一元回归_ols参数解读(推荐AAA)

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多重共线性测试需要改进

文件夹需要两个包

python3.0 anaconda

normality_check.py 正太检验

# -*- coding: utf-8 -*-
'''
Author：Toby
QQ：231469242，all right reversed,no commercial use
normality_check.py
正态性检验脚本

'''

import scipy
from scipy.stats import f
import numpy as np
import matplotlib.pyplot as plt
import scipy.stats as stats
# additional packages
from statsmodels.stats.diagnostic import lillifors

#正态分布测试
def check_normality(testData):
    #20<样本数<50用normal test算法检验正态分布性
    if 20<len(testData) <50:
       p_value= stats.normaltest(testData)[1]
       if p_value<0.05:
           print("use normaltest")
           print ("data are not normal distributed")
           return  False
       else:
           print("use normaltest")
           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 ("data are not normal distributed")
           return  False
       else:
           print ("use shapiro:")
           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 ("data are not normal distributed")
           return  False
       else:
           print ("use lillifors:")
           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 ("data are not normal distributed")
           return  False
       else:
           print ("use kstest:")
           print ("data are normal distributed")
           return True

#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
    return True

Rsquare_multimode.py   多种模型计算R平方

加入了线性显著检测和ｒ相关系数显著检测，多重共线性，自相关，残差正太检验等等

# -*- coding: utf-8 -*-
#斯皮尔曼等级相关（Spearman’s correlation coefficient for ranked data）
import math,pylab,scipy
import numpy as np
import scipy.stats as stats
from scipy.stats import t
from scipy.stats import f
import pandas as pd
import matplotlib.pyplot as plt
from statsmodels.stats.diagnostic import lillifors
import normality_check
import statsmodels.formula.api as sm
x=[4.03,3.76,3.77,3.34,3.47,2.92,3.20,2.71,3.53,4.51]
y=[6.47,6.13,6.19,4.89,5.63,4.52,5.89,4.79,5.27,6.08]

list_group=[x,y]
sample=len(x)
#显著性
a=0.05

#数据可视化
plt.plot(x,y,'ro')
#斯皮尔曼等级相关，非参数检验
def Spearmanr(x,y):
    print("use spearmanr,Nonparametric tests")
    #样本不一致时，发出警告
    if len(x)!=len(y):
        print ("warming,the samples are not equal!")
    r,p=stats.spearmanr(x,y)
    print("spearman r**2:",r**2)
    print("spearman p:",p)
    if sample<500 and p>0.05:
        print("when sample < 500，p has no mean（>0.05）")
        print("when sample > 500，p has mean")

#皮尔森 ，参数检验
def Pearsonr(x,y):
    print("use Pearson,parametric tests")
    r,p=stats.pearsonr(x,y)
    print("pearson r**2:",r**2)
    print("pearson p:",p)
    if sample<30:
        print("when sample <30,pearson has no mean")

#皮尔森 ，参数检验,带有详细参数
def Pearsonr_details(x,y,xLabel,yLabel,formula):
    n=len(x)
    df=n-2
    data=pd.DataFrame({yLabel:y,xLabel:x})
    result = sm.ols(formula, data).fit()
    print(result.summary()) 

    #模型F分布显著性分析
    print('\n')
    print("linear relation Significant test:...................................")
    #如果F检验的P值<0.05，拒绝H0，x和y无显著关系，H1成立，x和y有显著关系
    if result.f_pvalue<0.05:
        print ("P value of f test<0.05,the linear relation is right.")

    #R的显著检验
    print('\n')
    print("R significant test:...................................")
    r_square=result.rsquared
    r=math.sqrt(r_square)
    t_score=r*math.sqrt(n-2)/(math.sqrt(1-r**2))
    t_std=t.isf(a/2,df)
    if t_score<-t_std or t_score>t_std:
        print ("R is significant according to its sample size")
    else:
        print ("R is not significant")

    #残差分析
    print('\n')
    print("residual error analysis:...................................")
    states=normality_check.check_normality(result.resid)
    if states==True:
        print("the residual error are normal distributed")
    else:
        print("the residual error are not normal distributed")

    #残差偏态和峰态
    Skew = stats.skew(result.resid, bias=True)
    Kurtosis = stats.kurtosis(result.resid, fisher=False,bias=True)
    if round(Skew,1)==0:
        print("residual errors normality Skew:in middle,perfect match")
    elif  round(Skew,1)>0:
        print("residual errors normality Skew:close right")
    elif  round(Skew,1)<0:
        print("residual errors normality Skew:close left")

    if round(Kurtosis,1)==3:
        print("residual errors normality Kurtosis:in middle,perfect match")
    elif  round(Kurtosis,1)>3:
        print("residual errors normality Kurtosis:more peak")
    elif  round(Kurtosis,1)<3:
        print("residual errors normality Kurtosis:more flat")    

    #自相关分析autocorrelation
    print('\n')
    print("autocorrelation test:...................................")
    DW = np.sum( np.diff( result.resid.values )**2.0 )/ result.ssr
    if round(DW,1)==2:
        print("Durbin-Watson close to 2,there is no autocorrelation.OLS model works well")    

    #共线性检查
    print('\n')
    print("multicollinearity test:")
    conditionNumber=result.condition_number
    if conditionNumber>30:
        print("conditionNumber>30,multicollinearity exists")
    else:
        print("conditionNumber<=30,multicollinearity not exists")

    #绘制残差图，用于方差齐性检验
    Draw_residual(list(result.resid))
'''
result.rsquared
Out[28]: 0.61510660055413524
''' 

#kendalltau非参数检验
def Kendalltau(x,y):
    print("use kendalltau,Nonparametric tests")
    r,p=stats.kendalltau(x,y)
    print("kendalltau r**2:",r**2)
    print("kendalltau p:",p)

#选择模型
def R_mode(x,y,xLabel,yLabel,formula):
    #正态性检验
    Normal_result=normality_check.NormalTest(list_group)
    print ("normality result:",Normal_result)
    if len(list_group)>2:
        Kendalltau(x,y)
    if Normal_result==False:
        Spearmanr(x,y)
        Kendalltau(x,y)
    if Normal_result==True:
        Pearsonr_details(x,y,xLabel,yLabel,formula)

#调整的R方
def Adjust_Rsquare(r_square,n,k):
    adjust_rSquare=1-((1-r_square)*(n-1)*1.0/(n-k-1))
    return adjust_rSquare
'''
n=len(x)
n=10
k=1
 r_square=0.615
 Adjust_Rsquare(r_square,n,k)
Out[11]: 0.566875
'''    

#绘图
def Plot(x,y,yLabel,xLabel,Title):
    plt.plot(x,y,'ro')
    plt.ylabel(yLabel)
    plt.xlabel(xLabel)
    plt.title(Title)
    plt.show()

#绘图参数
yLabel='Alcohol'
xLabel='Tobacco'
Title='Sales in Several UK Regions'
Plot(x,y,yLabel,xLabel,Title)
formula='Alcohol ~ Tobacco'    

#绘制残点图
def Draw_residual(residual_list):
    x=[i for i in range(1,len(residual_list)+1)]
    y=residual_list
    pylab.plot(x,y,'ro')
    pylab.title("draw residual to check wrong number")

    # Pad margins so that markers don't get clipped by the axes,让点不与坐标轴重合
    pylab.margins(0.3)

    #绘制网格
    pylab.grid(True)

    pylab.show()

R_mode(x,y,xLabel,yLabel,formula)

'''
result.fittedvalues表示预测的y值阵列
result.fittedvalues
Out[42]:
0    6.094983
1    5.823391
2    5.833450
3    5.400915
4    5.531682
5    4.978439
6    5.260090
7    4.767201
8    5.592035
9    6.577813
dtype: float64

#计算残差的偏态
S = stats.skew(result.resid, bias=True)
Out[44]: -0.013678125910039975

K = stats.kurtosis(result.resid, fisher=False,bias=True)
K
Out[47]: 1.5271300905736027
'''

result.params 得到两个参数：x的系数和截距

截距

result.params[0]

x系数

result.params[1]

 

 

 dubin watson解读

--残差是否符合正太分布

D.W统计量是用来检验残差分布是否为正态分布的，因为用OLS进行回归估计是假设模型残差服从正态分布的，因此，如果残差不服从正态分布，那么，模型将是有偏的，也就是说模型的解释能力是不强的。
D.W统计量在2左右说明残差是服从正态分布的，若偏离2太远，那么你所构建的模型

的解释能力就要受影响了。

jarque-bera解读
----样本是否符合正太分布

JB统计量全称叫Jarque-Bera统计量，是用来检验一组样本是否能够认为来自正态总体的一种方法，它依据OLS残差，对大样本进行检验（或称为渐进检验）。

 

首先计算偏度系数S(对概率密度函数对称性的度量)：

及峰度系数K(对概率密度函数的“胖瘦”的度量)：

对于正态分布变量，偏度为零，峰度为3.

Jarque和Bera建立了如下检验统计量——JB统计量：

其中，n为样本容量，S为偏度，K为峰度。

在正态分布的假设下，JB统计量渐进地服从自由度为2的卡方分布, JBasy~χ2(2)。

若变量服从正态分布，则S为零，K为3，因而JB统计量的值为零；如果变量不是正态变量，则JB统计量将为一个逐渐增大值。

如果JB统计量值较大，比如为11，则可以计算出卡方值大于11的概率为0.004，这个概率过小，因此不能认为样本来自正态分布。反之，成立。

Jarque-Bera的P值接近于0，表明显著性高，数据服从正态分布。

Omnibus解读

Omnibus统计量的P值都接近于0，自变量的作用显著。

Omnibus tests are a kind of statistical test. They test whether the explained variance in a set of data is significantly greater than the unexplained variance, overall. One example is the F-test in the analysis of variance. There can be legitimate significant effects within a model even if the omnibus test is not significant. For instance, in a model with two independent variables, if only one variable exerts a significant effect on the dependent variable and the other does not, then the omnibus test may be non-significant. This fact does not affect the conclusions that may be drawn from the one significant variable. In order to test effects within an omnibus test, researchers often use contrasts.

https://en.wikipedia.org/wiki/Omnibus_test

python信用评分卡建模（附代码，博主录制）

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