Unbalanced nested designs. Consider an unbalanced two-stage nested design with bj levels of B under the ith level of A and nij replicates in the ijth cell.

Factor A 1 2 Factor B 1 2 1 2 3 6 −3 5 2 1 4 1 7 4 0 8 9 3 −3 6

(a) Write down the least squares normal equations for this situation. Solve the normal equations.

(b) Construct the analysis of variance table for the unbalanced two-stage nested design.

(c) Analyze the following data, using the results in part (b).