通过实现线性回归讨论数据

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)

通过实现线性回归讨论数据

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