실습_3차시_2015131406_박가은.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "실습 3차시",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MH4dGAvhuPm7"
      },
      "source": [
        "# **실습 3차시**\n",
        "\n",
        "제출 기한: 2020년 10월 14일 수요일 15시 29분\n",
        "\n",
        "실습 3차시 내용\n",
        "\n",
        "* Linear Regression\n",
        "\n",
        "* Logistic Regression"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "o84SHFveual0"
      },
      "source": [
        "# **활동 1: Simple Linear Regression**\n",
        "\n",
        "* machine learning의 목적은 real-world data를 잘 설명해줄 수 있는 모델을 설계하는 것입니다. 이를 통해 우리는 미래에 다른 input이 들어 왔을 때 무슨 일이 일어날지 예측할 수 있게됩니다.\n",
        "\n",
        "* 가장 간단하고 직관적인 방법은 data의 경향에 맞게 선을 그어주는 것입니다. 이때 data에 대해 가장 잘 맞는 선을 찾아가는 과정을 \"Linear Regression\"이라고 합니다.\n",
        "\n",
        "### [Example: Sandra’s lemonade stand’s revenue over its first 12 months of being open]\n",
        "\n",
        "주어진 data(months, revenue)에 대해 x축은 months y축은 revenue로 하여 그래프를 그린 후 둘의 관계를 확인해 봅시다."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NmFuHPinn-yR",
        "outputId": "48da731f-c7d5-4ad3-ba90-d5309537e8f5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        }
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "months = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]\n",
        "revenue = [52, 74, 79, 95, 115, 110, 129, 126, 147, 146, 156, 184]\n",
        "\n",
        "plt.plot(months, revenue, \"o\")\n",
        "plt.title(\"Sandra's Lemonade Stand\")\n",
        "plt.xlabel(\"Months\")\n",
        "plt.ylabel(\"Revenue ($)\")\n",
        "plt.show()"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "G7yME6q3ujcs"
      },
      "source": [
        "### [Points and Lines]\n",
        "* line은 아래의 수식처럼 slope(=m)와 intercept(=b)에 의해 결정됩니다. \n",
        "\n",
        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        "* Linear Regression에서의 목표는 우리가 가지고 있는 data에서 \"가장 좋은\"(=\"최적의\") m과 b를 찾는 것입니다.       \n",
        "* 위의 data에 대해 최적의 m과 b를 미리 구해 놓았다고 가정하겠습니다. 이때 최적의 m과 b 는 각각 10과 53입니다."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wx9mhn1nujA0"
      },
      "source": [
        "# TODO: slope\n",
        "m = 10\n",
        "# TODO: intercept\n",
        "b = 53"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yEPdU6rAuoAf"
      },
      "source": [
        "### [Practice 1]\n",
        "\n",
        "위에서 주어진 최적의 m과 b를 이용하여 months에 대한 예측값 y를 생성하고 이를 실제 관측값인 revenue와 그래프를 그려 비교해봅시다. (앞에서와 마찬가지로 그래프를 그릴 때 x축은 months로 설정하십시오.)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dhqYXyVLughx"
      },
      "source": [
        "# TODO: m과 b를 이용하여 months에 대한 예측값 y 생성하기\n",
        "y = [m * x + b for x in months]"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FtE-_LgiBbD7",
        "outputId": "1df66e81-3005-44cf-834d-43fbe2c08938",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        }
      },
      "source": [
        "# y와 revenue를 그래프를 그려 비교하기\n",
        "plt.plot(months, revenue, \"o\")\n",
        "plt.plot(months, y)\n",
        "plt.show()"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RQykEvhmGMSZ"
      },
      "source": [
        ""
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4QsojpiuuseB"
      },
      "source": [
        "### [Loss]\n",
        "* 최적의 parameter(m과 b)를 찾기 위해서는 Loss를 정의해야합니다. 이때 Loss는 fitting된 line이 실제값과 얼마나 차이가 있는지를 수치로 표현한 것을 의미합니다. 즉, Loss가 낮을 수록 최적의 parameter에 가까운 것이고 Loss가 높을 수록 최적의 parameter와는 거리가 있는 것입니다.\n",
        "\n",
        "* 여기서는 아래 그림처럼 해당 point에서 line까지의 squared distance를 Loss라고 정의합니다."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VrGWQbOSBcgv"
      },
      "source": [
        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        "\n",
        "A의 squared distance는 9이고 B의 squared distance는 1입니다. 그래서 total Loss는 10이 됩니다. 만약 10보다 작은 Loss를 갖는 line을 찾는다면 그 line은 이 data에 대해 더욱 최적인 parameter라고 할 수 있습니다. \n",
        "* 결론적으로, 이러한 Loss를 기준으로 최적의 parameter인지 아닌지를 판단합니다. 즉, 주어진 전체 data에 대해 Loss를 최소로 하는 parameter(m, b)를 찾는 것이 목표입니다.\n",
        "이를 식으로 표현하면 아래와 같습니다.\n",
        "\n",
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      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "W47h0BiFuvX7"
      },
      "source": [
        "### [Example]\n",
        "\n",
        "3개의 point (1, 5), (2, 1), (3, 3)가 주어졌을 때, y = x와 y = 0.5x +1인 두가지 line이 있다고 가정해보겠습니다."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TrM53_Rbus2y"
      },
      "source": [
        "x = [1, 2, 3]\n",
        "y = [5, 1, 3]"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7OQKdIeNBdnl"
      },
      "source": [
        "# TODO: y = x\n",
        "m1 = 1\n",
        "b1 = 0  "
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FiB4UTFvBewf"
      },
      "source": [
        "# TODO: y = 0.5x + 1\n",
        "m2 = 0.5\n",
        "b2 = 1"
      ],
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TUZ-alqaBf6g"
      },
      "source": [
        "# TODO:\n",
        "y_predicted1 = [m1 * x_val + b1 for x_val in x]\n",
        "y_predicted2 = [m2 * x_val + b2 for x_val in x]"
      ],
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hkYSdePiuzA6"
      },
      "source": [
        "### [ Practice 2 ]\n",
        "\n",
        "이 두가지 line 중 위의 식을 토대로 Loss를 계산하고, 그 중 Loss가 더 작은 line을 골라봅시다."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hXIyONi0uxRg",
        "outputId": "fee96835-2e06-4c15-9eff-276b5cd07669",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "# TODO: \n",
        "total_loss1 = 0\n",
        "total_loss2 = 0\n",
        "\n",
        "N = len(x)\n",
        "for i in range (N) :\n",
        "    total_loss1 += (y[i] - y_predicted1[i])**2 / N\n",
        "    total_loss2 += (y[i] - y_predicted2[i])**2 / N\n",
        "\n",
        "print(total_loss1, total_loss2)"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "5.666666666666666 4.499999999999999\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "btohyn2CN8yL"
      },
      "source": [
        "### **Gradient Descent for Intercept**\n",
        "* 최소의 loss를 찾는 것은 마치 아래의 그림처럼 언덕을 내려가다가 바닥에 도착하면 멈추는 것과 비슷합니다. 즉, parameter(m과 b)를 loss가 작아지는 방향으로 조정하다가 최소가되면 멈추게됩니다. 이때 loss가 작아지는 방향은 현재의 경사(=gradient)의 반대 방향을 의미합니다. (실제 Loss도 아래의 그림과 같은 형태입니다.)\n",
        "* 이러한 과정을 \"Gradient Descent\"라고 합니다.\n",
        "\n",
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        "\n",
        "* 먼저 intercept(=b)에 대해서 gradient descent를 수행해보겠습니다. 우리는 앞에서 정의한 loss를 b에 대해 미분하여 gradient를 구할 수 있습니다. 결과는 아래와 같습니다.\n",
        "\n",
        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      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9dei5EOfOESP"
      },
      "source": [
        "# TODO: gradient descent을 함수로 구현해봅니다.\n",
        "def get_gradient_at_b(x, y, b, m) : \n",
        "    N = len(x)\n",
        "    diff = 0\n",
        "    for i in range(N) :\n",
        "        x_val = x[i]\n",
        "        y_val = y[i]\n",
        "        diff += y_val - (m * x_val + b)\n",
        "    b_gradient = -(2 / N) * diff\n",
        "    return b_gradient"
      ],
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7TxZ0NXpOOKR"
      },
      "source": [
        "### **Gradient Descent for Slope**\n",
        "* 마찬가지 방식으로 slope(=m)에 대한 gradient descent를 수행해보겠습니다.\n",
        "이번에는 앞에서 정의한 loss를 m에 대해 미분하여 gradient를 구하면 됩니다.\n",
        "결과는 아래와 같습니다.\n",
        "\n",
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      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YeH1bBejOVbX"
      },
      "source": [
        "##### **[ Practice 3 ]**\n",
        "\n",
        "intercept와 마찬가지 방식으로 slop에 대한 gradient식을 직접 함수로 구현해봅시다."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OE6mWHagOXOW"
      },
      "source": [
        "# TODO: 이때 사용하는 변수명은 위와 동일하게 하되, 함수명은 get_gradient_at_m()로 하십시오.\n",
        "def get_gradient_at_b(x, y, b, m) : \n",
        "    N = len(x)\n",
        "    diff = 0\n",
        "    for i in range(N) :\n",
        "        x_val = x[i]\n",
        "        y_val = y[i]\n",
        "        diff += x_val * (y_val - (m * x_val + b))\n",
        "    m_gradient = -(2 / N) * diff\n",
        "    return m_gradient"
      ],
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dfp948DhOZAg"
      },
      "source": [
        "### **Put it Together**\n",
        "* b에 대한 gradient와 m에 대한 gradient를 계산하는 방법을 알았으므로 b와 m의 gradient를 이용하여 loss가 감소하는 방향으로 b와 m을 update합니다. 그리고 loss가 최소가 되면 update가 멈추게 되는데, 그때의 b와 m이 최적의 parameter가 됩니다.\n",
        "* 이때 언덕을 내려가는 보폭을 조절할 수 있는데 이때 사용되는 것이 \"learning rate\"입니다. 즉, learning rate가 크면 큰 보폭으로 언덕을 내려가고 learning rate가 작으면 작은 보폭으로 언덕을 내려갑니다. \n",
        "* 즉, \"learning rate\"를 gradient에 곱해주어 보폭을 사용자가 정할 수 있게합니다.\n",
        "* 그러나 learning rate는 신중하게 정할 필요가 있습니다.\n",
        "  1. learning rate가 너무 작으면 loss의 최솟값에 수렴하는데 시간이 오래 걸립니다.\n",
        "  2. learning rate가 너무 크면 최적의 parameter를 얻지 못할 수 있습니다."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nmr2sADdOa8g"
      },
      "source": [
        "# TODO: step_gradient 함수\n",
        "def step_gradient(b_current, m_current, x, y, learning_rate) :\n",
        "    b_gradient = get_gradient_at_b(x, y, b_current, m_current)\n",
        "    m_gradient = get_gradient_at_b(x, y, b_current, m_current)\n",
        "    b = b_current - (b_gradient * learning_rate)\n",
        "    m = m_current - (m_gradient * learning_rate)\n",
        "\n",
        "    return [b, m]"
      ],
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "E35qQZvKOenm"
      },
      "source": [
        "### **Example: Sandra’s lemonade stand’s revenue over its first 12 months of being open**\n",
        "* 이 함수들을 통해 앞에서 생성했던 data에 대해 한 step 후의 update된 parameter를 구해보겠습니다."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Vu8I6A73OgBj",
        "outputId": "e8c7dccc-f24b-4aa4-e821-f073aeec8fa1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "months = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]\n",
        "revenue = [52, 74, 79, 95, 115, 110, 129, 126, 147, 146, 156, 184]\n",
        "\n",
        "# current intercept guess:\n",
        "b = 0\n",
        "# current slope guess:\n",
        "m = 0\n",
        "# TODO: learning rate\n",
        "learning_rate = 0.01\n",
        "\n",
        "# TODO: perform step_gradient\n",
        "b, m = step_gradient(b, m, months, revenue, learning_rate)\n",
        "print(b, m)"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "17.78333333333333 17.78333333333333\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "k5JXx7MnOpsI"
      },
      "source": [
        "지금까지 gradient를 계산하는 법과 learning_rate를 설정하는 이유도 알았으므로 최적의 parameter를 찾을 때까지 위의 과정을 반복해보겠습니다. (여기서는 앞의 과정을 1000번만 반복해보겠습니다.=> `num_iterations=1000`)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uAsDf9VjOrVZ"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "  \n",
        "# TODO: gradient_descent 함수\n",
        "def gradient_descent(x, y, learning_rate, num_iteration) :\n",
        "    b = 0\n",
        "    m = 0\n",
        "    for i in range(num_iteration) :\n",
        "        step_gradient(b, m, x, y, learning_rate)\n",
        "    return b, m"
      ],
      "execution_count": 23,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FGq41hhEBVlp"
      },
      "source": [
        "months = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]\n",
        "revenue = [52, 74, 79, 95, 115, 110, 129, 126, 147, 146, 156, 184]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XhWFPDxsBWm7",
        "outputId": "c22274ec-f056-4142-8ebb-3110f05fc4dc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "# TODO: gradient_descent 호출\n",
        "gradient_descent(months, revenue, 0.01, 1000)\n",
        "print(b, m)"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "17.78333333333333 17.78333333333333\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9RD9MewwOtru"
      },
      "source": [
        "위에서 찾은 최적의 parameter로 그래프를 그려보겠습니다."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Q79Odl_OOvVA"
      },
      "source": [
        "# TODO: 최적의 parameter로 linear regression line 만들기\n",
        "y = [m * x + b for x in months]"
      ],
      "execution_count": 26,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "g3_yt0J6BYQc",
        "outputId": "2e47b21a-e00f-4039-ed75-eca7ddb6751d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        }
      },
      "source": [
        "plt.plot(months, revenue, \"o\")\n",
        "plt.plot(months, y)\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f3LbDtZNxRme"
      },
      "source": [
        "### [Scikit-Learn]\n",
        "* 지금까지 linear regression algorithm을 직접 구현했습니다. scikit-learn library를 이용하여 보다 간단하게 linear regression을 사용할 수 있습니다. [다큐멘테이션](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html)\n",
        "* scikit-learn에 있는 linear_model 모듈을 통해 linear regression을 실습해보겠습니다.(단, 위에서 언급했던 `learning_rate`와 `num_iterations`은 scikit-learn의 기본값을 사용합니다.)\n",
        "* 아래의 temperature/sales 데이터를 scikit-learn을 이용하여 fitting 해보겠습니다.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "H0rVhogUu1AQ",
        "outputId": "0fe62968-bdfc-4f1f-942b-7b189197260e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "temperature = np.array(range(60, 100, 2))\n",
        "temperature = temperature.reshape(-1, 1)\n",
        "sales = [65, 58, 46, 45, 44, 42, 40, 40, 36, 38, 38, 28, 30, 22, 27, 25, 25, 20, 15, 5]\n",
        "\n",
        "plt.plot(temperature, sales, 'o')"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f54de3466d8>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 28
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mYEE-w4WxT9B"
      },
      "source": [
        "# TODO:\n",
        "from sklearn.linear_model import LinearRegression\n",
        "line_fitter = LinearRegression()\n",
        "line_fitter.fit(temperature, sales)\n",
        "sales_predict = line_fitter.predict(temperature)"
      ],
      "execution_count": 30,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2zE0If-urj8d",
        "outputId": "d82d7284-3177-4e82-8213-38250c12eaab",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        }
      },
      "source": [
        "plt.plot(temperature, sales, 'o')\n",
        "plt.plot(temperature, sales_predict)\n",
        "plt.show()"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5Sf1e7WW537l"
      },
      "source": [
        "### [Coefficients]\n",
        "\n",
        "fitting된 모델에서 계수(coefficients)를 출력해보겠습니다."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xg1tcCKlxX5Z",
        "outputId": "f334c318-ac0f-487f-9fff-a6a4f6cb35d9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "# TODO:\n",
        "line_fitter.coef_"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-1.15225564])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yxL64B5J56xa",
        "outputId": "9af80b0c-5bef-4a67-d7ca-e49429b71698",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "# TODO:\n",
        "line_fitter.intercept_"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "125.47819548872182"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xQMxvvUV7EyM"
      },
      "source": [
        "### [Evaluating the Model's Performance]\n",
        "\n",
        "R-Squared (Coefficient of Determination)은 0과 1사이의 값으로 선형 회귀 모델이 데이터에 얼마나 fit 되었는지 나타냅니다. R-Squared가 1에 가까울 수록 모델은 종속 변수를 잘 예측할 수 있습니다."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xOOUvkQp6V9Z"
      },
      "source": [
        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      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1BI8bmqG6VdG",
        "outputId": "3f41d871-00af-4387-bac3-a1c4c0ff0997",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "# TODO:\n",
        "line_fitter.score(temperature, sales)"
      ],
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.9114088011031334"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 35
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vQCQkCLhsfUD"
      },
      "source": [
        "# **활동 2: Logistic Regression**\n",
        "\n",
        "Logistic Regression은 데이터가 특정 카테고리에 속할지를 0과 1사이의 연속적인 확률로 예측하는 회귀 알고리즘 중 하나입니다. 그런 다음, 확률에 기반하여 특정 데이터가 어떤 카테고리에 속할지를 결정하게 되고, 궁극적으로 classification문제를 풀게 됩니다.\n",
        "\n",
        "Logistic Regression을 활용하면 수신한 이메일이 스팸일지 아닐지를 예측할 수 있습니다. 만약 특정 이메일의 예측된 확률값이 0.5보다 크다면 해당 이메일을 정상메일으로 분류합니다. 여기서 정상메일은 positive class라고 불리고, label을 1로 설정합니다. positive class란 모델이 detect하고자 하는 class를 말합니다. 만약 특정 이메일의 예측된 확률값이 0.5보다 작다면, 해당 이메일을 스팸메일으로 분류합니다. 여기서 스팸메일은 negative class라고 불리고, label을 0으로 설정합니다. 이렇게 두 가지 class중 데이터가 어떤 class에 속할지 결정하는 일을 binary classification이라고 합니다."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "t8iOPJCJtRjg"
      },
      "source": [
        "### [Linear Regression Approach]\n",
        "\n",
        "만약 대학교 강의에서 학생들이 기말 시험을 pass할 수 있을지를 예측한다고 생각해봅시다. 첫 번째로 해야할 일은 각 학생들이 시험을 pass할 확률을 예측하는 것입니다. 여기서 Linear Regression을 활용하면 어떨까요? 한번 해봅시다.\n",
        "\n",
        "우선 기말 시험 data를 확인 해보겠습니다.\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UX62ShUutUEh",
        "outputId": "ff7e5320-908e-4def-e33e-53627fd00af1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        }
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "passed_exam = np.array([0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1])\n",
        "passed_exam = passed_exam.reshape(-1, 1) \n",
        "hours_studied = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19])\n",
        "hours_studied = hours_studied.reshape(-1, 1) \n",
        "\n",
        "# Scatter plot of exam passage vs number of hours studied\n",
        "plt.scatter(hours_studied, passed_exam)\n",
        "plt.ylabel('passed/failed')\n",
        "plt.xlabel('hours studied')\n",
        "plt.show()"
      ],
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ftDPoi94tSWq"
      },
      "source": [
        "각 학생들이 공부한 시간을 num_hours_studied이라 하고 해당 학생이 중간 시험을 통과한 여부를 y  (y 는 통과한 경우 1, 그렇지 않은 경우 0) 라고 한다면 Linear Regression을 통해 다음과 같이 직선을 그릴 수 있습니다."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ApcFAdactag8",
        "outputId": "0885b41f-8b1a-40e5-b4ea-10675b949ab0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "# TODO:\n",
        "model = LinearRegression()\n",
        "model.fit(hours_studied, passed_exam)"
      ],
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 37
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fjV8H8aNtbC1"
      },
      "source": [
        "# TODO: Plug sample data into fitted model\n",
        "sample_x = np.linspace(0, 20, 100).reshape(-1, 1)\n",
        "probability = model.predict(sample_x).ravel()"
      ],
      "execution_count": 43,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-DmC8p5IMz7y",
        "outputId": "95b350c7-8ad6-4f97-ff89-46ca90b999e1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        }
      },
      "source": [
        "plt.plot(hours_studied, passed_exam, 'o')\n",
        "plt.plot(sample_x, probability)\n",
        "plt.show()"
      ],
      "execution_count": 104,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pBSH_QzpteMZ"
      },
      "source": [
        "여기에는 한 가지 문제가 존재합니다. 바로 낮은 num_hours_studied값을 보유한 학생에 대해서는 확률이 음의 값으로 예측된다는 것입니다. 마찬가지로 높은 값을 보유한 학생의 예측값은 1을 초과하게 됩니다. 이렇게 기준을 벗어나는 확률 값은 의미가 없습니다. 이러한 문제가 발생하는 이유는 바로 Linear Regression의 출력 범위가 - ∞ 부터 + ∞ 까지이기 떄문입니다."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9qhzQc0ttgx7"
      },
      "source": [
        "Logistic Regression의 출력은 0과 1사이이므로 위와 같은 Linear Regression의 한계를 극복할 수 있습니다. Logistic Regression은 다음과 같은 과정으로 수행됩니다.\n",
        "\n",
        "1. 모든 coefficients와 intercept를 0으로 초기화합니다.\n",
        "2. 각각의 feature를 이에 상응하는 coefficient와 곱한 값과 intercept를 모두 더해 log-odds를 계산합니다.\n",
        "3. 계산한 log-odds 값을 sigmoid 함수에 전달하여 0 과 1 사이의 확률값을 구합니다.\n",
        "4. 계산한 확률값과 실제 label을 비교하여 Loss를 계산하고, gradient descent로 최적의 coefficients와 intercept를 찾습니다.\n",
        "5. 최적의 파라미터를 찾았다면 classification threshold 값을 조절하여 positive class와 negative class를 어떻게 나눌지를 설정합니다.\n",
        "\n",
        "위 방법대로 Logistic Regression을 구현해봅시다.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gmUfn8qOtksg"
      },
      "source": [
        "## [ Log-Odds ]\n",
        "Linear Regression에서는 각 feature를 이에 상응하는 coefficient에 곱한 값과 intercept를 더해 predict를 하였습니다. Logistic Regression에서도 마찬가지지만 log-odds를 계산합니다.\n",
        "\n",
        "log-odds는 특정 데이터가 positive class에 속할 확률을 표현하는 또 다른 방법입니다. 확률론에서 특정 사건의 odds(승산)을 계산하는 공식은 다음과 같습니다.\n",
        "\n",
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d0zTIrzTL2e7k3SxR2EiGKBfvSEmc47AZHJPtXT3aXElrItlNHBOR8kkkZkVT6lQRn8xXN6dJaabeXg02z1LX79nKX16BHksP4N7siYGSNicLjkA9V1H0F1PxBqaX+jwppd7p0dxqCRSyTm3ZXQq52/LIxBOAc4HTrV3WdcuLXWLHRtNhia9vkkdZbhiI4lTGTgcueR8oxn1FYqaZoVxr2mwxaKvh3Ube5+0xq9jGpuUVTlVkjJU/eyRuJ46d619bsL7VGMEmiaXeW8bBoZZ7+SKVG/vLthJRvdWz70dAe+n9asj1S+1/QNNm1O7m03ULa2QvNDHbvbPsA5KsZHBP+yQM+orSvtW+yaINUit5JoVRZZE+66x4yWC45IHO3joa5LSrW41aa5YaDbXP9n3bQFNR1+5uEEigfMqvEy9+DgH6V2tqbqa0I1O3ghlbIaOGYyrj/eKr/KjW2gdSaGaO4gjmgcSRyKGR1OQwIyDT65n4eSM/gm0jck/Z5JYFJ/upIyr+gFdNTduga9QooopAFZkHiTR7nWP7KtdQhnvdrMYom37Qpw2SOAQexOa06427/wCSzaf/ANgiT/0ZR1S/rYOjf9bnZUU12KRsyozkAkKuMt7DPFZn9r3v/Qu6l/38tv8A49QBq1R1nVF0XSZtQltpriKBS8iwFNyqBkt87KOMeufapbK6mulcz2FxZFTgCdoyW+mx2/XFcx8ULqSPwXJY23/HxqU8dnEPUs3I/IEUne2g1a+pYPjmGLRYtYutF1S30yRVf7U6wsqq2MMVWQvjkfw1rXWsxx3Vha2iC5nvvnQBsBYhgtITg8DIA9SQPcYmpeHtV1zQYtBuks9O04CNJXt7h5pHRMfIoMaBc4HPP0p2ixp/wsTWY1XbHYWNrbQL/dQ7mIH5D8qrS/8AWxOtrnV1l6f4hsNU1rUdMs2Z59NKCdsDbls8A55IxzUXifWH0rTAtqJHvbpvKt1jhaVlJ6vsUEkKMscDtjvXI+CUtLL4k61aaelwkEljBIPtMDxO5X5WYq4BJJJJOOSTSWrt/Xcb0V/63O30zVVv5bu3ki8i7s5PLmhLbsZGVYHjKkcg/Udq0K5dmMHxWjVPu3WkHzB6lJRtP/j5FdRQtk/67B1aCiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACobqF7i2eKK5ltXbpNCFLLz23Kw/MGpqKAMTw54Yh8Mx3EVrf3lzHcStM63Pln526tlUU5PuSKua7pi61oF7prnaLqFow390kcH8Dg1fopNXVhp2dzL8O3z3uiwi5Xyry3Ahuoj1jkUYI+h6g9wQa1KKKpu7uSlZWMe30meLxle6szxmCezigVQTuDKzkkjGMfMO9T6xo0esQwZnmtZ7aUTW9xARujcAjOGBBBBIIIIwa0aKXSw+pifYPErwiKTXbFRgBpYtMKyY7kFpWUH6qR7Ve0jSoNF02OytWkdELMzytueRmJZmY+pJJq7RQBUj0uzi1WbUkh/0yZFjeZmLEIOijJ+Ud8DGTyear6/o8WsaTcwiG3a7a2lit5pUBMTOhUkNglQc847Vp0Umrqw02ncgsIGtdOtreQgvFEqMV6EgAVlt4cZdTvL2y1nULJr11kljhWBlLBQoI3xMRwo71t0VTd3clKysZMWj30cyO/iPU5VVgSjx22GHocQg4+hBrWoopDCqVjpcNhd31xC0jPfTCaQOQQGCKvHHTCj1q7RQBR1nSodb0mbT7mSWKObGXiIDDBBGMgjqPSqv9iX/AP0M+q/9+rT/AOMVsUUARWsL29skUtzLdOvWaYKGb67VUfkBWZqGhTS6qNV0q/axvvLWKTdGJYpkDZAdMg8ZOCrKee/StiijrcOljn7zQdU1iBrTWtXhaxcYlhsbMwNMP7rO0jnae4XB963XhjkgMMkavEy7GRhkEYxgj0p9FAFSx0nTtLSRdLsLWyWTlxbwrGGPbO0DNQ6BpX9h6Daab53n/Zk2eZs27uc9MnHX1rRooAitrW3s4fKtII4I8ltkSBVyTknA9TzVDVtBttR0fU7K3WK0k1GJklnSIZYlcbmxjcQPU1qUUANiTy4UTOdqgZ9ax5PDjDVby/stY1Cye8ZGmSFYGUlVCgjfGxHA9a2qKOtwWiscteeFNUudSluE8SXKRvIrLzKHjAABChJVi7HrGevO6t7VdNi1fSLrTrlpFhuomidoyAwBGDjIIz+FW6KOlg63MWPQb2KJY4/E2qhUAVR5drwB/wBsK0LCzns43W41G5vyxyGuFiBX2Hloo/PNWqKACsGPQL/TbmZtB1VLe3nkeV7W8tvPRHY5JQq6MuTkkEsOeMVvUUAYkOhXU+q2+oa3qIvJbQs1tDbweRDGSu0sVLMzNgkZLYGeB3rboooAzNG0f+yG1A+f53228e6+5t2bgPl6nOMdal1jURpmly3AQyy42wwr96WQ8Ko9yf8AGr1FJ6qw+tzK8MaQdC8NWWnOwaSKPMrDoXYlmP5k1q0UVTd3cQUUUUgCudm8I+d4gXWjrmppeJG0SFRb7UjJzsAMXT3OT710VFHW4eQUUUUAFYGt+E013UbW7udW1CH7HKJreKEQ7I3Axu+aMk/iTW/RQAigqgBYsQMFjjJ9+K525i/snxwmpuMWmpW62ssnaOVWJjJ9mDFc+oA710dFHW4dLGRDoBj8QnV5dUvriTy2iWGXyvLRCc7QAgI5xznJwMk1WTwnHH4qbXxq2oG7ZPKZMQ+WYt27Zjy84987veugoo2A5zSof7T8X32ugf6PFALG1b/noAxaRx7bsKD32mujooo6WDrcKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAP/Z)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "m12fDrIetre4"
      },
      "source": [
        "Odds는 특정 사건이 일어나는 횟수가 특정 사건이 일어나지 않는 횟수보다 얼마나 더 많은지를 의미합니다. 만약 특정 학생이 시험에서 pass할 확률이 0.7이라면, pass하지 못 할 확률은 1 - 0.7 = 0.3 이고, 이 경우 odds를 다음과 같이 계산할 수 있습니다.\n",
        "\n",
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      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5YOE759xtw4W"
      },
      "source": [
        "Odds는 0과 양의 무한대의 값을 범위로 갖습니다. log-odds는 odds에 log를 취한 것으로 음의 무한대부터 양의 무한대까지의 범위를 갖습니다.\n",
        "\n",
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      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6ymAXF9EtzbK"
      },
      "source": [
        "Logistic Regression 모델에서, 우리는 아래와 같이 z 값으로 나타내지는 log-odds 값을 계산할 수 있습니다.\n",
        "\n",
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      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wFvQsAT6t16p"
      },
      "source": [
        "이로써 특정 데이터의 feature values를 해당 데이터가 positive class에 속할 가능성으로 매핑할 수 있습니다. 이 때 이러한 곱의 합을 dot product(내적) 이라고 합니다. 내적은 numpy의 np.dot() 메서드를 활용하여 쉽게 계산할 수 있습니다.\n",
        "\n",
        "기말 시험 data에서 최적의 coefficient와 intercept가 각각 0.03, -0.3이라고 가정했을 때의 log-odds를 계산 해봅시다."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "f_kVrpKHt3mQ"
      },
      "source": [
        "calculated_coefficients = 0.03\n",
        "intercept = -0.3"
      ],
      "execution_count": 48,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OyCNCJw8BrVj"
      },
      "source": [
        "# TODO: log_odds() 함수 정의\n",
        "def log_odds(features, coefficients, intercept) :\n",
        "    return np.dot(features, coefficients) + intercept"
      ],
      "execution_count": 105,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3dMENDo1Bt3z",
        "outputId": "6c58acf5-82b8-4c84-ca3a-88f02a5195c0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 377
        }
      },
      "source": [
        "# TODO: hours_studied 데이터에 대해서 log-odds를 계산해봅니다.\n",
        "calculate_log_odds = log_odds(hours_studied, calculated_coefficients, intercept)\n",
        "print(calculate_log_odds)"
      ],
      "execution_count": 53,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[-0.3 ]\n",
            " [-0.27]\n",
            " [-0.24]\n",
            " [-0.21]\n",
            " [-0.18]\n",
            " [-0.15]\n",
            " [-0.12]\n",
            " [-0.09]\n",
            " [-0.06]\n",
            " [-0.03]\n",
            " [ 0.  ]\n",
            " [ 0.03]\n",
            " [ 0.06]\n",
            " [ 0.09]\n",
            " [ 0.12]\n",
            " [ 0.15]\n",
            " [ 0.18]\n",
            " [ 0.21]\n",
            " [ 0.24]\n",
            " [ 0.27]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HAITYm5vt6Gz"
      },
      "source": [
        "## [ Sigmoid Function ]\n",
        "\n",
        "Sigmoid Function은 log-odds인 z 값을 취해서 아래와 같이 0 과 1 사이의 값을 반환합니다.\n",
        "\n",
        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      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bCNzOiFjt_bO"
      },
      "source": [
        "이는 궁극적으로 Logistic Regression이 특정 데이터가 positive class에 속할 확률을 계산하게 합니다. 이를 python 코드로 구현해보겠습니다. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ubBWUhMUuBTf"
      },
      "source": [
        "# TODO: sigmoid 함수 정의하기\n",
        "def sigmoid(z) :\n",
        "    return 1 / (1 + np.exp(-z))"
      ],
      "execution_count": 51,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ojkQQVuEuBxh",
        "outputId": "d15f1d4f-5523-4969-f6b7-171f08aeca6b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 377
        }
      },
      "source": [
        "# TODO: 확률 계산해보기\n",
        "probabilities = sigmoid(calculate_log_odds)\n",
        "print(probabilities)"
      ],
      "execution_count": 54,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[0.42555748]\n",
            " [0.4329071 ]\n",
            " [0.44028635]\n",
            " [0.44769209]\n",
            " [0.45512111]\n",
            " [0.46257015]\n",
            " [0.47003595]\n",
            " [0.47751518]\n",
            " [0.4850045 ]\n",
            " [0.49250056]\n",
            " [0.5       ]\n",
            " [0.50749944]\n",
            " [0.5149955 ]\n",
            " [0.52248482]\n",
            " [0.52996405]\n",
            " [0.53742985]\n",
            " [0.54487889]\n",
            " [0.55230791]\n",
            " [0.55971365]\n",
            " [0.5670929 ]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cbkSRDI_uEbf"
      },
      "source": [
        "0 과 1 사이의 값을 반환함을 확인했습니다."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qzFpMJdVuG0o"
      },
      "source": [
        "## [ Log-Loss ]\n",
        "\n",
        "지금까지 Logistic Regression 모델이 어떻게 확률을 예측하는지 알아보았습니다. 그렇다면 이제 남은 것은 최적의 coefficients와 intercept를 구하는 일입니다. 그런데 어떻게 이를 구할 수 있을까요? 이에 대답하기 위해선 주어진 모델이 데이터에 얼마나 fit한지를 측정하는 기준이 필요합니다. 이를 loss function 혹은 cost function이라고 합니다.\n",
        "\n",
        "모델이 데이터에 ‘fit’ 하단걸 측정하기 위해선 먼저 각 데이터에 대한 loss를 계산한뒤 loss의 평균을 내야합니다. Logistic Regression에서의 loss function은 Log Loss라고 불리며, 공식은 다음과 같습니다.\n",
        "\n",
        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        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rz_WLSYyuMu9"
      },
      "source": [
        "* m 은 전체 데이터의 개수입니다.\n",
        "* $y^{(i)}$는 $i$ 번째 데이터의 class 입니다.\n",
        "* $a^{(i)}$는 $i$ 번째 데이터의 log-odds 값에 sigmoid 를 취한 값입니다. 즉 $i$ 번째 데이터가 positive class에 속할 확률을 나타낸 값입니다."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gccoAJP3uO_B"
      },
      "source": [
        "왜 위와 같은 공식이 유도되는 걸까요? 만약 i 번째 데이터의 class가 y=1 이라면 해당 데이터에 대한 loss는 다음과 같습니다.\n",
        "\n",
        "![3.JPG](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAeAB4AAD/4RDsRXhpZgAATU0AKgAAAAgABAE7AAIAAAALAAAISodpAAQAAAABAAAIVpydAAEAAAAWAAAQzuocAAcAAAgMAAAAPgAAAAAc6gAAAAgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAHNlam9uZ3N0YXQAAAAFkAMAAgAAABQAABCkkAQAAgAAABQAABC4kpEAAgAAAAM2NAAAkpIAAgAAAAM2NAAA6hwABwAACAwAAAiYAAAAABzqAAAACAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA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      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Y0h47rVluRhH"
      },
      "source": [
        "loss를 최소화 시키려면 $a^{(i)}$ 값이 커야 합니다. 즉, 예측된 확률 값이 원래 class인 1 에 가까울수록 loss는 줄어들게 됩니다.\n",
        "\n",
        "이번에는 반대로 $i$ 번째 데이터의 class가 y=0 인 경우를 생각해봅시다."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x9EGjwnT0zS5"
      },
      "source": [
        " 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      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "P7YrdoKyuUQl"
      },
      "source": [
        "loss를 최소화 시키려면 $a^{(i)}$값이 작아야 합니다. 즉, 예측된 확률 값이 원래 class이 0에 가까울수록 loss는 줄어들게 됩니다. \n",
        "\n",
        " 아래의 그래프는 class가 y=1, y=0 일 때 a값에 따라 loss가 어떻게 변화하는지를 나타냅니다."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9weE3nLC1Cl2"
      },
      "source": [
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) "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "I_ZDaytBuW5p"
      },
      "source": [
        "그래프를 보면 올바르게 예측할수록 loss가 줄어드는 것을 볼 수 있습니다. 반대로 잘 못 예측하게 되면 loss가 크게 증가하는데, 이는 모델이 잘못 예측할 때 패널티를 강하게 줌으로써 올바른 예측을 할 수 있도록 유도할 수 있습니다.\n",
        "\n",
        "이제는 Linear Regression과 마찬가지로 gradient descent를 활용해서 loss를 최소화시키는 coefficients와 intercept를 찾으면 됩니다. 여기서는 따로 다루지 않겠습니다."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Syx2nmM_uZo5"
      },
      "source": [
        "이를 python 코드로 구현해보겠습니다. 그런 후 현재의 coefficients와 intercept의 log-loss를 구해봅시다."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "I8Do1Rreubb5"
      },
      "source": [
        "# TODO: log_loss 함수 구현해보기\n",
        "# probabilities는 log_odds에 sigmoid를 취한 확률값이며, acutal_class는 실제 class label입니다.\n",
        "def log_loss(probabilities, actual_class) :\n",
        "    return np.sum(-(1 / actual_class.shape[0] * (actual_class * np.log(probabilities) + (1 - actual_class) * np.log(1 - probabilities))))"
      ],
      "execution_count": 55,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "coSRQ_mJudQN",
        "outputId": "cedd0952-fe0c-4c20-d3ce-a956518fec41",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "# TODO: 구한 probabilities와  passed_exam의 log_loss 구하기\n",
        "loss = log_loss(probabilities, passed_exam)\n",
        "print(loss)"
      ],
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.6279073897953891\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AJN-6GZTue6D"
      },
      "source": [
        "## [ Classification Thresholding ]\n",
        "\n",
        "Logistic Regression은 예측된 확률 값이 임계값을 넘느냐 못 넘느냐에 따라서 class를 분류합니다. 이 임계값을 classification threshold 라고 합니다.\n",
        "\n",
        "Classification threshold의 디폴트 값은 0.5 입니다. 만약 특정 데이터의 예측된 확률 값이 0.5 보다 크거나 같다면 해당 데이터는 positive class로 분류됩니다. 반대로 예측된 확률 값이 0.5 보다 낮다면 negative class로 분류됩니다.\n",
        "\n",
        "만약 더욱 엄격하게하고자 한다면 threshold를 0.6이나 0.7로 조정할 수 있습니다. 즉, 모델이 positive class를 더 적게 예측할 수 있도록 하는 것입니다. \n",
        "\n",
        "이에 대해 예측된 확률값이 임계값을 넘으면 1, 그렇지 않으면 0 을 반환하는 함수를 구현해보겠습니다."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YxLMeNdXuijr"
      },
      "source": [
        "# TODO: predict_class함수 구현하기\n",
        "def predict_class(features, coefficients, intercept, threshold) :\n",
        "    z = log_odds(features, coefficients, intercept)\n",
        "    a = sigmoid(z)\n",
        "    return np.where(a >= threshold, 1, 0)"
      ],
      "execution_count": 62,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Tu2noRSXukDT",
        "outputId": "c4c13815-9cb1-45d2-982e-c0e8d52a067a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 377
        }
      },
      "source": [
        "# TODO: threshold=0.5로 최종 예측 해보기\n",
        "final_result = predict_class(hours_studied, calculated_coefficients, intercept, 0.5)\n",
        "print(final_result)"
      ],
      "execution_count": 63,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[0]\n",
            " [0]\n",
            " [0]\n",
            " [0]\n",
            " [0]\n",
            " [0]\n",
            " [0]\n",
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            " [0]\n",
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            " [1]\n",
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            " [1]\n",
            " [1]\n",
            " [1]\n",
            " [1]\n",
            " [1]\n",
            " [1]\n",
            " [1]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FlFSgM1numI4"
      },
      "source": [
        "이번에는 더욱 엄격하게 threshold를 0.55로 설정하여 위의 결과와 비교해봅시다.  "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XTtDq5hwuoAz",
        "outputId": "4c35866a-aae3-458a-8e56-69cdf0f74d12",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 377
        }
      },
      "source": [
        "# TODO: threshold=0.55로 최종 예측 해보기\n",
        "final_result2 = predict_class(hours_studied, calculated_coefficients, intercept, 0.55)\n",
        "print(final_result2)"
      ],
      "execution_count": 64,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[0]\n",
            " [0]\n",
            " [0]\n",
            " [0]\n",
            " [0]\n",
            " [0]\n",
            " [0]\n",
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            " [0]\n",
            " [1]\n",
            " [1]\n",
            " [1]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JmFuhb82uqGi"
      },
      "source": [
        "1로 예측한 개수가 확실히 줄어들었습니다."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MMS2MSknushP"
      },
      "source": [
        "## [ Scikit-Learn ]\n",
        "\n",
        "지금까지 Logistic Regression이 어떤 과정으로 이뤄지는지 알아보았습니다. 이제 sklearn에서 제공하는 메서드를 활용하여 Logistic Regression을 구현해봅시다.\n",
        "\n",
        "* 먼저 sklearn의 linear_model 모듈에서 LogisticRegression을 임포트한 뒤, LogisticRegression 객체를 생성해 줍니다. \n",
        "* 그런 다음, .fit() 함수에 features와 labels을 파라미터로 전달하여 모델을 학습시킵니다. .fit() 함수는 내부적으로 gradient descent를 수행해서 최적의 coefficients와 intercept를 찾아줍니다.\n",
        "* 마지막으로 .predict() 함수로 테스트할 데이터를 전달하여 1과 0으로 예측된 결과를 확인할 수 있습니다. 이때 sklearn은 디폴트로 classification threshold를 0.5로 설정합니다.\n",
        "* 만약 데이터의 class가 아닌 예측된 확률을 얻고자 한다면 .predict_proba() 함수에 동일한 파라미터를 전달하면 됩니다. 이 함수는 0 과 1사이의 예측된 확률값을 반환합니다.\n",
        "\n",
        "기말 시험 data에 대해 LogisticRegression을 수행하여 앞에서 확인했던 Linear Regression의 결과를 plot을 그려 비교 해봅시다."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dya9b1hvuvQe",
        "outputId": "e8e6f92a-6fda-4de5-8d0c-cc5ac5f68311",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 163
        }
      },
      "source": [
        "from sklearn.linear_model import LogisticRegression\n",
        "\n",
        "# TODO: logistic regression model 생성하기\n",
        "model = LogisticRegression()\n",
        "model.fit(hours_studied, passed_exam)"
      ],
      "execution_count": 69,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/sklearn/utils/validation.py:760: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
            "  y = column_or_1d(y, warn=True)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
              "                   intercept_scaling=1, l1_ratio=None, max_iter=100,\n",
              "                   multi_class='auto', n_jobs=None, penalty='l2',\n",
              "                   random_state=None, solver='lbfgs', tol=0.0001, verbose=0,\n",
              "                   warm_start=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 69
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "c2EKrGROuwoE"
      },
      "source": [
        "# TODO: Plug sample data into fitted model\n",
        "sample_x = np.linspace(0, 20, 100).reshape(-1, 1)\n",
        "probability = model.predict_proba(sample_x)[:, 1]"
      ],
      "execution_count": 71,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eYDPSioUlmMd",
        "outputId": "10d5dbfa-da2e-482c-abbc-a69a2e7f610b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        }
      },
      "source": [
        "plt.plot(hours_studied, passed_exam, 'o')\n",
        "plt.plot(sample_x, probability)\n",
        "plt.show()"
      ],
      "execution_count": 72,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bxZh5Yw3uzVY"
      },
      "source": [
        "낮은 num_hours_studied 값을 보유한 학생에 대해서는 확률이 음의 값으로 예측된다는 것과 높은 값을 보유한 학생의 예측값은 1을 초과한다는 Linear Regression의 문제점을 Logistic Regression이 해결했음을 확인 할 수 있습니다.\n",
        "\n",
        "그렇다면 최적의 coefficients와 intercept는 무엇일까요? 이를 확인하려면 아래와 같이 하면됩니다."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TEVH9CYDu2dD",
        "outputId": "ad83887d-9f0f-46fa-ca63-1ac632b20d92",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "# TODO: 최적의 coefficient와 intercept 프린트하기\n",
        "model.coef_"
      ],
      "execution_count": 73,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.59365161]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 73
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "i-nwj9tBUe_U",
        "outputId": "c2dce4ce-abf1-488c-bf31-471f9cb51330",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "model.intercept_"
      ],
      "execution_count": 74,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-6.23665281])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 74
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ri0VS9pzA_V8"
      },
      "source": [
        "# **과제**\n",
        "\n",
        "1. 이전 실습2 과제의 코드를 이용하여 titanic.csv 데이터의 url를 통해 `pandas` `DataFrame`으로 데이터를 가져옵니다.\n",
        "2. 이전 실습2 과제처럼 동일하게 1) 전체 데이터에서 `Survived`, `Pclass`, `Sex`, `Age`, `SibSp`, `Parch`, `Fare`, `Embarked` feature을 고르고, 2) `Age` feature의 NA값을 drop하고, 3) `Sex` feature을 `scikit-learn`의 `LabelEncoder`을 사용하여 정수형으로 변환합니다.\n",
        "3. `.head()`를 사용하여 데이터의 첫 다섯개 instance를 프린트해봅니다.\n",
        "4. 주어진 `onehot()` 함수를 사용하여 `Embarked` feature을 one-hot encoding 합니다.\n",
        "```python\n",
        "def onehot(data, feature):\n",
        "  '''\n",
        "  data의 feature column을 one hot으로 변환해줍니다.\n",
        "  data: pandas DataFrame\n",
        "  feature: string, 데이터 프레임의 column 이름\n",
        "  '''\n",
        "  return pd.concat([data, pd.get_dummies(data[feature], prefix=feature)], axis=1).drop([feature], axis=1)\n",
        "```\n",
        "5. `.head()`를 사용하여 one-hot encoding이 올바르게 되었는지 확인합니다.\n",
        "6. 아래 주어진 코드를 이용하여 데이터를 feature 변수 `x`와 label 변수 `y`로 분리하고 `train_test_split()`함수를 이용하여 데이터를 train data과 test data으로 나눕니다. 만약 deterministic한 결과를 원한다면 `random_state` 파라미터를 지정해줍니다. (지정하지 않아도 과제 점수에는 상관이 없습니다.) [train_test_split() 다큐멘테이션](https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.train_test_split.html)\n",
        "```python\n",
        "# 데이터를 feature X와 label y로 나눕니다.\n",
        "y = df[['Survived']].to_numpy().ravel()\n",
        "x = df.drop(columns=['Survived'])\n",
        "```\n",
        "\n",
        "7. `LogisticRegression()` 모델을 생성합니다. 이때, 모델 파라미터는 `max_iter`을 `1000`으로 지정해줍니다. 이 모델을 train data에 fit 해봅니다.\n",
        "8. test data에 대하여 score을 계산합니다. \n",
        "9. 훈련된 Logistic regression 모델의 `.coef_`를 프린트해보고, `.coef_`의 절대값이 큰 feature 2개와 절대값이 작은 feature 2개가 무엇인지, 그리고 각각에 대해 그 값이 몇인지 서술합니다.\n",
        "10. https://www.kaggle.com/masumrumi/a-statistical-analysis-ml-workflow-of-titanic#Part-3.-Visualization-and-Feature-Relations\n",
        "위 링크의 Part 3에서 제공하는 각 feature와 생존여부에 대한 시각화 통계자료를 활용하여, \n",
        "9번에서 `.coef_`의 절대값이 크게 나온 2개의 feature는 왜 `.coef_`가 크게 나왔는지, 반대로 절대값이 작게 나온 2개의 feature는 왜 `.coef_`가 작게 나왔는지에 대한 분석을 서술합니다."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OvJphLOXzDLB",
        "outputId": "c72d7abd-7670-4de1-ffa7-8a3e4b447149",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 255
        }
      },
      "source": [
        "import pandas as pd\n",
        "data_url = \"https://raw.githubusercontent.com/inikoreaackr/2020_Fall_ML/master/titanic.csv\"\n",
        "data = pd.read_csv(data_url)\n",
        "data.head()"
      ],
      "execution_count": 129,
      "outputs": [
        {
          "output_type": "execute_result",
          "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>PassengerId</th>\n",
              "      <th>Survived</th>\n",
              "      <th>Pclass</th>\n",
              "      <th>Name</th>\n",
              "      <th>Sex</th>\n",
              "      <th>Age</th>\n",
              "      <th>SibSp</th>\n",
              "      <th>Parch</th>\n",
              "      <th>Ticket</th>\n",
              "      <th>Fare</th>\n",
              "      <th>Cabin</th>\n",
              "      <th>Embarked</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>Braund, Mr. Owen Harris</td>\n",
              "      <td>male</td>\n",
              "      <td>22.0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>A/5 21171</td>\n",
              "      <td>7.2500</td>\n",
              "      <td>NaN</td>\n",
              "      <td>S</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>Cumings, Mrs. John Bradley (Florence Briggs Th...</td>\n",
              "      <td>female</td>\n",
              "      <td>38.0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>PC 17599</td>\n",
              "      <td>71.2833</td>\n",
              "      <td>C85</td>\n",
              "      <td>C</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>3</td>\n",
              "      <td>Heikkinen, Miss. Laina</td>\n",
              "      <td>female</td>\n",
              "      <td>26.0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>STON/O2. 3101282</td>\n",
              "      <td>7.9250</td>\n",
              "      <td>NaN</td>\n",
              "      <td>S</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>4</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>Futrelle, Mrs. Jacques Heath (Lily May Peel)</td>\n",
              "      <td>female</td>\n",
              "      <td>35.0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>113803</td>\n",
              "      <td>53.1000</td>\n",
              "      <td>C123</td>\n",
              "      <td>S</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>5</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>Allen, Mr. William Henry</td>\n",
              "      <td>male</td>\n",
              "      <td>35.0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>373450</td>\n",
              "      <td>8.0500</td>\n",
              "      <td>NaN</td>\n",
              "      <td>S</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   PassengerId  Survived  Pclass  ...     Fare Cabin  Embarked\n",
              "0            1         0       3  ...   7.2500   NaN         S\n",
              "1            2         1       1  ...  71.2833   C85         C\n",
              "2            3         1       3  ...   7.9250   NaN         S\n",
              "3            4         1       1  ...  53.1000  C123         S\n",
              "4            5         0       3  ...   8.0500   NaN         S\n",
              "\n",
              "[5 rows x 12 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 129
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dS2qJqD4XCEq"
      },
      "source": [
        "from sklearn.preprocessing import LabelEncoder\n",
        "data = data[['Survived', 'Pclass', 'Sex', 'Age', 'SibSp', 'Parch', 'Fare', 'Embarked']]\n",
        "\n",
        "data = data.dropna()\n",
        "\n",
        "le = LabelEncoder()\n",
        "data.Sex = le.fit_transform(data.Sex)"
      ],
      "execution_count": 130,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "i14Qrm_dXf5D",
        "outputId": "abc31253-896d-4bb1-f9db-1e3f4ef338bd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 204
        }
      },
      "source": [
        "data.head()"
      ],
      "execution_count": 92,
      "outputs": [
        {
          "output_type": "execute_result",
          "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>Survived</th>\n",
              "      <th>Pclass</th>\n",
              "      <th>Sex</th>\n",
              "      <th>Age</th>\n",
              "      <th>SibSp</th>\n",
              "      <th>Parch</th>\n",
              "      <th>Fare</th>\n",
              "      <th>Embarked</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>22.0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>7.2500</td>\n",
              "      <td>S</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>38.0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>71.2833</td>\n",
              "      <td>C</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>26.0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>7.9250</td>\n",
              "      <td>S</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>35.0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>53.1000</td>\n",
              "      <td>S</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>35.0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>8.0500</td>\n",
              "      <td>S</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   Survived  Pclass  Sex   Age  SibSp  Parch     Fare Embarked\n",
              "0         0       3    1  22.0      1      0   7.2500        S\n",
              "1         1       1    0  38.0      1      0  71.2833        C\n",
              "2         1       3    0  26.0      0      0   7.9250        S\n",
              "3         1       1    0  35.0      1      0  53.1000        S\n",
              "4         0       3    1  35.0      0      0   8.0500        S"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 92
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uwG81JI3gsT3"
      },
      "source": [
        "def onehot(data, feature):\n",
        "  '''\n",
        "  data의 feature column을 one hot으로 변환해줍니다.\n",
        "  data: pandas DataFrame\n",
        "  feature: string, 데이터 프레임의 column 이름\n",
        "  '''\n",
        "  return pd.concat([data, pd.get_dummies(data[feature], prefix=feature)], axis=1).drop([feature], axis=1)\n"
      ],
      "execution_count": 131,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FY8KZJg0agzK"
      },
      "source": [
        "data.Embarked = onehot(data, 'Embarked')"
      ],
      "execution_count": 132,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0GNt58v4fN4a",
        "outputId": "25e166f2-4b14-4668-9d61-8cb5863b5440",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 204
        }
      },
      "source": [
        "data.head()"
      ],
      "execution_count": 133,
      "outputs": [
        {
          "output_type": "execute_result",
          "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>Survived</th>\n",
              "      <th>Pclass</th>\n",
              "      <th>Sex</th>\n",
              "      <th>Age</th>\n",
              "      <th>SibSp</th>\n",
              "      <th>Parch</th>\n",
              "      <th>Fare</th>\n",
              "      <th>Embarked</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>22.0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>7.2500</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>38.0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>71.2833</td>\n",
              "      <td>1.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>26.0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>7.9250</td>\n",
              "      <td>1.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>35.0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>53.1000</td>\n",
              "      <td>1.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>35.0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>8.0500</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   Survived  Pclass  Sex   Age  SibSp  Parch     Fare  Embarked\n",
              "0         0       3    1  22.0      1      0   7.2500       0.0\n",
              "1         1       1    0  38.0      1      0  71.2833       1.0\n",
              "2         1       3    0  26.0      0      0   7.9250       1.0\n",
              "3         1       1    0  35.0      1      0  53.1000       1.0\n",
              "4         0       3    1  35.0      0      0   8.0500       0.0"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 133
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qZen0ddwgkiU"
      },
      "source": [
        "# 데이터를 feature X와 label y로 나눕니다.\n",
        "df = pd.DataFrame(data)\n",
        "y = df[['Survived']].to_numpy().ravel()\n",
        "x = df.drop(columns=['Survived'])"
      ],
      "execution_count": 134,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wxlJorPGoeU5"
      },
      "source": [
        "from sklearn.model_selection import train_test_split \n",
        "\n",
        "x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.3)"
      ],
      "execution_count": 135,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PSgmEupQh5wJ",
        "outputId": "f561e007-dc4a-4eaa-b36b-43514026ec1a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 107
        }
      },
      "source": [
        "from sklearn.linear_model import LogisticRegression\n",
        "\n",
        "model = LogisticRegression(max_iter=1000)\n",
        "model.fit(x_train, y_train)"
      ],
      "execution_count": 136,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
              "                   intercept_scaling=1, l1_ratio=None, max_iter=1000,\n",
              "                   multi_class='auto', n_jobs=None, penalty='l2',\n",
              "                   random_state=None, solver='lbfgs', tol=0.0001, verbose=0,\n",
              "                   warm_start=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 136
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AVzyKrtaiMDT",
        "outputId": "ce326768-a340-44dd-974c-6780c941839b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "print(model.score(x_test, y_test))"
      ],
      "execution_count": 137,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "1.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2J0U_eQHpR18",
        "outputId": "be973000-4530-43fe-f8b3-3b95b492f24a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 71
        }
      },
      "source": [
        "model.coef_\n"
      ],
      "execution_count": 138,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-5.78195834e-01, -1.07950273e+00, -2.25348992e-02,\n",
              "        -1.20727239e-01, -5.71270358e-02,  2.27392043e-03,\n",
              "         6.51330198e+00]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 138
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JnoWuJYRpXCc",
        "outputId": "fb57ef4c-bbdc-48dd-c513-0e5efbc81da5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "model.intercept_"
      ],
      "execution_count": 139,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-0.86716194])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 139
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "v4lXmpRWp8YO"
      },
      "source": [
        "# coefficient가 가장 높은 feature : Pclass, Fare\n",
        "# 그 이유: 타이타닉이 침몰할 때 구조의 우선순위는 높은 등급의 선실에 앉아있는 승객들, 즉 Fare를 많이 지불하고, Pclass(승선 등급)이 높은 사람들이 많이 구조되었다.\n",
        "# 때문에 Fare가 높을 수록, Pclass의 등급이 높을 수록 survived될 확률이 높기 때문이다.\n",
        "# coefficient가 낮은 feature: Embarked와 SibSp이다. 형제자매의 유무와 어디서 승선했는지는 승객을 구조할 때 고려한 사항이 아니었다. "
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}