Polynomial Regression

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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

2. Load and Prepare Data: Load your dataset and organize it into the independent variable (feature) and the dependent variable (target).

   # Example data
   data = pd.read_csv('your_dataset.csv')

   # Separate the feature (independent variable) and the target (dependent variable)
   X = data['Feature']  # Independent variable (feature)
   y = data['Target']   # Dependent variable (target)

3. 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)

4. 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.

5. 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)

6. 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)

7. 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.