Researchers at the Upjohn Company utilized multiple regression analysis in the development of sustained-release tablet. One of the objectives of the research was to develop a model relating the dissolution y of a tablet (i.e., the percentage of the tablet dissolved over a specified period of time) to the following independent variables:

x ₁ = Excipient level (i.e., amount of non drug ingredient in the tablet)

x ₂ = Process variable (e.g., machine setting under which tablet is processed)

(a) Write the complete second-order model for E(y).

(b) Write a model that hypothesizes straightline relationships between E(y), x _l . and x ₂ .Assume that x ₁ and x ₂ do not interact.

(c) Repeat part b, but add interaction to the model.

(d) For the model in part c. what is the slope of the E(y), x ₁ line for fixed x ₂ ?

(e) For the model in part c, what is the slope of the E(y), x ₂ line for fixed x ₁ ?