The task is to predict housing prices (denoted by **MEDV**) based on the percentage of lower-income population (**LSTAT**) in a neighborhood. A **Decision Tree Regressor** is used to model this relationship. However, earlier attempts with a tree of **maximum depth 5** resulted in overfitting, where the model captured too much noise and did not generalize well. To mitigate overfitting, the tree's maximum depth was reduced to **2**, simplifying the model.
---
### Explanation of the Plot
1. **Scatter Plot**:
- The blue points represent the actual data points showing the relationship between **LSTAT** (x-axis) and **MEDV** (y-axis).
- Each point corresponds to the housing price (MEDV) for a given percentage of lower-income residents (LSTAT).
2. **Model Prediction Line**:
- The black line represents the predictions made by the Decision Tree Regressor with a maximum depth of 2.
- The line is piecewise constant, divided into distinct horizontal segments that reflect the simplified decision rules of the tree.
---
### Solution Explanation
Reducing the **max_depth** of the tree to 2 addresses overfitting by simplifying the model.
1. **Simplified Decision Boundaries**:
- A shallow tree with depth 2 creates fewer decision rules, focusing only on the most significant splits in the data.
- This generalizes better to unseen data, as it avoids overfitting to minor fluctuations or noise in the training dataset.
2. **Trade-off**:
- While the model may not capture all intricate patterns in the data, it provides a more stable and interpretable solution that balances bias and variance.
---
### Key Takeaway
By limiting the depth of the decision tree, the model becomes less sensitive to noise and achieves better generalization at the expense of capturing fewer details in the training data. This approach is effective for improving performance on unseen data, especially in small or noisy datasets.
