Air pollution is the introduction of chemicals and biological materials into the atmosphere that causes damage to the natural environment. We focused

Air pollution is the introduction of chemicals and biological materials into the atmosphere that causes damage to the natural environment.

We focused on Sulfur Dioxide as a major contributor to air pollution.

Sulfur is:• Highly reactive gas• Cause of acid rain• Precursor to respiratory and cardiovascular problems

Air pollution is an ongoing problem worldwide, now more than ever.

We conduct a cross-sectional study of the air pollution levels in terms of Sulfur and related factors for 41 US cities using the means over the years 1969-1971. By running several regressions we attempt to determine the likely causes of air pollution.

City SO2 Temperature Man Population Wind Rain RainDays

Phoenix 10 70.3 213 582 6 7.05 36

Little Rock 13 61 91 132 8.2 48.52 100

San Francisco 12 56.7 453 716 8.7 20.66 67

Denver 17 51.9 454 515 9 12.95 86

Hartford 56 49.1 412 158 9 43.37 127

Wilmington 36 54 80 80 9 40.25 114

Washington 29 57.3 434 757 9.3 38.89 111

Jacksonville 14 68.4 136 529 8.8 54.47 116

……. …. …. …. …. …. …. ….

The data are means over the years 1969-1971.

1. City: City

2. SO2: Sulfur dioxide content of air in micrograms per cubic meter

3. Temp: Average annual temperature in degrees Fahrenheit

4. Man: Number of manufacturing enterprises employing 20 or more workers

5. Pop: Population size in thousands from the 1970 census

6. Wind: Average annual wind speed in miles per hour

7. Rain: Average annual precipitation in inches

8. RainDays: Average number of days with precipitation per year

Histogram of sulfur levels:

Since the data has a high Jarque-Bera test and are positively skewed, sulfur levels are not normally distributed.

We ran a number of bi-variate regressions to find out which independent variables significantly explain SO2 levels, both including and excluding dummy variables.

Next we ran a multi-variate regression to see if the variables that we found to be significant are significant in explaining SO2 levels when combined.

We then tested for multicollinearity and lastly investigated an interesting problem.

Dependent Variable: SO2Method: Least SquaresDate: 11/22/09 Time: 14:03Sample: 1 41Included observations: 41

Variable Coefficient Std. Error t-Statistic Prob.

TEMPERATURE -1.408133 0.468595 -3.005012 0.0046C 108.5711 26.34371 4.121328 0.0002

R-squared 0.188009 Mean dependent var 30.04878Adjusted R-squared 0.167189 S.D. dependent var 23.47227S.E. of regression 21.42044 Akaike info criterion 9.014119Sum squared resid 17894.58 Schwarz criterion 9.097708Log likelihood -182.7894 F-statistic 9.030097Durbin-Watson stat 1.848386 Prob(F-statistic) 0.004624

Temperature significantly explains SO2 levels due to the high t-statistic and low p-values.The coefficient of temperature is negative meaning SO2 levels decrease as temperature increases.



MAN 0.026859 0.005099 5.267788 0.0000C 17.61057 3.691587 4.770462 0.0000


Manufacturing Enterprises significantly explains SO2 levels due to the high t-statistic and low p-values. The positive coefficient of man means that as number of manufacturing enterprises increases so do SO2 levels.



POPULATION 0.020014 0.005644 3.546111 0.0010C 17.86832 4.713844 3.790604 0.0005


Population significantly explains SO2 levels due to the high t-statistic and low p-values.The coefficient of population is positive meaning as population increases, so does SO2.



WIND 1.555741 2.619045 0.594011 0.5559C 15.35652 25.00859 0.614050 0.5427

R-squared 0.008966 Mean dependent var 30.04878Adjusted R-squared -0.016445 S.D. dependent var 23.47227S.E. of regression 23.66448 Akaike info criterion 9.213378Sum squared resid 21840.30 Schwarz criterion 9.296967Log likelihood -186.8743 F-statistic 0.352849Durbin-Watson stat 1.818109 Prob(F-statistic) 0.555935

Wind does not significantly explain SO2 levels as can be seen by the low t-statistic and low R-square.It thus makes sense to take the wind variable out of our regression model.



RAIN 0.108262 0.318822 0.339569 0.7360C 26.06809 12.29492 2.120233 0.0404

R-squared 0.002948 Mean dependent var 30.04878Adjusted R-squared -0.022618 S.D. dependent var 23.47227S.E. of regression 23.73623 Akaike info criterion 9.219433Sum squared resid 21972.94 Schwarz criterion 9.303022Log likelihood -186.9984 F-statistic 0.115307Durbin-Watson stat 1.820565 Prob(F-statistic) 0.736003

Rain does not significantly explain SO2 levels due to the low t-statistic and low R-squared. We thus remove the wind variable from our regression model.



RAINYDAYS 0.327260 0.131760 2.483761 0.0174C -7.226963 15.39914 -0.469310 0.6415


RainyDays does significantly explain the SO2 levels due to the high t-statistic and low p-value.The coefficient of rainydays is positive meaning the SO2 levels will increase as the number of rainy days increases.



TEMPERATURE -0.417243 0.391666 -1.065304 0.2938RAINYDAYS 0.127634 0.100713 1.267308 0.2132

POPULATION -0.043929 0.015398 -2.852937 0.0071MAN 0.068179 0.016111 4.231909 0.0002

C 33.93991 27.91632 1.215773 0.2320


Dependent Variable: RAINYDAYSMethod: Least SquaresDate: 11/22/09 Time: 14:35Sample: 1 41Included observations: 41


TEMPERATURE -1.577840 0.530112 -2.976427 0.0050C 201.8882 29.80212 6.774289 0.0000


Multicollinearity does exist because the two variables are significantly correlated; they have a high t-statistic and high R-square. RainyDays and Temperature are negatively correlated, as temperature goes up, rainy days goes down.




C 68.42054 38.36511 1.783405 0.0825


Since multicollinearity exists, we cannot look at the t-statistic for a regression using these two variables as the independent variables. We can however, continue to use the F-statistic to determine if these two variables collectively significantly impact SO2 levels. As it turns out we cannot tell which variable significantly impacts the SO2 level.

Box plot indicating the two outliers: Providence (94) and Chicago (110)

Smallest = 8 (Wichita)Q1 = 12.5 Median = 26 (Richmond)Q3 = 35.5 Largest = 110 (Chicago)IQR = 23

94 110



TEMPERATURE -1.046409 0.342685 -3.053562 0.0042C2 61.31696 15.76031 3.890593 0.0004C1 77.94481 15.73461 4.953716 0.0000C 85.00347 19.36350 4.389881 0.0001


Temperature still significantly explains SO2 levels due to the high t-statistic and low p-values.



MAN 0.025836 0.007284 3.546764 0.0011C2 68.91495 15.10630 4.562001 0.0001C1 7.380472 26.27515 0.280892 0.7804C 16.22323 3.724041 4.356351 0.0001


Manufacturing Enterprises still significantly explains SO2 levels due to the high t-statistic and low p-values.



POPULATION 0.012183 0.007103 1.715259 0.0947C2 72.14691 17.02945 4.236597 0.0001C1 49.28269 26.15993 1.883900 0.0675C 19.67230 4.719600 4.168214 0.0002


Population no longer significantly explains SO2 levels due to the low t-statistic and high p-values.

0

500

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0 20 40 60 80 100 120

SO2

PO

PULA

TIO

NPOPULATION vs. SO2



WIND -0.393012 1.937653 -0.202829 0.8404C2 68.11667 17.62874 3.863956 0.0004C1 84.03807 17.58138 4.779946 0.0000C 30.04926 18.40261 1.632881 0.1110


Wind still does not significantly explain SO2 levels as can be seen by the low t-statistic and low R-square.



RAIN 0.070950 0.232440 0.305241 0.7619C2 67.21003 17.51681 3.836887 0.0005C1 83.79963 17.46754 4.797449 0.0000C 23.75684 8.960694 2.651228 0.0117


Rain still does not significantly explain SO2 levels due to the low t-statistic and low R-squared.



RAINYDAYS 0.278414 0.092644 3.005193 0.0047C2 64.41428 15.71003 4.100200 0.0002C1 81.24952 15.69349 5.177276 0.0000C -5.215998 10.79510 -0.483182 0.6318


Rainy Days still significantly explains the SO2 levels due to the high t-statistic and low p-value.

Dependent Variable: TEMPERATUREMethod: Least SquaresDate: 12/02/09 Time: 15:38Sample: 1 41Included observations: 41


RAINYDAYS -0.114168 0.040132 -2.844797 0.0072C2 -4.720416 6.805350 -0.693633 0.4922C1 -4.462919 6.798183 -0.656487 0.5156C 68.99137 4.676276 14.75349 0.0000


Multicollinearity still exists because the two variables are significantly correlated.




C2 60.91225 15.17959 4.012773 0.0003C1 77.93852 15.15345 5.143285 0.0000C 45.96809 27.18869 1.690706 0.0995


According to the F-statistic temperature and rainy days are significantly related to SO2 levels. However since multicollinearity exists we cannot refer to the t-statistic and therefore do not know how significant each variable is.

Our final model includes the two dummy variables. This regression model has a significant F-statistic and a small p-value.

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-30 -20 -10 0 10 20 30

Series: ResidualsSample 1 41Observations 41

Mean 5.20e-16Median -1.262938Maximum 26.55544Minimum -29.56690Std. Dev. 12.37240Skewness 0.169384Kurtosis 2.795795

Jarque-Bera 0.267292Probability 0.874900

Histogram of sulfur levels with dummy variables:

The data has a low Jarque-Bera test, a high probability and is slightly positively skewed, so sulfur levels are normally distributed.

According to the figure above, there is an indication of heteroskedasticity. However since this is a cross sectional analysis, it does not have a significant impact on our final regression.

From our regression model, we find that temperature, rainy days and manufacturing all have a significant effect on SO2 levels, explaining 72% of the sulfur levels.

Out of the three variables however, manufacturing enterprises is the most significant explanatory variable.

Economic Impact:• Given that SO2 is a threat to human wellbeing and the environment, lowering the SO2 levels can reduce future costs.• SO2 pollution is preventable as it stems from human activity.• Lower SO2 levels could be achieved by future restrictions on the number of manufacturing enterprises or on the emission levels of SO2 they release.

Documents

Air pollution is the introduction of chemicals and biological materials into the atmosphere that causes damage to the natural environment. We focused