This is the data and R code data <- scan(what = list(aggregate=\"\",compaction=\

Question

This is the data and R code

data <- scan(what = list(aggregate="",compaction="",strength=0), multi.line=F)
Basalt Static 68 Basalt Static 63 Basalt Static 65
Basalt Basalt Regular 128   Basalt Regular 133
Basalt Low 93   Basalt Low 101 Basalt Low 98
Basalt VeryLow 56   Basalt VeryLow 59   Basalt VeryLow 57
Silicious Static 71 Silicious Static 66 Silicious Static 66
Silicious Regular 107   Silicious Regular 110 Silicious Regular 116
Silicious Low 63 Silicious Low 60 Silicious Low 59
Silicious VeryLow 40   Silicious VeryLow 44

data

concrete <- data.frame(data)
rm(data)

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 "VeryLow". 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 stuns of squares (I, II, and III). For the Type I SS, 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 = SS Aggregate + SS Compaction + SS Aggregate x Compact ion+ RSS? iii) For this set of data, which Type of SS should be used?

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data

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