General Linear Model uses a regression approach to fit the model that you specify. First Minitab creates a design matrix, from the factors and covariates, and the model that you specify. The columns of this matrix are the predictors for the regression.
The design matrix has n rows, where n = number of observations, and one block of columns, often called indicator variables, for each term in the model. There are as many columns in a block as there are degrees of freedom for the term. The first block is for the constant and contains one column, a column of all ones. The block for a covariate also contains one column, the covariate column itself.
|Level of A||A1||A2||A3|
|Level of A||Level of B||B11||B12||B21||B22||B31||B32||B41||B42|
To calculate the indicator variables for an interaction term, multiply all the corresponding dummy variables for the factors and/or covariates in the interaction. For example, suppose factor A has 6 levels, C has 3 levels, D has 4 levels, and Z and W are covariates. Then the term A * C * D * Z * W * W has 5 x 2 x 3 x 1 x 1 x 1 = 30 indicator variables. To obtain them, multiply each indicator variable for A by each for C, by each for D, by the covariates Z one time and W twice.