Consider the numerical examples given in Section 8.8 of Chapter 8, involving assessment of the relationship of the independent variables HGT, AGE, and (AGE)2 to the dependent variable WGT. Suppose that HGT is the independent variable of primary concern, so interest lies in evaluating the relationship of HGT to WGT, controlling for the possible confounding effects of AGE and (AGE)2.
a. Assuming that no interaction of any kind exists, state an appropriate regression model to use as the baseline (i.e., standard) for decisions about confounding.
b. Using an appropriate regression coefficient given in part (a) as your measure of association, determine whether confounding exists due to AGE and/or (AGE)2.
c. Can (AGE)2 be dropped from your initial model in part (a) because it is not needed to control adequately for confounding? Explain your answer (using a regression coefficient as your measure of association).
d. Should (AGE)2 be retained in the final model for the sake of precision? Explain.
e. In light of both confounding and precision, what should be your final model? Why?
f. How would you modify your initial model in part (a) to allow for assessing interactions?
g. Regarding your answer to part (f), how would you test for interaction?