我在玩scikit elarn和statsmodels，我从make_regression函数生成了数组，以适合statsmodels
from sklearn.datasets import make_regression
x,y,coef = make_regression(n_samples=10000,n_informative=10,coef=True)
所以我有10个变量在回归中似乎很重要。
但是，当我从statsmodels运行api来检查哪个是“真正的生成器”时：
import statsmodels.api as sm
x = sm.add_constant(x, prepend=False)
mod = sm.OLS(y,x)
res = mod.fit()
res.summary()
它给了我：
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 1.000
Model: OLS Adj. R-squared: 1.000
Method: Least Squares F-statistic: 2.336e+31
Date: Fri, 20 Sep 2019 Prob (F-statistic): 0.00
Time: 15:38:01 Log-Likelihood: 2.7280e+05
No. Observations: 10000 AIC: -5.454e+05
Df Residuals: 9899 BIC: -5.447e+05
Df Model: 100
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
x1 24.0004 3.5e-15 6.85e+15 0.000 24.000 24.000
x2 1.11e-14 3.49e-15 3.183 0.001 4.27e-15 1.79e-14
x3 2.953e-14 3.46e-15 8.546 0.000 2.28e-14 3.63e-14
x4 40.4471 3.46e-15 1.17e+16 0.000 40.447 40.447
x5 -2.665e-14 3.49e-15 -7.629 0.000 -3.35e-14 -1.98e-14
x6 -1.887e-15 3.43e-15 -0.550 0.583 -8.62e-15 4.84e-15
x7 2.578e-14 3.45e-15 7.474 0.000 1.9e-14 3.25e-14
x8 -2.265e-14 3.45e-15 -6.568 0.000 -2.94e-14 -1.59e-14
x9 5.662e-15 3.49e-15 1.621 0.105 -1.19e-15 1.25e-14
x10 -7.772e-14 3.45e-15 -22.497 0.000 -8.45e-14 -7.09e-14
x11 2.143e-14 3.51e-15 6.109 0.000 1.46e-14 2.83e-14
x12 5.318e-14 3.48e-15 15.269 0.000 4.64e-14 6e-14
x13 -3.952e-14 3.49e-15 -11.340 0.000 -4.64e-14 -3.27e-14
x14 3.642e-14 3.45e-15 10.556 0.000 2.97e-14 4.32e-14
x15 -6.661e-16 3.51e-15 -0.190 0.849 -7.54e-15 6.21e-15
x16 -2.637e-14 3.49e-15 -7.556 0.000 -3.32e-14 -1.95e-14
x17 5.135e-14 3.5e-15 14.672 0.000 4.45e-14 5.82e-14
x18 4.718e-15 3.45e-15 1.369 0.171 -2.04e-15 1.15e-14
x19 3.186e-14 3.5e-15 9.112 0.000 2.5e-14 3.87e-14
x20 -1.488e-14 3.44e-15 -4.319 0.000 -2.16e-14 -8.13e-15
x21 -2.998e-14 3.41e-15 -8.790 0.000 -3.67e-14 -2.33e-14
x22 -5.118e-14 3.52e-15 -14.560 0.000 -5.81e-14 -4.43e-14
x23 -2.354e-14 3.5e-15 -6.717 0.000 -3.04e-14 -1.67e-14
x24 -8.16e-15 3.44e-15 -2.375 0.018 -1.49e-14 -1.42e-15
x25 1.443e-15 3.45e-15 0.418 0.676 -5.33e-15 8.21e-15
x26 -2.331e-15 3.51e-15 -0.664 0.507 -9.22e-15 4.55e-15
x27 -7.383e-15 3.44e-15 -2.144 0.032 -1.41e-14 -6.34e-16
x28 -3.175e-14 3.48e-15 -9.128 0.000 -3.86e-14 -2.49e-14
x29 1.887e-15 3.52e-15 0.537 0.591 -5e-15 8.78e-15
x30 -8.993e-15 3.5e-15 -2.571 0.010 -1.58e-14 -2.14e-15
x31 -1.432e-14 3.46e-15 -4.138 0.000 -2.11e-14 -7.54e-15
x32 -5.307e-14 3.47e-15 -15.309 0.000 -5.99e-14 -4.63e-14
x33 -4.036e-14 3.49e-15 -11.550 0.000 -4.72e-14 -3.35e-14
x34 -2.297e-14 3.46e-15 -6.631 0.000 -2.98e-14 -1.62e-14
x35 1.776e-15 3.48e-15 0.510 0.610 -5.05e-15 8.6e-15
x36 2.184e-14 3.48e-15 6.278 0.000 1.5e-14 2.87e-14
x37 61.7653 3.46e-15 1.79e+16 0.000 61.765 61.765
x38 -1.332e-15 3.48e-15 -0.383 0.702 -8.16e-15 5.49e-15
x39 -1.577e-14 3.52e-15 -4.478 0.000 -2.27e-14 -8.86e-15
x40 1.849e-14 3.48e-15 5.317 0.000 1.17e-14 2.53e-14
x41 -1.965e-14 3.46e-15 -5.685 0.000 -2.64e-14 -1.29e-14
x42 -2.265e-14 3.42e-15 -6.614 0.000 -2.94e-14 -1.59e-14
x43 -4.73e-14 3.48e-15 -13.594 0.000 -5.41e-14 -4.05e-14
x44 -2.176e-14 3.44e-15 -6.324 0.000 -2.85e-14 -1.5e-14
x45 -5.568e-14 3.49e-15 -15.959 0.000 -6.25e-14 -4.88e-14
x46 6.883e-15 3.5e-15 1.967 0.049 2.29e-17 1.37e-14
x47 2.454e-14 3.5e-15 7.005 0.000 1.77e-14 3.14e-14
x48 3.12e-14 3.46e-15 9.016 0.000 2.44e-14 3.8e-14
x49 -1.515e-14 3.42e-15 -4.432 0.000 -2.19e-14 -8.45e-15
x50 3.553e-15 3.48e-15 1.021 0.307 -3.27e-15 1.04e-14
x51 7.484e-14 3.48e-15 21.533 0.000 6.8e-14 8.17e-14
x52 -2.276e-15 3.43e-15 -0.663 0.507 -9e-15 4.45e-15
x53 -3.908e-14 3.44e-15 -11.377 0.000 -4.58e-14 -3.23e-14
x54 -5.329e-15 3.48e-15 -1.531 0.126 -1.22e-14 1.49e-15
x55 -2.176e-14 3.43e-15 -6.352 0.000 -2.85e-14 -1.5e-14
x56 -5.917e-14 3.41e-15 -17.334 0.000 -6.59e-14 -5.25e-14
x57 5.54e-14 3.51e-15 15.769 0.000 4.85e-14 6.23e-14
x58 1.532e-14 3.48e-15 4.406 0.000 8.5e-15 2.21e-14
x59 -3.064e-14 3.48e-15 -8.805 0.000 -3.75e-14 -2.38e-14
x60 12.2240 3.45e-15 3.54e+15 0.000 12.224 12.224
x61 -2.964e-14 3.49e-15 -8.504 0.000 -3.65e-14 -2.28e-14
x62 -6.384e-16 3.48e-15 -0.184 0.854 -7.45e-15 6.18e-15
x63 75.2689 3.5e-15 2.15e+16 0.000 75.269 75.269
x64 -3.264e-14 3.46e-15 -9.445 0.000 -3.94e-14 -2.59e-14
x65 5.085e-14 3.49e-15 14.574 0.000 4.4e-14 5.77e-14
x66 -1.743e-14 3.48e-15 -5.010 0.000 -2.43e-14 -1.06e-14
x67 3.131e-14 3.46e-15 9.057 0.000 2.45e-14 3.81e-14
x68 3.63e-14 3.52e-15 10.308 0.000 2.94e-14 4.32e-14
x69 3.919e-14 3.52e-15 11.143 0.000 3.23e-14 4.61e-14
x70 14.7147 3.5e-15 4.21e+15 0.000 14.715 14.715
x71 7.438e-15 3.43e-15 2.168 0.030 7.14e-16 1.42e-14
x72 6.106e-16 3.48e-15 0.176 0.861 -6.2e-15 7.42e-15
x73 1.826e-14 3.48e-15 5.247 0.000 1.14e-14 2.51e-14
x74 1.565e-14 3.48e-15 4.498 0.000 8.83e-15 2.25e-14
x75 5.662e-15 3.47e-15 1.631 0.103 -1.14e-15 1.25e-14
x76 1.821e-14 3.51e-15 5.193 0.000 1.13e-14 2.51e-14
x77 2.798e-14 3.48e-15 8.036 0.000 2.12e-14 3.48e-14
x78 47.3326 3.5e-15 1.35e+16 0.000 47.333 47.333
x79 -2.376e-14 3.47e-15 -6.838 0.000 -3.06e-14 -1.69e-14
x80 -1.266e-14 3.47e-15 -3.644 0.000 -1.95e-14 -5.85e-15
x81 2.953e-14 3.49e-15 8.454 0.000 2.27e-14 3.64e-14
x82 30.8112 3.47e-15 8.88e+15 0.000 30.811 30.811
x83 6.117e-14 3.51e-15 17.453 0.000 5.43e-14 6.8e-14
x84 51.1612 3.48e-15 1.47e+16 0.000 51.161 51.161
x85 -2.603e-14 3.51e-15 -7.411 0.000 -3.29e-14 -1.91e-14
x86 -2.953e-14 3.46e-15 -8.525 0.000 -3.63e-14 -2.27e-14
x87 97.7774 3.44e-15 2.84e+16 0.000 97.777 97.777
x88 4.108e-14 3.46e-15 11.863 0.000 3.43e-14 4.79e-14
x89 5.24e-14 3.49e-15 15.009 0.000 4.56e-14 5.92e-14
x90 6.772e-15 3.49e-15 1.940 0.052 -7.08e-17 1.36e-14
x91 1.332e-14 3.48e-15 3.829 0.000 6.5e-15 2.01e-14
x92 -9.881e-15 3.49e-15 -2.828 0.005 -1.67e-14 -3.03e-15
x93 -1.166e-14 3.51e-15 -3.321 0.001 -1.85e-14 -4.78e-15
x94 3.431e-14 3.52e-15 9.754 0.000 2.74e-14 4.12e-14
x95 -2.531e-14 3.46e-15 -7.321 0.000 -3.21e-14 -1.85e-14
x96 7.105e-15 3.49e-15 2.036 0.042 2.63e-16 1.39e-14
x97 1.732e-14 3.46e-15 5.009 0.000 1.05e-14 2.41e-14
x98 -2.315e-14 3.45e-15 -6.704 0.000 -2.99e-14 -1.64e-14
x99 2.665e-14 3.5e-15 7.618 0.000 1.98e-14 3.35e-14
x100 7.235e-14 3.51e-15 20.639 0.000 6.55e-14 7.92e-14
const 6.883e-15 3.48e-15 1.980 0.048 6.83e-17 1.37e-14
==============================================================================
Omnibus: 0.635 Durbin-Watson: 1.959
Prob(Omnibus): 0.728 Jarque-Bera (JB): 0.653
Skew: 0.018 Prob(JB): 0.721
Kurtosis: 2.986 Cond. No. 1.22
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
不是statsmodels的p值仅返回约10个变量的“好” p值吗？