(단순) 선형 회귀 분석, ols, LinearRegression

 

선형 회귀 분석 (단순)¶

¶

많이 사용하는 두가지 패키지가 있음¶

In [2]:

# statsmodels ols
from statsmodels.formula.api import ols 

In [12]:

# sklearn LinearRegression
from sklearn.linear_model import LinearRegression 

In [20]:

# 오차 계산
from sklearn.metrics import mean_squared_error # MSE -> 제곱근 RMSE
from sklearn.metrics import mean_absolute_error # MAE

In [21]:

# 테스트 셋을 나누기
from sklearn.model_selection import train_test_split

https://github.com/tidyverse/ggplot2/blob/main/data-raw/diamonds.csv 시험용 여기에서 다운로드¶

In [22]:

import pandas as pd
dia = pd.read_csv("diamonds.csv")
dia_train, dia_test = train_test_split(dia ,train_size=0.7,random_state=123)

In [35]:

dia.head()

Out[35]:

	carat	cut	color	clarity	depth	table	price	x	y	z
0	0.23	Ideal	E	SI2	61.5	55.0	326	3.95	3.98	2.43
1	0.21	Premium	E	SI1	59.8	61.0	326	3.89	3.84	2.31
2	0.23	Good	E	VS1	56.9	65.0	327	4.05	4.07	2.31
3	0.29	Premium	I	VS2	62.4	58.0	334	4.20	4.23	2.63
4	0.31	Good	J	SI2	63.3	58.0	335	4.34	4.35	2.75

¶

ols¶

In [9]:

from statsmodels.formula.api import ols

기본 패턴¶

model = ols(formula=" y ~ X1 ",data=df).fit() # X가 여러개인 경우 formula y ~ X1 + X2 + X3 형태로 표현¶

model.summary() # 결정 계수 R제곱 값이 나옴, 절편 intercept 나옴¶

model.predict(df.iloc[xxx,xxx])¶

In [14]:

# X가 1개인 경우 X:carat y:price

In [16]:

formula="price~carat"

In [23]:

model = ols(formula=formula,data=dia_train).fit()
model

Out[23]:

<statsmodels.regression.linear_model.RegressionResultsWrapper at 0x25888935d90>

In [24]:

model.summary()

Out[24]:

OLS Regression Results

Dep. Variable:	price	R-squared:	0.849
Model:	OLS	Adj. R-squared:	0.849
Method:	Least Squares	F-statistic:	2.125e+05
Date:	Sun, 27 Nov 2022	Prob (F-statistic):	0.00
Time:	19:14:35	Log-Likelihood:	-3.3090e+05
No. Observations:	37758	AIC:	6.618e+05
Df Residuals:	37756	BIC:	6.618e+05
Df Model:	1
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
Intercept	-2261.4691	15.636	-144.630	0.000	-2292.117	-2230.822
carat	7760.7979	16.835	460.985	0.000	7727.800	7793.795

Omnibus:	9750.769	Durbin-Watson:	1.990
Prob(Omnibus):	0.000	Jarque-Bera (JB):	108813.279
Skew:	0.923	Prob(JB):	0.00
Kurtosis:	11.109	Cond. No.	3.66

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

In [29]:

dia_test["predict"] = model.predict(dia_test)

In [30]:

mean_squared_error(y_true=dia_test["price"],y_pred=dia_test["predict"])**0.5

Out[30]:

1549.1452107597029

¶

sklearn LinerRegression()¶

In [ ]:

from sklearn.linear_model import LinearRegression

기본 패턴¶

model = LinearRegression().fit(X=df[["X컬럼"]],y=df[["Y컬럼"]])¶

model.coef_¶

model.intercept_¶

model.predict(df[["X컬럼"]])¶

In [31]:

# X가 1개인 경우 X:carat y:price

In [32]:

model = LinearRegression().fit(X=dia_train[["carat"]],y=dia_train[["price"]])
model

Out[32]:

LinearRegression()

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In [33]:

model.coef_

Out[33]:

array([[7760.79786937]])

In [34]:

model.intercept_

Out[34]:

array([-2261.46912291])

In [36]:

dia_test["predict"] = model.predict(dia_test[["carat"]])

In [37]:

mean_squared_error(y_true=dia_test["price"],y_pred=dia_test["predict"])**0.5

Out[37]:

1549.1452107597036