In this section we re-examine the two-way contingency tables studied in Independence Testing using the following log-linear regression model:

where all the *x _{ij}* are dummy variables coded to represent categorical variables. In addition, we also consider more complicated models which contain factors consisting of interactions between the same variables, as described in the sections listed below, and the y

*are used to express the frequency of outcomes.*

_{i}In particular we will address the following example:

**Example 1**: Determine which of the log-linear models is the best fit for the data in Example 2 of Independence Testing.

As we will see there are the following types of log-linear models for two-way contingency tables: