Refer to the Marine Mammal Science (Apr. 2010) study of whales entangled in fishing gear, Exercise 12.87, (p. 703). Now consider a model for the length (y) of an entangled whale (in meters) that is a function of water depth of the entanglement (in meters) and gear type (set nets, pots, or gill nets).
a. Write a main-effects-only model for E(y).
b. Sketch the relationships hypothesized by the model, part a. (Hint: Plot length on the vertical axis and water depth on the horizontal axis.)
c. Add terms to the model, part a, that include interaction between water depth and gear type. (Hint: Be sure to interact each dummy variable for gear type with water depth.)
d. Sketch the relationships hypothesized by the model, part c.
e. In terms of the β's in the model of part c, give the rate of change of whale length with water depth for set nets.
f. Repeat part e for pots.
g. Repeat part e for gill nets.
h. In terms of the β's in the model of part c, how would you test to determine if the rate of change of whale length with water depth is the same for all three types of fishing gear?