通过实现线性回归讨论数据

川长思鸟来 2022-05-19 10:41 132阅读 0赞

分析数据：

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

boston = datasets.load_boston()
    
    X = boston.data
    y = boston.target
    
    X = X[y < 50.0]
    y = y[y < 50.0]

from sklearn.linear_model import LinearRegression
    
    lin_reg = LinearRegression()
    lin_reg.fit(X, y)

LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)

lin_reg.coef_
    #系数为正即为正相关，特征越大，房价越高；反之特征越小，房价越低

array([ -1.05574295e-01,   3.52748549e-02,  -4.35179251e-02,
             4.55405227e-01,  -1.24268073e+01,   3.75411229e+00,
            -2.36116881e-02, -1.21088069e+00, 2.50740082e-01,         -1.37702943e-02, -8.38888137e-01, 7.93577159e-03,         -3.50952134e-01])

np.argsort(lin_reg.coef_)#将各特征对房价的影响排序

array([ 4, 7, 10, 12, 0, 2, 6, 9, 11, 1, 8, 3, 5])

boston.feature_names[np.argsort(lin_reg.coef_)]#NOX为一氧化氮，可知一氧化氮浓度越大，房价越低，系数为负值，最小

array(['NOX', 'DIS', 'PTRATIO', 'LSTAT', 'CRIM', 'INDUS', 'AGE', 'TAX',
           'B', 'ZN', 'RAD', 'CHAS', 'RM'], 
          dtype='<U7')

print(boston.DESCR)

Boston House Prices dataset
    =========================== 
    Notes
    ------ Data Set Characteristics:  
    
        :Number of Instances: 506 
    
        :Number of Attributes: 13 numeric/categorical predictive
    
        :Median Value (attribute 14) is usually the target
    
        :Attribute Information (in order):
            - CRIM per capita crime rate by town         - ZN proportion of residential land zoned for lots over 25,000 sq.ft.         - INDUS proportion of non-retail business acres per town         - CHAS Charles River dummy variable (= 1 if tract bounds river; 0 otherwise)         - NOX nitric oxides concentration (parts per 10 million)         - RM average number of rooms per dwelling         - AGE proportion of owner-occupied units built prior to 1940         - DIS weighted distances to five Boston employment centres         - RAD index of accessibility to radial highways         - TAX full-value property-tax rate per $10,000         - PTRATIO pupil-teacher ratio by town         - B 1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town         - LSTAT % lower status of the population         - MEDV Median value of owner-occupied homes in $1000's 
        :Missing Attribute Values: None
    
        :Creator: Harrison, D. and Rubinfeld, D.L.
    
    This is a copy of UCI ML housing dataset.
    http://archive.ics.uci.edu/ml/datasets/Housing

This dataset was taken from the StatLib library which is maintained at Carnegie Mellon University.
    
    The Boston house-price data of Harrison, D. and Rubinfeld, D.L. 'Hedonic
    prices and the demand for clean air', J. Environ. Economics & Management,
    vol.5, 81-102, 1978.   Used in Belsley, Kuh & Welsch, 'Regression diagnostics
    ...', Wiley, 1980.   N.B. Various transformations are used in the table on
    pages 244-261 of the latter.
    
    The Boston house-price data has been used in many machine learning papers that address regression
    problems.   
    
    **References**
    
       - Belsley, Kuh & Welsch, 'Regression diagnostics: Identifying Influential Data and Sources of Collinearity', Wiley, 1980. 244-261.
       - Quinlan,R. (1993). Combining Instance-Based and Model-Based Learning. In Proceedings on the Tenth International Conference of Machine Learning, 236-243, University of Massachusetts, Amherst. Morgan Kaufmann.
       - many more! (see http://archive.ics.uci.edu/ml/datasets/Housing)