The factors that influence the breaking strength of a synthetic fiber are being studied. Four production machines and three operators are available to produce the fiber and a factorial design experiment is run using figure from the same production batch. The data for these experiments is below:

Operator Machine
1 2 3 4
1 109 110 108 110
110 115 109 108
2 110 110 111 114
112 111 109 112
3 116 112 114 120
114 115 119 117

(a) Analyze the data and draw conclusions. Use α=0.05.
(b) Prepare appropriate residual plots and comment on the model's adequacy.