Ordinary least squares regression in Python

From: Bayesian Models for Astrophysical Data, Cambridge Univ. Press

you are kindly asked to include the complete citation if you used this material in a publication

Code 3.2 Ordinary least squares regression in Python without formula.
==================================================
import numpy as np
import statsmodels.api as sm
from scipy.stats import uniform, norm

# Data
np.random.seed(1056) # set seed to replicate example
nobs = 250 # number of obs in model
x1 = uniform.rvs(size=nobs) # random uniform variable
alpha = 2.0 # intercept
beta = 3.0 # slope
xb = alpha + beta * x1 # linear predictor
y = norm.rvs(loc=xb, scale=1.0, size=nobs) # create y as adjusted random normal variate

# Fit

unity_vec = np.full((nobs,),1, np.float) # unity vector
X = np.column_stack((unity_vec, x1)) # build data matrix with intercept
results = sm.OLS(y, X).fit()

# Output
print(str(results.summary()))
==================================================

GET SOURCE

Output on screen:

OLS Regression Results
==============================================================================
Dep. Variable:    y R-squared:    0.455
Model: OLS    Adj. R-squared:    0.453
Method: Least Squares F-statistic: 207.0
Date: Sat, 17 Dec 2016 Prob (F-statistic): 1.56e-34
Time: 02:15:19 Log-Likelihood: -339.11
No. Observations: 250 AIC: 682.2
Df Residuals: 248 BIC:    689.3
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t|    [95.0% Conf. Int.]
-------------------------------------------------------------------------------------------------------------------------------------
const 2.0398 0.127 16.010 0.000 1.789 2.291
x1    3.1363    0.218 14.387 0.000    2.707 3.566
==============================================================================
Omnibus: 1.101 Durbin-Watson:    1.967
Prob(Omnibus): 0.577 Jarque-Bera (JB):    1.186
Skew: -0.109 Prob(JB): 0.553
Kurtosis: 2.743    Cond. No.    4.69
==============================================================================

Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

HSI

HSI