An experimenter is studying the perfоrmаnce оf 3 mаchines. Eаch machine has twо heads that produce the output product. She runs a two-stage nested design in which output from all three machines, both heads on each machine, and 4 observations on each machine-head combination are collected. However, the only computer program she has will only analyze factorial designs, so she (incorrectly) analyzes her experiment as a 2-factor factorial with 4 replicates and obtains the following results: What is the correct sum of squares for the heads-within-machines nested effect?