19기_컴퓨터과학과_배지호.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "eU9gqjFNLzn_"
   },
   "source": [
    "# 회귀분석 과제\n",
    "22 July 2021(Thu)\n",
    "\n",
    "---\n",
    "\n",
    "제출 형식: 본인 Github에 다음과 같은 파일명으로 두 개의 파일을 업로드하시면 됩니다.  \n",
    "- 19기_학과명_이름.ipynb  \n",
    "- graduate_submission.csv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "lI_Syv8WPOY-"
   },
   "source": [
    "# 구글 드라이브 mount **(Colab을 사용하는 경우에만 해당)**\n",
    "Jupyter Notebook을 사용하시는 경우 이 부분은 무시하고 진행하시면 됩니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "executionInfo": {
     "elapsed": 33874,
     "status": "ok",
     "timestamp": 1627390844260,
     "user": {
      "displayName": "Soo Min Park",
      "photoUrl": "",
      "userId": "04363060217763346939"
     },
     "user_tz": -540
    },
    "id": "B9EBLKXCtpjH",
    "outputId": "c45b6c9d-9a22-4c4e-b211-b9d1eafd5827"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mounted at /content/gdrive\n"
     ]
    }
   ],
   "source": [
    "from google.colab import drive\n",
    "drive.mount('/content/gdrive')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "No9fyWe9LzoI"
   },
   "source": [
    "# 목표: 대학원 합격 확률 및 합격 여부 예측\n",
    "\n",
    "- 회귀: 학습 데이터로 선형 회귀, Ridge, Lasso를 통해 학습시켜 봅시다.\n",
    "\n",
    "완성된 모델로 테스트 데이터의 **합격 여부**를 예측해보세요. (합격 여부를 예측하는 것은 분류 문제입니다.)  \n",
    "아래의 빈칸(코드+서술 답안)을 모두 채워 넣어주시면 됩니다.  \n",
    "\"## TODO\"라고 적힌 부분에는 코드를 작성하여 주시고, \"A.\"라고 적힌 부분에는 서술 답안을 작성하여 주세요.  \n",
    "이를 모두 완성한 **(1) ipynb 파일**과 최종 예측을  **(2) csv 파일**로 저장하여 본인 Github에 업로드하시면 됩니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "CxB8Z4zKLzoJ"
   },
   "outputs": [],
   "source": [
    "# 패키지 불러오기\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "id": "32d8uA69LzoK"
   },
   "outputs": [],
   "source": [
    "# 경고 무시\n",
    "import warnings\n",
    "warnings.filterwarnings(action='ignore')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "gAsUjAOALzoK"
   },
   "source": [
    "# 데이터 로드 및 확인\n",
    "graduate_train.csv 파일과 graduate_test.csv 파일을 My Drive에 넣어주세요.  \n",
    "(Jupyter Notebook을 사용하시는 경우에는 graduate_train.csv 파일과 graduate_test.csv 파일 경로를 각각의 로컬 디렉토리 위치로 변경해주세요.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 438
    },
    "executionInfo": {
     "elapsed": 314,
     "status": "error",
     "timestamp": 1627390866838,
     "user": {
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      "userId": "04363060217763346939"
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "data size: (400, 8)\n"
     ]
    },
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>GRE Score</th>\n",
       "      <th>TOEFL Score</th>\n",
       "      <th>University Rating</th>\n",
       "      <th>SOP</th>\n",
       "      <th>LOR</th>\n",
       "      <th>CGPA</th>\n",
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       "      <td>3.5</td>\n",
       "      <td>8.01</td>\n",
       "      <td>No</td>\n",
       "      <td>0.71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
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       "      <td>No</td>\n",
       "      <td>0.58</td>\n",
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       "      <th>4</th>\n",
       "      <td>329</td>\n",
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       "      <td>5</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>9.30</td>\n",
       "      <td>Yes</td>\n",
       "      <td>0.86</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>300</td>\n",
       "      <td>104</td>\n",
       "      <td>3</td>\n",
       "      <td>3.5</td>\n",
       "      <td>3.0</td>\n",
       "      <td>8.16</td>\n",
       "      <td>No</td>\n",
       "      <td>0.71</td>\n",
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       "      <th>6</th>\n",
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       "      <td>Yes</td>\n",
       "      <td>0.71</td>\n",
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       "      <td>110</td>\n",
       "      <td>4</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>9.13</td>\n",
       "      <td>Yes</td>\n",
       "      <td>0.86</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>315</td>\n",
       "      <td>105</td>\n",
       "      <td>2</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.5</td>\n",
       "      <td>7.65</td>\n",
       "      <td>No</td>\n",
       "      <td>0.39</td>\n",
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       "      <th>9</th>\n",
       "      <td>332</td>\n",
       "      <td>119</td>\n",
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       "      <td>5.0</td>\n",
       "      <td>4.5</td>\n",
       "      <td>9.24</td>\n",
       "      <td>Yes</td>\n",
       "      <td>0.90</td>\n",
       "    </tr>\n",
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      "text/plain": [
       "   GRE Score  TOEFL Score  University Rating  SOP  LOR  CGPA Research  \\\n",
       "0        310          105                  2  3.0  3.5  8.01       No   \n",
       "1        307          105                  2  2.5  4.5  8.12      Yes   \n",
       "2        329          111                  4  4.5  4.0  9.01      Yes   \n",
       "3        300          105                  1  1.0  2.0  7.80       No   \n",
       "4        329          114                  5  4.0  5.0  9.30      Yes   \n",
       "5        300          104                  3  3.5  3.0  8.16       No   \n",
       "6        318          103                  3  4.0  4.5  8.49      Yes   \n",
       "7        322          110                  4  4.0  5.0  9.13      Yes   \n",
       "8        315          105                  2  2.0  2.5  7.65       No   \n",
       "9        332          119                  4  5.0  4.5  9.24      Yes   \n",
       "\n",
       "   Chance of Admit  \n",
       "0             0.71  \n",
       "1             0.67  \n",
       "2             0.81  \n",
       "3             0.58  \n",
       "4             0.86  \n",
       "5             0.71  \n",
       "6             0.71  \n",
       "7             0.86  \n",
       "8             0.39  \n",
       "9             0.90  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# train 데이터 불러오기\n",
    "df = pd.read_csv(\"graduate_train.csv\")\n",
    "\n",
    "# train 데이터 크기 확인\n",
    "print(\"data size:\", df.shape)\n",
    "\n",
    "# train 데이터 훑어보기\n",
    "df.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "id": "kv3NdZusLzoL",
    "scrolled": false
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "data size: (100, 7)\n"
     ]
    },
    {
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       "      <th>TOEFL Score</th>\n",
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       "      <th>SOP</th>\n",
       "      <th>LOR</th>\n",
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       "      <td>5.0</td>\n",
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       "      <td>Yes</td>\n",
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       "      <td>No</td>\n",
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       "      <td>114</td>\n",
       "      <td>3</td>\n",
       "      <td>4.5</td>\n",
       "      <td>4.5</td>\n",
       "      <td>9.24</td>\n",
       "      <td>Yes</td>\n",
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       "      <th>9</th>\n",
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       "      <td>111</td>\n",
       "      <td>5</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>9.86</td>\n",
       "      <td>Yes</td>\n",
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      "text/plain": [
       "   GRE Score  TOEFL Score  University Rating  SOP  LOR  CGPA Research\n",
       "0        304          103                  5  5.0  4.0  8.64       No\n",
       "1        297           96                  2  2.5  1.5  7.89       No\n",
       "2        302          101                  2  2.5  3.5  7.96       No\n",
       "3        318          112                  3  4.0  3.5  8.67       No\n",
       "4        304          100                  4  1.5  2.5  7.84       No\n",
       "5        330          116                  4  5.0  4.5  9.45      Yes\n",
       "6        315          110                  2  3.5  3.0  8.46      Yes\n",
       "7        317          107                  3  4.0  3.0  8.70       No\n",
       "8        330          114                  3  4.5  4.5  9.24      Yes\n",
       "9        323          111                  5  4.0  5.0  9.86      Yes"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# test 데이터 불러오기\n",
    "test = pd.read_csv(\"graduate_test.csv\")\n",
    "\n",
    "# test 데이터 크기 확인\n",
    "print(\"data size:\", test.shape)\n",
    "\n",
    "# test 데이터 훑어보기\n",
    "test.head(10)\n",
    "\n",
    "# test 데이터에는 'Chance of Admit'이 없습니다. 이 확률을 예측해보는 것이 과제입니다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "6ExYVssaLzoL"
   },
   "source": [
    "# 1. 결측치"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "6q8hhS-ULzoL"
   },
   "source": [
    "데이터에 결측치가 있는지 확인해보세요."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "mxSoKLulLzoL"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GRE Score            0\n",
       "TOEFL Score          0\n",
       "University Rating    0\n",
       "SOP                  0\n",
       "LOR                  0\n",
       "CGPA                 0\n",
       "Research             0\n",
       "Chance of Admit      0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.isnull().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "tymuetEVLzoM"
   },
   "source": [
    "Q. 데이터에 결측치가 있나요? 어떤 방법으로 처리하였나요?  \n",
    "A. 결측치가 없습니다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2EQrNaMzLzoM"
   },
   "source": [
    "# 2. 범주형 변수"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ukXfwUXwLzoM"
   },
   "source": [
    "설명변수 중 범주형 변수가 존재하나요?  \n",
    "존재한다면 어떻게 처리해주어야 할까요?  \n",
    "**학습 데이터를 수정하는 경우 테스트 데이터도 그에 맞게 수정해주어야 된다는 점에 유의하세요.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "id": "ctkoPnBFLzoM"
   },
   "outputs": [
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       "    }\n",
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       "    .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 Score</th>\n",
       "      <th>TOEFL Score</th>\n",
       "      <th>University Rating</th>\n",
       "      <th>SOP</th>\n",
       "      <th>LOR</th>\n",
       "      <th>CGPA</th>\n",
       "      <th>Chance of Admit</th>\n",
       "      <th>Research_No</th>\n",
       "      <th>Research_Yes</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>310</td>\n",
       "      <td>105</td>\n",
       "      <td>2</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.5</td>\n",
       "      <td>8.01</td>\n",
       "      <td>0.71</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>307</td>\n",
       "      <td>105</td>\n",
       "      <td>2</td>\n",
       "      <td>2.5</td>\n",
       "      <td>4.5</td>\n",
       "      <td>8.12</td>\n",
       "      <td>0.67</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>329</td>\n",
       "      <td>111</td>\n",
       "      <td>4</td>\n",
       "      <td>4.5</td>\n",
       "      <td>4.0</td>\n",
       "      <td>9.01</td>\n",
       "      <td>0.81</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>300</td>\n",
       "      <td>105</td>\n",
       "      <td>1</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>7.80</td>\n",
       "      <td>0.58</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>329</td>\n",
       "      <td>114</td>\n",
       "      <td>5</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>9.30</td>\n",
       "      <td>0.86</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   GRE Score  TOEFL Score  University Rating  SOP  LOR  CGPA  Chance of Admit  \\\n",
       "0        310          105                  2  3.0  3.5  8.01             0.71   \n",
       "1        307          105                  2  2.5  4.5  8.12             0.67   \n",
       "2        329          111                  4  4.5  4.0  9.01             0.81   \n",
       "3        300          105                  1  1.0  2.0  7.80             0.58   \n",
       "4        329          114                  5  4.0  5.0  9.30             0.86   \n",
       "\n",
       "   Research_No  Research_Yes  \n",
       "0            1             0  \n",
       "1            0             1  \n",
       "2            0             1  \n",
       "3            1             0  \n",
       "4            0             1  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.dtypes\n",
    "df = pd.get_dummies(df)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "RvuamBECLzoN"
   },
   "source": [
    "Q. 어떤 변수가 범주형인가요? 어떻게 처리해 주었나요?  \n",
    "A. Research가 범주형이고 더미화 했다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ELLpIte3LzoN"
   },
   "source": [
    "# 3. 선형(Linear) 회귀"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "id": "go7iVXmaLzoN"
   },
   "outputs": [],
   "source": [
    "# 먼저 데이터를 설명변수와 종속변수로 분리합니다.\n",
    "X = df.drop('Chance of Admit', axis=1)\n",
    "y = df['Chance of Admit']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "id": "8EHoXKvwLzoN"
   },
   "outputs": [],
   "source": [
    "# 데이터를 train과 test로 분리하여 사용합니다.\n",
    "from sklearn.model_selection import train_test_split\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=1234)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "id": "1NWnrQpALzoN"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "training predictors size: (320, 8)\n",
      "training response size: (320,)\n",
      "test predictors size: (80, 8)\n",
      "test response size: (80,)\n"
     ]
    }
   ],
   "source": [
    "# 각각의 크기 확인\n",
    "print(\"training predictors size:\", X_train.shape)\n",
    "print(\"training response size:\", y_train.shape)\n",
    "print(\"test predictors size:\", X_test.shape)\n",
    "print(\"test response size:\", y_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "aL1jjly2LzoO"
   },
   "source": [
    "### 3.1. scikit-learn으로 선형 회귀"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "id": "ZiETNl1zLzoO"
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "id": "meo5SRoBLzoO"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training R^2: 0.83\n",
      "Testing R^2: 0.77\n"
     ]
    }
   ],
   "source": [
    "# 1. 먼저 모델을 만들어 줍니다.\n",
    "linear = LinearRegression()\n",
    "\n",
    "# 2. 모델을 적합시킵니다.\n",
    "linear.fit(X_train, y_train)\n",
    "\n",
    "# 3. train 세트와 test 세트에서의 성능을 확인합니다. (이 경우 결정계수 R^2)\n",
    "print(\"Training R^2: %.2f\" % model.score(X_train, y_train))\n",
    "print(\"Testing R^2: %.2f\" % model.score(X_test, y_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "fIMiipaoLzoO"
   },
   "source": [
    "#### 3.1.1. 모델의 MSE와 R^2를 구해봅시다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "id": "cp7MbB5zLzoP"
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_squared_error, r2_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "id": "Y-uqZTxKLzoP"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE: 0.0040\n",
      "Variance score: 0.7729\n"
     ]
    }
   ],
   "source": [
    "y_pred = linear.predict(X_test)\n",
    "\n",
    "print('MSE: %.4f' % mean_squared_error(y_test, y_pred))\n",
    "print('Variance score: %.4f' % r2_score(y_test, y_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "RENlNFn3LzoP"
   },
   "source": [
    "#### 3.1.2. 모델의 절편 계수를 확인해봅시다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "id": "gjB76NUNLzoP"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "intercept: -1.2419421437018687\n"
     ]
    }
   ],
   "source": [
    "print(\"intercept:\", linear.intercept_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "PtBtzTWALzoP"
   },
   "source": [
    "Q. 절편 계수의 의미는 무엇인가요?  \n",
    "A. 모든 독립 변수의 값이 0일때의 종속 변수의 값"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "1k1Z3SYbLzoP"
   },
   "source": [
    "#### 3.1.3. 모델의 기울기 계수를 확인해 보세요."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "id": "QuL165twLzoQ"
   },
   "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>slope</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Research_No</th>\n",
       "      <td>-0.013241</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GRE Score</th>\n",
       "      <td>0.001640</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>University Rating</th>\n",
       "      <td>0.002748</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TOEFL Score</th>\n",
       "      <td>0.003606</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SOP</th>\n",
       "      <td>0.007253</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Research_Yes</th>\n",
       "      <td>0.013241</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LOR</th>\n",
       "      <td>0.017343</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CGPA</th>\n",
       "      <td>0.112079</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                      slope\n",
       "Research_No       -0.013241\n",
       "GRE Score          0.001640\n",
       "University Rating  0.002748\n",
       "TOEFL Score        0.003606\n",
       "SOP                0.007253\n",
       "Research_Yes       0.013241\n",
       "LOR                0.017343\n",
       "CGPA               0.112079"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta = pd.DataFrame(linear.coef_, index=X.columns, columns=[\"slope\"])\n",
    "beta.sort_values(\"slope\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "iBS0dVQULzoQ"
   },
   "source": [
    "Q. 기울기 계수의 의미는 무엇인가요? 어떤 예측변인이 대학원 합격 확률과 유의미한 관계를 가지고 있으며 이것을 어떻게 해석할 수 있나요?  \n",
    "A. 해당 변수가 1만큼 증가했을 때의 대학원 합격 확률의 변화량을 나타낸다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "9PI6NLMCLzoQ"
   },
   "source": [
    "#### 3.1.4. 연속형 설명변수 중 하나를 골라 종속변수와의 관계를 scatter plot으로 그려 보세요."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "id": "AWSYGxUDLzoQ",
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(x=\"TOEFL Score\", y=\"Chance of Admit\", data=df)\n",
    "plt.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "6Tmr_FxuLzoQ"
   },
   "source": [
    "#### 3.1.5. 범주형 설명변수와 종속변수의 관계를 box plot으로 그려 보세요."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "id": "7FBIR7INLzoQ",
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='Research_Yes', ylabel='Chance of Admit'>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(x=\"Research_Yes\", y='Chance of Admit', data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2rTH7VlnLzoR"
   },
   "source": [
    "### 3.2. StatsModels로 선형 회귀 시행하기"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "id": "c6uzmVC5LzoR"
   },
   "outputs": [],
   "source": [
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "id": "9hqrkhXrLzoR",
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>     <td>Chance of Admit</td> <th>  R-squared:         </th> <td>   0.826</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.822</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   211.6</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Thu, 29 Jul 2021</td> <th>  Prob (F-statistic):</th> <td>1.99e-114</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>02:11:50</td>     <th>  Log-Likelihood:    </th> <td>  449.18</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   320</td>      <th>  AIC:               </th> <td>  -882.4</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   312</td>      <th>  BIC:               </th> <td>  -852.2</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     7</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "          <td></td>             <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>GRE Score</th>         <td>    0.0016</td> <td>    0.001</td> <td>    2.571</td> <td> 0.011</td> <td>    0.000</td> <td>    0.003</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>TOEFL Score</th>       <td>    0.0036</td> <td>    0.001</td> <td>    3.161</td> <td> 0.002</td> <td>    0.001</td> <td>    0.006</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>University Rating</th> <td>    0.0027</td> <td>    0.005</td> <td>    0.582</td> <td> 0.561</td> <td>   -0.007</td> <td>    0.012</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SOP</th>               <td>    0.0073</td> <td>    0.006</td> <td>    1.273</td> <td> 0.204</td> <td>   -0.004</td> <td>    0.018</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>LOR</th>               <td>    0.0173</td> <td>    0.005</td> <td>    3.391</td> <td> 0.001</td> <td>    0.007</td> <td>    0.027</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>CGPA</th>              <td>    0.1121</td> <td>    0.012</td> <td>    9.237</td> <td> 0.000</td> <td>    0.088</td> <td>    0.136</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Research_No</th>       <td>   -1.2552</td> <td>    0.132</td> <td>   -9.498</td> <td> 0.000</td> <td>   -1.515</td> <td>   -0.995</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Research_Yes</th>      <td>   -1.2287</td> <td>    0.136</td> <td>   -9.065</td> <td> 0.000</td> <td>   -1.495</td> <td>   -0.962</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>72.061</td> <th>  Durbin-Watson:     </th> <td>   1.968</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td> 163.598</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-1.110</td> <th>  Prob(JB):          </th> <td>2.99e-36</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 5.710</td> <th>  Cond. No.          </th> <td>1.88e+04</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 1.88e+04. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:        Chance of Admit   R-squared:                       0.826\n",
       "Model:                            OLS   Adj. R-squared:                  0.822\n",
       "Method:                 Least Squares   F-statistic:                     211.6\n",
       "Date:                Thu, 29 Jul 2021   Prob (F-statistic):          1.99e-114\n",
       "Time:                        02:11:50   Log-Likelihood:                 449.18\n",
       "No. Observations:                 320   AIC:                            -882.4\n",
       "Df Residuals:                     312   BIC:                            -852.2\n",
       "Df Model:                           7                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "=====================================================================================\n",
       "                        coef    std err          t      P>|t|      [0.025      0.975]\n",
       "-------------------------------------------------------------------------------------\n",
       "GRE Score             0.0016      0.001      2.571      0.011       0.000       0.003\n",
       "TOEFL Score           0.0036      0.001      3.161      0.002       0.001       0.006\n",
       "University Rating     0.0027      0.005      0.582      0.561      -0.007       0.012\n",
       "SOP                   0.0073      0.006      1.273      0.204      -0.004       0.018\n",
       "LOR                   0.0173      0.005      3.391      0.001       0.007       0.027\n",
       "CGPA                  0.1121      0.012      9.237      0.000       0.088       0.136\n",
       "Research_No          -1.2552      0.132     -9.498      0.000      -1.515      -0.995\n",
       "Research_Yes         -1.2287      0.136     -9.065      0.000      -1.495      -0.962\n",
       "==============================================================================\n",
       "Omnibus:                       72.061   Durbin-Watson:                   1.968\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              163.598\n",
       "Skew:                          -1.110   Prob(JB):                     2.99e-36\n",
       "Kurtosis:                       5.710   Cond. No.                     1.88e+04\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 1.88e+04. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = sm.OLS(y_train, X_train)\n",
    "results = model.fit()\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Vsmwmmn2LzoR"
   },
   "source": [
    "Q. R^2와 F-statistic을 고려해 볼 때, 이 모델은 좋은 모델이라고 볼 수 있나요?  \n",
    "A. R^2값이 1과 가깝고, Prob 값이 0.05보다 작으므로 좋은 모델이다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "BnbzqDp-LzoR"
   },
   "source": [
    "Q. 계수에 대한 가설 검정 결과를 바탕으로 'University Rating'이 대학원 합격률에 미치는 영향을 어떻게 해석할 수 있을까요?  \n",
    "A. 대학 등급의 Prob 값이 0.561로 0.05보다 크다. 따라서 영향을 미치지 않는다고 판단된다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "NMeP1XG_LzoS"
   },
   "source": [
    "# 4. Ridge, Lasso 회귀"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "L2s42qvnLzoS"
   },
   "source": [
    "이번에는 scikit-learn으로 Ridge와 Lasso를 시도해 보세요.  \n",
    "**가장 적절한 수준의 alpha를 찾아 모델에 적용해 보세요.**  \n",
    "(힌트: cross-validation을 사용하세요.)  \n",
    "(참고자료:\n",
    "https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.RidgeCV.html  \n",
    "https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LassoCV.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "id": "Kwg6rP8eLzoS"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training R^2: 0.83\n",
      "Training R^2: 0.77\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import RidgeCV\n",
    "\n",
    "# 1. 먼저 모델을 만들어 줍니다.\n",
    "ridge = RidgeCV()\n",
    "\n",
    "# 2. 모델을 적합시킵니다.\n",
    "ridge.fit(X_train, y_train)\n",
    "\n",
    "# 3. train 세트와 test 세트에서의 성능을 확인합니다. (이 경우 결정계수 R^2)\n",
    "print(\"Training R^2: %.2f\" % ridge.score(X_train, y_train))\n",
    "print(\"Training R^2: %.2f\" % ridge.score(X_test, y_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "id": "c2YiywA_LzoS"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training R^2: 0.82\n",
      "Training R^2: 0.77\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LassoCV\n",
    "\n",
    "# 1. 먼저 모델을 만들어 줍니다.\n",
    "lasso = LassoCV()\n",
    "\n",
    "# 2. 모델을 적합시킵니다.\n",
    "lasso.fit(X_train, y_train)\n",
    "\n",
    "# 3. train 세트와 test 세트에서의 성능을 확인합니다. (이 경우 결정계수 R^2)\n",
    "print(\"Training R^2: %.2f\" % lasso.score(X_train, y_train))\n",
    "print(\"Training R^2: %.2f\" % lasso.score(X_test, y_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "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>GRE Score</th>\n",
       "      <th>TOEFL Score</th>\n",
       "      <th>University Rating</th>\n",
       "      <th>SOP</th>\n",
       "      <th>LOR</th>\n",
       "      <th>CGPA</th>\n",
       "      <th>Research_No</th>\n",
       "      <th>Research_Yes</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>304</td>\n",
       "      <td>103</td>\n",
       "      <td>5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>8.64</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>297</td>\n",
       "      <td>96</td>\n",
       "      <td>2</td>\n",
       "      <td>2.5</td>\n",
       "      <td>1.5</td>\n",
       "      <td>7.89</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>302</td>\n",
       "      <td>101</td>\n",
       "      <td>2</td>\n",
       "      <td>2.5</td>\n",
       "      <td>3.5</td>\n",
       "      <td>7.96</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>318</td>\n",
       "      <td>112</td>\n",
       "      <td>3</td>\n",
       "      <td>4.0</td>\n",
       "      <td>3.5</td>\n",
       "      <td>8.67</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>304</td>\n",
       "      <td>100</td>\n",
       "      <td>4</td>\n",
       "      <td>1.5</td>\n",
       "      <td>2.5</td>\n",
       "      <td>7.84</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   GRE Score  TOEFL Score  University Rating  SOP  LOR  CGPA  Research_No  \\\n",
       "0        304          103                  5  5.0  4.0  8.64            1   \n",
       "1        297           96                  2  2.5  1.5  7.89            1   \n",
       "2        302          101                  2  2.5  3.5  7.96            1   \n",
       "3        318          112                  3  4.0  3.5  8.67            1   \n",
       "4        304          100                  4  1.5  2.5  7.84            1   \n",
       "\n",
       "   Research_Yes  \n",
       "0             0  \n",
       "1             0  \n",
       "2             0  \n",
       "3             0  \n",
       "4             0  "
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_dum = pd.get_dummies(test)\n",
    "test_dum.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "predict = pd.DataFrame(lasso.predict(test_dum), columns=['Chance of Admit'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "predict.to_csv('graduate_submission.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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