A study was conducted to assess the combined effects of patient attitude and patient physician communication on patient satisfaction with medical care during pregnancy. A random sample of 110 pregnant women under the care of private physicians was followed from the first visit with the physician until delivery. On the basis of specially devised questionnaires, the following variables were measured for each patient: Y = Satisfaction score; X1 = Attitude score; and X2 = Communication score. Each score was developed as an interval variable, but some question remains as to whether the analysis should treat the attitude and/or communication scores as nominal variables.
a. What would be an appropriate regression model for describing the joint effect of X1 and X2 on Y if an interaction between communication and attitude is possible and if all variables are treated as interval variables?
b. What would be an appropriate regression model (using dummy variables) if the analyst wished to allow for an interaction effect but desired only to compare high values versus low values (i.e., to make group comparisons) for both the communication and attitude variables? What kind of ANOVA model would this regression model correspond to?
c. When would the model in part (a) be preferable to that in part (b), and vice versa?
d. If both independent variables are treated nominally, as in part (b), would you expect the associated 2 × 2 table to have equal numbers in each of the four cells?