Consider a multiple regression model for a response y, with one quantitative independent variable x1 and one qualitative variable at three levels.
a. Write a first-order model that relates the mean response E(y) to the quantitative independent variable.
b. Add the main effect terms for the qualitative independent variable to the model of part a. Specify the coding scheme you use.
c. Add terms to the model of part b to allow for interaction between the quantitative and qualitative independent variables.
d. Under what circumstances will the response lines of the model in part c be parallel?
e. Under what circumstances will the model in part c have only one response line?