Eli Lilly and Company has developed three methods (G, R₁, and R₂) for estimating the shelf life of its drug products based on the potency of the drug.* One way to compare the three methods is to build a regression model for the dependent variable, estimated shelf life y (as a percent of true shelf life), with potency of the drug (x₁) as a quantitative predictor and method as a qualitative predictor.

a. Write a first-order, main effects model for E(y) as a function of potency (x₁) and method. 

b. Interpret the β coefficients of the model, part a.

c. Write a first-order model for E(y) that will allow the slopes to differ for the three methods.

d. Refer to part c. For each method, write the slope of the y–x₁ line in terms of the β’s.