The Questions
1. Consider the multiple sclerosis data given in Chapter 1 of Johnson and Wichern.
(a) Examine the univariate normality of the variables x1 and x3 using a Q - Q plot.
(b) Examine the univariate normality of the variables x1 and x3 using a test based on the correlation coefficient r0.
(c) Examine the multivariate normality of the variables x1 and x3 using a chi-square plot of ordered squared generalised distances.
(d) What are the conditions under which we can make meaningful inferences from the chi-square plot?
(e) Find the best power transformation to make each of these variables near-normal. (If you have not met power transformations yet in your course, I have in mind the Box-Cox power transformation, available in Minitab, for instance.)
(f) Show the Q - Q plot of each transformed variable. Comment.
2. Richard-Hansen et al (1999) give information about species capture and collection of morphological measurements prior to the flooding of a large area of rainforest in French Guiana. Email me to collect your data set of readings for a subset of the Coendou prehensilis. Use your data to answer the following questions.
(a) Find and sketch the 95% confidence ellipse for the population means weight and hbl (head and body length).
(b) Suppose that it is known that µw = 3.6 kg and µhbl = 470 mm for Coendou prehensilis caught in a nearby area. Are these plausible values for Coendou prehensilis from this area? Explain.
(c) Construct the simultaneous 95% T2 -intervals for the means for the four variables in these data.
(d) Construct the simultaneous 95% Bonferroni intervals for the means for the four variables in these data.
(e) Compare these intervals. What are the advantages and disadvantages of each type of interval?
(f) Use appropriate plots and tests to investigate whether a normal distribution with p = 4 is appropriate for these data. What is your conclusion?