Chapter 12.3, Problem 12.18ACI

Contamination from a plant's discharge. Refer to the U.S. Army Corps of Engineers data (Example 1.5, p. 14 ) 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. E (y) = β_{0 +} β₁ x_{1 +} β₂x_{2 +} β₃x₃, to the data. where y = DDT level. x₁ = mile, x₂ = length, and x₃ = weight. Report the least squares prediction equation.

Data for Exercise 12.18

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

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

e.    Find and interpret a 95% confidence interval for β₃.