Based on prior knowledge, we can analyze the relationship between the `lug_boot` feature and the task of rating the decision to buy a car. 

The size of the luggage boot can be an important factor in determining the rating of the decision to buy a car. A larger luggage boot provides more storage space, which can be desirable for many buyers. 

Here is the dictionary with the analysis:

```json
{
	"unacceptable": ["small"],  
	"acceptable": ["small", "med"],  
	"very good": ["med", "big"],  
	"good": ["med", "big"]  
}
```

Explanation:

- For the "unacceptable" rating, cars with a small luggage boot may be considered not suitable for certain buyers.
- For the "acceptable" rating, cars with both small and medium-sized luggage boots are considered suitable for purchase.
- For the "very good" rating, cars with medium and big luggage boots are more likely to receive a higher rating as they offer a sufficient amount of storage space.
- For the "good" rating, cars with medium and big luggage boots are also more likely to be rated as good, but the size of the luggage boot may not be as crucial as in the "very good" rating.

Please note that this analysis is based on prior knowledge and assumptions. The actual relationship between the `lug_boot` feature and the target rating can be determined by analyzing the specific dataset and performing statistical tests.