Python statsmodel 输出和 Excel/Google Sheet 输出不匹配
Python statsmodel outpput and Excel/Google Sheet output doesn't match
我有一个小数据集，由于某种原因，输出与 Excel 的不匹配。
这是我所做的。我必须列：
Miles Traveled
Travel Time
89
7.0
66
5.4
78
6.6
111
7.4
44
4.8
77
6.4
80
7.0
66
5.6
109
7.3
76
6.4
这是我在 Google Sheet:
上得到的输出
Slope
Intercept
Coefficient
0.04025678079
3.185560249
Standard Error
0.005706415564
0.4669507938
R Squared, Standard Error
0.8615153295
0.3423088398
F Stat
49.76812677
8
Regression SS / Residual SS
5.831597265
0.9374027345
此输出也与 excel 输出匹配。
但是，当我在 statsmodel 上执行以下操作时：
milesTravelled = [89.0, 66.0, 78.0, 111.0, 44.0, 77.0, 80.0, 66.0, 109.0, 76.0]
travelTime = [7.0, 5.4, 6.6, 7.4, 4.8, 6.4, 7.0, 5.6, 7.3, 6.4]
model = sm.OLS(travelTime, milesTraveled).fit()
print(model.summary())
我得到以下信息：
OLS Regression Results
=======================================================================================
Dep. Variable: Travel Time R-squared (uncentered): 0.985
Model: OLS Adj. R-squared (uncentered): 0.983
Method: Least Squares F-statistic: 575.6
Date: Mon, 01 Feb 2021 Prob (F-statistic): 1.82e-09
Time: 10:18:44 Log-Likelihood: -11.951
No. Observations: 10 AIC: 25.90
Df Residuals: 9 BIC: 26.20
Df Model: 1
Covariance Type: nonrobust
==================================================================================
coef std err t P>|t| [0.025 0.975]
----------------------------------------------------------------------------------
Miles Traveled 0.0781 0.003 23.991 0.000 0.071 0.085
==============================================================================
Omnibus: 2.179 Durbin-Watson: 2.654
Prob(Omnibus): 0.336 Jarque-Bera (JB): 1.033
Skew: -0.777 Prob(JB): 0.597
Kurtosis: 2.741 Cond. No. 1.00
==============================================================================
如您所见，标准误差、R 平方等的值与 Google Sheet/Excel 完全不匹配。我究竟做错了什么？我该怎么做才能获得准确的结果摘要，例如 Google Sheet/Excel?
默认情况下，OLS class 不包括线性模型中的常数项。您可以使用 sm.add_constant 为 OLS:
创建适当的 exog 参数
In [36]: milesTraveled = [89.0, 66.0, 78.0, 111.0, 44.0, 77.0, 80.0, 66.0, 109.0, 76.0]
In [37]: travelTime = [7.0, 5.4, 6.6, 7.4, 4.8, 6.4, 7.0, 5.6, 7.3, 6.4]
In [38]: X = sm.add_constant(milesTraveled)
In [39]: model = sm.OLS(travelTime, X).fit()
In [40]: print(model.summary())
/Users/warren/a2020.11/lib/python3.8/site-packages/scipy/stats/stats.py:1603: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=10
warnings.warn("kurtosistest only valid for n>=20 ... continuing "
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 0.862
Model: OLS Adj. R-squared: 0.844
Method: Least Squares F-statistic: 49.77
Date: Mon, 01 Feb 2021 Prob (F-statistic): 0.000107
Time: 13:04:53 Log-Likelihood: -2.3532
No. Observations: 10 AIC: 8.706
Df Residuals: 8 BIC: 9.312
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 3.1856 0.467 6.822 0.000 2.109 4.262
x1 0.0403 0.006 7.055 0.000 0.027 0.053
==============================================================================
Omnibus: 0.542 Durbin-Watson: 2.608
Prob(Omnibus): 0.763 Jarque-Bera (JB): 0.554
Skew: 0.370 Prob(JB): 0.758
Kurtosis: 2.115 Cond. No. 353.
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
我有一个小数据集，由于某种原因，输出与 Excel 的不匹配。
这是我所做的。我必须列：
| Miles Traveled | Travel Time |
|---|---|
| 89 | 7.0 |
| 66 | 5.4 |
| 78 | 6.6 |
| 111 | 7.4 |
| 44 | 4.8 |
| 77 | 6.4 |
| 80 | 7.0 |
| 66 | 5.6 |
| 109 | 7.3 |
| 76 | 6.4 |
这是我在 Google Sheet:
上得到的输出| Slope | Intercept | |
|---|---|---|
| Coefficient | 0.04025678079 | 3.185560249 |
| Standard Error | 0.005706415564 | 0.4669507938 |
| R Squared, Standard Error | 0.8615153295 | 0.3423088398 |
| F Stat | 49.76812677 | 8 |
| Regression SS / Residual SS | 5.831597265 | 0.9374027345 |
此输出也与 excel 输出匹配。
但是，当我在 statsmodel 上执行以下操作时：
milesTravelled = [89.0, 66.0, 78.0, 111.0, 44.0, 77.0, 80.0, 66.0, 109.0, 76.0]
travelTime = [7.0, 5.4, 6.6, 7.4, 4.8, 6.4, 7.0, 5.6, 7.3, 6.4]
model = sm.OLS(travelTime, milesTraveled).fit()
print(model.summary())
我得到以下信息：
OLS Regression Results
=======================================================================================
Dep. Variable: Travel Time R-squared (uncentered): 0.985
Model: OLS Adj. R-squared (uncentered): 0.983
Method: Least Squares F-statistic: 575.6
Date: Mon, 01 Feb 2021 Prob (F-statistic): 1.82e-09
Time: 10:18:44 Log-Likelihood: -11.951
No. Observations: 10 AIC: 25.90
Df Residuals: 9 BIC: 26.20
Df Model: 1
Covariance Type: nonrobust
==================================================================================
coef std err t P>|t| [0.025 0.975]
----------------------------------------------------------------------------------
Miles Traveled 0.0781 0.003 23.991 0.000 0.071 0.085
==============================================================================
Omnibus: 2.179 Durbin-Watson: 2.654
Prob(Omnibus): 0.336 Jarque-Bera (JB): 1.033
Skew: -0.777 Prob(JB): 0.597
Kurtosis: 2.741 Cond. No. 1.00
==============================================================================
如您所见，标准误差、R 平方等的值与 Google Sheet/Excel 完全不匹配。我究竟做错了什么？我该怎么做才能获得准确的结果摘要，例如 Google Sheet/Excel?
默认情况下，OLS class 不包括线性模型中的常数项。您可以使用 sm.add_constant 为 OLS:
exog 参数
In [36]: milesTraveled = [89.0, 66.0, 78.0, 111.0, 44.0, 77.0, 80.0, 66.0, 109.0, 76.0]
In [37]: travelTime = [7.0, 5.4, 6.6, 7.4, 4.8, 6.4, 7.0, 5.6, 7.3, 6.4]
In [38]: X = sm.add_constant(milesTraveled)
In [39]: model = sm.OLS(travelTime, X).fit()
In [40]: print(model.summary())
/Users/warren/a2020.11/lib/python3.8/site-packages/scipy/stats/stats.py:1603: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=10
warnings.warn("kurtosistest only valid for n>=20 ... continuing "
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 0.862
Model: OLS Adj. R-squared: 0.844
Method: Least Squares F-statistic: 49.77
Date: Mon, 01 Feb 2021 Prob (F-statistic): 0.000107
Time: 13:04:53 Log-Likelihood: -2.3532
No. Observations: 10 AIC: 8.706
Df Residuals: 8 BIC: 9.312
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 3.1856 0.467 6.822 0.000 2.109 4.262
x1 0.0403 0.006 7.055 0.000 0.027 0.053
==============================================================================
Omnibus: 0.542 Durbin-Watson: 2.608
Prob(Omnibus): 0.763 Jarque-Bera (JB): 0.554
Skew: 0.370 Prob(JB): 0.758
Kurtosis: 2.115 Cond. No. 353.
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.