4) Consider the two-factor ANOVA concrete data available in a separate file (ada

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4) Consider the two-factor ANOVA concrete data available in a separate file (adapted from Kuehl's nice Design of Experiments text). The first factor, called Aggregate has levels of "Basalt" and "Silicious while the second factor, called Compaction, has levels of "Static", Regular "Low", and "Very Low". The response is the strength of a sample of concrete produced with those factor levels. i) By fitting a series of regression models (using deviation coding), obtain sums of squares for all tests of interest (Aggregate and Compaction main effects, and the two-way interaction) using all three Types of sums of squares (I, II, and III). For the Type ISS, fit in the order of Aggregate, Compaction, and Aggregate x Compaction. You can check your sums of squares using factors with SAS or R to be sure they are correct) ii) Do any of the three types of sums of squares satisfy Total SS SSAggregate- SSCompaction+SSAggregate x Compaction +RSS? iii) For this set of data, which Type of SS should be used?

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