6.31. Peanuts are an important crop in parts of the southern United States. In an effort to de- velop improved plants, crop scientists routinely compare varieties with respect to sever- al variables. The data for one two-factor experiment are given in Table 6.17 on page 354. Three varieties (5, 6, and 8) were grown at two geographical locations (1, 2) and, in this case, the three variables representing yield and the two important grade-grain charac- teristics were measured. The three variables are X1 = Yield (plot weight) X2 = Sound mature kernels (weight in grams-maximum of 250 grams) X3 = Seed size (weight, in grams, of 100 seeds) There were two replications of the experiment. (a) Perform a two-factor MANOVA using the data in Table 6.17. Test for a location effect, a variety effect, and a location-variety interaction. Use a = .05. (b) Analyze the residuals from Part a. Do the usual MANOVA assumptions appear to be satisfied? Discuss. (c) Using the results in Part a, can we conclude that the location and/or variety effects are additive? If not, does the interaction effect show up for some variables, but not for others? Check by running three separate univariate two-factor ANOVAs. for others? Check by running three separate univariate two-factor ANOVAs. chapter 6 Comparisons of Several Multivariate Means Table 6.17 Peanut Data Factor 1 Factor 2 *1 *2 X3 Location Variety Yield SdMatKer SeedSize 195.3 153.1 51.4 194.3 167.7 53.7 189.7 139.5 55.5 180.4 121.1 44.4 203.0 156.8 498 195.9 166.0 45.8 202.7 166.1 60.4 197.6 161.8 54.1 193.5 164.5 57.8 on 00 00 00 a 187.0 165.1 58.6 201.5 166.8 65.0 200.0 173.8 67.2 Source: Data courtesy of Yolanda Lopez. (d) Larger numbers correspond to better yield and grade-grain characteristics. Using lo- cation 2, can we conclude that one variety is better than the other two for each char- acteristic? Discuss your answer, using 95% Bonferroni simultaneous intervals for pairs of varieties