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

# Generate Synthetic Data
np.random.seed(42)
X = np.random.rand(100, 1) * 10
y = 3 * X**2 + 2 * X + np.random.randn(100, 1) * 5

# Transform features to polynomial
poly_features = PolynomialFeatures(degree=2, include_bias=False)
X_poly = poly_features.fit_transform(X)

# Fit Polynomial Regression
model = LinearRegression()
model.fit(X_poly, y)
y_pred = model.predict(X_poly)

# Plot results
plt.scatter(X, y, color="blue", label="Actual Data")
plt.scatter(X, y_pred, color="red", label="Predicted Data")
plt.title("Polynomial Regression")
plt.xlabel("X")
plt.ylabel("y")
plt.legend()
plt.show()

# Evaluate Model
mse = mean_squared_error(y, y_pred)
print("Mean Square Error (MSE): ", mse)