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):
Mid-Month of Quarter
Year Feb May Aug Nov Yearly Totals
2004 3.5 2.9 2.0 3.2 11.6
2005 4.1 3.4 2.9 3.6 14.0
2006 5.2 4.5 3.1 4.5 17.3
2007 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 1 through 4.
b. Determine the seasonal index for each quarter.
c. Do the best you can to project the cycle factor through 2008.
d. Make a forecast for each quarter of 2008.
e. The actual numbers of customers served per quarter in 2008 were 6.8, 5.1, 4.7, and 6.5 for quarters 1 through 4, respectively (numbers are in hundreds). Calculate the RMSE for 2008.
f. 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 2004 through 2008 (where data are available).