{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Logistic Regression\n",
    "\n",
    "* [Logistic Regression in Python](http://blog.yhathq.com/posts/logistic-regression-and-python.html)\n",
    "* [Regression Analysis with Python, pandas, and StatsModels.pptx](http://allendowney.blogspot.kr/2014/09/regression-with-python-pandas-and.html)\n",
    "* https://stats.oarc.ucla.edu/r/dae/logit-regression/\n",
    "\n",
    "\n",
    "* GRE (Graduate Record Examinations) - 미국 ETS(Educational Testing Service)에서 주관하는 대학원 입학 자격시험\n",
    "  * 구(old) GRE 점수 체계 (2011년 8월 이전)\n",
    "    * Verbal Reasoning (언어): 200점 ~ 800점\n",
    "    * Quantitative Reasoning (수리): 200점 ~ 800점\n",
    "    * 두 영역 모두 만점을 받으면 총 1600점\n",
    "  * 현(new) GRE 점수 체계 (2011년 8월 이후)\n",
    "    * Verbal Reasoning (언어)\t130~170점\n",
    "    * Quantitative Reasoning (수리)\t130~170점\n",
    "    * Analytical Writing (작문) 0.0~6.0점\n",
    "* GPA (Grade Point Average) - '평균 평점' 또는 '내신 성적'. 4.0 만점 스케일을 사용. (A=4.0, B=3.0, C=2.0, D=1.0, F=0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   admit  gre   gpa  rank\n",
      "0      0  380  3.61     3\n",
      "1      1  660  3.67     3\n",
      "2      1  800  4.00     1\n",
      "3      1  640  3.19     4\n",
      "4      0  520  2.93     4\n",
      "Index(['admit', 'gre', 'gpa', 'prestige'], dtype='object')\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "import pylab as pl\n",
    "import numpy as np\n",
    "\n",
    "# read the data in\n",
    "df = pd.read_csv(\"https://stats.idre.ucla.edu/stat/data/binary.csv\")\n",
    "\n",
    "# take a look at the dataset\n",
    "print(df.head())\n",
    "#    admit  gre   gpa  rank\n",
    "# 0      0  380  3.61     3\n",
    "# 1      1  660  3.67     3\n",
    "# 2      1  800  4.00     1\n",
    "# 3      1  640  3.19     4\n",
    "# 4      0  520  2.93     4\n",
    "\n",
    "# rename the 'rank' column because there is also a DataFrame method called 'rank'\n",
    "# prestige: 대학교 평판 수준\n",
    "df.columns = [\"admit\", \"gre\", \"gpa\", \"prestige\"]\n",
    "print(df.columns)\n",
    "# array([admit, gre, gpa, prestige], dtype=object)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            admit         gre         gpa   prestige\n",
      "count  400.000000  400.000000  400.000000  400.00000\n",
      "mean     0.317500  587.700000    3.389900    2.48500\n",
      "std      0.466087  115.516536    0.380567    0.94446\n",
      "min      0.000000  220.000000    2.260000    1.00000\n",
      "25%      0.000000  520.000000    3.130000    2.00000\n",
      "50%      0.000000  580.000000    3.395000    2.00000\n",
      "75%      1.000000  660.000000    3.670000    3.00000\n",
      "max      1.000000  800.000000    4.000000    4.00000\n",
      "admit         0.466087\n",
      "gre         115.516536\n",
      "gpa           0.380567\n",
      "prestige      0.944460\n",
      "dtype: float64\n",
      "prestige   1   2   3   4\n",
      "admit                   \n",
      "0         28  97  93  55\n",
      "1         33  54  28  12\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# summarize the data\n",
    "print(df.describe())\n",
    "#             admit         gre         gpa   prestige\n",
    "# count  400.000000  400.000000  400.000000  400.00000\n",
    "# mean     0.317500  587.700000    3.389900    2.48500\n",
    "# std      0.466087  115.516536    0.380567    0.94446\n",
    "# min      0.000000  220.000000    2.260000    1.00000\n",
    "# 25%      0.000000  520.000000    3.130000    2.00000\n",
    "# 50%      0.000000  580.000000    3.395000    2.00000\n",
    "# 75%      1.000000  660.000000    3.670000    3.00000\n",
    "# max      1.000000  800.000000    4.000000    4.00000\n",
    " \n",
    "# take a look at the standard deviation of each column\n",
    "print(df.std())\n",
    "# admit      0.466087\n",
    "# gre      115.516536\n",
    "# gpa        0.380567\n",
    "# prestige   0.944460\n",
    " \n",
    "# frequency table cutting presitge and whether or not someone was admitted\n",
    "print(pd.crosstab(df['admit'], df['prestige'], rownames=['admit']))\n",
    "# prestige   1   2   3   4\n",
    "# admit                   \n",
    "# 0         28  97  93  55\n",
    "# 1         33  54  28  12\n",
    " \n",
    "# plot all of the columns\n",
    "df.hist()\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "get_dummies() 메서드는 주어진 열 값에 따라 이진화 열과 값을 생성해낸다. 아래 예는 prestige 열의 값을 dummify한 것이다.\n",
    "이 table을 기존의 table과 합친다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   prestige_1  prestige_2  prestige_3  prestige_4\n",
      "0           0           0           1           0\n",
      "1           0           0           1           0\n",
      "2           1           0           0           0\n",
      "3           0           0           0           1\n",
      "4           0           0           0           1\n",
      "   admit  gre   gpa  prestige_2  prestige_3  prestige_4\n",
      "0      0  380  3.61           0           1           0\n",
      "1      1  660  3.67           0           1           0\n",
      "2      1  800  4.00           0           0           0\n",
      "3      1  640  3.19           0           0           1\n",
      "4      0  520  2.93           0           0           1\n"
     ]
    }
   ],
   "source": [
    "# dummify rank\n",
    "dummy_ranks = pd.get_dummies(df['prestige'], prefix='prestige', dtype=int)\n",
    "print(dummy_ranks.head())\n",
    "#    prestige_1  prestige_2  prestige_3  prestige_4\n",
    "# 0           0           0           1           0\n",
    "# 1           0           0           1           0\n",
    "# 2           1           0           0           0\n",
    "# 3           0           0           0           1\n",
    "# 4           0           0           0           1\n",
    " \n",
    "# create a clean data frame for the regression\n",
    "cols_to_keep = ['admit', 'gre', 'gpa']\n",
    "data = df[cols_to_keep].join(dummy_ranks.loc[:, 'prestige_2':])\n",
    "print(data.head())\n",
    "#    admit  gre   gpa  prestige_2  prestige_3  prestige_4\n",
    "# 0      0  380  3.61           0           1           0\n",
    "# 1      1  660  3.67           0           1           0\n",
    "# 2      1  800  4.00           0           0           0\n",
    "# 3      1  640  3.19           0           0           1\n",
    "# 4      0  520  2.93           0           0           1\n",
    " \n",
    "# manually add the intercept\n",
    "data['intercept'] = 1.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 로짓 변환\n",
    "\n",
    "gre, gpa, prestige_2, prestige_3, prestige_4를 이용하여 admit을 예측해보자.\n",
    "statsmodels.api 모듈의 Logit 클래스를 이용한다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>admit</th>\n",
       "      <th>gre</th>\n",
       "      <th>gpa</th>\n",
       "      <th>prestige_2</th>\n",
       "      <th>prestige_3</th>\n",
       "      <th>prestige_4</th>\n",
       "      <th>intercept</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>380</td>\n",
       "      <td>3.61</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>660</td>\n",
       "      <td>3.67</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>800</td>\n",
       "      <td>4.00</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>640</td>\n",
       "      <td>3.19</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>520</td>\n",
       "      <td>2.93</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   admit  gre   gpa  prestige_2  prestige_3  prestige_4  intercept\n",
       "0      0  380  3.61           0           1           0        1.0\n",
       "1      1  660  3.67           0           1           0        1.0\n",
       "2      1  800  4.00           0           0           0        1.0\n",
       "3      1  640  3.19           0           0           1        1.0\n",
       "4      0  520  2.93           0           0           1        1.0"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.573147\n",
      "         Iterations 6\n"
     ]
    }
   ],
   "source": [
    "train_cols = data.columns[1:]\n",
    "# Index([gre, gpa, prestige_2, prestige_3, prestige_4], dtype=object)\n",
    " \n",
    "logit = sm.Logit(data['admit'], data[train_cols])\n",
    "\n",
    "# fit the model\n",
    "result = logit.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Logit Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>         <td>admit</td>      <th>  No. Observations:  </th>  <td>   400</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                 <td>Logit</td>      <th>  Df Residuals:      </th>  <td>   394</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>                 <td>MLE</td>       <th>  Df Model:          </th>  <td>     5</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Tue, 28 Oct 2025</td> <th>  Pseudo R-squ.:     </th>  <td>0.08292</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>07:17:19</td>     <th>  Log-Likelihood:    </th> <td> -229.26</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>converged:</th>             <td>True</td>       <th>  LL-Null:           </th> <td> -249.99</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>     <td>nonrobust</td>    <th>  LLR p-value:       </th> <td>7.578e-08</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td></td>         <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>gre</th>        <td>    0.0023</td> <td>    0.001</td> <td>    2.070</td> <td> 0.038</td> <td>    0.000</td> <td>    0.004</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>gpa</th>        <td>    0.8040</td> <td>    0.332</td> <td>    2.423</td> <td> 0.015</td> <td>    0.154</td> <td>    1.454</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>prestige_2</th> <td>   -0.6754</td> <td>    0.316</td> <td>   -2.134</td> <td> 0.033</td> <td>   -1.296</td> <td>   -0.055</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>prestige_3</th> <td>   -1.3402</td> <td>    0.345</td> <td>   -3.881</td> <td> 0.000</td> <td>   -2.017</td> <td>   -0.663</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>prestige_4</th> <td>   -1.5515</td> <td>    0.418</td> <td>   -3.713</td> <td> 0.000</td> <td>   -2.370</td> <td>   -0.733</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>intercept</th>  <td>   -3.9900</td> <td>    1.140</td> <td>   -3.500</td> <td> 0.000</td> <td>   -6.224</td> <td>   -1.756</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/latex": [
       "\\begin{center}\n",
       "\\begin{tabular}{lclc}\n",
       "\\toprule\n",
       "\\textbf{Dep. Variable:}   &      admit       & \\textbf{  No. Observations:  } &      400    \\\\\n",
       "\\textbf{Model:}           &      Logit       & \\textbf{  Df Residuals:      } &      394    \\\\\n",
       "\\textbf{Method:}          &       MLE        & \\textbf{  Df Model:          } &        5    \\\\\n",
       "\\textbf{Date:}            & Tue, 28 Oct 2025 & \\textbf{  Pseudo R-squ.:     } &  0.08292    \\\\\n",
       "\\textbf{Time:}            &     07:17:19     & \\textbf{  Log-Likelihood:    } &   -229.26   \\\\\n",
       "\\textbf{converged:}       &       True       & \\textbf{  LL-Null:           } &   -249.99   \\\\\n",
       "\\textbf{Covariance Type:} &    nonrobust     & \\textbf{  LLR p-value:       } & 7.578e-08   \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lcccccc}\n",
       "                     & \\textbf{coef} & \\textbf{std err} & \\textbf{z} & \\textbf{P$> |$z$|$} & \\textbf{[0.025} & \\textbf{0.975]}  \\\\\n",
       "\\midrule\n",
       "\\textbf{gre}         &       0.0023  &        0.001     &     2.070  &         0.038        &        0.000    &        0.004     \\\\\n",
       "\\textbf{gpa}         &       0.8040  &        0.332     &     2.423  &         0.015        &        0.154    &        1.454     \\\\\n",
       "\\textbf{prestige\\_2} &      -0.6754  &        0.316     &    -2.134  &         0.033        &       -1.296    &       -0.055     \\\\\n",
       "\\textbf{prestige\\_3} &      -1.3402  &        0.345     &    -3.881  &         0.000        &       -2.017    &       -0.663     \\\\\n",
       "\\textbf{prestige\\_4} &      -1.5515  &        0.418     &    -3.713  &         0.000        &       -2.370    &       -0.733     \\\\\n",
       "\\textbf{intercept}   &      -3.9900  &        1.140     &    -3.500  &         0.000        &       -6.224    &       -1.756     \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "%\\caption{Logit Regression Results}\n",
       "\\end{center}"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                           Logit Regression Results                           \n",
       "==============================================================================\n",
       "Dep. Variable:                  admit   No. Observations:                  400\n",
       "Model:                          Logit   Df Residuals:                      394\n",
       "Method:                           MLE   Df Model:                            5\n",
       "Date:                Tue, 28 Oct 2025   Pseudo R-squ.:                 0.08292\n",
       "Time:                        07:17:19   Log-Likelihood:                -229.26\n",
       "converged:                       True   LL-Null:                       -249.99\n",
       "Covariance Type:            nonrobust   LLR p-value:                 7.578e-08\n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "gre            0.0023      0.001      2.070      0.038       0.000       0.004\n",
       "gpa            0.8040      0.332      2.423      0.015       0.154       1.454\n",
       "prestige_2    -0.6754      0.316     -2.134      0.033      -1.296      -0.055\n",
       "prestige_3    -1.3402      0.345     -3.881      0.000      -2.017      -0.663\n",
       "prestige_4    -1.5515      0.418     -3.713      0.000      -2.370      -0.733\n",
       "intercept     -3.9900      1.140     -3.500      0.000      -6.224      -1.756\n",
       "==============================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Df Residuals: 394\"는 **잔차 자유도(Degrees of Freedom for Residuals)** - 모델을 추정하는 데 사용되지 않고 남은 정보의 양\n",
    "  * $\\text{Df Residuals} = (\\text{관측치 수}) - (\\text{모델에 추정된 모수(계수)의 총 수})$\n",
    "  * 400 - (5+1, 독립변수 수, 절편) = 394\n",
    "  * 394라는 잔차 자유도는 400개의 관측치 중 6개의 모수(5개의 독립 변수 계수와 1개의 절편)를 추정하는 데 정보가 사용되었으며, 나머지 394개의 독립적인 정보가 **모델의 오차(잔차)** 를 추정하는 데 남아 있음을 의미합니다.\n",
    "  * 잔차 자유도는 모델이 데이터에 얼마나 잘 적합되었는지 평가하는 데 중요한 역할을 합니다. 특히 이 값이 클수록(보통 수십 이상), 모델 추정치가 안정적이고 신뢰할 수 있다는 것을 나타냅니다.\n",
    "* Df Model:\t5 모델 자유도 (변수)\n",
    "* Method MLE: 최대 우도 추정(Maximum Likelihood Estimation) 방식으로 모델을 추정\n",
    "* Pseudo R-squ.0.08292: 이 모델의 설명력. 일반적인 $R^2$과 달리 로지스틱 회귀에서는 유사 $R^2$을 사용하며, 이 값이 0.08292라는 것은 모델이 종속 변수의 변동을 약 8.29% 설명한다는 의미입니다.\n",
    "* converged\tTrue: 모델 추정 과정이 성공적으로 수렴했음을 의미\n",
    "* LLR p-value:\t7.578e-08 우도 비율 검정(Likelihood Ratio Test)의 p-값. 이 값이 매우 작기 때문에(0.05보다 훨씬 작음), 최소한 하나의 독립 변수가 종속 변수에 유의한 영향을 미친다고 결론 내릴 수 있습니다. 즉, 이 모델은 아무런 변수도 포함하지 않은 모델(Null Model)보다 유의하게 더 낫습니다.\n",
    "* $z$는 z 통계량\n",
    "* $\\text{P>|z|}$ 값이 0.05보다 작으면 해당 변수는 합격 확률에 통계적으로 유의한 영향을 미친다고 해석\n",
    "* 대학교 평판 수준이 1(가장 높음)에서 2, 3, 4로 낮아질수록 (대학원에) 합격할 확률은 점점 더 낮아짐"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "신뢰 구간 값을 좀 더 정확히 살펴 볼 수 있다.\n",
    "\n",
    "각 계수($\\text{coef}$)에 대한 95% 신뢰 구간\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>gre</th>\n",
       "      <td>0.000120</td>\n",
       "      <td>0.004409</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gpa</th>\n",
       "      <td>0.153684</td>\n",
       "      <td>1.454391</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>prestige_2</th>\n",
       "      <td>-1.295751</td>\n",
       "      <td>-0.055135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>prestige_3</th>\n",
       "      <td>-2.016992</td>\n",
       "      <td>-0.663416</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>prestige_4</th>\n",
       "      <td>-2.370399</td>\n",
       "      <td>-0.732529</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>intercept</th>\n",
       "      <td>-6.224242</td>\n",
       "      <td>-1.755716</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   0         1\n",
       "gre         0.000120  0.004409\n",
       "gpa         0.153684  1.454391\n",
       "prestige_2 -1.295751 -0.055135\n",
       "prestige_3 -2.016992 -0.663416\n",
       "prestige_4 -2.370399 -0.732529\n",
       "intercept  -6.224242 -1.755716"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result.conf_int()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "gre           0.002264\n",
       "gpa           0.804038\n",
       "prestige_2   -0.675443\n",
       "prestige_3   -1.340204\n",
       "prestige_4   -1.551464\n",
       "intercept    -3.989979\n",
       "dtype: float64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result.params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "계수에 지수함수를 취하면 odds ratio를 얻는다. 이 값은 변수의 1단위가 증감할 때 합격 odds에 얼마나 영향을 미치는지 말해준다. 예를 들어, prestige_2가 감소할 때 50%의 합격 오즈가 감소한다는 것을 알 수 있다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gre           1.002267\n",
      "gpa           2.234545\n",
      "prestige_2    0.508931\n",
      "prestige_3    0.261792\n",
      "prestige_4    0.211938\n",
      "intercept     0.018500\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# odds ratios only\n",
    "print(np.exp(result.params))\n",
    "# gre           1.002267\n",
    "# gpa           2.234545\n",
    "# prestige_2    0.508931\n",
    "# prestige_3    0.261792\n",
    "# prestige_4    0.211938\n",
    "# intercept     0.018500"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "신뢰 구간으로 표시하면 불확실한 변수에 대해 좀 더 확실히 알 수 있다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                2.5%     97.5%        OR\n",
      "gre         1.000120  1.004418  1.002267\n",
      "gpa         1.166122  4.281877  2.234545\n",
      "prestige_2  0.273692  0.946358  0.508931\n",
      "prestige_3  0.133055  0.515089  0.261792\n",
      "prestige_4  0.093443  0.480692  0.211938\n",
      "intercept   0.001981  0.172783  0.018500\n"
     ]
    }
   ],
   "source": [
    "# odds ratios and 95% CI\n",
    "params = result.params\n",
    "conf = result.conf_int()\n",
    "conf['OR'] = params\n",
    "conf.columns = ['2.5%', '97.5%', 'OR']\n",
    "print(np.exp(conf))\n",
    "#                   2.5%     97.5%        OR\n",
    "# gre           1.000120  1.004418  1.002267\n",
    "# gpa           1.166122  4.281877  2.234545\n",
    "# prestige_2    0.273692  0.946358  0.508931\n",
    "# prestige_3    0.133055  0.515089  0.261792\n",
    "# prestige_4    0.093443  0.480692  0.211938\n",
    "# intercept     0.001981  0.172783  0.018500"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def cartesian(arrays, out=None):\n",
    "    \"\"\"\n",
    "    Generate a cartesian product of input arrays.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    arrays : list of array-like\n",
    "        1-D arrays to form the cartesian product of.\n",
    "    out : ndarray\n",
    "        Array to place the cartesian product in.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    out : ndarray\n",
    "        2-D array of shape (M, len(arrays)) containing cartesian products\n",
    "        formed of input arrays.\n",
    "\n",
    "    Examples\n",
    "    --------\n",
    "    >>> cartesian(([1, 2, 3], [4, 5], [6, 7]))\n",
    "    array([[1, 4, 6],\n",
    "           [1, 4, 7],\n",
    "           [1, 5, 6],\n",
    "           [1, 5, 7],\n",
    "           [2, 4, 6],\n",
    "           [2, 4, 7],\n",
    "           [2, 5, 6],\n",
    "           [2, 5, 7],\n",
    "           [3, 4, 6],\n",
    "           [3, 4, 7],\n",
    "           [3, 5, 6],\n",
    "           [3, 5, 7]])\n",
    "\n",
    "    \"\"\"\n",
    "\n",
    "    arrays = [np.asarray(x) for x in arrays]\n",
    "    dtype = arrays[0].dtype\n",
    "\n",
    "    n = np.prod([x.size for x in arrays])\n",
    "    if out is None:\n",
    "        out = np.zeros([n, len(arrays)], dtype=dtype)\n",
    "\n",
    "    m = n // arrays[0].size\n",
    "    out[:,0] = np.repeat(arrays[0], m)\n",
    "    if arrays[1:]:\n",
    "        cartesian(arrays[1:], out=out[0:m,1:])\n",
    "        for j in range(1, arrays[0].size):\n",
    "            out[j*m:(j+1)*m,1:] = out[0:m,1:]\n",
    "    return out"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "GRE 점수에 따른 합격률을 계산해보자"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[220.         284.44444444 348.88888889 413.33333333 477.77777778\n",
      " 542.22222222 606.66666667 671.11111111 735.55555556 800.        ]\n",
      "[2.26       2.45333333 2.64666667 2.84       3.03333333 3.22666667\n",
      " 3.42       3.61333333 3.80666667 4.        ]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>gre</th>\n",
       "      <th>gpa</th>\n",
       "      <th>prestige</th>\n",
       "      <th>intercept</th>\n",
       "      <th>prestige_2</th>\n",
       "      <th>prestige_3</th>\n",
       "      <th>prestige_4</th>\n",
       "      <th>admit_pred</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>220.0</td>\n",
       "      <td>2.260000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.157801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>220.0</td>\n",
       "      <td>2.260000</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.087056</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>220.0</td>\n",
       "      <td>2.260000</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.046758</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>220.0</td>\n",
       "      <td>2.260000</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.038194</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>220.0</td>\n",
       "      <td>2.453333</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.179574</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     gre       gpa  prestige  intercept  prestige_2  prestige_3  prestige_4  \\\n",
       "0  220.0  2.260000       1.0        1.0           0           0           0   \n",
       "1  220.0  2.260000       2.0        1.0           1           0           0   \n",
       "2  220.0  2.260000       3.0        1.0           0           1           0   \n",
       "3  220.0  2.260000       4.0        1.0           0           0           1   \n",
       "4  220.0  2.453333       1.0        1.0           0           0           0   \n",
       "\n",
       "   admit_pred  \n",
       "0    0.157801  \n",
       "1    0.087056  \n",
       "2    0.046758  \n",
       "3    0.038194  \n",
       "4    0.179574  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# instead of generating all possible values of GRE and GPA, we're going\n",
    "# to use an evenly spaced range of 10 values from the min to the max \n",
    "gres = np.linspace(data['gre'].min(), data['gre'].max(), 10)\n",
    "print(gres)\n",
    "# array([ 220.        ,  284.44444444,  348.88888889,  413.33333333,\n",
    "#         477.77777778,  542.22222222,  606.66666667,  671.11111111,\n",
    "#         735.55555556,  800.        ])\n",
    "gpas = np.linspace(data['gpa'].min(), data['gpa'].max(), 10)\n",
    "print(gpas)\n",
    "# array([ 2.26      ,  2.45333333,  2.64666667,  2.84      ,  3.03333333,\n",
    "#         3.22666667,  3.42      ,  3.61333333,  3.80666667,  4.        ])\n",
    " \n",
    " \n",
    "# enumerate all possibilities\n",
    "combos = pd.DataFrame(cartesian([gres, gpas, [1, 2, 3, 4], [1.]]))\n",
    "# recreate the dummy variables\n",
    "combos.columns = ['gre', 'gpa', 'prestige', 'intercept']\n",
    "dummy_ranks = pd.get_dummies(combos['prestige'], prefix='prestige', dtype=int)\n",
    "dummy_ranks.columns = ['prestige_1', 'prestige_2', 'prestige_3', 'prestige_4']\n",
    "\n",
    "# keep only what we need for making predictions\n",
    "cols_to_keep = ['gre', 'gpa', 'prestige', 'intercept']\n",
    "combos = combos[cols_to_keep].join(dummy_ranks.loc[:, 'prestige_2':])\n",
    "\n",
    "# make predictions on the enumerated dataset\n",
    "combos['admit_pred'] = result.predict(combos[train_cols])\n",
    "combos.head()\n",
    "#    gre       gpa  prestige  intercept  prestige_2  prestige_3  prestige_4  admit_pred\n",
    "# 0  220  2.260000         1          1           0           0           0    0.157801\n",
    "# 1  220  2.260000         2          1           1           0           0    0.087056\n",
    "# 2  220  2.260000         3          1           0           1           0    0.046758\n",
    "# 3  220  2.260000         4          1           0           0           1    0.038194\n",
    "# 4  220  2.453333         1          1           0           0           0    0.179574"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "GPA 점수에 따른 합격률을 계산해보자"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def isolate_and_plot(variable):\n",
    "    # isolate gre and class rank\n",
    "    grouped = pd.pivot_table(combos, values=['admit_pred'], index=[variable, 'prestige'],\n",
    "                            aggfunc='mean')\n",
    "    \n",
    "    # in case you're curious as to what this looks like\n",
    "    # print grouped.head()\n",
    "    #                      admit_pred\n",
    "    # gre        prestige            \n",
    "    # 220.000000 1           0.282462\n",
    "    #            2           0.169987\n",
    "    #            3           0.096544\n",
    "    #            4           0.079859\n",
    "    # 284.444444 1           0.311718\n",
    "    \n",
    "    # make a plot\n",
    "    colors = 'rbgyrbgy'\n",
    "    for col in combos.prestige.unique():\n",
    "        plt_data = grouped.loc[grouped.index.get_level_values(1)==col]\n",
    "        pl.plot(plt_data.index.get_level_values(0), plt_data['admit_pred'],\n",
    "                color=colors[int(col)])\n",
    " \n",
    "    pl.xlabel(variable)\n",
    "    pl.ylabel(\"P(admit=1)\")\n",
    "    pl.legend(['1', '2', '3', '4'], loc='upper left', title='Prestige')\n",
    "    pl.title(\"Prob(admit=1) isolating \" + variable + \" and presitge\")\n",
    "    pl.show()\n",
    " \n",
    "isolate_and_plot('gre')\n",
    "isolate_and_plot('gpa')"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.11.15"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}