You may work in groups of no more than three students and submit your assignment jointly. Each student will receive the same mark.
The exercises are from McCulloch, C.E. & Searle, S.R. (2001) Generalized, Linear and Mixed Models, Wiley.
Chapter 1:
E 1.1, 1.2, 1.3, 1.4
Chapter 2:
E 2.1, 2.2, 2.3
Chapter 3:
E 3.1
Chapter 4:
E 4.1, 4.2, 4.3
Likelihood-based Confidence Regions:
In class we derived 5 different pivotal quantities that give likelihood-based confidence regions. Pick any 2 of these and code them in R for the case of the mean and shape parameter of the gamma distribution. Show the resulting contour plots for a few different values of the shape parameter and for small and large samples. For each example, overlay the rectangular region you get from the confidence interval for each parameter separately.
Simple Linear Regression with Lack of Fit Test:
In the class computer labs, you analysed the following data in R and in SAS to get an ANOVA for simple linear regression with a test for lack of fit (nonlinearity). Set this up as a General Linear Model with fixed effects and complete the calculations, writing out each matrix involved in the analysis. Do you need to use a generalized inverse?
Effluent Decline 20 22 14 13 12 11 pH 7 7 9 9 10.5 10.5