Air pollution control specialists in southern g California monitor the amount of
ID: 3124461 • Letter: A
Question
Air pollution control specialists in southern g California monitor the amount of ozone, I carbon dioxide, and nitrogen dioxide in the I air on an hourly basis. The hourly time I series data exhibit seasonality, with the levels of pollutants showing patterns that I vary over the hours in the day. On July 15, I 16, and 17, the following levels of nitrogen I dioxide were observed for the 12 hours from I 6:00 A.M. to 6:00 P.M. Use a multiple linear regression model with I dummy variables as follows to develop an I equation to account for seasonal effects in I the data: Hourl 1= 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 can you please tell me how to make this regression analysis?????????????? how do i set up the information in excel to get the desired results????? have tried the way i know how and it wont let me....Explanation / Answer
Data setup
You set up data like this.
Score is dependent variable y
t1 to t11 are independent variables.( dummy variables).
day
score
t1
t2
t3
t4
t5
t6
t7
t8
t9
t10
t11
15
25
1
0
0
0
0
0
0
0
0
0
0
15
28
0
1
0
0
0
0
0
0
0
0
0
15
35
0
0
1
0
0
0
0
0
0
0
0
15
50
0
0
0
1
0
0
0
0
0
0
0
15
60
0
0
0
0
1
0
0
0
0
0
0
15
60
0
0
0
0
0
1
0
0
0
0
0
15
40
0
0
0
0
0
0
1
0
0
0
0
15
35
0
0
0
0
0
0
0
1
0
0
0
15
30
0
0
0
0
0
0
0
0
1
0
0
15
25
0
0
0
0
0
0
0
0
0
1
0
15
25
0
0
0
0
0
0
0
0
0
0
1
15
20
0
0
0
0
0
0
0
0
0
0
0
16
28
1
0
0
0
0
0
0
0
0
0
0
16
30
0
1
0
0
0
0
0
0
0
0
0
16
35
0
0
1
0
0
0
0
0
0
0
0
16
48
0
0
0
1
0
0
0
0
0
0
0
16
60
0
0
0
0
1
0
0
0
0
0
0
16
65
0
0
0
0
0
1
0
0
0
0
0
16
50
0
0
0
0
0
0
1
0
0
0
0
16
40
0
0
0
0
0
0
0
1
0
0
0
16
35
0
0
0
0
0
0
0
0
1
0
0
16
25
0
0
0
0
0
0
0
0
0
1
0
16
20
0
0
0
0
0
0
0
0
0
0
1
16
20
0
0
0
0
0
0
0
0
0
0
0
17
35
1
0
0
0
0
0
0
0
0
0
0
17
42
0
1
0
0
0
0
0
0
0
0
0
17
45
0
0
1
0
0
0
0
0
0
0
0
17
70
0
0
0
1
0
0
0
0
0
0
0
17
72
0
0
0
0
1
0
0
0
0
0
0
17
75
0
0
0
0
0
1
0
0
0
0
0
17
60
0
0
0
0
0
0
1
0
0
0
0
17
45
0
0
0
0
0
0
0
1
0
0
0
17
40
0
0
0
0
0
0
0
0
1
0
0
17
25
0
0
0
0
0
0
0
0
0
1
0
17
25
0
0
0
0
0
0
0
0
0
0
1
17
25
0
0
0
0
0
0
0
0
0
0
0
Regression Analysis
R²
0.881
Adjusted R²
0.827
n
36
R
0.939
k
11
Std. Error
6.696
Dep. Var.
score
ANOVA table
Source
SS
df
MS
F
p-value
Regression
8,002.2222
11
727.4747
16.23
1.56E-08
Residual
1,076.0000
24
44.8333
Total
9,078.2222
35
Regression output
confidence interval
variables
coefficients
std. error
t (df=24)
p-value
95% lower
95% upper
Intercept
21.6667
3.8658
5.605
9.07E-06
13.6880
29.6453
t1
7.6667
5.4671
1.402
.1736
-3.6168
18.9502
t2
11.6667
5.4671
2.134
.0433
0.3832
22.9502
t3
16.6667
5.4671
3.049
.0055
5.3832
27.9502
t4
34.3333
5.4671
6.280
1.72E-06
23.0498
45.6168
t5
42.3333
5.4671
7.743
5.59E-08
31.0498
53.6168
t6
45.0000
5.4671
8.231
1.90E-08
33.7165
56.2835
t7
28.3333
5.4671
5.183
2.62E-05
17.0498
39.6168
t8
18.3333
5.4671
3.353
.0026
7.0498
29.6168
t9
13.3333
5.4671
2.439
.0225
2.0498
24.6168
t10
3.3333
5.4671
0.610
.5478
-7.9502
14.6168
t11
1.6667
5.4671
0.305
.7631
-9.6168
12.9502
day
score
t1
t2
t3
t4
t5
t6
t7
t8
t9
t10
t11
15
25
1
0
0
0
0
0
0
0
0
0
0
15
28
0
1
0
0
0
0
0
0
0
0
0
15
35
0
0
1
0
0
0
0
0
0
0
0
15
50
0
0
0
1
0
0
0
0
0
0
0
15
60
0
0
0
0
1
0
0
0
0
0
0
15
60
0
0
0
0
0
1
0
0
0
0
0
15
40
0
0
0
0
0
0
1
0
0
0
0
15
35
0
0
0
0
0
0
0
1
0
0
0
15
30
0
0
0
0
0
0
0
0
1
0
0
15
25
0
0
0
0
0
0
0
0
0
1
0
15
25
0
0
0
0
0
0
0
0
0
0
1
15
20
0
0
0
0
0
0
0
0
0
0
0
16
28
1
0
0
0
0
0
0
0
0
0
0
16
30
0
1
0
0
0
0
0
0
0
0
0
16
35
0
0
1
0
0
0
0
0
0
0
0
16
48
0
0
0
1
0
0
0
0
0
0
0
16
60
0
0
0
0
1
0
0
0
0
0
0
16
65
0
0
0
0
0
1
0
0
0
0
0
16
50
0
0
0
0
0
0
1
0
0
0
0
16
40
0
0
0
0
0
0
0
1
0
0
0
16
35
0
0
0
0
0
0
0
0
1
0
0
16
25
0
0
0
0
0
0
0
0
0
1
0
16
20
0
0
0
0
0
0
0
0
0
0
1
16
20
0
0
0
0
0
0
0
0
0
0
0
17
35
1
0
0
0
0
0
0
0
0
0
0
17
42
0
1
0
0
0
0
0
0
0
0
0
17
45
0
0
1
0
0
0
0
0
0
0
0
17
70
0
0
0
1
0
0
0
0
0
0
0
17
72
0
0
0
0
1
0
0
0
0
0
0
17
75
0
0
0
0
0
1
0
0
0
0
0
17
60
0
0
0
0
0
0
1
0
0
0
0
17
45
0
0
0
0
0
0
0
1
0
0
0
17
40
0
0
0
0
0
0
0
0
1
0
0
17
25
0
0
0
0
0
0
0
0
0
1
0
17
25
0
0
0
0
0
0
0
0
0
0
1
17
25
0
0
0
0
0
0
0
0
0
0
0
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