Air pollution control specialists in southern California monitor the amount of ozone, carbon 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.
Use a multiple linear regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data:
Hour1 = 1 if the reading was made between 6:00 A. M. and 7:00A. M.; 0 otherwise
Hour2 = 1 if the reading was made between 7:00 A. M. and 8:00 A. M.; 0 otherwise
Hour11 = 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.
If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
Value=21.7 +7.67 hour1+11.7 hour2+16.7 hour3+34.3 hour4+42.3 hour5+45.0 hour6+28.3 hour7+18.3 hour8+13.3 hour9+3.33 hour10+1.67 hour11
6:00 a. m. - 7:00 a. m. forecast
29.31
7:00 a. m. - 8:00 a. m. forecast
33.4
8:00 a. m. - 9:00 a. m. forecast
38.4
9:00 a. m. - 10:00 a. m. forecast
56
10:00 a. m. - 11:00 a. m. forecast
64
11:00 a. m. - noon forecast
66.7
noon - 1:00 p. m. forecast
50
1:00 p. m. - 2:00 p. m. forecast
40
2:00 p. m. - 3:00 p. m. forecast
35
3:00 p. m. - 4:00 p. m. forecast
25.03
4:00 p. m. - 5:00 p. m. forecast
23.37
5:00 p. m. - 6:00 p. m. forecast
21.7
Let t = 1 to refer to the observation in hour 1 on July 15; t = 2 to refer to the observation in hour 2 of July 15; ...; and t = 36 to refer to the observation in hour 12 of July 17. Using the dummy variables defined in part (b) and ts, develop an equation to account for seasonal effects and any linear trend in the time series.
If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
Value=11.2 +12.5 hour1+16.0 hour2+20.06 hour3+37.8 hour4+45.4 hour5+47.6 hour6+30.5 hour7+20.1 hour8+14.6 hour9+4.21 hour10+2.10 hour11+0.437 t
Based upon the seasonal effects in the data and linear trend estimated in part (d), compute estimates of the levels of nitrogen dioxide for July 18.
6:00 a. m. - 7:00 a. m. forecast
40
7:00 a. m. - 8:00 a. m. forecast
44
8:00 a. m. - 9:00 a. m. forecast
49
9:00 a. m. - 10:00 a. m. forecast
66
10:00 a. m. - 11:00 a. m. forecast
75
11:00 a. m. - noon forecast
77
noon - 1:00 p. m. forecast
60
1:00 p. m. - 2:00 p. m. forecast
51
2:00 p. m. - 3:00 p. m. forecast
45
3:00 p. m. - 4:00 p. m. forecast
36
4:00 p. m. - 5:00 p. m. forecast
34
5:00 p. m. - 6:00 p. m. forecast
32
This is the part I cant figure out, please help me find the MSE's
Is this model you developed in part (b) or the model you developed in part (d) more effective?
Model developed in part (b)
Model developed in part (d)
MSE
Answers: 2
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