2. For a regression problem with a dummy variable in the design matrix (such as D in Equation 7.1 of Fox), consider replacing the 0 and 1 values in the dummy variable with 0.5 and 0.5 respectively. What is the resulting regression equation? Describe how to interpret the parameters of the model. Is this model an acceptable alternative to the usual one for modeling the effects of a binary variable? Is there a reason to prefer one coding to another? (3 points) Yi = a + BXityDi+ Ei (7.1) where D, called a dummy-variable regressor or an indicator variable, is coded 1 for men and 0 for women: for men Di = 0 for women Thus, for women, the model becomes Yi = a + BXity(0) + si = a+ BXit Ei and for men Yi = a + BXity(1) + si = (at y) + BXit Ei