Statistics: Hypothesis Testing – #29507


Question: The quarterly sales data in number of copies sold for a college textbook over the past three years is as follows:

Quarter Year 1 Year 2 Year 3
1 1690 1800 1850
2 940 900 1100
3 2625 2900 2390
4 2500 2360 2615

a. Construct a time series plot. What type of patterns exists in the data?

b. Use a regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data. Qtr 1 = 1 if Quarter 1; 0 otherwise, Qtr 2 = 1 if Quarter 2, 0 otherwise; Qtr 3 = 1 if Quarter 3, 0 otherwise; Qtr 4 = 1 if Quarter 4, 0 otherwise.

c. Compute the quarterly forecasts for the next year.

d. Let t=1 to refer to the observations in quarter 1 of year 1; t=2 to refer to the observation in quarter 2 of year 1; …; and t=12 to refer to the observations in quarter 4 or year 3 (see table below). Using the dummy variables defined in part (b) above, and also using t, develop a regression equation to account for seasonal effects and any linear trend in the time series. Based upon the seasonal effects in the data and the linear trend, compute the quarterly forecasts for the next year (Year 4).

Year Quarter t Textbook Sales
1 Quarter 1 1 1690
1 Quarter 2 2 940
1 Quarter 3 3 2625
1 Quarter 4 4 2500
2 Quarter 1 5 1800
2 Quarter 2 6 900
2 Quarter 3 7 2900
2 Quarter 4 8 2360
3 Quarter 1 9 1850
3 Quarter 2 10 1100
3 Quarter 3 11 2930
3 Quarter 4 12 2615

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