Researchers in toxicology study were interested in evaluating the effects of air pollution on vasoconstriction of small pulmonary arteries in rats. Also, they wanted to know if these health effects differed according to whether the rats had preexisting pulmonary disease. Thus, chronic bronchitis was induced in some of the rats by exposing them to 802 for 6 weeks prior to pollution exposure. All rats were randomized to one of four groups: 0 ?ltered air, not exposed to 802o concentrated air particles (CAPS), not exposed to 802o ?ltered air, exposed to 802 o concentrated air particles (CAPS), exposed to 802 and the amount of pulmonary in?ammation, as measured by neutrophil numerical density (Nn) in each animal was measured after three successive days of air pollution exposure. A large value of Nn denotes pulmonary in?ammation. The data are contained in the ?le pollution. sas7bdat, and variables CAPS, 802 and Nn are named as caps, $02, and 1m therein.
(a) Consider the main effect model and the interaction model (which contains both main effects and interactions) that simultaneously assess two categorical factors (802 and CAPS). Write down these two regression models, making sure to explicitly de?ne all independent variables. Write out the interpretation of each regression coefficient Speci?ed in each of these two models.
(b) Consider a test of whether there is a difference in the health effects of air pollution inhalation for healthy animals and that for chronic bronchitic animals (i.e. those who received 802) under the interaction model. What is the null hypothesis correSponding to this test, in terms of the regression coef?cients under the interaction model?