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Polychlorinated biphenyls (PCBs) are synthetic compounds, called congeners, that are particularly toxic to fetuses and young children. Although PCBs are no longer produced in the United States, they are stillfound in the environment. Since human exposure to these PCBsis primarily through the consumption of fish, the EnvironmentalProtection Agency (EPA) monitors PCB levels in fish. Unfortunately,there are 209 different congeners and measuring all ofthem in a fish specimen is an expensive and time-consuming process.You’ve been asked to see if the total amount of PCBs in aspecimen can be estimated with only a few, easily quantifiablecongeners.26 If this can be done, costs can be greatly reduced.Consider the following variables: PCB (the total amount of PCB)and four congeners, PCB52, PCB118, PCB138, and PCB180.

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DATA FILE

PCB

(a) Using numerical and graphical summaries, describe the distributionof each of these variables.

(b) Using numerical and graphical summaries, describe the relationshipbetween each pair of variables in this set.

(c) Use the four congeners, PCB52, PCB118, PCB138, and PCB180, in a multiple regression to predict PCB.

(d) Examine the residuals. Do they appear to be approximately Normal? When you plot them versus each of the explanatory

variables, are any patterns evident?

(e) There may be two outliers, one with a high residual and one with a low residual. Because of safety issues, we are more concerned about underestimating total PCB in a specimen than about overestimating. Give the specimen number for each of the two suspected outliers. Which one corresponds to an overestimate of

PCB?

(f) Rerun the analysis with the two suspected outliers deleted, summarize these results, and compare them with those you obtained in part (c).

 

 
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