In response to a health advisory regarding mercury poisoning in Maine lakes, the Environmental Protection Agency conducted a field study of 120 Maine lakes. (Statistical Case Studies: A Collaboration Between Academe and Industry, American Statistical Association, 1998.) In addition to the mercury level (parts per million) of each lake, the EPA measured the lake elevation (feet). The data are saved in the MAINELAKE file.

a. Consider the simple linear model, E(y) = β_o + β₁x, where y = mercury level and x = elevation. Is there evidence that mercury level decreases linearly as elevation increases?
b. Conduct a residual analysis for the linear model. Do the assumptions on ∈ appear to be satisfied?

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MAINELAKE (Data for first 10 lakes shown) Lake Mercury Level Elevation Allen Pond 1.080 425 Alligator Pond 0.025 1494 Anasagunticook Lake 0.570 402 Balch & Stump Ponds 0.770 557 Baskahegan Lake 0.790 417 Bauneag Beg Lake 0.750 205 Beaver Pond 0.270 397 Belden Pond 0.660 350 Ben Annis Pond 0.180 122 Bottle Lake 1.050 298