Chemical plant contamination. Refer to Exercise 12.18 (p. 725) and the U.S. Army Corps of Engineers study. You fit the first-order model, E(y) = 0 + 1x1 + b2x2 + 3 x3, to the data, where y = DDT level (parts per million), x1 = number of miles upstream, x2 = length (centimeters), and x3 = weight (grams). Use the Excel/XLSTAT printout below to predict, with 90% confidence, the DDT level of a fish caught 300 miles upstream with a length of 40 centimeters and a weight of 1,000 grams. Interpret the result.

Exercise 12.18

Contamination from a plant’s discharge. Refer to the U.S. Army Corps of Engineers data (Example 1.5, p. 38) on fish contaminated from the toxic discharges of a chemical plant located on the banks of the Tennessee River in Alabama. Recall that the engineers measured the length (in centimeters), weight (in grams), and DDT level (in parts per million) for 144 captured fish. In addition, the number of miles upstream from the river was recorded. The data are saved in the file. (The first and last five observations are shown in the table on the next page.)

a. Fit the first-order model,   to the data, where y = DDT level, 1 = mile, 2 = length, and 3 = weight. Report the least squares prediction equation.


b. Find the estimate of the standard deviation of  for the model and give a practical interpretation of its value.

c. Conduct a test of the global utility of the model. Use  = .05.

d. Do the data provide sufficient evidence to conclude that DDT level increases as length increases? Report the observed significance level of the test and reach a conclusion using  = .05.

e. Find and interpret a 95% confidence interval for 3.

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