import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import LinearRegression
from sklearn.preprocessing import PolynomialFeatures

# Generate random data
np.random.seed(0)
X = np.linspace(-3, 3, 100)
y = 0.5 * X**2 + X + np.random.normal(0, 1, 100)

# Reshape the input data
X = X.reshape(-1, 1)

# Plot the original data
plt.scatter(X, y, color='b', label='Data')

# Fit polynomial regression models of different degrees
degrees = [1, 4, 15]
colors = ['r', 'g', 'm']
for degree, color in zip(degrees, colors):
    # Create polynomial features
    polynomial_features = PolynomialFeatures(degree=degree)
    X_poly = polynomial_features.fit_transform(X)

    # Fit the polynomial regression model
    model = LinearRegression()
    model.fit(X_poly, y)

    # Predict the values
    y_pred = model.predict(X_poly)

    # Plot the fitted curve
    plt.plot(X, y_pred, color=color, linewidth=2, label=f'Degree {degree}')

# Add labels and title to the plot
plt.xlabel('X')
plt.ylabel('y')
plt.title('Polynomial Regression - Overfitting Example')
plt.legend(loc='upper left')

# Display the plot
plt.show()