demonstrates the diminishing dependence as features increase

experiment.py

import numpy as np
import matplotlib.pylab as plt

def run_with_samples(feats=1):
    n = 1000
    xs = np.random.uniform(0, 2, (n, feats))
    ys = 1.5 + xs.sum(axis=1) + np.random.normal(0, 1, (n,))
    
    size_subset = 500
    n_samples = 2000
    samples = np.zeros((n_samples, 2))

    for i in range(n_samples):
        idx = np.random.choice(np.arange(n), size=size_subset, replace=False)
        X = xs[idx]
        Y = ys[idx]
        sk_model = LinearRegression().fit(X, Y)
        samples[i, 0] = sk_model.intercept_
        samples[i, 1] = sk_model.coef_[0]
    return samples

plt.figure(figsize=(15, 3))
for idx, i in enumerate([1,2,4,8,16]):
    samples = run_with_samples(feats=i)
    plt.subplot(150 + idx + 1)
    plt.scatter(samples[:, 0], samples[:, 1], alpha=0.2)
    plt.title(f"feats={i}");