Question

The concentration of pollutants in the atmosphere is affected by some meteorological variables such as relative humidity, temperature, atmospheric pressure, among others. On the other hand, the dispersion of these pollutants is influenced by the stability that prevails in the atmosphere. At the regional level, attention has been paid to the problem of air pollution, mainly due to the oil activities that take place in southwestern Mexico. Through an automated monitoring network known as the Automated System of the Southern Region (SAMARS) of Petróleos Mexicanos (PEMEX), the main air pollutants (except ozone) and meteorological variables are monitored. This network has been operating since 1999 and has six monitoring stations located on the outskirts of the oil facilities (Batteries and Compressors). The information collected to date has been used mainly in the evaluation of air quality in the periphery of these facilities, in the calibration of pollutant dispersion models, and in their spatial distribution. The pollutants whose concentrations were studied are SO2 (sulfur dioxide), NO2 (nitrogen dioxide), and H2S (hydrogen sulfide); In this activity we will focus only on sulfur dioxide and its relationship with some meteorological variables. This information was obtained at a monitoring station in northern Chiapas.

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

b) Obtain the Pearson correlation coefficient between both variables and make an interpretation of it

 

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.

Expert Answer

Answer 1

Correlation coefficient is given by -0.93.

There is strong negative correlation between two variables.

With every year the PPB is decreasing.

Used excel function correl(data) for above calculations

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SUMMARY OUTPUT
Regression Statistics
Multiple R	0.755
R Square	0.571
Adjusted R Square	0.325
Standard Error	1.449
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	4	19.546	4.887	2.327	0.155
Residual	7	14.701	2.100
Total	11	34.247
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-34.610	17.832	-1.941	0.093	-76.776	7.556
t	-0.329	0.194	-1.696	0.134	-0.787	0.130
T	0.051	0.213	0.241	0.816	-0.452	0.555
RH	0.006	0.085	0.071	0.945	-0.195	0.207
P	0.044	0.018	2.437	0.045	0.001	0.087

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