Complete the following problems starting on p. 230: 26 and 27.
1. Your work should include, at a minimum, the below items:
2. Worked out solutions, including any computer generated solutions.
3. The answer clearly labeled at the end of the problem.
4. As much narrative as needed to back up your solutions.
Problem 26 & 27 are located below:
WEBFILE: Textbook Sales.
26.The quarterly sales data (number of copies sold) for a college textbook over the past three years follow.
Quarter
Year 1
Year 2
Year 3
1
1690
1800
1850
2
940
900
1100
3
2626
2900
2930
4
2500
2360
2615
a.Construct a time series plot. What type of pattern 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.
Qtr1 5 1 if Quarter 1, 0 otherwise; Qtr2 5 1 if Quarter 2, 0 otherwise; Qtr3 5 1 if Quarter 3, 0 otherwise.
c. Compute the quarterly forecasts for next year.
d. let t 5 1 to refer to the observation in quarter 1 of year 1; t 5 2 to refer to the observation in quarter 2 of year 1; . . . ; and t 5 12 to refer to the observation in quarter 4 of year 3. using the dummy variables defined in part (b) and also using t, develop an equation to account for seasonal effects and any linear trend in the time series. Based upon the seasonal effects in the data and linear trend, compute the quarterly forecasts for next year.
27. Air pollution control specialists in southern California monitor the amount of ozone, car- bon dioxide, and nitrogen dioxide in the air on an hourly basis. The hourly time series data exhibit seasonality, with the levels of pollutants showing patterns that vary over the hours in the day. on July 15, 16, and 17, the following levels of nitrogen dioxide were observed for the 12 hours from 6:00 a.m. to 6:00 p.m.
WEBFILE: Pollution.
July 15: 25 28 35 50 60 60 40 35 30 25 25 20
July 16: 28 30 35 48 60 65 50 40 35 25 20 20
July 17: 35 42 45 70 72 75 60 45 40 25 25 25
a.Construct a time series plot. What type of pattern exists in the data?
b. Use a multiple linear regression model with dummy variables as follows to develop
an equation to account for seasonal effects in the data:
Hour 1 = 1 if the reading was made between 6:00 a.m. and 7:00 a.m.; 0 otherwise
Hour 2 =1 if the reading was made between 7:00 a.m. and 8:00 a.m.; 0 otherwise .
Hour 11 = 1 if the reading was made between 4:00 p.m. and 5:00 p.m.; 0 otherwise
(note that when the values of the 11 dummy variables are equal to 0, the observation
corresponds to the 5:00 p.m. to 6:00 p.m. hour).
c. Using the equation developed in part (b), compute estimates of the levels of nitrogen dioxide for July 18.
d. let t = 1 to refer to the observation in hour 1 on July 15; t 5 2 to refer to the obser-
vation in hour 2 of July 15; . . . ; and t 5 36 to refer to the observation in hour 12 of July 17. using the dummy variables defined in part (b) and t, develop an equation to account for seasonal effects and any linear trend in the time series. Based upon the seasonal effects in the data and linear trend, compute estimates of the levels of nitrogen dioxide for July 18.
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