Refer to the Marine Mammal Science (Apr. 2010) study of whales entangled in fishing gear, Exercise 12.109 (p. 713). A first-order model for the length (y) of an entangled whale that is a function of water depth of the entanglement (x1) and gear type (set nets, pots, or gill nets) is written as follows:
E(y) = β0 + β1x1 + β2x2 + β3x3 + β4x1x2 + β5x1x3, where x2 = {1 if set net, 0 if not} and x2 = {1 if pot, 0 if not}. Consider this model the complete model in a nested model F-test.
a. Suppose you want to determine if there are any differences in the mean lengths of entangled whales for the three gear types. Give the appropriate null hypothesis to test.
b. Refer to part a. Give the reduced model for the test.
c. Refer to parts a and b. If you reject the null hypothesis, what would you conclude?
d. Suppose you want to determine if the rate of change of whale length (y) with water depth (x1) is the same for all three types of fishing gear. Give the appropriate null hypothesis to test.
e. Refer to part d. Give the reduced model for the test.
f. Refer to parts d and e. If you fail to reject the null hypothesis, what would you conclude?