{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# 09wk-1: Numpy와 Pandas의 활용\n",
        "\n",
        "최규빈  \n",
        "2023-05-01\n",
        "\n",
        "<a href=\"https://colab.research.google.com/github/guebin/PP2023/blob/main/posts/02_DataScience/2023-05-01-9wk-1.ipynb\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" style=\"text-align: left\"></a>\n",
        "\n",
        "# 강의영상\n",
        "\n",
        "> youtube:\n",
        "> <https://youtube.com/playlist?list=PLQqh36zP38-w-stglh0uVkQxHpCT9lH9C>\n",
        "\n",
        "# imports"
      ],
      "id": "6f980ee2-b662-4301-8cfa-c4a6bf6c5b08"
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {},
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import pandas as pd \n",
        "import matplotlib.pyplot as plt \n",
        "import urllib.request"
      ],
      "id": "8bc45346-052d-4da4-beb6-aec2d6167161"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# 회귀분석\n",
        "\n",
        "`1--7`.\n",
        "\n",
        "`1`. $x_i$가 아래와 같이 주어졌다고 가정하자."
      ],
      "id": "7a706cb2-fdf7-4357-93b3-04bcfc590fd0"
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {},
      "outputs": [],
      "source": [
        "x =  np.array([0.00983, 0.01098, 0.02951, 0.0384 , 0.03973, 0.04178, 0.0533 ,\n",
        "               0.058  , 0.09454, 0.1103 , 0.1328 , 0.1412 , 0.1497 , 0.1664 ,\n",
        "               0.1906 , 0.1923 , 0.198  , 0.2141 , 0.2393 , 0.2433 , 0.3157 ,\n",
        "               0.3228 , 0.3418 , 0.3552 , 0.3918 , 0.3962 , 0.4    , 0.4482 ,\n",
        "               0.496  , 0.507  , 0.53   , 0.5654 , 0.582  , 0.5854 , 0.5854 ,\n",
        "               0.6606 , 0.7007 , 0.723  , 0.7305 , 0.7383 , 0.7656 , 0.7725 ,\n",
        "               0.831  , 0.8896 , 0.9053 , 0.914  , 0.949  , 0.952  , 0.9727 ,\n",
        "               0.982  ])"
      ],
      "id": "72bc70cb-964c-4f64-a535-4cf8fd6ab0d5"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "아래의 수식에 따라 $y_i$를 생성하라.\n",
        "\n",
        "-   $y_i = 2+3x_i +\\epsilon_i,\\quad \\epsilon_i \\overset{iid}{\\sim} N(0,1)$\n",
        "\n",
        "$(x_i,y_i)$를 산점도를 이용하여 시각화하라.\n",
        "\n",
        "(풀이)"
      ],
      "id": "f3009f11-79c3-406e-bfe2-2be279c42472"
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {},
      "outputs": [],
      "source": [
        "y = 2+3*x + np.random.randn(50) "
      ],
      "id": "cc4d9ead-a7fc-4734-9f85-fb1dddb8698b"
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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          }
        }
      ],
      "source": [
        "plt.plot(x,y,'o',label=r'$(x_i,y_i)$')\n",
        "plt.legend()"
      ],
      "id": "26a8d9a3-6ee3-4618-aae6-152419e0733d"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "`2`. `1`과 같은 자료를 잘 표현할 수 있는 적절한 추세선\n",
        "$(x_i, \\hat{y}_i)$를 그리기 위하여 아래의 수식을 고려하자.\n",
        "\n",
        "-   $\\hat{y}_i = ax_i+b$\n",
        "\n",
        "a,b를 각각 아래의 표에 의하여 선택하였을 경우 추세선을 문제하단에 명시된\n",
        "요구사항에 맞추어 시각화하라.\n",
        "\n",
        "|       |  $a$  | $b$ |\n",
        "|:-----:|:-----:|:---:|\n",
        "| \\(a\\) |  $1$  | $0$ |\n",
        "| \\(b\\) | $2.5$ | $2$ |\n",
        "| \\(c\\) |  $3$  | $2$ |\n",
        "\n",
        "**요구사항**\n",
        "\n",
        "-   $(x_i,y_i)$를 산점도로 그리고 각 (a),(b),(c)에 대한\n",
        "    $(x_i,\\hat{y}_i)$를 lineplot으로 겹쳐그릴 것\n",
        "-   범례를 포함할 것"
      ],
      "id": "131e55ea-70e6-4665-b8f4-17f898661eaf"
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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LLiMiJ5uw8RMwR4S3fbJ2OnruKOuPrXeOYz5ZeRKrycpnN3xGsDmYezLuISQo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\nws9JoBZCCD/3/wEg2lmT6mirfAAAAABJRU5ErkJggg==\n"
          }
        }
      ],
      "source": [
        "plt.plot(x,y,'o',label=r'$(x_i,y_i)$')\n",
        "plt.plot(x,1*x+0,'--',label=r'(a) $(x_i,\\hat{y}_i)$')\n",
        "plt.plot(x,2.5*x+2,'--',label=r'(b) $(x_i,\\hat{y}_i)$')\n",
        "plt.plot(x,3*x+2,'--',label=r'(c) $(x_i,\\hat{y}_i)$')\n",
        "plt.legend()"
      ],
      "id": "47a01002-de75-434b-b2a5-681134588bf8"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "`3`. 아래를 각각 계산하라.\n",
        "\n",
        "`(a)` $\\frac{1}{n}\\sum_{i=1}^{n}(y_i-x_i)^2$\n",
        "\n",
        "`(b)` $\\frac{1}{n}\\sum_{i=1}^{n}(y_i-2-2.5x_i)^2$\n",
        "\n",
        "`(c)` $\\frac{1}{n}\\sum_{i=1}^{n}(y_i-2-3x_i)^2$\n",
        "\n",
        "가장 작은 값을 가지는 것은 무엇인가?\n",
        "\n",
        "(풀이)"
      ],
      "id": "55edf863-5f2a-497c-8a06-4383f44c9607"
    },
    {
      "cell_type": "code",
      "execution_count": 32,
      "metadata": {},
      "outputs": [],
      "source": [
        "np.mean((y-(1*x+0))**2), np.mean((y-(2.5*x+2))**2), np.mean((y-(3*x+2))**2)"
      ],
      "id": "258cd06f-aa42-4293-aaee-589d2acd81da"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "가장 작은 값을 가지는 것은 (c)이다.\n",
        "\n",
        "`4`. 3의 결과를 근거로 (a)-(c)중 가장 적절한 추세선을 판단하고 적절한\n",
        "순서대로 나열하라.\n",
        "\n",
        "`(풀이)`\n",
        "\n",
        "3-(a),(b),(c)는 각각\n",
        "\n",
        "-   $\\hat{y}_i=x_i$\n",
        "-   $\\hat{y}_i=2+2.5x_i$\n",
        "-   $\\hat{y}_i=2+3x_i$\n",
        "\n",
        "일 경우\n",
        "\n",
        "$${\\tt mse}({\\boldsymbol y}, \\hat{\\boldsymbol y}) = \\frac{1}{n}\\sum_{i=1}^{n}(y_i -\\hat{y}_i)^2$$\n",
        "\n",
        "를 계산한 것이라 해석할 수 있다. 그런데\n",
        "${\\tt mse}({\\boldsymbol y}, \\hat{\\boldsymbol y})$의 값은\n",
        "\n",
        "-   $y_1 \\approx \\hat{y}_1$\n",
        "-   $y_2 \\approx \\hat{y}_2$\n",
        "-   $\\dots$\n",
        "-   $y_n \\approx \\hat{y}_n$\n",
        "\n",
        "일수록 작은 값을 가진다. 그리고 위의 조건은 더 적절하게 추세선을\n",
        "그렸을때 만족된다. 요약하면\n",
        "\n",
        "-   적절한 추세선을 그림 $\\Rightarrow$ $y_i \\approx \\hat{y}_i$\n",
        "    $\\Rightarrow$ ${\\tt mse}({\\boldsymbol y}, \\hat{\\boldsymbol y})$ 값이\n",
        "    작아짐\n",
        "\n",
        "와 같은 관계가 있음을 파악할 수 있다. 따라서\n",
        "${\\tt mse}({\\boldsymbol y}, \\hat{\\boldsymbol y})$의 값이 작을수록 적절한\n",
        "추세선이라 생각할 수 있다.\n",
        "\n",
        "`5`. 아래와 같은 수식을 이용하여 $\\hat{\\beta}_0, \\hat{\\beta}_1$ 을\n",
        "계산하라.\n",
        "\n",
        "$$\\begin{bmatrix} \\hat{\\beta}_0 \\\\ \\hat{\\beta}_1 \\end{bmatrix} = ({\\bf X}^T {\\bf X})^{-1}{\\bf X}^T {\\boldsymbol y}, \\quad {\\bf X}=\\begin{bmatrix} 1 & x_1 \\\\ 1 & x_2 \\\\ \\dots \\\\ 1 & x_n \\end{bmatrix}$$\n",
        "\n",
        "`(풀이)`"
      ],
      "id": "106b038c-371a-42f2-ab67-aad89bdd2673"
    },
    {
      "cell_type": "code",
      "execution_count": 40,
      "metadata": {},
      "outputs": [],
      "source": [
        "X = np.stack([[1]*50 ,x],axis=1)\n",
        "np.linalg.inv(X.T @ X)@X.T@y "
      ],
      "id": "8909caef-073e-4227-842d-f4442e26ac18"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "$\\hat{\\beta}_0=1.97914281$ 이고 $\\hat{\\beta}_1= 2.90834079$ 이다.\n",
        "\n",
        "`6`. `5`에서 계산된 $\\hat{\\beta}_0, \\hat{\\beta}_1$을 각각\n",
        "$b=\\hat{\\beta}_0, a=\\hat{\\beta}_1$으로 생각하고 적절한 추세선\n",
        "$(x_i, \\hat{y}_i)$를 그려라. (단, $\\hat{y}_i=ax_i+b$ 이다)\n",
        "\n",
        "`(풀이)`"
      ],
      "id": "ca74f46d-5761-47e0-b495-63d838a627c7"
    },
    {
      "cell_type": "code",
      "execution_count": 43,
      "metadata": {},
      "outputs": [],
      "source": [
        "b, a = np.linalg.inv(X.T @ X)@X.T@y \n",
        "yhat = a*x +b "
      ],
      "id": "363dd1fc-c037-447c-b5c1-938b29c6e48b"
    },
    {
      "cell_type": "code",
      "execution_count": 47,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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zNGudiOS7YBJ1RwazqBtCRPJZEIlaI/1ERFoWRNWHRvqJiLSs1URtZnea2WYz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\nCPfNqquoKqUAAAAASUVORK5CYII=\n"
          }
        }
      ],
      "source": [
        "plt.plot(x,y,'o',label=r'$(x_i,y_i)$')\n",
        "plt.plot(x,yhat,'--',label=r'$(x_i,\\hat{y}_i)$')\n",
        "plt.legend()"
      ],
      "id": "35857d1c-1994-4f15-9abe-d0b12e037211"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "`7`. 4의 기준에 따르면, $(a,b)=(3,2)$ 일때 만들어지는 추세선과\n",
        "$(a,b)=(\\hat{\\beta}_1,\\hat{\\beta}_0)$ 일때 만들어지는 추세선은 어떤 것이\n",
        "더 적절한가?\n",
        "\n",
        "`(풀이)`"
      ],
      "id": "46b06f67-1db5-41e6-9e15-b62d1334d37d"
    },
    {
      "cell_type": "code",
      "execution_count": 51,
      "metadata": {},
      "outputs": [],
      "source": [
        "np.mean((y-(3*x+2))**2), np.mean((y-yhat)**2)"
      ],
      "id": "e4c90c43-3b82-4205-bee8-c45b4d7247ec"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# MNIST data\n",
        "\n",
        "아래는 0~9가지의 숫자이미지가 저장된 이미지데이터를 불러오는 코드이다."
      ],
      "id": "6c10974b-8666-4a0c-8595-a34946d63f5c"
    },
    {
      "cell_type": "code",
      "execution_count": 52,
      "metadata": {},
      "outputs": [],
      "source": [
        "# URL 설정\n",
        "url = 'https://github.com/guebin/PP2023/raw/main/posts/02_PY4DS/mnist.npz'\n",
        "\n",
        "# URL에서 파일 다운로드\n",
        "urllib.request.urlretrieve(url, './mnist.npz')\n",
        "\n",
        "# 데이터 로드\n",
        "data = np.load('./mnist.npz')\n",
        "xtrain, ytrain, xtest, ytest = data['x_train'], data['y_train'], data['x_test'], data['y_test']"
      ],
      "id": "f7d26003-a978-4cf0-91b2-e36087a2a38d"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "아래는 데이터에 대한 설명이다.\n",
        "\n",
        "-   전체의 이미지의 수는 70000개이며, 60000개의 이미지 ${\\tt xtrain}$에\n",
        "    10000개의 이미지는 ${\\tt xtest}$에 저장되어 있다.\n",
        "-   이미지에 대한 라벨은 각각 ${\\tt ytrain}$과 $\\tt ytest$에 저장되어\n",
        "    있다. 따라서 $\\tt ytrain$에는 60000개의 이미지에 해당하는 라벨이,\n",
        "    $\\tt ytest$에는 10000개의 이미지에 해당하는 라벨이 기록되어 있다.\n",
        "-   보통 분석에서는 60000개의 이미지를 가지고 라벨을 맞추는 “훈련”을\n",
        "    하고 (${\\tt xtrain}$을 이용하여 ${\\tt ytrain}$을 맞추는 방법을\n",
        "    학습하고), 그러한 훈련이 잘 되었는지 10000개의 이미지를 이용하여\n",
        "    “테스트”한다.\n",
        "-   위와 같은 의미로 $({\\tt xtrain}, {\\tt ytrain})$ 을 training data\n",
        "    set, $({\\tt xtest},{\\tt ytest})$ 를 test data set 이라고 부른다.\n",
        "    (ref:\n",
        "    [위키참고](https://en.wikipedia.org/wiki/Training,_validation,_and_test_data_sets))\n",
        "\n",
        "아래는 이미지자료와 시각화에 대한 설명이다.\n",
        "\n",
        "-   각 이미지는 (28,28) 픽셀의 흑백이미지이다. 따라서 각 이미지는\n",
        "    (28,28,3) 이 아니라 (28,28) 의 shape을 가진 텐서로 구성되어있다.\n",
        "-   흑백이미지를 시각화 하기 위해서는 `plt.imshow(img, cmap='gray')`를\n",
        "    이용한다. 여기에서 ${\\tt img}$은 임의의 2차원 텐서이며 이 예제의\n",
        "    경우 (28,28)의 shape을 가진다.\n",
        "\n",
        "아래는 ${\\tt xtrain}$의 두번째 이미지, 즉 ${\\tt xtrain[1,:,:]}$를\n",
        "확인하는 코드의 예시이다."
      ],
      "id": "0e3e1397-bcc6-41c2-b39a-6f60e359c54b"
    },
    {
      "cell_type": "code",
      "execution_count": 78,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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s4weSzpK0VdIbkn4v6cwO6u1Xakzt/bIaweqqqbfL1NhFf1nSjuxnft3vXaKvtrxvnC4L\nBMEBOiAIwg4EQdiBIAg7EARhB4Ig7EAQhB0I4u8I826N2+OQkQAAAABJRU5ErkJggg==\n"
          }
        }
      ],
      "source": [
        "# plt.imshow(xtrain[1,:,:],cmap='gray')\n",
        "plt.imshow(xtrain[1],cmap='gray') ## 같은코드임"
      ],
      "id": "5d1eb0c2-c7a5-4bbb-b860-408747fd7863"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "이 이미지에 대한 label은 ${\\tt ytrain[1]}$의 값으로 확인가능하다."
      ],
      "id": "8e4d6b7f-a140-4a91-8fb5-31faa93c7270"
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {},
      "outputs": [],
      "source": [
        "ytrain[1]"
      ],
      "id": "43f9b361-6543-499c-b060-260bd3819f26"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "이미지와 라벨을 한번에 표현하는 코드는 아래와 같이 작성가능하다."
      ],
      "id": "c087244e-a154-47d2-939e-1c163108ebb1"
    },
    {
      "cell_type": "code",
      "execution_count": 88,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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2Be6tUa3s7aRahY5ez/6FjUtrImJ8aQ0kdGtv3doXuLdGdao3H8abZcJhN8tE2WFfUPL2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\nh90sEw67WSYcdrNM/B+rgFPq3xIxpwAAAABJRU5ErkJggg==\n"
          }
        }
      ],
      "source": [
        "plt.imshow(xtrain[1],cmap='gray')\n",
        "plt.title('label={}'.format(ytrain[1]));"
      ],
      "id": "39c31132-a451-4c8b-b979-08628de4923f"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "아래는 10개의 이미지를 라벨과 함께 출력하는 코드의 예시이다."
      ],
      "id": "318146fc-4de9-49c8-9a68-6fe40b674974"
    },
    {
      "cell_type": "code",
      "execution_count": 95,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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2hZm9V+vxoD6Y2dlm9q6ZLTazj8zsD2a2Rq3HhWzj5w1KYWZrmdkbZja31mNp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\nSBSKYgAAAABJRU5ErkJggg==\n"
          }
        }
      ],
      "source": [
        "fig, ax = plt.subplots(2,5,figsize=(10,5))\n",
        "\n",
        "ax[0][0].imshow(xtrain[0],cmap='gray'); ax[0][0].set_title('label={}'.format(ytrain[0]));\n",
        "ax[0][1].imshow(xtrain[1],cmap='gray'); ax[0][1].set_title('label={}'.format(ytrain[1]));\n",
        "ax[0][2].imshow(xtrain[2],cmap='gray'); ax[0][2].set_title('label={}'.format(ytrain[2]));\n",
        "ax[0][3].imshow(xtrain[3],cmap='gray'); ax[0][3].set_title('label={}'.format(ytrain[3]));\n",
        "ax[0][4].imshow(xtrain[4],cmap='gray'); ax[0][4].set_title('label={}'.format(ytrain[4]));\n",
        "\n",
        "ax[1][0].imshow(xtrain[5],cmap='gray'); ax[1][0].set_title('label={}'.format(ytrain[5]));\n",
        "ax[1][1].imshow(xtrain[6],cmap='gray'); ax[1][1].set_title('label={}'.format(ytrain[6]));\n",
        "ax[1][2].imshow(xtrain[7],cmap='gray'); ax[1][2].set_title('label={}'.format(ytrain[7]));\n",
        "ax[1][3].imshow(xtrain[8],cmap='gray'); ax[1][3].set_title('label={}'.format(ytrain[8]));\n",
        "ax[1][4].imshow(xtrain[9],cmap='gray'); ax[1][4].set_title('label={}'.format(ytrain[9]));\n",
        "\n",
        "fig.tight_layout()\n"
      ],
      "id": "17405393-3dbc-4771-be5f-b54fdadf21f5"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "`(1)` 70000개의 이미지중 0~9에 해당하는 이미지는 각각 몇장씩 들어있는가?\n",
        "\n",
        "(풀이)"
      ],
      "id": "7c5b4328-293c-4d69-99b7-ea0bc3868b20"
    },
    {
      "cell_type": "code",
      "execution_count": 105,
      "metadata": {},
      "outputs": [],
      "source": [
        "_y = ytrain.tolist()+ytest.tolist()"
      ],
      "id": "827c7a10-385e-47ef-be4d-ca970969dcec"
    },
    {
      "cell_type": "code",
      "execution_count": 111,
      "metadata": {},
      "outputs": [],
      "source": [
        "{s:_y.count(s) for s in set(_y)}"
      ],
      "id": "b197d528-afca-4b5f-a2a6-29a36e4f6ed0"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "`(2)` ${\\tt xtrain}$에서 손글씨 0을 의미하는 이미지만을 모아서 새로운\n",
        "텐서 ${\\tt xtrain0}$를 만들어라. 이 텐서에서 처음과 마지막 이미지를\n",
        "출력하라.\n",
        "\n",
        "**hint:** ${\\tt xtrain0}$ 의 shape은 (5923,28,28)이어야 한다.\n",
        "\n",
        "(풀이)"
      ],
      "id": "7a3daba6-d641-4ca0-a056-b6d9a0f7ba76"
    },
    {
      "cell_type": "code",
      "execution_count": 117,
      "metadata": {},
      "outputs": [],
      "source": [
        "xtrain0 = xtrain[ytrain==0]\n",
        "xtrain0.shape"
      ],
      "id": "3743e66a-7f15-4506-bc5c-f89e0972a897"
    },
    {
      "cell_type": "code",
      "execution_count": 119,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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s4weSzpK0VdIbkn4v6cwO6u1Xakzt/bIaweqqqbfL1NhFf1nSjuxnft3vXaKvtrxvnC4L\nBMEBOiAIwg4EQdiBIAg7EARhB4Ig7EAQhB0I4u8I826N2+OQkQAAAABJRU5ErkJggg==\n"
          }
        }
      ],
      "source": [
        "plt.imshow(xtrain0[0],cmap='gray') # 처음이미지"
      ],
      "id": "b5d0fcdc-c46a-4210-b09d-e0602fe6abe9"
    },
    {
      "cell_type": "code",
      "execution_count": 120,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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ZpZLmqfWGot4k6c7s+Z2S/lRiL1/QKsN45w0zrpI/u9KHP3f3pv9IWqDKHvn/l/TLMnrI\n6etbkt7Kft4puzdJXaps1n2uyr6NeyT9m6Stkt6X9L+SJrVQb/+jytDePaoEq62k3marsoneI+nN\n7GdB2Z9doq+mfG6cLgsEwQ46IAjCDgRB2IEgCDsQBGEHgiDsQBCEHQjin2A2p0O+O2dFAAAAAElF\nTkSuQmCC\n"
          }
        }
      ],
      "source": [
        "plt.imshow(xtrain0[-1],cmap='gray') # 마지막이미지"
      ],
      "id": "4f0b72cf-9a5c-48d1-993a-22de33bda1b8"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "`(3)` ${\\tt xtrain}$에서 손글씨 0을 의미하는 이미지의 평균을 계산하라.\n",
        "즉 아래를 계산하라.\n",
        "\n",
        "-   ${\\tt xtrain0mean} = \\frac{1}{5923}\\sum_{i=1}^{5923} {\\tt xtrain0[i, :, :]}$\n",
        "\n",
        "계산결과를 출력하라.\n",
        "\n",
        "(풀이)"
      ],
      "id": "0188cf78-7631-4af0-848e-5f427deb05dc"
    },
    {
      "cell_type": "code",
      "execution_count": 131,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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          }
        }
      ],
      "source": [
        "plt.imshow(xtrain0.mean(axis=0),cmap='gray')"
      ],
      "id": "0713aaac-51a2-4018-9e8a-9d697eb65892"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "`(4)` ${\\tt xtrain}$에서 각 라벨에 대한 평균이미지를 계산하고 계산결과를\n",
        "${\\tt imgmean}$에 길이가 10인 `list`로 저장하라. 즉 ${\\tt imgmean}$은\n",
        "아래와 같은 자료구조를 가지고 있어야 한다.\n",
        "\n",
        "-   ${\\tt imgmean}=\\big[{\\tt imgmean[0]},\\dots, {\\tt imgmean[9]}\\big]$\n",
        "-   ${\\tt imgmean[0]}, \\dots, {\\tt imgmean[9]}$ 는 각각 (28,28)의\n",
        "    shape을 가진 numpy array\n",
        "-   ${\\tt imgmean[0]}, \\dots, {\\tt imgmean[9]}$ 는 각각 숫자 0,1, …, 9의\n",
        "    평균이미지를 의미\n",
        "\n",
        "${\\tt imgmean[0]},\\dots, {\\tt imgmean[9]}$를 시각화 하라.\n",
        "\n",
        "(풀이)"
      ],
      "id": "b200b920-7bb2-41ef-bfbc-59b302a861f5"
    },
    {
      "cell_type": "code",
      "execution_count": 133,
      "metadata": {},
      "outputs": [],
      "source": [
        "imgmean = [xtrain[ytrain==i].mean(axis=0) for i in range(10)] "
      ],
      "id": "d9503a9f-1eac-450e-84bf-e9709983eace"
    },
    {
      "cell_type": "code",
      "execution_count": 137,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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bU0pZF1ca6HtN0/xw4cuD2sYxs296sG/smz7sG/umK3smIuybzmahbya5QP55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\n+MuIuD8ivlJKuX9Sj38VT0bE5/G1xyL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          }
        }
      ],
      "source": [
        "fig, ax = plt.subplots(2,5,figsize=(10,5))\n",
        "\n",
        "ax[0][0].imshow(imgmean[0],cmap='gray')\n",
        "ax[0][1].imshow(imgmean[1],cmap='gray')\n",
        "ax[0][2].imshow(imgmean[2],cmap='gray')\n",
        "ax[0][3].imshow(imgmean[3],cmap='gray')\n",
        "ax[0][4].imshow(imgmean[4],cmap='gray')\n",
        "\n",
        "ax[1][0].imshow(imgmean[5],cmap='gray')\n",
        "ax[1][1].imshow(imgmean[6],cmap='gray')\n",
        "ax[1][2].imshow(imgmean[7],cmap='gray')\n",
        "ax[1][3].imshow(imgmean[8],cmap='gray')\n",
        "ax[1][4].imshow(imgmean[9],cmap='gray')\n",
        "\n",
        "fig.tight_layout()\n"
      ],
      "id": "9a4812f4-b5cb-4d5a-b73f-54ef5d261221"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "`(5)` ${\\tt xtrain}$의 두번째 이미지와 ${\\tt imgmean[0]}$의 차이를\n",
        "제곱한 값의 평균을 구하라. 즉 아래를 계산하라.\n",
        "\n",
        "-   $\\frac{1}{28\\times 28} \\sum_{p=0}^{27}\\sum_{q=0}^{27}\\big({\\tt xtrain[1,p,q]}-{\\tt imgmean[0][p,q]}\\big)^2$\n",
        "\n",
        "(풀이)"
      ],
      "id": "076471c5-5eb2-43a1-8295-c48c3cb17e5e"
    },
    {
      "cell_type": "code",
      "execution_count": 151,
      "metadata": {},
      "outputs": [],
      "source": [
        "np.mean((xtrain[1,:,:]- imgmean[0])**2)"
      ],
      "id": "33cd18e2-c6d8-43c0-adde-c9129818bab6"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "`(6)` 모든 $j=0,1,\\dots,9$ 에 대하여 아래를 계산하라.\n",
        "\n",
        "-   $\\frac{1}{28\\times 28} \\sum_{p=0}^{27}\\sum_{q=0}^{27}\\big({\\tt xtrain[1,p,q]}-{\\tt imgmean[j][p,q]}\\big)^2$\n",
        "\n",
        "계산값이 가장 작게 나오는 $j$는 얼마인가? 위의 계산결과를 토대로\n",
        "${\\tt xtrain}$의 두번째 이미지는 어떠한 숫자를 의미한다고 “분류”하는\n",
        "것이 타당한가?"
      ],
      "id": "1098fc66-2184-4f03-8c5c-76b79d3c0e16"
    },
    {
      "cell_type": "code",
      "execution_count": 152,
      "metadata": {},
      "outputs": [],
      "source": [
        "[np.mean((xtrain[1,:,:]- imgmean[i])**2) for i in range(10)]"
      ],
      "id": "11059ad0-e5c7-4ce6-85f6-c7236d932d9c"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "`(7)` 아래와 같은 numpy array 를 생성하라.\n",
        "\n",
        "$${\\tt loss}= \n",
        "\\begin{bmatrix} \n",
        "{\\tt loss[0,0]} & \\dots & {\\tt loss[0,9]} \\\\ \n",
        "{\\tt loss[1,0]} & \\dots & {\\tt loss[1,9]} \\\\ \n",
        "\\dots & \\dots &  \\dots \\\\ \n",
        "{\\tt loss[59999,0]}& \\dots &{\\tt loss[59999,9]} \\\\ \n",
        "\\end{bmatrix}$$\n",
        "\n",
        "단,\n",
        "${\\tt loss[i,j]} = \\frac{1}{28\\times 28} \\sum_{p=0}^{27}\\sum_{q=0}^{27}\\big({\\tt xtrain[i,p,q]}-{\\tt imgmean[j][p,q]}\\big)^2$\n",
        "\n",
        "위에서 생성한 ${\\tt loss}$를 이용해 (6)와 같은 방식으로 ${\\tt xtrain}$의\n",
        "모든 이미지에 대한 분류를 수행하라.\n",
        "\n",
        "**hint**: ${\\tt loss}$에서 “최소값을 가지는 원소의 인덱스를 출력”하는\n",
        "함수를 각 행별로 적용하면 된다.\n",
        "\n",
        "(풀이)"
      ],
      "id": "54faf91f-9ea6-4ea6-8c51-ca620b489fe9"
    },
    {
      "cell_type": "code",
      "execution_count": 169,
      "metadata": {},
      "outputs": [],
      "source": [
        "loss = np.array([[np.mean((xtrain[j,:,:]- imgmean[i])**2) for i in range(10)] for j in range(60000)])"
      ],
      "id": "b440cd25-443c-4e96-bd86-2ff0ce52497a"
    },
    {
      "cell_type": "code",
      "execution_count": 171,
      "metadata": {},
      "outputs": [],
      "source": [
        "loss.argmin(axis=1)"
      ],
      "id": "d46a617f-6c97-47c2-99c7-5b5a4c54a99c"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "`(8)` `(7)`에서 수행한 분류결과와 실제 라벨 ${\\tt ytrain}$을 비교하라.\n",
        "얼마나 많은 결과가 일치하는지 비율을 계산하라.\n",
        "\n",
        "(풀이)"
      ],
      "id": "539ff34d-a08b-4811-b961-bd77cf732aed"
    },
    {
      "cell_type": "code",
      "execution_count": 176,
      "metadata": {},
      "outputs": [],
      "source": [
        "np.sum(ytrain == loss.argmin(axis=1)) / 60000"
      ],
      "id": "351ef726-4c04-43de-ad7a-6436c55d935d"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "`(9)` ${\\tt xtrain}$에서 학습한 평균이미지 ${\\tt imgmean}$를 바탕으로\n",
        "${\\tt xtest}$의 이미지를 분류하라. 분류결과를 ${\\tt ytest}$와 비교하라.\n",
        "얼마나 많은 결과가 일치하는지 비율을 계산하라.\n",
        "\n",
        "(풀이)"
      ],
      "id": "2ee2d598-a52d-42ba-ad57-840bef048545"
    },
    {
      "cell_type": "code",
      "execution_count": 183,
      "metadata": {},
      "outputs": [],
      "source": [
        "est = np.array([[np.mean((xtest[j,:,:]- imgmean[i])**2) for i in range(10)] for j in range(10000)]).argmin(axis=1)"
      ],
      "id": "e58202b3-684b-44e5-9719-2a1792f530fb"
    },
    {
      "cell_type": "code",
      "execution_count": 186,
      "metadata": {},
      "outputs": [],
      "source": [
        "np.sum(est == ytest)/10000"
      ],
      "id": "251c6cb9-a733-44ae-bf89-6c6ce4b88920"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "`(10)` `(9)`의 과정에서 잘못분류된 이미지 10개를 선택하여 시각화 하라.\n",
        "\n",
        "-   실제 라벨과 잘못된 라벨을 구분하여 시각화 할 것"
      ],
      "id": "ee72d599-4a5b-42a0-9f04-acdde723d776"
    },
    {
      "cell_type": "code",
      "execution_count": 191,
      "metadata": {},
      "outputs": [],
      "source": [
        "_ytest = ytest[est != ytest]\n",
        "_xtest = xtest[est != ytest]\n",
        "_est = est[est != ytest]"
      ],
      "id": "c7158777-cf48-4ae1-85d9-63b06c9cc149"
    },
    {
      "cell_type": "code",
      "execution_count": 196,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
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Hjh3r8je/+c1SS6yHhuubeC105plnFrx9/Dtm/PjxFa+pHPFrY3z+2LXXXuvyBx98UJU6\n0o5YTJE0JP/1EEl3VqYctHD0DdKgb5AGfYM06BtIat42b7dImiFpWzObb2bHSfqFpAPMbK6k/fMZ\n+AJ9gzToG6RB3yAN+gaFFB2xCCH8YA1X7VfhWtCC0DdIg75BGvQN0qBvUEjZJ+nV06GHHuryqFGj\nXI73Id57771d/vDDD6tSFxpbvB9tjx7+JOZS57U23nhjl+OZ3/POO6/g/d966y2Xb7zxRpevuuoq\nl+fPn1/w8aZMmeLywIEDXe7Zs6fLGZhBbkinnXaay4cddljB28+ePdvlSy+91OVHH33U5Xiv0HLN\nnTvX5RNPPLGij4/6i/c9Hjx4cMHbH3XUUS7HM8axeE692OOjMuK97Hv37l3w9qNHj65mOWU79thj\n612CJD5qGgAAAHBYIAMAAAAJLJABAACAhIaeQS62p+IzzzzjcrHZTECSdt5554LXx7OaxcQzxvFs\nZwh+C83p06e7PGLECJdfeumlkp4/Vmr9aJ527dq5PHLkyJLuH+9bfMsttxS8/fvv+0/IvfLKK13e\nbz9/ntFee+1V8PGuv/56l5k9b3nifYxjpc4cl+rII4+s6uO3FgcffLDLxWa9X3/9dZfj8x3qbb31\n1nO5e/fudarE4wgyAAAAkMACGQAAAEhggQwAAAAkNPQM8hFHHFHw+gEDBrj8s5/9zOU77/SfIPns\ns89WpC40tnjf4lLFe1DGc32x+HPlTz/9dJc//fTTsuopZtasWQUzmmfVqlUu//Of/3Q53k87tnz5\ncpdXrFjh8m9+8xuXx44d6/Kmm27qcrEZ6JkzZ7p89dVXF7w9Ku/NN98seH2vXr3Kevy4J+JZ1Rkz\nZrjMTHA2rbvuui6ff/75Ba+Pff/733f5k08+qUxhFbLlllu63KdPn4K3nzBhQhWr+TeOIAMAAAAJ\nLJABAACABBbIAAAAQEJDzyB369bN5XgGsH379i5fcMEFLsf7015zzTUux58rv9lmm7n86quvulxs\nf9qvfvWrLsfzX+zTnA2dO3d22cxKuv+wYcNc7tKli8s333yzyyeddFJJj1+u+Pv77LPPXK72zHNL\n9fnnn7s8aNAglw866CCXV65c6XJ8DsQrr7xS8Pk6derkcnyORfz6t3TpUpeHDBni8pIlSwo+Hyrv\niiuucDnepzieMx83blxJj3/55ZcXvH7SpEklPV4xm2yyicvxjDUzzunE+wJ/4xvfKHj7yZMnu/zC\nCy9UvKZ6eu+992ryPBxBBgAAABJYIAMAAAAJLJABAACAhIaeQb7ssstcLvY587G11vL/Pjj55JML\n5kp79913Xf7b3/7m8tFHH13V50fTQggFczE9e/YseP/4+mqL93U+7rjjXL7jjjtqWU6r8cEHH7j8\nhz/8oaKPf/jhh7t82GGHFbz9H//4R5fnzJlT0XpQunhGNz4vpW/fvi6PGDHC5VJnkmMLFiwo6/5H\nHnmky3G9pf5ORk7//v1dvvjiiwvePj4f6tRTT3U5Pj8iPq+mY8eOJdUXn7fSrl27grdftmyZy6X+\nTo1nquM95quFI8gAAABAAgtkAAAAIIEFMgAAAJDQ0DPIo0aNcjmesYv3m23b1n+78efUxzPJ1Rbv\n43zEEUe4HO/TfNFFF1W9JpTvxBNPdHmvvfYqmM8++2yXx48f73K5ez7GM8Yff/yxy8X2SkU2rL/+\n+i6feeaZBW8fz7eecsopFa8JlRXvixzP9Mb7Ihe7fvDgwQWfL555LiaeOY7PA4p77vbbby/p8ZFz\nyCGHuLzLLrsUvH285/k555xT8PbxWij+nRWLZ5ZnzZrl8s4771zw/j/60Y9cvuuuu1z+7ne/W/D+\n8fkcpc4wp8URZAAAACCBBTIAAACQwAIZAAAASGjoGeR4b7+nnnrK5d69exe8/3777edyvJffhRde\n6PJuu+1WYoWlied8in3eOioj3ie43H2K45nheH5sypQpLo8ZM8blAQMGuHzQQQe5/NFHHxW8Pp5d\nj+fD4ln2J554Qsi+qVOnurzjjjsWvP3o0aNd/vTTTyteEyrrtttuc7lXr14ux/sgxzPGxWaOY/EM\nc5zj82KKPX58/3gmGc0T73FeTHw+VaXPN4hnfjt37uxy/HNesmSJyzfddJPLTz/9tMvx+Vixq6++\null1VhpHkAEAAIAEFsgAAABAAgtkAAAAIKGhZ5DL9cADDxS8vk+fPi7HM8grV650+Xe/+53L1157\nrcvDhw93+Yc//GEzqkS1vfXWWy7PnTvX5c0339zl73znOy7/9re/dTneZ3jhwoUux30UzxC//PLL\nLnfp0sXleN/i4447ruDzxzPH8cwzsmmrrbZy+Wtf+1rB2999990uT5w4sdIlocbGjRvncryvcPw7\n5Ywzzijp8ePPDigm3jf5qKOOcpmZ48qIzx/49a9/XfD2b7zxhstvv/22y0uXLi14/+nTp7scn88V\n+7//+z+XO3To4PLixYtd3meffVweNmyYy/H5Vs8995zL8e/kWuEIMgAAAJDAAhkAAABIKLpANrNN\nzexBM/u7mb1kZqfnL1/fzO4zs7n5v7tWv1w0CvoGadA3KBU9gzToGxRjxT7T2sx6SuoZQphlZp0l\nPS3pUEn/Jen9EMIvzGyUpK4hhJFFHqs2H6BdIfH+tU8++WRJ93/wwQdd7tevn8vxvsexq666yuV4\nbqfWQgiFC05o5L7ZZJNNXI5nO+P9Zx9//HGXx44d63I8gxwbNGiQy/GM8x577OFy3DezZ892+dxz\nz3V58uTJBZ+/2lpL35Qr3vP20UcfdTmehY/nPffee2+X47nERtPcvmnNPVNM3APxfrmx+LVr5syZ\nLsf7NGfQ0yGEXZtzwyz3Tdu2/vSw+Hyo2KJFi1x+//33XY7PS6m3eKY63rf5mmuucfnkk0+udklN\n9k3RI8ghhIUhhFn5rz+S9LKkXpIOkXRD/mY3KNdYgCT6BunQNygVPYM06BsUU9IuFma2haSdJc2U\n1COEsPrQ2CJJPdZwn6GShpZRIxocfYM06BuUip5BGvQNmtLsk/TMrJOkP0kaHkJwnyMYcnMaTb7F\nEEIYH0LYtblve6BloW+QBn2DUtEzSIO+wZo06wiymbVTroFuCiHckb/4bTPrGUJYmJ/leadaRdZL\nvB9tPH915JFHFrz/vvvuW/D6zz//3OV41nXUqFHFSsy0Ru2b+fPnuzxgwACX49nyvn37ujxp0qSC\njx/PEBc7DyAW77c9cqQfj3vvvfdKerysadS+KVd8zkM8cxz3zfXXX+9yo88cl6O19kwx8WtRsX2S\n4xnlOMc99sQTT5RRXf1ltW/iz1goti9xo4n3eb7iiitcLnbeTq00ZxcLkzRB0sshhOQE/xRJQ/Jf\nD5F0Z+XLQ6Oib5AGfYNS0TNIg75BMc05gryXpGMkvWBmz+YvO0fSLyTdZmbHSZonqfDhVLQ29A3S\noG9QKnoGadA3KKjoAjmE8KikNW23s19ly0FLQd8gDfoGpaJnkAZ9g2JK2sWitVm+fLnL8efed+rU\nyeVdd/Wz+t27d3f59ddfd/nGG290+cILLyy9SFRdPA+15557unzUUUe5vPXWW7t8wgknuHzddde5\nXGwGecKECS6/8sorBW+PxrD77ru7fMMNN6zhljkrVqxwOT5nAYideeaZBa8fPHhwwetnzJjh8oIF\nC8quCXj33XcL5qzgo6YBAACABBbIAAAAQAILZAAAACDBSt2Dtawna2Gfcx875phjXI5nVX/+85+7\n/M47jbUtZwhhTSc0VFVL75uWjr7J6dixo8u33367y/379y94/7ffftvleJ/1ljabXo++yVrPoGRP\n1+ODO+ibhtdk33AEGQAAAEhggQwAAAAksEAGAAAAEphBRrMxS4o06JucESNGuHz55ZcXvP2iRYtc\nHjhwoMvPPvtsRerKKmaQkQIzyEiDGWQAAACgGBbIAAAAQAILZAAAACChbb0LAIDW4PPPP3f5ww8/\ndHncuHEuX3vttS4vXLiwOoUBAL6EI8gAAABAAgtkAAAAIIEFMgAAAJDAPshoNvazRRr0DdJgH2Sk\nwD7ISIN9kAEAAIBiWCADAAAACSyQAQAAgAQWyAAAAEACC2QAAAAggQUyAAAAkMACGQAAAEhoW+Pn\nWyxpnqQN819nVZbrq1dtm9fhOVdrhL7Jcm1S6+2bZeLnUo7W1jeN8FojUd+a0DeFUV/Tmuybmn5Q\nyBdPavZUPTbzbq4s15fl2qoty997lmuTsl9ftWT9+6a+bMr690192ZT175v6SsOIBQAAAJDAAhkA\nAABIqNcCeXydnre5slxflmurtix/71muTcp+fdWS9e+b+rIp69839WVT1r9v6itBXWaQAQAAgKxi\nxAIAAABIYIEMAAAAJNR0gWxmA8xstpm9amajavnca6jnejN7x8xeTFy2vpndZ2Zz8393rWN9m5rZ\ng2b2dzN7ycxOz1qNtUDflFwffSP6JkV99I3omxJro2fy6JuSamuIvqnZAtnM2kj6jaQDJe0g6Qdm\ntkOtnn8NJkoaEF02StIDIYRtJD2Qz/WyUtKZIYQdJO0p6ZT8f7Ms1VhV9E0q9A19kwZ9Q9+UqtX3\njETfpNAYfRNCqMkfSX0l/SWRz5Z0dq2ev0BdW0h6MZFnS+qZ/7qnpNn1rjFR252SDshyjfRN9n4m\n9A19Q9/QN/QMfZPVn0tW+6aWIxa9JL2ZyPPzl2VNjxDCwvzXiyT1qGcxq5nZFpJ2ljRTGa2xSuib\nMtA3X6BvSkDffIG+aaZW3DMSfZNalvuGk/QKCLl/xtR9Hzwz6yTpT5KGhxCWJK/LSo34t6z8TOib\nxpKVnwl901iy8DOhZxpPFn4uWe+bWi6QF0jaNJE3yV+WNW+bWU9Jyv/9Tj2LMbN2yjXQTSGEO/IX\nZ6rGKqNvUqBv6Js06Bv6plT0jCT6pmSN0De1XCA/KWkbM9vSzNaWdLSkKTV8/uaaImlI/ushys3G\n1IWZmaQJkl4OIYxNXJWZGmuAvikRfSOJvikZfSOJvikJPfMF+qYEDdM3NR7EHihpjqR/SDq3nsPX\n+XpukbRQ0mfKzQwdJ2kD5c6enCvpfknr17G+byn3FsPzkp7N/xmYpRrpG/omq3/oG/qGvqFn6Bv6\nJu0fPmoaAAAASOAkPQAAACCBBTIAAACQwAIZAAAASGCBDAAAACSwQAYAAAASWCADAAAACSyQAQAA\ngAQWyAAAAEACC2QAAAAggQUyAAAAkMACGQAAAEhggQwAAAAksEAGAAAAElggAwAAAAkskAEAAIAE\nFsgAAABAAgtkAAAAIIEFMgAAAJDAAhkAAABIYIEMAAAAJLBABgAAABJYIAMAAAAJLJABAACABBbI\nAAAAQAILZAAAACCBBTIAAACQwAIZAAAASGCBDAAAACSwQAYAAAASWCADAAAACSyQAQAAgAQWyAAA\nAEACC+RmMrP2ZjbBzOaZ2Udm9qyZHRjd5mwzu8TMdjCzp8zsX/k/95vZDvWqHfVTYt+sbWa3m9nr\nZhbMrF99qka9mdmp+deQFWY2sYnrV/fMFvleWZr4c34dSkZGmNnRZvaymS0zs3+Y2d6J61b3zZ5m\ndp+ZvW9m75rZJDPrWc+6UT9mtr6ZTc73zDwz+2F0/W/NbKiZ9TOzVdHrzZB61V1tLJCbr62kNyV9\nW9J6ks6TdJuZbZG4zSBJ0yS9JekISetL2lDSFEm31rJYZEYpfSNJj0r6T0mLalgjsuctSRdJun4N\n1yd7RpK6hBA65f+MqXp1yCQzO0DSpZL+W1JnSftI+mfiJqv7pquk8ZK2kLS5pI8k/a6WtSJTfiPp\nU0k9JP1I0tVm9tXE9Qfq3683byVeazqFEG6oca0107beBTSKEMIySRcmLrrLzF6T9A1Jr5tZV0m9\nJc0IIXwu6QNJMjOT9LmkrWtaMDIhRd9cIUlm9nmNS0WGhBDukCQz21XSJsnrkj0jadPaV4cM+7mk\n0SGEJ/J5weormnitUeK6KyU9VLMqkRlm1lHS4ZJ2DCEslfSomU2RdIykUWb2dUkfhBDmm1mrWsdw\nBDklM+uh3IvNS/mL+kt6IPnCY2YfSPpE0q8lXVLrGpE9zekboIimemaemc03s9+Z2Yb1Kgz1Y2Zt\nJO0qqZuZvZrvhyvNbJ38TQq91uyjf78moXXpLWllCGFO4rLnJK0+gjxQ0t2J67qb2dtm9pqZjcsv\nsFskFsgpmFk7STdJuiGE8Er+4vgtT4UQuij3tvqpkp6pZY3Inub2DVBEsmcWS9pNubfJv6Hc2+o3\n1aku1FcPSe2UG+/bW1IfSTsrN9YlreG1Jn+E8AJJP61JlciaTpKWRJd9qNxrieT75hXl+qqnpO8o\n95oztvol1gcL5BKZ2VqSblRuXufUxGUHSLo3vn3+LfZrJP3ezLrXsFRkSKl9AzQl7pkQwtIQwlMh\nhJUhhLeV663vmlnnQo+DFml5/u9fhxAWhhAWK7d4Gbim15r8W+b3SDo9hPBITatFViyVtG502bqS\nPjKzLpK2k/S4JIUQFoUQ/h5CWBVCeE3S/1NuPKNFYoFcgvw88QTl/qV+eAjhs/xVu0maF0J4dw13\nXUtSB0m9ql8lsqaMvgFixXom5P/mtb2VCSH8S9J8/bsHlPj6S31jZptLul/SmBDCjTUrFFkzR1Jb\nM9smcdlOyo3c9Jc0vcAIYFALfq1psd9YlVwtaXtJ3wshLE9c7mZ0zOwAM9vZzNqY2brK/Sv+X5Je\nrmm1yIpm9Y30xbZw/5GPa5vZf+QX2GhFzKxtvg/aSGqT74O2+vJrzR5mtq2ZrWVmG0j6laS/hRA+\nrE/lqLPfSRpmZt3zJ+WNkHSXvtw3vSRNl3RlCOGaulSKTMi/y32HpNFm1tHM9pJ0iHLveMZ9s6+Z\nbW45m0r6haQ761F3LbBAbqb8v7ZPVG7+ZlFiD8AfqYktlyTdotwczz8kfUXSgBDCJzUtGnVXYt9I\n0mzl3irtJekv+a83r13FyIjzlPvZj1Ju27/l+cvintlKubfNP5L0oqQVkn5Q00qRJWMkPancUcGX\nlTv35WJ9uW+OV653LkzuaVvrYpEZJ0taR9I7yq1dTpL0d+WOICfHcnZWbtxiWf7vFySdVtNKa8hC\nCMVvhTXK70rwjKRegf+YaCb6BqWiZ5AGfYM0zGx35d5h2L3etdQLR5DLt56kM3nhQYnoG5SKnkEa\n9A3S+lm9C6gnjiADAAAACRxBBgAAABLKWiCb2QAzm53/1J5RlSoKLRt9gzToG6RB3yAN+gapRyzy\nH2s5R7nNx+crd+bsD0IIfy9wH+Y5GlgIoeztxuib1oe+QRr16Bt6puEtDiF0K/dB6JtWp8m+KecI\n8u6SXg0h/DOE8KmkW5XbOw8ohL5BGvQN0qBvWpd5FXoc+qZ1abJvylkg95L0ZiLPVxOfFGdmQ83s\nKTN7qoznQstB3yAN+gZpFO0begZNoG+gttV+ghDCeEnjJd6GQPPRN0iDvkGp6BmkQd+0fOUcQV4g\nadNE3iR/GVAIfYM06BukQd8gDfoGZS2Qn5S0jZltaWZrSzpa0pTKlIUWjL5BGvQN0qBvkAZ9g/Qj\nFiGElWZ2qqS/SGoj6foQwksVqwwtEn2DNOgbpEHfIA36BlKNP0mPOZ3GVoltl9KgbxobfYM06tE3\n9EzDezqEsGutn5S+aXhN9g2fpAcAAAAksEAGAAAAElggAwAAAAkskAEAAICEqn9QCAAAKF2XLl1c\nnj59ussdO3Z0edttt612SUCrwRFkAAAAIIEFMgAAAJDAAhkAAABIYAa5DLvssovLo0aNcvmII45w\nee+993b5scceq05haCjbbbedy/vss0/B248fP76a5aBGrr76apeHDh3q8m233ebyscce6/Ly5cur\nUxjqpmvXri7ff//9Lu+0004uz507t+o1Aa0VR5ABAACABBbIAAAAQAILZAAAACCBGeQCtt56a5ev\nvfZal3fffXeX11lnnYKPd9ZZZ7nMDDIkafvtt3d5+PDhLsd7m8az7Mccc0xV6kJl9ezZ0+X+/fu7\nHEJwefDgwS7Hs+cPPvhgBatDPRSbOe7Tp4/Lq1atcnnq1KlVqQstW4cOHVzeYIMNXF64cKHLxx9/\nvMvnn3++yxtttJHLF110kcuXXnqpyx9//HHzi60jjiADAAAACSyQAQAAgAQWyAAAAEBCq55BbtOm\njcv77befy7fffrvLnTp1cvm9995zeenSpS5369bN5fbt26eqEy3b5MmTXZ41a5bLM2fOdPlb3/qW\nyxtuuKHLixcvrmB1qJR4rm/RokUub7bZZgXvf84557j81FNPufzRRx+VUR3qYeTIkS7HM8exeA79\npz/9aaVLQiswaNAgl2+55RaX77nnHpcPPPDAgo8Xnz9x3nnnufzJJ5+4fOWVV7qc1dcujiADAAAA\nCSyQAQAAgAQWyAAAAEBCq5pB7tGjh8s33HCDy9/97nddXrZsmcsnnHCCy/fee6/Lhx9+uMtXXHFF\nmjLRys2bN8/lN9980+XtttvOZWaQG9Pjjz/ucryvemzfffd1+aCDDnI5niNE9sT/rw4YMKDg7T/8\n8EOXf/WrX1W8JrQ+vXv3Lnj9wIEDXY5njK+++mqXb7rpJpfjz3gYM2aMy927d3d5xIgRBeupF44g\nAwAAAAkskAEAAIAEFsgAAABAQoueQY7nvaZNm+byDjvs4PJxxx3n8l/+8heX33rrrbLqee2118q6\nP1qHeMY4zvG+ya+88krVa0Ll/fWvf3X51FNPdblt28Ivz7vttpvLzCBn3wMPPODyjjvuWPD28c90\n9uzZFa8JLd83vvENl88999yS7n/yySe7PHHiRJc//fRTl6+77jqX47VVz549S3r+euEIMgAAAJDA\nAhkAAABIYIEMAAAAJLSqGeRrr73W5dtvv93lau8f+8tf/rKqj4+WYYsttnC5Q4cOLl9yySU1rAbV\nEs8gz5w50+W99tqr4P2POuool3/729+6zLxq9nzta19zOd5fdunSpS6PGzeu6jWh5Rs5cqTL7du3\nL3j7tdbyx07ff/99l+OZ49hZZ53lcrzH++DBg12eOnWqy/G+yvXCEWQAAAAggQUyAAAAkFB0gWxm\n15vZO2b2YuKy9c3sPjObm/+7a3XLRKOhb5AGfYM06BukQd+gEItnoL50A7N9JC2V9PsQwo75y/5X\n0vshhF+Y2ShJXUMIIws9Tv5+hZ+swZ122mkun3feeS7Hnz/eaEII1tzb0jfNF+9z/NBDD7n8zjvv\nuBzPMWYdfdM8BxxwgMv33HNPSfd/+eWXXW60PonVo2+q3TPx79tVq1a5HM96duvWrZrlfEnv3r1d\n7tSpU0Uf/4UXXnD5s88+q+jjS3o6hLBrc2/cKH1Trj/+8Y8uH3744QVvH/9cBg4c6PKDDz5Y0eef\nO3euy9tvv31Jj18BTfZN0SPIIYSHJb0fXXyIpBvyX98g6dByq0PLQt8gDfoGadA3SIO+QSFpd7Ho\nEUJYmP96kaQea7qhmQ2VNDTl86BloW+QBn2DNJrVN/QMIvQNJFVgm7cQQij09kIIYbyk8VL234ZA\n7dA3SIO+QRqF+oaewZrQN61b2gXy22bWM4Sw0Mx6Snqn6D1aoHi/2p/85CcuT5o0qYbVNAT6RlLH\njh1dvvjii11evny5y/vuu2/Va8q4VtE3jz32mMv/+te/XO7atfC5Quutt57L6667rstLliwpo7qG\nlLm+KXbOT7Xtv//+Lp9++uku9+3b1+ViPVeq6dOnu/zII4+4PHHiRJffeOONij5/M2Wub2pt2LBh\nLpc6cxy79dZbXY5nkLfZZpuyHr9a0m7zNkXSkPzXQyTdWZly0MLRN0iDvkEa9A3SoG8gqXnbvN0i\naYakbc1svpkdJ+kXkg4ws7mS9s9n4Av0DdKgb5AGfYM06BsUUnTEIoTwgzVctV+Fa0ELQt8gDfoG\nadA3SIO+QSFln6TXmg0d6k9gjWf8zj333FqWgwYxatQolw855BCXb775ZpcXL15c9ZpQfx9//LHL\nY8eOdXnMmDEF79+rVy+Xv/3tb7s8derUMqpDI+rcubPLo0ePdnmPPfYoeP9nnnnG5Y8++sjlF198\n0eX33nvP5T59+rjcv39/l7/zne+4/F//9V8uxzPJcf1o2sYbb+xyvI9xMdddd10ly9HChQuL3yiD\n+KhpAAAAIIEFMgAAAJDAAhkAAABIsFruy9jom2lvuOGGLsefKx9/3vjw4cOrXVJNhRCsHs/b6H3T\nrVs3l99++22XH374YZf79etX7ZJqir5JZ+2113b5gQcecDnes9bM/2d+6qmnXI7nEON50aypR99U\nu2dWrVrlcvz7d9y4cS6fddZZZT3fFVdc4XK8v20s3ru/2Hk2pTr11FNdPuWUU1zu3bt3wfu3adOm\n2FM8HULYNUVpZcnaa812223n8ksvvVTS/Zvx37kke+65p8vxnu/Vfv5maLJvOIIMAAAAJLBABgAA\nABJYIAMAAAAJ7INcggsuuMDlTp06uXzvvffWshxkVDxzPG3aNJffffddl88444yq14TG8+mnn7q8\nYsUKl+OZ47XW8sc7dt3Vj9T17NnT5azPILdG+++/f0Ufb7PNNivp9ldeeaXL5c4cF3v8tm39EuTy\nyy+v6PO1VieccILLtTzXrDmyVs+acAQZAAAASGCBDAAAACSwQAYAAAASmEEuoEuXLi7Hn1sf7zHJ\nDDIk6bTTTnN5l112cfmkk05yedasWS5vvvnmLsf7bxezzz77uBzPe8Wzq9tuu63L8Yz0//zP/7j8\n8ccfl1QPKuONN95wOf65Fttj93vf+57LL774YgWrQyX06tWr3iVkyuzZs+tdQkM6+uijC14/f/58\nl5944olqltOwOIIMAAAAJLBABgAAABJYIAMAAAAJzCAX8Otf/9rleB/R6667rpblfEnHjh1djmdf\njzjiCJePPfZYl5977rnqFNbKHHbYYS6fc845LsezoGeffbbL8Z6V8d6lG2ywgcvxDHGxGeNyr3/l\nlVdcvummm4Ta+/Of/+zyj3/845Lu379/f5d/+ctfurxy5cpUdaFy1l57bZe33nprl1999dWqPv+J\nJ57o8qOPPlrV5yvm5z//eV2fv1FttNFGLsev8fHMcbGZ5daKI8gAAABAAgtkAAAAIIEFMgAAAJDA\nDHLCIYcc4vJ//ud/uhzPQ82bN6+q9ay33nouH3DAAS5fdNFFLm+11VYuX3XVVS7/4x//qGB1LVc8\n273ddtu5HM8YH3rooS7HM7yxeJ/jeF/h888/v+D9x48fX/D6ct14440uDx8+3GVmkOtj2rRpLr/8\n8ssu77DDDgXv/61vfcvl+Od62WWXpS8OzRLvgR6/Rnfq1MnleAZ42LBhLk+aNKng851yyikuP/PM\nMy7/5Cc/cTl+Lbv77rtdjufW//a3vxV8/mK+9rWvFbw+Pu8HzVPsd1Ct9evXz+W4voceeqiG1TQf\nR5ABAACABBbIAAAAQAILZAAAACDB4v3xqvpkZrV7smZo3769y/HegBtuuKHL++67r8vl7kkZP/5Z\nZ53l8tChQ13u0qWLywsWLHA5npmu9FxPCKEug03V7ptzzz3X5R/+8Icub7vttnE9Lsf/D8Vzg5Mn\nT3b5kUcecTneZzieSa63eAY7rreYlto39Xb66ae7PHbsWJeLvbbHfRrPCdZbPfqm2j3Ttq0/7efJ\nJ590+etf/3rB+7/wwgsu9+nTp6x6RowY4XL8OyjeTzd+bTr++ONd/uMf/1jw+eI5+ZkzZ7rcoUMH\nl+O9/OPX0iY8HULYtdiNKi1rrzWff/65y/FrwX//93+7HJ93UmlxXxx++OEux+dXPfjgg1WtpwlN\n9g1HkAEAAIAEFsgAAABAAgtkAAAAIKFV74N84YUXurzTTju5vN9++7lc6szxrrv6kZb//d//dbnY\nzN+MGTNc/vOf/+xyvCclmudPf/qTy/Hen2ut5f/duGrVKpfffPNNlwcMGOByqTO6WdfSvp+WYvbs\n2WXdP553jffnrvY+763RypUrXR44cKDL8+fPL3j/eIY33kc5nkMv9jtr3LhxLsfnRwwZMsTleK/9\n66+/3uV4tvXOO+90Od5DPp45PvbYY12Of+ehMubOnVvVx49/rptssknB21e7nrQ4ggwAAAAkFF0g\nm9mmZvagmf3dzF4ys9Pzl69vZveZ2dz8312rXy4aBX2DNOgblIqeQRr0DYppzhHklZLODCHsIGlP\nSaeY2Q6SRkl6IISwjaQH8hlYjb5BGvQNSkXPIA36BgWVvA+ymd0p6cr8n34hhIVm1lPS30II2xa5\nb133CuzWrZvLzz//vMvx59TH82FbbLGFy/HeffHefvG+yfEekvE+pPFs7B/+8AeX4/m1WitnX9Is\n9U2xPSLjfY4vvvhil3/1q1+5vHjx4gpW1/K0lL7Jungf9/gciGKuuOIKl+M9cWstbd80Us/ErzVH\nHXWUyyNHjnS52D7Jy5YtczmeI58wYUKpJTprr722y7vvvrvLhx12WMH7x79zBw0a5PLChQtdTvE5\nDan3QW6kvimm2O+4iRMnuhzvZ12uqVOnunzggQe6fPfdd7v8/e9/3+W4/hoofx9kM9tC0s6SZkrq\nEUJY3c2LJPUot0K0TPQN0qBvUCp6BmnQN2hKs3exMLNOkv4kaXgIYUnyX74hhLCmf0GZ2VBJQ5u6\nDi0ffYM06BuUip5BGvQN1qRZR5DNrJ1yDXRTCOGO/MVv599+UP7vd5q6bwhhfAhh13p8/CPqi75B\nGvQNSkXPIA36BoUUPYJsuX9OTZD0cgghucniFElDJP0i//edTdw9U0455RSXe/Tw75zEM8DxPsk/\n+clPXO7evbvL8dzM9OnTXR49erTLjz32WOGCG1iW++akk04qeP3DDz/sMvsA106W+ybr4rm+UmeQ\n+/btW8lyaqaReyaeDb311ltd/uSTT1zeY489XI5neL/61a+6HO+bfPnll6eqc03i18Z4r/9nn33W\n5Xhf4xUrVlS0nlI0ct8UM23aNJfj86nitUuXLl1c/uCDD1zeYIMNXI5n4S+44AKXv/3tb7v8wgsv\nuByvpeowc9wszRmx2EvSMZJeMLNn85edo1zz3GZmx0maJ+nIqlSIRkXfIA36BqWiZ5AGfYOCii6Q\nQwiPSlrT2cT7reFytHL0DdKgb1AqegZp0Dcohk/SAwAAABJK3ge5rCer8V6Bbdv6A+SzZ892ecst\ntyzr8eNZ1UsuucTlv/71r2U9ftaUs59tObK2xyRKQ9/UxlZbbeXynDlzSrr/qFH+8xAuu+yysmsq\nRz36ptF6Jv4dF59XM3RodTdZuOaaa1yO9zGug9T7IJcja30Tzxi/+OKLLq+//vouz5071+V4v+o9\n99zT5V69ehV8/pdeesnleFZ+/vz5Be9fB+XvgwwAAAC0dCyQAQAAgAQWyAAAAEBCi55BjveMnDFj\nRsHbx/sWx/siv/baay4/8sgjLi9btqzUEhsKs6RIg76pjXbt2rkc7/d97rnnutyhQweX471LZ82a\nVcHqSscMMlJgBrkJY8aMcfnss88uePvkpwlKX96vOxaf77Dffn4TkAzMphfDDDIAAABQDAtkAAAA\nIIEFMgAAAJDQomeQUVnMkiIN+gZpMIOMFJhBbkL79u1d/uY3v+ny5MmTXe7cubPLd911l8vTpk1z\n+dZbb3X5ww8/TFVnHTGDDAAAABTDAhkAAABIYIEMAAAAJDCDjGZjlhRp0DdIgxlkpMAMMtJgBhkA\nAAAohgUyAAAAkMACGQAAAEhggQwAAAAksEAGAAAAElggAwAAAAkskAEAAIAEFsgAAABAAgtkAAAA\nIIEFMgAAAJDAAhkAAABIaFvj51ssaZ6kDfNfZ1WW66tXbZvX4TlXa4S+yXJtUuvtm2Xi51KO1tY3\njfBaI1HfmtA3hVFf05rsGwsh1LoQmdlTIYRda/7EzZTl+rJcW7Vl+XvPcm1S9uurlqx/39SXTVn/\nvqkvm7L+fVNfaRixAAAAABJYIAMAAAAJ9Vogj6/T8zZXluvLcm3VluXvPcu1Sdmvr1qy/n1TXzZl\n/fumvmzK+vdNfSWoywwyAAAAkFWMWAAAAAAJNV0gm9kAM5ttZq+a2ahaPvca6rnezN4xsxcTl61v\nZveZ2dz8313rWN+mZvagmf3dzF4ys9OzVmMt0Dcl10ffiL5JUR99I/qmxNromTz6pqTaGqJvarZA\nNrM2kn4j6UBJO0j6gZntUKvnX4OJkgZEl42S9EAIYRtJD+RzvayUdGYIYQdJe0o6Jf/fLEs1VhV9\nkwp9Q9+kQd/QN6Vq9T0j0TcpNEbfhBBq8kdSX0l/SeSzJZ1dq+cvUNcWkl5M5NmSeua/7ilpdr1r\nTNR2p6QDslwjfZO9nwl9Q9/QN/QNPUPfZPXnktW+qeWIRS9Jbyby/PxlWdMjhLAw//UiST3qWcxq\nZraFpJ0lzVRGa6wS+qYM9M0X6JsS0DdfoG+aqRX3jETfpJblvuEkvQJC7p8xdd/mw8w6SfqTpOEh\nhCXJ67JSI/4tKz8T+qaxZOVnQt80liz8TOiZxpOFn0vW+6aWC+QFkjZN5E3yl2XN22bWU5Lyf79T\nz2LMrJ1yDXRTCOGO/MWZqrHK6JsU6Bv6Jg36hr4pFT0jib4pWSP0TS0XyE9K2sbMtjSztSUdLWlK\nDZ+/uaZIGpL/eohyszF1YWYmaYKkl0MIYxNXZabGGqBvSkTfSKJvSkbfSKJvSkLPfIG+KUHD9E2N\nB7EHSpoj6R+Szq3n8HW+nlskLZT0mXIzQ8dJ2kC5syfnSrpf0vp1rO9byr3F8LykZ/N/BmapRvqG\nvsnqH/qGvqFv6Bn6hr5J+4dP0gMAAAASOEkPAAAASGCBDAAAACSwQAYAAAASWCADAAAACSyQAQAA\ngAQWyAAAAEACC2QAAAAggQUyAAAAkPD/AV4Y/sVlo+RvAAAAAElFTkSuQmCC\n"
          }
        }
      ],
      "source": [
        "fig, ax = plt.subplots(2,5,figsize=(10,5))\n",
        "\n",
        "ax[0][0].imshow(_xtest[0],cmap='gray'); ax[0][0].set_title('{}/{}'.format(_ytest[0],_est[0]));\n",
        "ax[0][1].imshow(_xtest[1],cmap='gray'); ax[0][1].set_title('{}/{}'.format(_ytest[1],_est[1]));\n",
        "ax[0][2].imshow(_xtest[2],cmap='gray'); ax[0][2].set_title('{}/{}'.format(_ytest[2],_est[2]));\n",
        "ax[0][3].imshow(_xtest[3],cmap='gray'); ax[0][3].set_title('{}/{}'.format(_ytest[3],_est[3]));\n",
        "ax[0][4].imshow(_xtest[4],cmap='gray'); ax[0][4].set_title('{}/{}'.format(_ytest[4],_est[4]));\n",
        "\n",
        "ax[1][0].imshow(_xtest[5],cmap='gray'); ax[1][0].set_title('{}/{}'.format(_ytest[5],_est[5]));\n",
        "ax[1][1].imshow(_xtest[6],cmap='gray'); ax[1][1].set_title('{}/{}'.format(_ytest[6],_est[6]));\n",
        "ax[1][2].imshow(_xtest[7],cmap='gray'); ax[1][2].set_title('{}/{}'.format(_ytest[7],_est[7]));\n",
        "ax[1][3].imshow(_xtest[8],cmap='gray'); ax[1][3].set_title('{}/{}'.format(_ytest[8],_est[8]));\n",
        "ax[1][4].imshow(_xtest[9],cmap='gray'); ax[1][4].set_title('{}/{}'.format(_ytest[9],_est[9]));\n",
        "\n",
        "fig.tight_layout()"
      ],
      "id": "2a56cf69-230f-4aed-ae66-40e0998e4509"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# FIFA23 자료분석\n",
        "\n",
        "아래는 FIFA23 자료를 불러오는 코드이다."
      ],
      "id": "00e8982f-fa08-4c94-aaf9-8b51445489da"
    },
    {
      "cell_type": "code",
      "execution_count": 201,
      "metadata": {},
      "outputs": [],
      "source": [
        "df=pd.read_csv('https://raw.githubusercontent.com/guebin/DV2022/master/posts/FIFA23_official_data.csv').drop(columns=['Loaned From', 'Best Overall Rating']).dropna()\n",
        "df.head()"
      ],
      "id": "e3928e66-58bc-43b0-abf9-23a7c21877ba"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "`(1)` 선수들의 평균임금(Wage)을 구하라.\n",
        "\n",
        "# 삼성전자와 SK하이닉스\n",
        "\n",
        "아래는 삼성전자와 SK하이닉스의 주가를 load하는 코드이다."
      ],
      "id": "98c7a615-ae50-476f-982a-b58b11a125c5"
    },
    {
      "cell_type": "code",
      "execution_count": 227,
      "metadata": {},
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[*********************100%***********************]  2 of 2 completed"
          ]
        }
      ],
      "source": [
        "import yfinance as yf\n",
        "\n",
        "# 삼성전자와 SK하이닉스의 종목 코드\n",
        "tickers = [\"005930.KS\", \"017670.KS\"]\n",
        "\n",
        "# 주가 데이터를 불러올 기간\n",
        "start_date = \"2021-01-01\"\n",
        "end_date = \"2023-05-02\"\n",
        "\n",
        "# yfinance를 이용하여 데이터 다운로드\n",
        "df = yf.download(tickers, start=start_date, end=end_date)['Adj Close']\n",
        "df.columns = pd.Index(['삼성전자','SKT']) \n",
        "\n",
        "# 데이터 확인\n",
        "df"
      ],
      "id": "c1e15c74-5a08-442d-a9d5-a633fb6f1524"
    }
  ],
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