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Multi Class Regression with scikit-learn: Predicting Categorical Variables

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In machine learning, regression models are commonly used to predict continuous variables such as price or yield. However, scikit-learn, a popular machine learning library in Python, also includes methods for multi-class regression, enabling the prediction of categorical variables. In this description, we'll discuss the underlying concepts and implementation details of multi-class regression using scikit-learn.

Multi-class regression extends the standard regression models to handle multiple target classes. One popular approach is the multinomial logistic regression, which transforms the problem into several binary classification tasks. It is essential to note that these models predict the log-odds, so post-processing is required to obtain classes.

First, let's start by creating a dataset, setting up our environment, and importing the necessary libraries:

```python
import numpy as np
import pandas as pd
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import train_test_split

dataset prep
np.random.seed(42)
X = np.random.rand(100, 5)
y = np.random.randint(6, size=(100,))
```

Now, we'll split the dataset into features (X) and labels (y) and perform train-test splits for model evaluation.

```python
splitting data
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42)
```

Before implementing the multi-class regression model, let's create a simple single-class regression model as a starting point:

```python
single class regression
Olivetti Face Dataset as an example
from sklearn.datasets import fetch_openml
X, y = fetch_openml('olivetti_faces', version=1, return_X_y=True)

train-test split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_

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