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


    

In [2]:

    

auto = pd.read_csv('data/Auto.csv', na_values=['?'])
auto.describe()


    

    
Out[2]:






  

    

      

      
mpg
      
cylinders
      
displacement
      
horsepower
      
weight
      
acceleration
      
year
      
origin
    
  
  

    

      
count
      
397.000000
      
397.000000
      
397.000000
      
392.000000
      
397.000000
      
397.000000
      
397.000000
      
397.000000
    
    

      
mean
      
23.515869
      
5.458438
      
193.532746
      
104.469388
      
2970.261965
      
15.555668
      
75.994962
      
1.574307
    
    

      
std
      
7.825804
      
1.701577
      
104.379583
      
38.491160
      
847.904119
      
2.749995
      
3.690005
      
0.802549
    
    

      
min
      
9.000000
      
3.000000
      
68.000000
      
46.000000
      
1613.000000
      
8.000000
      
70.000000
      
1.000000
    
    

      
25%
      
17.500000
      
4.000000
      
104.000000
      
75.000000
      
2223.000000
      
13.800000
      
73.000000
      
1.000000
    
    

      
50%
      
23.000000
      
4.000000
      
146.000000
      
93.500000
      
2800.000000
      
15.500000
      
76.000000
      
1.000000
    
    

      
75%
      
29.000000
      
8.000000
      
262.000000
      
126.000000
      
3609.000000
      
17.100000
      
79.000000
      
2.000000
    
    

      
max
      
46.600000
      
8.000000
      
455.000000
      
230.000000
      
5140.000000
      
24.800000
      
82.000000
      
3.000000
    
  

In [3]:

    

fit = smf.ols('mpg ~ horsepower', data=auto).fit()
print(fit.summary())


    

    




                            OLS Regression Results                            
==============================================================================
Dep. Variable:                    mpg   R-squared:                       0.606
Model:                            OLS   Adj. R-squared:                  0.605
Method:                 Least Squares   F-statistic:                     599.7
Date:                Sun, 09 Aug 2015   Prob (F-statistic):           7.03e-81
Time:                        13:15:54   Log-Likelihood:                -1178.7
No. Observations:                 392   AIC:                             2361.
Df Residuals:                     390   BIC:                             2369.
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [95.0% Conf. Int.]
------------------------------------------------------------------------------
Intercept     39.9359      0.717     55.660      0.000        38.525    41.347
horsepower    -0.1578      0.006    -24.489      0.000        -0.171    -0.145
==============================================================================
Omnibus:                       16.432   Durbin-Watson:                   0.920
Prob(Omnibus):                  0.000   Jarque-Bera (JB):               17.305
Skew:                           0.492   Prob(JB):                     0.000175
Kurtosis:                       3.299   Cond. No.                         322.
==============================================================================

Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

In [4]:

    

# fit.predict has a bug in statsmodels 6.1 that should be corrected for 7.0
estimate = fit.params['Intercept'] + 98 * fit.params['horsepower']
print('The mpg associated with a horsepower of 98 is', estimate)


    

    




The mpg associated with a horsepower of 98 is 24.4670771525

In [5]:

    

sns.regplot(y='mpg', x='horsepower', data=auto, scatter_kws={'color': 'red'})


    

    
Out[5]:





<matplotlib.axes._subplots.AxesSubplot at 0x9af1080>






    

In [6]:

    

plt.figure(figsize=(18, 6))
plt.subplot(131)
sns.residplot(y='mpg', x='horsepower', data=auto, scatter_kws={'color': 'red'})
ax = plt.subplot(132)
fig = sm.qqplot(fit.resid, line='s', ax=ax)
ax = plt.subplot(133)
fig = sm.graphics.influence_plot(fit, ax=ax, size=10)
xmin, xmax = plt.xlim((-0.001, 0.04))