Box-Cox Transformation Practice Problem

This data science coding problem helps you practice Feature Scaling & Transformation, box-cox transformation, and implementation skills. Read the problem statement, write your solution, and strengthen your understanding of Feature Scaling & Transformation.

• Problem ID: 33
• Problem key: 33-box-cox-transformation
• URL: https://datacrack.app/solve/33-box-cox-transformation
• Difficulty: hard
• Topic: Feature Scaling & Transformation
• Module: Data Cleaning

Problem Statement

# Box-Cox Transformation

### 🎯 Goal
Apply the Box-Cox power transformation to a specified column to make its distribution more normal-like.

### 💻 Task
Implement `box_cox_transform(data, column, lam)` that:
1. Converts the input dictionary to a DataFrame
2. Validates that all values in the target column are positive
3. Applies the Box-Cox formula based on lambda:
   - If `lam == 0`: `ln(x)` (natural logarithm)
   - Otherwise: `(x^lam - 1) / lam`
4. Returns the DataFrame with the transformed column, rounded to 2 decimal places

---

### 📥 Input
- `data`: A dictionary where keys are column names and values are lists of numeric data
- `column`: The name of the column to transform
- `lam`: The lambda parameter for the Box-Cox transformation

### 📤 Output
- A pandas DataFrame with the specified column transformed, rounded to 2 decimals

---

### 🧩 Starter Code

```python
import pandas as pd
import numpy as np

def box_cox_transform(data, column, lam):
    """
    Apply Box-Cox power transformation to a column.

    Args:
        data (dict): Input data as dictionary (from JSON)
        column (str): Name of the column to transform
        lam (float): Lambda parameter (0 = log transform)

    Returns:
        pd.DataFrame: DataFrame with the column transformed, rounded to 2 decimals
    """
    # TODO: Convert the input dictionary to a DataFrame
    # TODO: Check if lambda is 0 (use natural log) or not (use power formula)
    # TODO: Apply the appropriate Box-Cox formula to the specified column
    # TODO: Round the result to 2 decimal places and return
    pass
```

---

### 💡 Examples

**Example 1:** Lambda = 0 (natural log)
```python
data = {"A": [1.0, 2.0, 3.0, 4.0, 5.0]}
box_cox_transform(data, column="A", lam=0)
```
```
      A
0  0.00
1  0.69
2  1.10
3  1.39
4  1.61
```

**Example 2:** Lambda = 0.5 (square root variant)
```python
data = {"A": [1.0, 4.0, 9.0, 16.0]}
box_cox_transform(data, column="A", lam=0.5)
```
```
     A
0  0.0
1  2.0
2  4.0
3  6.0
```

**Example 3:** Lambda = 2 (quadratic variant)
```python
data = {"A": [1.0, 2.0, 3.0]}
box_cox_transform(data, column="A", lam=2)
```
```
     A
0  0.0
1  1.5
2  4.0
```

Starter Code

import pandas as pd
import numpy as np

def box_cox_transform(data, column, lam):
    """
    Apply Box-Cox power transformation to a column.

    Args:
        data (dict): Input data as dictionary (from JSON)
        column (str): Name of the column to transform
        lam (float): Lambda parameter (0 = log transform)

    Returns:
        pd.DataFrame: DataFrame with the column transformed, rounded to 2 decimals
    """
    # TODO: Convert the input dictionary to a DataFrame
    # TODO: Check if lambda is 0 (use natural log) or not (use power formula)
    # TODO: Apply the appropriate Box-Cox formula to the specified column
    # TODO: Round the result to 2 decimal places and return
    pass