The catch basin in a storm-sewer system is the interface between surface runoff and the sewer. The catch-basin insert is a device for retrofitting catch basins to improve pollutantremoval properties. The article "An Evaluation of the Urban Stormwater Pollutant Removal Efficiency of Catch Basin Inserts" (Water Envir. Res., 2005: 500-510) reported on tests of various inserts under controlled conditions for which inflow is close to what can be expected in the field. Consider the following data, read from a graph in the article, for one particular type of insert on x = amount filtered (1000s of liters) and y = % total suspended solids removed.

Summary quantities are

a. Does a scatter-plot support the choice of the simple linear regression model? Explain.
b. Obtain the equation of the least squares line.
c. What proportion of observed variation in % removed can be attributed to the model relationship?
d. Does the simple linear regression model specify a useful relationship? Carry out an appropriate test of hypotheses using a significance level of .05.
e. Is there strong evidence for concluding that there is at least a 2% decrease in true average suspended solid removal associated with a 10,000 liter increase in the amount filtered? Test appropriate hypotheses using α = .05.
f. Calculate and interpret a 95% CI for true average % removed when amount filtered is 100,000 liters. How does this interval compare in width to a CI when amount filtered is 200,000 liters?
g. Calculate and interpret a 95% PI for % removed when amount filtered is 100,000 liters. How does this interval compare in width to the CI calculated in (f) and to a PI when amount filtered is 200,000 liters?

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x| 23 45 68 91 114 136 159 182 205 228 y53.3 26.9 54.8 33.8 29.9 8.2 17.2 12.2 3.2 11.1 yi = 125 1, ΣΧ2-199365, y-250.6, y-9249.36. ΣΑΧ = 21,904.4 〉V