Решение_Метод_наименьших_квадратов.ipynb

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      "authorship_tag": "ABX9TyMnfD+PMMxZrlUBfLvoiBlN",
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      "name": "python3",
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    "language_info": {
      "name": "python"
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
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      "source": [
        "<a href=\"https://colab.research.google.com/github/vn322/Cod_future/blob/main/%D0%A0%D0%B5%D1%88%D0%B5%D0%BD%D0%B8%D0%B5_%D0%9C%D0%B5%D1%82%D0%BE%D0%B4_%D0%BD%D0%B0%D0%B8%D0%BC%D0%B5%D0%BD%D1%8C%D1%88%D0%B8%D1%85_%D0%BA%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%BE%D0%B2.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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    {
      "cell_type": "markdown",
      "source": [
        "# Подготовка данных"
      ],
      "metadata": {
        "id": "qqSHd9jVM6qA"
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    {
      "cell_type": "markdown",
      "source": [
        "Метод наименьших квадратов один из методов регрессионного анализа (изучения влияния независимых переменных на целевую с использованием статистических методов) который позволяет найти неизвестные параметры регрессионной модели по имеющимся для анализа данным. Упрощая можно сказать, что метод позволяет найти ту линию (прямую или кривую) которая лучшим образом описыват имеющийся набор данных (на которую наши данные похожи больше всего).\n",
        "\n",
        "\n",
        "Следует сразу отметито, что статистическая зависимость не означает автоматически наличие причинно-следственных отношений.\n",
        "\n"
      ],
      "metadata": {
        "id": "_l6EPPQgAgX4"
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    {
      "cell_type": "markdown",
      "source": [
        "Сформируем набор данных для исследования и для этого выберем несколько игроков с разным уровнем развития определённого качества (Level) и соотнесём его с количеством убитых монстров за первые пять минут игры (Frags)\n",
        "\n",
        "\n",
        "\n",
        "Level|1|2|3|4|5|\n",
        "--|--|--|--|--|--|\n",
        "Frags|3| 6| 5| 7| 10\n",
        "\n",
        "\n",
        "Как можно видеть разному уровню навыка соответствует различное количество монстров. Давайте посмотрим как это выглядит на простом точечном графике."
      ],
      "metadata": {
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)"
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      "source": [
        "Просто точки дают нам мало понимания о закономерности этого соотношения, поэтому попробуем соединитить их непрерывной линией и обратим внимание, что мы можем изобразить такую кривую, расстояние до которой от каждой из наших точек будет минимальным."
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)"
      ],
      "metadata": {
        "id": "ccpXmjtZ8vh3"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Как можно убедиться, действительно возможно подобрать линию, которая описывает наш набор данных. Однако, мы не можем сказать, что именно эта линия справляется с задачей лучше других и поэтому нам надо научиться получать формулу, которая позволит свести отклонения точки данных от линии к минимуму."
      ],
      "metadata": {
        "id": "NKECZWWNMlIX"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![image.png](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAX4AAAEGCAYAAABiq/5QAAAdzklEQVR4nO3dd3hUdfbH8XcE/CkCFowrC0LEQgeBKCpY0RWVFX/7W1fZYBdc24plWRVXdK2IsKBICWVhAUEB6UjvSksoITRBBARRg0ozaIDM748zLEhJJmTufO+d+byeZ57MXCaZ8/jIyeH7/d5zQERERERERERERERERERERERE/CXJdQCRKF++fCglJcV1GCIigZKZmbkdSD7yekkHsRRZSkoKGRkZrsMQEQmUpKSkTce6flKsAxEREbeU+EVEEowSv4hIglHiFxFJMEr8IiIJRolfRCTBKPGLiCQYJX4RER/6/nto2xZ27oz+z1biFxHxkVAIhg+HmjXh/fdhzpzof4aXib8/8B2Qfdi1TsAaIAsYBZzh4eeLiATKtm3whz/An/4E550HmZnw+99H/3O8TPwDgGZHXJsK1AbqAp8Dz3v4+SIigRAKQf/+UKMGTJoEb78NCxZA3brefJ6XiX8O8MMR16YA+8PPFwCVPPx8ERHf27ABbrwRHnwQ6tWDrCz429+gpIed1Fyu8T8AfFLAn7cBMoCMnJyc2EQkIhIjBw5A165Qpw4sWgQ9e8LMmXDRRd5/tqvunO2xyn9IAe9JDz9ITk4OxSIoEZFYWLXKKvwFC+CWW6BXL1vTjxUXFf99QHMgDVBCF5GEkZcHr74K9evDunUweDCMHx/bpA+xr/ibAe2Aa4DcGH+2iIgzGRlW5WdlwV13QbducM45bmLxsuIfCswHqgFbgAeB7kBZ7HTPMqCXh58vIuLc3r3Qrh00agTbt8OYMTB0qLukD95W/C2Pca2fh58nIuIrs2fDQw/B+vXQujV06gSnn+46Kt25KyISdbt2wSOPwLXXQn4+TJ8O6en+SPqgxC8iElUTJkCtWpbon34aVqyA6693HdWvKfGLiETB9u3QqhU0b26V/WefQefOULq068iOpsQvIlIMoRAMG2btFj76CDp0gCVLbDPXr1zdwCUiEnhbt8Kjj8LYsXDppdCvn92J63eq+EVEiigUgj59rHXy1Km2pDN/fjCSPqjiFxEpki++sKOZM2fCddfZL4ALLnAdVdGo4hcRicCBA9Cli1X1mZl2amf69OAlfVDFLyJSqOxsa7ewaJENRunZEypWdB3ViVPFLyJyHHl58Mor0KCB9c0fOtRaLgQ56YMqfhGRY1q0yKr87GxIS7Pe+Wef7Tqq6FDFLyJymNxceOYZuOIK2LHD2iYPHhw/SR9U8YuI/NfMmdZUbcMG+MtfoGNHKFfOdVTRp4pfRBLezp3Qpo311DnpJJg1yzZw4zHpgxK/iCS4cePsRqx+/WzI+fLlcM01rqPylhK/iCSknBxo2RJuuw3Kl4eFC+Htt/3ZVC3alPhFJKGEQvDBB9ZUbeRI+Oc/bSxiaqrryGJHm7sikjC2bLFN2wkT4PLLbXmnZk3XUcWeKn4RiXv5+dCrlyX5mTPtTP68eYmZ9EEVv4jEuXXrrKna7NnQtKn12Kla1XVUbqniF5G4tH+/DTevWxeWLbNlnalTlfRBFb+IxKGsLGu3kJEBLVpAjx7w29+6jso/VPGLSNz45Rd46SVo2BA2b7ZRiKNGKekfSRW/iMSF+fOtyl+9Gu65x3rnly/vOip/UsUvIoH200/Qti00bgx79sDEiTBwoJJ+QVTxi0hgTZtmJ3Y2boTHHoM334SyZV1H5X+q+EUkcHbssGWdG2+EUqVgzhzo3l1JP1JK/CISKKNH241XAwfCc89ZU7WrrnIdVbBoqUdEAuHbb+GJJ2D4cLjkEhuQ0qCB66iCycuKvz/wHZB92LWzgKnAuvDXMz38fBHx2pAhkJJiTexTUux1lIVCMGiQVfljxsDrr9tYRCX9E+dl4h8ANDvi2nPAdOCi8NfnPPx8EfHSkCE2vWTTJsvOmzbZ6ygm/82b4ZZb7Hhm9eq2rPPCC7auLyfOy8Q/B/jhiGstgIHh5wOB2z38fBHxUvv2NqD2cLm5dr2Y8vPh/fehVi2YOxfefde+Vq9e7B8txH6N/zfAtvDzb8Kvj6dN+EFOTo7HYYlIkW3eXLTrEVq71ubezptnp3bS020VSaLH5ameUPhxPOlAKpCanJwcm4hEJHKVKxfteiH274e33oJ69WDlShgwACZPVtL3QqwT/7dAhfDzCtjmr4gE0euvHz2nsHRpu15Ey5ZBo0bw/PPQvDmsWgX33gtJSVGKVX4l1ol/LHBv+Pm9wJgYf76IREtamq3DVKliGbpKFXudlhbxj/j5Z9sSSE2FrVthxAh7nHuuh3ELXv4+HQpcC5yNVfodgNHAR0BlYBPwJ47eAD5Kw4YNQxkZGd5FKiIx9+mndvft2rVw333QuTOcdZbrqOJLUlJSJrZk/itebu62PM71ph5+poj43J49diSze3fbDpg8GX73O9dRJRa1bBCRmJkyBWrXtqT/+OOQna2k74ISv4h47ocf4P774aab4NRTD53NL1PGdWSJSYlfRDw1cqS1Wxg0yDZyly613vnijpq0iYgntm2z5ZyPP4b69WHSJGuuJu6p4heRqAqF7OarmjVhwgS7KWvRIiV9P1HFLyJRs3Gj9WmbOhWaNIG+faFaNddRyZFU8YtIseXnw3vv2Ymd+fOtwdrs2Ur6fqWKX0SKZfVqa6r22WfQrBn07n3C7XokRlTxi8gJ2bcP3njD1u7XrIH//AcmTlTSDwJV/CJSZEuWwAMP2GCUO+6wZZ7fFNRkXXxFFb+IRGzvXhtwftllNgN31Cj46CMl/aBRxS8iEZk719byP//cmqt16gRnamp2IKniF5EC7d4Njz0GV19t6/pTp9oxTSX94FLiF5Hj+uQTm3vbsye0bQsrVsANN7iOSopLSz0icpTvv4ennrL+OjVr2lHNyy93HZVEiyp+EfmvUMg2a2vUgKFD4R//sBM8SvrxRRW/iADw9de2lj96NDRsCNOmQd26rqMSL6jiF0lwoRD062dLOpMm2WmdBQuU9OOZKn6RBLZhgzVVmz4drrnGTutceKHrqMRrqvhFEtCBA9C1K9SpYy2Te/WCGTOU9BOFKn6RBLNypd2AtXAh3HqrJf1KlVxHJbGkil8kQeTlwauv2jSs9ethyBAYN05JPxGp4hdJAIsXW5W/YgXcdZcNOk9Odh2VuKKKXySO5eZCu3Z2Dv/772HMGDufr6Sf2FTxi8SpWbOgdWtb1mnTBt5+G04/3XVU4geq+EXizM6d8Je/wHXX2Rn9GTNsKpaSvhykxC8SRyZMsKZqffrAM89AVpb9AhA5nBK/SBzIyYG0NGje3Nolz58P77wDpUu7jkz8yFXifwpYCWQDQ4FTHMUhEmihEAwbZu0Whg+Hl1+GzEybkCVyPC4Sf0Xgr0AqUBsoAdzlIA6RQNuyBVq0gJYtoWpV66LZoQOcfLLryMTvXFX8JYFTw19LA187ikMkcPLzIT3d1vKnTYMuXaxffu3ariOToHCR+LcC7wCbgW3ATmDKMd7XBsgAMnJycmIXnYiPrV8PTZvCww9b6+QVK2xgSokSriOTIHGR+M8EWgDnA78FTgNaHeN96dhyUGqy7jaRBHfgAHTubK2SlyyxUzvTp8MFF7iOTILIReK/AfgSyAH2AR8DVzqIQyQQsrPhiivg2Wdt3u2qVfDQQ5CU5DoyCSoXiX8zcDm2tp8ENAVWO4hDxNfy8uyUToMGsHGjnd4ZMwYqVnQdmQSdi5YNC4ERwBJgP7AUW9YRkbCFC62p2sqV0KoV/OtfcPbZrqOSeOHqVE8HoDp2nPNu4BdHcYj4yk8/2R23V15prRfGj4dBg5T0JbrUpE3EJ2bMsKZqGzZYr52OHaFcOddRSTxSywYRx3bssITftCmcdJJ11ezZU0lfvKPEL+LQ2LF2I1b//tY3PyvLhp6LeCnSxH/aYe+9GLgNKOVJRCIJ4LvvbBJWixa2fr9woS3tnHqq68gkEUSa+OdgjdQqYnfZ3g0M8CookXgVCsHgwVCjBowaZTNwMzIgNdV1ZJJIIk38SUAu8AegB3AHUMuroETi0VdfWdvku++Giy+GpUvhxRehlP7tLDFWlMR/BZAGTAhfU3cQkQjk59tmba1atnHbtSvMm2etlEVciPQ4Z1vgeWAU1ke/KjDTq6BE4sW6ddZeYc4ca7eQng7nn+86Kkl0kSb+2eHHQRuwnvoicgz791u75A4d4JRT7NTOffepv474Q6SJfxwQOuLaTqxtcm/g52gGJRJky5dbu4XMTPjf/4X334cKFVxHJXJIpGv8G4A9QJ/wYxewGzva2ceb0ESC5Zdf4B//sBM6X31loxBHjixi0h8yBFJS7E6ulBR7LRJlkVb8VwKXHvZ6HLA4fG1ltIMSCZr5863KX70a7rnHlnnKly/iDxkyBNq0gdxce71pk70Gm6QuEiWRVvxlgMqHva4cvgaQF9WIRAJkzx5o2xYaN7YGa598AgMHnkDSB2jf/lDSPyg3166LRFGkFf8zwDzgC+xo5/nAo9gdvQO9CU3E36ZOtYJ840Z4/HF44w0oW7YYP3Dz5qJdFzlBkSb+icBFWCtlgLUc2tDtGu2gRPzsxx9tGlb//lCtGsydC02aROEHV65syzvHui4SRUVp0nYRUA2oB/wJuMeTiER8bNQou/Fq4EB4/nlYtixKSR/g9dehdOlfXytd2q6LRFGkFX8H4FqgJlb934wt/fzHo7hEfOWbb+CJJ2DECLjkEpgwwUYiRtXBDdz27W15p3JlS/ra2JUoizTx/xGr9JcC9wO/AQZ7FZSIX4RCNgGrbVvbZ33jDVvm8ay/TlqaEr14LtLEvxfIx2bklgO+A87zKigRP9i0CR5+GCZPtlGI/fpB9eqFf5+I30W6xp8BnIHdrJWJDUqf71VQIi7l59vdtrVrWzO1996zDVwlfYkXkVT8ScCbwA6gFzAJq/qzPIxLxIm1a62p2rx5cNNN0Ls3VKniOiqR6Iqk4g9hG7oHbURJX+LMvn3w5ptQrx6sXAkDBtjNWEr6Eo8iXeNfgrVnWOxhLCJOLF1q7RaWLoU//tGWds4913VUIt6JdI2/EbAAu3M3C1iBqn4JuJ9/hhdegEsvha+/toZqw4cr6Uv8K6zirwxsBm6KQSwiMfPpp1blr10L998PnTvDmWe6jkokNgqr+EeHv24CuoS/Hv4QCZTdu+1GrKuusjbKU6ZY6wUlfUkkhSX+w+cFVfUyEBGvTZ5sRzTff9+S/4oVcOONrqMSib3CEn/oOM9FAuOHH2zsYbNm1vpm3jzo1g3KlCn8e0XiUWFr/PWwaVtJwKnh54Rfh7Dz/CK+NWIEPPaYJf/27eHFF20GrkgiK6ziL4El97LYL4lyh70uTtI/AxgBrAFWA1cU42dJrAVgPOC2bfB//wd33AGVKsHixfDaa0r6IhD5Of5o64bdAfxH4GSgdMFvF9/w+XjAUMhuvnr6aTuu2bGjPS/p6v90ER8qSj/+aDkduBroF36dh7WDkCDw8XjAL7+E3/0OHngA6tSB5cuhXTslfZEjuUj85wM5wL+xNs99sRGOR2qDNYfLyMnJiV10UjAfjgc8cADefddO7CxYAD16wKxZcPHFzkIS8TUXib8k0ADoCdQHfgKeO8b70oFUIDU5OTl20UnBjjcG0NF4wNWr7Uz+k0/CNddYn51HHrHtBxE5Nhd/PbaEHwvDr0dgvwgkCHwyHnDfPvvISy6xu28HDbKpWBpPK1I4F4n/G+ArbH4vQFNglYM45ESkpUF6urWtTEqyr+npMd3YzcyE1FQ7mnn77Vb1t2pl4YhI4Vxtez0BDMFO9GzAxjlKUDgaD7h3L7z8svXVOeccG3x+++0xD0Mk8Fwl/mXY+r1IRObMsQEp69bZ106d4IwzXEclEkzaAhNf27ULHn3UNm7374dp06BPHyV9keJQ4hffmjjRjmj26gVPPWVN1Zo2dR2VSPDp1hbxne3bLdEPHgw1a8Jnn8Hll7uOSiR+qOIX3wiF4MMPLdkPGwYvvQRLlijpi0SbKn7xha+/thuvxo61o5rTpkHduq6jEolPqvjFqVAI+va1Kn/KFHjnHZg/X0lfxEuq+MWZDRugdWuYMcNO7fTtCxde6Doqkfinil9i7sAB+Ne/7MTO4sXQu7clfyV9kdhQxS8xtXIlPPggLFwIt95qRzUrVXIdlUhiUcUvMZGXB//8J9SvD198AR98AOPGKemLuKDEL55bvBgaNoQOHWwU4qpV0LJlDJuqBWBUpEgsKfGLZ3Jz4dln7Rz+jz/aUc0hQyCm4xUOjorctMmOEB0cFankLwlMiV88MWuWHcns3NlO7qxcCb//vYNAfDwqUsQVJX6Jqp074eGH4brr7PWMGbaBe/rpjgLy4ahIEdeU+CVqxo2DWrXsPP6zz0JW1qFfAM74bFSkiB8o8Uux5eTAn/8Mt90GZ51lA887dTp6QqMTPhkVKeInSvxywkIhO5ZZowaMGAGvvAIZGXDppa4jO4wPRkWK+I1u4JITsmWLNVUbPx4aNYJ+/WyZx5ccjYoU8StV/FIk+fnWYqFmTZg+Hbp0gU8/9XHSF5GjqOKXiK1fb0czZ82C66+3EYhVq7qOSkSKShW/FGr/fmuXXKeODUbp08f65SvpiwSTKn4pUFaWNVXLyLBTOz16QMWKrqMSkeJQxS/H9Msv1lunYUPrcvDhhzB6tJK+SDxQxS9HWbDAqvxVq6BVK+jaFcqXdx2ViESLKn75r59+gqefhiuvhF27YMIEGDRISV8k3qjiF8COZrZuDV9+aefz33oLypVzHZWIeEEVf4LbsQMeeghuuAFKloTZs20DV0lfJH4p8SewMWPsRqwBA+Dvf4fly+Hqq11HJSJec5n4SwBLgfEOY0hI334Ld94Jt98O55xj82/fegtOPdV1ZCISCy4T/5PAaoefn3BCIRg82Kr80aPhtdcOjUUUkcThKvFXAm4F+jr6/ISzeTPceivcfTdUqwbLltkQqlKlXEcmIrHmKvF3BdoB+Y4+P2Hk59tmba1atnHbrRvMnWutlEUkMblI/M2B74DMQt7XBsgAMnJycjwPKh59/jlcey089hhccQVkZ8Nf/wolSriOTERccpH4GwO3ARuBYcD1wOBjvC8dSAVSk5OTYxddHNi/Hzp2tGHnK1bAv/8NkyfD+ee7jkxE/MBF4n8eW+NPAe4CZgCtHMQRl5Yvt8Eozz0Ht9xibRfuu8+GT4mIgM7xx42ff4YXX4TUVNi61UYhfvwxVKjgOjIR8RvXLRtmhR9SDJ99Zk3V1qyBe++1qVhnneU6KhHxK1X8AbZnj23WNmkCubkwaZLdhaukLyIFUeIPqClToHZt6N7dTu1kZ8NNN7mOSkSCQIk/YH78Ee6/35L8KafAnDnw3ntQtqzryEQkKJT4A+Tjj63dwqBB8PzzdvdtkyauoxKRoHG9uSsR+OYbePxxGDkSLrkEJk6E+vVdRyUiQaWK38dCIdusrVkTxo+HN96ARYuU9EWkeFTx+9TGjfDww7aJ27gx9O0L1au7jkpE4oEqfp/Jz7fN2tq17Xx+9+62gaukLyLRoorfR9assTGIn35qp3Z694YqVVxHJSLxRhW/D+zbZ+v39epZb52BA+GTT5T0RcQbSvyOLVkCl11mQ1FuKzmB1T+eyz0vpZD0wRDXoYlInFLid2TvXjuLf9ll8M2Xexl5ckuG5zbnN3wLmzZBmzYwRMlfRKJPid+BefPsPP5bb8E998Cqso34Q96wX78pN9f+GSAiEmVK/DG0e7fdiHXVVZCXZ0c1+/eHM7dmH/sbNm+ObYAikhCU+GNk0iQ7otmjBzz5pE3GuvHG8B9WrnzsbzredRGRYlDi99j331uP/JtvhtNOs6OaXbtCmTKHven116F06V9/Y+nSdl1EJMqU+D0SCsHw4dZu4YMPbDrW0qU29PwoaWmQnm7nN5OS7Gt6ul0XEYky3cDlgW3b4NFHYfRoaNjQ1vLr1Svkm9LSlOhFJCZU8UdRKGSbtTVq2Jp+x46wYEEESV9EJIZU8UfJl1/a0ftp0+Dqq6FPH7j4YtdRiYgcTRV/MR04AN262YmdhQuhZ0+YOVNJX0T8SxV/MaxaBQ8+aMs5N99sTdXOO891VCIiBVPFfwLy8uDVV20gyrp1MHgwTJigpC8iwaCKv4gyMqzKz8qCO++Ed9+Fc85xHZWISORU8Udo715o1w4aNYLt2+2o5rBhSvoiEjyq+CMwe7YNSFm/Hlq3hrffhjPOcB2ViMiJUcVfgF274JFH4NprbSTi9Ol2Q62SvogEmRL/cUyYALVqWaJ/+mlb07/+etdRiYgUnxL/EbZvh1atoHlzKFfOBp537mwN1kRE4oGLxH8eMBNYBawEnnQQw1FCIdusrVEDPvwQOnSwsYiNGrmOTEQkulxs7u4HngGWAGWBTGAq9ovAia1brana2LFw6aXQrx/UqeMqGhERb7mo+LdhSR9gN7AaqOggDkIh66lTsyZMnQrvvAPz5yvpi0h8c32cMwWoDyw8xp+1CT/IycmJ+gd/8YUdzZw5007t9OkDF14Y9Y8REfEdl5u7ZYCRQFtg1zH+PB1IBVKTk5Oj9qEHDkCXLlbVZ2Zaf53p05X0RSRxuKr4S2FJfwjwcaw+NDvb2i0sWmSndnr2hEqVYvXpIiL+4KLiTwL6YWv7XWLxgXl58Mor0KABbNhgoxDHjlXSF5HE5KLibwzcDawAloWvvQBM9OLDFi2yKj87G/78Zxt0HsWVIxGRwHGR+OdhVb/nXnvNzuNXqADjxtnyjohIoovrO3cvuMBO7qxcqaQvInKQ6+OcnmrZ0h4iInJIXFf8IiJytLhK/KGQ6whERPwvrhK/iIgULq4Sf1JMzgqJiARbXCV+EREpnBK/iEiCUeIXEUkwSvwiIgkmKNuhOcCmE/zes4HtUYzFa0GKN0ixQrDiDVKsEKx4gxQrFC/eKkBCdifLcB1AEQUp3iDFCsGKN0ixQrDiDVKs4EG8WuoREUkwSvwiIgmmhOsAYiTTdQBFFKR4gxQrBCveIMUKwYo3SLFC8OIVERERERERERGJhmbAWmA98JzjWArTH/gOyHYdSATOA2YCq4CVwJNuwynQKcAiYDkW6ytuw4lICWApMN51IBHYyKH52UE4JnkGMAJYA6wGrnAbznFVw/6bHnzsAto6jSggSgBfAFWBk7G/+DWdRlSwq4EGBCPxV8BiBSgLfI5//9smAWXCz0sBC4HL3YUTkaeBDwhO4j/bdRBFMBB4KPz8ZOwXgd+VAL7BbsaKing+znkZVulvAPKAYUALpxEVbA7wg+sgIrQNWBJ+vhurnCq6C6dAIWBP+Hmp8MPPI3sqAbcCfV0HEodOxwqsfuHXecAOd+FErClWxJ5o94KjxHPirwh8ddjrLfg3OQVZClAfq6T9qgT2z+XvgKn4O9auQDsg33UgEQoBU7Djhm0cx1KY87H2L//GltL6Aqc5jSgydwFDo/kD4znxi/fKACOxtcddjmMpyAHgEqyavgyo7Tac42qO/XIK0pntJtiy383AY1hF7VclsVh7YsXKT/h/7+9k4DZgeDR/aDwn/q3YJuRBlcLXJDpKYUl/CPCx41gitQPblG7mOpDjaIz9Jd+ILU1eDwx2GlHhDv6d+g4Yhf1i9ast4cfBf/GN4NBelV/djC2rfus6kKAoia3vn8+hzd1aTiMqXArB2NxNAv6DLUv4XTKHNvBOBeZilbXfXYv/N3dPwzb3Dz7/DP/+Uj1oLnZiBuBloJPDWCIxDLjfdRBBcwt24uQLoL3jWAozFNs03YdVJQ+6DadATbC13SwOHTe7xWlEx1cXW8/Nwn6pvuQ2nIgFIfFXxQqqg0dl/f53DGzJLwP7/2E0cKbbcAp0GvA9tiktIiIiIiIiIiIiIiIiIiIiIiIikkD2FP6WE/Yy8KyHP18kIvF8566IiByDEr9I4S4AJmE9dOYC1bGbajZx6O/QaVhTwFLHeb+IiPjUsZZ6pgMXhZ83AmaEn48Brgs/v5NDrZSP934t9YgvlHQdgIjPlQGu5NfdEf8n/PVDLOHPxFrn9ijk/SIi4kNHVvzlsB5Kx1IG66R5FrAZ6/tf0PtV8YsvaI1fpGC7gC+BO8Kvk4B64ed7gMVAN6yh2oFC3i/iC0r8Ir9WmkN927dg82/TsG6pB7tQHj7C80OgVfjrQQW9X0RERERERERERERERERERERERERERERERBLI/wNncaMaifft+QAAAABJRU5ErkJggg==)"
      ],
      "metadata": {
        "id": "cHAfe0ZQMTMu"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Вычисление формулы описывающей набор данных"
      ],
      "metadata": {
        "id": "ZYflp-oJM5ma"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Мы можем сделать предположение, что для функции $y = f(x)$ , которая наилучшим образом приближает эмпирические (опытные) данные хорошо подойдёт прямая, а формула прямой нам хорошо известна $f(x) = ax+b$\n",
        "\n",
        "Для того чтобы выбрать метрику оценивающую качество нашего приближения кривой к данным (апроксимации) мы заметим, что отклонения от линии $y - f(x)$ могут быть как положительными, так и отрицательными и если мы попробуем посчитать их сумму, то они могут компенсировать друг друга. Чтобы избежать этого, нужно оставить только значения отклонений и избавиться от знака. \n",
        "\n",
        "Для этого можно применять различные средства и методы, мы же используем возведение в квадрат, что даст нам возможность найти минимальное значение этих ошибок решив систему уравнений. Итак ошибка $e = y-f(x)$ должна быть вычислена для каждой точки данных и возведена в квадрат $$\\sum_{i=1}^n e^2= \\sum_{i=1}^n (y_i - f(x_i))^2 = \\sum_{i=1}^n (y_i - (ax_i+b))^2 = F(a,b)$$\n",
        "\n",
        "Для получения формулы прямой нам нужно найти два параметра $a$ и $b$, а для этого необходимо определить минимум функции двух переменных, так как именно эти параметры и являются нашими неизвестными. Мы знаем, что  своего минимума функция достигает в точке, где функция меняет убывание на возрастание,а её производная в этот момент будет равна нулю. Мы уже умеем находить производную функции одной переменной. Для нахождения производной функции двух переменных необходимо зафиусировать сначала одну из них и найти производную от второй, а затем зафиксировать вторую и найти производную от первой. В результате мы получим систему из двух уравнений, успешно решив которую найдём искомые коэффициенты."
      ],
      "metadata": {
        "id": "Lmhwr15ONsVn"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        " $$\\begin{cases} a\\sum_{i=1}^n x_i^2 +b\\sum_{i=1}^n x_i=\\sum_{i=1}^n x_iy_i, \\\\\\\\ a\\sum_{i=1}^n x_i +bn=\\sum_{i=1}^n y_i\\end{cases}$$"
      ],
      "metadata": {
        "id": "emqA8IZ9ef7i"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "<tr><th>$x_i$<th>1<th><th>2<th><th>3<th><th>4<th><th>5<th><th> $∑x_i$=<th>15\n",
        "<tr><th>$y_i$ <th>3<th><th>6<th><th>5<th><th>7<th><th>10<th><th> $∑x_i$=<th>31\n",
        "<tr><th>$x_i^2$ <th>1<th><th>4<th><th>9<th><th>16<th><th>25<th><th> $∑x_i^2$=<th>55\n",
        "<tr><th>$x_iy_i$ <th>3<th><th>12<th><th>15<th><th>28<th><th>50<th><th> $∑x_iy_i$=<th>108"
      ],
      "metadata": {
        "id": "ReVAWfaLjLaz"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        " Так мы получили систему уравнений, где неизвестные вместо $x$ и $y$ стали  $a$ и $b$ \n",
        " $$\\begin{cases} 55a +15b=108 \\\\\\\\ 15a + 5b=31\\end{cases}$$"
      ],
      "metadata": {
        "id": "9ybO5NFIKFQR"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Эту систему можно решить разными способами, в том числе записав систему в виде матриц, но сейчас мы используем известный уже вам способ выразив сначала  переменную $b$ з второго уравнения\n",
        "$$b =\\frac{31-15a}{5}$$ \n",
        "Теперь подставим получившееся выражение в первое уравнение и найдём переменную $a$\n",
        "$$55a + 3(31-15a)=108$$\n",
        "$$55a-45a=108-93$$\n",
        "$$10a=15$$\n",
        "$$a= 1.5$$\n",
        "Зная переменную $a$ мы без труда найдём переменную $b$\n",
        "$$b=\\frac{31-15*1.5}{5}=\\frac{8.5}{5}$$\n",
        "$$b=1.7$$\n"
      ],
      "metadata": {
        "id": "jb9G9U2pLKS5"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Таким образом мы получили формулу задающую прямую линию максимально точно описывающую наш набор данных\n",
        "$$y = 1.5x+1.7$$\n",
        "или подставив наши переменные это будет выглядеть так\n",
        "$$\\hat{Frags} = 1.5*Level+1.7$$"
      ],
      "metadata": {
        "id": "nmMz4lpQrel_"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Подставив значение независимой переменной в формулу можно заметить, что несмотря на различие наблюдается сходство в изменении зависимой и независимой перемееных.\n",
        "\n",
        "Зная формулу для прогноза мы можем подставив в неё два следующих значения независимой переменной получить ожидаемое значение зависимой (целевой)."
      ],
      "metadata": {
        "id": "z5WhZE44fRCy"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "|Level|1\\.0|2\\.0|3\\.0|4\\.0|5\\.0|6\\.0|7\\.0|\n",
        "|---|---|---|---|---|---|---|---|\n",
        "|Frags|3\\.0|6\\.0|5\\.0|7\\.0|10\\.0|---|---|\n",
        "|Прогноз|3\\.2|4\\.7|6\\.2|7\\.7|9\\.2|10\\.7|12\\.2|"
      ],
      "metadata": {
        "id": "Yemsw6Eee3GM"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Задание"
      ],
      "metadata": {
        "id": "D91k2Njs2bhW"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "- Создать набор данных не менее чем 2 строк х 5 столбцов. \n",
        "- Одну из переменных назначить зависимой (целевой). \n",
        "- Методом наименьших квадратов найти коэффициенты линейной зависимости между независимой и зависимой переменной. \n",
        "- Создать прогноз для изменения зависимой переменной на следующие два значения независимой."
      ],
      "metadata": {
        "id": "UFCBTRTI3GQv"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Код для графиков и решения"
      ],
      "metadata": {
        "id": "nm9Ykdw-MWkE"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Создание таблицы"
      ],
      "metadata": {
        "id": "CGKB0iUC9cWn"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import pandas as pd\n",
        "df = pd.DataFrame({'Frags':[3, 6, 5, 7, 10]})\n",
        "df['Level'] = df.index+1\n",
        "df['Прогноз'] = df['Level']*1.5+1.7\n",
        "df.T\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 143
        },
        "id": "bVqCvVmodqA1",
        "outputId": "84a01559-6d7e-4377-9a26-b1f1da93df5b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "           0    1    2    3     4\n",
              "Frags    3.0  6.0  5.0  7.0  10.0\n",
              "Level    1.0  2.0  3.0  4.0   5.0\n",
              "Прогноз  3.2  4.7  6.2  7.7   9.2"
            ],
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              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
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              "  "
            ]
          },
          "metadata": {},
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        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Расчёт двух следующих значений"
      ],
      "metadata": {
        "id": "dnfn9uwa9XJA"
      }
    },
    {
      "cell_type": "code",
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        "pd.DataFrame([6,7])*1.5+1.7"
      ],
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        },
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      },
      "execution_count": null,
      "outputs": [
        {
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          "data": {
            "text/plain": [
              "      0\n",
              "0  10.7\n",
              "1  12.2"
            ],
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              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
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              "            + ' to learn more about interactive tables.';\n",
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              "  "
            ]
          },
          "metadata": {},
          "execution_count": 43
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Точечный и линейный графики"
      ],
      "metadata": {
        "id": "tqj0Xiic9gqp"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "df.plot(x=\"Level\", y=\"Frags\", kind=\"scatter\", c='Red')\n",
        "df.plot(x=\"Level\", y=\"Frags\")\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 541
        },
        "id": "_oU1JY-k4zdp",
        "outputId": "58889222-a7b5-42af-e981-7d4bb551bb62"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Получение графика и коэффициентов линейной регрессии"
      ],
      "metadata": {
        "id": "LHgA_MMW9oYA"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "model = np.polyfit(df[\"Level\"], df[\"Frags\"], 1)\n",
        "print(model)\n",
        "prognoz = np.poly1d(model)\n",
        "x_axis = range(8)\n",
        "y_axis = prognoz(x_axis)\n",
        "plt.xlabel('Level')\n",
        "plt.ylabel('Frags')    \n",
        "plt.scatter(df[\"Level\"], df[\"Frags\"], c = 'r')\n",
        "plt.plot(x_axis, y_axis, c = 'b')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 314
        },
        "id": "EERPyKGWGwO8",
        "outputId": "0bbb03d6-8cb4-4c7d-886b-3000798de532"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1.5 1.7]\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fbd60bea2e0>]"
            ]
          },
          "metadata": {},
          "execution_count": 10
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}