There is only one problem, which I hope is pretty straightforward.

1) A nutrition study of serum glucose levels over time after eating. There are 3 foods; each was fed to 4 subjects, so there are a total of 12 subjects in the study. Foods were randomly assigned to subjects. Blood samples were taken from each subject at 15 minutes, 30 minutes, and 45 minutes after injestion of the food. The data are in serum.txt.
a) Plot the means for each food over time. Without worrying about the variation or tests, describe the effect of each diet on serum glucose concentration.
b) Consider 5 models for the correlation between observations on the same subject: Independence, split-plot-in-time, AR(1), AR(1) with random effects, and Unstructured. Which appears to be the most appropriate model for the correlation structure?
c) To illustrate why there is a non-zero correlation (at least why from a statistical point-of-view), consider subjects 2 and 4, two of the four people who ate diet 1. You have already calculated the means for each diet and time in part a. Calculate the residuals for each time for subject 2 and the residuals for each time for subject 4. This is probably easiest by hand. If the residual for the first time (15 minutes) is positive, are those for 30min and 45 min also positive? If the residual for the first time (15 minutes) is negative, are those for 30min and 45min also negative?
d) Fit a model with fixed effects for diet, time, and diet*time using the most appropriate correlation model. Report the F statistics and p-values for each effect.
e) Is the effect of diet consistent over time? For example, is the difference between diet 1 and 2 (or diets 1 and 3, or diets 2 and 3) the same at 15min, 30min and 45min? Explain why or why not?
f) Construct 2 d.f. F tests that test whether there is an effect of diet at 15 min. Repeat for 30 min and 45 min. Report the F statistics and p-values.
Hint: slicing.
g) An alternative way to examine the time-specific differences between diets would be to consider each time separately. I.e. analyze just the data from 15 minutes to test equality of diets at 15min. You do not need to do this analysis. This analysis is certainly simpler. Is there any benefit to doing the repeated measures analysis (e.g. the analysis in parts d, e, and f)?
Hint: write out the skeleton ANOVA table for a '15 min' only analysis. What, if anything, is different between the two analyses?