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## A More Complex ANCOVA: Two Factors and One Continuous Covariate

The following experiment, with Weight as the response variable, involved Genotype and Sex as two categorical explanatory variables and Age as a continuous covariate. There are six levels of Genotype and two levels of Sex.

```Gain <-read.table("c:\\temp\\Gain.txt",header=T)
attach(Gain)
names(Gain)

[1] "Weight" "Sex" "Age" "Genotype" "Score"```

We begin by fitting the maximal model with its 24 parameters: different slopes and intercepts for every combination of Sex and Genotype.

```m1<-lm(Weight~Sex*Age*Genotype)
summary(m1)```
`Coefficients: Estimate Std. Error t value Pr (>|t|) (Intercept) 7.80053 0.24941 31.276 < 2e-16 *** Sexmale -0.51966 0.35272 -1.473 0.14936 Age 0.34950 0.07520 4.648 4.39e-05 *** GenotypeCloneB 1.19870 0.35272 3.398 0.00167 ** GenotypeCloneC -0.41751 0.35272 -1.184 0.24429 GenotypeCloneD 0.95600 0.35272 2.710 0.01023 * GenotypeCloneE -0.81604 0.35272 -2.314 0.02651 * GenotypeCloneF 1.66851 0.35272 4.730 3.41e-05 *** Sexmale:Age -0.11283 0.10635 -1.061 0.29579 Sexmale:GenotypeCloneB -0.31716 0.49882 -0.636 0.52891 Sexmale:GenotypeCloneC -1.06234 0.49882 -2.130 0.04010 * Sexmale:GenotypeCloneD -0.73547 0.49882 -1.474 0.14906 Sexmale:GenotypeCloneE -0.28533 0.49882 -0.572 0.57087 Sexmale:GenotypeCloneF -0.19839 0.49882 -0.398 0.69319 Age:GenotypeCloneB -0.10146 0.10635 -0.954 0.34643 Age:GenotypeCloneC -0.20825 0.10635 -1.958 0.05799 . Age:GenotypeCloneD -0.01757 0.10635 -0.165 0.86970 Age:GenotypeCloneE ...`

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