Air pollution control specialists in southern California monitor the amount of o
ID: 3229488 • Letter: A
Question
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.
d. 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 t, develop an estimated regression equation to account for seasonal effects and any linear trend in the time series (to 3 decimals if necessary).
The regression equation is:
Level = ______ + ______ Hour1 + ______ Hour2 + ______ Hour3 + ______ Hour4 + ______ Hour5 + ______ Hour6 + ______ Hour7 + ______ Hour8 + ______ Hour9 + ______ Hour10 + ______ Hour11 + ______ t
Explanation / Answer
Answer:
Regression Analysis
R²
0.954
Adjusted R²
0.931
n
36
R
0.977
k
12
Std. Error
4.245
Dep. Var.
data
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
H1
12.479
3.5560
3.509
.0019
5.1229
19.8354
H2
16.042
3.5406
4.531
.0001
8.7173
23.3660
H3
20.604
3.5266
5.843
5.92E-06
13.3088
27.8995
H4
37.833
3.5140
10.766
1.86E-10
30.5641
45.1026
H5
45.396
3.5029
12.960
4.69E-12
38.1496
52.6420
H6
47.625
3.4932
13.634
1.66E-12
40.3988
54.8512
H7
30.521
3.4849
8.758
8.77E-09
23.3117
37.7300
H8
20.083
3.4782
5.774
6.99E-06
12.8881
27.2786
H9
14.646
3.4730
4.217
.0003
7.4615
21.8302
H10
4.208
3.4692
1.213
.2374
-2.9683
11.3849
H11
2.104
3.4669
0.607
.5498
-5.0678
9.2761
t
0.438
0.0722
6.059
3.53E-06
0.2881
0.5869
The regression equation is:
Level = 11.167 + 12.479 Hour1 +16.042 Hour2 + 20.604 Hour3 + 37.833 Hour4 + 45.396 Hour5 + 47.625 Hour6 + 30.521 Hour7 + 20.083 Hour8 + 14.646 Hour9 + 4.208 Hour10 +2.104 Hour11 + 0.438 t
t
hour
Predicted
37
1
39.833
38
2
43.833
39
3
48.833
40
4
66.500
41
5
74.500
42
6
77.167
43
7
60.500
44
8
50.500
45
9
45.500
46
10
35.500
47
11
33.833
48
12
32.167
Regression Analysis
R²
0.954
Adjusted R²
0.931
n
36
R
0.977
k
12
Std. Error
4.245
Dep. Var.
data
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
H1
12.479
3.5560
3.509
.0019
5.1229
19.8354
H2
16.042
3.5406
4.531
.0001
8.7173
23.3660
H3
20.604
3.5266
5.843
5.92E-06
13.3088
27.8995
H4
37.833
3.5140
10.766
1.86E-10
30.5641
45.1026
H5
45.396
3.5029
12.960
4.69E-12
38.1496
52.6420
H6
47.625
3.4932
13.634
1.66E-12
40.3988
54.8512
H7
30.521
3.4849
8.758
8.77E-09
23.3117
37.7300
H8
20.083
3.4782
5.774
6.99E-06
12.8881
27.2786
H9
14.646
3.4730
4.217
.0003
7.4615
21.8302
H10
4.208
3.4692
1.213
.2374
-2.9683
11.3849
H11
2.104
3.4669
0.607
.5498
-5.0678
9.2761
t
0.438
0.0722
6.059
3.53E-06
0.2881
0.5869
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