Milk production of shaded cows. Because of the hot, humid weather conditions in Florida, the growth rates of beef cattle and the milk production of dairy cows typically decline during the summer. However, agricultural and environmental engineers have found that a well-designed shade structure can significantly increase the milk production 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.