Exercise 3.10

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]:

    

carseats = pd.read_csv('data/carseats.csv')
model = smf.ols('Sales ~ Price + Urban + US', data=carseats)
fit = model.fit()
print(fit.summary())


    

    




                            OLS Regression Results                            
==============================================================================
Dep. Variable:                  Sales   R-squared:                       0.239
Model:                            OLS   Adj. R-squared:                  0.234
Method:                 Least Squares   F-statistic:                     41.52
Date:                Sun, 09 Aug 2015   Prob (F-statistic):           2.39e-23
Time:                        12:56:45   Log-Likelihood:                -927.66
No. Observations:                 400   AIC:                             1863.
Df Residuals:                     396   BIC:                             1879.
Df Model:                           3                                         
Covariance Type:            nonrobust                                         
================================================================================
                   coef    std err          t      P>|t|      [95.0% Conf. Int.]
--------------------------------------------------------------------------------
Intercept       13.0435      0.651     20.036      0.000        11.764    14.323
Urban[T.Yes]    -0.0219      0.272     -0.081      0.936        -0.556     0.512
US[T.Yes]        1.2006      0.259      4.635      0.000         0.691     1.710
Price           -0.0545      0.005    -10.389      0.000        -0.065    -0.044
==============================================================================
Omnibus:                        0.676   Durbin-Watson:                   1.912
Prob(Omnibus):                  0.713   Jarque-Bera (JB):                0.758
Skew:                           0.093   Prob(JB):                        0.684
Kurtosis:                       2.897   Cond. No.                         628.
==============================================================================

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

In [3]:

    

model2 = smf.ols('Sales ~ Price + US', data=carseats)
fit2 = model2.fit()
print(fit2.summary())


    

    




                            OLS Regression Results                            
==============================================================================
Dep. Variable:                  Sales   R-squared:                       0.239
Model:                            OLS   Adj. R-squared:                  0.235
Method:                 Least Squares   F-statistic:                     62.43
Date:                Sun, 09 Aug 2015   Prob (F-statistic):           2.66e-24
Time:                        12:57:26   Log-Likelihood:                -927.66
No. Observations:                 400   AIC:                             1861.
Df Residuals:                     397   BIC:                             1873.
Df Model:                           2                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [95.0% Conf. Int.]
------------------------------------------------------------------------------
Intercept     13.0308      0.631     20.652      0.000        11.790    14.271
US[T.Yes]      1.1996      0.258      4.641      0.000         0.692     1.708
Price         -0.0545      0.005    -10.416      0.000        -0.065    -0.044
==============================================================================
Omnibus:                        0.666   Durbin-Watson:                   1.912
Prob(Omnibus):                  0.717   Jarque-Bera (JB):                0.749
Skew:                           0.092   Prob(JB):                        0.688
Kurtosis:                       2.895   Cond. No.                         607.
==============================================================================

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

In [13]:

    

plt.figure(figsize=(18, 6))
ax = plt.subplot(131)
plt.plot(carseats['Price'], fit2.resid, 'o', [20, 200], [0, 0], 'r-')
ax = plt.subplot(132)
fig = sm.qqplot(fit2.resid, line='s', ax=ax)
ax = plt.subplot(133)
fig = sm.graphics.influence_plot(fit2, ax=ax, size=10)
xmin, xmax = plt.xlim(-0.001, 0.04)


    

In [ ]: