Copyright 2016 Allen B. Downey

MIT License: https://opensource.org/licenses/MIT

```
In [1]:
```%matplotlib inline
import numpy as np
import pandas as pd
import thinkstats2
import thinkplot

```
In [2]:
```import first
live, firsts, others = first.MakeFrames()

Here's birth weight as a function of mother's age (which we saw in the previous chapter).

```
In [3]:
```import statsmodels.formula.api as smf
formula = 'totalwgt_lb ~ agepreg'
model = smf.ols(formula, data=live)
results = model.fit()
results.summary()

```
Out[3]:
```
OLS Regression Results
Dep. Variable: totalwgt_lb R-squared: 0.005
Model: OLS Adj. R-squared: 0.005
Method: Least Squares F-statistic: 43.02
Date: Thu, 28 Feb 2019 Prob (F-statistic): 5.72e-11
Time: 09:58:53 Log-Likelihood: -15897.
No. Observations: 9038 AIC: 3.180e+04
Df Residuals: 9036 BIC: 3.181e+04
Df Model: 1
Covariance Type: nonrobust

coef std err t P>|t| [0.025 0.975]
Intercept 6.8304 0.068 100.470 0.000 6.697 6.964
agepreg 0.0175 0.003 6.559 0.000 0.012 0.023

Omnibus: 1024.052 Durbin-Watson: 1.618
Prob(Omnibus): 0.000 Jarque-Bera (JB): 3081.833
Skew: -0.601 Prob(JB): 0.00
Kurtosis: 5.596 Cond. No. 118.

Warnings:

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

We can extract the parameters.

```
In [4]:
```inter = results.params['Intercept']
slope = results.params['agepreg']
inter, slope

```
Out[4]:
```(6.830396973311047, 0.017453851471802877)

And the p-value of the slope estimate.

```
In [5]:
```slope_pvalue = results.pvalues['agepreg']
slope_pvalue

```
Out[5]:
```5.722947107312786e-11

And the coefficient of determination.

```
In [6]:
```results.rsquared

```
Out[6]:
```0.004738115474710369

The difference in birth weight between first babies and others.

```
In [7]:
```diff_weight = firsts.totalwgt_lb.mean() - others.totalwgt_lb.mean()
diff_weight

```
Out[7]:
```-0.12476118453549034

The difference in age between mothers of first babies and others.

```
In [8]:
```diff_age = firsts.agepreg.mean() - others.agepreg.mean()
diff_age

```
Out[8]:
```-3.5864347661500275

The age difference plausibly explains about half of the difference in weight.

```
In [9]:
```slope * diff_age

```
Out[9]:
```-0.06259709972169267

Running a single regression with a categorical variable, `isfirst`

:

```
In [10]:
```live['isfirst'] = live.birthord == 1
formula = 'totalwgt_lb ~ isfirst'
results = smf.ols(formula, data=live).fit()
results.summary()

```
Out[10]:
```
OLS Regression Results
Dep. Variable: totalwgt_lb R-squared: 0.002
Model: OLS Adj. R-squared: 0.002
Method: Least Squares F-statistic: 17.74
Date: Thu, 28 Feb 2019 Prob (F-statistic): 2.55e-05
Time: 09:58:53 Log-Likelihood: -15909.
No. Observations: 9038 AIC: 3.182e+04
Df Residuals: 9036 BIC: 3.184e+04
Df Model: 1
Covariance Type: nonrobust

coef std err t P>|t| [0.025 0.975]
Intercept 7.3259 0.021 356.007 0.000 7.286 7.366
isfirst[T.True] -0.1248 0.030 -4.212 0.000 -0.183 -0.067

Omnibus: 988.919 Durbin-Watson: 1.613
Prob(Omnibus): 0.000 Jarque-Bera (JB): 2897.107
Skew: -0.589 Prob(JB): 0.00
Kurtosis: 5.511 Cond. No. 2.58

Warnings:

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

Now finally running a multiple regression:

```
In [11]:
```formula = 'totalwgt_lb ~ isfirst + agepreg'
results = smf.ols(formula, data=live).fit()
results.summary()

```
Out[11]:
```
OLS Regression Results
Dep. Variable: totalwgt_lb R-squared: 0.005
Model: OLS Adj. R-squared: 0.005
Method: Least Squares F-statistic: 24.02
Date: Thu, 28 Feb 2019 Prob (F-statistic): 3.95e-11
Time: 09:58:53 Log-Likelihood: -15894.
No. Observations: 9038 AIC: 3.179e+04
Df Residuals: 9035 BIC: 3.182e+04
Df Model: 2
Covariance Type: nonrobust

coef std err t P>|t| [0.025 0.975]
Intercept 6.9142 0.078 89.073 0.000 6.762 7.066
isfirst[T.True] -0.0698 0.031 -2.236 0.025 -0.131 -0.009
agepreg 0.0154 0.003 5.499 0.000 0.010 0.021

Omnibus: 1019.945 Durbin-Watson: 1.618
Prob(Omnibus): 0.000 Jarque-Bera (JB): 3063.682
Skew: -0.599 Prob(JB): 0.00
Kurtosis: 5.588 Cond. No. 137.

Warnings:

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

As expected, when we control for mother's age, the apparent difference due to `isfirst`

is cut in half.

If we add age squared, we can control for a quadratic relationship between age and weight.

```
In [12]:
```live['agepreg2'] = live.agepreg**2
formula = 'totalwgt_lb ~ isfirst + agepreg + agepreg2'
results = smf.ols(formula, data=live).fit()
results.summary()

```
Out[12]:
```
OLS Regression Results
Dep. Variable: totalwgt_lb R-squared: 0.007
Model: OLS Adj. R-squared: 0.007
Method: Least Squares F-statistic: 22.64
Date: Thu, 28 Feb 2019 Prob (F-statistic): 1.35e-14
Time: 09:58:54 Log-Likelihood: -15884.
No. Observations: 9038 AIC: 3.178e+04
Df Residuals: 9034 BIC: 3.181e+04
Df Model: 3
Covariance Type: nonrobust

coef std err t P>|t| [0.025 0.975]
Intercept 5.6923 0.286 19.937 0.000 5.133 6.252
isfirst[T.True] -0.0504 0.031 -1.602 0.109 -0.112 0.011
agepreg 0.1124 0.022 5.113 0.000 0.069 0.155
agepreg2 -0.0018 0.000 -4.447 0.000 -0.003 -0.001

Omnibus: 1007.149 Durbin-Watson: 1.616
Prob(Omnibus): 0.000 Jarque-Bera (JB): 3003.343
Skew: -0.594 Prob(JB): 0.00
Kurtosis: 5.562 Cond. No. 1.39e+04

Warnings:

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

[2] The condition number is large, 1.39e+04. This might indicate that there are

strong multicollinearity or other numerical problems.

When we do that, the apparent effect of `isfirst`

gets even smaller, and is no longer statistically significant.

These results suggest that the apparent difference in weight between first babies and others might be explained by difference in mothers' ages, at least in part.

```
In [13]:
```import nsfg
live = live[live.prglngth>30]
resp = nsfg.ReadFemResp()
resp.index = resp.caseid
join = live.join(resp, on='caseid', rsuffix='_r')

And we can search for variables with explanatory power.

Because we don't clean most of the variables, we are probably missing some good ones.

```
In [14]:
```import patsy
def GoMining(df):
"""Searches for variables that predict birth weight.
df: DataFrame of pregnancy records
returns: list of (rsquared, variable name) pairs
"""
variables = []
for name in df.columns:
try:
if df[name].var() < 1e-7:
continue
formula = 'totalwgt_lb ~ agepreg + ' + name
formula = formula.encode('ascii')
model = smf.ols(formula, data=df)
if model.nobs < len(df)/2:
continue
results = model.fit()
except (ValueError, TypeError, patsy.PatsyError):
continue
variables.append((results.rsquared, name))
return variables

```
In [15]:
```variables = GoMining(join)

The following functions report the variables with the highest values of $R^2$.

```
In [16]:
```import re
def ReadVariables():
"""Reads Stata dictionary files for NSFG data.
returns: DataFrame that maps variables names to descriptions
"""
vars1 = thinkstats2.ReadStataDct('2002FemPreg.dct').variables
vars2 = thinkstats2.ReadStataDct('2002FemResp.dct').variables
all_vars = vars1.append(vars2)
all_vars.index = all_vars.name
return all_vars
def MiningReport(variables, n=30):
"""Prints variables with the highest R^2.
t: list of (R^2, variable name) pairs
n: number of pairs to print
"""
all_vars = ReadVariables()
variables.sort(reverse=True)
for r2, name in variables[:n]:
key = re.sub('_r$', '', name)
try:
desc = all_vars.loc[key].desc
if isinstance(desc, pd.Series):
desc = desc[0]
print(name, r2, desc)
except (KeyError, IndexError):
print(name, r2)

```
In [17]:
```MiningReport(variables)

Combining the variables that seem to have the most explanatory power.

```
In [18]:
```formula = ('totalwgt_lb ~ agepreg + C(race) + babysex==1 + '
'nbrnaliv>1 + paydu==1 + totincr')
results = smf.ols(formula, data=join).fit()
results.summary()

```
Out[18]:
```
OLS Regression Results
Dep. Variable: totalwgt_lb R-squared: 0.060
Model: OLS Adj. R-squared: 0.059
Method: Least Squares F-statistic: 79.98
Date: Thu, 28 Feb 2019 Prob (F-statistic): 4.86e-113
Time: 09:59:13 Log-Likelihood: -14295.
No. Observations: 8781 AIC: 2.861e+04
Df Residuals: 8773 BIC: 2.866e+04
Df Model: 7
Covariance Type: nonrobust

coef std err t P>|t| [0.025 0.975]
Intercept 6.6303 0.065 102.223 0.000 6.503 6.757
C(race)[T.2] 0.3570 0.032 11.215 0.000 0.295 0.419
C(race)[T.3] 0.2665 0.051 5.175 0.000 0.166 0.367
babysex == 1[T.True] 0.2952 0.026 11.216 0.000 0.244 0.347
nbrnaliv > 1[T.True] -1.3783 0.108 -12.771 0.000 -1.590 -1.167
paydu == 1[T.True] 0.1196 0.031 3.861 0.000 0.059 0.180
agepreg 0.0074 0.003 2.921 0.004 0.002 0.012
totincr 0.0122 0.004 3.110 0.002 0.005 0.020

Omnibus: 398.813 Durbin-Watson: 1.604
Prob(Omnibus): 0.000 Jarque-Bera (JB): 1388.362
Skew: -0.037 Prob(JB): 3.32e-302
Kurtosis: 4.947 Cond. No. 221.

Warnings:

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

```
In [19]:
```y = np.array([0, 1, 0, 1])
x1 = np.array([0, 0, 0, 1])
x2 = np.array([0, 1, 1, 1])

According to the logit model the log odds for the $i$th element of $y$ is

$\log o = \beta_0 + \beta_1 x_1 + \beta_2 x_2 $

So let's start with an arbitrary guess about the elements of $\beta$:

```
In [20]:
```beta = [-1.5, 2.8, 1.1]

Plugging in the model, we get log odds.

```
In [21]:
```log_o = beta[0] + beta[1] * x1 + beta[2] * x2
log_o

```
Out[21]:
```array([-1.5, -0.4, -0.4, 2.4])

Which we can convert to odds.

```
In [22]:
```o = np.exp(log_o)
o

```
Out[22]:
```array([ 0.22313016, 0.67032005, 0.67032005, 11.02317638])

And then convert to probabilities.

```
In [23]:
```p = o / (o+1)
p

```
Out[23]:
```array([0.18242552, 0.40131234, 0.40131234, 0.9168273 ])

The likelihoods of the actual outcomes are $p$ where $y$ is 1 and $1-p$ where $y$ is 0.

```
In [24]:
```likes = np.where(y, p, 1-p)
likes

```
Out[24]:
```array([0.81757448, 0.40131234, 0.59868766, 0.9168273 ])

The likelihood of $y$ given $\beta$ is the product of `likes`

:

```
In [25]:
```like = np.prod(likes)
like

```
Out[25]:
```0.1800933529673034

Logistic regression works by searching for the values in $\beta$ that maximize `like`

.

Here's an example using variables in the NSFG respondent file to predict whether a baby will be a boy or a girl.

```
In [26]:
```import first
live, firsts, others = first.MakeFrames()
live = live[live.prglngth>30]
live['boy'] = (live.babysex==1).astype(int)

The mother's age seems to have a small effect.

```
In [27]:
```model = smf.logit('boy ~ agepreg', data=live)
results = model.fit()
results.summary()

```
```Optimization terminated successfully.
Current function value: 0.693015
Iterations 3

Out[27]:
Logit Regression Results
Dep. Variable: boy No. Observations: 8884
Model: Logit Df Residuals: 8882
Method: MLE Df Model: 1
Date: Thu, 28 Feb 2019 Pseudo R-squ.: 6.144e-06
Time: 09:59:16 Log-Likelihood: -6156.7
converged: True LL-Null: -6156.8
LLR p-value: 0.7833

coef std err z P>|z| [0.025 0.975]
Intercept 0.0058 0.098 0.059 0.953 -0.185 0.197
agepreg 0.0010 0.004 0.275 0.783 -0.006 0.009

Here are the variables that seemed most promising.

```
In [28]:
```formula = 'boy ~ agepreg + hpagelb + birthord + C(race)'
model = smf.logit(formula, data=live)
results = model.fit()
results.summary()

```
```Optimization terminated successfully.
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Out[28]:
Logit Regression Results
Dep. Variable: boy No. Observations: 8782
Model: Logit Df Residuals: 8776
Method: MLE Df Model: 5
Date: Thu, 28 Feb 2019 Pseudo R-squ.: 0.0001440
Time: 09:59:16 Log-Likelihood: -6085.4
converged: True LL-Null: -6086.3
LLR p-value: 0.8822

coef std err z P>|z| [0.025 0.975]
Intercept -0.0301 0.104 -0.290 0.772 -0.234 0.173
C(race)[T.2] -0.0224 0.051 -0.439 0.660 -0.122 0.077
C(race)[T.3] -0.0005 0.083 -0.005 0.996 -0.163 0.162
agepreg -0.0027 0.006 -0.484 0.629 -0.014 0.008
hpagelb 0.0047 0.004 1.112 0.266 -0.004 0.013
birthord 0.0050 0.022 0.227 0.821 -0.038 0.048

To make a prediction, we have to extract the exogenous and endogenous variables.

```
In [29]:
```endog = pd.DataFrame(model.endog, columns=[model.endog_names])
exog = pd.DataFrame(model.exog, columns=model.exog_names)

```
In [30]:
```actual = endog['boy']
baseline = actual.mean()
baseline

```
Out[30]:
```0.507173764518333

If we use the previous model, we can compute the number of predictions we get right.

```
In [31]:
```predict = (results.predict() >= 0.5)
true_pos = predict * actual
true_neg = (1 - predict) * (1 - actual)
sum(true_pos), sum(true_neg)

```
Out[31]:
```(3944.0, 548.0)

And the accuracy, which is slightly higher than the baseline.

```
In [32]:
```acc = (sum(true_pos) + sum(true_neg)) / len(actual)
acc

```
Out[32]:
```0.5115007970849464

To make a prediction for an individual, we have to get their information into a `DataFrame`

.

```
In [33]:
```columns = ['agepreg', 'hpagelb', 'birthord', 'race']
new = pd.DataFrame([[35, 39, 3, 2]], columns=columns)
y = results.predict(new)
y

```
Out[33]:
```0 0.513091
dtype: float64

This person has a 51% chance of having a boy (according to the model).

**Exercise:** Suppose one of your co-workers is expecting a baby and you are participating in an office pool to predict the date of birth. Assuming that bets are placed during the 30th week of pregnancy, what variables could you use to make the best prediction? You should limit yourself to variables that are known before the birth, and likely to be available to the people in the pool.

```
In [34]:
```import first
live, firsts, others = first.MakeFrames()
live = live[live.prglngth>30]

```
In [35]:
```import statsmodels.formula.api as smf
model = smf.ols('prglngth ~ birthord==1 + race==2 + nbrnaliv>1', data=live)
results = model.fit()
results.summary()

```
Out[35]:
```
OLS Regression Results
Dep. Variable: prglngth R-squared: 0.011
Model: OLS Adj. R-squared: 0.011
Method: Least Squares F-statistic: 34.28
Date: Thu, 28 Feb 2019 Prob (F-statistic): 5.09e-22
Time: 09:59:18 Log-Likelihood: -18247.
No. Observations: 8884 AIC: 3.650e+04
Df Residuals: 8880 BIC: 3.653e+04
Df Model: 3
Covariance Type: nonrobust

coef std err t P>|t| [0.025 0.975]
Intercept 38.7617 0.039 1006.410 0.000 38.686 38.837
birthord == 1[T.True] 0.1015 0.040 2.528 0.011 0.023 0.180
race == 2[T.True] 0.1390 0.042 3.311 0.001 0.057 0.221
nbrnaliv > 1[T.True] -1.4944 0.164 -9.086 0.000 -1.817 -1.172

Omnibus: 1587.470 Durbin-Watson: 1.619
Prob(Omnibus): 0.000 Jarque-Bera (JB): 6160.751
Skew: -0.852 Prob(JB): 0.00
Kurtosis: 6.707 Cond. No. 10.9

Warnings:

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

**Exercise:** The Trivers-Willard hypothesis suggests that for many mammals the sex ratio depends on “maternal condition”; that is, factors like the mother’s age, size, health, and social status. See https://en.wikipedia.org/wiki/Trivers-Willard_hypothesis

Some studies have shown this effect among humans, but results are mixed. In this chapter we tested some variables related to these factors, but didn’t find any with a statistically significant effect on sex ratio.

As an exercise, use a data mining approach to test the other variables in the pregnancy and respondent files. Can you find any factors with a substantial effect?

```
In [36]:
```# Solution
def GoMining(df):
"""Searches for variables that predict birth weight.
df: DataFrame of pregnancy records
returns: list of (rsquared, variable name) pairs
"""
df['boy'] = (df.babysex==1).astype(int)
variables = []
for name in df.columns:
try:
if df[name].var() < 1e-7:
continue
formula='boy ~ agepreg + ' + name
model = smf.logit(formula, data=df)
nobs = len(model.endog)
if nobs < len(df)/2:
continue
results = model.fit()
except:
continue
variables.append((results.prsquared, name))
return variables
variables = GoMining(join)

```
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Optimization terminated successfully.
Current function value: 0.692652
Iterations 5
Optimization terminated successfully.
Current function value: 0.692991
Iterations 3
Optimization terminated successfully.
Current function value: 0.692918
Iterations 4
Optimization terminated successfully.
Current function value: 0.692984
Iterations 3
Optimization terminated successfully.
Current function value: 0.692952
Iterations 3
Optimization terminated successfully.
Current function value: 0.693008
Iterations 3
Optimization terminated successfully.
Current function value: 0.692893
Iterations 5
Warning: Maximum number of iterations has been exceeded.
Current function value: 0.692776
Iterations: 35
Optimization terminated successfully.
Current function value: 0.692638
Iterations 6
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3

/home/downey/anaconda3/envs/ThinkStats2/lib/python3.7/site-packages/statsmodels/base/model.py:508: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
"Check mle_retvals", ConvergenceWarning)

Optimization terminated successfully.
Current function value: 0.692838
Iterations 5
Optimization terminated successfully.
Current function value: 0.692971
Iterations 3
Optimization terminated successfully.
Current function value: 0.692985
Iterations 4
Optimization terminated successfully.
Current function value: 0.692971
Iterations 3
Optimization terminated successfully.
Current function value: 0.693003
Iterations 3
Optimization terminated successfully.
Current function value: 0.692998
Iterations 4
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.692973
Iterations 3
Optimization terminated successfully.
Current function value: 0.692973
Iterations 4
Optimization terminated successfully.
Current function value: 0.692810
Iterations 4
Optimization terminated successfully.
Current function value: 0.693014
Iterations 3
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.693011
Iterations 3
Optimization terminated successfully.
Current function value: 0.693003
Iterations 3
Optimization terminated successfully.
Current function value: 0.692995
Iterations 3
Optimization terminated successfully.
Current function value: 0.692979
Iterations 3
Optimization terminated successfully.
Current function value: 0.693014
Iterations 3
Optimization terminated successfully.
Current function value: 0.693003
Iterations 3
Optimization terminated successfully.
Current function value: 0.686305
Iterations 4
Optimization terminated successfully.
Current function value: 0.693006
Iterations 3
Optimization terminated successfully.
Current function value: 0.692959
Iterations 3
Optimization terminated successfully.
Current function value: 0.692991
Iterations 3
Optimization terminated successfully.
Current function value: 0.692984
Iterations 3
Optimization terminated successfully.
Current function value: 0.692928
Iterations 5
Optimization terminated successfully.
Current function value: 0.692910
Iterations 3
Optimization terminated successfully.
Current function value: 0.693007
Iterations 3
Optimization terminated successfully.
Current function value: 0.693008
Iterations 3
Optimization terminated successfully.
Current function value: 0.692881
Iterations 3
Optimization terminated successfully.
Current function value: 0.692866
Iterations 3
Optimization terminated successfully.
Current function value: 0.692861
Iterations 3
Optimization terminated successfully.
Current function value: 0.692866
Iterations 3
Optimization terminated successfully.
Current function value: 0.692930
Iterations 3
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Current function value: 0.692806
Iterations 3
Optimization terminated successfully.
Current function value: 0.692808
Iterations 3
Optimization terminated successfully.
Current function value: 0.692986
Iterations 3
Optimization terminated successfully.
Current function value: 0.693004
Iterations 3
Optimization terminated successfully.
Current function value: 0.692985
Iterations 3
Optimization terminated successfully.
Current function value: 0.693039
Iterations 4
Optimization terminated successfully.
Current function value: 0.692886
Iterations 3
Optimization terminated successfully.
Current function value: 0.692957
Iterations 3
Optimization terminated successfully.
Current function value: 0.692888
Iterations 4
Optimization terminated successfully.
Current function value: 0.692989
Iterations 3
Optimization terminated successfully.
Current function value: 0.693006
Iterations 3
Optimization terminated successfully.
Current function value: 0.692921
Iterations 3
Optimization terminated successfully.
Current function value: 0.692996
Iterations 3
Optimization terminated successfully.
Current function value: 0.692907
Iterations 3
Optimization terminated successfully.
Current function value: 0.692439
Iterations 3
Optimization terminated successfully.
Current function value: 0.692916
Iterations 4
Optimization terminated successfully.
Current function value: 0.692951
Iterations 3
Optimization terminated successfully.
Current function value: 0.693014
Iterations 3
Optimization terminated successfully.
Current function value: 0.692950
Iterations 3
Optimization terminated successfully.
Current function value: 0.693037
Iterations 3
Optimization terminated successfully.
Current function value: 0.693021
Iterations 3
Optimization terminated successfully.
Current function value: 0.693018
Iterations 3
Optimization terminated successfully.
Current function value: 0.692850
Iterations 3
Optimization terminated successfully.
Current function value: 0.693056
Iterations 3
Optimization terminated successfully.
Current function value: 0.692885
Iterations 4
Optimization terminated successfully.
Current function value: 0.693007
Iterations 3
Optimization terminated successfully.
Current function value: 0.692963
Iterations 3
Optimization terminated successfully.
Current function value: 0.692994
Iterations 3
Optimization terminated successfully.
Current function value: 0.692959
Iterations 4
Optimization terminated successfully.
Current function value: 0.692319
Iterations 6
Optimization terminated successfully.
Current function value: 0.692984
Iterations 5
Optimization terminated successfully.
Current function value: 0.692841
Iterations 4
Optimization terminated successfully.
Current function value: 0.693006
Iterations 3
Optimization terminated successfully.
Current function value: 0.693014
Iterations 3
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.692879
Iterations 4
Optimization terminated successfully.
Current function value: 0.693007
Iterations 3
Optimization terminated successfully.
Current function value: 0.692871
Iterations 3
Optimization terminated successfully.
Current function value: 0.692993
Iterations 3
Optimization terminated successfully.
Current function value: 0.692997
Iterations 3
Optimization terminated successfully.
Current function value: 0.693013
Iterations 3
Optimization terminated successfully.
Current function value: 0.692956
Iterations 3
Optimization terminated successfully.
Current function value: 0.693010
Iterations 3
Optimization terminated successfully.
Current function value: 0.692780
Iterations 3
Optimization terminated successfully.
Current function value: 0.693055
Iterations 4
Optimization terminated successfully.
Current function value: 0.693104
Iterations 4
Optimization terminated successfully.
Current function value: 0.693022
Iterations 3
Optimization terminated successfully.
Current function value: 0.693069
Iterations 3
Optimization terminated successfully.
Current function value: 0.693052
Iterations 3
Optimization terminated successfully.
Current function value: 0.692988
Iterations 3
Optimization terminated successfully.
Current function value: 0.693037
Iterations 3
Optimization terminated successfully.
Current function value: 0.693063
Iterations 3
Optimization terminated successfully.
Current function value: 0.693052
Iterations 3
Optimization terminated successfully.
Current function value: 0.693078
Iterations 3
Optimization terminated successfully.
Current function value: 0.693078
Iterations 3
Optimization terminated successfully.
Current function value: 0.692964
Iterations 4
Optimization terminated successfully.
Current function value: 0.692801
Iterations 4
Optimization terminated successfully.
Current function value: 0.693074
Iterations 3
Optimization terminated successfully.
Current function value: 0.692959
Iterations 4
Optimization terminated successfully.
Current function value: 0.692995
Iterations 3
Optimization terminated successfully.
Current function value: 0.693013
Iterations 3
Optimization terminated successfully.
Current function value: 0.693004
Iterations 3
Optimization terminated successfully.
Current function value: 0.692911
Iterations 3
Optimization terminated successfully.
Current function value: 0.693014
Iterations 3
Optimization terminated successfully.
Current function value: 0.692833
Iterations 3
Optimization terminated successfully.
Current function value: 0.693025
Iterations 3
Optimization terminated successfully.
Current function value: 0.692823
Iterations 3
Optimization terminated successfully.
Current function value: 0.692970
Iterations 4
Optimization terminated successfully.
Current function value: 0.692945
Iterations 3
Optimization terminated successfully.
Current function value: 0.693014
Iterations 3
Optimization terminated successfully.
Current function value: 0.693014
Iterations 3
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.693013
Iterations 3
Optimization terminated successfully.
Current function value: 0.693055
Iterations 3
Optimization terminated successfully.
Current function value: 0.692908
Iterations 4
Optimization terminated successfully.
Current function value: 0.692703
Iterations 4
Optimization terminated successfully.
Current function value: 0.692853
Iterations 5
Optimization terminated successfully.
Current function value: 0.692981
Iterations 3
Optimization terminated successfully.
Current function value: 0.693053
Iterations 3
Optimization terminated successfully.
Current function value: 0.692991
Iterations 3
Optimization terminated successfully.
Current function value: 0.692962
Iterations 3
Optimization terminated successfully.
Current function value: 0.692928
Iterations 4
Optimization terminated successfully.
Current function value: 0.693013
Iterations 3
Optimization terminated successfully.
Current function value: 0.693009
Iterations 3
Optimization terminated successfully.
Current function value: 0.692999
Iterations 3
Optimization terminated successfully.
Current function value: 0.692943
Iterations 3
Optimization terminated successfully.
Current function value: 0.693049
Iterations 4
Optimization terminated successfully.
Current function value: 0.692901
Iterations 3
Optimization terminated successfully.
Current function value: 0.692951
Iterations 3
Optimization terminated successfully.
Current function value: 0.692998
Iterations 3
Optimization terminated successfully.
Current function value: 0.692843
Iterations 4
Optimization terminated successfully.
Current function value: 0.692834
Iterations 3
Optimization terminated successfully.
Current function value: 0.693011
Iterations 3
Optimization terminated successfully.
Current function value: 0.692783
Iterations 3
Optimization terminated successfully.
Current function value: 0.692799
Iterations 3
Optimization terminated successfully.
Current function value: 0.692850
Iterations 3
Optimization terminated successfully.
Current function value: 0.692841
Iterations 3
Optimization terminated successfully.
Current function value: 0.693012
Iterations 3
Optimization terminated successfully.
Current function value: 0.692986
Iterations 3
Optimization terminated successfully.
Current function value: 0.693118
Iterations 3
Optimization terminated successfully.
Current function value: 0.693128
Iterations 3
Optimization terminated successfully.
Current function value: 0.692958
Iterations 3
Optimization terminated successfully.
Current function value: 0.692898
Iterations 3
Optimization terminated successfully.
Current function value: 0.693003
Iterations 3
Optimization terminated successfully.
Current function value: 0.693005
Iterations 3
Optimization terminated successfully.
Current function value: 0.692829
Iterations 3
Optimization terminated successfully.
Current function value: 0.692999
Iterations 3
Optimization terminated successfully.
Current function value: 0.692972
Iterations 3
Optimization terminated successfully.
Current function value: 0.692901
Iterations 4
Optimization terminated successfully.
Current function value: 0.692929
Iterations 3
Optimization terminated successfully.
Current function value: 0.692894
Iterations 3
Optimization terminated successfully.
Current function value: 0.692820
Iterations 4
Optimization terminated successfully.
Current function value: 0.692973
Iterations 3
Optimization terminated successfully.
Current function value: 0.692960
Iterations 3
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.692999
Iterations 3
Optimization terminated successfully.
Current function value: 0.693011
Iterations 3
Optimization terminated successfully.
Current function value: 0.693007
Iterations 3
Optimization terminated successfully.
Current function value: 0.692993
Iterations 3
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.692986
Iterations 3
Optimization terminated successfully.
Current function value: 0.693002
Iterations 3
Optimization terminated successfully.
Current function value: 0.692968
Iterations 4
Optimization terminated successfully.
Current function value: 0.692995
Iterations 3
Optimization terminated successfully.
Current function value: 0.693028
Iterations 3
Optimization terminated successfully.
Current function value: 0.692992
Iterations 3
Optimization terminated successfully.
Current function value: 0.693010
Iterations 3
Optimization terminated successfully.
Current function value: 0.692733
Iterations 4
Optimization terminated successfully.
Current function value: 0.692645
Iterations 3
Optimization terminated successfully.
Current function value: 0.693029
Iterations 3
Optimization terminated successfully.
Current function value: 0.692842
Iterations 3
Optimization terminated successfully.
Current function value: 0.692821
Iterations 3
Optimization terminated successfully.
Current function value: 0.692986
Iterations 3
Optimization terminated successfully.
Current function value: 0.693012
Iterations 3
Optimization terminated successfully.
Current function value: 0.692721
Iterations 4
Optimization terminated successfully.
Current function value: 0.693054
Iterations 3
Optimization terminated successfully.
Current function value: 0.692742
Iterations 3
Optimization terminated successfully.
Current function value: 0.693012
Iterations 3
Optimization terminated successfully.
Current function value: 0.693007
Iterations 3
Optimization terminated successfully.
Current function value: 0.693013
Iterations 3
Optimization terminated successfully.
Current function value: 0.692958
Iterations 3
Optimization terminated successfully.
Current function value: 0.692975
Iterations 3
Optimization terminated successfully.
Current function value: 0.692848
Iterations 3
Optimization terminated successfully.
Current function value: 0.692942
Iterations 3
Optimization terminated successfully.
Current function value: 0.692953
Iterations 3
Optimization terminated successfully.
Current function value: 0.692915
Iterations 3
Optimization terminated successfully.
Current function value: 0.692931
Iterations 3
Optimization terminated successfully.
Current function value: 0.692973
Iterations 3
Optimization terminated successfully.
Current function value: 0.692940
Iterations 3
Optimization terminated successfully.
Current function value: 0.692992
Iterations 3
Optimization terminated successfully.
Current function value: 0.693006
Iterations 3
Optimization terminated successfully.
Current function value: 0.693013
Iterations 3
Optimization terminated successfully.
Current function value: 0.693000
Iterations 3
Optimization terminated successfully.
Current function value: 0.693008
Iterations 3
Optimization terminated successfully.
Current function value: 0.693012
Iterations 3
Optimization terminated successfully.
Current function value: 0.693012
Iterations 3
Optimization terminated successfully.
Current function value: 0.693013
Iterations 3
Optimization terminated successfully.
Current function value: 0.693013
Iterations 3
Optimization terminated successfully.
Current function value: 0.693014
Iterations 3
Optimization terminated successfully.
Current function value: 0.693011
Iterations 3
Optimization terminated successfully.
Current function value: 0.692999
Iterations 3
Optimization terminated successfully.
Current function value: 0.692979
Iterations 3
Optimization terminated successfully.
Current function value: 0.693000
Iterations 3
Optimization terminated successfully.
Current function value: 0.692984
Iterations 3
Optimization terminated successfully.
Current function value: 0.692978
Iterations 3
Optimization terminated successfully.
Current function value: 0.692930
Iterations 3
Optimization terminated successfully.
Current function value: 0.692829
Iterations 3
Optimization terminated successfully.
Current function value: 0.692992
Iterations 3
Optimization terminated successfully.
Current function value: 0.692980
Iterations 3
Optimization terminated successfully.
Current function value: 0.692971
Iterations 3
Optimization terminated successfully.
Current function value: 0.693010
Iterations 3
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.693014
Iterations 3
Optimization terminated successfully.
Current function value: 0.693000
Iterations 3
Optimization terminated successfully.
Current function value: 0.693000
Iterations 3
Optimization terminated successfully.
Current function value: 0.692979
Iterations 3
Optimization terminated successfully.
Current function value: 0.692996
Iterations 3
Optimization terminated successfully.
Current function value: 0.693008
Iterations 3
Optimization terminated successfully.
Current function value: 0.693006
Iterations 3
Optimization terminated successfully.
Current function value: 0.692985
Iterations 3
Optimization terminated successfully.
Current function value: 0.693010
Iterations 3
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.693003
Iterations 3
Optimization terminated successfully.
Current function value: 0.692990
Iterations 3
Optimization terminated successfully.
Current function value: 0.693012
Iterations 3
Optimization terminated successfully.
Current function value: 0.693012
Iterations 3
Optimization terminated successfully.
Current function value: 0.693011
Iterations 3
Optimization terminated successfully.
Current function value: 0.692950
Iterations 3
Optimization terminated successfully.
Current function value: 0.693037
Iterations 3
Optimization terminated successfully.
Current function value: 0.693039
Iterations 3
Optimization terminated successfully.
Current function value: 0.693091
Iterations 3
Optimization terminated successfully.
Current function value: 0.693065
Iterations 3
Optimization terminated successfully.
Current function value: 0.692992
Iterations 3
Optimization terminated successfully.
Current function value: 0.692998
Iterations 4
Optimization terminated successfully.
Current function value: 0.692987
Iterations 4
Optimization terminated successfully.
Current function value: 0.693011
Iterations 3
Optimization terminated successfully.
Current function value: 0.692840
Iterations 3
Optimization terminated successfully.
Current function value: 0.693013
Iterations 3
Optimization terminated successfully.
Current function value: 0.693011
Iterations 3
Optimization terminated successfully.
Current function value: 0.692984
Iterations 3
Optimization terminated successfully.
Current function value: 0.693008
Iterations 3
Optimization terminated successfully.
Current function value: 0.693002
Iterations 3
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.693023
Iterations 3
Optimization terminated successfully.
Current function value: 0.693001
Iterations 3
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.692998
Iterations 3
Optimization terminated successfully.
Current function value: 0.693016
Iterations 3
Optimization terminated successfully.
Current function value: 0.693006
Iterations 3
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.692970
Iterations 3
Optimization terminated successfully.
Current function value: 0.693006
Iterations 3
Optimization terminated successfully.
Current function value: 0.692980
Iterations 3
Optimization terminated successfully.
Current function value: 0.692989
Iterations 3
Optimization terminated successfully.
Current function value: 0.693007
Iterations 3
Optimization terminated successfully.
Current function value: 0.693014
Iterations 3
Optimization terminated successfully.
Current function value: 0.692985
Iterations 3
Optimization terminated successfully.
Current function value: 0.693003
Iterations 3
Optimization terminated successfully.
Current function value: 0.692994
Iterations 3
Optimization terminated successfully.
Current function value: 0.692990
Iterations 3
Optimization terminated successfully.
Current function value: 0.693011
Iterations 3
Optimization terminated successfully.
Current function value: 0.693003
Iterations 3
Optimization terminated successfully.
Current function value: 0.692985
Iterations 3
Optimization terminated successfully.
Current function value: 0.692965
Iterations 3
Optimization terminated successfully.
Current function value: 0.692994
Iterations 3
Optimization terminated successfully.
Current function value: 0.692818
Iterations 3
Optimization terminated successfully.
Current function value: 0.692980
Iterations 3
Optimization terminated successfully.
Current function value: 0.692680
Iterations 4
Optimization terminated successfully.
Current function value: 0.693011
Iterations 3
Optimization terminated successfully.
Current function value: 0.692674
Iterations 4
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.692884
Iterations 3
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.692865
Iterations 3
Optimization terminated successfully.
Current function value: 0.693007
Iterations 3
Optimization terminated successfully.
Current function value: 0.692883
Iterations 3
Optimization terminated successfully.
Current function value: 0.692994
Iterations 3
Optimization terminated successfully.
Current function value: 0.692941
Iterations 3
Optimization terminated successfully.
Current function value: 0.692998
Iterations 3
Optimization terminated successfully.
Current function value: 0.692948
Iterations 3
Optimization terminated successfully.
Current function value: 0.693008
Iterations 3
Optimization terminated successfully.
Current function value: 0.692917
Iterations 3
Optimization terminated successfully.
Current function value: 0.692993
Iterations 3
Optimization terminated successfully.
Current function value: 0.692999
Iterations 3
Optimization terminated successfully.
Current function value: 0.692968
Iterations 3
Optimization terminated successfully.
Current function value: 0.692850
Iterations 3
Optimization terminated successfully.
Current function value: 0.692971
Iterations 3
Optimization terminated successfully.
Current function value: 0.692844
Iterations 3
Optimization terminated successfully.
Current function value: 0.692963
Iterations 4
Optimization terminated successfully.
Current function value: 0.692980
Iterations 3
Optimization terminated successfully.
Current function value: 0.692984
Iterations 3
Optimization terminated successfully.
Current function value: 0.692937
Iterations 3
Optimization terminated successfully.
Current function value: 0.692960
Iterations 4
Optimization terminated successfully.
Current function value: 0.692970
Iterations 3
Optimization terminated successfully.
Current function value: 0.693001
Iterations 3
Optimization terminated successfully.
Current function value: 0.692911
Iterations 3
Optimization terminated successfully.
Current function value: 0.693002
Iterations 3
Optimization terminated successfully.
Current function value: 0.692929
Iterations 3
Optimization terminated successfully.
Current function value: 0.692995
Iterations 3
Optimization terminated successfully.
Current function value: 0.692845
Iterations 3
Optimization terminated successfully.
Current function value: 0.692981
Iterations 3
Optimization terminated successfully.
Current function value: 0.692718
Iterations 4
Optimization terminated successfully.
Current function value: 0.692973
Iterations 3
Optimization terminated successfully.
Current function value: 0.692575
Iterations 4
Optimization terminated successfully.
Current function value: 0.692985
Iterations 3
Optimization terminated successfully.
Current function value: 0.692673
Iterations 4
Optimization terminated successfully.
Current function value: 0.692988
Iterations 3
Optimization terminated successfully.
Current function value: 0.692778
Iterations 3
Optimization terminated successfully.
Current function value: 0.693018
Iterations 3
Optimization terminated successfully.
Current function value: 0.692804
Iterations 3
Optimization terminated successfully.
Current function value: 0.693023
Iterations 3
Optimization terminated successfully.
Current function value: 0.692752
Iterations 4
Optimization terminated successfully.
Current function value: 0.693023
Iterations 3
Optimization terminated successfully.
Current function value: 0.692671
Iterations 4
Optimization terminated successfully.
Current function value: 0.692986
Iterations 3
Optimization terminated successfully.
Current function value: 0.692709
Iterations 4
Optimization terminated successfully.
Current function value: 0.693046
Iterations 3
Optimization terminated successfully.
Current function value: 0.692650
Iterations 4
Optimization terminated successfully.
Current function value: 0.693063
Iterations 3
Optimization terminated successfully.
Current function value: 0.692875
Iterations 3
Optimization terminated successfully.
Current function value: 0.693098
Iterations 3
Optimization terminated successfully.
Current function value: 0.692806
Iterations 4
Optimization terminated successfully.
Current function value: 0.693074
Iterations 3
Optimization terminated successfully.
Current function value: 0.693058
Iterations 3
Optimization terminated successfully.
Current function value: 0.693024
Iterations 3
Optimization terminated successfully.
Current function value: 0.692892
Iterations 3
Optimization terminated successfully.
Current function value: 0.692998
Iterations 3
Optimization terminated successfully.
Current function value: 0.693013
Iterations 3
Optimization terminated successfully.
Current function value: 0.692959
Iterations 3
Optimization terminated successfully.
Current function value: 0.692853
Iterations 3
Optimization terminated successfully.
Current function value: 0.692615
Iterations 3
Optimization terminated successfully.
Current function value: 0.692979
Iterations 3
Optimization terminated successfully.
Current function value: 0.693046
Iterations 3
Optimization terminated successfully.
Current function value: 0.692917
Iterations 3
Optimization terminated successfully.
Current function value: 0.692977
Iterations 3
Optimization terminated successfully.
Current function value: 0.693011
Iterations 3
Optimization terminated successfully.
Current function value: 0.692985
Iterations 3
Optimization terminated successfully.
Current function value: 0.693004
Iterations 3
Optimization terminated successfully.
Current function value: 0.692985
Iterations 3
Optimization terminated successfully.
Current function value: 0.692932
Iterations 3
Optimization terminated successfully.
Current function value: 0.692619
Iterations 4
Optimization terminated successfully.
Current function value: 0.692779
Iterations 3
Optimization terminated successfully.
Current function value: 0.692886
Iterations 3
Optimization terminated successfully.
Current function value: 0.692739
Iterations 3
Optimization terminated successfully.
Current function value: 0.692662
Iterations 3
Optimization terminated successfully.
Current function value: 0.692621
Iterations 3
Optimization terminated successfully.
Current function value: 0.692792
Iterations 3
Optimization terminated successfully.
Current function value: 0.692926
Iterations 3
Optimization terminated successfully.
Current function value: 0.692879
Iterations 3
Optimization terminated successfully.
Current function value: 0.692805
Iterations 4
Optimization terminated successfully.
Current function value: 0.693009
Iterations 3
Optimization terminated successfully.
Current function value: 0.692673
Iterations 4
Optimization terminated successfully.
Current function value: 0.692940
Iterations 3
Optimization terminated successfully.
Current function value: 0.692903
Iterations 3
Optimization terminated successfully.
Current function value: 0.693005
Iterations 3
Optimization terminated successfully.
Current function value: 0.693006
Iterations 3
Optimization terminated successfully.
Current function value: 0.692994
Iterations 3
Optimization terminated successfully.
Current function value: 0.693011
Iterations 3
Optimization terminated successfully.
Current function value: 0.692992
Iterations 3
Optimization terminated successfully.
Current function value: 0.692980
Iterations 3
Optimization terminated successfully.
Current function value: 0.693001
Iterations 3
Optimization terminated successfully.
Current function value: 0.692999
Iterations 3
Optimization terminated successfully.
Current function value: 0.693002
Iterations 3
Optimization terminated successfully.
Current function value: 0.692941
Iterations 4
Optimization terminated successfully.
Current function value: 0.692972
Iterations 3
Optimization terminated successfully.
Current function value: 0.692952
Iterations 3
Optimization terminated successfully.
Current function value: 0.692977
Iterations 3
Optimization terminated successfully.
Current function value: 0.692920
Iterations 3
Optimization terminated successfully.
Current function value: 0.692856
Iterations 3
Optimization terminated successfully.
Current function value: 0.692955
Iterations 4
Optimization terminated successfully.
Current function value: 0.692852
Iterations 3
Optimization terminated successfully.
Current function value: 0.692573
Iterations 3
Optimization terminated successfully.
Current function value: 0.692976
Iterations 3
Optimization terminated successfully.
Current function value: 0.692879
Iterations 4
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.693069
Iterations 3
Optimization terminated successfully.
Current function value: 0.692955
Iterations 3
Optimization terminated successfully.
Current function value: 0.692868
Iterations 3
Optimization terminated successfully.
Current function value: 0.693003
Iterations 3
Optimization terminated successfully.
Current function value: 0.693018
Iterations 3
Optimization terminated successfully.
Current function value: 0.693027
Iterations 3
Optimization terminated successfully.
Current function value: 0.693011
Iterations 3
Optimization terminated successfully.
Current function value: 0.692949
Iterations 3
Optimization terminated successfully.
Current function value: 0.693012
Iterations 3
Optimization terminated successfully.
Current function value: 0.692945
Iterations 3
Optimization terminated successfully.
Current function value: 0.692962
Iterations 3
Optimization terminated successfully.
Current function value: 0.693013
Iterations 3
Optimization terminated successfully.
Current function value: 0.693014
Iterations 3
Optimization terminated successfully.
Current function value: 0.692971
Iterations 4
Optimization terminated successfully.
Current function value: 0.693012
Iterations 3
Optimization terminated successfully.
Current function value: 0.693011
Iterations 3
Optimization terminated successfully.
Current function value: 0.692579
Iterations 4
Optimization terminated successfully.
Current function value: 0.692949
Iterations 3
Optimization terminated successfully.
Current function value: 0.692801
Iterations 4
Optimization terminated successfully.
Current function value: 0.692987
Iterations 4
Optimization terminated successfully.
Current function value: 0.693094
Iterations 3
Optimization terminated successfully.
Current function value: 0.693036
Iterations 3
Optimization terminated successfully.
Current function value: 0.692917
Iterations 3
Optimization terminated successfully.
Current function value: 0.693013
Iterations 3
Optimization terminated successfully.
Current function value: 0.692971
Iterations 3
Optimization terminated successfully.
Current function value: 0.693006
Iterations 3
Optimization terminated successfully.
Current function value: 0.692824
Iterations 3
Optimization terminated successfully.
Current function value: 0.692862
Iterations 3
Optimization terminated successfully.
Current function value: 0.692862
Iterations 3
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.692976
Iterations 3
Optimization terminated successfully.
Current function value: 0.693009
Iterations 3
Optimization terminated successfully.
Current function value: 0.693009
Iterations 3
Optimization terminated successfully.
Current function value: 0.692965
Iterations 3
Optimization terminated successfully.
Current function value: 0.692967
Iterations 3
Optimization terminated successfully.
Current function value: 0.692973
Iterations 3
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.693014
Iterations 3
Optimization terminated successfully.
Current function value: 0.693008
Iterations 3
Optimization terminated successfully.
Current function value: 0.692998
Iterations 3
Optimization terminated successfully.
Current function value: 0.692916
Iterations 4
Optimization terminated successfully.
Current function value: 0.693005
Iterations 3
Optimization terminated successfully.
Current function value: 0.692951
Iterations 3
Optimization terminated successfully.
Current function value: 0.692962
Iterations 3
Optimization terminated successfully.
Current function value: 0.692985
Iterations 3
Optimization terminated successfully.
Current function value: 0.692952
Iterations 3
Optimization terminated successfully.
Current function value: 0.692946
Iterations 3
Optimization terminated successfully.
Current function value: 0.692995
Iterations 3
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.693013
Iterations 3
Optimization terminated successfully.
Current function value: 0.692974
Iterations 3
Optimization terminated successfully.
Current function value: 0.692992
Iterations 3
Optimization terminated successfully.
Current function value: 0.693012
Iterations 3
Optimization terminated successfully.
Current function value: 0.692995
Iterations 3
Optimization terminated successfully.
Current function value: 0.692994
Iterations 3
Optimization terminated successfully.
Current function value: 0.692866
Iterations 3
Optimization terminated successfully.
Current function value: 0.692806
Iterations 3
Optimization terminated successfully.
Current function value: 0.692989
Iterations 3
Optimization terminated successfully.
Current function value: 0.692987
Iterations 3
Optimization terminated successfully.
Current function value: 0.692985
Iterations 3
Optimization terminated successfully.
Current function value: 0.693008
Iterations 3
Optimization terminated successfully.
Current function value: 0.693006
Iterations 3
Optimization terminated successfully.
Current function value: 0.693013
Iterations 3
Optimization terminated successfully.
Current function value: 0.693005
Iterations 3
Optimization terminated successfully.
Current function value: 0.693007
Iterations 3
Optimization terminated successfully.
Current function value: 0.693008
Iterations 3
Optimization terminated successfully.
Current function value: 0.692610
Iterations 4
Optimization terminated successfully.
Current function value: 0.692904
Iterations 3
Optimization terminated successfully.
Current function value: 0.692998
Iterations 4
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.692859
Iterations 5
Optimization terminated successfully.
Current function value: 0.692712
Iterations 4
Optimization terminated successfully.
Current function value: 0.692948
Iterations 4
Optimization terminated successfully.
Current function value: 0.692993
Iterations 3
Optimization terminated successfully.
Current function value: 0.692871
Iterations 3
Optimization terminated successfully.
Current function value: 0.692883
Iterations 3
Optimization terminated successfully.
Current function value: 0.692801
Iterations 4
Optimization terminated successfully.
Current function value: 0.692998
Iterations 3
Optimization terminated successfully.
Current function value: 0.693001
Iterations 3
Optimization terminated successfully.
Current function value: 0.692994
Iterations 3
Optimization terminated successfully.
Current function value: 0.692722
Iterations 3
Optimization terminated successfully.
Current function value: 0.692909
Iterations 3
Optimization terminated successfully.
Current function value: 0.692561
Iterations 3
Optimization terminated successfully.
Current function value: 0.692803
Iterations 3
Optimization terminated successfully.
Current function value: 0.692870
Iterations 3
Optimization terminated successfully.
Current function value: 0.692755
Iterations 3
Optimization terminated successfully.
Current function value: 0.692702
Iterations 3
Optimization terminated successfully.
Current function value: 0.693008
Iterations 3
Optimization terminated successfully.
Current function value: 0.692963
Iterations 3
Optimization terminated successfully.
Current function value: 0.692879
Iterations 3
Optimization terminated successfully.
Current function value: 0.692855
Iterations 3
Optimization terminated successfully.
Current function value: 0.692837
Iterations 3
Optimization terminated successfully.
Current function value: 0.692729
Iterations 3
Optimization terminated successfully.
Current function value: 0.693001
Iterations 3
Optimization terminated successfully.
Current function value: 0.692990
Iterations 3
Optimization terminated successfully.
Current function value: 0.692875
Iterations 3
Optimization terminated successfully.
Current function value: 0.692989
Iterations 3
Optimization terminated successfully.
Current function value: 0.692813
Iterations 3
Optimization terminated successfully.
Current function value: 0.692475
Iterations 3
Optimization terminated successfully.
Current function value: 0.693001
Iterations 3
Optimization terminated successfully.
Current function value: 0.692833
Iterations 3
Optimization terminated successfully.
Current function value: 0.692529
Iterations 3
Optimization terminated successfully.
Current function value: 0.693013
Iterations 3
Optimization terminated successfully.
Current function value: 0.692898
Iterations 3
Optimization terminated successfully.
Current function value: 0.692640
Iterations 3
Optimization terminated successfully.
Current function value: 0.692784
Iterations 3
Optimization terminated successfully.
Current function value: 0.692875
Iterations 3
Optimization terminated successfully.
Current function value: 0.692782
Iterations 3
Optimization terminated successfully.
Current function value: 0.692938
Iterations 3
Optimization terminated successfully.
Current function value: 0.692871
Iterations 3
Optimization terminated successfully.
Current function value: 0.692973
Iterations 3
Optimization terminated successfully.
Current function value: 0.692973
Iterations 3
Optimization terminated successfully.
Current function value: 0.692973
Iterations 3
Optimization terminated successfully.
Current function value: 0.692973
Iterations 3
Optimization terminated successfully.
Current function value: 0.692973
Iterations 3
Optimization terminated successfully.
Current function value: 0.692939
Iterations 18
Optimization terminated successfully.
Current function value: 0.693009
Iterations 4
Optimization terminated successfully.
Current function value: 0.693005
Iterations 4
Optimization terminated successfully.
Current function value: 0.692976
Iterations 4
Optimization terminated successfully.
Current function value: 0.693012
Iterations 3
Optimization terminated successfully.
Current function value: 0.692995
Iterations 4
Optimization terminated successfully.
Current function value: 0.692958
Iterations 4
Optimization terminated successfully.
Current function value: 0.693002
Iterations 4
Optimization terminated successfully.
Current function value: 0.692983
Iterations 4
Optimization terminated successfully.
Current function value: 0.693010
Iterations 3
Optimization terminated successfully.
Current function value: 0.693014
Iterations 3
Optimization terminated successfully.
Current function value: 0.692955
Iterations 4
Optimization terminated successfully.
Current function value: 0.692967
Iterations 4
Optimization terminated successfully.
Current function value: 0.693009
Iterations 3
Optimization terminated successfully.
Current function value: 0.692859
Iterations 4
Optimization terminated successfully.
Current function value: 0.693010
Iterations 3
Optimization terminated successfully.
Current function value: 0.692925
Iterations 4
Optimization terminated successfully.
Current function value: 0.692969
Iterations 4
Optimization terminated successfully.
Current function value: 0.692983
Iterations 4
Optimization terminated successfully.
Current function value: 0.692998
Iterations 4
Optimization terminated successfully.
Current function value: 0.692998
Iterations 4
Optimization terminated successfully.
Current function value: 0.692894
Iterations 4
Optimization terminated successfully.
Current function value: 0.692874
Iterations 4
Optimization terminated successfully.
Current function value: 0.692859
Iterations 4
Optimization terminated successfully.
Current function value: 0.693010
Iterations 3
Optimization terminated successfully.
Current function value: 0.693014
Iterations 3
Optimization terminated successfully.
Current function value: 0.692924
Iterations 4
Optimization terminated successfully.
Current function value: 0.692982
Iterations 4
Optimization terminated successfully.
Current function value: 0.692914
Iterations 4
Optimization terminated successfully.
Current function value: 0.692969
Iterations 4
Optimization terminated successfully.
Current function value: 0.692983
Iterations 4
Optimization terminated successfully.
Current function value: 0.692998
Iterations 4
Optimization terminated successfully.
Current function value: 0.692998
Iterations 4
Optimization terminated successfully.
Current function value: 0.692695
Iterations 4
Optimization terminated successfully.
Current function value: 0.693014
Iterations 3
Optimization terminated successfully.
Current function value: 0.692955
Iterations 4
Optimization terminated successfully.
Current function value: 0.692946
Iterations 4
Optimization terminated successfully.
Current function value: 0.693009
Iterations 3
Optimization terminated successfully.
Current function value: 0.692859
Iterations 4
Optimization terminated successfully.
Current function value: 0.693010
Iterations 3
Optimization terminated successfully.
Current function value: 0.692925
Iterations 4
Optimization terminated successfully.
Current function value: 0.692969
Iterations 4
Optimization terminated successfully.
Current function value: 0.692983
Iterations 4
Optimization terminated successfully.
Current function value: 0.692998
Iterations 4
Optimization terminated successfully.
Current function value: 0.692998
Iterations 4
Optimization terminated successfully.
Current function value: 0.692955
Iterations 4
Optimization terminated successfully.
Current function value: 0.692889
Iterations 4
Optimization terminated successfully.
Current function value: 0.692823
Iterations 4
Optimization terminated successfully.
Current function value: 0.692968
Iterations 4
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.692859
Iterations 4
Optimization terminated successfully.
Current function value: 0.692998
Iterations 3
Optimization terminated successfully.
Current function value: 0.692925
Iterations 4
Optimization terminated successfully.
Current function value: 0.692969
Iterations 4
Optimization terminated successfully.
Current function value: 0.692983
Iterations 4
Optimization terminated successfully.
Current function value: 0.692998
Iterations 4
Optimization terminated successfully.
Current function value: 0.692998
Iterations 4
Optimization terminated successfully.
Current function value: 0.692989
Iterations 3
Optimization terminated successfully.
Current function value: 0.692997
Iterations 3
Optimization terminated successfully.
Current function value: 0.693014
Iterations 3
Optimization terminated successfully.
Current function value: 0.693014
Iterations 3
Optimization terminated successfully.
Current function value: 0.693010
Iterations 3
Optimization terminated successfully.
Current function value: 0.692923
Iterations 4
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.692990
Iterations 4
Optimization terminated successfully.
Current function value: 0.692986
Iterations 4
Optimization terminated successfully.
Current function value: 0.692929
Iterations 5
Optimization terminated successfully.
Current function value: 0.693001
Iterations 3
Optimization terminated successfully.
Current function value: 0.693005
Iterations 3
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.693014
Iterations 3
Optimization terminated successfully.
Current function value: 0.692939
Iterations 4
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.692990
Iterations 4
Optimization terminated successfully.
Current function value: 0.692986
Iterations 4
Optimization terminated successfully.
Current function value: 0.692929
Iterations 5
Optimization terminated successfully.
Current function value: 0.692991
Iterations 3
Optimization terminated successfully.
Current function value: 0.692966
Iterations 3
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.692941
Iterations 4
Optimization terminated successfully.
Current function value: 0.693013
Iterations 3
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.692978
Iterations 4
Optimization terminated successfully.
Current function value: 0.692986
Iterations 4
Optimization terminated successfully.
Current function value: 0.692929
Iterations 5
Optimization terminated successfully.
Current function value: 0.692973
Iterations 3
Optimization terminated successfully.
Current function value: 0.692973
Iterations 3
Optimization terminated successfully.
Current function value: 0.692974
Iterations 3
Optimization terminated successfully.
Current function value: 0.693011
Iterations 3
Optimization terminated successfully.
Current function value: 0.692973
Iterations 3
Optimization terminated successfully.
Current function value: 0.692930
Iterations 3
Optimization terminated successfully.
Current function value: 0.692929
Iterations 3
Optimization terminated successfully.
Current function value: 0.692933
Iterations 3
Optimization terminated successfully.
Current function value: 0.693045
Iterations 3
Optimization terminated successfully.
Current function value: 0.693078
Iterations 3
Optimization terminated successfully.
Current function value: 0.692739
Iterations 3
Optimization terminated successfully.
Current function value: 0.693012
Iterations 3
Optimization terminated successfully.
Current function value: 0.692997
Iterations 3
Optimization terminated successfully.
Current function value: 0.692750
Iterations 3
Optimization terminated successfully.
Current function value: 0.692991
Iterations 3
Optimization terminated successfully.
Current function value: 0.692873
Iterations 3
Optimization terminated successfully.
Current function value: 0.692830
Iterations 3
Optimization terminated successfully.
Current function value: 0.692998
Iterations 3
Optimization terminated successfully.
Current function value: 0.693082
Iterations 3
Optimization terminated successfully.
Current function value: 0.692636
Iterations 3
Warning: Maximum number of iterations has been exceeded.
Current function value: 0.692709
Iterations: 35
Optimization terminated successfully.
Current function value: 0.692863
Iterations 3
Optimization terminated successfully.
Current function value: 0.692926
Iterations 3

/home/downey/anaconda3/envs/ThinkStats2/lib/python3.7/site-packages/statsmodels/base/model.py:508: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
"Check mle_retvals", ConvergenceWarning)

Optimization terminated successfully.
Current function value: 0.692726
Iterations 3
Optimization terminated successfully.
Current function value: 0.692774
Iterations 3
Optimization terminated successfully.
Current function value: 0.692999
Iterations 4
Optimization terminated successfully.
Current function value: 0.692861
Iterations 3
Optimization terminated successfully.
Current function value: 0.692705
Iterations 4
Optimization terminated successfully.
Current function value: 0.692723
Iterations 4
Optimization terminated successfully.
Current function value: 0.692803
Iterations 4
Optimization terminated successfully.
Current function value: 0.692956
Iterations 3
Optimization terminated successfully.
Current function value: 0.692786
Iterations 3
Optimization terminated successfully.
Current function value: 0.693007
Iterations 3
Optimization terminated successfully.
Current function value: 0.692989
Iterations 4
Optimization terminated successfully.
Current function value: 0.692993
Iterations 3
Optimization terminated successfully.
Current function value: 0.693013
Iterations 3
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.692952
Iterations 3
Optimization terminated successfully.
Current function value: 0.693012
Iterations 3
Optimization terminated successfully.
Current function value: 0.692970
Iterations 4
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.693014
Iterations 3
Optimization terminated successfully.
Current function value: 0.693009
Iterations 3
Optimization terminated successfully.
Current function value: 0.693011
Iterations 4
Warning: Maximum number of iterations has been exceeded.
Current function value: 0.692862
Iterations: 35
Optimization terminated successfully.
Current function value: 0.692861
Iterations 4
Optimization terminated successfully.
Current function value: 0.693014
Iterations 3
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3

/home/downey/anaconda3/envs/ThinkStats2/lib/python3.7/site-packages/statsmodels/base/model.py:508: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
"Check mle_retvals", ConvergenceWarning)

Optimization terminated successfully.
Current function value: 0.693011
Iterations 3
Optimization terminated successfully.
Current function value: 0.693010
Iterations 3
Optimization terminated successfully.
Current function value: 0.692658
Iterations 4
Optimization terminated successfully.
Current function value: 0.692789
Iterations 4
Optimization terminated successfully.
Current function value: 0.693008
Iterations 3
Optimization terminated successfully.
Current function value: 0.692855
Iterations 4
Optimization terminated successfully.
Current function value: 0.692855
Iterations 4
Optimization terminated successfully.
Current function value: 0.693013
Iterations 3
Optimization terminated successfully.
Current function value: 0.692749
Iterations 4
Optimization terminated successfully.
Current function value: 0.692862
Iterations 4
Optimization terminated successfully.
Current function value: 0.692862
Iterations 3
Optimization terminated successfully.
Current function value: 0.692821
Iterations 3
Optimization terminated successfully.
Current function value: 0.692772
Iterations 3
Optimization terminated successfully.
Current function value: 0.692687
Iterations 4
Optimization terminated successfully.
Current function value: 0.692947
Iterations 4
Optimization terminated successfully.
Current function value: 0.692771
Iterations 4
Optimization terminated successfully.
Current function value: 0.692755
Iterations 4
Optimization terminated successfully.
Current function value: 0.693011
Iterations 3
Optimization terminated successfully.
Current function value: 0.693006
Iterations 3
Optimization terminated successfully.
Current function value: 0.692998
Iterations 3
Optimization terminated successfully.
Current function value: 0.693012
Iterations 3
Optimization terminated successfully.
Current function value: 0.692949
Iterations 3
Optimization terminated successfully.
Current function value: 0.692912
Iterations 3
Optimization terminated successfully.
Current function value: 0.692879
Iterations 3
Optimization terminated successfully.
Current function value: 0.692950
Iterations 3
Optimization terminated successfully.
Current function value: 0.692991
Iterations 3
Optimization terminated successfully.
Current function value: 0.692929
Iterations 4
Warning: Maximum number of iterations has been exceeded.
Current function value: 0.692960
Iterations: 35
Optimization terminated successfully.
Current function value: 0.693007
Iterations 3
Optimization terminated successfully.
Current function value: 0.692981
Iterations 3
Optimization terminated successfully.
Current function value: 0.692975
Iterations 3
Optimization terminated successfully.
Current function value: 0.692961
Iterations 3
Optimization terminated successfully.
Current function value: 0.693005
Iterations 3
Optimization terminated successfully.
Current function value: 0.692995
Iterations 3
Optimization terminated successfully.
Current function value: 0.693001
Iterations 3
Optimization terminated successfully.
Current function value: 0.693014
Iterations 3

/home/downey/anaconda3/envs/ThinkStats2/lib/python3.7/site-packages/statsmodels/base/model.py:508: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
"Check mle_retvals", ConvergenceWarning)

Optimization terminated successfully.
Current function value: 0.692957
Iterations 3
Optimization terminated successfully.
Current function value: 0.693015
Iterations 3
Optimization terminated successfully.
Current function value: 0.692983
Iterations 3
Optimization terminated successfully.
Current function value: 0.692258
Iterations 5
Warning: Maximum number of iterations has been exceeded.
Current function value: 0.692696
Iterations: 35
Optimization terminated successfully.
Current function value: 0.692993
Iterations 3
Optimization terminated successfully.
Current function value: 0.693009
Iterations 3
Optimization terminated successfully.
Current function value: 0.693011
Iterations 3
Optimization terminated successfully.
Current function value: 0.692853
Iterations 3

/home/downey/anaconda3/envs/ThinkStats2/lib/python3.7/site-packages/statsmodels/base/model.py:508: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
"Check mle_retvals", ConvergenceWarning)

Optimization terminated successfully.
Current function value: 0.692971
Iterations 3
Optimization terminated successfully.
Current function value: 0.692639
Iterations 3
Optimization terminated successfully.
Current function value: 0.692917
Iterations 3
Optimization terminated successfully.
Current function value: 0.692760
Iterations 3
Optimization terminated successfully.
Current function value: 0.693013
Iterations 3
Optimization terminated successfully.
Current function value: 0.692832
Iterations 3
Optimization terminated successfully.
Current function value: 0.693028
Iterations 3
Optimization terminated successfully.
Current function value: 0.693014
Iterations 3
Optimization terminated successfully.
Current function value: 0.692888
Iterations 3
Optimization terminated successfully.
Current function value: 0.692770
Iterations 3
Optimization terminated successfully.
Current function value: 0.692992
Iterations 3
Optimization terminated successfully.
Current function value: 0.692976
Iterations 3
Optimization terminated successfully.
Current function value: 0.692866
Iterations 3
Optimization terminated successfully.
Current function value: 0.692992
Iterations 3
Optimization terminated successfully.
Current function value: 0.692976
Iterations 3
Optimization terminated successfully.
Current function value: 0.692866
Iterations 3
Optimization terminated successfully.
Current function value: 0.693010
Iterations 3
Optimization terminated successfully.
Current function value: 0.692896
Iterations 3
Optimization terminated successfully.
Current function value: 0.692758
Iterations 3
Optimization terminated successfully.
Current function value: 0.693081
Iterations 3
Optimization terminated successfully.
Current function value: 0.692986
Iterations 4
Optimization terminated successfully.
Current function value: 0.692927
Iterations 4
Optimization terminated successfully.
Current function value: 0.692827
Iterations 4
Optimization terminated successfully.
Current function value: 0.693008
Iterations 3
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/home/downey/anaconda3/envs/ThinkStats2/lib/python3.7/site-packages/statsmodels/base/model.py:508: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
"Check mle_retvals", ConvergenceWarning)

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```
In [37]:
```# Solution
#Here are the 30 variables that yield the highest pseudo-R^2 values.
MiningReport(variables)

```
```totalwgt_lb 0.009696855253233383
birthwgt_lb 0.009274460080281988 BD-3 BIRTHWEIGHT IN POUNDS - 1ST BABY FROM THIS PREGNANCY
constat3 0.0010985419170438382 3RD PRIORITY CODE FOR CURRENT CONTRACEPTIVE STATUS
lbw1 0.0010519527860076705 LOW BIRTHWEIGHT - BABY 1
nplaced 0.001010368752280555 # OF R'S BIO CHILDREN SHE PLACED FOR ADOPTION (BASED ON BPA)
fmarout5 0.0009096579032891183 FORMAL MARITAL STATUS AT PREGNANCY OUTCOME
rmarout6 0.000818252143711895 INFORMAL MARITAL STATUS AT PREGNANCY OUTCOME - 6 CATEGORIES
infever 0.0008115919859909004 EVER USED INFERTILITY SERVICES OF ANY KIND
frsteatd 0.0007675331422082321 AGE (IN MOS) WHEN 1ST SUPPLEMENTED - 1ST FROM THIS PREG
splstwk1 0.0007334122339932581 IF-1 H/P DOING WHAT LAST WEEK (EMPLOYMENT STATUS) 1ST MENTION
pmarpreg 0.0007245809157658822 WHETHER PREGNANCY ENDED BEFORE R'S 1ST MARRIAGE (PREMARITALLY)
usefstp 0.0007122387685902787 EF-3 USE METHOD AT FIRST SEX WITH 1ST PARTNER IN PAST 12 MONTHS?
outcom02 0.0007015744602576479 OUTCOME OF PREGNANCY - 2ND
nummult34 0.0006606172426639745 NUMBER OF METHODS REPORTED IN (OCT 2001)
coh1dur 0.0006550110146368304 DURATION (IN MONTHS) OF R'S FIRST COHABITATION
brnout_r 0.0006438582787924307
brnout 0.0006438582787924307
bpa_bdscheck1 0.0006384992730465999 WHETHER 1ST LIVEBORN BABY FROM THIS PREGNANCY WAS BPA OR BDS
nummult41 0.000624852395994635 NUMBER OF METHODS REPORTED IN (MAY 2002)
agepreg_i 0.0006221097878729154 AGEPREG IMPUTATION FLAG
educmom 0.0005903653895802385 MOTHER'S (OR MOTHER-FIGURE'S) EDUCATION
marout03 0.0005883792792801268 FORMAL MARITAL STATUS WHEN PREGNANCY ENDED - 3RD
abort12 0.0005779076671296179 FA-3B RECEIVED ABORTION LAST 12 MONTHS
p1yhsage 0.0005631662500977797 CI-6 PARTNER'S AGE AT 1ST SEX-1ST REPORTED PARTNER IN LAST 12 MOS
numfirsm1 0.0005601782001567468 TOTAL NUMBER OF RESPONSES IN EB-1 FIRSMETH - PRESCRIPTION METHODS
lbw1_i 0.0005499451546340239 LBW1 IMPUTATION FLAG
agecon_i 0.0005303754891523571 AGECON IMPUTATION FLAG
mar1con1_i 0.0005217496825273837 MAR1CON1 IMPUTATION FLAG
nummult35 0.0005188253090530059 NUMBER OF METHODS REPORTED IN (NOV 2001)
nummult39 0.0005146121683266003 NUMBER OF METHODS REPORTED IN (MAR 2002)

```
In [38]:
```# Solution
# Eliminating variables that are not known during pregnancy and
# others that are fishy for various reasons, here's the best model I could find:
formula='boy ~ agepreg + fmarout5==5 + infever==1'
model = smf.logit(formula, data=join)
results = model.fit()
results.summary()

```
```Optimization terminated successfully.
Current function value: 0.691874
Iterations 4

Out[38]:
Logit Regression Results
Dep. Variable: boy No. Observations: 8884
Model: Logit Df Residuals: 8880
Method: MLE Df Model: 3
Date: Thu, 28 Feb 2019 Pseudo R-squ.: 0.001653
Time: 09:59:57 Log-Likelihood: -6146.6
converged: True LL-Null: -6156.8
LLR p-value: 0.0001432

coef std err z P>|z| [0.025 0.975]
Intercept -0.1805 0.118 -1.534 0.125 -0.411 0.050
fmarout5 == 5[T.True] 0.1582 0.049 3.217 0.001 0.062 0.255
infever == 1[T.True] 0.2194 0.065 3.374 0.001 0.092 0.347
agepreg 0.0050 0.004 1.172 0.241 -0.003 0.013

**Exercise:** If the quantity you want to predict is a count, you can use Poisson regression, which is implemented in StatsModels with a function called `poisson`

. It works the same way as `ols`

and `logit`

. As an exercise, let’s use it to predict how many children a woman has born; in the NSFG dataset, this variable is called `numbabes`

.

Suppose you meet a woman who is 35 years old, black, and a college graduate whose annual household income exceeds $75,000. How many children would you predict she has born?

```
In [39]:
```# Solution
# I used a nonlinear model of age.
join.numbabes.replace([97], np.nan, inplace=True)
join['age2'] = join.age_r**2

```
In [40]:
```# Solution
formula='numbabes ~ age_r + age2 + age3 + C(race) + totincr + educat'
formula='numbabes ~ age_r + age2 + C(race) + totincr + educat'
model = smf.poisson(formula, data=join)
results = model.fit()
results.summary()

```
```Optimization terminated successfully.
Current function value: 1.677002
Iterations 7

Out[40]:
Poisson Regression Results
Dep. Variable: numbabes No. Observations: 8884
Model: Poisson Df Residuals: 8877
Method: MLE Df Model: 6
Date: Thu, 28 Feb 2019 Pseudo R-squ.: 0.03686
Time: 09:59:57 Log-Likelihood: -14898.
converged: True LL-Null: -15469.
LLR p-value: 3.681e-243

coef std err z P>|z| [0.025 0.975]
Intercept -1.0324 0.169 -6.098 0.000 -1.364 -0.701
C(race)[T.2] -0.1401 0.015 -9.479 0.000 -0.169 -0.111
C(race)[T.3] -0.0991 0.025 -4.029 0.000 -0.147 -0.051
age_r 0.1556 0.010 15.006 0.000 0.135 0.176
age2 -0.0020 0.000 -13.102 0.000 -0.002 -0.002
totincr -0.0187 0.002 -9.830 0.000 -0.022 -0.015
educat -0.0471 0.003 -16.076 0.000 -0.053 -0.041

```
In [41]:
```# Solution
columns = ['age_r', 'age2', 'age3', 'race', 'totincr', 'educat']
new = pd.DataFrame([[35, 35**2, 35**3, 1, 14, 16]], columns=columns)
results.predict(new)

```
Out[41]:
```0 2.496802
dtype: float64

**Exercise:** If the quantity you want to predict is categorical, you can use multinomial logistic regression, which is implemented in StatsModels with a function called `mnlogit`

. As an exercise, let’s use it to guess whether a woman is married, cohabitating, widowed, divorced, separated, or never married; in the NSFG dataset, marital status is encoded in a variable called `rmarital`

.

Suppose you meet a woman who is 25 years old, white, and a high school graduate whose annual household income is about $45,000. What is the probability that she is married, cohabitating, etc?

```
In [42]:
```# Solution
# Here's the best model I could find.
formula='rmarital ~ age_r + age2 + C(race) + totincr + educat'
model = smf.mnlogit(formula, data=join)
results = model.fit()
results.summary()

```
```Optimization terminated successfully.
Current function value: 1.084053
Iterations 8

Out[42]:
MNLogit Regression Results
Dep. Variable: rmarital No. Observations: 8884
Model: MNLogit Df Residuals: 8849
Method: MLE Df Model: 30
Date: Thu, 28 Feb 2019 Pseudo R-squ.: 0.1682
Time: 09:59:58 Log-Likelihood: -9630.7
converged: True LL-Null: -11579.
LLR p-value: 0.000

rmarital=2 coef std err z P>|z| [0.025 0.975]
Intercept 9.0156 0.805 11.199 0.000 7.438 10.593
C(race)[T.2] -0.9237 0.089 -10.418 0.000 -1.097 -0.750
C(race)[T.3] -0.6179 0.136 -4.536 0.000 -0.885 -0.351
age_r -0.3635 0.051 -7.150 0.000 -0.463 -0.264
age2 0.0048 0.001 6.103 0.000 0.003 0.006
totincr -0.1310 0.012 -11.337 0.000 -0.154 -0.108
educat -0.1953 0.019 -10.424 0.000 -0.232 -0.159
rmarital=3 coef std err z P>|z| [0.025 0.975]
Intercept 2.9570 3.020 0.979 0.328 -2.963 8.877
C(race)[T.2] -0.4411 0.237 -1.863 0.062 -0.905 0.023
C(race)[T.3] 0.0591 0.336 0.176 0.860 -0.600 0.718
age_r -0.3177 0.177 -1.798 0.072 -0.664 0.029
age2 0.0064 0.003 2.528 0.011 0.001 0.011
totincr -0.3258 0.032 -10.175 0.000 -0.389 -0.263
educat -0.0991 0.048 -2.050 0.040 -0.194 -0.004
rmarital=4 coef std err z P>|z| [0.025 0.975]
Intercept -3.5238 1.205 -2.924 0.003 -5.886 -1.162
C(race)[T.2] -0.3213 0.093 -3.445 0.001 -0.504 -0.139
C(race)[T.3] -0.7706 0.171 -4.509 0.000 -1.106 -0.436
age_r 0.1155 0.071 1.626 0.104 -0.024 0.255
age2 -0.0007 0.001 -0.701 0.483 -0.003 0.001
totincr -0.2276 0.012 -19.621 0.000 -0.250 -0.205
educat 0.0667 0.017 3.995 0.000 0.034 0.099
rmarital=5 coef std err z P>|z| [0.025 0.975]
Intercept -2.8963 1.305 -2.220 0.026 -5.453 -0.339
C(race)[T.2] -1.0407 0.104 -10.038 0.000 -1.244 -0.837
C(race)[T.3] -0.5661 0.156 -3.635 0.000 -0.871 -0.261
age_r 0.2411 0.079 3.038 0.002 0.086 0.397
age2 -0.0035 0.001 -2.977 0.003 -0.006 -0.001
totincr -0.2932 0.015 -20.159 0.000 -0.322 -0.265
educat -0.0174 0.021 -0.813 0.416 -0.059 0.025
rmarital=6 coef std err z P>|z| [0.025 0.975]
Intercept 8.0533 0.814 9.890 0.000 6.457 9.649
C(race)[T.2] -2.1871 0.080 -27.211 0.000 -2.345 -2.030
C(race)[T.3] -1.9611 0.138 -14.188 0.000 -2.232 -1.690
age_r -0.2127 0.052 -4.122 0.000 -0.314 -0.112
age2 0.0019 0.001 2.321 0.020 0.000 0.003
totincr -0.2945 0.012 -25.320 0.000 -0.317 -0.272
educat -0.0742 0.018 -4.169 0.000 -0.109 -0.039

```
In [43]:
```# Solution
# This person has a 75% chance of being currently married,
# a 13% chance of being "not married but living with opposite
# sex partner", etc.
columns = ['age_r', 'age2', 'race', 'totincr', 'educat']
new = pd.DataFrame([[25, 25**2, 2, 11, 12]], columns=columns)
results.predict(new)

```
Out[43]:
```
0
1
2
3
4
5
0
0.750028
0.126397
0.001564
0.033403
0.021485
0.067122

```
In [ ]:
```