Statsmodels Library -- linear regression model

Catalog

Simple linear regression model

Multiple linear regression model

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Yes statsmodels The linear regression model collation of the library can be compared with sklearn The arrangement of the linear regression model of the library can be used for reference ​​​​​​​https://blog.csdn.net/qq_57099024/article/details/122324764https://blog.csdn.net/qq_57099024/article/details/122324764

Simple linear regression model

import statsmodels.formula.api as smf
import seaborn as sns
import pandas as pd
tips=sns.load_dataset('tips')# download seaborn Native data set tips
print(tips.head())# View the acquired dataset tips The first five elements of 

   total_bill   tip     sex smoker  day    time  size
0       16.99  1.01  Female     No  Sun  Dinner     2
1       10.34  1.66    Male     No  Sun  Dinner     3
2       21.01  3.50    Male     No  Sun  Dinner     3
3       23.68  3.31    Male     No  Sun  Dinner     2
4       24.59  3.61  Female     No  Sun  Dinner     4

# Specify the model , To the left of the wave line is the response variable , On the right is the independent variable 
model=smf.ols(formula='tip~total_bill',data=tips)
# Use fit Methods to fit the model 
results=model.fit()
# Use summary Method to view the results of the fitted model 
print(results.summary())

OLS Regression Results                            
==============================================================================
Dep. Variable:                    tip   R-squared:                       0.457
Model:                            OLS   Adj. R-squared:                  0.454
Method:                 Least Squares   F-statistic:                     203.4
Date:                Wed, 05 Jan 2022   Prob (F-statistic):           6.69e-34
Time:                        14:34:42   Log-Likelihood:                -350.54
No. Observations:                 244   AIC:                             705.1
Df Residuals:                     242   BIC:                             712.1
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept      0.9203      0.160      5.761      0.000       0.606       1.235
total_bill     0.1050      0.007     14.260      0.000       0.091       0.120
==============================================================================
Omnibus:                       20.185   Durbin-Watson:                   2.151
Prob(Omnibus):                  0.000   Jarque-Bera (JB):               37.750
Skew:                           0.443   Prob(JB):                     6.35e-09
Kurtosis:                       4.711   Cond. No.                         53.0
==============================================================================

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

The results include the Intercept（ intercept ） and total_bill. With these parameters, we can get the linear equation y=0.105x+0.920. These figures can be interpreted as ：total_bill Every additional unit （ That is, the amount of each consumption increase 1 dollar ）, Consumption increases 0.105 Units if you only need a coefficient , Can end results Of params Property to get .

print(results.params)

Intercept     0.920270
total_bill    0.105025
dtype: float64

Multiple linear regression model

statsmodels Will automatically create a dummy variable , And remove reference variables to avoid multicollinearity , For example, gender is divided into male and female , Then the system will select the first male as the reference variable , After deletion, the male column will not be converted into a dummy variable , It will not become a factor that affects the response variable

import statsmodels.formula.api as smf
import seaborn as sns
import pandas as pd
tips=sns.load_dataset('tips')
print(tips.head())
print('----'*10)# Output horizontal lines to distinguish output 
# Use the plus sign to pass multiple arguments into 
model=smf.ols(formula='tip~total_bill+size+sex+smoker+day+time',data=tips)
results=model.fit()
print(results.summary())
print('----'*10)
print(results.params)

   total_bill   tip     sex smoker  day    time  size
0       16.99  1.01  Female     No  Sun  Dinner     2
1       10.34  1.66    Male     No  Sun  Dinner     3
2       21.01  3.50    Male     No  Sun  Dinner     3
3       23.68  3.31    Male     No  Sun  Dinner     2
4       24.59  3.61  Female     No  Sun  Dinner     4
----------------------------------------
                            OLS Regression Results                            
==============================================================================
Dep. Variable:                    tip   R-squared:                       0.470
Model:                            OLS   Adj. R-squared:                  0.452
Method:                 Least Squares   F-statistic:                     26.06
Date:                Wed, 05 Jan 2022   Prob (F-statistic):           1.20e-28
Time:                        16:27:12   Log-Likelihood:                -347.48
No. Observations:                 244   AIC:                             713.0
Df Residuals:                     235   BIC:                             744.4
Df Model:                           8                                         
Covariance Type:            nonrobust                                         
==================================================================================
                     coef    std err          t      P>|t|      [0.025      0.975]
----------------------------------------------------------------------------------
Intercept          0.5908      0.256      2.310      0.022       0.087       1.095
sex[T.Female]      0.0324      0.142      0.229      0.819      -0.247       0.311
smoker[T.No]       0.0864      0.147      0.589      0.556      -0.202       0.375
day[T.Fri]         0.1623      0.393      0.412      0.680      -0.613       0.937
day[T.Sat]         0.0408      0.471      0.087      0.931      -0.886       0.968
day[T.Sun]         0.1368      0.472      0.290      0.772      -0.793       1.066
time[T.Dinner]    -0.0681      0.445     -0.153      0.878      -0.944       0.808
total_bill         0.0945      0.010      9.841      0.000       0.076       0.113
size               0.1760      0.090      1.966      0.051      -0.000       0.352
==============================================================================
Omnibus:                       27.860   Durbin-Watson:                   2.096
Prob(Omnibus):                  0.000   Jarque-Bera (JB):               52.555
Skew:                           0.607   Prob(JB):                     3.87e-12
Kurtosis:                       4.923   Cond. No.                         281.
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
----------------------------------------
Intercept         0.590837
sex[T.Female]     0.032441
smoker[T.No]      0.086408
day[T.Fri]        0.162259
day[T.Sat]        0.040801
day[T.Sun]        0.136779
time[T.Dinner]   -0.068129
total_bill        0.094487
size              0.175992
dtype: float64