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import numpy as np
import matplotlib.pyplot as plt
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LogisticRegression
from sklearn.metrics import accuracy_score, confusion_matrix
from sklearn.datasets import make_classification
from sklearn.preprocessing import StandardScaler

# Sigmoid function
def sigmoid(z):
    return 1 / (1 + np.exp(-z))

# Create synthetic dataset
X, y = make_classification(n_samples=1000, n_features=2, n_informative=2, n_redundant=0, n_clusters_per_class=1, random_state=42)

# Split the dataset into training and testing sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

# Standardize the features (optional but often recommended for logistic regression)
scaler = StandardScaler()
X_train = scaler.fit_transform(X_train)
X_test = scaler.transform(X_test)

# Create a logistic regression model
model = LogisticRegression()

# Train the model
model.fit(X_train, y_train)

# Plot sigmoid function
x_values = np.linspace(-7, 7, 300)
y_values = sigmoid(x_values)

plt.plot(x_values, y_values, label='Sigmoid Function')
plt.title('Sigmoid Function')
plt.xlabel('z')
plt.ylabel('sigmoid(z)')
plt.legend()
plt.show()

# Plot decision boundary on the test set along with sigmoid function
def plot_decision_boundary_with_sigmoid(X, y, model, title="Decision Boundary"):
    h = .02  # step size in the mesh
    x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1
    y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1
    xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
    Z = model.predict(np.c_[xx.ravel(), yy.ravel()])
    Z = Z.reshape(xx.shape)

    # Plot the decision boundary
    plt.contourf(xx, yy, Z, cmap=plt.cm.coolwarm, alpha=0.8)

    # Plot the sigmoid function
    plt.plot(x_values, y_values, label='Sigmoid Function', color='black', linestyle='--')

    # Plot the test points
    plt.scatter(X[:, 0], X[:, 1], c=y, edgecolors='k', cmap=plt.cm.coolwarm)
    plt.title(title)
    plt.xlabel('Feature 1')
    plt.ylabel('Feature 2')
    plt.legend()
    plt.show()

# Plot decision boundary and sigmoid function on the test set
plot_decision_boundary_with_sigmoid(X_test, y_test, model, title="Decision Boundary with Sigmoid Function on Test Set")
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