# Residual vs fits for 2-level factorial design

So I'm analysing a 2-level factorial design, and get the residual vs fits plot below. I don't understand why it's symmetrical around 0. In any form of linear regression I've learned that the plot in question should be randomly scattered (given the assumptions in the model are correct).

However, I've read that this symmetry in fact is the correct pattern for a factorial design, but the source doesn't explain why. (See page 6 of this source: http://www.calpoly.edu/~pan/teaching/Minitab%20DOE%20Tutorial.pdf.)

Can you explain why the residuals vs fits plot for a 2-factorial design is symmetrical around 0?

• thanks! On a side note, this is a split-plot design (i.e. some of the factors are blocked), meaning there are two levels of factors and hence two levels of error, say $\sigma_W$ at the whole-plot level and $\sigma_S$ at the split-plot level. Which error do you think the residuals explain? – harisf Apr 21 '15 at 18:36