Refer to the Marine Mammal Science (Apr. 2010) study of whales entangled in fishing gear, Exercise 12.17 (p. 670). These entanglements involved one of three types of fishing gear: set nets, pots, and gill nets. Consequently, the researchers used gear type as a predictor of the body length (y, in meters) of the entangled whale. Consider the regression model E(y) = β0 + β1x1 + β2x2, where x1 = 51 if set net, 0 if not6 and x2 = 51 if pots, 0 if not6. [Note: Gill nets is the "base" level of gear type]
a. The researchers want to know the mean body length of whales entangled in gill nets. Give an expression for this value in terms of the β's in the model.
b. Practically interpret the value of b1 in the model.
c. In terms of the β's in the model, how would you test to determine if the mean body lengths of entangled whales differ for the three types of fishing gear?