# -*- coding: UTF-8 -*-
"""
此脚本用于展示使用sklearn搭建线性回归模型
"""import os
import sysimport numpy as np
import matplotlib.pyplot as plt
import pandas as pd
from sklearn import linear_modeldef evaluateModel(model, testData, features, labels):"""计算线性模型的均方差和决定系数参数----model : LinearRegression, 训练完成的线性模型testData : DataFrame，测试数据features : list[str]，特征名列表labels : list[str]，标签名列表返回----error : np.float64，均方差score : np.float64，决定系数"""# 均方差(The mean squared error)，均方差越小越好error = np.mean((model.predict(testData[features]) - testData[labels]) ** 2)# 决定系数(Coefficient of determination)，决定系数越接近1越好score = model.score(testData[features], testData[labels])return error, scoredef visualizeModel(model, data, features, labels, error, score):"""模型可视化"""# 为在Matplotlib中显示中文，设置特殊字体plt.rcParams['font.sans-serif']=['SimHei']# 创建一个图形框fig = plt.figure(figsize=(6, 6), dpi=80)# 在图形框里只画一幅图ax = fig.add_subplot(111)# 在Matplotlib中显示中文，需要使用unicode# 在Python3中，str不需要decodeif sys.version_info[0] == 3:ax.set_title(u'%s' % "线性回归示例")else:ax.set_title(u'%s' % "线性回归示例".decode("utf-8"))ax.set_xlabel('$x$')ax.set_ylabel('$y$')# 画点图，用蓝色圆点表示原始数据# 在Python3中，str不需要decodeif sys.version_info[0] == 3:ax.scatter(data[features], data[labels], color='b',label=u'%s: $y = x + epsilon$' % "真实值")else:ax.scatter(data[features], data[labels], color='b',label=u'%s: $y = x + epsilon$' % "真实值".decode("utf-8"))# 根据截距的正负，打印不同的标签if model.intercept_ > 0:# 画线图，用红色线条表示模型结果# 在Python3中，str不需要decodeif sys.version_info[0] == 3:ax.plot(data[features], model.predict(data[features]), color='r',label=u'%s: $y = %.3fx$ + %.3f'% ("预测值", model.coef_, model.intercept_))else:ax.plot(data[features], model.predict(data[features]), color='r',label=u'%s: $y = %.3fx$ + %.3f'% ("预测值".decode("utf-8"), model.coef_, model.intercept_))else:# 在Python3中，str不需要decodeif sys.version_info[0] == 3:ax.plot(data[features], model.predict(data[features]), color='r',label=u'%s: $y = %.3fx$ - %.3f'% ("预测值", model.coef_, abs(model.intercept_)))else:ax.plot(data[features], model.predict(data[features]), color='r',label=u'%s: $y = %.3fx$ - %.3f'% ("预测值".decode("utf-8"), model.coef_, abs(model.intercept_)))legend = plt.legend(shadow=True)legend.get_frame().set_facecolor('#6F93AE')# 显示均方差和决定系数# 在Python3中，str不需要decodeif sys.version_info[0] == 3:ax.text(0.99, 0.01, u'%s%.3fn%s%.3f'% ("均方差：", error, "决定系数：", score),style='italic', verticalalignment='bottom', horizontalalignment='right',transform=ax.transAxes, color='m', fontsize=13)else:ax.text(0.99, 0.01, u'%s%.3fn%s%.3f'% ("均方差：".decode("utf-8"), error, "决定系数：".decode("utf-8"), score),style='italic', verticalalignment='bottom', horizontalalignment='right',transform=ax.transAxes, color='m', fontsize=13)# 展示上面所画的图片。图片将阻断程序的运行，直至所有的图片被关闭# 在Python shell里面，可以设置参数"block=False"，使阻断失效。plt.show()def trainModel(trainData, features, labels):"""利用训练数据，估计模型参数参数----trainData : DataFrame，训练数据集，包含特征和标签features : 特征名列表labels : 标签名列表返回----model : LinearRegression, 训练好的线性模型"""# 创建一个线性回归模型model = linear_model.LinearRegression()# 训练模型，估计模型参数model.fit(trainData[features], trainData[labels])return modeldef linearModel(data):"""线性回归模型建模步骤展示参数----data : DataFrame，建模数据"""features = ["x"]labels = ["y"]# 划分训练集和测试集trainData = data[:15]testData = data[15:]# 产生并训练模型model = trainModel(trainData, features, labels)# 评价模型效果error, score = evaluateModel(model, testData, features, labels)# 图形化模型结果visualizeModel(model, data, features, labels, error, score)def readData(path):"""使用pandas读取数据"""data = pd.read_csv(path)return dataif __name__ == "__main__":homePath = os.path.dirname(os.path.abspath(__file__))# Windows下的存储路径与Linux并不相同if os.name == "nt":dataPath = "%sdatasimple_example.csv" % homePathelse:dataPath = "%s/data/simple_example.csv" % homePathdata = readData(dataPath)linea

"""
此脚本用于如何使用统计方法解决模型幻觉
"""# 保证脚本与Python3兼容
from __future__ import print_functionimport osimport numpy as np
import statsmodels.api as sm
import matplotlib.pyplot as plt
import pandas as pddef generateRandomVar():""""""np.random.seed(4873)return np.random.randint(2, size=20) def evaluateModel(res):"""分析线性回归模型的统计性质"""# 整体统计分析结果print(res.summary())# 用f test检测x对应的系数a是否显著print("检验假设z的系数等于0：")print(res.f_test("z=0"))# 用f test检测常量b是否显著print("检测假设const的系数等于0：")print(res.f_test("const=0"))# 用f test检测a=1, b=0同时成立的显著性print("检测假设z和const的系数同时等于0：")print(res.f_test(["z=0", "const=0"]))def trainModel(X, Y):"""训练模型"""model = sm.OLS(Y, X)res = model.fit()return resdef confidenceInterval(data):""""""features = ["x"]labels = ["y"]Y = data[labels]_X = data[features]# 加入新的随机变量，次变量的系数应为0_X["z"] = generateRandomVar()# 加入常量变量X = sm.add_constant(_X)res = trainModel(X, Y)evaluateModel(res)def generateData():"""生成模型数据"""np.random.seed(5320)x = np.array(range(0, 20)) / 2error = np.round(np.random.randn(20), 2)y = 0.05 * x + error# 新加入的无关变量z恒等于1z = np.zeros(20) + 1return pd.DataFrame({"x": x, "z": z, "y": y})def wrongCoef():"""由于新变量的加入，正效应变为负效应"""features = ["x", "z"]labels = ["y"]data = generateData()X = data[features]Y = data[labels]# 没有多余变量时，x系数符号估计正确，为正model = sm.OLS(Y, X["x"])res = model.fit()print("没有加入新变量时：")print(res.summary())# 加入多余变量时，x系数符号估计错误，为负model1 = sm.OLS(Y, X)res1 = model1.fit()print("加入新变量后：")print(res1.summary())def readData(path):"""使用pandas读取数据"""data = pd.read_csv(path)return dataif __name__ == "__main__":homePath = os.path.dirname(os.path.abspath(__file__))# Windows下的存储路径与Linux并不相同if os.name == "nt":dataPath = "%sdatasimple_example.csv" % homePathelse:dataPath = "%s/data/simple_example.csv" % homePathdata = readData(dataPath)print("***************************************************")# 在Windows下运行此脚本需确保Windows下的命令提示符(cmd)能显示中文print("加入不相关的新变量，新变量的系数被错误估计为不等于0")print("***************************************************")confidenceInterval(data)print("**********************************************")print("加入不相关的新变量，旧变量系数的符号被错误估计")print("**********************************************