numpy.polyfit 系数的 t 值和 Pr(>|t|)

问题描述

我想使用 numpy.polyfit 确定拟合到某些数据的多项式模型中系数的显着性.

I want to determine the significance of the coefficients in a polynomial model fitted to some data using numpy.polyfit.

这个是我想使用 R 实现的一个例子.基本上，我需要使用 scipy/numpy 获取 R 的摘要"函数输出.有没有一种简单的方法可以使用 scipy/numpy(一些内置的帮助函数?)或者我应该使用 rpy 代替?

This is an example of what I want to achieve using R. Basically, I need to get what R's "summary" function outputs with scipy/numpy. Is there an easy way to do this with scipy/numpy (some built-in helper function?) or should I just go with rpy instead?

推荐答案

使用 statsmodels:

Use statsmodels:

import pandas as pd
import statsmodels.formula.api as smf
df = pd.DataFrame(
    {"year":[1959, 1960, 1961, 1962, 1963, 1964, 1965, 1966, 1967, 1968, 1969],
    "population":[4835, 4970, 5085, 5160, 5310, 5260, 5235, 5255, 5235, 5210, 5175]})
df.year -= 1964

results = smf.ols('population ~ year + I(year**2)', data=df).fit()
print results.summary()

这里是输出:

                            OLS Regression Results
==============================================================================
Dep. Variable:             population   R-squared:                       0.941
Model:                            OLS   Adj. R-squared:                  0.926
Method:                 Least Squares   F-statistic:                     63.48
Date:                Fri, 07 Mar 2014   Prob (F-statistic):           1.23e-05
Time:                        14:53:22   Log-Likelihood:                -54.089
No. Observations:                  11   AIC:                             114.2
Df Residuals:                       8   BIC:                             115.4
Df Model:                           2
================================================================================
                   coef    std err          t      P>|t|      [95.0% Conf. Int.]
--------------------------------------------------------------------------------
Intercept     5263.1585     17.655    298.110      0.000      5222.446  5303.871
year            29.3182      3.696      7.933      0.000        20.796    37.841
I(year ** 2)   -10.5886      1.323     -8.002      0.000       -13.640    -7.537
==============================================================================
Omnibus:                       10.349   Durbin-Watson:                   1.669
Prob(Omnibus):                  0.006   Jarque-Bera (JB):                4.954
Skew:                           1.379   Prob(JB):                       0.0840
Kurtosis:                       4.789   Cond. No.                         20.2
==============================================================================

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