Acid rain affects the environment by increasing the acidity of lakes and streams

Question

Acid rain affects the environment by increasing the acidity of lakes and streams to dangerous levels, damaging trees and soil, accelerating the decay of building materials and paint, and destroying national monuments. The goal of the environment protection agency’s (EPA) Acid Rain Program is to achieve environmental health benefits by reducing the emissions of the primary causes of acid rain: sulfur dioxide and nitrogen oxides. You work for the EPA and you want to determine whether there is a significant correlation between the average concentrations of sulfur dioxide and nitrogen dioxide.

sulfur dioxide

nitrogen dioxide

x

y

4.6

15.6

4.4

15.4

4

14.9

3.8

13.5

3.9

13.4

3.4

12.7

3.3

12.3

2.9

11.4

2.4

10.5

2.2

10.2

The data in the table show the average concentrations’ of Sulphur dioxide (in parts per billion) and nitrogen dioxide (in parts per billion) for 11 years. Construct a scatter plot of the data and make a conclusion about the type of correlation between the average concentrations of sulfur dioxide and nitrogen dioxide.

Calculate the correlation coefficient r and verify your conclusion in part (a).

Test the significance of the correlation coefficient found in part (b). Use = 0.05

Find the equation of the regression line to your scatter plot in part (a). Does the regression line appear to be a good fit?

Can you use the equation of the regression line to predict the average concentration of nitrogen dioxide given the average concentration of sulfur dioxide? Why or why not?

Find the coefficient of determination r2 and the standard error of estimate se interpret your results.

sulfur dioxide

nitrogen dioxide

x

y

4.6

15.6

4.4

15.4

4

14.9

3.8

13.5

3.9

13.4

3.4

12.7

3.3

12.3

2.9

11.4

2.4

10.5

2.2

10.2

Explanation / Answer

Scatter Plot of Sulpher Dioxide and Nitrogen Dioxide using by MS Excel

Correlation coefficient r = 0.9836

Here we observed by Scatter plot and Correlation coefficient r, we say that the strong correlation between these two variables. Moreover their is near linear relationship among them.

Here P-value is very small as compared to level of signficant = 0.05, so we reject null hypothesis Ho means there is significant relationship between these variables (X and Y) at 5% level of significant.

coefficient of determination r2 = 0.9673 and standard error of estimate is 0.1538

SUMMARY OUTPUT Regression Statistics Multiple R 0.983538777 R Square 0.967348525 Adjusted R Square 0.963267091 Standard Error 0.371249184 Observations 10 ANOVA df SS MS F Significance F Regression 1 32.66639235 32.66639 237.011904 3.14936E-07 Residual 8 1.102607651 0.137826 Total 9 33.769 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 4.728118031 0.549344606 8.606834 2.57037E-05 3.461327098 5.99490896 3.461327098 5.994908963 Sulpher Dioxide (X) 2.367301424 0.15376889 15.39519 3.14936E-07 2.012709727 2.72189312 2.012709727 2.72189312

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