In [1]:

    

from __future__ import print_function
import numpy as np
import statsmodels.api as sm
import matplotlib.pyplot as plt
from statsmodels.sandbox.regression.predstd import wls_prediction_std

np.random.seed(9876789)


    

In [2]:

    

nsample = 100
x = np.linspace(0, 10, 100)
X = np.column_stack((x, x**2))
beta = np.array([1, 0.1, 10])
e = np.random.normal(size=nsample)


    

In [4]:

    




    

    
Out[4]:





array([  1. ,   0.1,  10. ])

In [5]:

    

X = sm.add_constant(X)
y = np.dot(X, beta) + e


    

In [8]:

    

sm?


    

In [9]:

    

model = sm.OLS(y, X)
results = model.fit()
print(results.summary())


    

    




                            OLS Regression Results                            
==============================================================================
Dep. Variable:                      y   R-squared:                       1.000
Model:                            OLS   Adj. R-squared:                  1.000
Method:                 Least Squares   F-statistic:                 4.020e+06
Date:                Wed, 14 May 2014   Prob (F-statistic):          2.83e-239
Time:                        22:31:29   Log-Likelihood:                -146.51
No. Observations:                 100   AIC:                             299.0
Df Residuals:                      97   BIC:                             306.8
Df Model:                           2                                         
==============================================================================
                 coef    std err          t      P>|t|      [95.0% Conf. Int.]
------------------------------------------------------------------------------
const          1.3423      0.313      4.292      0.000         0.722     1.963
x1            -0.0402      0.145     -0.278      0.781        -0.327     0.247
x2            10.0103      0.014    715.745      0.000         9.982    10.038
==============================================================================
Omnibus:                        2.042   Durbin-Watson:                   2.274
Prob(Omnibus):                  0.360   Jarque-Bera (JB):                1.875
Skew:                           0.234   Prob(JB):                        0.392
Kurtosis:                       2.519   Cond. No.                         144.
==============================================================================

In [10]:

    

print('Parameters: ', results.params)
print('R2: ', results.rsquared)


    

    




Parameters:  [  1.34233516  -0.04024948  10.01025357]
R2:  0.999987936503

In [11]:

    

nsample = 50
sig = 0.5
x = np.linspace(0, 20, nsample)
X = np.column_stack((x, np.sin(x), (x-5)**2, np.ones(nsample)))
beta = [0.5, 0.5, -0.02, 5.]

y_true = np.dot(X, beta)
y = y_true + sig * np.random.normal(size=nsample)


    

In [12]:

    

res = sm.OLS(y, X).fit()
print(res.summary())


    

    




                            OLS Regression Results                            
==============================================================================
Dep. Variable:                      y   R-squared:                       0.933
Model:                            OLS   Adj. R-squared:                  0.928
Method:                 Least Squares   F-statistic:                     211.8
Date:                Wed, 14 May 2014   Prob (F-statistic):           6.30e-27
Time:                        22:32:31   Log-Likelihood:                -34.438
No. Observations:                  50   AIC:                             76.88
Df Residuals:                      46   BIC:                             84.52
Df Model:                           3                                         
==============================================================================
                 coef    std err          t      P>|t|      [95.0% Conf. Int.]
------------------------------------------------------------------------------
x1             0.4687      0.026     17.751      0.000         0.416     0.522
x2             0.4836      0.104      4.659      0.000         0.275     0.693
x3            -0.0174      0.002     -7.507      0.000        -0.022    -0.013
const          5.2058      0.171     30.405      0.000         4.861     5.550
==============================================================================
Omnibus:                        0.655   Durbin-Watson:                   2.896
Prob(Omnibus):                  0.721   Jarque-Bera (JB):                0.360
Skew:                           0.207   Prob(JB):                        0.835
Kurtosis:                       3.026   Cond. No.                         221.
==============================================================================

In [13]:

    

print('Parameters: ', res.params)
print('Standard errors: ', res.bse)
print('Predicted values: ', res.predict())


    

    




Parameters:  [ 0.46872448  0.48360119 -0.01740479  5.20584496]
Standard errors:  [ 0.02640602  0.10380518  0.00231847  0.17121765]
Predicted values:  [  4.77072516   5.22213464   5.63620761   5.98658823   6.25643234
   6.44117491   6.54928009   6.60085051   6.62432454   6.6518039
   6.71377946   6.83412169   7.02615877   7.29048685   7.61487206
   7.97626054   8.34456611   8.68761335   8.97642389   9.18997755
   9.31866582   9.36587056   9.34740836   9.28893189   9.22171529
   9.17751587   9.1833565    9.25708583   9.40444579   9.61812821
   9.87897556  10.15912843  10.42660281  10.65054491  10.8063004
  10.87946503  10.86825119  10.78378163  10.64826203  10.49133265
  10.34519853  10.23933827  10.19566084  10.22490593  10.32487947
  10.48081414  10.66779556  10.85485568  11.01006072  11.10575781]

In [14]:

    

prstd, iv_l, iv_u = wls_prediction_std(res)

fig, ax = plt.subplots(figsize=(8,6))

ax.plot(x, y, 'o', label="data")
ax.plot(x, y_true, 'b-', label="True")
ax.plot(x, res.fittedvalues, 'r--.', label="OLS")
ax.plot(x, iv_u, 'r--')
ax.plot(x, iv_l, 'r--')
ax.legend(loc='best');


    

In [ ]: