```json
{
	"yes": ["own", "for free"],
	"no": ["rent"]
}
```
Explanation:
Based on the given feature description, the feature "housing" is a categorical variable with three possible categories: "own", "for free", and "rent". 

After analyzing the relationship between the feature and the task of determining whether a person receives credit, it can be observed that individuals who own their housing or live in housing provided for free are more likely to receive credit (target class 'yes'). On the other hand, individuals who rent their housing are less likely to receive credit (target class 'no'). 

Therefore, the dictionary for the relationship between the feature "housing" and the target class can be constructed as shown above.