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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