Based on prior knowledge, the relationship feature describes what an individual is relative to others. It is a categorical variable with the following categories: ['Own-child', 'Husband', 'Not-in-family', 'Unmarried', 'Wife', 'Other-relative'].

To analyze the relationship between this feature and the task of earning more than $50,000 per year, we can examine the potential relationship categories that are more likely to have a positive or negative impact on the target variable.

According to common knowledge, individuals who are married or have a spouse (categories: 'Husband', 'Wife') are more likely to have higher household incomes. On the other hand, individuals who are children (category: 'Own-child') or have no family attachments (categories: 'Not-in-family', 'Unmarried', 'Other-relative') might have lower household incomes.

Based on this analysis, we can create the following dictionary with the specific details:

```json
{
	"no": ["Own-child", "Not-in-family", "Unmarried", "Other-relative"],
	"yes": ["Husband", "Wife"]
}
```

Please note that this analysis is based on general knowledge and should be further validated with the dataset at hand.