Phenolic compounds are found in the effluents of coal conversion processes, petroleum refineries, herbicide manufacturing, and fiberglass manufacturing. These compounds are toxic, carcinogenic, and have contributed over the past decades to environmental pollution of aquatic environments. In one study reported in "Photolysis, Biodegradation, and Sorption Behavior of Three Selected Phenolic Compounds on the Surface and Sediment of Rivers" (J. of Envir. Engr., 2011: 1114-1121), the authors examined the sorption characteristics of three selected phenolic compounds. The following data on y = sorbed concentration (mg/g) and x = equilibrium concentration (mg/mL) of 2, 4-Dinitrophenol (DNP) in a particular natural river sediment was read from a graph in the article.

a. Calculate point estimates of the slope and intercept of the population regression line.
b. Does the simple linear regression model specify a useful relationship between y and x?
c. Confirm that y^ = 3.404, SY^ = .107 when x = .2, and y^ = 6.616, SY^ = .088 when x = .4. Explain why sY^ is larger when x = .2 than when x = .4.
d. Calculate a confidence interval with a confidence level of 95% for the true average DNP sorbed concentration of all river sediment specimens having an equilibrium concentration of .4.
e. Calculate a prediction interval with a prediction level of 95% for the DNP sorbed concentration of a single river sediment specimen having an equilibrium concentration of .4.

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x.11 .13 .14 .18 .29 44 67 .78 .93 y 1.72 2.17 2.33 3.00 5.17 7.61 11.17 12.72 14.78