机器学习测试笔记（11）——线性回归方法（上）

# 导入NumPy库 
import numpy as np
# 导入画图工具
import matplotlib.pyplot as plt

def Line_base():
    x = np.linspace(-5,5,100)
    y = 0.5 * x + 3
    plt.plot(x,y,c='green')
    plt.title('Straight Line')
    plt.show()

# 通过两个点（[2,3]和[3,4]）画出直线
from sklearn.linear_model import LinearRegression
def Line_base_by_two_point():
    X = [[2],[3]]
    y = [3,4]
# 用线性模型拟合这；两个点
    lr =LinearRegression().fit(X,y)
# 画出通过两个点（[2,3]和[3,4]）直线
    z = np.linspace(-5,5,20)
    plt.scatter(X,y,s=80)
   plt.plot(z,lr.predict(z.reshape(-1,1)),c='k')
    plt.title('Straight Line')
    plt.show()

# 显示这条线的斜率和截距
print('y={:.3f}'.format(lr.coef_[0]),'x','+{:.3f}'.format(lr.intercept_))

y=1.000 x +1.000

# 画出通过三个点（[2,3]、[3,4]和[4,4]）直线
def Line_base_by_three_point():
    X = [[2],[3],[4]]
    y = [3,4,4]
# 用线性模型拟合这；两个点
    lr =LinearRegression().fit(X,y)
# 画出通过三个点（[2,3]、[3,4]和[4,4]）直线
    z = np.linspace(-5,5,20)
    plt.scatter(X,y,s=80)
   plt.plot(z,lr.predict(z.reshape(-1,1)),c='k')
    plt.title('Straight Line')
    plt.show()
# 显示这条线的斜率和截距 
   print('y={:.3f}'.format(lr.coef_[0]),'x','+{:.3f}'.format(lr.intercept_))

y=0.500 x +2.167

#导入make_regression数据集成生成器
from sklearn.datasets import make_regression
# 画出多个点的直线
def Line_base_by_multiple_point():
    X,y =make_regression(n_samples=50,n_features=1,n_informative=1,noise=50,random_state=1)
# 使用线性模型进行拟合
    reg = LinearRegression()
    reg.fit(X,y)
# z 是我们生成的等差数列，用来画出线性模型
    z =np.linspace(-3,3,200).reshape(-1,1)
   plt.scatter(X,y,c='b',s=60)
   plt.plot(z,reg.predict(z),c='k')
    plt.title('LinearRegression')
    plt.show()
# 显示这条线的斜率和截距
    print('y={:.3f}'.format(reg.coef_[0]),'x','+{:.3f}'.format(reg.intercept_))

y=79.525 x +10.922

# 导入数据划分模块、分为训练集和测试集
from sklearn.model_selection import train_test_split
def Line_for_sklearn_data():
        X,y =make_regression(n_samples=100,n_features=2,n_informative=2,random_state=8)
       X_train,X_test,y_train,y_test = train_test_split(X, y,random_state=8,test_size=0.3)#测试集占30%
        lr =LinearRegression().fit(X,y)
        print('lr.coef_: {} '.format(lr.coef_[:]))
        print('reg.intercept_:{}'.format(lr.intercept_))
        print('训练集得分:{}'.format(lr.score(X_train,y_train)))
        print('测试集得分: {}'.format(lr.score(X_test,y_test)))

lr.coef_: [82.06262736 7.73658023]
reg.intercept_: -8.881784197001252e-16
训练集得分: 1.0
测试集得分: 1.0

from sklearn import datasets
#用线性回归对sklearn数据进行分析
def useing_sklearn_datasets_for_LinearRegression():
        X,y =datasets.load_diabetes().data,datasets.load_diabetes().target
       X_train,X_test,y_train,y_test = train_test_split(X, y,random_state=8,test_size=0.3)
        lr = LinearRegression().fit(X_train,y_train)
        print('斜率: {} '.format(lr.coef_[0))
        print('截距: {:.3f}'.format(lr.intercept_))
        print('糖尿病训练集得分:{:.3f}'.format(lr.score(X_train,y_train)))
        print('糖尿病测试集得分: {:.3f}'.format(lr.score(X_test,y_test)))

斜率: [12.8821982   -280.25543507   525.99221876   407.85755317 -1120.30092255   698.91189157 234.67105524   208.41900324   816.01470258   114.97615609]
截距: 152.535
糖尿病训练集得分: 0.535
糖尿病测试集得分: 0.454

Boston =datasets.load_boston()
X,y =Boston.data,Boston.target
X_train,X_test,y_train,y_test= train_test_split(X, y)
lr =LinearRegression().fit(X_train,y_train)
print('斜率: {} '.format(lr.coef_[:]))
print('截距: {}'.format(lr.intercept_))
print('波士顿房价训练集得分:{:.3f}'.format(lr.score(X_train,y_train)))
print('波士顿房价测试集得分:{:.3f}'.format(lr.score(X_test,y_test)))

斜率: [-9.68961053e-02 4.87033096e-02-2.55499190e-02 3.92145072e+00 -1.52816098e+01 4.23762130e+00 -1.84848509e-02-1.56942479e+00 2.79115671e-01 -1.13985910e-02 -9.27575541e-01 1.05878888e-02-4.14823758e-01]
截距: 32.06878785459298
波士顿房价训练集得分: 0.743
波士顿房价测试集得分: 0.716

# 导入StatsModels的API库,C:\Users\xiang>pip3 install statsmodels
import statsmodels.api as sm
#StatsModels 库
# y = w^x+e(e 误差，符合均值为0的正态分布)
def StatsModels_linear_regression():
# 前四行训练构造函数，自变量x 因变量y
# 通过自变量x准备数据，将1~10 数据分割成20份
    x = np.linspace(0,10,20)
# 向数组中添加一列，构成20组x
    X = sm.add_constant(x)
    ratio = np.array([1,10]) #ratio：比例
# 使回归方程的系数点乘x数据集，构成因变量y
#numpy.random.normal(loc=0.0, scale=1.0, size=None)
# loc:float,概率分布的均值，对应着整个分布的中心center
# scale: 概率分布的标准差，对应于分布的宽度，scale越大越矮胖，scale越小，越瘦高
# size: 输出的shape，默认为None，只输出一个值
# np.random.randn(size)所谓标准正太分布（μ=0, σ=1），对应于np.random.normal(loc=0, scale=1, size)
    y = np.dot(X,ratio) +np.random.normal(size=20)
# 执行OLS模型
    testmodel = sm.OLS(y,X)
# 使用fit方法启动模型训练
    results = testmodel.fit()
   print("results.params:\n",results.params,"\nresults.summary():\n",results.summary())

from sklearn import datasets
def StatsModels_linear_regression_for_sklearn_dataset():
#Load Boston
        Boston =datasets.load_boston()
        X,y =Boston.data[:,5].reshape(-1,1),Boston.target.reshape(-1,1)
        testmodel =sm.OLS(y,X)
        results =testmodel.fit()
       print("results.params(Boston):\n",results.params,"\nresults.summary(Boston):\n",results.summary())
#Load diabetes
        X,y = datasets.load_diabetes().data,datasets.load_diabetes().target
        testmodel =sm.OLS(y,X)
        results =testmodel.fit()
       print("results.params(diabetes):\n",results.params,"\nresults.summary(diabetes):\n",results.summary())

results.params(Boston):
[3.6533504]
R-squared (uncentered): 0.901
results.params(diabetes):
[ -10.01219782 -239.81908937 519.83978679  324.39042769-792.18416163 476.74583782 101.04457032  177.06417623  751.27932109  67.62538639]
R-squared(uncentered):   0.106

def StatsModels_linear_regression_for_all_model():
#Load Boston
        Boston =datasets.load_boston()
        X,y =Boston.data[:,5].reshape(-1,1),Boston.target.reshape(-1,1)
        testmodel =sm.OLS(y,X)
        results =testmodel.fit()
       print("OLS:\n",results.params,"\nOLS:\n",results.summary())
        Boston =datasets.load_boston()
        X,y =Boston.data[:,5].reshape(-1,1),Boston.target.reshape(-1,1)
        testmodel =sm.WLS(y,X)
        results =testmodel.fit()
       print("WLS:\n",results.params,"\nWLS:\n",results.summary())
        Boston =datasets.load_boston()
        X,y =Boston.data[:,5].reshape(-1,1),Boston.target.reshape(-1,1)
        testmodel =sm.GLS(y,X)
        results =testmodel.fit()
       print("GLS:\n",results.params,"\nGLS:\n",results.summary())