In: Statistics and Probability
1) The following average SO2 concentrations per year were obtained in ppb (parts per billion):
Year |
2015 |
2016 |
2017 |
2018 |
2019 |
PPB |
12.1 |
8.7 |
8.3 |
5.8 |
6.1 |
2) The following data refer to the SO2 concentration time (t), temperature (T), relative humidity (RH) and atmospheric pressure (P) in the last 12 months:
(ppb) |
Time |
Temperature () |
Relative Humidity (%) |
Atmosferic Pressure (mb) |
10.3 |
1 |
14 |
31 |
980 |
9.9 |
2 |
17 |
42 |
1010 |
9.4 |
3 |
21 |
52 |
1003 |
10.6 |
4 |
28 |
63 |
1020 |
10.1 |
5 |
33 |
74 |
990 |
14.3 |
6 |
35 |
88 |
1050 |
13.3 |
7 |
36 |
84 |
1070 |
8.2 |
8 |
35 |
86 |
1025 |
8.8 |
9 |
32 |
90 |
995 |
9.1 |
10 |
27 |
81 |
1005 |
10 |
11 |
23 |
62 |
1080 |
10.4 |
12 |
18 |
42 |
1056 |
Fit a multiple linear regression model to estimate the SO2 concentration in the coming months.
2. The multiple linear regression model is:
PPB = -34.6098 - 0.3287Time + 0.0514Temperature + 0.0061Relative Humidity + 0.0443Atmospheric Pressure
The output is:
R² | 0.571 | |||||
Adjusted R² | 0.325 | |||||
R | 0.755 | |||||
Std. Error | 1.449 | |||||
n | 12 | |||||
k | 4 | |||||
Dep. Var. | (ppb) | |||||
ANOVA table | ||||||
Source | SS | df | MS | F | p-value | |
Regression | 19.5461 | 4 | 4.8865 | 2.33 | .1553 | |
Residual | 14.7006 | 7 | 2.1001 | |||
Total | 34.2467 | 11 | ||||
Regression output | confidence interval | |||||
variables | coefficients | std. error | t (df=7) | p-value | 95% lower | 95% upper |
Intercept | -34.6098 | |||||
Time | -0.3287 | 0.1938 | -1.696 | .1338 | -0.7871 | 0.1297 |
Temperature () | 0.0514 | 0.2128 | 0.241 | .8161 | -0.4519 | 0.5547 |
Relative Humidity (%) | 0.0061 | 0.0851 | 0.071 | .9452 | -0.1953 | 0.2074 |
Atmosferic Pressure (mb) | 0.0443 | 0.0182 | 2.437 | .0450 | 0.0013 | 0.0873 |