线性回归:通过拟合线性模型的回归系数W =(w_1,…,w_p)来减少数据中观察到的结果和实际结果之间的残差平方和,并通过线性逼近进行预测。

从数学上讲,它解决了下面这个形式的问题:     

LinearRegression()模型在Sklearn.linear_model下,他主要是通过fit(x,y)的方法来训练模型,其中x为数据的属性,y为所属类型。线性模型的回归系数W会保存在他的coef_方法中。

例如:

>>> from sklearn import linear_model
>>> clf = linear_model.LinearRegression()
>>> clf.fit ([[0, 0], [1, 1], [2, 2]], [0, 1, 2])
LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)
>>> clf.coef_
array([ 0.5, 0.5])

实例:

使用的数据集为Sklearn.dataset.load_diabetes()一个关于糖尿病的数据集。

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" alt="" width="677" height="236" />

为了说明这个回归技术的一个二维图,例子仅仅使用了糖尿病数据集的第一个特征。

代码如下:

# -*- encoding:utf-8 -*-
"""
Line Regression Example
DataBase:diavetes
""" import matplotlib.pyplot as plt
import numpy as np
from sklearn import datasets,linear_model
import time a=time.time()
####加载数据集
diabetes=datasets.load_diabetes() ####仅仅使用一个特征:
diabetes_X=diabetes.data[:,np.newaxis,2] ###s数据划分训练集和测试集
diabetes_X_train=diabetes_X[:-20]
diabetes_X_test=diabetes_X[-20:] ###目标划分为训练集和测试集
diabetes_y_train=diabetes.target[:-20]
diabetes_y_test=diabetes.target[-20:] ###训练模型
regr=linear_model.LogisticRegression()
regr.fit(diabetes_X_train,diabetes_y_train) ###回归系数
print('Coefficients:\n',regr.coef_) ###均方误差
print('the mean sqare error:%.2f' %np.mean((regr.predict(diabetes_X_test)-diabetes_y_test)**2))
print('Variance score:%.2f' %regr.score(diabetes_X_test,diabetes_y_test))
##散点图
plt.scatter(diabetes_X_test,diabetes_y_test,color='black')
plt.plot(diabetes_X_test,regr.predict(diabetes_X_test),color='blue',linewidth=3)
plt.xticks()
plt.yticks()
b=time.time()
print('the running time is %.2f' %(b-a))
plt.show()

实验结果:

Coefficients:
[ 938.23786125]
Residual sum of squares: 2548.07
Variance score: 0.47
the running time is 0.31


 

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