A statistical program is recommended. A company that sells musical instruments has been in business for five years. During that time, sales of pianos increased
A statistical program is recommended.
A company that sells musical instruments has been in business for five years. During that time, sales of pianos increased from 12 units in the first year to 76 units in the most recent year. The firm's owner wants to develop a forecast of piano sales for the coming year. The quarterly sales data follow.
| Year | Quarter 1 | Quarter 2 | Quarter 3 | Quarter 4 | Total Yearly Sales |
|---|---|---|---|---|---|
| 1 | 4 | 2 | 1 | 5 | 12 |
| 2 | 6 | 4 | 4 | 14 | 28 |
| 3 | 10 | 3 | 5 | 16 | 34 |
| 4 | 13 | 9 | 7 | 22 | 51 |
| 5 | 18 | 10 | 13 | 35 | 76 |
(a)Deseasonalize the data. (Round your answers to four decimal places.)
| Year | Quarter | Sales | Adjusted Seasonal Index | Deseasonalized Sales |
|---|---|---|---|---|
| 1 | 1 | 4 | 1.2888 | |
| 2 | 2 | 0.6081 | ||
| 3 | 1 | 0.4946 | ||
| 4 | 5 | 1.6084 | ||
| 2 | 1 | 6 | 1.2888 | |
| 2 | 4 | 0.6081 | ||
| 3 | 4 | 0.4946 | ||
| 4 | 14 | 1.6084 | ||
| 3 | 1 | 10 | 1.2888 | |
| 2 | 3 | 0.6081 | ||
| 3 | 5 | 0.4946 | ||
| 4 | 16 | 1.6084 | ||
| 4 | 1 | 13 | 1.2888 | |
| 2 | 9 | 0.6081 | ||
| 3 | 7 | 0.4946 | ||
| 4 | 22 | 1.6084 | ||
| 5 | 1 | 18 | 1.2888 | |
| 2 | 10 | 0.6081 | ||
| 3 | 13 | 0.4946 | ||
| 4 | 35 | 1.6084 |
Use the deseasonalized time series to identify the trend. (Let
t = 1 denote the time series value in quarter 1 of year 1; t = 2 denote the time series value in quarter 2 of year 1; and t = 20 denote the time series value in quarter 4 of year 5. Round your numerical values to two decimal places.)
Tt =
(b)Use the results of part (a) to develop a quarterly forecast for next year based on trend. (Round your answers to two decimal places.)
forecast for quarter 1.....?
forecast for quarter 2.......?
forecast for quarter 3.......?
forecast for quarter 4........?
(c)Use the adjusted seasonal indexes given in part (a) to adjust the forecasts developed in part (b) to account for the effect of season. (Round your answers to one decimal place.)
forecast for quarter 1 is..........?
forecast for quarter 2 is.......?
forecast for quarter 3 is.......?
forecast for quarter 4 is....?
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Authors: Michael Sullivan
10th Edition
0134178785, 9780134178783
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