The U.S. Army Corps of Engineers data 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 below in the table.)
a. Fit the first-order model, E(y) = β0 + β1x1 + β2x2 + β3x3, to the data, where y = DDT level, x1 = mile, x2 = length, and x3 = weight. Report the least squares prediction equation.
b. Find the estimate of the standard deviation of ε 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.

For information: (Example 1.5)

River Mile Species Length Weight DDT FC 5 CHANNELCATFISH 42.5 732 10.00 FC 5 CHANNELCATFISH44.0 795 16.00 FC 5 CHANNELCATFISH 41.5 547 23.00 FC 5 CHANNELCATFISH 39.0 465 21.00 FC 5 CHNNELCATFISH 50.5 1252 50.00 TR 345 LARGEMOUTHBASS 23.5 358 2.00 TR 345 LARGEMOUTHBASS 300 856 2.20 TR 345 LARGEMOUTHBASS 29.0 793 740 TR 345 LARGEMOUTHBASS 75 173 0.35 TR 345 LARGEMOUTHBASS 36.0 1,433 190