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# Polynomial Regression

Polynomial linear regression is a variation of linear regression where the relationship between the independent variable(s) and the dependent variable is modeled as an nth-degree polynomial. In Python, you can perform polynomial linear regression using the scikit-learn library. Here’s how you can do it:

1. Import Necessary Libraries:
``````   import numpy as np
import pandas as pd
from sklearn.linear_model import LinearRegression
from sklearn.preprocessing import PolynomialFeatures
from sklearn.model_selection import train_test_split``````
1. Load and Prepare Data: Load your dataset and organize it into the independent variable (feature) and the dependent variable (target).
``````   # Example data

# Separate the feature (independent variable) and the target (dependent variable)
X = data['Feature']  # Independent variable (feature)
y = data['Target']   # Dependent variable (target)``````
1. Split Data: Split your dataset into a training set and a test set to evaluate the model’s performance on unseen data.
``   X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)``
1. Create Polynomial Features: Use scikit-learn’s `PolynomialFeatures` to create polynomial features from your original feature(s). You specify the degree of the polynomial.
``````   degree = 2  # Choose the degree of the polynomial (e.g., 2 for quadratic)
poly_features = PolynomialFeatures(degree=degree)

X_train_poly = poly_features.fit_transform(X_train.values.reshape(-1, 1))
X_test_poly = poly_features.transform(X_test.values.reshape(-1, 1))``````

This step transforms your original feature(s) into a set of features including the original feature(s) and their polynomial combinations.

1. Create and Fit the Model: Create a LinearRegression model and fit it to your training data with the polynomial features.
``````   # Create a linear regression model
model = LinearRegression()

# Fit the model to the training data with polynomial features
model.fit(X_train_poly, y_train)``````
1. Predictions: Once the model is trained, you can use it to make predictions on the test data with polynomial features.
``   y_pred = model.predict(X_test_poly)``
1. Evaluate the Model: You can evaluate the model’s performance using various metrics, such as Mean Squared Error (MSE), R-squared (R^2), or others, depending on your specific goals.
``````   from sklearn.metrics import mean_squared_error, r2_score

mse = mean_squared_error(y_test, y_pred)
r_squared = r2_score(y_test, y_pred)

print(f"Mean Squared Error: {mse}")
print(f"R-squared: {r_squared}")``````

This example demonstrates how to perform polynomial linear regression using scikit-learn in Python. By introducing polynomial features, you can model more complex relationships between the independent and dependent variables. You can adjust the `degree` parameter to control the complexity of the polynomial model. 