Problem 6-27 Air pollution control specialists in southern California monitor th
ID: 3204795 • Letter: P
Question
Problem 6-27 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.
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
Using the equation developed in part (b), compute estimates of the levels of nitrogen dioxide for July 18. If required, round your answers to three decimal places.
Explanation / Answer
Result:
Problem 6-27 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.
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
Use a multiple linear regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data:
Regression Analysis
R²
0.954
Adjusted R²
0.931
n
36
R
0.977
k
12
Std. Error
4.245
Dep. Var.
value
ANOVA table
Source
SS
df
MS
F
p-value
Regression
8,663.7222
12
721.9769
40.06
1.62E-12
Residual
414.5000
23
18.0217
Total
9,078.2222
35
Regression output
confidence interval
variables
coefficients
std. error
t (df=23)
p-value
95% lower
95% upper
Intercept
11.167
3.0018
3.720
.0011
4.9569
17.3764
hour1
7.667
3.4662
2.212
.0372
0.4963
14.8370
hour2
11.667
3.4662
3.366
.0027
4.4963
18.8370
hour3
16.667
3.4662
4.808
.0001
9.4963
23.8370
hour4
34.333
3.4662
9.905
9.15E-10
27.1630
41.5037
hour5
42.333
3.4662
12.213
1.55E-11
35.1630
49.5037
hour6
45.000
3.4662
12.983
4.52E-12
37.8296
52.1704
hour7
28.333
3.4662
8.174
2.96E-08
21.1630
35.5037
hour8
18.333
3.4662
5.289
2.28E-05
11.1630
25.5037
hour9
13.333
3.4662
3.847
.0008
6.1630
20.5037
hour10
3.333
3.4662
0.962
.3462
-3.8370
10.5037
hour11
1.667
3.4662
0.481
.6352
-5.5037
8.8370
t
5.250
0.8665
6.059
3.53E-06
3.4574
7.0426
Value =11.167 + 7.667 HOUR1 + 11.667HOUR2 + 16.667HOUR3 +
34.333HOUR4 + 42.333HOUR5 + 45.000HOUR6 + 28.333HOUR7 +
18.333HOUR8 + 13.333 HOUR9 + 3.333HOUR10 + 1.667 HOUR11 + 5.250 t
Using the equation developed in part (b), compute estimates of the levels of nitrogen dioxide for July 18. If required, round your answers to three decimal places.
Period
Forecast
6:00 a.m. 7:00 a.m.
39.833
7:00 a.m. 8:00 a.m.
43.833
8:00 a.m. 9:00 a.m.
48.833
9:00 a.m. 10:00 a.m.
66.500
10:00 a.m. 11:00 a.m.
74.500
11:00 a.m. noon
77.167
noon 1:00 p.m.
60.500
1:00 p.m. 2:00 p.m.
50.500
2:00 p.m. 3:00 p.m.
45.500
3:00 p.m. 4:00 p.m.
35.500
4:00 p.m. 5:00 p.m.
33.833
5:00 p.m. 6:00 p.m.
32.167
Predicted values for: value
95% Confidence Intervals
95% Prediction Intervals
hour1
hour2
hour3
hour4
hour5
hour6
hour7
hour8
hour9
hour10
hour11
t
Predicted
lower
upper
lower
upper
Leverage
1
0
0
0
0
0
0
0
0
0
0
4
39.833
33.624
46.043
29.078
50.589
0.500
0
1
0
0
0
0
0
0
0
0
0
4
43.833
37.624
50.043
33.078
54.589
0.500
0
0
1
0
0
0
0
0
0
0
0
4
48.833
42.624
55.043
38.078
59.589
0.500
0
0
0
1
0
0
0
0
0
0
0
4
66.500
60.290
72.710
55.744
77.256
0.500
0
0
0
0
1
0
0
0
0
0
0
4
74.500
68.290
80.710
63.744
85.256
0.500
0
0
0
0
0
1
0
0
0
0
0
4
77.167
70.957
83.376
66.411
87.922
0.500
0
0
0
0
0
0
1
0
0
0
0
4
60.500
54.290
66.710
49.744
71.256
0.500
0
0
0
0
0
0
0
1
0
0
0
4
50.500
44.290
56.710
39.744
61.256
0.500
0
0
0
0
0
0
0
0
1
0
0
4
45.500
39.290
51.710
34.744
56.256
0.500
0
0
0
0
0
0
0
0
0
1
0
4
35.500
29.290
41.710
24.744
46.256
0.500
0
0
0
0
0
0
0
0
0
0
1
4
33.833
27.624
40.043
23.078
44.589
0.500
0
0
0
0
0
0
0
0
0
0
0
4
32.167
25.957
38.376
21.411
42.922
0.500
Regression Analysis
R²
0.954
Adjusted R²
0.931
n
36
R
0.977
k
12
Std. Error
4.245
Dep. Var.
value
ANOVA table
Source
SS
df
MS
F
p-value
Regression
8,663.7222
12
721.9769
40.06
1.62E-12
Residual
414.5000
23
18.0217
Total
9,078.2222
35
Regression output
confidence interval
variables
coefficients
std. error
t (df=23)
p-value
95% lower
95% upper
Intercept
11.167
3.0018
3.720
.0011
4.9569
17.3764
hour1
7.667
3.4662
2.212
.0372
0.4963
14.8370
hour2
11.667
3.4662
3.366
.0027
4.4963
18.8370
hour3
16.667
3.4662
4.808
.0001
9.4963
23.8370
hour4
34.333
3.4662
9.905
9.15E-10
27.1630
41.5037
hour5
42.333
3.4662
12.213
1.55E-11
35.1630
49.5037
hour6
45.000
3.4662
12.983
4.52E-12
37.8296
52.1704
hour7
28.333
3.4662
8.174
2.96E-08
21.1630
35.5037
hour8
18.333
3.4662
5.289
2.28E-05
11.1630
25.5037
hour9
13.333
3.4662
3.847
.0008
6.1630
20.5037
hour10
3.333
3.4662
0.962
.3462
-3.8370
10.5037
hour11
1.667
3.4662
0.481
.6352
-5.5037
8.8370
t
5.250
0.8665
6.059
3.53E-06
3.4574
7.0426
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