多元迴歸中的常量值

Question

我已經編寫了一個代碼，用WLS的多元迴歸形成最佳擬合線的方程式。下面是我使用的代碼：

import numpy as np 
import csv 
import pandas as pd 
import statsmodels.api as sm 
from statsmodels.sandbox.regression.predstd import wls_prediction_std 

#read data from csv 
readCSV=pd.read_csv('test2.csv') 

#store data into corresponding month lists 
mJan=readCSV['month__Jan'] 
mFeb=readCSV['month__Feb'] 
mMar=readCSV['month__Mar'] 
mApr=readCSV['month__Apr'] 
mMay=readCSV['month__May'] 
mJun=readCSV['month__Jun'] 
mJul=readCSV['month__Jul'] 
mAug=readCSV['month__Aug'] 
mSep=readCSV['month__Sep'] 
mOct=readCSV['month__Oct'] 
mNov=readCSV['month__Nov'] 
mDec=readCSV['month__Dec'] 

#store data into corresponding weekdays lists 
wMon=readCSV['weekday__Mon'] 
wTue=readCSV['weekday__Tue'] 
wWed=readCSV['weekday__Wed'] 
wThu=readCSV['weekday__Thu'] 
wFri=readCSV['weekday__Fri'] 

#convert month pandas data to numpy arrays 
mJan=mJan.as_matrix() 
mFeb=mFeb.as_matrix() 
mMar=mMar.as_matrix() 
mApr=mApr.as_matrix() 
mMay=mMay.as_matrix() 
mJun=mJun.as_matrix() 
mJul=mJul.as_matrix() 
mAug=mAug.as_matrix() 
mSep=mSep.as_matrix() 
mOct=mOct.as_matrix() 
mNov=mNov.as_matrix() 
mDec=mDec.as_matrix() 

#convert weekday pandas data frame to numpy arrays 
wMon=wMon.as_matrix() 
wTue=wTue.as_matrix() 
wWed=wWed.as_matrix() 
wThu=wThu.as_matrix() 
wFri=wFri.as_matrix() 

prices=[] 
dayNum=[] 
with open('aapl.csv','rb') as csvfile: 
    csvFileReader=csv.reader(csvfile) 
    next(csvFileReader) 
    for row in csvFileReader: 
     fullDate=row[0] 
     #print(fullDate[7:])    
     l=row[0].split() 
     s=l[1].strip(',') 
     dayNum.append(int(s)) 
     prices.append(float(row[1])) 

#final input data set 
X=np.vstack((dayNum,mJan,mFeb,mMar,mApr,mMay,mJun,mJul,mAug,mSep,mOct,mNov,mDec,wMon,wTue,wWed,wThu,wFri)).T 

#final target parameter 
mod_wls = sm.WLS(prices, X) 
res_wls = mod_wls.fit() 
print res_wls.params 
print res_wls.summary() 

代碼工作得很好，並且我得到的輸出看起來是這樣的：

> [ 6.74096438e-03 4.18506571e+01 5.60244116e+01 3.54806772e+01 
> 2.83052274e+01 1.74134713e+01 1.86328033e+01 2.11088939e+01 
> 2.97457264e+01 3.31973702e+01 3.80025208e+01 3.21529043e+01 
> 3.64722064e+01 7.74843964e+01 7.77925151e+01 7.79671536e+01 
> 7.76580605e+01 7.74847444e+01] 
>        WLS Regression Results        
> ============================================================================== Dep. Variable:      y R-squared:      
> 0.999 Model:       WLS Adj. R-squared:     0.999 Method:     Least Squares F-statistic:     1.041e+04 Date:    Thu, 16 Mar 2017 Prob (F-statistic):   9.43e-313 Time:      13:51:47 Log-Likelihood:    -668.01 No. Observations:     240 AIC:        1370. Df Residuals:      223 BIC:        1429. Df Model:       17           
> ============================================================================== 
>     coef std err   t  P>|t|  [95.0% Conf. Int.] 
> ------------------------------------------------------------------------------ x1    0.0067  0.030  0.227  0.821  -0.052 
> 0.065 x2   41.8507  0.888  47.124  0.000  40.101 43.601 x3   56.0244  0.899  62.321  0.000  54.253 57.796 x4   35.4807  1.257  28.221  0.000  33.003 37.958 x5   28.3052  0.864  32.746  0.000  26.602 30.009 x6   17.4135  0.862  20.207  0.000  15.715 19.112 x7   18.6328  0.845  22.043  0.000  16.967 20.299 x8   21.1089  0.887  23.792  0.000  19.360 22.857 x9   29.7457  0.828  35.922  0.000  28.114 31.378 x10   33.1974  0.870  38.178  0.000  31.484 34.911 x11   38.0025  0.866  43.872  0.000  36.296 39.710 x12   32.1529  0.861  37.338  0.000  30.456 33.850 x13   36.4722  0.865  42.188  0.000  34.769 38.176 x14   77.4844  0.699 110.787  0.000  76.106 78.863 x15   77.7925  0.642 121.266  0.000  76.528 79.057 x16   77.9672  0.632 123.309  0.000  76.721 79.213 x17   77.6581  0.635 122.371  0.000  76.407 78.909 x18   77.4847  0.662 117.132  0.000  76.181 78.788 
> ============================================================================== Omnibus:      142.534 Durbin-Watson:     
> 0.414 Prob(Omnibus):     0.000 Jarque-Bera (JB):    2512.436 Skew:       1.927 Prob(JB):       0.00 Kurtosis:      18.375 Cond. No.       nan 
> ============================================================================== 
> 
> Warnings: [1] The smallest eigenvalue is -7.44e-15. This might 
> indicate that there are strong multicollinearity problems or that the 
> design matrix is singular. 

全部18個參數的係數被計算並顯​​示。我怎樣才能知道常數或攔截的價值？方程式必須爲y = m1x1 + m2x2 + ...... + m18x18 + K 我應該如何計算該值？另外，請解釋我得到的關於特徵值的警告的含義。謝謝！

Answer 1

只是想通了！我們可以爲此使用statsmodels。

#final input data set 
X=np.vstack((dayNum,mJan,mFeb,mMar,mApr,mMay,mJun,mJul,mAug,mSep,mOct,mNov,mDec,wMon,wTue,wWed,wThu,wFri)).T 
X=sm.add_constant(X)  #adds constant to the input array 
#final target parameter 
mod_wls = sm.WLS(prices, X) 
res_wls = mod_wls.fit() 
print res_wls.params 
print res_wls.summary() 

常量值與其他參數一起顯示爲輸出。