Interaction plot in factorial design

Question

How to investigate the effect of a main factor on a respone with ANOVA?

Answer 1

You can quite easily calculate the mean of y at different levels of A, B and C:

by( y, B, mean ) # mean of y at each level
diff( by( y, B, mean ) ) # the difference of the means at the two available levels of y

# same for A and C:

by( y, C, mean )
# etc.

I don't really see your newdata variable that you plot, but assuming its just data.frame(A,B,C,y) , my figure matches the mean's of y at levels of predictors. Though my figure is slightly different from yours.