Statsmodels.formula.api OLS does not show statistical values of intercept

Question

I am running the following source code:

import statsmodels.formula.api as sm

# Add one column of ones for the intercept term
X = np.append(arr= np.ones((50, 1)).astype(int), values=X, axis=1)

regressor_OLS = sm.OLS(endog=y, exog=X).fit()
print(regressor_OLS.summary())

where

X is an 50x5 (before adding the intercept term) numpy array which looks like this:

[[0 1 165349.20 136897.80 471784.10]
 [0 0 162597.70 151377.59 443898.53]...]

and y is a a 50x1 numpy array with float values for the dependent variable.

The first two columns are for a dummy variable with three different values. The rest of the columns are three different indepedent variables.

Although, it is said that the statsmodels.formula.api.OLS adds automatically an intercept term (see @stellacia's answer here: OLS using statsmodel.formula.api versus statsmodel.api) its summary does not show the statistical values of the intercept term as it evident below in my case:

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                 Profit   R-squared:                       0.988
Model:                            OLS   Adj. R-squared:                  0.986
Method:                 Least Squares   F-statistic:                     727.1
Date:                Sun, 01 Jul 2018   Prob (F-statistic):           7.87e-42
Time:                        21:40:23   Log-Likelihood:                -545.15
No. Observations:                  50   AIC:                             1100.
Df Residuals:                      45   BIC:                             1110.
Df Model:                           5                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
x1          3464.4536   4905.406      0.706      0.484   -6415.541    1.33e+04
x2          5067.8937   4668.238      1.086      0.283   -4334.419    1.45e+04
x3             0.7182      0.066     10.916      0.000       0.586       0.851
x4             0.3113      0.035      8.885      0.000       0.241       0.382
x5             0.0786      0.023      3.429      0.001       0.032       0.125
==============================================================================
Omnibus:                        1.355   Durbin-Watson:                   1.288
Prob(Omnibus):                  0.508   Jarque-Bera (JB):                1.241
Skew:                          -0.237   Prob(JB):                        0.538
Kurtosis:                       2.391   Cond. No.                     8.28e+05
==============================================================================

For this reason, I added to my source code the line:

X = np.append(arr= np.ones((50, 1)).astype(int), values=X, axis=1)

as you can see at the beginning of my post and the statistical values of the intercept/constant are shown as below:

 OLS Regression Results                            
==============================================================================
Dep. Variable:                 Profit   R-squared:                       0.951
Model:                            OLS   Adj. R-squared:                  0.945
Method:                 Least Squares   F-statistic:                     169.9
Date:                Sun, 01 Jul 2018   Prob (F-statistic):           1.34e-27
Time:                        20:25:21   Log-Likelihood:                -525.38
No. Observations:                  50   AIC:                             1063.
Df Residuals:                      44   BIC:                             1074.
Df Model:                           5                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const       5.013e+04   6884.820      7.281      0.000    3.62e+04     6.4e+04
x1           198.7888   3371.007      0.059      0.953   -6595.030    6992.607
x2           -41.8870   3256.039     -0.013      0.990   -6604.003    6520.229
x3             0.8060      0.046     17.369      0.000       0.712       0.900
x4            -0.0270      0.052     -0.517      0.608      -0.132       0.078
x5             0.0270      0.017      1.574      0.123      -0.008       0.062
==============================================================================
Omnibus:                       14.782   Durbin-Watson:                   1.283
Prob(Omnibus):                  0.001   Jarque-Bera (JB):               21.266
Skew:                          -0.948   Prob(JB):                     2.41e-05
Kurtosis:                       5.572   Cond. No.                     1.45e+06
==============================================================================

Why the statistical values of the intercept are not showing when I do not add my myself an intercept term even though it is said that statsmodels.formula.api.OLS is adding this automatically?

Answer 1

Can use this X = sm.add_constant(X)

Answer 2

"No constant is added by the model unless you are using formulas." Therefore try something like below example. Variable names should be defined according to your data set.

Use,

regressor_OLS  = smf.ols(formula='Y_variable ~ X_variable', data=df).fit()

instead of,

regressor_OLS = sm.OLS(endog=y, exog=X).fit()