(博客主亲自录制视频教程)

 

 

貌似一个不相关的变量，可能对结果有显著影响

多元回归可以分析独立变量与因变量是否显著相关。但解释能力不如因子分析

因子分析对变量相关性解释能力更强

 

正态分布检验OK

三组数据呈现正态分布，可以用回归检测

# -*- coding: utf-8 -*-'''Author：TobyQQ：231469242，all right reversed,no commercial usenormality_check.py正态性检验脚本  '''  import scipyfrom scipy.stats import fimport numpy as npimport matplotlib.pyplot as pltimport scipy.stats as stats# additional packagesfrom statsmodels.stats.diagnostic import lillifors  #对一列数据进行正态分布测试def check_normality(testData):    print("one group normality check begin:")    #20
     <样本数>
      <50用normal test算法检验正态分布性    if 20
      
       <50:       p_value= stats.normaltest(testData)[1]       if p_value<0.05:           print("use normaltest")           print("p value:",p_value)           print ("data are not normal distributed")           return  False       else:           print("use normaltest")           print("p value:",p_value)           print ("data are normal distributed")           return True          #样本数小于50用Shapiro-Wilk算法检验正态分布性    if len(testData) <50:       p_value= stats.shapiro(testData)[1]       if p_value<0.05:           print ("use shapiro:")           print("p value:",p_value)           print ("data are not normal distributed")           return  False       else:           print ("use shapiro:")           print("p value:",p_value)           print ("data are normal distributed")           return True            if 300>=len(testData) >=50:       p_value= lillifors(testData)[1]              if p_value<0.05:           print ("use lillifors:")           print("p value:",p_value)           print ("data are not normal distributed")           return  False       else:           print ("use lillifors:")           print("p value:",p_value)           print ("data are normal distributed")           return True          if len(testData) >300:       p_value= stats.kstest(testData,'norm')[1]       if p_value<0.05:           print ("use kstest:")           print("p value:",p_value)           print ("data are not normal distributed")           return  False       else:           print ("use kstest:")           print("p value:",p_value)           print ("data are normal distributed")           return True    #测试结束    print("-"*100)  #对所有样本组进行正态性检验def NormalTest(list_groups):    for group in list_groups:        #正态性检验        status=check_normality(group)        if status==False :            return False               group1=[5,2,4,2.5,3,3.5,2.5,3]group2=[1.5,2,1.5,2.5,3.3,2.3,4.2,2.5]group3=[96,90,95,92,95,94,94,94]list_groups=[group1,group2,group3]list_total=group1+group2+group3#对所有样本组进行正态性检验  NormalTest(list_groups)
      
     

　　

 

下图可见，独立变量x1和x2没有相关，R调整平方为0.19

x1和yR调整平方0.59的关系--存在很弱关系

x2和y存在R调整平方-0.19，即没有关系

但x1和x2与y存在0.886R调整平方关系，非常强

 

 

且x1和x2与y结合后，残差服从正态分布，AIC和BIC值很小，

prob (F-statistic)=0.00187,小于0.05，说明回归方程显著

参数t检验显著，x1和x2的t分数P值分别为0.001和0.01,小于0.05，否定H0，表示x1和x2显著，说明此模型拟合度很好

说明貌似一个不相关的变量，可能对结果有显著影响

 

# -*- coding: utf-8 -*-"""Created on Tue Jul 18 09:37:15 2017@author: toby"""# Import standard packagesimport numpy as npimport matplotlib.pyplot as pltimport pandas as pdimport seaborn as snsfrom sklearn import datasets, linear_modelfrom matplotlib.font_manager import FontProperties font_set = FontProperties(fname=r"c:\windows\fonts\simsun.ttc", size=15)  # additional packagesimport sysimport ossys.path.append(os.path.join('..', '..', 'Utilities'))try:# Import formatting commands if directory "Utilities" is available    from ISP_mystyle import showData     except ImportError:# Ensure correct performance otherwise    def showData(*options):        plt.show()        return# additional packages ...# ... for the 3d plot ...from mpl_toolkits.mplot3d import Axes3Dfrom matplotlib import cm# ... and for the statisticfrom statsmodels.formula.api import ols#生成组合from itertools import combinationsx1=[5,2,4,2.5,3,3.5,2.5,3]x2=[1.5,2,1.5,2.5,3.3,2.3,4.2,2.5]y=[96,90,95,92,95,94,94,94]#自变量列表list_x=[x1,x2]#绘制多元回归三维图def Draw_multilinear():        df = pd.DataFrame({'x1':x1,'x2':x2,'y':y})    # --- >>> START stats <<< ---    # Fit the model    model = ols("y~x1+x2", df).fit()    param_intercept=model.params[0]    param_x1=model.params[1]    param_x2=model.params[2]    rSquared_adj=model.rsquared_adj        #generate data,产生矩阵然后把数值附上去    x = np.linspace(-5,5,101)    (X,Y) = np.meshgrid(x,x)        # To get reproducable values, I provide a seed value    np.random.seed(987654321)       Z = param_intercept + param_x1*X+param_x2*Y+np.random.randn(np.shape(X)[0], np.shape(X)[1])    # 绘图    #Set the color    myCmap = cm.GnBu_r    # If you want a colormap from seaborn use:    #from matplotlib.colors import ListedColormap    #myCmap = ListedColormap(sns.color_palette("Blues", 20))        # Plot the figure    fig = plt.figure("multi")    ax = fig.gca(projection='3d')    surf = ax.plot_surface(X,Y,Z, cmap=myCmap, rstride=2, cstride=2,         linewidth=0, antialiased=False)    ax.view_init(20,-120)    ax.set_xlabel('X')    ax.set_ylabel('Y')    ax.set_zlabel('Z')    ax.set_title("multilinear with adj_Rsquare %f"%(rSquared_adj))    fig.colorbar(surf, shrink=0.6)        outFile = '3dSurface.png'    showData(outFile)    #检查独立变量之间共线性关系def Two_dependentVariables_compare(x1,x2):    # Convert the data into a Pandas DataFrame    df = pd.DataFrame({'x':x1, 'y':x2})    # Fit the model    model = ols("y~x", df).fit()    rSquared_adj=model.rsquared_adj    print("rSquared_adj",rSquared_adj)    if rSquared_adj>=0.8:        print("high relation")        return True    elif 0.6<=rSquared_adj<0.8:         print("middle relation")         return False    elif rSquared_adj<0.6:         print("low relation")         return False#比较所有参数，观察是否存在多重共线def All_dependentVariables_compare(list_x):      list_status=[]    list_combine=list(combinations(list_x, 2))    for i in list_combine:        x1=i[0]        x2=i[1]        status=Two_dependentVariables_compare(x1,x2)        list_status.append(status)    if True in list_status:        print("there is multicorrelation exist in dependent variables")        return True    else:        return False            #回归方程，支持哑铃变量def regressionModel(x1,x2,y):    '''Multilinear regression model, calculating fit, P-values, confidence intervals etc.'''    # Convert the data into a Pandas DataFrame    df = pd.DataFrame({'x1':x1,'x2':x2,'y':y})        # --- >>> START stats <<< ---    # Fit the model    model = ols("y~x1+x2", df).fit()    # Print the summary    print((model.summary()))    return model._results.params  # should be array([-4.99754526,  3.00250049, -0.50514907])    # Function to show the resutls of linear fit modeldef Draw_linear_line(X_parameters,Y_parameters,figname,x1Name,x2Name):    #figname表示图表名字，用于生成独立图表fig1 = plt.figure('fig1')，fig2 = plt.figure('fig2')    plt.figure(figname)    #获取调整R方参数        df = pd.DataFrame({'x':X_parameters, 'y':Y_parameters})    # Fit the model    model = ols("y~x", df).fit()    rSquared_adj=model.rsquared_adj         #处理X_parameter1数据    X_parameter1 = []    for i in X_parameters:        X_parameter1.append([i])        # Create linear regression object    regr = linear_model.LinearRegression()    regr.fit(X_parameter1, Y_parameters)    plt.scatter(X_parameter1,Y_parameters,color='blue',label="real value")    plt.plot(X_parameter1,regr.predict(X_parameter1),color='red',linewidth=4,label="prediction line")    plt.title("linear regression %s and %s with adj_rSquare:%f"%(x1Name,x2Name,rSquared_adj))    plt.xlabel('x', fontproperties=font_set)      plt.ylabel('y', fontproperties=font_set)      plt.xticks(())    plt.yticks(())    plt.legend()    plt.show()          #绘制多元回归三维图Draw_multilinear()  #比较所有参数，观察是否存在多重共线All_dependentVariables_compare(list_x)              Draw_linear_line(x1,x2,"fig1","x1","x2")Draw_linear_line(x1,y,"fig4","x1","y")Draw_linear_line(x2,y,"fig5","x2","y")regressionModel(x1,x2,y)        '''训练数据x1=[2,6,8,3,2,7,9,8,4,6]x2=[1,0,1,0,1,1,0,0,1,1]y=[2900,3000,4800,1800,2900,4900,4200,4800,4400,4500]x=[89,66,78,111,44,77,80,66,109,76]y=[4,1,3,6,1,3,3,2,5,3]z=[7,5.4,6.6,7.4,4.8,6.4,7,5.6,7.3,6.4]x1=[89,66,78,111,44,77,80,66,109,76]x2=[4,1,3,6,1,3,3,2,5,3]x3=[3.84,3.19,3.78,3.89,3.57,3.57,3.03,3.51,3.54,3.25]y=[7,5.4,6.6,7.4,4.8,6.4,7,5.6,7.3,6.4]   '''