1. Cook and Weisberg (1999) describe an experiment with turkey growth. Methionine is an amino acid essential for normal growth in turkeys; if they have too little, the birds can be malnourished, but if they have too much, it could be toxic. To find the optimal level of methionine for the birds, an experiment was conducted. A total of 60 pens of turkeys were randomly assigned to one of three commercial sources of methionine and one of four doses of methionine, ranging from 0.04% to 0.28% of the total diet. (Five pens were assigned to each treatment combination.)
An additional 10 pens were assigned to a control group receiving no methionine at all. A plot of the relationship between dosage and average weight gain for the birds from each of the groups of five pens, along with the average from the 10 control pens, is shown below. (Black squares are the averages for Source 1, red circles for Source 2, and green triangles for Source 3.)
(a) Would you suggest weighting this model? Why or why not? If so, what weights would you use?
(b) Would you suggest using a polynomial model? Why or why not? If so, what order polynomial would you use?
(c) Would you suggest using separate lines or polynomials for the three groups? Would you use separate intercepts? Would you use interactions? Explain.
(d) Write down your suggested model, using variables x = dosage, iSource2 = indicator for being methionine from Source 2, and iSource3 = indicator for being methionine from Source 3.
2. A mom noticed that girls’ shoes are narrower than boys’ shoes and wondered whether their feet were also narrower. More specifically, she wondered whether 4th grade girls actually had narrower feet than boys, given the same length foot. She went to her daughter’s classroom to measure the children’s feet. The measurements taken for the children included foot width, foot length, and sex.
(a) In order to answer the mom’s question, is it necessary to have an interaction term? Why or why not?
(b) Develop a linear model for this study, interpreting all parameters in the context of the problem.
(c) Write down your hypotheses to be tested in terms of your model parameters. (You don’t have any data to conduct the test; just write down the hypotheses.)