Sustained-release drug study. Researchers at the Upjohn Company utilized multiple regression analysis in the development of a 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: x1 = Excipient level (i.e., amount of nondrug ingredient in the tablet) x2 = 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),x1, and x2. Assume that x1 and x2 do not interact.
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(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),x1 line for fixed x2?
(e) For the model in part c, what is the slope of the E(y),x2 line for fixed x1?