Minitab generates a design matrix for each design. The first column is a
column of one's for the constant term. If the design was blocked into k blocks,
there are (k − 1) columns for blocks. Minitab uses the same method of coding
blocks as in Factorial Models. This is followed by one column for each main
effect. Terms with categorical factors can have more than one column. If the
model has squared terms, there is one column for each squared term. The column
for a squared term is the product of the corresponding factor with itself. If
the model has interaction terms, then there is one column for each interaction
term. Interactions that include categorical factors can have more than one
column. The column for an interaction term is the product of the two columns
that are crossed.
If Minitab removes some terms because the data cannot support them, these
terms are not in the stored design matrix. The columns stored match the
coefficients that are displayed.