Editing Analysis of variance (section)

====Example====
We can consider the 2-way interaction example where we assume that the first factor has 2 levels and the second factor has 3 levels.

Define <math>a_i = 1</math> if <math>Z_{k,1}=i</math> and <math>b_i = 1</math> if <math>Z_{k,2} = i</math>, i.e. <math>a</math> is the one-hot encoding of the first factor and <math>b</math> is the one-hot encoding of the second factor.

With that,
<math display="block">
X_k = [a_1, a_2, b_1, b_2, b_3 ,a_1 \times b_1, a_1 \times b_2, a_1 \times b_3, a_2 \times b_1, a_2 \times b_2, a_2 \times b_3, 1]
</math>
where the last term is an intercept term. For a more concrete example suppose that
<math display="block">\begin{align}
Z_{k,1} & = 2 \\
Z_{k,2} & = 1
\end{align}</math>
Then, <math display="block">X_k = [0,1,1,0,0,0,0,0,1,0,0,1]</math>