(6) Linear regression algorithm

1. Import the package

import numpy as np
import matplotlib.pylab as plt
from sklearn import datasets

boston = datasets.load_boston()
boston.keys()

 dict_keys(['data', 'target', 'feature_names', 'DESCR', 'filename'])

print(boston.DESCR)

 

2. Get data: No data cleaning is done here

x = boston.data
y = boston.target

x.shape   # (506, 13)
y.shape   # (506,)

3. Data segmentation 

from sklearn.model_selection  import train_test_split

X_train, X_test, y_train, y_test = train_test_split(x,y,test_size=0.2,random_state=666)

from  sklearn.linear_model import LinearRegression

reg = LinearRegression()

4. Model training 

reg.fit(X_train, y_train)

 LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)

5. Feature parameters, that is, the coefficients of the model in each feature dimension 

# 每一个特征对应的参数
reg.coef_

array([-7.56857766e-02,  4.93306230e-02,  6.85902135e-02,  2.55876122e+00,
       -1.60400649e+01,  4.09692993e+00,  6.55718540e-03, -1.41742836e+00,
        2.92373287e-01, -1.41859462e-02, -9.68019957e-01,  1.16809189e-02,
       -5.33536333e-01])

# 截距
reg.intercept_

32.926954792283404

6. Model accuracy evaluation index: R square

# R Squared(r2 score)
reg.score(X_test, y_test)

0.6336069713055628

R2_score can be understood as the proportion of model fitting characteristics, taking the benchmark (mean) error as a reference.

• R2_score = 1, the predicted value is exactly the same as the true value without any error;
• R2_score = 0. At this time, the numerator is equal to the denominator, and the model is the same as the benchmark model;
• R2_score<0, the foolish model is not as good as the prediction of the average benchmark model. At this time, the data does not have any linear correlation.