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

#statsmodel package
#ImportError: Install xlrd >= 0.9.0 for Excel support , need xlrd.

apt-get install python3-xlrd
import pandas as pd
df=pd.read_excel("")
df.head()

1st version code

import statsmodels.api as sm
from sklearn.preprocessing import StandardScaler

scale= StandardScaler()
X=df[['Mileage','Cylinder', 'Doors', 'Model_ord']]
y=df[['Price']]

X[['Mileage', 'Cylinder', 'Doors']]=scale.fit_transform(X[['Mileage', 'Cylinder', 'Doors']].as_matrix())
print(X)
est=sm.OLS(y, X).fit()
est.summary()

2nd version

'''2nd version code '''
df['Model_ord'] = pd.Categorical(df.Model).codes
X=df[['Mileage','Cylinder', 'Doors', 'Model_ord']]
y=df[['Price']]
X1=sm.add_constant(X)
est=sm.OLS(y, X1).fit()

est.summary()

2种方式得到的summary page是完全一样的.

"""
                            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
==============================================================================

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', ]]

In [13]: df['Model_ord'] = pd.Categorical(df.Model).codes
    ...: X=df[['Mileage', 'Doors', 'Model_ord']]
    ...: y=df[['Price']]
    ...: X1=sm.add_constant(X)
    ...: est=sm.OLS(y, X1).fit()
    ...:
    ...: est.summary()
    ...:
Out[13]:
<class 'statsmodels.iolib.summary.Summary'>
"""
                            OLS Regression Results
==============================================================================
Dep. Variable:                  Price   R-squared:                       0.042
Model:                            OLS   Adj. R-squared:                  0.038
Method:                 Least Squares   F-statistic:                     11.57
Date:                Sun, 08 Jul 2018   Prob (F-statistic):           1.98e-07
Time:                        20:52:16   Log-Likelihood:                -8519.1
No. Observations:                 804   AIC:                         1.705e+04
Df Residuals:                     800   BIC:                         1.706e+04
Df Model:                           3
Covariance Type:            nonrobust
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const       3.125e+04   1809.549     17.272      0.000    2.77e+04    3.48e+04
Mileage       -0.1765      0.042     -4.227      0.000      -0.259      -0.095
Doors      -1652.9303    402.649     -4.105      0.000   -2443.303    -862.558
Model_ord    -39.0387     39.326     -0.993      0.321    -116.234      38.157
==============================================================================
Omnibus:                      206.410   Durbin-Watson:                   0.080
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              470.872
Skew:                           1.379   Prob(JB):                    5.64e-103
Kurtosis:                       5.541   Cond. No.                     1.15e+05
==============================================================================

Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.15e+05. This might indicate that there are
strong multicollinearity or other numerical problems.
"""

3. 最后

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