[time-series]
회귀분석
import pandas as pd
from statsmodels.formula.api import ols
# 가져오기
df = pd.read_excel('car.xlsx')
# 분석
m = ols("price ~ mileage", data = df).fit()
# 결과
m.summary()
:::note[output]
c:\Users\eupho\anaconda3\lib\site-packages\pandas\core\arrays\masked.py:60: UserWarning: Pandas requires version '1.3.6' or newer of 'bottleneck' (version '1.3.5' currently installed).
from pandas.core import (
<class 'statsmodels.iolib.summary.Summary'>
"""
OLS Regression Results
==============================================================================
Dep. Variable: price R-squared: 0.457
Model: OLS Adj. R-squared: 0.455
Method: Least Squares F-statistic: 229.1
Date: Thu, 08 Aug 2024 Prob (F-statistic): 5.81e-38
Time: 16:58:38 Log-Likelihood: -1895.7
No. Observations: 274 AIC: 3795.
Df Residuals: 272 BIC: 3803.
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
Intercept 1258.7668 30.599 41.137 0.000 1198.526 1319.008
mileage -0.0052 0.000 -15.136 0.000 -0.006 -0.005
==============================================================================
Omnibus: 0.258 Durbin-Watson: 1.101
Prob(Omnibus): 0.879 Jarque-Bera (JB): 0.108
Skew: 0.032 Prob(JB): 0.947
Kurtosis: 3.074 Cond. No. 1.83e+05
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.83e+05. This might indicate that there are
strong multicollinearity or other numerical problems.
"""
:::
예측
# 새로운 데이터 만들기
new_df = pd.DataFrame({'mileage': [10000, 20000]})
# 모형에 입력하여 예측
m.predict(new_df)
:::note[output]
0 1206.483684
1 1154.200600
dtype: float64
:::
다중회귀분석
ols("price ~ mileage + year", data = df).fit().summary()
:::note[output]
<class 'statsmodels.iolib.summary.Summary'>
"""
OLS Regression Results
==============================================================================
Dep. Variable: price R-squared: 0.749
Model: OLS Adj. R-squared: 0.747
Method: Least Squares F-statistic: 403.5
Date: Thu, 08 Aug 2024 Prob (F-statistic): 5.62e-82
Time: 16:58:39 Log-Likelihood: -1790.2
No. Observations: 274 AIC: 3586.
Df Residuals: 271 BIC: 3597.
Df Model: 2
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
Intercept -1.688e+05 9597.865 -17.592 0.000 -1.88e+05 -1.5e+05
mileage -0.0023 0.000 -8.143 0.000 -0.003 -0.002
year 84.3822 4.761 17.724 0.000 75.009 93.755
==============================================================================
Omnibus: 11.272 Durbin-Watson: 1.598
Prob(Omnibus): 0.004 Jarque-Bera (JB): 11.786
Skew: 0.435 Prob(JB): 0.00276
Kurtosis: 3.523 Cond. No. 8.41e+07
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 8.41e+07. This might indicate that there are
strong multicollinearity or other numerical problems.
"""
:::
표준화
ols("price ~ scale(mileage) + scale(year)", data = df).fit().summary()
:::note[output]
<class 'statsmodels.iolib.summary.Summary'>
"""
OLS Regression Results
==============================================================================
Dep. Variable: price R-squared: 0.749
Model: OLS Adj. R-squared: 0.747
Method: Least Squares F-statistic: 403.5
Date: Thu, 08 Aug 2024 Prob (F-statistic): 5.62e-82
Time: 16:58:39 Log-Likelihood: -1790.2
No. Observations: 274 AIC: 3586.
Df Residuals: 271 BIC: 3597.
Df Model: 2
Covariance Type: nonrobust
==================================================================================
coef std err t P>|t| [0.025 0.975]
----------------------------------------------------------------------------------
Intercept 853.6606 10.112 84.419 0.000 833.752 873.569
scale(mileage) -100.2044 12.306 -8.143 0.000 -124.431 -75.978
scale(year) 218.1006 12.306 17.724 0.000 193.874 242.327
==============================================================================
Omnibus: 11.272 Durbin-Watson: 1.598
Prob(Omnibus): 0.004 Jarque-Bera (JB): 11.786
Skew: 0.435 Prob(JB): 0.00276
Kurtosis: 3.523 Cond. No. 1.91
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
"""
:::
더미코딩
ols("price ~ model", data = df).fit().summary()
:::note[output]
<class 'statsmodels.iolib.summary.Summary'>
"""
OLS Regression Results
==============================================================================
Dep. Variable: price R-squared: 0.011
Model: OLS Adj. R-squared: 0.007
Method: Least Squares F-statistic: 3.039
Date: Thu, 08 Aug 2024 Prob (F-statistic): 0.0824
Time: 16:58:39 Log-Likelihood: -1977.9
No. Observations: 274 AIC: 3960.
Df Residuals: 272 BIC: 3967.
Df Model: 1
Covariance Type: nonrobust
===============================================================================
coef std err t P>|t| [0.025 0.975]
-------------------------------------------------------------------------------
Intercept 833.4146 23.144 36.009 0.000 787.850 878.980
model[T.K3] 80.3970 46.121 1.743 0.082 -10.402 171.196
==============================================================================
Omnibus: 13.893 Durbin-Watson: 0.528
Prob(Omnibus): 0.001 Jarque-Bera (JB): 15.007
Skew: 0.573 Prob(JB): 0.000551
Kurtosis: 3.002 Cond. No. 2.48
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
"""
:::
범주가 3개일 경우
dep = pd.read_excel('depression.xlsx')
ols('y ~ TRT', dep).fit().summary()
:::note[output]
<class 'statsmodels.iolib.summary.Summary'>
"""
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 0.172
Model: OLS Adj. R-squared: 0.122
Method: Least Squares F-statistic: 3.424
Date: Thu, 08 Aug 2024 Prob (F-statistic): 0.0445
Time: 16:58:39 Log-Likelihood: -137.86
No. Observations: 36 AIC: 281.7
Df Residuals: 33 BIC: 286.5
Df Model: 2
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
Intercept 62.3333 3.359 18.557 0.000 55.500 69.167
TRT[T.B] -10.4167 4.750 -2.193 0.035 -20.081 -0.752
TRT[T.C] -11.0833 4.750 -2.333 0.026 -20.748 -1.419
==============================================================================
Omnibus: 0.553 Durbin-Watson: 1.488
Prob(Omnibus): 0.758 Jarque-Bera (JB): 0.544
Skew: -0.267 Prob(JB): 0.762
Kurtosis: 2.721 Cond. No. 3.73
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
"""
:::
선형 회귀분석과 분산 분석
import pingouin as pg
pg.anova(dep, dv='y', between='TRT')
:::note[output]
Source ddof1 ddof2 F p-unc np2
0 TRT 2 33 3.424087 0.044539 0.171857
c:\Users\eupho\anaconda3\lib\site-packages\outdated\utils.py:14: OutdatedPackageWarning: The package pingouin is out of date. Your version is 0.5.3, the latest is 0.5.4.
Set the environment variable OUTDATED_IGNORE=1 to disable these warnings.
return warn(
:::
기준 범주 바꾸기
ols('price ~ C(model, Treatment("K3"))', df).fit().summary()
:::note[output]
<class 'statsmodels.iolib.summary.Summary'>
"""
OLS Regression Results
==============================================================================
Dep. Variable: price R-squared: 0.011
Model: OLS Adj. R-squared: 0.007
Method: Least Squares F-statistic: 3.039
Date: Thu, 08 Aug 2024 Prob (F-statistic): 0.0824
Time: 16:58:40 Log-Likelihood: -1977.9
No. Observations: 274 AIC: 3960.
Df Residuals: 272 BIC: 3967.
Df Model: 1
Covariance Type: nonrobust
=======================================================================================================
coef std err t P>|t| [0.025 0.975]
-------------------------------------------------------------------------------------------------------
Intercept 913.8116 39.893 22.906 0.000 835.273 992.350
C(model, Treatment("K3"))[T.Avante] -80.3970 46.121 -1.743 0.082 -171.196 10.402
==============================================================================
Omnibus: 13.893 Durbin-Watson: 0.528
Prob(Omnibus): 0.001 Jarque-Bera (JB): 15.007
Skew: 0.573 Prob(JB): 0.000551
Kurtosis: 3.002 Cond. No. 3.76
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
"""
:::
무작위 데이터의 예시
무작위로 만든 데이터도 독립변수가 많으면 R제곱이 높게 나옴
import numpy as np
d = np.random.random(size=(10, 21))
d = pd.DataFrame(d, columns=['y'] + [f'x{i}' for i in range(20)])
ols('y ~ x0 + x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8', d).fit().summary()
:::note[output]
<class 'statsmodels.iolib.summary.Summary'>
"""
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 1.000
Model: OLS Adj. R-squared: nan
Method: Least Squares F-statistic: nan
Date: Thu, 08 Aug 2024 Prob (F-statistic): nan
Time: 16:59:03 Log-Likelihood: 318.98
No. Observations: 10 AIC: -618.0
Df Residuals: 0 BIC: -614.9
Df Model: 9
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
Intercept 0.9427 inf 0 nan nan nan
x0 -0.4604 inf -0 nan nan nan
x1 1.2115 inf 0 nan nan nan
x2 -0.2894 inf -0 nan nan nan
x3 -0.5839 inf -0 nan nan nan
x4 -1.0369 inf -0 nan nan nan
x5 -1.5566 inf -0 nan nan nan
x6 1.7873 inf 0 nan nan nan
x7 -1.2252 inf -0 nan nan nan
x8 0.4618 inf 0 nan nan nan
==============================================================================
Omnibus: 1.046 Durbin-Watson: 0.071
Prob(Omnibus): 0.593 Jarque-Bera (JB): 0.826
Skew: 0.543 Prob(JB): 0.662
Kurtosis: 2.104 Cond. No. 69.6
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
"""
:::
교차 검증
from sklearn.model_selection import train_test_split
# 분할
train_df, test_df = train_test_split(
df, # 원자료
test_size=0.2, # 테스트 데이터의 비율(0.2 = 20%)
random_state=42) # 난수 생성의 seed를을 고정(동일한 분할을 위해)
# 분석
m = ols('price ~ year', train_df).fit()
# 예측
y_pred = m.predict(test_df)
# 잔차 분산
from sklearn.metrics import mean_squared_error
mean_squared_error(test_df.price, y_pred)
:::note[output]
34805.44825035994
:::