A tanning parlor located in a major shopping center near a large New England city has the following history of customers over the last four years (data are in hundreds of customers and months are the midmonth of each quarter):
|
Year |
Feb |
May |
Aug |
Nov |
Yearly Totals |
|
2012 |
3.5 |
2.9 |
2.0 |
3.2 |
11.6 |
|
2013 |
4.1 |
3.4 |
2.9 |
3.6 |
14.0 |
|
2014 |
5.2 |
4.5 |
3.1 |
4.5 |
17.3 |
|
2015 |
6.1 |
5.0 |
4.4 |
6.0 |
21.5 |
a. Construct a table in which you show the actual data (given in the table), the centered moving average, the centered moving-average trend, the seasonal factors, and the cycle factors for every quarter for which they can be calculated in years 2012 through 2015.
b. Look at the seasonal index for each quarter as calculated in Forecast X™. Do they make sense to you? Explain why or why not.
c. Make a forecast of the number of customers for each quarter of 2016.
d. The actual numbers of customers served per quarter in 2016 were 6.8, 5.1, 4.7, and 6.5 for quarters 1 through 4, respectively (numbers are in hundreds). Calculate the MAPE for 2016.
e. Using the results provided in the tables produced by Forecast X™, prepare a time-series plot of the actual data, the centered moving averages, the long-term trend, and the values predicted by your model for 2012 through 2016 (where data are available).
