3.2: Multiple predictors



In [1]:

    
from __future__ import print_function, division
%matplotlib inline

import matplotlib
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
# use matplotlib style sheet
plt.style.use('ggplot')

# import statsmodels for R-style regression
import statsmodels.formula.api as smf

Read the data

Data are in the child.iq directory of the ARM_Data download-- you might have to change the path I use below to reflect the path on your computer.



In [2]:

    
kidiq  = pd.read_stata("../../ARM_Data/child.iq/kidiq.dta")
kidiq.head()

Regression -- multiple predictors, Pg 33



In [3]:

    
fit= smf.ols('kid_score ~ mom_hs + mom_iq', data=kidiq).fit()
print(fit.summary())









    



                            OLS Regression Results                            
==============================================================================
Dep. Variable:              kid_score   R-squared:                       0.214
Model:                            OLS   Adj. R-squared:                  0.210
Method:                 Least Squares   F-statistic:                     58.72
Date:                Thu, 30 Jul 2015   Prob (F-statistic):           2.79e-23
Time:                        13:24:50   Log-Likelihood:                -1872.0
No. Observations:                 434   AIC:                             3750.
Df Residuals:                     431   BIC:                             3762.
Df Model:                           2                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [95.0% Conf. Int.]
------------------------------------------------------------------------------
Intercept     25.7315      5.875      4.380      0.000        14.184    37.279
mom_hs         5.9501      2.212      2.690      0.007         1.603    10.297
mom_iq         0.5639      0.061      9.309      0.000         0.445     0.683
==============================================================================
Omnibus:                        7.327   Durbin-Watson:                   1.625
Prob(Omnibus):                  0.026   Jarque-Bera (JB):                7.530
Skew:                          -0.313   Prob(JB):                       0.0232
Kurtosis:                       2.845   Cond. No.                         683.
==============================================================================

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

Figure 3.3, Pg 33



In [4]:

    
fig, ax = plt.subplots(figsize=(8, 6))
iq_linspace = np.linspace(kidiq['mom_iq'].min(), kidiq['mom_iq'].max(), 50)

# default color cycle
colors = plt.rcParams['axes.color_cycle']

# mom_hs == 0
hs0 = (kidiq['mom_hs'] == 0)
plt.scatter(kidiq[hs0]['mom_iq'], kidiq[hs0]['kid_score'],
            s=60, alpha=0.5, c=colors[0])
# mom_hs == 1
hs1 = (kidiq['mom_hs'] == 1)
plt.scatter(kidiq[hs1]['mom_iq'], kidiq[hs1]['kid_score'],
            s=60, alpha=0.5, c=colors[1])

# add fits
# mom_hs == 0
plt.plot(iq_linspace, fit.params[0] + fit.params[1] * 0. + fit.params[2] * iq_linspace,
         lw=3, c=colors[0])
# mom_hs == 1
plt.plot(iq_linspace, fit.params[0] + fit.params[1] * 1. + fit.params[2] * iq_linspace,
         lw=3, c=colors[1])

plt.xlabel("Mother IQ score")
plt.ylabel("Child test score")









    Out[4]:





<matplotlib.text.Text at 0x7f8736a66290>

	kid_score	mom_hs	mom_iq	mom_work	mom_age
0	65	1	121.117529	4	27
1	98	1	89.361882	4	25
2	85	1	115.443165	4	27
3	83	1	99.449639	3	25
4	115	1	92.745710	4	27