Python_Data_Science_第八课

multivariate regression. (multiple regression)

1. What if more than 1 variable influence the one you are interested in ?
Example:
  predicting a price for a car based on its many attributes(body style, brand, mileage, etc.) 例如有多个因素都会影响车辆的价格，车型，品牌，公里数，车门数。

#still use least squares
We just end up with coefficients for each factor.
  For example, prices = a + b(mileage) + c(doors)
  These coefficients imply how important each factor is (if the data is all normalized)
  Get rid of ones that don't matter.
Can still measure fit with r-squared.
Need to assume the different factors are not themselves dependent on each other.

2.  直接上代码了.
使用pandas 来读一个excel. 有可能碰到ImportError

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1. #statsmodel package
   
2. #ImportError: Install xlrd >= 0.9.0 for Excel support , need xlrd.
3. 
   
4. apt-get install python3-xlrd
   
5. import pandas as pd
6. df=pd.read_excel("http://cdn.sundog-soft.com/Udemy/DataScience/cars.xls")
   
7. df.head()
8. 
   

1st version code

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1. import statsmodels.api as sm
   
2. from sklearn.preprocessing import StandardScaler
   
3. 
   
4. scale= StandardScaler()
   
5. X=df[['Mileage','Cylinder', 'Doors', 'Model_ord']]
   
6. y=df[['Price']]
   
7. 
   
8. X[['Mileage', 'Cylinder', 'Doors']]=scale.fit_transform(X[['Mileage', 'Cylinder', 'Doors']].as_matrix())
   
9. print(X)
   
10. est=sm.OLS(y, X).fit()
    
11. est.summary()

2nd version

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1. '''2nd version code '''
   
2. df['Model_ord'] = pd.Categorical(df.Model).codes
   
3. X=df[['Mileage','Cylinder', 'Doors', 'Model_ord']]
   
4. y=df[['Price']]
   
5. X1=sm.add_constant(X)
   
6. est=sm.OLS(y, X1).fit()
   
7. 
   
8. est.summary()

2种方式得到的summary page是完全一样的.

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1. 
   """
                               OLS Regression Results                            
   ==============================================================================
   Dep. Variable:                  Price   R-squared:                       0.425
   Model:                            OLS   Adj. R-squared:                  0.422
   Method:                 Least Squares   F-statistic:                     147.4
   Date:                Sun, 08 Jul 2018   Prob (F-statistic):           2.10e-94
   Time:                        20:51:27   Log-Likelihood:                -8313.9
   No. Observations:                 804   AIC:                         1.664e+04
   Df Residuals:                     799   BIC:                         1.666e+04
   Df Model:                           4                                         
   Covariance Type:            nonrobust                                         
   ==============================================================================
                    coef    std err          t      P>|t|      [0.025      0.975]
   ------------------------------------------------------------------------------
   const       1.037e+04   1669.695      6.211      0.000    7093.297    1.36e+04
   Mileage       -0.1608      0.032     -4.966      0.000      -0.224      -0.097
   Cylinder    4726.1696    204.906     23.065      0.000    4323.952    5128.387
   Doors      -1742.6007    312.188     -5.582      0.000   -2355.406   -1129.795
   Model_ord   -309.4669     32.666     -9.474      0.000    -373.587    -245.346
   ==============================================================================
   Omnibus:                      193.097   Durbin-Watson:                   0.081
   Prob(Omnibus):                  0.000   Jarque-Bera (JB):              440.016
   Skew:                           1.288   Prob(JB):                     2.83e-96
   Kurtosis:                       5.549   Cond. No.                     1.37e+05
   ==============================================================================
   
   
2. 
   
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.37e+05. This might indicate that there are
strong multicollinearity or other numerical problems.
"""

注意这里的R-squared ，1是完美，0是极差，0.425, 算是不那么差。如果把使用的columns 减少一个，例如：使用三列，这个R-squared 就会变得很比较糟， 0.042.

X=df[['Mileage','Cylinder', 'Doors', ]]

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1. In [13]: df['Model_ord'] = pd.Categorical(df.Model).codes
   
2.     ...: X=df[['Mileage', 'Doors', 'Model_ord']]
   
3.     ...: y=df[['Price']]
   
4.     ...: X1=sm.add_constant(X)
   
5.     ...: est=sm.OLS(y, X1).fit()
   
6.     ...:
   
7.     ...: est.summary()
   
8.     ...:
   
9. Out[13]:
   
10. <class 'statsmodels.iolib.summary.Summary'>
    
11. """
    
12.                             OLS Regression Results
    
13. ==============================================================================
    
14. Dep. Variable: Price R-squared: 0.042
    
15. Model: OLS Adj. R-squared: 0.038
    
16. Method: Least Squares F-statistic: 11.57
    
17. Date: Sun, 08 Jul 2018 Prob (F-statistic): 1.98e-07
    
18. Time: 20:52:16 Log-Likelihood: -8519.1
    
19. No. Observations: 804 AIC: 1.705e+04
    
20. Df Residuals: 800 BIC: 1.706e+04
    
21. Df Model: 3
    
22. Covariance Type: nonrobust
    
23. ==============================================================================
    
24.                  coef std err t P>|t| [0.025 0.975]
    
25. ------------------------------------------------------------------------------
    
26. const 3.125e+04 1809.549 17.272 0.000 2.77e+04 3.48e+04
    
27. Mileage -0.1765 0.042 -4.227 0.000 -0.259 -0.095
    
28. Doors -1652.9303 402.649 -4.105 0.000 -2443.303 -862.558
    
29. Model_ord -39.0387 39.326 -0.993 0.321 -116.234 38.157
    
30. ==============================================================================
    
31. Omnibus: 206.410 Durbin-Watson: 0.080
    
32. Prob(Omnibus): 0.000 Jarque-Bera (JB): 470.872
    
33. Skew: 1.379 Prob(JB): 5.64e-103
    
34. Kurtosis: 5.541 Cond. No. 1.15e+05
    
35. ==============================================================================
    
36. 
    
37. Warnings:
    
38. [1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
    
39. [2] The condition number is large, 1.15e+05. This might indicate that there are
    
40. strong multicollinearity or other numerical problems.
    
41. """

3. 最后

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1. #The table of coefficients above give us the values to plug into an equation of form B0 + B1 mileage + B2 model_ord + B3 * doors
   
2. #In this example it's pretty clear that the number of cylinders is more important than anything based on the coefficient.
   
3. #Could we have figured that outliers?
   
4. y.groupby(df.Doors).mean()
   
5. #surpringly , more doors does not mean a higher price, so it's not surprising that it's pretty useless as a predictor here.