11.4 Consider a 22 factorial experiment in a completely randomized design with r replications for each treatment combination. Suppose that for each observation, y, information on a covariate, x, is available. (i) Using the supplementary information, give the general expression for the (adjusted) estimator for the main effect A. (ii) Let A Buy (AB) and Eyy be the sums of squares for A, B, AB and Error, respectively, in the ANOVA table without the covariate. Using similar notation, give general expressions for the corresponding sums of squares when the covariate is included in the analysis.