Example of linear regression in Python

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

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Code 2.3 Example of linear regression in Python.
==================================================

import numpy as np
import statsmodels.formula.api as smf

# Data
y = np.array([13, 15, 9, 17, 8, 5, 19, 23, 10, 7, 10, 6]) # continuous response variable
x1 = np.array([1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0]) # binary predictor
x2 = np.array([1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3]) # categorical predictor

mydata = {} # create data dictionary
mydata['x1'] = x1
mydata['x2'] = x2
mydata['y'] = y

# Fit using ordinary least squares
results = smf.ols(formula = 'y ~ x1 + x2', data = mydata).fit()

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

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GET SOURCE

Output on screen:

OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 0.763
Model: OLS Adj. R-squared: 0.711
Method: Least Squares F-statistic: 14.51
Date:    Sat, 17 Dec 2016 Prob (F-statistic): 0.00153
Time: 01:22:54 Log-Likelihood:    -28.579
No. Observations: 1 AIC: 63.16
Df Residuals: 9 BIC: 64.61
Df Model: 2
Covariance Type: nonrobust
==============================================================================
coef std err    t      P>|t| [95.0% Conf. Int.]
------------------------------------------------------------------------------------------------------------------------------------
Intercept    38.8333 5.090 7.630 0.000   27.319 50.347
x1 -14.5000   3.024 -4.795    0.001    -21.340 -7.660
x2 -9.8750 1.852 -5.333 0.000    -14.064 -5.686
==============================================================================
Omnibus: 0.687 Durbin-Watson: 2.112
Prob(Omnibus): 0.709 Jarque-Bera (JB): 0.467
Skew: -0.426    Prob(JB): 0.792
Kurtosis: 2.545 Cond. No.    16.5
==============================================================================

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

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