import numpy as np
import statsmodels.api as sm
import matplotlib.pyplot as plt

N, M = 100, 10
b_N, b_M = [], []

for i in range(5000):
    x = np.random.random(N)
    y = 2*x + 1 + np.random.random(N)
    _, b_1 = sm.OLS(y, sm.add_constant(x)).fit().params
    b_N.append(b_1)
    _, b_1 = sm.OLS(y[:M], sm.add_constant(x[:M])).fit().params
    b_M.append(b_1)

plt.hist(b_M)
plt.hist(b_N)
plt.show()