Exercise 10.6.2. Smith, Gnanadesikan, and Hughes (1962) provide data on characteristics of the urine of young men. The men are categorized into four groups based on their degree of obesity. The four variables given in Table 10.4 consist of a covariate x = 103((specific gravity)−1) and three dependent variables:

y1 = pigment creatinine, y2 = chloride, and y3 = chlorine.

(a) Do a one-way MANOVA on these data ignoring the covariate.

(b) Do a one-way multivariate ACOVA (MACOVA) on these data.