Example of single linear regression (closed form equation)

single_linear_regression.py

import numpy as np
import statsmodels.api as sm
from sklearn.linear_model import LinearRegression

# generate sample data (single linear)
X = 2 * np.random.rand(200, 1)
y = 1.2 * X + 1 + 0.8 * np.random.randn(200, 1)
X_ = sm.add_constant(X)  # add constant for intercept computation

print('Method 1: matrix formulation')
print(np.dot(np.linalg.inv(np.dot(X_.T, X_)), np.dot(X_.T, y)))

# statsmodels lib
model = sm.OLS(y, X_).fit()
print('Method 2: statsmodels')
print(f'{model.params}')

# LinearRegression
print('Method 3: sklearn.linear_model.LinearRegression')
lr_model = LinearRegression(fit_intercept=True)
lr_model.fit(X, y)
print(f'Intercept: {lr_model.intercept_}, coeff: {lr_model.coef_}')