Return to Practice Exercise 2 and the data in Table 11.16. Based on their experience with other vaccines, the researchers believed that the variability in the immune responses might be greater in younger volunteers.
(a) Produce a plot of the jackknifed residuals (the studentized deleted residuals) versus age. Is there a suggestion that the researchers’ suspicion is correct?
(b) The researchers believe that the standard deviation of the errors is proportional to 1/AGE. Fit an appropriate weighted regression model and compare the results to those of Practice Exercise 2.
Exercise 2
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 = βo
+ 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?