Exercise 3.9



In [1]:

    
%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import seaborn as sns
import statsmodels.api as sm
import statsmodels.formula.api as smf

3.9 a



In [2]:

    
auto = pd.read_csv('data/Auto.csv', na_values=['?'])
subset = auto.dropna()
sns.pairplot(subset[:-1]) # pairplot doesn't like NaN's









    Out[2]:





<seaborn.axisgrid.PairGrid at 0x8fb7f98>

3.9 b



In [3]:

    
auto.corr()









    Out[3]:






  
    
      
      mpg
      cylinders
      displacement
      horsepower
      weight
      acceleration
      year
      origin
    
  
  
    
      mpg
      1.000000
      -0.776260
      -0.804443
      -0.778427
      -0.831739
      0.422297
      0.581469
      0.563698
    
    
      cylinders
      -0.776260
      1.000000
      0.950920
      0.842983
      0.897017
      -0.504061
      -0.346717
      -0.564972
    
    
      displacement
      -0.804443
      0.950920
      1.000000
      0.897257
      0.933104
      -0.544162
      -0.369804
      -0.610664
    
    
      horsepower
      -0.778427
      0.842983
      0.897257
      1.000000
      0.864538
      -0.689196
      -0.416361
      -0.455171
    
    
      weight
      -0.831739
      0.897017
      0.933104
      0.864538
      1.000000
      -0.419502
      -0.307900
      -0.581265
    
    
      acceleration
      0.422297
      -0.504061
      -0.544162
      -0.689196
      -0.419502
      1.000000
      0.282901
      0.210084
    
    
      year
      0.581469
      -0.346717
      -0.369804
      -0.416361
      -0.307900
      0.282901
      1.000000
      0.184314
    
    
      origin
      0.563698
      -0.564972
      -0.610664
      -0.455171
      -0.581265
      0.210084
      0.184314
      1.000000

3.9 c



In [4]:

    
formula = 'mpg ~ ' + '+'.join(auto.columns.difference(['mpg', 'name']))
model = smf.ols(formula, data=auto)
fit = model.fit()
print(fit.summary())









    



                            OLS Regression Results                            
==============================================================================
Dep. Variable:                    mpg   R-squared:                       0.821
Model:                            OLS   Adj. R-squared:                  0.818
Method:                 Least Squares   F-statistic:                     252.4
Date:                Sun, 09 Aug 2015   Prob (F-statistic):          2.04e-139
Time:                        13:14:41   Log-Likelihood:                -1023.5
No. Observations:                 392   AIC:                             2063.
Df Residuals:                     384   BIC:                             2095.
Df Model:                           7                                         
Covariance Type:            nonrobust                                         
================================================================================
                   coef    std err          t      P>|t|      [95.0% Conf. Int.]
--------------------------------------------------------------------------------
Intercept      -17.2184      4.644     -3.707      0.000       -26.350    -8.087
acceleration     0.0806      0.099      0.815      0.415        -0.114     0.275
cylinders       -0.4934      0.323     -1.526      0.128        -1.129     0.142
displacement     0.0199      0.008      2.647      0.008         0.005     0.035
horsepower      -0.0170      0.014     -1.230      0.220        -0.044     0.010
origin           1.4261      0.278      5.127      0.000         0.879     1.973
weight          -0.0065      0.001     -9.929      0.000        -0.008    -0.005
year             0.7508      0.051     14.729      0.000         0.651     0.851
==============================================================================
Omnibus:                       31.906   Durbin-Watson:                   1.309
Prob(Omnibus):                  0.000   Jarque-Bera (JB):               53.100
Skew:                           0.529   Prob(JB):                     2.95e-12
Kurtosis:                       4.460   Cond. No.                     8.59e+04
==============================================================================

Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 8.59e+04. This might indicate that there are
strong multicollinearity or other numerical problems.



In [ ]:

	mpg	cylinders	displacement	horsepower	weight	acceleration	year	origin
mpg	1.000000	-0.776260	-0.804443	-0.778427	-0.831739	0.422297	0.581469	0.563698
cylinders	-0.776260	1.000000	0.950920	0.842983	0.897017	-0.504061	-0.346717	-0.564972
displacement	-0.804443	0.950920	1.000000	0.897257	0.933104	-0.544162	-0.369804	-0.610664
horsepower	-0.778427	0.842983	0.897257	1.000000	0.864538	-0.689196	-0.416361	-0.455171
weight	-0.831739	0.897017	0.933104	0.864538	1.000000	-0.419502	-0.307900	-0.581265
acceleration	0.422297	-0.504061	-0.544162	-0.689196	-0.419502	1.000000	0.282901	0.210084
year	0.581469	-0.346717	-0.369804	-0.416361	-0.307900	0.282901	1.000000	0.184314
origin	0.563698	-0.564972	-0.610664	-0.455171	-0.581265	0.210084	0.184314	1.000000