Milk production of shaded cows. Because of the hot, humid weather conditions in Florida, the growth rates of beef cattle and the milk produc- tion of dairy cows typically decline during the summer. However, agricultural and environmen- tal engineers have found that a well-designed shade structure can signi?cantly increase the milk pro- duction of dairy cows. In one experiment, 30 cows were selected and divided into three groups of 10 cows each. Group 1 cows were provided with a man-made shade structure, group 2 cows with tree shade, and group 3 cows with no shade. Of interest was the mean milk production (in gallons) of the cows in each group.

(a) Identify the independent variables in the experiment.

(b) Write a model relating the mean milk production, E(y), to the independent variables. Identify and code all dummy variables.

(c) Interpret the β parameters of the model.