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 Environmental 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.

EXERCISES
1.

(a) The data in the table show the annual averages of the daily maximum concentrations of sulfur dioxide (in parts per billion) and nitrogen dioxide (in parts per billion) for 12 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.

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

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

(d) Find the equation of the regression line for the average concentrations of sulfur dioxide and nitrogen dioxide. Add the graph of the regression line to your scatter plot in part (a). Does the regression line appear to be a good fit?

(e) 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?

(f) Find the coefficient of determination \(r^{2}\) and the standard error of estimate \(s_{e}\). Interpret your results.

2. Construct a \(95 \%\) prediction interval for the average concentration of nitrogen dioxide when the average concentration of sulfur dioxide is 28 parts per billion. Interpret the results.