from sklearn.metrics import roc_curve, roc_auc_score
import matplotlib.pyplot as plt

y_pred_proba = model.predict_proba(X_test)[:, 1]
fpr, tpr, _ = roc_curve(y_test, y_pred_proba)
auc = roc_auc_score(y_test, y_pred_proba)

plt.plot(fpr, tpr, label=f'ROC Curve (AUC = {auc:.2f})')
plt.xlabel('False Positive Rate')
plt.ylabel('True Positive Rate')
plt.title('Receiver Operating Characteristic')
plt.legend(loc='lower right')
plt.show()

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