{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Examples and Exercises from Think Stats, 2nd Edition\n", "\n", "http://thinkstats2.com\n", "\n", "Copyright 2016 Allen B. Downey\n", "\n", "MIT License: https://opensource.org/licenses/MIT\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import numpy as np\n", "import pandas as pd\n", "\n", "import thinkstats2\n", "import thinkplot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multiple regression\n", "\n", "Let's load up the NSFG data again." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import first\n", "\n", "live, firsts, others = first.MakeFrames()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's birth weight as a function of mother's age (which we saw in the previous chapter)." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
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
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
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
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
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." ], "text/plain": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: totalwgt_lb R-squared: 0.005\n", "Model: OLS Adj. R-squared: 0.005\n", "Method: Least Squares F-statistic: 43.02\n", "Date: Thu, 28 Feb 2019 Prob (F-statistic): 5.72e-11\n", "Time: 09:58:53 Log-Likelihood: -15897.\n", "No. Observations: 9038 AIC: 3.180e+04\n", "Df Residuals: 9036 BIC: 3.181e+04\n", "Df Model: 1 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept 6.8304 0.068 100.470 0.000 6.697 6.964\n", "agepreg 0.0175 0.003 6.559 0.000 0.012 0.023\n", "==============================================================================\n", "Omnibus: 1024.052 Durbin-Watson: 1.618\n", "Prob(Omnibus): 0.000 Jarque-Bera (JB): 3081.833\n", "Skew: -0.601 Prob(JB): 0.00\n", "Kurtosis: 5.596 Cond. No. 118.\n", "==============================================================================\n", "\n", "Warnings:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "\"\"\"" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import statsmodels.formula.api as smf\n", "\n", "formula = 'totalwgt_lb ~ agepreg'\n", "model = smf.ols(formula, data=live)\n", "results = model.fit()\n", "results.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can extract the parameters." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(6.830396973311047, 0.017453851471802877)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "inter = results.params['Intercept']\n", "slope = results.params['agepreg']\n", "inter, slope" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And the p-value of the slope estimate." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "5.722947107312786e-11" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "slope_pvalue = results.pvalues['agepreg']\n", "slope_pvalue" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And the coefficient of determination." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.004738115474710369" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "results.rsquared" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The difference in birth weight between first babies and others." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-0.12476118453549034" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "diff_weight = firsts.totalwgt_lb.mean() - others.totalwgt_lb.mean()\n", "diff_weight" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The difference in age between mothers of first babies and others." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-3.5864347661500275" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "diff_age = firsts.agepreg.mean() - others.agepreg.mean()\n", "diff_age" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The age difference plausibly explains about half of the difference in weight." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-0.06259709972169267" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "slope * diff_age" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Running a single regression with a categorical variable, `isfirst`:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
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
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
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
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
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." ], "text/plain": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: totalwgt_lb R-squared: 0.002\n", "Model: OLS Adj. R-squared: 0.002\n", "Method: Least Squares F-statistic: 17.74\n", "Date: Thu, 28 Feb 2019 Prob (F-statistic): 2.55e-05\n", "Time: 09:58:53 Log-Likelihood: -15909.\n", "No. Observations: 9038 AIC: 3.182e+04\n", "Df Residuals: 9036 BIC: 3.184e+04\n", "Df Model: 1 \n", "Covariance Type: nonrobust \n", "===================================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "-----------------------------------------------------------------------------------\n", "Intercept 7.3259 0.021 356.007 0.000 7.286 7.366\n", "isfirst[T.True] -0.1248 0.030 -4.212 0.000 -0.183 -0.067\n", "==============================================================================\n", "Omnibus: 988.919 Durbin-Watson: 1.613\n", "Prob(Omnibus): 0.000 Jarque-Bera (JB): 2897.107\n", "Skew: -0.589 Prob(JB): 0.00\n", "Kurtosis: 5.511 Cond. No. 2.58\n", "==============================================================================\n", "\n", "Warnings:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "\"\"\"" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "live['isfirst'] = live.birthord == 1\n", "formula = 'totalwgt_lb ~ isfirst'\n", "results = smf.ols(formula, data=live).fit()\n", "results.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now finally running a multiple regression:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
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
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
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
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
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." ], "text/plain": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: totalwgt_lb R-squared: 0.005\n", "Model: OLS Adj. R-squared: 0.005\n", "Method: Least Squares F-statistic: 24.02\n", "Date: Thu, 28 Feb 2019 Prob (F-statistic): 3.95e-11\n", "Time: 09:58:53 Log-Likelihood: -15894.\n", "No. Observations: 9038 AIC: 3.179e+04\n", "Df Residuals: 9035 BIC: 3.182e+04\n", "Df Model: 2 \n", "Covariance Type: nonrobust \n", "===================================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "-----------------------------------------------------------------------------------\n", "Intercept 6.9142 0.078 89.073 0.000 6.762 7.066\n", "isfirst[T.True] -0.0698 0.031 -2.236 0.025 -0.131 -0.009\n", "agepreg 0.0154 0.003 5.499 0.000 0.010 0.021\n", "==============================================================================\n", "Omnibus: 1019.945 Durbin-Watson: 1.618\n", "Prob(Omnibus): 0.000 Jarque-Bera (JB): 3063.682\n", "Skew: -0.599 Prob(JB): 0.00\n", "Kurtosis: 5.588 Cond. No. 137.\n", "==============================================================================\n", "\n", "Warnings:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "\"\"\"" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "formula = 'totalwgt_lb ~ isfirst + agepreg'\n", "results = smf.ols(formula, data=live).fit()\n", "results.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As expected, when we control for mother's age, the apparent difference due to `isfirst` is cut in half.\n", "\n", "If we add age squared, we can control for a quadratic relationship between age and weight." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
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
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
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
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
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." ], "text/plain": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: totalwgt_lb R-squared: 0.007\n", "Model: OLS Adj. R-squared: 0.007\n", "Method: Least Squares F-statistic: 22.64\n", "Date: Thu, 28 Feb 2019 Prob (F-statistic): 1.35e-14\n", "Time: 09:58:54 Log-Likelihood: -15884.\n", "No. Observations: 9038 AIC: 3.178e+04\n", "Df Residuals: 9034 BIC: 3.181e+04\n", "Df Model: 3 \n", "Covariance Type: nonrobust \n", "===================================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "-----------------------------------------------------------------------------------\n", "Intercept 5.6923 0.286 19.937 0.000 5.133 6.252\n", "isfirst[T.True] -0.0504 0.031 -1.602 0.109 -0.112 0.011\n", "agepreg 0.1124 0.022 5.113 0.000 0.069 0.155\n", "agepreg2 -0.0018 0.000 -4.447 0.000 -0.003 -0.001\n", "==============================================================================\n", "Omnibus: 1007.149 Durbin-Watson: 1.616\n", "Prob(Omnibus): 0.000 Jarque-Bera (JB): 3003.343\n", "Skew: -0.594 Prob(JB): 0.00\n", "Kurtosis: 5.562 Cond. No. 1.39e+04\n", "==============================================================================\n", "\n", "Warnings:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 1.39e+04. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n", "\"\"\"" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "live['agepreg2'] = live.agepreg**2\n", "formula = 'totalwgt_lb ~ isfirst + agepreg + agepreg2'\n", "results = smf.ols(formula, data=live).fit()\n", "results.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When we do that, the apparent effect of `isfirst` gets even smaller, and is no longer statistically significant.\n", "\n", "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." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Data Mining\n", "\n", "We can use `join` to combine variables from the preganancy and respondent tables." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "import nsfg\n", "\n", "live = live[live.prglngth>30]\n", "resp = nsfg.ReadFemResp()\n", "resp.index = resp.caseid\n", "join = live.join(resp, on='caseid', rsuffix='_r')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And we can search for variables with explanatory power.\n", "\n", "Because we don't clean most of the variables, we are probably missing some good ones." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "import patsy\n", "\n", "def GoMining(df):\n", " \"\"\"Searches for variables that predict birth weight.\n", "\n", " df: DataFrame of pregnancy records\n", "\n", " returns: list of (rsquared, variable name) pairs\n", " \"\"\"\n", " variables = []\n", " for name in df.columns:\n", " try:\n", " if df[name].var() < 1e-7:\n", " continue\n", "\n", " formula = 'totalwgt_lb ~ agepreg + ' + name\n", " formula = formula.encode('ascii')\n", "\n", " model = smf.ols(formula, data=df)\n", " if model.nobs < len(df)/2:\n", " continue\n", "\n", " results = model.fit()\n", " except (ValueError, TypeError, patsy.PatsyError):\n", " continue\n", " \n", " variables.append((results.rsquared, name))\n", "\n", " return variables" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "variables = GoMining(join)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following functions report the variables with the highest values of $R^2$." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "import re\n", "\n", "def ReadVariables():\n", " \"\"\"Reads Stata dictionary files for NSFG data.\n", "\n", " returns: DataFrame that maps variables names to descriptions\n", " \"\"\"\n", " vars1 = thinkstats2.ReadStataDct('2002FemPreg.dct').variables\n", " vars2 = thinkstats2.ReadStataDct('2002FemResp.dct').variables\n", "\n", " all_vars = vars1.append(vars2)\n", " all_vars.index = all_vars.name\n", " return all_vars\n", "\n", "def MiningReport(variables, n=30):\n", " \"\"\"Prints variables with the highest R^2.\n", "\n", " t: list of (R^2, variable name) pairs\n", " n: number of pairs to print\n", " \"\"\"\n", " all_vars = ReadVariables()\n", "\n", " variables.sort(reverse=True)\n", " for r2, name in variables[:n]:\n", " key = re.sub('_r$', '', name)\n", " try:\n", " desc = all_vars.loc[key].desc\n", " if isinstance(desc, pd.Series):\n", " desc = desc[0]\n", " print(name, r2, desc)\n", " except (KeyError, IndexError):\n", " print(name, r2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Some of the variables that do well are not useful for prediction because they are not known ahead of time." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "MiningReport(variables)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Combining the variables that seem to have the most explanatory power." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
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
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
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
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
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." ], "text/plain": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: totalwgt_lb R-squared: 0.060\n", "Model: OLS Adj. R-squared: 0.059\n", "Method: Least Squares F-statistic: 79.98\n", "Date: Thu, 28 Feb 2019 Prob (F-statistic): 4.86e-113\n", "Time: 09:59:13 Log-Likelihood: -14295.\n", "No. Observations: 8781 AIC: 2.861e+04\n", "Df Residuals: 8773 BIC: 2.866e+04\n", "Df Model: 7 \n", "Covariance Type: nonrobust \n", "========================================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "----------------------------------------------------------------------------------------\n", "Intercept 6.6303 0.065 102.223 0.000 6.503 6.757\n", "C(race)[T.2] 0.3570 0.032 11.215 0.000 0.295 0.419\n", "C(race)[T.3] 0.2665 0.051 5.175 0.000 0.166 0.367\n", "babysex == 1[T.True] 0.2952 0.026 11.216 0.000 0.244 0.347\n", "nbrnaliv > 1[T.True] -1.3783 0.108 -12.771 0.000 -1.590 -1.167\n", "paydu == 1[T.True] 0.1196 0.031 3.861 0.000 0.059 0.180\n", "agepreg 0.0074 0.003 2.921 0.004 0.002 0.012\n", "totincr 0.0122 0.004 3.110 0.002 0.005 0.020\n", "==============================================================================\n", "Omnibus: 398.813 Durbin-Watson: 1.604\n", "Prob(Omnibus): 0.000 Jarque-Bera (JB): 1388.362\n", "Skew: -0.037 Prob(JB): 3.32e-302\n", "Kurtosis: 4.947 Cond. No. 221.\n", "==============================================================================\n", "\n", "Warnings:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "\"\"\"" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "formula = ('totalwgt_lb ~ agepreg + C(race) + babysex==1 + '\n", " 'nbrnaliv>1 + paydu==1 + totincr')\n", "results = smf.ols(formula, data=join).fit()\n", "results.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Logistic regression\n", "\n", "Example: suppose we are trying to predict `y` using explanatory variables `x1` and `x2`." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "y = np.array([0, 1, 0, 1])\n", "x1 = np.array([0, 0, 0, 1])\n", "x2 = np.array([0, 1, 1, 1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "According to the logit model the log odds for the $i$th element of $y$ is\n", "\n", "$\\log o = \\beta_0 + \\beta_1 x_1 + \\beta_2 x_2 $\n", "\n", "So let's start with an arbitrary guess about the elements of $\\beta$:\n", "\n" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "beta = [-1.5, 2.8, 1.1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plugging in the model, we get log odds." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([-1.5, -0.4, -0.4, 2.4])" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "log_o = beta[0] + beta[1] * x1 + beta[2] * x2\n", "log_o" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Which we can convert to odds." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 0.22313016, 0.67032005, 0.67032005, 11.02317638])" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "o = np.exp(log_o)\n", "o" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And then convert to probabilities." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.18242552, 0.40131234, 0.40131234, 0.9168273 ])" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p = o / (o+1)\n", "p" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The likelihoods of the actual outcomes are $p$ where $y$ is 1 and $1-p$ where $y$ is 0. " ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.81757448, 0.40131234, 0.59868766, 0.9168273 ])" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "likes = np.where(y, p, 1-p)\n", "likes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The likelihood of $y$ given $\\beta$ is the product of `likes`:" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.1800933529673034" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "like = np.prod(likes)\n", "like" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Logistic regression works by searching for the values in $\\beta$ that maximize `like`.\n", "\n", "Here's an example using variables in the NSFG respondent file to predict whether a baby will be a boy or a girl." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "import first\n", "live, firsts, others = first.MakeFrames()\n", "live = live[live.prglngth>30]\n", "live['boy'] = (live.babysex==1).astype(int)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The mother's age seems to have a small effect." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n" ] }, { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
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
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
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
" ], "text/plain": [ "\n", "\"\"\"\n", " Logit Regression Results \n", "==============================================================================\n", "Dep. Variable: boy No. Observations: 8884\n", "Model: Logit Df Residuals: 8882\n", "Method: MLE Df Model: 1\n", "Date: Thu, 28 Feb 2019 Pseudo R-squ.: 6.144e-06\n", "Time: 09:59:16 Log-Likelihood: -6156.7\n", "converged: True LL-Null: -6156.8\n", " LLR p-value: 0.7833\n", "==============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept 0.0058 0.098 0.059 0.953 -0.185 0.197\n", "agepreg 0.0010 0.004 0.275 0.783 -0.006 0.009\n", "==============================================================================\n", "\"\"\"" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model = smf.logit('boy ~ agepreg', data=live)\n", "results = model.fit()\n", "results.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here are the variables that seemed most promising." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 0.692944\n", " Iterations 3\n" ] }, { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
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
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
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
" ], "text/plain": [ "\n", "\"\"\"\n", " Logit Regression Results \n", "==============================================================================\n", "Dep. Variable: boy No. Observations: 8782\n", "Model: Logit Df Residuals: 8776\n", "Method: MLE Df Model: 5\n", "Date: Thu, 28 Feb 2019 Pseudo R-squ.: 0.0001440\n", "Time: 09:59:16 Log-Likelihood: -6085.4\n", "converged: True LL-Null: -6086.3\n", " LLR p-value: 0.8822\n", "================================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "--------------------------------------------------------------------------------\n", "Intercept -0.0301 0.104 -0.290 0.772 -0.234 0.173\n", "C(race)[T.2] -0.0224 0.051 -0.439 0.660 -0.122 0.077\n", "C(race)[T.3] -0.0005 0.083 -0.005 0.996 -0.163 0.162\n", "agepreg -0.0027 0.006 -0.484 0.629 -0.014 0.008\n", "hpagelb 0.0047 0.004 1.112 0.266 -0.004 0.013\n", "birthord 0.0050 0.022 0.227 0.821 -0.038 0.048\n", "================================================================================\n", "\"\"\"" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "formula = 'boy ~ agepreg + hpagelb + birthord + C(race)'\n", "model = smf.logit(formula, data=live)\n", "results = model.fit()\n", "results.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To make a prediction, we have to extract the exogenous and endogenous variables." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "endog = pd.DataFrame(model.endog, columns=[model.endog_names])\n", "exog = pd.DataFrame(model.exog, columns=model.exog_names)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The baseline prediction strategy is to guess \"boy\". In that case, we're right almost 51% of the time." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.507173764518333" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "actual = endog['boy']\n", "baseline = actual.mean()\n", "baseline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we use the previous model, we can compute the number of predictions we get right." ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(3944.0, 548.0)" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "predict = (results.predict() >= 0.5)\n", "true_pos = predict * actual\n", "true_neg = (1 - predict) * (1 - actual)\n", "sum(true_pos), sum(true_neg)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And the accuracy, which is slightly higher than the baseline." ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.5115007970849464" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "acc = (sum(true_pos) + sum(true_neg)) / len(actual)\n", "acc" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To make a prediction for an individual, we have to get their information into a `DataFrame`." ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0 0.513091\n", "dtype: float64" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "columns = ['agepreg', 'hpagelb', 'birthord', 'race']\n", "new = pd.DataFrame([[35, 39, 3, 2]], columns=columns)\n", "y = results.predict(new)\n", "y" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This person has a 51% chance of having a boy (according to the model)." ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## Exercises" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "**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." ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [], "source": [ "import first\n", "live, firsts, others = first.MakeFrames()\n", "live = live[live.prglngth>30]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following are the only variables I found that have a statistically significant effect on pregnancy length." ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
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
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
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
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
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." ], "text/plain": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: prglngth R-squared: 0.011\n", "Model: OLS Adj. R-squared: 0.011\n", "Method: Least Squares F-statistic: 34.28\n", "Date: Thu, 28 Feb 2019 Prob (F-statistic): 5.09e-22\n", "Time: 09:59:18 Log-Likelihood: -18247.\n", "No. Observations: 8884 AIC: 3.650e+04\n", "Df Residuals: 8880 BIC: 3.653e+04\n", "Df Model: 3 \n", "Covariance Type: nonrobust \n", "=========================================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "-----------------------------------------------------------------------------------------\n", "Intercept 38.7617 0.039 1006.410 0.000 38.686 38.837\n", "birthord == 1[T.True] 0.1015 0.040 2.528 0.011 0.023 0.180\n", "race == 2[T.True] 0.1390 0.042 3.311 0.001 0.057 0.221\n", "nbrnaliv > 1[T.True] -1.4944 0.164 -9.086 0.000 -1.817 -1.172\n", "==============================================================================\n", "Omnibus: 1587.470 Durbin-Watson: 1.619\n", "Prob(Omnibus): 0.000 Jarque-Bera (JB): 6160.751\n", "Skew: -0.852 Prob(JB): 0.00\n", "Kurtosis: 6.707 Cond. No. 10.9\n", "==============================================================================\n", "\n", "Warnings:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "\"\"\"" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import statsmodels.formula.api as smf\n", "model = smf.ols('prglngth ~ birthord==1 + race==2 + nbrnaliv>1', data=live)\n", "results = model.fit()\n", "results.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**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\n", "\n", "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.\n", "\n", "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?" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 0.692991\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692961\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692849\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692996\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692903\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692724\n", " Iterations 6\n", "Optimization terminated successfully.\n", " Current function value: 0.693014\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692992\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693010\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692985\n", " Iterations 5\n", "Optimization terminated successfully.\n", " Current function value: 0.692577\n", " Iterations 6\n", "Optimization terminated successfully.\n", " Current function value: 0.686599\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693022\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692903\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693031\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692963\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692964\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692905\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693092\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693107\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692589\n", " Iterations 6\n", "Optimization terminated successfully.\n", " Current function value: 0.693006\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693014\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692774\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692843\n", " Iterations 5\n", "Optimization terminated successfully.\n", " Current function value: 0.692612\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692947\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692817\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692947\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693023\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692967\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692995\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692645\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692555\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693021\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693066\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692911\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692917\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693003\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692861\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692859\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692814\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692389\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692517\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692452\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692701\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692290\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692930\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693003\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692926\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693004\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692930\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692861\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692866\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692866\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692806\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692930\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692989\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692987\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693008\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692985\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693006\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692993\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692871\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692994\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692985\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693001\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692942\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693011\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692922\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692986\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692573\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692988\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692817\n", " Iterations 5\n", "Optimization terminated successfully.\n", " Current function value: 0.692588\n", " Iterations 5\n", "Optimization terminated successfully.\n", " Current function value: 0.692877\n", " Iterations 5\n", "Optimization terminated successfully.\n", " Current function value: 0.692652\n", " Iterations 5\n", "Optimization terminated successfully.\n", " Current function value: 0.692991\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692918\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692984\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692952\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693008\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692893\n", " Iterations 5\n", "Warning: Maximum number of iterations has been exceeded.\n", " Current function value: 0.692776\n", " Iterations: 35\n", "Optimization terminated successfully.\n", " Current function value: 0.692638\n", " Iterations 6\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/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\n", " \"Check mle_retvals\", ConvergenceWarning)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 0.692838\n", " Iterations 5\n", "Optimization terminated successfully.\n", " Current function value: 0.692971\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692985\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692971\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693003\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692998\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692973\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692973\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692810\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693014\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693011\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693003\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692995\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692979\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693014\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693003\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.686305\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693006\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692959\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692991\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692984\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692928\n", " Iterations 5\n", "Optimization terminated successfully.\n", " Current function value: 0.692910\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693007\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693008\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692881\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692866\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692861\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692866\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692930\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692806\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692808\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692986\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693004\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692985\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693039\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692886\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692957\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692888\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692989\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693006\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692921\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692996\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692907\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692439\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692916\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692951\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693014\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692950\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693037\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693021\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693018\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692850\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693056\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692885\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693007\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692963\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692994\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692959\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692319\n", " Iterations 6\n", "Optimization terminated successfully.\n", " Current function value: 0.692984\n", " Iterations 5\n", "Optimization terminated successfully.\n", " Current function value: 0.692841\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693006\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693014\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692879\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693007\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692871\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692993\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692997\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693013\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692956\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693010\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692780\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693055\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693104\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693022\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693069\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693052\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692988\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693037\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693063\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693052\n", " Iterations 3\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 0.693078\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693078\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692964\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692801\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693074\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692959\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692995\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693013\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693004\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692911\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693014\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692833\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693025\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692823\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692970\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692945\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693014\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693014\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693013\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693055\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692908\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692703\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692853\n", " Iterations 5\n", "Optimization terminated successfully.\n", " Current function value: 0.692981\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693053\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692991\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692962\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692928\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693013\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693009\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692999\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692943\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693049\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692901\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692951\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692998\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692843\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692834\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693011\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692783\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692799\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692850\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692841\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693012\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692986\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693118\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693128\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692958\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692898\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693003\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693005\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692829\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692999\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692972\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692901\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692929\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692894\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692820\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692973\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692960\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692999\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693011\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693007\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692993\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692986\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693002\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692968\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692995\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693028\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692992\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693010\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692733\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692645\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693029\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692842\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692821\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692986\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693012\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692721\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693054\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692742\n", " Iterations 3\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 0.693012\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693007\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693013\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692958\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692975\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692848\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692942\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692953\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692915\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692931\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692973\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692940\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692992\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693006\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693013\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693000\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693008\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693012\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693012\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693013\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693013\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693014\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693011\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692999\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692979\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693000\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692984\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692978\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692930\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692829\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692992\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692980\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692971\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693010\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693014\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693000\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693000\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692979\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692996\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693008\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693006\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692985\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693010\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693003\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692990\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693012\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693012\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693011\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692950\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693037\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693039\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693091\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693065\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692992\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692998\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692987\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693011\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692840\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693013\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693011\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692984\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693008\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693002\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693023\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693001\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692998\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693016\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693006\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692970\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693006\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692980\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692989\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693007\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693014\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692985\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693003\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692994\n", " Iterations 3\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 0.692990\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693011\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693003\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692985\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692965\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692994\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692818\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692980\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692680\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693011\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692674\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692884\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692865\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693007\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692883\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692994\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692941\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692998\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692948\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693008\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692917\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692993\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692999\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692968\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692850\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692971\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692844\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692963\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692980\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692984\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692937\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692960\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692970\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693001\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692911\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693002\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692929\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692995\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692845\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692981\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692718\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692973\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692575\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692985\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692673\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692988\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692778\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693018\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692804\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693023\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692752\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693023\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692671\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692986\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692709\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693046\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692650\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693063\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692875\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693098\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692806\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693074\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693058\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693024\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692892\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692998\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693013\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692959\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692853\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692615\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692979\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693046\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692917\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692977\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693011\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692985\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693004\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692985\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692932\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692619\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692779\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692886\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692739\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692662\n", " Iterations 3\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 0.692621\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692792\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692926\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692879\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692805\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693009\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692673\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692940\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692903\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693005\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693006\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692994\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693011\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692992\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692980\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693001\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692999\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693002\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692941\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692972\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692952\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692977\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692920\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692856\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692955\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692852\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692573\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692976\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692879\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693069\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692955\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692868\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693003\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693018\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693027\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693011\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692949\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693012\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692945\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692962\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693013\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693014\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692971\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693012\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693011\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692579\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692949\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692801\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692987\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693094\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693036\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692917\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693013\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692971\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693006\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692824\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692862\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692862\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692976\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693009\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693009\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692965\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692967\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692973\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693014\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693008\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692998\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692916\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693005\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692951\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692962\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692985\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692952\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692946\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692995\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693013\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692974\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692992\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693012\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692995\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692994\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692866\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692806\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692989\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692987\n", " Iterations 3\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 0.692985\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693008\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693006\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693013\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693005\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693007\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693008\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692610\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692904\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692998\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692859\n", " Iterations 5\n", "Optimization terminated successfully.\n", " Current function value: 0.692712\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692948\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692993\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692871\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692883\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692801\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692998\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693001\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692994\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692722\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692909\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692561\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692803\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692870\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692755\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692702\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693008\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692963\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692879\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692855\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692837\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692729\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693001\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692990\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692875\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692989\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692813\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692475\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693001\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692833\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692529\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693013\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692898\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692640\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692784\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692875\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692782\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692938\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692871\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692973\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692973\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692973\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692973\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692973\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692939\n", " Iterations 18\n", "Optimization terminated successfully.\n", " Current function value: 0.693009\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693005\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692976\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693012\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692995\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692958\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693002\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692983\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693010\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693014\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692955\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692967\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693009\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692859\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693010\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692925\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692969\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692983\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692998\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692998\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692894\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692874\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692859\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693010\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693014\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692924\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692982\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692914\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692969\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692983\n", " Iterations 4\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 0.692998\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692998\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692695\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693014\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692955\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692946\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693009\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692859\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693010\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692925\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692969\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692983\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692998\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692998\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692955\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692889\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692823\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692968\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692859\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692998\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692925\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692969\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692983\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692998\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692998\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692989\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692997\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693014\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693014\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693010\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692923\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692990\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692986\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692929\n", " Iterations 5\n", "Optimization terminated successfully.\n", " Current function value: 0.693001\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693005\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693014\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692939\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692990\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692986\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692929\n", " Iterations 5\n", "Optimization terminated successfully.\n", " Current function value: 0.692991\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692966\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692941\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693013\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692978\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692986\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692929\n", " Iterations 5\n", "Optimization terminated successfully.\n", " Current function value: 0.692973\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692973\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692974\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693011\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692973\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692930\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692929\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692933\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693045\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693078\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692739\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693012\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692997\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692750\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692991\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692873\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692830\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692998\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693082\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692636\n", " Iterations 3\n", "Warning: Maximum number of iterations has been exceeded.\n", " Current function value: 0.692709\n", " Iterations: 35\n", "Optimization terminated successfully.\n", " Current function value: 0.692863\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692926\n", " Iterations 3\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/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\n", " \"Check mle_retvals\", ConvergenceWarning)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 0.692726\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692774\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692999\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692861\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692705\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692723\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692803\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692956\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692786\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693007\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692989\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692993\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693013\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692952\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693012\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692970\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693014\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693009\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693011\n", " Iterations 4\n", "Warning: Maximum number of iterations has been exceeded.\n", " Current function value: 0.692862\n", " Iterations: 35\n", "Optimization terminated successfully.\n", " Current function value: 0.692861\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693014\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/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\n", " \"Check mle_retvals\", ConvergenceWarning)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 0.693011\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693010\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692658\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692789\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693008\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692855\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692855\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693013\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692749\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692862\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692862\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692821\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692772\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692687\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692947\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692771\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692755\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693011\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693006\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692998\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693012\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692949\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692912\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692879\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692950\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692991\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692929\n", " Iterations 4\n", "Warning: Maximum number of iterations has been exceeded.\n", " Current function value: 0.692960\n", " Iterations: 35\n", "Optimization terminated successfully.\n", " Current function value: 0.693007\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692981\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692975\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692961\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693005\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692995\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693001\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693014\n", " Iterations 3\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/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\n", " \"Check mle_retvals\", ConvergenceWarning)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 0.692957\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692983\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692258\n", " Iterations 5\n", "Warning: Maximum number of iterations has been exceeded.\n", " Current function value: 0.692696\n", " Iterations: 35\n", "Optimization terminated successfully.\n", " Current function value: 0.692993\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693009\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693011\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692853\n", " Iterations 3\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/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\n", " \"Check mle_retvals\", ConvergenceWarning)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 0.692971\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692639\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692917\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692760\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693013\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692832\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693028\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693014\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692888\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692770\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692992\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692976\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692866\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692992\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692976\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692866\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693010\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692896\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692758\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693081\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692986\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692927\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692827\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693008\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692890\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692941\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692920\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692920\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692982\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692998\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692998\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692998\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693001\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693014\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692997\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693011\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693008\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693008\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692998\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693005\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692956\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692931\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692996\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692996\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692730\n", " Iterations 5\n", "Optimization terminated successfully.\n", " Current function value: 0.693014\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692898\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692879\n", " Iterations 5\n", "Optimization terminated successfully.\n", " Current function value: 0.692887\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692987\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692986\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692995\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693013\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692980\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692849\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692998\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692974\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692987\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692957\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693009\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693002\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693013\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692980\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692849\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692998\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692974\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692987\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692957\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693009\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693002\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692969\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693005\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692946\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692862\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692905\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692962\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692977\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693010\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693000\n", " Iterations 3\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 0.692998\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693012\n", " Iterations 3\n", "Warning: Maximum number of iterations has been exceeded.\n", " Current function value: 0.692939\n", " Iterations: 35\n", "Optimization terminated successfully.\n", " Current function value: 0.693003\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692831\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692999\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693003\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692997\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692795\n", " Iterations 4\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/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\n", " \"Check mle_retvals\", ConvergenceWarning)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 0.692693\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692457\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692815\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693002\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693011\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692989\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693008\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693011\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693011\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693011\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693011\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693011\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693011\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693011\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693011\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693011\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692673\n", " Iterations 5\n", "Optimization terminated successfully.\n", " Current function value: 0.692982\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692985\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692986\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692922\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693011\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692973\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693011\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693015\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692942\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692921\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693002\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693014\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693014\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692810\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.693003\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692995\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692979\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693014\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.693003\n", " Iterations 3\n", "Optimization terminated successfully.\n", " Current function value: 0.692996\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692996\n", " Iterations 4\n", "Optimization terminated successfully.\n", " Current function value: 0.692971\n", " Iterations 3\n" ] } ], "source": [ "# Solution\n", "\n", "def GoMining(df):\n", " \"\"\"Searches for variables that predict birth weight.\n", "\n", " df: DataFrame of pregnancy records\n", "\n", " returns: list of (rsquared, variable name) pairs\n", " \"\"\"\n", " df['boy'] = (df.babysex==1).astype(int)\n", " variables = []\n", " for name in df.columns:\n", " try:\n", " if df[name].var() < 1e-7:\n", " continue\n", "\n", " formula='boy ~ agepreg + ' + name\n", " model = smf.logit(formula, data=df)\n", " nobs = len(model.endog)\n", " if nobs < len(df)/2:\n", " continue\n", "\n", " results = model.fit()\n", " except:\n", " continue\n", "\n", " variables.append((results.prsquared, name))\n", "\n", " return variables\n", "\n", "variables = GoMining(join)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "totalwgt_lb 0.009696855253233383\n", "birthwgt_lb 0.009274460080281988 BD-3 BIRTHWEIGHT IN POUNDS - 1ST BABY FROM THIS PREGNANCY\n", "constat3 0.0010985419170438382 3RD PRIORITY CODE FOR CURRENT CONTRACEPTIVE STATUS\n", "lbw1 0.0010519527860076705 LOW BIRTHWEIGHT - BABY 1\n", "nplaced 0.001010368752280555 # OF R'S BIO CHILDREN SHE PLACED FOR ADOPTION (BASED ON BPA)\n", "fmarout5 0.0009096579032891183 FORMAL MARITAL STATUS AT PREGNANCY OUTCOME\n", "rmarout6 0.000818252143711895 INFORMAL MARITAL STATUS AT PREGNANCY OUTCOME - 6 CATEGORIES\n", "infever 0.0008115919859909004 EVER USED INFERTILITY SERVICES OF ANY KIND\n", "frsteatd 0.0007675331422082321 AGE (IN MOS) WHEN 1ST SUPPLEMENTED - 1ST FROM THIS PREG\n", "splstwk1 0.0007334122339932581 IF-1 H/P DOING WHAT LAST WEEK (EMPLOYMENT STATUS) 1ST MENTION\n", "pmarpreg 0.0007245809157658822 WHETHER PREGNANCY ENDED BEFORE R'S 1ST MARRIAGE (PREMARITALLY)\n", "usefstp 0.0007122387685902787 EF-3 USE METHOD AT FIRST SEX WITH 1ST PARTNER IN PAST 12 MONTHS?\n", "outcom02 0.0007015744602576479 OUTCOME OF PREGNANCY - 2ND\n", "nummult34 0.0006606172426639745 NUMBER OF METHODS REPORTED IN (OCT 2001)\n", "coh1dur 0.0006550110146368304 DURATION (IN MONTHS) OF R'S FIRST COHABITATION\n", "brnout_r 0.0006438582787924307\n", "brnout 0.0006438582787924307\n", "bpa_bdscheck1 0.0006384992730465999 WHETHER 1ST LIVEBORN BABY FROM THIS PREGNANCY WAS BPA OR BDS\n", "nummult41 0.000624852395994635 NUMBER OF METHODS REPORTED IN (MAY 2002)\n", "agepreg_i 0.0006221097878729154 AGEPREG IMPUTATION FLAG\n", "educmom 0.0005903653895802385 MOTHER'S (OR MOTHER-FIGURE'S) EDUCATION\n", "marout03 0.0005883792792801268 FORMAL MARITAL STATUS WHEN PREGNANCY ENDED - 3RD\n", "abort12 0.0005779076671296179 FA-3B RECEIVED ABORTION LAST 12 MONTHS\n", "p1yhsage 0.0005631662500977797 CI-6 PARTNER'S AGE AT 1ST SEX-1ST REPORTED PARTNER IN LAST 12 MOS\n", "numfirsm1 0.0005601782001567468 TOTAL NUMBER OF RESPONSES IN EB-1 FIRSMETH - PRESCRIPTION METHODS\n", "lbw1_i 0.0005499451546340239 LBW1 IMPUTATION FLAG\n", "agecon_i 0.0005303754891523571 AGECON IMPUTATION FLAG\n", "mar1con1_i 0.0005217496825273837 MAR1CON1 IMPUTATION FLAG\n", "nummult35 0.0005188253090530059 NUMBER OF METHODS REPORTED IN (NOV 2001)\n", "nummult39 0.0005146121683266003 NUMBER OF METHODS REPORTED IN (MAR 2002)\n" ] } ], "source": [ "# Solution\n", "\n", "#Here are the 30 variables that yield the highest pseudo-R^2 values.\n", "\n", "MiningReport(variables)" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 0.691874\n", " Iterations 4\n" ] }, { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
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
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
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
" ], "text/plain": [ "\n", "\"\"\"\n", " Logit Regression Results \n", "==============================================================================\n", "Dep. Variable: boy No. Observations: 8884\n", "Model: Logit Df Residuals: 8880\n", "Method: MLE Df Model: 3\n", "Date: Thu, 28 Feb 2019 Pseudo R-squ.: 0.001653\n", "Time: 09:59:57 Log-Likelihood: -6146.6\n", "converged: True LL-Null: -6156.8\n", " LLR p-value: 0.0001432\n", "=========================================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "-----------------------------------------------------------------------------------------\n", "Intercept -0.1805 0.118 -1.534 0.125 -0.411 0.050\n", "fmarout5 == 5[T.True] 0.1582 0.049 3.217 0.001 0.062 0.255\n", "infever == 1[T.True] 0.2194 0.065 3.374 0.001 0.092 0.347\n", "agepreg 0.0050 0.004 1.172 0.241 -0.003 0.013\n", "=========================================================================================\n", "\"\"\"" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Solution\n", "\n", "# Eliminating variables that are not known during pregnancy and \n", "# others that are fishy for various reasons, here's the best model I could find:\n", "\n", "formula='boy ~ agepreg + fmarout5==5 + infever==1'\n", "model = smf.logit(formula, data=join)\n", "results = model.fit()\n", "results.summary() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**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`.\n", "\n", "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?" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [], "source": [ "# Solution\n", "\n", "# I used a nonlinear model of age.\n", "\n", "join.numbabes.replace([97], np.nan, inplace=True)\n", "join['age2'] = join.age_r**2" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 1.677002\n", " Iterations 7\n" ] }, { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
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
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
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
" ], "text/plain": [ "\n", "\"\"\"\n", " Poisson Regression Results \n", "==============================================================================\n", "Dep. Variable: numbabes No. Observations: 8884\n", "Model: Poisson Df Residuals: 8877\n", "Method: MLE Df Model: 6\n", "Date: Thu, 28 Feb 2019 Pseudo R-squ.: 0.03686\n", "Time: 09:59:57 Log-Likelihood: -14898.\n", "converged: True LL-Null: -15469.\n", " LLR p-value: 3.681e-243\n", "================================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "--------------------------------------------------------------------------------\n", "Intercept -1.0324 0.169 -6.098 0.000 -1.364 -0.701\n", "C(race)[T.2] -0.1401 0.015 -9.479 0.000 -0.169 -0.111\n", "C(race)[T.3] -0.0991 0.025 -4.029 0.000 -0.147 -0.051\n", "age_r 0.1556 0.010 15.006 0.000 0.135 0.176\n", "age2 -0.0020 0.000 -13.102 0.000 -0.002 -0.002\n", "totincr -0.0187 0.002 -9.830 0.000 -0.022 -0.015\n", "educat -0.0471 0.003 -16.076 0.000 -0.053 -0.041\n", "================================================================================\n", "\"\"\"" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Solution\n", "\n", "formula='numbabes ~ age_r + age2 + age3 + C(race) + totincr + educat'\n", "formula='numbabes ~ age_r + age2 + C(race) + totincr + educat'\n", "model = smf.poisson(formula, data=join)\n", "results = model.fit()\n", "results.summary() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can predict the number of children for a woman who is 35 years old, black, and a college\n", "graduate whose annual household income exceeds $75,000" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0 2.496802\n", "dtype: float64" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Solution\n", "\n", "columns = ['age_r', 'age2', 'age3', 'race', 'totincr', 'educat']\n", "new = pd.DataFrame([[35, 35**2, 35**3, 1, 14, 16]], columns=columns)\n", "results.predict(new)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**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`.\n", "\n", "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?" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 1.084053\n", " Iterations 8\n" ] }, { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
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
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
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
" ], "text/plain": [ "\n", "\"\"\"\n", " MNLogit Regression Results \n", "==============================================================================\n", "Dep. Variable: rmarital No. Observations: 8884\n", "Model: MNLogit Df Residuals: 8849\n", "Method: MLE Df Model: 30\n", "Date: Thu, 28 Feb 2019 Pseudo R-squ.: 0.1682\n", "Time: 09:59:58 Log-Likelihood: -9630.7\n", "converged: True LL-Null: -11579.\n", " LLR p-value: 0.000\n", "================================================================================\n", " rmarital=2 coef std err z P>|z| [0.025 0.975]\n", "--------------------------------------------------------------------------------\n", "Intercept 9.0156 0.805 11.199 0.000 7.438 10.593\n", "C(race)[T.2] -0.9237 0.089 -10.418 0.000 -1.097 -0.750\n", "C(race)[T.3] -0.6179 0.136 -4.536 0.000 -0.885 -0.351\n", "age_r -0.3635 0.051 -7.150 0.000 -0.463 -0.264\n", "age2 0.0048 0.001 6.103 0.000 0.003 0.006\n", "totincr -0.1310 0.012 -11.337 0.000 -0.154 -0.108\n", "educat -0.1953 0.019 -10.424 0.000 -0.232 -0.159\n", "--------------------------------------------------------------------------------\n", " rmarital=3 coef std err z P>|z| [0.025 0.975]\n", "--------------------------------------------------------------------------------\n", "Intercept 2.9570 3.020 0.979 0.328 -2.963 8.877\n", "C(race)[T.2] -0.4411 0.237 -1.863 0.062 -0.905 0.023\n", "C(race)[T.3] 0.0591 0.336 0.176 0.860 -0.600 0.718\n", "age_r -0.3177 0.177 -1.798 0.072 -0.664 0.029\n", "age2 0.0064 0.003 2.528 0.011 0.001 0.011\n", "totincr -0.3258 0.032 -10.175 0.000 -0.389 -0.263\n", "educat -0.0991 0.048 -2.050 0.040 -0.194 -0.004\n", "--------------------------------------------------------------------------------\n", " rmarital=4 coef std err z P>|z| [0.025 0.975]\n", "--------------------------------------------------------------------------------\n", "Intercept -3.5238 1.205 -2.924 0.003 -5.886 -1.162\n", "C(race)[T.2] -0.3213 0.093 -3.445 0.001 -0.504 -0.139\n", "C(race)[T.3] -0.7706 0.171 -4.509 0.000 -1.106 -0.436\n", "age_r 0.1155 0.071 1.626 0.104 -0.024 0.255\n", "age2 -0.0007 0.001 -0.701 0.483 -0.003 0.001\n", "totincr -0.2276 0.012 -19.621 0.000 -0.250 -0.205\n", "educat 0.0667 0.017 3.995 0.000 0.034 0.099\n", "--------------------------------------------------------------------------------\n", " rmarital=5 coef std err z P>|z| [0.025 0.975]\n", "--------------------------------------------------------------------------------\n", "Intercept -2.8963 1.305 -2.220 0.026 -5.453 -0.339\n", "C(race)[T.2] -1.0407 0.104 -10.038 0.000 -1.244 -0.837\n", "C(race)[T.3] -0.5661 0.156 -3.635 0.000 -0.871 -0.261\n", "age_r 0.2411 0.079 3.038 0.002 0.086 0.397\n", "age2 -0.0035 0.001 -2.977 0.003 -0.006 -0.001\n", "totincr -0.2932 0.015 -20.159 0.000 -0.322 -0.265\n", "educat -0.0174 0.021 -0.813 0.416 -0.059 0.025\n", "--------------------------------------------------------------------------------\n", " rmarital=6 coef std err z P>|z| [0.025 0.975]\n", "--------------------------------------------------------------------------------\n", "Intercept 8.0533 0.814 9.890 0.000 6.457 9.649\n", "C(race)[T.2] -2.1871 0.080 -27.211 0.000 -2.345 -2.030\n", "C(race)[T.3] -1.9611 0.138 -14.188 0.000 -2.232 -1.690\n", "age_r -0.2127 0.052 -4.122 0.000 -0.314 -0.112\n", "age2 0.0019 0.001 2.321 0.020 0.000 0.003\n", "totincr -0.2945 0.012 -25.320 0.000 -0.317 -0.272\n", "educat -0.0742 0.018 -4.169 0.000 -0.109 -0.039\n", "================================================================================\n", "\"\"\"" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Solution\n", "\n", "# Here's the best model I could find.\n", "\n", "formula='rmarital ~ age_r + age2 + C(race) + totincr + educat'\n", "model = smf.mnlogit(formula, data=join)\n", "results = model.fit()\n", "results.summary() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Make a prediction for a woman who is 25 years old, white, and a high\n", "school graduate whose annual household income is about $45,000." ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
012345
00.7500280.1263970.0015640.0334030.0214850.067122
\n", "
" ], "text/plain": [ " 0 1 2 3 4 5\n", "0 0.750028 0.126397 0.001564 0.033403 0.021485 0.067122" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Solution\n", "\n", "# This person has a 75% chance of being currently married, \n", "# a 13% chance of being \"not married but living with opposite \n", "# sex partner\", etc.\n", "\n", "columns = ['age_r', 'age2', 'race', 'totincr', 'educat']\n", "new = pd.DataFrame([[25, 25**2, 2, 11, 12]], columns=columns)\n", "results.predict(new)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.2" } }, "nbformat": 4, "nbformat_minor": 1 }