AmeriPlas, Inc., produces 20-ounce plastic drinking cups that are embossed with the names of prominent beers and soft drinks. The sales data are:
|
Date |
Sales |
|
Jan-13 |
40,358 |
|
Feb-13 |
45,002 |
|
Mar-13 |
63,165 |
|
Apr-13 |
57,479 |
|
May-13 |
52,308 |
|
Jun-13 |
60,062 |
|
Jul-13 |
51,694 |
|
Aug-13 |
54,469 |
|
Sep-13 |
48,284 |
|
Oct-13 |
45,239 |
|
Nov-13 |
40,665 |
|
Dec-13 |
47,968 |
|
Jan-14 |
37,255 |
|
Feb-14 |
38,521 |
|
Mar-14 |
55,110 |
|
Apr-14 |
51,389 |
|
May-14 |
58,068 |
|
Jun-14 |
64,028 |
|
Jul-14 |
52,873 |
|
Aug-14 |
62,584 |
|
Sep-14 |
53,373 |
|
Oct-14 |
52,060 |
|
Nov-14 |
51,727 |
|
Dec-14 |
51,455 |
|
Jan-15 |
47,906 |
|
Feb-15 |
53,570 |
|
Mar-15 |
69,189 |
|
Apr-15 |
64,346 |
|
May-15 |
77,267 |
|
Jun-15 |
75,787 |
|
Jul-15 |
74,052 |
|
Aug-15 |
79,756 |
|
Sep-15 |
73,292 |
|
Oct-15 |
77,207 |
|
Nov-15 |
68,423 |
|
Dec-15 |
67,274 |
|
Jan-16 |
65,711 |
|
Feb-16 |
68,005 |
|
Mar-16 |
78,029 |
|
Apr-16 |
92,764 |
|
May-16 |
97,175 |
|
Jun-16 |
86,255 |
|
Jul-16 |
90,496 |
|
Aug-16 |
87,602 |
|
Sep-16 |
83,577 |
|
Oct-16 |
92,610 |
|
Nov-16 |
73,949 |
|
Dec-16 |
77,711 |
a. Prepare a time-series plot of the sales data. Does there appear to be a regular pattern of movement in the data that may be seasonal? Ronnie Mills, the product manager for this product line, believes that her brief review of sales data for the four-year period indicates that sales are slowest in November, December, January, and February than in other months. Do you agree?
b. Since production is closely related to orders for current shipment, Ronnie would like to have a monthly sales forecast that incorporates monthly fluctuations. She has asked you to develop a trend model that includes a time index and dummy variables for all but the above mentioned four months. Do these results support Ronnie’s observations? Explain.
c. Ronnie believes that there has been some increase in the rate of sales growth. To test this and to include such a possibility in the forecasting effort, she has asked that you add the square of the time index (T) to your model (call this new term T2). Is there any evidence of increasing of sales growth? Compare the results of this model with those found in part (b).
d. Use the model in part (c) to forecast sales for 2017. Calculate the mean absolute percentage error (MAPE) for the first six months of 2017. Actual sales for those six months were as shown below:
