statsmodels の summary の t について

どうやら、tは 標本分布を t分布と仮定した際の coef=0 の T の値っぽい。
t が 0から遠ければ遠いほど、coef が 0でない確率が高い。要は相関がある。

from patsy import dmatrices
import statsmodels.api as sm

df = sm.datasets.get_rdataset("Guerry", "HistData").data

vars = ['Department', 'Lottery', 'Literacy', 'Wealth', 'Region']

df = df[vars].dropna()

y, X = dmatrices('Lottery ~ Literacy + Wealth + Region', data=df, return_type='dataframe')
mod = sm.OLS(y, X) 
res = mod.fit()
res.summary()
 OLS Regression Results                            
==============================================================================
Dep. Variable:                Lottery   R-squared:                       0.338
Model:                            OLS   Adj. R-squared:                  0.287
Method:                 Least Squares   F-statistic:                     6.636
Date:                Wed, 17 Apr 2019   Prob (F-statistic):           1.07e-05
Time:                        14:49:35   Log-Likelihood:                -375.30
No. Observations:                  85   AIC:                             764.6
Df Residuals:                      78   BIC:                             781.7
Df Model:                           6                                         
Covariance Type:            nonrobust                                         
===============================================================================
                  coef    std err          t      P>|t|      [0.025      0.975]
-------------------------------------------------------------------------------
Intercept      38.6517      9.456      4.087      0.000      19.826      57.478
Region[T.E]   -15.4278      9.727     -1.586      0.117     -34.793       3.938
Region[T.N]   -10.0170      9.260     -1.082      0.283     -28.453       8.419
Region[T.S]    -4.5483      7.279     -0.625      0.534     -19.039       9.943
Region[T.W]   -10.0913      7.196     -1.402      0.165     -24.418       4.235
Literacy       -0.1858      0.210     -0.886      0.378      -0.603       0.232
Wealth          0.4515      0.103      4.390      0.000       0.247       0.656
==============================================================================
Omnibus:                        3.049   Durbin-Watson:                   1.785
Prob(Omnibus):                  0.218   Jarque-Bera (JB):                2.694
Skew:                          -0.340   Prob(JB):                        0.260
Kurtosis:                       2.454   Cond. No.                         371.
==============================================================================

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

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