Untitled

import numpy as np
import matplotlib.pyplot as plt
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error
from sklearn.datasets import make_regression

# Step 1: Generate a synthetic dataset
X, y = make_regression(n_samples=1000, n_features=1, noise=10, random_state=42)

# Step 2: Split the data into training and test sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

# Step 3: Apply linear regression on subsets of increasing size and calculate MSE
subset_sizes = np.linspace(10, len(X_train), 10, dtype=int)
mse_values = []

for size in subset_sizes:
    mse_avg = 0
    # Averaging over 10 random permutations
    for _ in range(10):
        subset_idx = np.random.choice(len(X_train), size, replace=False)
        X_subset, y_subset = X_train[subset_idx], y_train[subset_idx]

        # Apply linear regression
        model = LinearRegression()
        model.fit(X_subset, y_subset)

        # Calculate MSE on the training subset
        y_pred = model.predict(X_subset)
        mse = mean_squared_error(y_subset, y_pred)
        mse_avg += mse

    mse_avg /= 10
    mse_values.append(mse_avg)

# Step 4: Plot the results
plt.figure(figsize=(10, 6))
plt.plot(subset_sizes, mse_values, marker='o')
plt.xlabel('Number of Samples (m)')
plt.ylabel('Mean Squared Error (MSE)')
plt.title('MSE on Training Set as a Function of Number of Samples')
plt.grid(True)
plt.show()