unbalanced two-way ANOVA model

e.g. we have recorded 4 observations at level 1 of factor A and level 1 for factor B, 5 observations at level 1 of factorA and level 2 for factor B, etc. (a) State explicitly what are the constraints imposed on the (15's, the l3j's and the 537's by the two-way AN OVA model in this situation. (b) Provide an interpretation of the two-way AN OVA parameters (1:, B} and 53-}- in a way that is understandable by a non-statistician. (c) Derive the MLE's of the two-way AN OVA parameters p, on, (12, a3, [31, B2, 311, 5215 . . . , 532 1. Suppose we have the following unbalanced two-way ANOVA model yijk = u + di + Bj + dij + Eijk iid Eijk ~ N(0, 62 ) where i = 1, 2,3 and j = 1, 2 denote, respectively, the number of levels for factor A and the number of levels for factor B. Suppose that the number of observations (Kij) per group is