# For 2008–2014, a company has collected the following data on quarterly sales of its product

November 24, 2016
• For 2008–2014, a company has collected the following data on quarterly sales of its product. (3 pts each)

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+ c2D2+ c3D3

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?

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