Question

Chapter 9, Problem 6 please walk through the steps. My subject is (Organizational Management)

A restaurant wants to forecast its weekly sales. Historical data (in dollars) for 15 weeks are shown below and can be found on worksheet C9P6 in the OM6 Data Workbook at OM6 Online. (Note: You may copy the data from the worksheet to the appropriate Excel template.)
a.   Plot the data and provide insights about the time series.
b.   What is the forecast for week 16, using a two- period moving average?
c.   What is the forecast for week 16, using a three- period moving average?
d.   Compute MSE for the two- and three-period moving average models and compare your results.
e.   Find the best number of periods for the moving average model based on MSE.

Time period is in weeks
Time period	Observation
1	1623
2	1533
3	1455
4	1386
5	1209
6	1348
7	1581
8	1332
9	1245
10	1521
11	1421
12	1502
13	1656
14	1614
15	1332

Answer 1

Time period	Observation
1	1623
2	1533
3	1455
4	1386
5	1209
6	1348
7	1581
8	1332
9	1245
10	1521
11	1421
12	1502
13	1656
14	1614
15	1332

The Observations are not following any trend or seasonality.

b)

Forecast for week 16 using a two- period moving average = (Observation of period 14+ Observation of period 15) / 2 = (1614+1332)/2 = 1473.0

c)

Forecast for week 16 using a three- period moving average = (Observation of period 13+Observation of period 14+ Observation of period 15) / 3 = (1656+1614+1332)/3 = 1534.0

d) MSE (Mean Square Error) = Average of all Error2

Average of all Error2 of Period 3 through 15 will be considered as it will be available for both 2 period and 3 period moving average.

e) The best number of periods for the moving average model based on MSE is forecast using 3 period moving averages as its MSE (27213.2) is lower than MSE of 2 period moving averages (33338.9).