Example 6.13 (A two-way multivariate analysis of variance of plastic film data) The optimum conditions for extruding plastic film have been examined using a tech- nique called Evolutionary Operation. (See [9].) In the course of the study that was done, three responses-X = tear resistance, X2 gloss, and X3 opacity-were measured at two levels of the factors, rate of extrusion and amount of an additive. The measurements were repeated n = 5 times at each combination of the factor levels. The data are displayed in Table 6.4. Table 6.4 Plastic Film Data xtear resistance, x2 = gloss, and x = opacity Factor 2: Amount of additive High (1.5%) XXX Low (1.0%) X2 X3 [6.5 9.5 4.4) [6.9 9.1 5.7] 6.2 9.9 6.4) 7.2 10.0 2.0 Low (-10)% 5.8 9.6 3.0 6.9 9.9 3.9 6.5 9.6 4.1 6.1 9.5 1.9 Factor 1: Change [6.5 9.2 0.8] [6.3 9.4 5.7] in rate of extrusion X1 X2 *3 X1 X2 X3 [6.7 9.1 2.8] [7.1 9.2 8.4] [6.6 93 4.1] 7.0 8.8 5.2] High (10%) 72 8.3 3.8 [7.2 9.7 6.9) 7.1 8.4 1.6] (7.5 10.1 2.7] [6.8 85 3.4] [7.6 9.2 1.9] Conduct a two-way MANOVA by manual on the data above. Then justify your answer.