
1458
62001.00
6
1348
1297.5
2550.25
1350
4.00
7
1581
1278.5
91506.25
1314.33
71111.11
8
1332
1464.5
17556.25
1379.33
2240.44
9
1245
1456.5
44732.25
1420.33
30741.78
10
1521
1288.5
54056.25
1386.00
18225.00
11
1421
1383
1444
1366.00
3025.00
12
1502
1471
961
1395.67
11306.78
13
1656
1461.5
37830.25
1481.33
30508.44
14
1614
1579
1225
1526.33
7685.44
15
1332
1635
91809
1590.67
66908.44
16
1473
1534.00
SUM =
415195.75
326558.44
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