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?