For 2008-2014, a company has collected the following data on quarterly sales of its product.
|
Year
|
Quarter
|
t
|
Sales (000)
|
|
2008
|
q1
|
1
|
1135
|
|
|
q2
|
2
|
900
|
|
|
q3
|
3
|
1005
|
|
|
q4
|
4
|
1025
|
|
2009
|
q1
|
5
|
1220
|
|
|
q2
|
6
|
950
|
|
|
q3
|
7
|
870
|
|
|
q4
|
8
|
1098
|
|
2010
|
q1
|
9
|
1205
|
|
|
q2
|
10
|
1025
|
|
|
q3
|
11
|
1050
|
|
|
q4
|
12
|
1300
|
|
2011
|
q1
|
13
|
1315
|
|
|
q2
|
14
|
1050
|
|
|
q3
|
15
|
1152
|
|
|
q4
|
16
|
1150
|
|
2012
|
q1
|
17
|
1155
|
|
|
q2
|
18
|
1075
|
|
|
q3
|
19
|
1190
|
|
|
q4
|
20
|
1316
|
|
2013
|
q1
|
21
|
1350
|
|
|
q2
|
22
|
1205
|
|
|
q3
|
23
|
1280
|
|
|
q4
|
24
|
1300
|
|
2014
|
q1
|
25
|
1450
|
|
|
q2
|
26
|
1250
|
|
|
q3
|
27
|
1225
|
|
|
q4
|
28
|
1340
|
a. The manager would like to know if there is an upward trend in sales of the product. Use the data above to estimate the quarterly trend in sales using a linear trend model of the form:
Qt = a + bt.
Where Qt = quarterly sales
(paste your computer printout here)
b. Does your statistical analysis indicate a trend? If so, is it an upward or downward trend and how great is it? Is it a statistically significant trend (use the 5 percent level of significance )?
c. Now adjust your statistical model to account for seasonal variation in sales. Estimate the following model of sales:
Qt= a + bt+ c1D1+ c2 D2+ c3 D3
WhereD1, D2andD3 are respectively dummy variables for quarters I, II, and III (e.g., D1 is equal to 1 in the first quarter of each year and 0 in other quarters).
(paste your computer printout here)
d. Does the data indicate a statistically significantseasonal pattern (use the 5 percent level of significance)? If so, what is theseasonal pattern of sales of the product?
e. Comparing your estimates of the trend in sales in parts a and c, which estimate is likely to be more accurate? Why?
f. Using the estimated forecast equation from part c, forecast sales for quarter 1, 2, 3 and 4 of 2015; quarter 1, 2, 3, and 4 of quarter 16, and quarter 1 of 2017. What possible concerns do you have about these forecasts?