Question

Because of the hot, humid weather conditions in Florida, the growth rates of beef cattle and the milk production of diary 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 diary cows. In one experiment, 30 cows were selected and divided into three groups of 10 cows each.

Group 1 cows were provided with an artificial shade structure, group 2 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.

Answer 1

a. Identify the independent variables in the experiment.
x1 - provided artificial shade

x2 - provided tree shade

x3 - provided no shade

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

$eta_0$ is the intercept it is the baseline milk production in the cow.

: If the cow is kept in artificial shade the milk production increases by

$eta_2$ : If the cow is kept in tree shade the milk production increases by $eta_2$ but this will be less than

$eta_3$ : If the cow is kept in no shade the milk production decreases by $eta_3$