Editing Design matrix (section)

===One-way ANOVA (cell means model)===
This section contains an example with a one-way analysis of variance ([[ANOVA]]) with three groups and seven observations. The given data set has the first three observations belonging to the first group, the following two observations belonging to the second group and the final two observations belonging to the third group.
If the model to be fit is just the mean of each group, then the model is
:<math> y_{ij} = \mu_i + \varepsilon_{ij}</math>
which can be written
:<math>
\begin{bmatrix}y_1 \\ y_2 \\ y_3 \\ y_4 \\ y_5 \\ y_6 \\ y_7 \end{bmatrix} = 
\begin{bmatrix}1 & 0 & 0 \\1 &0  &0 \\ 1 & 0 & 0 \\  0 & 1 & 0 \\  0 & 1 & 0 \\  0 & 0 & 1 \\  0 & 0 & 1\end{bmatrix}
\begin{bmatrix}\mu_1 \\ \mu_2 \\ \mu_3  \end{bmatrix}
+
\begin{bmatrix} \varepsilon_1 \\ \varepsilon_2 \\ \varepsilon_3 \\
\varepsilon_4 \\ \varepsilon_5 \\ \varepsilon_6 \\ \varepsilon_7 \end{bmatrix}
</math>
In this model <math>\mu_i</math> represents the mean of the <math>i</math>th group.