Entanglement of marine mammals (e.g., whales) in fishing gear is considered a significant threat to the species. A study published in Marine Mammal Science (April 2010) investigated the characteristics of whales entangled in fishing nets in the East Sea of Korea. A sample of 207 entanglements of whales in the area was used to model the body length (y, in meters) of the entangled whale. Two independent variables used to predict whale length were water depth of the entanglement (x₁ , in meters) and distance of the entanglement from land (x₂ , in miles).

a. Give the equation of a first-order model for length (y) as a function of the two independent variables.

b. The marine scientists theorize that the length of an entangled whale will increase linearly as the water depth increases, for entanglements that are a fixed distance from land. Explain how to use the model, part a, to test this theory.

c. The p-value for testing H_o: β₂ = 0 in the model, part a, was reported as .013. Interpret this result using α = .05.