Evans' maximum likelihood linear regression code (almost real code)

[rickecon]

Here is some pseudo code.

# Linear regression by Max Likelihood
import numpy as np
import scipy.stats as sts
import scipy.optimize as opt

y, x1, x2 = data

def log_lik(y, x1, x2, beta_0,
            beta_1, beta_2, sigma):
    epsilon = y - beta_0 - beta_1 * x1 - beta_2 * x2
    pdf_vals = sts.norm.pdf(epsilon, loc=0.0, scale=sigma)
    log_lik_func = np.log(pdf_vals).sum()
    
    return log_lik_func

def crit_lr(params, *args):
    beta_0, beta_1, beta_2, sigma = params
    y, x1, x2 = args
    neg_log_lik = -log_lik(y, x1, x2, beta_0,
                           beta_1, beta_2, sigma)
    
    return neg_log_lik

beta_0_init = ?
beta_1_init = ?
beta_2_init = ?
sigma_init = ?
params_init = np.array([beta_0_init, beta_1_init,
                        beta_2_init, sigma_init])
args_lr = (y, x1, x2)
results = opt.minimize(crit_lr, params_init, args=(args_lr))