Based on the feature description and task, we need to analyze how the level of education (feature: education) relates to whether a person earns more than $50,000 per year (target variable: income).

To analyze this relationship, we can look at the average income level for each category of education. Let's calculate the average income for each category and determine the relationship with the target variable.

Here is the dictionary with the analysis of the relationship between the feature education and the target variable income:

```json
{
  "no": ["11th", "HS-grad", "10th", "7th-8th", "Some-college", "9th", "12th", "5th-6th", "1st-4th", "Preschool"], 
  "yes": ["Assoc-acdm", "Prof-school", "Bachelors", "Masters", "Doctorate", "Assoc-voc"]
}
```

Explanation:
- People with education levels such as "11th", "HS-grad", "10th", "7th-8th", "Some-college", "9th", "12th", "5th-6th", "1st-4th", and "Preschool" are more likely to earn less than $50,000 per year.
- On the other hand, people with education levels such as "Assoc-acdm", "Prof-school", "Bachelors", "Masters", "Doctorate", and "Assoc-voc" are more likely to earn more than $50,000 per year.

Note: Some values of education (such as "Preschool" and "Doctorate") might be harder to predict due to the limited data available, but it is still important to include them in the dictionary to provide a comprehensive analysis.