Researchers randomly assign volunteers to a Low, Medium, or High dose of a potential vaccine. The dependent variable is Y = immune response. Because immune response weakens with age, they also record...

Researchers randomly assign volunteers to a Low, Medium, or High dose of a potential vaccine. The dependent variable is Y = immune response. Because immune response weakens with age, they also record each volunteer’s Age. They write a linear model as

Y = β_o
+ β₁D₁
+ β₂D₂
+ β₃Age + ε;

where D₁
= 0 if dose is Low and D₁
= 1 otherwise, and D₂
= 0 if dose is Low or Medium and D₂
= 1 otherwise. (This is called sequential coding.)

(a) Write the simplified regression equation separately for the Low, Medium, and High doses.

(b) The data is given in Table 11.16. Fit an ANCOVA model for this data, and interpret the regression coefficients for D₁
and D₂.

(c) Would including the interactions of AGE with D₁
or D₂
improve the model?