Yakushev_VP_Workbook4.ipynb

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    "Регрессия – это зависимость среднего значения какой-либо величины\n",
    "от некоторой другой величины или от нескольких других величин. В\n",
    "отличие от чисто функциональной зависимости 𝑦 = 𝑓(𝑥), когда каждому\n",
    "значению независимой переменной 𝑥 соответствует одно определённое\n",
    "значение зависимой переменной у, при регрессионной связи одному и тому\n",
    "же значению независимой переменной (фактору) 𝑥 могут соответствовать в\n",
    "зависимости от конкретного случая различные значения зависимой\n",
    "переменной (отклика) у.\n",
    "Изучение регрессии основано на том, что случайные величины Х и 𝑌\n",
    "связаны между собой вероятностной зависимостью: при каждом\n",
    "конкретном значении 𝑋 = 𝑥 величина 𝑌 является случайной величиной с\n",
    "вполне определённым распределением вероятностей. Зависимость\n",
    "зависимой переменной – отклика от одной независимой переменной –\n",
    "фактора или нескольких факторов называется уравнением регрессии. По\n",
    "количеству факторов выделяют парную (однофакторную) и\n",
    "множественную (многофакторную) регрессию. Для парной будем\n",
    "рассматривать следующие методы регрессии: линейную, показательную,\n",
    "экспоненциальную, гиперболическую и параболическую.\n",
    "Регрессионный анализ – это раздел математической статистики,\n",
    "изучающий регрессионную зависимость между случайными величинами по\n",
    "статистическим данным. Цель регрессионного анализа состоит в\n",
    "определении общего вида уравнения регрессии, вычислении оценок\n",
    "неизвестных параметров, входящих в уравнение регрессии проверке\n",
    "статистических гипотез о регрессионной связи.\n",
    "Таким образом, регрессионный анализ – набор статистических\n",
    "методов исследования влияния одной или нескольких независимых\n",
    "переменных 𝑋1, … , 𝑋𝑛 на зависимую переменную 𝑌. Независимые\n",
    "переменные иначе называют регрессорами или предикторами, а зависимые\n",
    "переменные – критериальными переменными."
   ],
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    "1.1. Теоретический материал – Линейные регрессионные модели\n",
    "\n",
    "Линейная регрессия\n",
    "Линейная регрессия (Linear regression) – модель зависимости переменной\n",
    "x от одной или нескольких других переменных (факторов, регрессоров,\n",
    "независимых переменных) с линейной функцией зависимости. Линейная\n",
    "регрессия относится к задаче определения «линии наилучшего соответствия»\n",
    "через набор точек данных и стала простым предшественником нелинейных\n",
    "методов, которые используют для обучения нейронных сетей.\n",
    "Цель линейной регрессии — поиск линии, которая наилучшим образом\n",
    "соответствует этим точкам. Напомним, что общее уравнение для прямой есть\n",
    "𝑓 (𝑥) = 𝑏 + 𝑚 ⋅ 𝑥 +, где 𝑚 – наклон линии, а 𝑏 – его сдвиг.\n",
    "Функция потерь — метод наименьших квадратов\n",
    "Функция потерь – это мера количества ошибок, которые наша линейная\n",
    "регрессия делает на наборе данных. Хотя есть разные функции потерь, все они\n",
    "вычисляют расстояние между предсказанным значением 𝑦(х) и его\n",
    "фактическим значением.\n",
    "Одна очень распространенная функция потерь называется средней\n",
    "квадратичной ошибкой MSE. Чтобы вычислить MSE, мы просто берем все\n",
    "значения ошибок, считаем их квадраты длин и усредняем.\n",
    "Задача экраполяции\n",
    "Допустим у нас есть много экспериментальных точек. Необходимо через\n",
    "них провести кривую, которая как можно ближе проходила к этим точкам. При\n",
    "этом необходимо минимизировать среднюю квадратичную ошибку (MSE).\n",
    "Для решения данной задачи в Python есть множество библиотек. Самыми\n",
    "распостраненными выступают:\n",
    "numpy - numpy.linalg.lstsq\n",
    "scipy - scipy.linalg (содержит все функции из numpy.linalg плюс часть\n",
    "новых функций, которых нет в numpy.linalg).\n"
   ],
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   "cell_type": "markdown",
   "source": [
    "1.1.1 Пример\n",
    "\n",
    "Проведем прямую 𝑦 = 𝑚𝑥 + 𝑏 через экспериментальные точки."
   ],
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   }
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[0., 1.],\n       [1., 1.],\n       [2., 1.],\n       [3., 1.]])"
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "x = np.array([0, 1, 2, 3])\n",
    "y = np.array([-1, 0.2, 0.9, 2.1])\n",
    "\n",
    "A = np.vstack([x, np.ones(len(x))]).T\n",
    "A"
   ],
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    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9999999999999997 -0.949999999999999\n"
     ]
    }
   ],
   "source": [
    "m, c = np.linalg.lstsq(A, y, rcond=None)[0]\n",
    "print(m, c)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.plot(x, y, 'o', label='Исходные данные', markersize=10)\n",
    "plt.plot(x, m * x + c, 'r', label='Линейная экстраполяция')\n",
    "plt.legend()\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "1.1.2 Пример\n",
    "\n",
    "Пусть 𝑥, 𝑦 – вектора длиной 𝑛 > 3 (точек > 3). Задача заключается в\n",
    "построении эстраполяционного полинома второго порядка (параболы). Таким\n",
    "образом, необходимо найти такие коэффициенты поринома 𝑎, 𝑏, 𝑐 по методу\n",
    "наименьших квадратов. Данные мтогут быть получены в результате\n",
    "измерений. Покажем пример генерации данных случайным образом и\n",
    "загрузки их из файла.\n"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "outputs": [],
   "source": [
    "from numpy import *\n",
    "from numpy.random import *\n",
    "\n",
    "delta = 1.0\n",
    "x = linspace(-5, 5, 11)\n",
    "y = x ** 2 + delta * (rand(11) - 0.5)\n",
    "x += delta * (rand(11) - 0.5)\n",
    "x.tofile('x_data.txt', '\\n')\n",
    "y.tofile('y_data.txt', '\\n')"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-5.44083541 -4.24337816 -2.7972939  -1.95730001 -0.7142697   0.2592018\n",
      "  1.4980812   1.8124045   2.73949203  4.14825341  4.535135  ]\n",
      "[25.48850235 16.01094544  8.92224257  4.19831421  0.702923   -0.41368714\n",
      "  0.76138014  3.80147509  8.5619731  16.3016166  24.54550792]\n"
     ]
    }
   ],
   "source": [
    "x = fromfile('x_data.txt', float, sep='\\n')\n",
    "y = fromfile('y_data.txt', float, sep='\\n')\n",
    "print(x)\n",
    "print(y)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m = vstack((x ** 2, x, ones(11))).T\n",
    "s = np.linalg.lstsq(m, y, rcond=None)[0]\n",
    "\n",
    "x_prec = linspace(-5, 5, 101)\n",
    "plt.plot(x, y, 'D')\n",
    "plt.plot(x_prec, s[0] * x_prec ** 2 + s[1] * x_prec + s[2], '-', lw=2)\n",
    "plt.grid()\n",
    "plt.savefig('парабола.png')"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "1.1.3 Пример\n",
    "\n",
    "По данным предыдущего примера постройте экстраполяционного полинома\n",
    "третьего порядка\n"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m = vstack((x ** 3, x ** 2, x, ones(11))).T\n",
    "s = np.linalg.lstsq(m, y, rcond=None)[0]\n",
    "\n",
    "x_prec = linspace(-5, 5, 101)\n",
    "plt.plot(x, y, 'D')\n",
    "plt.plot(x_prec, s[0] * x_prec ** 3 + s[1] * x_prec ** 2 + s[2] * x_prec + s[3], '-', lw=3)\n",
    "plt.grid()\n",
    "plt.savefig('полином 3-й степени.png')"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# linear\n",
    "import numpy as np\n",
    "\n",
    "x = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])\n",
    "y = np.random.random(10)\n",
    "\n",
    "A = np.vstack([x, np.ones(len(x))]).T\n",
    "m, c = np.linalg.lstsq(A, y, rcond=None)[0]\n",
    "plt.plot(x, y, 'o', label='Исходные данные', markersize=10)\n",
    "plt.plot(x, m * x + c, 'r', label='Линейная экстраполяция')\n",
    "plt.legend()\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Задание:\n",
    "\n",
    "Представьте собственные данные и постройте эктраполяцию полиномами\n",
    "первой, второй и третьей степени.\n"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# парабола\n",
    "\n",
    "delta = 1.0\n",
    "x = linspace(-10, 10, 20)\n",
    "y = x ** 2 + delta * (rand(20) - 0.5)\n",
    "x += delta * (rand(20) - 0.5)\n",
    "\n",
    "m = vstack((x ** 2, x, ones(20))).T\n",
    "s = np.linalg.lstsq(m, y, rcond=None)[0]\n",
    "\n",
    "x_prec = linspace(-10, 10, 101)\n",
    "plt.plot(x, y, 'D')\n",
    "plt.plot(x_prec, s[0] * x_prec ** 2 + s[1] * x_prec + s[2], '-', lw=2)\n",
    "plt.grid()\n",
    "plt.savefig('парабола.png')"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 3-й степени\n",
    "\n",
    "m = vstack((x ** 3, x ** 2, x, ones(20))).T\n",
    "s = np.linalg.lstsq(m, y, rcond=None)[0]\n",
    "\n",
    "x_prec = linspace(-10, 10, 101)\n",
    "plt.plot(x, y, 'D')\n",
    "plt.plot(x_prec, s[0] * x_prec ** 3 + s[1] * x_prec ** 2 + s[2] * x_prec + s[3], '-', lw=3)\n",
    "plt.grid()\n",
    "plt.savefig('полином 3-й степени.png')"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "1.1.4 Пример\n",
    "\n",
    "Необходимо проверить гипотезу, что наши точечно заданная функция ложится\n",
    "на кривую вида 𝑓(𝑥, 𝑏) = 𝑏0 + 𝑏1𝑒𝑥𝑝(−𝑏2𝑥2)\n"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.00014489798647308758\n",
      "0.07472195522288498\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import scipy as sp\n",
    "from scipy.optimize import curve_fit\n",
    "\n",
    "beta = (0.25, 0.75, 0.5)\n",
    "\n",
    "\n",
    "def f(x, b0, b1, b2):\n",
    "    return b0 + b1 * np.exp(-b2 * x ** 2)\n",
    "\n",
    "\n",
    "xdata = np.linspace(0, 5, 50)\n",
    "y = f(xdata, *beta)\n",
    "\n",
    "ydata = y + 0.05 * np.random.randn(len(xdata))\n",
    "\n",
    "beta_opt, beta_cov = sp.optimize.curve_fit(f, xdata, ydata)\n",
    "beta_opt\n",
    "\n",
    "lin_dev = sum(beta_cov[0])\n",
    "print(lin_dev)\n",
    "residuals = ydata - f(xdata, *beta_opt)\n",
    "fres = sum(residuals ** 2)\n",
    "print(fres)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(xdata, ydata)\n",
    "ax.plot(xdata, y, 'r', lw=2)\n",
    "ax.plot(xdata, f(xdata, *beta_opt), 'b', lw=2)\n",
    "ax.set_xlim(0, 5)\n",
    "ax.set_xlabel(r\"$x$\", fontsize=18)\n",
    "ax.set_ylabel(r\"$f(x,\\beta)$\", fontsize=18)\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "1.1.5 Пример\n",
    "\n",
    "Необходимо проверить гипотезу, что наши точечно заданная функция ложится\n",
    "на кривые вида:\n",
    "1) 𝑓(𝑥, 𝑏) = 𝑏0 + 𝑏1𝑥\n",
    "2) 𝑓(𝑥, 𝑏) = 𝑏0 + 𝑏1𝑥 + 𝑏2𝑥2\n",
    "3) 𝑓(𝑥, 𝑏) = 𝑏0 + 𝑏1𝑙𝑛(𝑥)\n",
    "4) 𝑓(𝑥, 𝑏) = 𝑏0 𝑥𝑏1\n"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.25421165 0.75184749]\n",
      "0.00012094321250497676\n",
      "0.10634661781087063\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.00012094321250497676\n",
      "0.07495488758196253\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.98225687 2.02332344]\n",
      "4.765550435117003e-05\n",
      "0.11020055927103826\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.00027228 2.00016952]\n",
      "4.561397658888153e-06\n",
      "0.10849679835292024\n"
     ]
    },
    {
     "data": {
      "text/plain": "Text(0, 0.5, '$f(x, \\\\beta)$')"
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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8Li4OKL1jFB9/9VloVlZWpbtHZfz9/fH392/YCYuIiDSyitt4tDh4mZSd4x3nnx39GTfNvtM1k3MzHll9ZhgGs2fP5uOPP2bVqlUkJSU5nU9KSiIuLo6VK1c6jhUXF7N27VoGDRrU2NMVERFxiYrbePhdtJOxbADFlN4EuDX8A5YOj8Bm9/iaq3rhkXeKZs2axeLFi/n0008xm82ONURhYWEEBgZiMpmYM2cOL774Ih07dqRjx468+OKLBAUFce+997p49iIiIo2j/DYeRgn4vt2as/bSJyh9fbZyZIaJfIuVbekXSG4f6cqpugWPDEULFiwAYPjw4U7HFy5cyAMPPADAY489RmFhIY888ggXL15kwIABrFixArPZ3MizFRERcY3y23MkvBfAlsJeAMRzBr87D3IuKLLSuObMI0PR9bRWMplMzJs3j3nz5jX8hERERNxQ2fYcCd/Y2HzmFgD8sNJv+Gd8l9iq0rjmziPXFImIiEj1+idF0O64iR0pVztWT++wiO8GlAai5raNR3UUikRERJqozEN57PugL5fxA+DWsP+wZXoCQLPcxqM6CkUiIiJNUFGBnenJZzhriwFgoO8mDv/IC8NU+tUfFxbAgvt7e9w2Hg3JI9cUiYiIiLPyHaujQwJ47fbjbLt0pWO16QRL18WRHt3Z0dG6OW7jUR2FIhEREQ9XsWN1yy/tbNpd2rE6kAI++b/TxA1MJs6Vk/QACkUiIiIerGLH6qi0y2zdPclx/vmJn3Pjz9Wx+npoTZGIiIiHqtixOvCsnaPLh2K7cs9jWuRiPhikjtXXS6FIRETEQ5XvWG0qgpLFHblolJbXD/Zby54ZAWRc6Vgt1VMoEhER8VBlnagNAyLfCudI8Q0AJJm+p/j+UxRf2ehcHauvj0KRiIiIhyrrRN3qYy9SLg4GwIyFThNWkxUdXmmc/DCFIhEREQ/VPymCjikGm46MB8CEnbG93+XAld5D6lhdMwpFIiIiHmr38gw2fTPC8fr2lm+yfXRrQB2ra0Ml+SIiIh4oKz2fKVOhgGAAxps/Z8c9kY7zcWEBPDO5qzpW14BCkYiIiAco37G6ha8fTw3L5sTlLgD09/+OD/Ylk2ZFHavrQKFIRETEzZXvWG0YEL8oiK3nSx+bJZjO8MmKIIJbRZLs4nl6OoUiERERN1axY3Xil3Y2ZpUGogAKmf+bVOKHTnDdBJsQLbQWERFxUxU7VsfsvMzmPVcD0JQub7Eg3F8dq+uJQpGIiIibKt+x2nzSxqGVw7HjDcC0qHfZMrklGTlF6lhdTxSKRERE3FRZJ2ofix3L+z3JIRyAYQHfsudHQWAyOY2TulEoEhERcVMx5gCMEgh6syUnbG0B6OK1F8uMLIp9/ZzGSd0pFImIiLipfm0jaL0kmN0FvQGI5iyx07dzISIUUMfq+qZQJCIi4qZe/UkqG04PB8APK8lDPyG9fTSgjtUNQaFIRETEDX35yiF+/VZPx+t7erzNd8mtHK/jwgJYcH9vdayuR+pTJCIi4gbKd6wuSsvnobnxjkqzp3ss49ldP2HbsYvqWN2AFIpERERcrHzHat9LBoWv9yLXMANwW+Qafrd1LF7eXiS3j/zhN5I6USgSERFxIaeO1ZfB781EjtgTAeju9R0PLI7GK9DfpXNsLrSmSERExEXKd6w2DIh7K5h9Rb0AiOcM4Xd+xwspmepY3UgUikRERFykfMfqxE9ga/ZwAAIpoPeoLzjZJlIdqxuRQpGIiIiLlHWibrn+MhsPTXQcn9jjHfb0Sag0ThqWQpGIiIiLxJgDiNpXTMqmcY5jtye8yfbxCZXGScPTQmsREREXiTpvkP75UKyUhp7x5k9JubeFY08zE6X9iNSxunHoTpGIiIgLXMwo4tbheVwwSsvsB/hu5NgDl7F7l/YmUsfqxqc7RSIiIo2gfHPGFn7+PDsikwOF3QHo7H2I8EcyyQwIdIyPCwvgmcld1bG6ESkUiYiINLDyzRkNA+IXBbE1awQA0Zzjy4+stJk83RGa1LHaNRSKREREGpBTc0Yg8VODjVcCkT9FvDRnK+2mTAJQx2oX05oiERGRBlK+OSNAwoZiNh6c5Dh/a7c3+WdMoJozugmFIhERkQZSvjljxP7L7NpYrvQ+/i22TWyp5oxuRKFIRESkgZQ1XQw5U8Lxz26miNKF1GNDPiPlvnBH6b2aM7oHhSIREZEGEmMOwMdiJ3dxz3Kl95s48WOro/S+bJy4nkKRiIhIA+kRHUbgojacsCUB0MnrACUzjlEQVHrHyATEqzmj21AoEhERaQB2O/ykz272FPYEIJZM4m7bSnZ0GKDmjO5IJfkiIiL1oHxzxhhzAB/9NJ0PjvQFIJg8RkxezuZ20Y7xas7ofhSKRERE6qh8c0aAVl/Z2Jh2KwDelPCfOZsZ+6eZas7o5hSKRERE6qBic8b4rVY2p01xnH9m6FIm/OUOQM0Z3Z3WFImIiNRSxeaMEQeLSVszFjullWXTohbz5dgWas7oIRSKREREaql8c8agjBJOfDqEAoIBuCXoK9JmBpFhsao5o4dQKBIREamlsqaLPhY7Be/25LxRupC6r89WMn+cR4mPr9M4cW8KRSIiIrUUYw7AZAW/f7fl+JVeRB1Nh2DGEfJCgpzGiftTKBIREaml3q1aEL0okv3WHgDEkUHC7Zs4FxMOqDmjp1EoEhERqQXDgF8O2cX2SwMBMGOh19gvOHalF5GaM3oeleSLiIhch4rNGb99NJ1/7ihtzuhLMVOGf8D6G682YlRzRs+jUCQiIlKNSs0Zv73Mxh1THecX3ruSu9/+iZozejiFIhERkR9QsTlj3HYrW3bc6jj/xE0fct87t4HJpOaMHk5rikRERK6hUnPGQ8XsWTUG25V7CpNbfMia6WHY1JuxSVAoEhERuYbyzRlDzpRw4pMh5BMCwIjAFex/wIeMvGI1Z2wiFIpERESuoazpov8FG5bFNzqaM/bx2UrWT3K47KfmjE2JQpGIiMg1xJgD8M43MN7syElbGwA6eR2AHx1Vc8YmSKFIRETkGnrFhhG6MIHDxV0AaMlJou/cRnZ0KKDmjE1NvVWfHTp0iM2bN3PmzBnOnTtHUVERkZGRREdH06VLFwYPHkxQUFD1byQiIuIGbCUGM29MIzW/NwARnOeGySs50iYWUHPGpqhOoWjz5s289tprLF++nKysrB/+IB8fevfuzX333ceMGTMICwur9eeuW7eOP/7xj6SkpJCRkcHSpUuZOnWq4/wDDzzAm2++6XTNgAED2LJlS60/U0REmg/DgF8MSuHD70ubMwaRz5gJn7G5a6xjjJozNj21CkXvvPMOL730Env37sUwrtYhhoSEEBkZSUREBIGBgVy4cIELFy6QnZ3N5cuX2bp1K9u2beOJJ57gnnvu4X//939JTEys8efn5+fTq1cvfvzjH3PbbbdVOWbcuHEsXLjQ8drPz6/mf1AREWk2ynesXv3rYyzYPhgAHy7z0a83M/qlmWrO2MTVKBStWbOGRx99lF27dmEYBhEREdx2220MHTqUAQMG0KFDhyqvy8vLY8eOHWzdupVly5axefNm3njjDd59911++ctf8tRTT2E2m697HuPHj2f8+PE/OMbf35+4uLia/PFERKSZKt+xOnF5CRu+m+I4t/DuFYx7eSKAmjM2cTUKRSNHjgRg7NixPPzww0yYMAFfX99qrwsJCWH48OEMHz6cxx9/nGPHjvHWW2/xt7/9jZdeeomgoCB++9vf1u5PcA1r1qwhJiaG8PBwhg0bxgsvvEBMTMw1x1utVqxWq+O1xWKp1/mIiIh7Kt+xuuXGYjaWC0S3Jy4i6umxrpucNKoaVZ+NHTuWzZs389VXXzFlypTrCkRVadu2Lf/7v//L8ePHmT9/PhER9btqf/z48bz77rusWrWKP/3pT2zfvp2RI0c6hZ6K5s+fT1hYmOOnNo/1RETEs5TvWB2bamXHhgkYV74ap0QtIeWeSJ79bB82u1pWNwcmo/yiIA9kMpkqLbSuKCMjgzZt2rBkyRKmT59e5Ziq7hQlJiaSk5NDaGhofU9bRETcwObvz3PP61uIPGjl0CejyKP03/djzJ9z5L9s2HxKH6i899BAPTrzEBaLhbCwsFp9fzeLDWHj4+Np06YNhw8fvuYYf39//P39G3FWIiLialm5RYQev0z6p8McgWiI/xqO/aQYm4+/0zhp+ppF88bz589z8uRJ4uNVNikiIld5nbRy7j/9uWiU3gXq67uViz/Nxhrg/B/J6ljdPNT4TpHVauXrr7/m3LlztG7dmiFDhhAYGNgQc7umvLw8jhw54nidnp5OamoqERERREREMG/ePG677Tbi4+M5duwYTz31FFFRUUybNq1R5ykiIu4r62gej97pTaY9AYBu3rspmZlOXsjVamgTpf2I1LG6eahRKMrOzmbIkCFOj6H8/Py4//77ee655xwl8K+88gr/+Mc/yMnJITExkdGjR/Pggw/Srl27epn0jh07GDFihOP13LlzAZg5cyYLFixg9+7dvPXWW1y6dIn4+HhGjBjB+++/X6OyfxERabpyzhYxrlcGh4o6AtDedISQ+9LIjAx3jFHH6uanRgut58yZw//7f/8PgM6dO3Px4kWysrIwmUwkJiayatUqPvroI5544gmnpo4mkwlvb28ee+wxnn/++fr/UzSAuizUEhER91PWnPFURj6vTM5h06UeALQyneaVfxzn5fOFZORcXTsUr47VHqnRFlovX74ck8nEokWLmDFjBoZh8PXXX/OrX/2KQ4cOcd9993Ho0CEMw2D06NHccccdnD17lqVLl7Jz507mz59Pbm4uf/3rX2s0SRERkbpwNGc8X0jka5HszE0GIIpzrFx8jhvuHsTUch2t1bG6earRnaLg4GBKSkooKirCZLr6f5Ts7GySk5M5evQoAMnJyaxfv95pzHvvvcdDDz1EYWEhGzduZODAgfX4x6h/ulMkItI0lDVntNsN4t8IYeuF4QCYsTB49Af88s8TdDeoCanL93eNqs/sdjv+/v5OYQcgKiqKxx57zPHIbPbs2ZXG3HPPPfzP//wPhmHw+uuv12iSIiIitVHWnNFuQOI7fo5A5E8Rwwe/z4HecWrOKA41CkUtW7YkPz/fcUeovPLNE/v161fl9Q899BAAGzZsqMnHioiI1Mq29Atk5BTR5n0TGzPGAOBNCRN6v03akAQMICOniG3pF1w7UXELNQpFI0aMwDAMnnzyyUrnoqOjHc0PW7ZsWeX1kZGRhIaGcvr06VpMVUREpGaycoto/bGd9ccnOI5NvWERO0cnVBonUqNQ9Ktf/Qo/Pz8+/PBDxo0bx7Zt25zO79+/n3fffZeAgKqbXJWUlJCfn09JSUntZywiInKddjx3nPWHJzte397u3+yYUnn9kJozCtQwFHXt2pV//OMfmEwmVq5cSXJyMgkJCUybNo0XXniBAwcOcMstt1zz+g8//BCbzUZsbGydJy4iIvJDFv4ylec/HuR4fVurN9l+e4zTGBOlpfdqzihQi47WDzzwADfccANPPPEE69atIzMzk08//ZRly5Y5xrRs2ZK+ffvSp08f+vTpQ9++fUlNTeWRRx7BZDIxatSoev1DiIhI82arUE5/YtFpfvr/ejjOT4tdTMq9kVCuCEjNGaWiGpXkV3Ty5ElWr17N9u3bSUlJIS0tjYKCgqtvXqECzTAMvLy8+Oc//8mkSZPc+o6RSvJFRDyDowfRlcaLCVutbF8zmRJ8AZjT+SvGLOnB7746qOaMzUBdvr/rFIoqstvt7N+/n507d5KSksLOnTtJTU0lLy/P+UOvhKW4uDhuuukmx8/06dPrayp1plAkIuL+ynoQlX2Rxe0qInXFRKyUrhG6L/4r3j42CpOfb6W7SWrO2DS5TSiqimEYHDp0yBGSUlJSSE1NJScnx2mcl5eXWy3AVigSEXFvNrvBkD+sctz9id5nZf9nY8gnBIBbgpdj/Y3Bmt+OU/hpRhptm4/aMJlMdO7cmc6dO3Pvvfc6jh85csQRklJSUti1a1dDT0VERJqQsh5EAJGHijj02ShHILo5YDWnHiygqNCfbekXSG4f6cqpiodo8FB0LR06dKBDhw7ceeedrpqCiIh4sLLeQi2+t3J06QgshAEwwG8j5396nqLAQKdxItWpUUm+iIiIu4gxBxB+vJiTHw3lEqUl9b19tpP/4GnygwOdxolcD4UiERHxSC3OlJDxfjLnjSgAevnsxPaTo+SGBgPqQSQ157LHZyIiIterYuVY9Hk7o0fayTJKy+m7e6dheuAQF1uYAfUgktpRKBIREbdWsQ9RUFYJuW/15pQtEYBuPvtp9fPD7A8yO66JUw8iqQWFIhERcVsV+xAFni8h/61ejkDU2fswqzYFEdlnunoQSZ0pFImIiFuy2Q2e/WyfIxAFXLRhXdSNE7a2ACSZvqfDg7uI7HMH3l4mld1LnTVqKPrd734HwMCBAxkzZkxjfrSIiHiY8n2I/HJs2BZ2Jr2kAwCtTceJv3MTe1pEqA+R1JtGDUXz5s1zbPFx88038+KLLzJo0KBqrhIRkeaorL+QX44N443OHLncGYAETtHmtjWcaBvlNE6krhq9JN8wDAzDYN26ddx8881MmjSpsacgIiIeIMYcgF+OHdMbHR2BKJ4zdJz2LSfaRzmNE6kPjXqnKD09HYDTp0+zevVqvv32W1atWtWYUxARETdU1WatHXz88fp3Bw5e7gJAHBl0mrqSY51KA5GJ0ioz9SGS+tLgG8JWp7i4GD8/P1dOoUraEFZEpHFULLkHaIkPeX9rS1pB6R2iWDLpOmU5R2+IBq72IVpwf2+V3YsTt94QtjruGIhERKRxVCy5B/DNtXH+X205WHwlEJnOMviub0lpE+0Yoz5E0hDqHIqeeOIJfv/739fHXEREpBmpWHIP4JNrx+df7ThQ3A2AaLL45t0Mutx1r/oQSYOrcyh66aWXOHfuHK+//jpeXtpKTURErk/5knsAnzwbfv9KYn9xdwCiyKLHpC/I7X+r+hBJo6hzigkKCmLRokVMnz4dq9V6Xdd89tlndf1YERHxcOVL6a8Goh5AaSDqNelLvu8Wo5J7aTR1DkXffvstERERfPbZZ4wdOxaLxXLNsZs3b2bo0KFMmzatrh8rIiIerqyU3jfXhu/r7dhvLQ1EkZyj14QvONIt2mmcSEOrcygaMGAAGzZsIDExkfXr1zNs2DAyMzOdxhw4cIBp06YxZMgQNmzYgIsL3kRExA30T4qgleGD9+sdOHDlkVkk57hpwucc6RGDCYhXyb00onpZBNS5c2c2bdpEt27d+O677xgyZAhHjx7lzJkzPPTQQ/Ts2ZNly5ZhGAYDBgxg5cqV9fGxIiLiwS6eyMfytyQOXu4KQDRnuXHSFxy+EogAnpncVQuqpdHUW0l+QkIC69atY8qUKaxfv54BAwZQUFBAUVERhmHQs2dPnnvuOSZPnlxfHykiIh7qXHoet3TPZHdhJ6C0D1G3W5dzpEvpIzOV3Isr1GufIrPZzPTp01m/fj0XLlzAMAzatWvH888/z913312fHyUiIh6kfMdqv/Ml/Gayjb2FpZu7xpsy+Ob9bHJ6T1bJvbhUvYQiwzB45513ePbZZx1beZhMJgzDIC8vj06dOtXHx4iIiAcq37E68HwJ1kXdHLvdtzSdYfXHF+k4tYeLZylSD2uKPvroI7p3784DDzzA0aNHCQgI4IknnuDUqVNMnDiRrKwsRo4cybffflsf8xUREQ9S1rE6I6eIoHOXKVrYvVwgOsmf/5ZOx6ndXDxLkVJ1DkV33HEH+/fvx8vLiwcffJDDhw/z4osvEhcXxyeffMKPfvQjLBYLEydO5P3336+POYuIiAco37E6+OxlCt7sxTFbewASTSdIun01f7EUYbOrIlncQ71Un02ZMoXdu3fz+uuvk5CQ4Dju7e3NokWL+PWvf01xcTH33Xcff/vb3+rjI0VExM2VdawOPV3Mpbf6cNyWBEBr0zES71jLyXaRZOQUsS39gotnKlKqzmuKNmzYwKBBg35wzB//+EdiY2N5/PHHmTNnDpmZmbzwwgt1/WgREXFjWblFhB8vJvP9gZw1SqvIkkzfE3/XJk63iXAaJ+IO6nynqLpAVObRRx9l4cKFeHt7awNZEZFmoCjlEqffH+IIRJ28DhBz3xanQATqWC3uo15L8qvzox/9iKioKO68887G/FgREWlg5UvuY8wBeO+08MhDCVwwWgDQ1XsPQTPSyIwNd1xjorQfkTpWi7to1FAEMGHCBL755pvG/lgREWkg5UvuAWL3FLH/i9HkEgpAL5+deM08zLmoMMc16lgt7qheFlrX1MCBA13xsSIiUs/Kl9wDxO0qYu8XYx2BaHDgdp77LAD/9lFO18WFBbDg/t7qWC1upUZ3il5++WVmzZpFYGBgvU1g+/btZGdnM378+Hp7TxERaXjlS+4BWm4rZOfqiRRR+h0x0G8j/r+8wIQxk5gwpovT4zV1rBZ3VKM7RY899hjt2rXjL3/5C5cuXarTB2/YsIFJkyYxcOBAtm/fXqf3EhGRxldWcg+QuKGQ7atvdQSiIQGrufRfmXxveLEt/QLeXiaS20cy5caWJLePVCASt1SjUPTUU09hsVh49NFHiY+P5/bbb+ejjz4iKyur2msvX77M9u3b+e1vf0v79u0ZNmwYX375Jf369WPq1Km1nb+IiLhIWSl9m2+sbNo4jcv4ATA8aAVZP7tIYXCA0zgRd2cyDKNGrURPnz7NU089xeLFi7HZbJhMpWk/MTGRXr16ER0dTUREBP7+/ly8eJELFy5w9OhRvvvuO4qLi4HSvdLat2/Pc88957YbxVosFsLCwsjJySE0NNTV0xERcTubvz/Pk7euZ+2+qY5jo82fc+ynJRT7+TqOvffQQJLbR7pghtIc1eX7u0Zrijp37sywYcN48803mT9/Pq+99hr//ve/OXXqFCdOnODEiROOkFReWe7y8fFh4sSJ/OxnP2Ps2LFVjhUREfdnGLDiv484BaIJER+x/ye+2L1LA5FK7sXT1OhOkZeXF3FxcZw5c8ZxLCUlBV9fXzZs2MDWrVs5c+YM586do6ioiMjISKKjo+natStDhw5l8ODBmM3mBvmD1DfdKRIRuap8H6LoYH8+/PER/rLxaiXxlLjFpM4wg1fpqoyy/+RVhZk0tka7U+Tj44Pdbnc61q9fPxISEjh16hSPPPJIjT5cRETcX/k+RIbNoNWbAWw6N8px/skBn7D61hiwWB3H4sICeGZyVwUi8Sg1CkVRUVGcO3eOwsJCp7L8ikFJRESahrI+RAZgumwn7o0wNuUMBcALG8+OXsb/rJhWqaO1Su7FE9Wo+qxPnz7Y7XZ+85vfYLVaq79AREQ8Vvk+RN5FdiL+GcPWK4HIl2Ju7bWIL0aEYrMbKrmXJqFGoWj27NkYhsGCBQuIjo5m4sSJABQXF3Pw4EFqWMgmIiJurKwPkZ/FRtA/EtmZPwCAQAoYO+Addo2LIyOniG3pF1w8U5H6UaNQNHbsWBYtWkRERAR5eXl89dVXmEwmLl68SNeuXQkNDWXw4MHMnj2bN954g127dnH58uWGmruIiDSgrNwigs9dxv76Deyx3ghAKDkMH7aE3cNjncaJNAU17lMEUFRUxIoVK1i3bh1//vOfK79puVJ7Hx8funbtyk033UTv3r256aab6NWrFyEhIXWbeQNT9ZmINHcfLz7Af88I5rQ9EYAYztJj/Fcc6RntNE59iMSd1OX7u1ahqLyyMv20tDR27tzJrl272LVrFzt37uT77793eqRWFpa8vLzc/g6SQpGINCcVF0p777Qw8e5Qsu2lYaeNKZ3W09dzosPV8FPWh2jD4yO1hkjcRqOV5FelZcuW2O12oqKiGDNmDGPGjHGcy8vLIzU11RGSdu3axf79+ykpKanrx4qISD0pX3IPkJBSwO5vxpFHaV+5G7z3EnrPd5xo6RyIAJ6Z3FWBSJqMOoeikydPUlBQUOW5kJAQhgwZwpAhQxzHiouL2bNnT10/VkRE6kH5knuA1usK2br5VorxByA5MIUn/uPP/N2xkHN17ZD6EElTVOdQBBAUFHTdY/38/Ojdu3d9fKyIiNRB+ZJ7gLZfWVmXNh3jSg3OkMDVeM/JZ+KEiUyc0E19iKTJq5dQJCIinqes5N4wIOlDG2uPTnecGx36BccevEyx3Zdt6RdIbh+pxdTS5NWoJN9drFu3jsmTJ5OQkIDJZOKTTz5xOm8YBvPmzSMhIYHAwECGDx/O3r17XTNZERE3lZVbBDaD1gv9WHv0VsfxidEfcPi/bI6d7lVyL82FR4ai/Px8evXqxauvvlrl+Zdeeok///nPvPrqq2zfvp24uDhGjx5Nbm5uI89URMR9hdm9iP5HCzacG+04NrXN2+z5cSCGt7fjWIw5wBXTE2l0Hvn4bPz48YwfP77Kc4Zh8Morr/D0008zfXrpreA333yT2NhYFi9ezM9+9rPGnKqIiFuoWHLfDl+eGHGJHXmDgdJtOyb0eIddE642ZSwrue+fFOGiWYs0Lo8MRT8kPT2dzMxMp9YA/v7+DBs2jE2bNl0zFFmtVqf93CwWS4PPVUSkMVQsuQ89U0zu4l4cs3UBwIyFm4d8SOpg50AEKrmX5sUjH5/9kMzMTABiY2OdjsfGxjrOVWX+/PmEhYU5fhITExt0niIijaGs5L4sEEUfLCTznUEcs7UDIN6Uwf89v5MLE9o4XRcXFsCC+3ur5F6alSZ3p6hM+a1GoPSxWsVj5T355JPMnTvX8dpisSgYiYhHq1hy32pHAd99e7UpYwevQ9zwQCr3PnkH94JK7qXZa3KhKC4uDii9YxQff/W/cLKysirdPSrP398ff3//Bp+fiEhjKSu5B0j6ppANKVMpobSi7EbfHZhmHGF3tFkl9yJXNLnHZ0lJScTFxbFy5UrHseLiYtauXcugQYNcODMRkcaVlXulB9F/SliTcrsjEN0cuArrz45zIdrsGCciHnqnKC8vjyNHjjhep6enk5qaSkREBK1bt2bOnDm8+OKLdOzYkY4dO/Liiy8SFBTEvffe68JZi4g0nIrVZf2TImjh40viGwGsOX+LY9y4Fks5/GMTJb5Xy+xVci9SyiND0Y4dOxgxYoTjddlaoJkzZ7Jo0SIee+wxCgsLeeSRR7h48SIDBgxgxYoVmM1mV01ZRKTBVKwuA2hl8sHrnzFsvHg1EE1p8w677gzHdGWtkEruRZyZDMMwqh/W/FgsFsLCwsjJySE0NNTV0xERqVLFDV0BzJnFFL7bje9LOgHgTxFjb3yP78bGOMaULaFWhZk0NXX5/vbIO0UiIlK5ugwg5mABxz+9mSyjtOgkgmz+8Ogu3ohorV3uRaqhUCQi4qHKV5cBJG4pYNfa8eQTAkCS6Sgtp2+k28MT2JAUoZJ7kWooFImIeKjyVWNJX1pZt3s6dkr3LLvRdwem+49wMiaCrNwivL1MKrkXqYZCkYiIh4oxB2DYDNq+682ajOmO48OCV3L2xxYKg82OcSJSPYUiEREP1SU4kLh/RrEud6Dj2KToD9j3Iz9sPgGqLhOpIYUiEREPdHzHOSYPzWF3YWkg8uEyEzu/S+qUKDCZtKGrSC0oFImIeIDyzRlzV53j0d8kcNbeAYAWXGD06C/Y2jvaMV7VZSI1p1AkIuLmyjdnbLOmgK1bJ2OldJ1QR5+jfP6hlfaT71d1mUgdKRSJiLixsuaMdrtBu49srDl6h+NcH9+t/PaDIDpN6QGg6jKROmpyG8KKiDQVZc0ZTUV2Wv4rmDVHpzjOjQ79nLxHTvP7fVnY7NqYQKQ+KBSJiLipbekXsBy2ELCgLZsvlu73aMLOlNbvcuhnBkUB/mTkFLEt/YKLZyrSNOjxmYiIm9r1n6NkL0p2bNkRTB4j+3xA6qgYp3HlmziKSO0pFImIuFj5yrKyRdJLHt3J3L/0cCyoTjSdoMOE1aR1j6l0vZozitQPhSIRERcqX1kGYNgMbvjQixXHJjjG9PbdBvcd5WhslNO1as4oUr8UikREXKSssqxsmbRPno0Wb0axIm+QY8x9rb5mx235WAPMTteqOaNI/dNCaxERFyirLCsLRGGniuCfN7DjSiDypoQ7O7/LovTRvPLTZOLCnB+RxYUFsOD+3mrOKFKPdKdIRMQFtqVfcDwya7U9n72rRnOJFkBph+rkwZ+ydUgM249fZFz3eEZ3jVNzRpEGplAkIuICWblFGHaD9p9cZu3h27DjDUAHr0PETtvG3g4xjnEA3l4mNWcUaWAKRSIiLhBa4kXCayGszhnuODY4cA2WGec41aKF45gqy0Qaj0KRiEgDq1hyH51ZzJwxeaQVDHeMmRy/hD33BWH3DgJUWSbiCgpFIiINqGLJfavt+exbNYqLlC6QNmNhWN+PSLvlav8hVZaJuIZCkYhIAylfcm/YDTp8WsyaQ1fXD3X0/p55L2fwt8LWkHO1K3VcWADPTO6qyjKRRqZQJCLSAMqX3PsW2Ih+y8yqnEmO84MC1xLwSA53/fdk7gJVlom4AYUiEZEGUFZyH3GsCMuHPdls6+g4Nyl+CXvvC8Lu7c229Askt49UZZmIG1AoEhFpAFm5RSStzWfHlvHkUdqN2oyFoX0/Yne59UPazFXEfSgUiYjUUcXqst4tw/nyJ0dYs+tOx5hOXvuJmZrCno7OG7qq5F7EfSgUiYjUQcXqsuDsYvwWtyG1cJhjzAjz12TNyOWk+Wr/IZXci7gfhSIRkVqquKFrwncFfP/1zWQZcQD4Usz4Du+TNi0cwyvQcZ1K7kXckzaEFRGphfLVZYbdoP2nVrYvn+oIRPGm09w66QN+9tEo4loEOV2rzVxF3JPuFImI1EJZdZmfxUaLd1qwKvdmx7m+fluw33OcHXHh/DrYjw2Pj1TJvYgHUCgSEamFrNwiYvcXcObzARy2t3YcnxD7IQfv86XEN8QxTpu5ingGhSIRkWpUrC7r1zaCXc8eIXXZrRTjD0A4FxjUfxl7R0Q7XavqMhHPoVAkIvIDKlaX+eaVELu4BRsvXq0u6+mzi8Db97O3zdVApOoyEc+jUCQicg0Vq8tiDhaQtawvG+1JjjHjopZy9D7ICQhzHFN1mYhnUvWZiEgVnKrLDGj/ZQFpn0zm+JVAFMYl7hz0Dr/4diARsaFO16q6TMQz6U6RiEgVyqrL/C0lRL4bzirLRMe5bj5phE7fzdakFsxRdZlIk6FQJCJShazcIuJ3F3By+UAO2RMdx8dGfMrR++2cCQx3jFN1mUjToFAkIs1exeqyvq1bsGHuYbavnobtyr8mw7nI4D6fsmeUqstEmiqFIhFp1ipWl4WcsxKwJJGUguGOMTf67sD/tkPsUXWZSJOmUCQizVbF6rI2W/LYu24k543S8GPCzsSEDzlwtz8XfVVdJtLUqfpMRJql8tVlXsUG7d42WLf2LkcgijOd4bYx7/Hzr24mKirE6VpVl4k0TbpTJCLNUll1WdTRQvKWdmV1SVfHuUGBa8m/5yzbo8OZq+oykWZDoUhEmryKC6n7J0VwNqeQDp8VsnHfRIoIBMAPK2Pbf8DuaaEY3sGAqstEmhOFIhFp0ioupAZoazXBm1GsvXi741hHr4O0HL+VtO7O4UfVZSLNh0KRiDRZFRdSA7TZlMeeDVcXUwOMjfyEY/faSQ+6GohUXSbS/CgUiUiTVH4hNYBPoZ1W7/my9txdjjExnKVP8nL2D41yCk6qLhNpnhSKRKRJKltIDRC3P59zX/Rmra2D4/ygwLUU3pXJ2PsGcXH7CafHa3FhATwzuauqy0SaGYUiEfF4VS2kzsotwnTZTruPbKw9Pt3RmTqQAkZ1+pC0KS3AK4S2UUGqLhMRQKFIRDxcVQup48MCmEQQAX9LYtXl7o7j3XzSaDE5jbROV9cOxZgDVF0mIoBCkYh4sKoWUht2g+BFl3ju0GCslFaOeVPCuISPOHSnPyf9WwBaSC0ilSkUiYhHqriQGiD8dCF82JZvi/o6jrX3Okzb0ZvYc2OU45gWUotIVRSKRMQjlV9IbdgNOqwoYNt348nDDJTuWzY2+hPG/r097x9uBVpILSLVUCgSEY+UlVsacsIyrPh9GM+qgkmOc61MJ+g6dDX7B0bxcIcoNkzvqYXUIlIthSIRcXtVVZdFB/vT/qt8tqWNI49Qx9hbwr4g8+5CDoaXPi7TQmoRuV4KRSLi1qqqLmtvsWNbksDai3c6jsWZznBT/5XsGx4FBGohtYjUmEKRiLititVlht2g01eFbNkzzrF2COCWsC85e1c++1qU3h3SQmoRqQ2FIhFxSxWry8JPFeH1USLfFPV3jEkwneaJh/awuK0/uTlX69C0kFpEakOhSETckqO6zGan4+dWNh8YRz4hjvOjwr8g464i+v5mOI8kRWghtYjUmUKRiLilrNwiYg7nU/B5Z74p7uU43tJ0ku6DV3FgcBQQQFZukRZSi0i98HL1BBrCvHnzMJlMTj9xcXGunpaIXIPNbrD5+/N8mnqazd+fJ/+SlW8fPsSuj6ext1wgGh3xGWEPb7sSiErFmANcMWURaYKa7J2ibt268c033zhee3t7u3A2InItFavLWu3KI+Pbvhy1jXCMae91mKThmznULxKubN2h6jIRqW9NNhT5+Pjo7pCImytfXeafe5mE//izJvsux3lfihmd8ClHbvfhcODVx2OqLhORhtAkH58BHD58mISEBJKSkrj77rs5evToD463Wq1YLBanHxFpOGXVZXYD2q3J49KCgazJHu8439N3F+PuXsqsr4YQERfqdG1cWAAL7u+t6jIRqVdN8k7RgAEDeOutt+jUqRNnz57l+eefZ9CgQezdu5fIyKoXY86fP59nn322kWcq0nxtS79A0d6LxCxNYHXBRMfxEHIZ3mEZe6eYSfMJoUWwHxseH6nqMhFpcCbDMIzqh3m2/Px82rdvz2OPPcbcuXOrHGO1WrFarY7XFouFxMREcnJyCA0NrfIaEbk+Fbfp6BVt5onx63h902CKCHSMSw5cR8m002QlXv0799e7b2TKjS1dMW0R8UAWi4WwsLBafX83yTtFFQUHB9OjRw8OHz58zTH+/v74+/s34qxEmoeKC6kTU/I4s7oPR22jHGPiTae5sc837B0RicnL+V9iqi4TkcbSLEKR1Wpl//793Hzzza6eikizUn4hdfD5YiI+MrPh4tVHZd6UMDr6M07cbmdfaBTlH4ipukxEGluTDEWPPvookydPpnXr1mRlZfH8889jsViYOXOmq6cm0mw4tumw2en4VSE79o5mHy0c53v4ptJq8n72d6x8e1vVZSLiCk0yFJ06dYp77rmH7OxsoqOjGThwIFu2bKFNmzaunppIs7Et/QJe67IJ/KY735R0cxwP5yKDb/iSvZPM7PMO5VejOrFk+wnH4zXQ3mUi4hpNMhQtWbLE1VMQaVYqLqRuXWjwp4n72HTiLqdxw0O/5tL0HPbEhjuOtY0KUnWZiLiFJhmKRKTxlF9Ibbpsp+PnRWw9NAYLQx1jOnvvo+WwFL7vFwEEO10fYw7Q3mUi4hYUikSk1sovpG69I5eMNb1ZaevkOB/ORQZ3+pL9k8x87+u8YFoLqUXE3SgUiUitlC2kDj9VSNBnUay3XK0qM2FnZIuvsN5TzF5zeKVrtZBaRNyRQpGI1MraracI/r88dp2ehJWrvYR6+KQSOWoPR3q1APy0kFpEPIZCkYj8oIqLqPu0CuftWdt46t/tyTKmOMZFk0X/bivYOz4Ui/fV0nstpBYRT6FQJCLXVFU36uy1PThwOdkxxg8rI+M+58RU2BPWotJ7aCG1iHgKhSKRZq7inaCyuzjlF1FHnijE/7NoNuRNdLp2mHkV1gln2d+26gaMWkgtIp5EoUikGat4JwggPiyA307swnNf7CfwYjFxn/qx4eytXMbPMaaL9x66jE3jwfkjmLW4EBNQfmdpLaQWEU9kMgzDqH5Y81OXXXZFPEH5O0HlmQCfQhttP7/M1qOjyCXMcS6GTPp1/4Z9Y0Ox+3jz3kMDySksrjJYaSG1iLhCXb6/dadIpBly7EtW+QQdVhawJ+1mvjESHIeDyGdYy684fquJPaFX1w1l5RYx5caWjO4ap4XUIuLxFIpEmriq1gxtS7/gdGfHMKDdllxObbqJb0o6O457YWNEi+VcmpzLvnhzpfeOMZeW4mshtYg0BQpFIk3YtdYMTege53jdKi2XgtXtWVPkvIh6UNA6TGNPcqRTOOAciLSIWkSaIoUikSbqWmuGMnOKeGPjMeIO5WFakcDGfOcw1N3nO2JvTuNI/wggXIuoRaTZUCgSaYKuuWYIiDieT9BXkWzMGY+Bl+N4G690uty4gf23hJPnFXGlCq0rz32xT92oRaRZUCgSaYIqrhkCCMssJOKLYDZkT6MEX8fxeNMZbrphNQfHhbDfL8LpTtC47vGM7a5F1CLSPCgUiTRBWblXA5E520rsFz5szJxIEYGO4xGc546+G9g71o+9JeGO4xXvBGkRtYg0FwpFIh6uquqyGHMAIdlW4r7wYVPmOPYQ5BhvxsLgxK85MdGLmY8Od1Sj6U6QiDR3CkUiHqyq6rIkK3T4xp+je8axt1wYCqCQYbHLyZhUwoGoIEf1mO4EiYiUUigS8VAVq8tCsouI+9KXTRmjWFMhDA2NWcG5cVYOxAdjurJdh6rHREScKRSJeKDy1WWhWUXELPdlc8Y49hLsGBNAIfd2Ws/J0QUcDPGl7K+7qsdERKqmUCTigbalX8C69wLtVgSz6dxEdhPgOOdPEUOjvyZ7vJWf/u8tWjMkInKdFIpE3FzFhdTmAxZefvgkaaemYSv3V7h8GDoUHwz4kJVbpDVDIiLXSaFIxI2VX0idsC8XVsezJe9mDJIcY0LIZVDcN2SNK+ZQbAjl/1qX7U0mIiLVUygScbGqSuq9vUws35PBw2+l0HZHLtFb2rK50Hk7jnAuMDBxFafGwcGIQLiygBq0N5mISG0oFIm40LU2bH1qZEfemLOFwB3dWFvSzemaGDLp224N56cGc8A3sOJbam8yEZFaUigScZGqNmz1z7tM2Mf5/Pzpzpw27nQan2g6TvfOGzk8Joi9gaW71v9qVCeWbD+hvclEROqBQpFIA6vq8RjgtGFr2NlCYlb4su3McA4R7nR9N580EnulcWhYKPt8w5zOtY0KYsPjI1VdJiJSDxSKRBrQtR6P3d0vkYycIlrtzsW0MYotOWNIK7dJK8DAwPUEJR/nSJ9w9nu1qPL9Y8wBqi4TEaknCkUiDaSqx2MA587l88XjKZh3d2Xj5V5O5/ywMjh8FdYRFzndKQxoQVX3fLSQWkSk/ikUidTR9TweAzCfLyJhJaSdGMRKw3m9TwTn6ZewlrOjSzgaFwxcfUxmAqf30UJqEZGGoVAkUgfVPR4DaLknF99NEWy5eAt7cO4b1Ml7P+1v2MmRkUEcCPIH/IGrd4J+O7Erz32xTwupRUQagckwjIp39wWwWCyEhYWRk5NDaGioq6cjbuhaj8dMgG/BZdqtLuTEwR7sv9y9wnk7ycHr8O9/iu/7huPlZaryTtCC+3szrnv8NfsYiYhIZXX5/tadIpFaKL8ha3lxR/IIWRfM9nPDOVyhiiyMSwyIXcOFkVZOtw4BWjD3OkrqtZBaRKRxKBSJ1MK29AuOIONjtdFufR7n9nRiq3VipbFdffbQpnMaR4cHcjDED/B1PB6bPbIDs0d20J0gERE3oFAkUo2qHl9l5RYRfzCX4E3B7Mwawvc4V4EFUEhy+Fpsyec53j2MfV7OC6fBeaG07gSJiLieQpHID6i4kDoop5jOm0pIP9SF74rurjS+vddhOrVP4fgIX462COBXo/qr47SIiIdQKBK5hrKF1Ha7QdJOC8aOaLbljGQ/zvuN+VPEgND1+PQ+y5F+4ezzMmOitApNj8dERDyHQpE0e9fqM/TKn7bQcSXsP9OXtUZipeu6+uyhTfvdnBjmx/EWAZQ1WtTjMRERz6RQJM1axcdj5uwi2m8xOPb9DXxXNK3S+HAu0Dd6A0UDcznZNZyxo/qyZPsJ8vR4TETE4ykUSbNV9njMp6CETpvysexvzY6Cseyp8NfCCxt9A7fQoks63w8J4XCgL1wpt9eGrCIiTYdCkTRp12p8mH+xiH/MXk+rXZHssgzgCCGVru3qs4fWbfeQMcSbs7FBnKXypqzakFVEpOlQKBKP9kPdnis+GvMuttEjrQifg3GsPNULC3dWer8E0yl6xG3DMrCIM53C2I+5ys/VhqwiIk2PQpF4rGvtO/bM5K4A/PydnXhbbbTfkYd9bwSpFwfxaRV3e1pwnptabIVeFzjaN5QD3lf3IANtyCoi0lxo77Nr0N5n7u2H9h3zy7tMp51WLu2N4jtLP3Kp/PsL4xI3hW/Bp1s26f3NlPhV/d8Hv6piG454LaQWEXFb2vtMmqxrlctX3HfMfL6IlluKuXS0FakF/ThUYTd6gBBy6R26hYCuZzk6wExOZBAX81tUClaAtuEQEWmGFIrEbV3r8djd/RI5c7GQhCN5hH3nzdnT7Uiz3sgevCu9RxgXuTFsO/6ds0gfEMzxID+48ght6o0JLNx47Loej2khtYhI06dQJG6pqsdjvgUlBG/IZNmfi7Cd78WWKhoqAsSZMugWmQLdLnGst5ljfj5QxVqi0V3j6J8UUSl4qc+QiEjzpFAkbsdmNxyPx8LPFhK3pYSLJ1qRVtCHIxW22CjTzusIHWJ3Y+2Vz7EeYRzx8qKqIATOlWPeXiZGd43T4zEREVEoEvezLf2C485NzD4rXx+4r9IYP6z0DNhJVOvjnO8NWW3MHMQP8MMEhAX5klNwGaj+0Zj6DImICCgUiRvKyr36KOtE3yB8txVzGT9iTZl0bbEL347nOdEniHNmf7IxVxl6fj+9B4AejYmIyHVTKBK3E2O+WjlWZPZjZK8PyUuEU13MHC33WKyqcvmKoUePxkRE5HopFInb6Z8UQXxYAJk5RRjAgXFhTudrUi6vR2MiInK9FIrE7Xh7mXhmcld+/s5OlcuLiEij8XL1BESqMq57PAvu701cmHMTxriwABbc31trgkREpN7pTpG4rXHd47UmSEREGo1Ckbg1rQkSEZHGosdnIiIiIigUiYiIiAAKRSIiIiJAEw9Ff//730lKSiIgIIA+ffqwfv16V09JRERE3FSTDUXvv/8+c+bM4emnn2bXrl3cfPPNjB8/nhMnTrh6aiIiIuKGTIZhGNUP8zwDBgygd+/eLFiwwHGsS5cuTJ06lfnz51d7vcViISwsjJycHEJDQxtyqiIiIlJP6vL93STvFBUXF5OSksKYMWOcjo8ZM4ZNmzZVeY3VasVisTj9iIiISPPRJENRdnY2NpuN2NhYp+OxsbFkZmZWec38+fMJCwtz/CQmJjbGVEVERMRNNMlQVMZkcu58bBhGpWNlnnzySXJychw/J0+ebIwpioiIiJtokh2to6Ki8Pb2rnRXKCsrq9LdozL+/v74+/s7XpcttdJjNBEREc9R9r1dmyXTTTIU+fn50adPH1auXMm0adMcx1euXMmUKVOu6z3Onz8PoMdoIiIiHuj8+fOEhYXV6JomGYoA5s6dy4wZM+jbty/Jycm89tprnDhxgocffvi6ro+IiADgxIkTNf6HKvXLYrGQmJjIyZMnVQnoYvpduBf9PtyHfhfuIycnh9atWzu+x2uiyYaiu+66i/Pnz/O73/2OjIwMunfvzpdffkmbNm2u63ovr9LlVmFhYfo/uJsIDQ3V78JN6HfhXvT7cB/6XbiPsu/xmmiyoQjgkUce4ZFHHnH1NERERMQDNOnqMxEREZHrpVB0Df7+/jzzzDNOFWniGvpduA/9LtyLfh/uQ78L91GX30WT3eZDREREpCZ0p0hEREQEhSIRERERQKFIREREBFAoEhEREQEUiqr097//naSkJAICAujTpw/r16939ZSapXXr1jF58mQSEhIwmUx88sknrp5SszV//nz69euH2WwmJiaGqVOncvDgQVdPq1lasGABPXv2dDQJTE5O5quvvnL1tITSvycmk4k5c+a4eirN0rx58zCZTE4/cXFxNXoPhaIK3n//febMmcPTTz/Nrl27uPnmmxk/fjwnTpxw9dSanfz8fHr16sWrr77q6qk0e2vXrmXWrFls2bKFlStXUlJSwpgxY8jPz3f11JqdVq1a8fvf/54dO3awY8cORo4cyZQpU9i7d6+rp9asbd++nddee42ePXu6eirNWrdu3cjIyHD87N69u0bXqyS/ggEDBtC7d28WLFjgONalSxemTp3K/PnzXTiz5s1kMrF06VKmTp3q6qkIcO7cOWJiYli7di1Dhw519XSavYiICP74xz/y4IMPunoqzVJeXh69e/fm73//O88//zw33ngjr7zyiqun1ezMmzePTz75hNTU1Fq/h+4UlVNcXExKSgpjxoxxOj5mzBg2bdrkolmJuJ+cnByAWm24KPXHZrOxZMkS8vPzSU5OdvV0mq1Zs2YxceJERo0a5eqpNHuHDx8mISGBpKQk7r77bo4ePVqj65v03mc1lZ2djc1mIzY21ul4bGwsmZmZLpqViHsxDIO5c+cyZMgQunfv7urpNEu7d+8mOTmZoqIiQkJCWLp0KV27dnX1tJqlJUuWkJKSwo4dO1w9lWZvwIABvPXWW3Tq1ImzZ8/y/PPPM2jQIPbu3UtkZOR1vYdCURVMJpPTa8MwKh0Taa5mz55NWloaGzZscPVUmq3OnTuTmprKpUuX+Oijj5g5cyZr165VMGpkJ0+e5Je//CUrVqwgICDA1dNp9saPH+/43z169CA5OZn27dvz5ptvMnfu3Ot6D4WicqKiovD29q50VygrK6vS3SOR5ugXv/gFy5YtY926dbRq1crV02m2/Pz86NChAwB9+/Zl+/bt/PWvf+Wf//yni2fWvKSkpJCVlUWfPn0cx2w2G+vWrePVV1/FarXi7e3twhk2b8HBwfTo0YPDhw9f9zVaU1SOn58fffr0YeXKlU7HV65cyaBBg1w0KxHXMwyD2bNn8/HHH7Nq1SqSkpJcPSUpxzAMrFarq6fR7Nxyyy3s3r2b1NRUx0/fvn257777SE1NVSByMavVyv79+4mPj7/ua3SnqIK5c+cyY8YM+vbtS3JyMq+99honTpzg4YcfdvXUmp28vDyOHDnieJ2enk5qaioRERG0bt3ahTNrfmbNmsXixYv59NNPMZvNjrupYWFhBAYGunh2zctTTz3F+PHjSUxMJDc3lyVLlrBmzRqWL1/u6qk1O2azudK6uuDgYCIjI7XezgUeffRRJk+eTOvWrcnKyuL555/HYrEwc+bM634PhaIK7rrrLs6fP8/vfvc7MjIy6N69O19++SVt2rRx9dSanR07djBixAjH67JnwjNnzmTRokUumlXzVNaiYvjw4U7HFy5cyAMPPND4E2rGzp49y4wZM8jIyCAsLIyePXuyfPlyRo8e7eqpibjUqVOnuOeee8jOziY6OpqBAweyZcuWGn1/q0+RiIiICFpTJCIiIgIoFImIiIgACkUiIiIigEKRiIiICKBQJCIiIgIoFImIiIgACkUiIiIigEKRiIiICKBQJCIiIgIoFImIiIgACkUiIiIigEKRiIiICKBQJCIiIgIoFIlIE7dx40ZMJhMmk4kPPvigyjFbt24lJCQEk8nEY4891sgzFBF3YTIMw3D1JEREGtKUKVNYtmwZN9xwA3v27MHb29tx7uDBgwwZMoTs7GxmzpzJwoULMZlMLpytiLiK7hSJSJP3+9//Hm9vbw4cOMA777zjOH7mzBnGjh1LdnY2kyZN4l//+pcCkUgzpjtFItIs/PSnP+WNN94gKSmJgwcPkp+fz9ChQ9m9ezdDhgxhxYoVBAYGunqaIuJCCkUi0iycPn2ajh07UlhYyF/+8heWLl3KunXr6NGjB+vWrSM8PNzVUxQRF1MoEpFm44knnuAPf/iD43Xbtm3ZuHEjCQkJLpyViLgLhSIRaTYyMjJo1aoVdrudiIgItmzZQseOHV09LRFxE1poLSLNQklJCf/1X/+F3W4HoKCgQGuIRMSJQpGINHmGYfDTn/6Uzz//nOjoaJKSkigqKuKZZ55x9dRExI3o8ZmINHm/+c1vePnllwkJCWHVqlUcOXKEe++9F29vb9LS0ujataurpygibkB3ikSkSXv55Zd5+eWX8fX15aOPPqJfv37cfffd9OzZE5vNxpNPPunqKYqIm1AoEpEm66233uKxxx7DZDKxaNEixowZA4DJZOK5554DYNmyZWzcuNGV0xQRN6HHZyLSJH355ZdMmTKFkpIS/vKXvzBnzpxKYwYOHMjWrVsZPHgwGzZsaPxJiohb0Z0iEWlyNm/ezB133EFJSQmPP/54lYEI4IUXXgBKN4399NNPG3GGIuKOdKdIREREBN0pEhEREQEUikREREQAhSIRERERQKFIREREBFAoEhEREQEUikREREQAhSIRERERQKFIREREBFAoEhEREQEUikREREQAhSIRERERQKFIREREBFAoEhEREQHg/wO2qaahKhMy3AAAAABJRU5ErkJggg==\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Решение\n",
    "#1\n",
    "import numpy as np\n",
    "from scipy.optimize import curve_fit\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#Добавим шума в данные, сделанные по функции f(x,b) с коэффициентами b = (0.25, 0.75)\n",
    "beta = (0.25, 0.75)\n",
    "\n",
    "\n",
    "def f(x, b0, b1):\n",
    "    return b0 + b1 * x\n",
    "\n",
    "\n",
    "#зададим массив точек xi\n",
    "xdata = np.linspace(0, 5, 50)\n",
    "#создаем теоретически правильные значения точек yi (без шума)\n",
    "y = f(xdata, *beta)\n",
    "#зашумляем эти данные\n",
    "ydata = y + 0.05 * np.random.randn(len(xdata))\n",
    "beta_opt, beta_cov = curve_fit(f, xdata, ydata)\n",
    "print(beta_opt)\n",
    "#Вычислим линейное отклонение\n",
    "lin_dev = sum(beta_cov[0])\n",
    "print(lin_dev)\n",
    "\n",
    "#Вычислим квадратичное отклонение\n",
    "residuals = ydata - f(xdata, *beta_opt)\n",
    "fres = sum(residuals ** 2)\n",
    "print(fres)\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(xdata, ydata)\n",
    "ax.plot(xdata, y, 'r', lw=2)\n",
    "ax.plot(xdata, f(xdata, *beta_opt), 'b', lw=2)\n",
    "ax.set_xlim(0, 5)\n",
    "ax.set_xlabel(r\"$x$\", fontsize=18)\n",
    "ax.set_ylabel(r\"$f(x, \\beta)$\", fontsize=18)\n",
    "plt.show()\n",
    "#Решение\n",
    "#2\n",
    "#Добавим шума в данные, сделанные по функции f(x,b) с коэффициентами b = (0.25, 0.75, 0.5)\n",
    "beta = (0.25, 0.75, 0.5)\n",
    "\n",
    "\n",
    "def f(x, b0, b1, b2):\n",
    "    return b0 + b1 * x + b2 * x * x\n",
    "\n",
    "\n",
    "#зададим массив точек xi\n",
    "xdata = np.linspace(0, 5, 50)\n",
    "#cоздаем теоретически правильные значения точек yi (без шума)\n",
    "y = f(xdata, *beta)\n",
    "#зашумляем эти данные\n",
    "ydata = y + 0.05 * np.random.randn(len(xdata))\n",
    "beta_opt, beta_cov = curve_fit(f, xdata, ydata)\n",
    "print(lin_dev)\n",
    "\n",
    "#Вычислим квадратичное отклонение\n",
    "residuals = ydata - f(xdata, *beta_opt)\n",
    "fres = sum(residuals ** 2)\n",
    "print(fres)\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(xdata, ydata)\n",
    "ax.plot(xdata, y, 'r', lw=2)\n",
    "ax.set_xlim(0, 5)\n",
    "ax.set_xlabel(r\"$x$\", fontsize=18)\n",
    "ax.set_ylabel(r\"$f(x, \\beta)$\", fontsize=18)\n",
    "plt.show()\n",
    "\n",
    "#Решение\n",
    "#3\n",
    "#Добавим шума в данные, сделанные по функции f(x,b) с коэффициентами b = (1, 2)\n",
    "beta = (1, 2)\n",
    "\n",
    "\n",
    "def f(x, b0, b1):\n",
    "    return b0 + b1 * np.log(x)\n",
    "\n",
    "\n",
    "#Зададим массив точек xi\n",
    "xdata = np.linspace(1, 5, 50)\n",
    "#Создаем теоретически правильные значения точек yi (без шума)\n",
    "y = f(xdata, *beta)\n",
    "#зашумляем эти данные\n",
    "ydata = y + 0.05 * np.random.randn(len(xdata))\n",
    "beta_opt, beta_cov = curve_fit(f, xdata, ydata)\n",
    "print(beta_opt)\n",
    "#Вычислим линейное отклонение\n",
    "lin_dev = sum(beta_cov[0])\n",
    "print(lin_dev)\n",
    "\n",
    "#Вычислим квадратичное отелонение\n",
    "residuals = ydata - f(xdata, *beta_opt)\n",
    "fres = sum(residuals ** 2)\n",
    "print(fres)\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(xdata, ydata)\n",
    "ax.plot(xdata, y, 'r', lw=2)\n",
    "ax.plot(xdata, f(xdata, *beta_opt), 'b', lw=2)\n",
    "ax.set_xlim(0, 5)\n",
    "ax.set_xlabel(r\"$x$\", fontsize=18)\n",
    "ax.set_ylabel(r\"$f(x, \\beta)$\", fontsize=18)\n",
    "plt.show()\n",
    "\n",
    "#Решение\n",
    "#4\n",
    "#Добавим шума в данные, сделанные по функции f(x,b) с коэффициентами b = (1,2)\n",
    "beta = (1, 2)\n",
    "\n",
    "\n",
    "def f(x, b0, b1):\n",
    "    return b0 * x ** b1\n",
    "\n",
    "\n",
    "#зададим массив точек xi\n",
    "xdata = np.linspace(1, 5, 50)\n",
    "#создаем теоретически правильные значения точек yi (без шума)\n",
    "y = f(xdata, *beta)\n",
    "#зашумляем эти данные\n",
    "ydata = y + 0.05 * np.random.randn(len(xdata))\n",
    "beta_opt, beta_cov = curve_fit(f, xdata, ydata)\n",
    "print(beta_opt)\n",
    "#Вычислим линейное отклонение\n",
    "lin_dev = sum(beta_cov[0])\n",
    "print(lin_dev)\n",
    "\n",
    "#Вычислим квадратичное отклонение\n",
    "residuals = ydata - f(xdata, *beta_opt)\n",
    "fres = sum(residuals ** 2)\n",
    "print(fres)\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(xdata, ydata)\n",
    "ax.plot(xdata, y, 'r', lw=2)\n",
    "ax.plot(xdata, f(xdata, *beta_opt), 'b', lw=2)\n",
    "ax.set_xlim(0, 5)\n",
    "ax.set_xlabel(r\"$x$\", fontsize=18)\n",
    "ax.set_ylabel(r\"$f(x, \\beta)$\", fontsize=18)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Задание:\n",
    "\n",
    "Подставьте собственные данные и поэкспериментируйте с представленными функциями. Проанализируйте динамику изменения данных.\n"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.12224761 0.33099972]\n",
      "0.00012046598205679071\n",
      "0.10592698681046578\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.00012046598205679071\n",
      "0.134404136624153\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 9.99125434 10.01054468]\n",
      "5.458734023243509e-05\n",
      "0.1262300212463373\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.00192702 2.998771  ]\n",
      "6.073765213332477e-07\n",
      "0.11843703676026932\n"
     ]
    },
    {
     "data": {
      "text/plain": "Text(0, 0.5, '$f(x, \\\\beta)$')"
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Решение\n",
    "#1\n",
    "import numpy as np\n",
    "from scipy.optimize import curve_fit\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#Добавим шума в данные, сделанные по функции f(x,b) с коэффициентами b = (0.25, 0.75)\n",
    "beta = (0.1, 0.34)\n",
    "\n",
    "\n",
    "def f(x, b0, b1):\n",
    "    return b0 + b1 * x\n",
    "\n",
    "\n",
    "#зададим массив точек xi\n",
    "xdata = np.linspace(0, 5, 50)\n",
    "#создаем теоретически правильные значения точек yi (без шума)\n",
    "y = f(xdata, *beta)\n",
    "#зашумляем эти данные\n",
    "ydata = y + 0.05 * np.random.randn(len(xdata))\n",
    "beta_opt, beta_cov = curve_fit(f, xdata, ydata)\n",
    "print(beta_opt)\n",
    "#Вычислим линейное отклонение\n",
    "lin_dev = sum(beta_cov[0])\n",
    "print(lin_dev)\n",
    "\n",
    "#Вычислим квадратичное отклонение\n",
    "residuals = ydata - f(xdata, *beta_opt)\n",
    "fres = sum(residuals ** 2)\n",
    "print(fres)\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(xdata, ydata)\n",
    "ax.plot(xdata, y, 'r', lw=2)\n",
    "ax.plot(xdata, f(xdata, *beta_opt), 'b', lw=2)\n",
    "ax.set_xlim(0, 5)\n",
    "ax.set_xlabel(r\"$x$\", fontsize=18)\n",
    "ax.set_ylabel(r\"$f(x, \\beta)$\", fontsize=18)\n",
    "plt.show()\n",
    "#Решение\n",
    "#2\n",
    "beta = (0.34, 0.7, 0.55)\n",
    "\n",
    "\n",
    "def f(x, b0, b1, b2):\n",
    "    return b0 + b1 * x + b2 * x * x\n",
    "\n",
    "\n",
    "#зададим массив точек xi\n",
    "xdata = np.linspace(0, 5, 50)\n",
    "#cоздаем теоретически правильные значения точек yi (без шума)\n",
    "y = f(xdata, *beta)\n",
    "#зашумляем эти данные\n",
    "ydata = y + 0.05 * np.random.randn(len(xdata))\n",
    "beta_opt, beta_cov = curve_fit(f, xdata, ydata)\n",
    "print(lin_dev)\n",
    "\n",
    "#Вычислим квадратичное отклонение\n",
    "residuals = ydata - f(xdata, *beta_opt)\n",
    "fres = sum(residuals ** 2)\n",
    "print(fres)\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(xdata, ydata)\n",
    "ax.plot(xdata, y, 'r', lw=2)\n",
    "ax.set_xlim(0, 5)\n",
    "ax.set_xlabel(r\"$x$\", fontsize=18)\n",
    "ax.set_ylabel(r\"$f(x, \\beta)$\", fontsize=18)\n",
    "plt.show()\n",
    "\n",
    "#Решение\n",
    "#3\n",
    "beta = (10, 10)\n",
    "\n",
    "\n",
    "def f(x, b0, b1):\n",
    "    return b0 + b1 * np.log(x)\n",
    "\n",
    "\n",
    "#Зададим массив точек xi\n",
    "xdata = np.linspace(1, 5, 50)\n",
    "#Создаем теоретически правильные значения точек yi (без шума)\n",
    "y = f(xdata, *beta)\n",
    "#зашумляем эти данные\n",
    "ydata = y + 0.05 * np.random.randn(len(xdata))\n",
    "beta_opt, beta_cov = curve_fit(f, xdata, ydata)\n",
    "print(beta_opt)\n",
    "#Вычислим линейное отклонение\n",
    "lin_dev = sum(beta_cov[0])\n",
    "print(lin_dev)\n",
    "\n",
    "#Вычислим квадратичное отелонение\n",
    "residuals = ydata - f(xdata, *beta_opt)\n",
    "fres = sum(residuals ** 2)\n",
    "print(fres)\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(xdata, ydata)\n",
    "ax.plot(xdata, y, 'r', lw=2)\n",
    "ax.plot(xdata, f(xdata, *beta_opt), 'b', lw=2)\n",
    "ax.set_xlim(0, 5)\n",
    "ax.set_xlabel(r\"$x$\", fontsize=18)\n",
    "ax.set_ylabel(r\"$f(x, \\beta)$\", fontsize=18)\n",
    "plt.show()\n",
    "\n",
    "#Решение\n",
    "#4\n",
    "#Добавим шума в данные, сделанные по функции f(x,b) с коэффициентами b = (1,2)\n",
    "beta = (1, 3)\n",
    "\n",
    "\n",
    "def f(x, b0, b1):\n",
    "    return b0 * x ** b1\n",
    "\n",
    "\n",
    "#зададим массив точек xi\n",
    "xdata = np.linspace(1, 5, 50)\n",
    "#создаем теоретически правильные значения точек yi (без шума)\n",
    "y = f(xdata, *beta)\n",
    "#зашумляем эти данные\n",
    "ydata = y + 0.05 * np.random.randn(len(xdata))\n",
    "beta_opt, beta_cov = curve_fit(f, xdata, ydata)\n",
    "print(beta_opt)\n",
    "#Вычислим линейное отклонение\n",
    "lin_dev = sum(beta_cov[0])\n",
    "print(lin_dev)\n",
    "\n",
    "#Вычислим квадратичное отклонение\n",
    "residuals = ydata - f(xdata, *beta_opt)\n",
    "fres = sum(residuals ** 2)\n",
    "print(fres)\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(xdata, ydata)\n",
    "ax.plot(xdata, y, 'r', lw=2)\n",
    "ax.plot(xdata, f(xdata, *beta_opt), 'b', lw=2)\n",
    "ax.set_xlim(0, 5)\n",
    "ax.set_xlabel(r\"$x$\", fontsize=18)\n",
    "ax.set_ylabel(r\"$f(x, \\beta)$\", fontsize=18)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "1.2 Теоретический материал - Задачи регрессии\n",
    "\n",
    "Линейная регрессия - это широко используемый метод статистического анализа, который использует регрессионный анализ в математической статистике для определения количественной взаимосвязи между двумя или более переменными. Если регрессионный анализ включает две или более независимых переменных, а связь между зависимой и независимой переменными является линейной, тогда имееи дело с множественной линейной регрессией. В этом разделе мы увидим, как библиотеку Scikit-Learn в Python для машинного обучения можно использовать для реализации функций регрессии. Мы начнем с простой линейной регрессии с участием двух переменных, а затем перейдем к линейной регрессии с участием нескольких переменных.\n"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "1.2.1 Пример\n",
    "\n",
    "Построим простую линейную регрессию в Python с использованием библиотеки scikit-learn\n"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from pandas import DataFrame, Series\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.linear_model import LinearRegression"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "outputs": [
    {
     "data": {
      "text/plain": "   Учебное время  Оценка\n0           0.50      10\n1           0.75      22\n2           1.00      13\n3           1.25      43\n4           1.50      20",
      "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>Учебное время</th>\n      <th>Оценка</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0.50</td>\n      <td>10</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>0.75</td>\n      <td>22</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>1.00</td>\n      <td>13</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>1.25</td>\n      <td>43</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>1.50</td>\n      <td>20</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_dict = {'Учебное время': [0.50, 0.75, 1.00, 1.25, 1.50, 1.75, 2.00,\n",
    "                             2.25, 2.50, 2.75, 3.00, 3.25, 3.50, 3.75,\n",
    "                             4.00, 4.25, 4.50, 4.75, 5.00, 5.50],\n",
    "           'Оценка': [10, 22, 13, 43, 20, 22, 33, 50, 62, 48, 55, 75,\n",
    "                      62, 73, 81, 76, 64, 82, 90, 93]}\n",
    "dataset = pd.DataFrame(my_dict)\n",
    "dataset.head()"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(20, 2)\n"
     ]
    },
    {
     "data": {
      "text/plain": "       Учебное время     Оценка\ncount      20.000000  20.000000\nmean        2.887500  53.700000\nstd         1.501041  26.435821\nmin         0.500000  10.000000\n25%         1.687500  30.250000\n50%         2.875000  58.500000\n75%         4.062500  75.250000\nmax         5.500000  93.000000",
      "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>Учебное время</th>\n      <th>Оценка</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>count</th>\n      <td>20.000000</td>\n      <td>20.000000</td>\n    </tr>\n    <tr>\n      <th>mean</th>\n      <td>2.887500</td>\n      <td>53.700000</td>\n    </tr>\n    <tr>\n      <th>std</th>\n      <td>1.501041</td>\n      <td>26.435821</td>\n    </tr>\n    <tr>\n      <th>min</th>\n      <td>0.500000</td>\n      <td>10.000000</td>\n    </tr>\n    <tr>\n      <th>25%</th>\n      <td>1.687500</td>\n      <td>30.250000</td>\n    </tr>\n    <tr>\n      <th>50%</th>\n      <td>2.875000</td>\n      <td>58.500000</td>\n    </tr>\n    <tr>\n      <th>75%</th>\n      <td>4.062500</td>\n      <td>75.250000</td>\n    </tr>\n    <tr>\n      <th>max</th>\n      <td>5.500000</td>\n      <td>93.000000</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(dataset.shape)\n",
    "dataset.describe()"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(dataset['Учебное время'], dataset['Оценка'], color='b', label=\"данные экзамена\")\n",
    "plt.xlabel(\"Часы\")\n",
    "plt.ylabel(\"Оценка\")\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "После того как мы получили представление о данных, разделим информацию\n",
    "на «атрибуты» и «метки». Атрибуты – это независимые переменные, а метки\n",
    "– это зависимые переменные, значения которых должны быть предсказаны. В\n",
    "нашем наборе всего два столбца и необходимо предсказать оценку в\n",
    "зависимости от количества часов. Чтобы извлечь атрибуты и метки,\n",
    "выполните следующий скрипт:"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.5 ]\n",
      " [0.75]\n",
      " [1.  ]\n",
      " [1.25]\n",
      " [1.5 ]\n",
      " [1.75]\n",
      " [2.  ]\n",
      " [2.25]\n",
      " [2.5 ]\n",
      " [2.75]\n",
      " [3.  ]\n",
      " [3.25]\n",
      " [3.5 ]\n",
      " [3.75]\n",
      " [4.  ]\n",
      " [4.25]\n",
      " [4.5 ]\n",
      " [4.75]\n",
      " [5.  ]\n",
      " [5.5 ]]\n",
      "[10 22 13 43 20 22 33 50 62 48 55 75 62 73 81 76 64 82 90 93]\n"
     ]
    }
   ],
   "source": [
    "x = dataset.iloc[:, :-1].values\n",
    "y = dataset.iloc[:, 1].values\n",
    "print(x)\n",
    "print(y)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.1686320754716846\n",
      "[17.18867925]\n"
     ]
    }
   ],
   "source": [
    "x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2, random_state=0)\n",
    "regressor = LinearRegression()\n",
    "regressor.fit(x_train, y_train)\n",
    "print(regressor.intercept_)\n",
    "print(regressor.coef_)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Получившийся результат можно интерпретировать следующим образом: с\n",
    "каждым затраченным часом на обучение результат экзамена повышается\n",
    "приблизительно на 17 баллов. Далее можно построить прогнозы. Для этого мы\n",
    "будем использовать наши тестовые данные и посмотрим, насколько точно наш\n",
    "алгоритм предсказывает процентную оценку. Чтобы сделать прогноз на\n",
    "тестовых данных необходимо выполнить следующий код:"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "outputs": [
    {
     "data": {
      "text/plain": "   Actual  Predicted\n0      90  89.112028\n1      22  16.060142\n2      93  97.706368\n3      62  46.140330",
      "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>Actual</th>\n      <th>Predicted</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>90</td>\n      <td>89.112028</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>22</td>\n      <td>16.060142</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>93</td>\n      <td>97.706368</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>62</td>\n      <td>46.140330</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = regressor.predict(x_test)\n",
    "df = pd.DataFrame({'Actual': y_test, 'Predicted': y_pred})\n",
    "df"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot(kind='bar')\n",
    "plt.grid(which='major', linestyle='-', linewidth='0.5', color='green')\n",
    "plt.grid(which='minor', linestyle=':', linewidth='0.5', color='black')\n",
    "plt.show()\n",
    "#Построим линию регрессии с тестовыми данными\n",
    "plt.scatter(x_test, y_test, color='gray')\n",
    "plt.plot(x_test, y_pred, color=\"red\", linewidth=2)\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Задание:\n",
    "\n",
    "Постройте модель линейной регрессии для произвольных данных из двух\n",
    "столбцов. Для примера можно взять точечную зависимость заработной платы от\n",
    "опыта работы:\n",
    "(https://raw.githubusercontent.com/AnnaShestova/salary-years-simple-linearregression/master/Salary_Data.csv).\n",
    "Найдите коэффициенты линии регрессии. Постройте прогноз.\n"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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WtFRvRY35z8L1043nkUce0f333+97XlVVRbgCgI4WGSlNmBDsUSAMheyMldPplNR8Nujw4cO+mSKn06na2lpVVlaetuazzz5r9vpHjhzxq2n6dyorK1VXV3famsOHD0tqPqvWmN1uV2xsrN8DALoNj0d65x1p+XLvT5pvIsyFbLAaOHCgnE6n1qxZ4ztWW1ur9evXa+zYsZKkESNGqGfPnn415eXl2rVrl69mzJgxcrvd2rp1q69my5YtcrvdfjW7du1SeaPeJqtXr5bdbteIESN8NRs2bPBrwbB69Wq5XC4NGDDA+g8AAEJdXp40YIB09dXS9OnenwMGsG0MwlvHr6Nv3fHjx82OHTvMjh07jCSzePFis2PHDnPgwAFjjDFPPPGEcTgcJi8vz+zcudNMmzbNJCUlmaqqKt9r3H333SY5OdmsXbvWbN++3VxzzTVm6NCh5tSpU76a6667zgwZMsQUFhaawsJCM3jwYJOenu47f+rUKZOammquvfZas337drN27VqTnJxssrKyfDXHjh0ziYmJZtq0aWbnzp0mLy/PxMbGmqeffrpd75m7AgF0Cw133zW+846779CNtfX7O6jBat26dUZSs8fMmTONMd6WC/PmzTNOp9PY7XZz1VVXmZ07d/q9xldffWWysrJMfHy8iY6ONunp6aakpMSv5ujRo2bGjBkmJibGxMTEmBkzZpjKykq/mgMHDpi0tDQTHR1t4uPjTVZWll9rBWOMef/99824ceOM3W43TqfTPProo+1qtWAMwQpAN3DqlDHJyc1DVeNwlZLirQO6ibZ+f9uMoXV4Z6qqqpLD4ZDb7Wa9FYCu6Z13vJf9vsm6dSwgR7fR1u/vkF1jBQAIUezJB7SKYAUAaB/25ANaRbACALQPe/IBrSJYAQDaJzJSeuYZ7z83DVcNz5cs8dYBYYZgBQBoP/bkA1oU8lvaAABCVEaGNHWqtHGjd6F6UpL38h8zVQhjBCsAQODYkw/ww6VAAAAAixCsAAAALEKwAgAAsAjBCgAAwCIEKwAAAItwVyAAdBaPh9YEQDdHsAKAzpCXJ82ZIx08+PWx5GRvB3OaaQLdBpcCAaCj5eVJN93kH6okqazMezwvLzjjAmA5ghUAdCSPxztTZUzzcw3HsrO9dQC6PIIVAHSkjRubz1Q1ZoxUWuqtA9DlEawAoCOVl1tbByCkEawAoCMlJVlbByCkEawAoCONG+e9+89ma/m8zSalpHjrAHR5BCsA6EiRkd6WClLzcNXwfMkS+lkB3QTBCgA6WkaGtGKF1K+f//HkZO/xYPex8nikd96Rli/3/uQORSBgNAgFgM6QkSFNnRp6nddpXApYymZMS81V0FGqqqrkcDjkdrsVGxsb7OEACGcNjUubfg00XKIMhdk0IES09fubS4EAEI5oXAp0CIIVAIQjGpcCHYJgBQDhiMalQIcgWAFAOKJxKdAhCFYAEI5oXAp0CIIVAIQjGpcCHYJgBQDhKtQblwJdEA1CASCchWrjUqCLIlgBQLiLjJQmTAj2KIBugUuBAAAAFiFYAQAAWIRgBQAAYBGCFQAAgEUIVgAAABYhWAEAAFiEYAUAAGARghUAAIBFAm4QevLkSa1fv14lJSWqra31Ozd79uwzHhgAAEBXE1Cw2rFjh66//np9+eWXOnnypOLj4/X555+rV69eSkhIIFgBAICwFNClwPvuu09TpkzRF198oejoaG3evFkHDhzQiBEj9PTTT1s9RgAAgC4hoGBVXFysBx54QJGRkYqMjFRNTY1SUlK0aNEi/eIXv7B6jAAAAF1CQMGqZ8+estlskqTExESVlJRIkhwOh++fAQAAwk1Aa6yGDx+ud999VxdeeKGuvvpq/frXv9bnn3+uv/zlLxo8eLDVYwQAAOgSApqxWrBggZKSkiRJ//M//6M+ffrov/7rv3T48GEtW7bM0gECAAB0FTZjjAn2IMJJVVWVHA6H3G63YmNjgz0cAADQBm39/g5oxuqaa67RsWPHAh0bAABAtxRQsHrnnXeaNQUFAAAIdwFvadNwVyAAAAC8At7S5vvf/76ioqJaPPf2228HPCAAAICuKuBgNWbMGJ199tlWjgUAAKBLCyhY2Ww2PfTQQ0pISLB6PAAAAF1WQMGKDg0AuhyPR9q4USovl5KSpHHjpMjIYI8KQDcTULCaN28elwEBdB15edKcOdLBg18fS06WnnlGysgI3rgAdDs0CO1kNAgFOllennTTTVLTf9U13Nm8YgXhCsA3auv3d8DBasWKFfrb3/6mkpKSZj2ttm/fHshLhgWCFdCJPB5pwAD/marGbDbvzNW+fVwWBHBaHdp5/Xe/+51+9KMfKSEhQTt27NDll1+uPn366NNPP9X3vve9gAcNAJbauLH1UCV5Z7FKS711AGCBgILV0qVLtWzZMuXk5CgqKko///nPtWbNGs2ePVtut9vqMQJAYMrLra0DgG8QULAqKSnR2LFjJUnR0dE6fvy4JCkzM1PLly+3bnQAcCaSkqytA4BvEFCwcjqdOnr0qCSpf//+2rx5syRp3759tGIAEDrGjfOuoWptCy6bTUpJ8dZZzeOR3nlHWr7c+9Pjsf5vAAg5AQWra665Rm+88YYk6c4779R9992niRMn6pZbbtH3v/99SwcIAAGLjPS2VJCah6uG50uWWL9wPS/Pu2j+6qul6dO9PwcM8B4H0K0FdFdgfX296uvr1aOHtw3W3/72NxUUFOiCCy7Q3Xff3eoeguCuQCAoWupjlZLiDVVWt1qgvQPQLXV4uwUEhmAFBElndF6nvQPQbbX1+zugzuuvv/76ac/fcMMNgbwsAHScyEhpwoSO/Rvtae/Q0WMBEBQBBasbb7yx1XM2m00eFmkCCEe0dwDCXkCL1yWpvLzct9aq8YNQBSBs0d4BCHsBB6uIiIB/tc1OnTqlX/3qVxo4cKCio6N1/vnn67HHHlN9fb2vxhijRx99VC6XS9HR0ZowYYJ2797t9zo1NTWaNWuW+vbtq969e+uGG27QwSbT9ZWVlcrMzJTD4ZDD4VBmZqaOHTvmV1NSUqIpU6aod+/e6tu3r2bPnt1sOx8AYSyY7R0AhISA09ELL7yg5557Tn/+85+1du1aff7551aOS5L05JNP6vnnn1dOTo4++OADLVq0SE899ZSeffZZX82iRYu0ePFi5eTkaNu2bXI6nZo4caKvaakkZWdna9WqVcrNzVVBQYFOnDih9PR0v9m16dOnq7i4WPn5+crPz1dxcbEyMzN95z0ej9LS0nTy5EkVFBQoNzdXK1eu1AMPPGD5+wbQRQWrvQOA0GEC0L9/f9O/f3/jcrnM2WefbWw2m4mMjDRTp041brc7kJdsUVpamvnxj3/sdywjI8Pcdtttxhhj6uvrjdPpNE888YTvfHV1tXE4HOb55583xhhz7Ngx07NnT5Obm+urKSsrMxERESY/P98YY8yePXuMJLN582ZfTWFhoZFk9u7da4wx5s033zQRERGmrKzMV7N8+XJjt9tP+56rq6uN2+32PUpLS40kSz8nACFm5UpjkpON8S5X9z5SUrzHAXRJbre7Td/fAc1Y7d+/X/v371dZWZmOHz8ut9utt956Sx9++KF+/vOfWxb6rrzySv3rX//SRx99JEl67733VFBQoOuvv16St9N7RUWFJk2a5Psdu92u8ePHa9OmTZKkoqIi1dXV+dW4XC6lpqb6agoLC+VwODRq1ChfzejRo+VwOPxqUlNT5XK5fDWTJ09WTU2NioqKWn0PCxcu9F1edDgcSklJOdOPBUCoy8iQ9u+X1q2TXn3V+3PfPvpXAWEgoLsCm4qJidG1116rpUuX6s4777TiJSVJc+fOldvt1kUXXaTIyEh5PB7Nnz9f06ZNkyRVVFRIkhITE/1+LzExUQcOHPDVREVFKS4urllNw+9XVFQoISGh2d9PSEjwq2n6d+Li4hQVFeWrackjjzyi+++/3/e8qqqKcAWEg85o7wAg5FgSrBpcffXV+vTTTy17vb/+9a96+eWX9eqrr+rSSy9VcXGxsrOz5XK5NHPmTF+drclaBmNMs2NNNa1pqT6QmqbsdrvsdvtpxwIAALqHgILV+++/f9rzQ4YMCWgwTT300EN6+OGHdeutt0qSBg8erAMHDmjhwoWaOXOmnE6nJO9sUlKj25cPHz7sm11yOp2qra1VZWWl36zV4cOHNXbsWF/NZ5991uzvHzlyxO91tmzZ4ne+srJSdXV1zWayAABAeApojdWwYcM0fPhwDRs2zPdoeD58+HDLBvfll182a+sQGRnpa7cwcOBAOZ1OrVmzxne+trZW69ev94WmESNGqGfPnn415eXl2rVrl69mzJgxcrvd2rp1q69my5YtcrvdfjW7du1SeaPGfqtXr5bdbteIESMse88AAKDrCvhS4JYtW3TuuedaOZZmpkyZovnz5+u8887TpZdeqh07dmjx4sX68Y9/LMl7aS47O1sLFizQoEGDNGjQIC1YsEC9evXS9OnTJUkOh0N33nmnHnjgAfXp00fx8fF68MEHNXjwYH33u9+VJF188cW67rrr9NOf/lR/+MMfJEl33XWX0tPT9e1vf1uSNGnSJF1yySXKzMzUU089pS+++EIPPvigfvrTn7LnHwAA8ArklkObzWY+++yzQH61XaqqqsycOXPMeeedZ8466yxz/vnnm1/+8pempqbGV1NfX2/mzZtnnE6nsdvt5qqrrjI7d+70e52vvvrKZGVlmfj4eBMdHW3S09NNSUmJX83Ro0fNjBkzTExMjImJiTEzZswwlZWVfjUHDhwwaWlpJjo62sTHx5usrCxTXV3drvfU1ts1AQBA6Gjr97fNGGPaG8YiIiJavZMOp9fW3bEBAEDoaOv3d0BrrGw22zfedQcAABBuAlpjZYzRhRde2Gq4+uKLL85oUAAAAF1RQMHqT3/6k9XjAAAA6PICClaNm3MCAADAK+B2Cx6PR6tWrdIHH3wgm82miy++WFOnTlWPHpY2cwcAAOgyAkpBu3bt0tSpU1VRUeHr8/TRRx/p3HPP1euvv67BgwdbOkgAAICuIKC7An/yk5/o0ksv1cGDB7V9+3Zt375dpaWlGjJkiO666y6rxwgAANAlBDRj9d577+ndd9/123svLi5O8+fP12WXXWbZ4AAAALqSgGasvv3tb7e4afHhw4d1wQUXnPGgAAAAuqKAgtWCBQs0e/ZsrVixQgcPHtTBgwe1YsUKZWdn68knn1RVVZXvAQAAEC4C3tLG9wL/aRLa8DKNn9tsNnk8HivG2W2wpQ0AAF1PW7+/A1pjtW7duoAHBgAA0F0FFKzGjx9v9TgAAAC6vDPq5vnll1+qpKREtbW1fseHDBlyRoMCAADoigIKVkeOHNGPfvQj/fOf/2zxPOuqAABAOArorsDs7GxVVlZq8+bNio6OVn5+vl566SUNGjRIr7/+utVjBAAA6BICmrF6++239fe//12XXXaZIiIi1L9/f02cOFGxsbFauHCh0tLSrB4nAABAyAtoxurkyZNKSEiQJMXHx+vIkSOSpMGDB2v79u3WjQ4AAKALCbjz+ocffihJGjZsmP7whz+orKxMzz//vJKSkiwdIAAAQFcR0KXA7OxslZeXS5LmzZunyZMn6+WXX1ZUVJReeuklSwcIAADQVQTUeb2pL7/8Unv37tV5552nvn37WjGubovO6wAAdD1t/f5u96XAF154QbfddpteeeUVSdKyZcs0bNgw3XLLLfrLX/4S+IgBAAC6uHZdCly+fLnuu+8+TZ48WQ8++KA++eQT/fa3v9VDDz0kj8ejefPmaeDAgbrxxhs7aLgAAAChq13BaunSpVq6dKluv/12bdu2TWPGjNHvf/97/exnP5MkJSUl6dlnnyVYAQCAsNSuS4G7d+/WFVdcIUm+HlajR4/2nR8/frzef/99a0cIAADQRbQrWFVXV6tXr16+53a7XTExMb7nvXr1arZvIAAAQLhoV7ByuVzav3+/7/kf//hHOZ1O3/OPP/5YAwYMsGpsAAAAXUq7gtWoUaOUl5fne37zzTf7zWD96U9/0qhRo6wbHQAAQBfSrj5WDaU2m63F8wcPHtQ555yjs88+25rRdUP0sQIAoOtp6/d3u+4KbC1QNUhOTm7PywEAAHQrAe0VCAAAgOYIVgAAABYhWAEAAFiEYAUAAGARghUAAIBF2nVXIAB0Go9H2rhRKi+XkpKkceOkyMhgjwoATotgBSD05OVJc+ZIBw9+fSw5WXrmGSkjI3jjAoBvwKVAAKElL0+66Sb/UCVJZWXe4412fwCAUEOwAhA6PB7vTFVLG0I0HMvO9tYBQAgiWAEIHRs3Np+paswYqbTUWwcAIYhgBSB0lJdbWwcAnYxgBSB0JCVZWwcAnYxgBSB0jBvnvfuvtQ3fbTYpJcVbBwAhiGAFIHRERnpbKkjNw1XD8yVL/PtZeTzSO+9Iy5d7f7KwHUAQEawAhJaMDGnFCqlfP//jycne4437WOXlSQMGSFdfLU2f7v05YAAtGQAEjc2Ylu5rRkepqqqSw+GQ2+1WbGxssIcDhK5v6rze0O+q6b/CGma2moYwADgDbf3+Jlh1MoIVYAGPxzsz1VprBpvNO8O1bx/b4ACwRFu/v7kUCKDrod8VgBBFsALQ9dDvCkCIYhNmoCN80/ognBn6XQEIUcxYAVbjTrWOR78rACGKYAVYqeFOtabrf8rKvMcJV9YIpN8VAHQCghVgFY9HmjOn+e3/0tfHsrNpYGmV9vS7AoBOwhorwCrtuVNtwoROG1a3lpEhTZ3KejYAIYNgBVgl1O5UC5cF9JGRBFUAIYNgBVgllO5Uy8vzXpZsPIOWnOxdl8QlMgDoMKyxAqwSKneqsYAeAIKGYAVYJRTuVGMBPQAEFcEKsFKw71RjqxcACCrWWAFWC+adaqG2gB4AwgzBCugIwbpTLZQW0ANAGOJSINCdhMoCegAIUwQroDsJ9gJ6j0d65x1p+XLvTxbJAwgzBCuguwnWAno2nwYA2Yxp6b5sdJSqqio5HA653W7FxsYGezjozjqz83pD76ym/zppmCVj7z4AXVxbv78JVp2MYIVux+Pxzky11ubBZvPOlu3b1z231AEQFtr6/c2lQKA9WEPUHL2zAMCHdgtAW7H/XsvonQUAPiE/Y1VWVqbbbrtNffr0Ua9evTRs2DAVFRX5zhtj9Oijj8rlcik6OloTJkzQ7t27/V6jpqZGs2bNUt++fdW7d2/dcMMNOtjk/2FXVlYqMzNTDodDDodDmZmZOnbsmF9NSUmJpkyZot69e6tv376aPXu2amtrO+y9I4Sw/17r6J0FAD4hHawqKyt1xRVXqGfPnvrnP/+pPXv26De/+Y3OOeccX82iRYu0ePFi5eTkaNu2bXI6nZo4caKOHz/uq8nOztaqVauUm5urgoICnThxQunp6fI0uowzffp0FRcXKz8/X/n5+SouLlZmZqbvvMfjUVpamk6ePKmCggLl5uZq5cqVeuCBBzrls0AQsf/e6dE7CwC+ZkLY3LlzzZVXXtnq+fr6euN0Os0TTzzhO1ZdXW0cDod5/vnnjTHGHDt2zPTs2dPk5ub6asrKykxERITJz883xhizZ88eI8ls3rzZV1NYWGgkmb179xpjjHnzzTdNRESEKSsr89UsX77c2O1243a7Wx1jdXW1cbvdvkdpaamRdNrfQYhZt84Yb4Q6/WPdumCPNHhWrjTGZvM+Gn8mDcdWrgz2CAHgjLjd7jZ9f4f0jNXrr7+ukSNH6oc//KESEhI0fPhwvfDCC77z+/btU0VFhSZNmuQ7ZrfbNX78eG3atEmSVFRUpLq6Or8al8ul1NRUX01hYaEcDodGjRrlqxk9erQcDodfTWpqqlwul69m8uTJqqmp8bs02dTChQt9lxcdDodSUlLO8FNBp2MN0TcL9ubTABAiQjpYffrpp3ruuec0aNAgvfXWW7r77rs1e/Zs/fnPf5YkVVRUSJISExP9fi8xMdF3rqKiQlFRUYqLizttTUJCQrO/n5CQ4FfT9O/ExcUpKirKV9OSRx55RG632/coLS1tz0eAUMAaorbJyJD275fWrZNefdX7c98+QhWAsBLSdwXW19dr5MiRWrBggSRp+PDh2r17t5577jndfvvtvjpbk7Udxphmx5pqWtNSfSA1Tdntdtnt9tOOBSGuYQ1RWVnL66wa+jSxhih4m08DQIgI6RmrpKQkXXLJJX7HLr74YpWUlEiSnE6nJDWbMTp8+LBvdsnpdKq2tlaVlZWnrfnss8+a/f0jR4741TT9O5WVlaqrq2s2k4VuJtj77wEAuoyQDlZXXHGFPvzwQ79jH330kfr37y9JGjhwoJxOp9asWeM7X1tbq/Xr12vs2LGSpBEjRqhnz55+NeXl5dq1a5evZsyYMXK73dq6dauvZsuWLXK73X41u3btUnmjdTSrV6+W3W7XiBEjLH7nCDmsIQIAtEUnLKQP2NatW02PHj3M/Pnzzccff2xeeeUV06tXL/Pyyy/7ap544gnjcDhMXl6e2blzp5k2bZpJSkoyVVVVvpq7777bJCcnm7Vr15rt27eba665xgwdOtScOnXKV3PdddeZIUOGmMLCQlNYWGgGDx5s0tPTfedPnTplUlNTzbXXXmu2b99u1q5da5KTk01WVla73lNb7ypAiDp1ynv336uven82+u8QAKD7auv3d0gHK2OMeeONN0xqaqqx2+3moosuMsuWLfM7X19fb+bNm2ecTqex2+3mqquuMjt37vSr+eqrr0xWVpaJj4830dHRJj093ZSUlPjVHD161MyYMcPExMSYmJgYM2PGDFNZWelXc+DAAZOWlmaio6NNfHy8ycrKMtXV1e16PwQrAAC6nrZ+f7MJcydjE2ZYwuPx7r1XXu69G3HcuMDXeFn5WgDQTbX1+zuk7woE0IIz2bOwaYj6/HPpvvvY/xAALMKMVSdjxqoLCcWZnIY9C5v+z7bh7sTTLaRvKZC1pC2vBQBhpq3f3wSrTkaw6iLOZFaoo3g80oABrQejhn5a+/Y1D4CtBbLWnO61ACAMtfX7O6TbLQBB0RBCmgaYsjLv8by84Ixr48bTzzYZI5WWeusaO90m0u19LQDAaRGsgMZOF0IajmVne+s6W6B7Fn5TILPibwIAJBGsAH+Bzgp1hkD3LDyTcBTu+x8CQDsRrIDGAp0V6gwNexa2tjelzSalpDTfszCQcNTaawEATotgBTQW6KxQZwh0z8KxY9u3AJ39DwEgYAQroLFAZ4U6SyB7Fm7a1L41Yex/CAABo0Eo0FjDrNBNN3lDVONF7KEyk5ORIU2d2vYeW229bJmVJf3gB6HRrwsAuiiCFdBUw6xQS32slixp20xORzcXjYyUJkxoW21bL1v+4Adtf00AQItoENrJaBDahQQajkKtuWhDY9GyspbbSNAMFAC+EXsFAmeqPbNCDVrrcN7QXDQYa5e6wuVNAOgmWLwOWCWUm4sGsugdANBuzFgBVmlPc9FgrGVq76J3AEC7EawAq4Ryc9EGgVzeBAC0GZcCAauEcnNRAECnIFgBVgn15qIAgA5HsAKsEuiWMwCAboNgBViJu+8AIKyxeB2wGnffAUDYIlgBHYG77wAgLHEpEAAAwCIEKwAAAIsQrAAAACxCsAIAALAIwQoAAMAiBCsAAACLEKwAAAAsQrACAACwCMEKAADAIgQrAAAAixCsAAAALEKwAgAAsAjBCgAAwCIEKwAAAIsQrAAAACxCsAIAALAIwQoAAMAiBCsAAACLEKwAAAAsQrACAACwSI9gDwCdyOORNm6UysulpCRp3DgpMjLYowIAoNsgWIWLvDxpzhzp4MGvjyUnS888I2VkBG9cAAB0I1wKDAd5edJNN/mHKkkqK/Mez8sLzrgAAOhmCFbdncfjnakypvm5hmPZ2d46AABwRghW3d3Gjc1nqhozRiot9dYBAIAzQrDq7srLra0DAACtIlh1d0lJ1tYBAIBWEay6u3HjvHf/2Wwtn7fZpJQUbx0AADgjBKvuLjLS21JBah6uGp4vWUI/KwAALECwCgcZGdKKFVK/fv7Hk5O9x+ljBQCAJWgQGi4yMqSpU+m8DgBAByJYhZPISGnChOCOgW11AADdGMEKnYdtdQAA3RxrrNA52FYHABAGCFboeGyrAwAIEwQrdDy21QEAhAmCFToe2+oAAMIEwQodj211AABhgmCFjse2OgCAMEGwQsdjWx0AQJggWKFzsK0OACAM0CAUnYdtdQAA3RzBCp0rFLbVAQCgg3ApEAAAwCIEKwAAAItwKRChyeNhLRYAoMvpUjNWCxculM1mU3Z2tu+YMUaPPvqoXC6XoqOjNWHCBO3evdvv92pqajRr1iz17dtXvXv31g033KCDTbZYqaysVGZmphwOhxwOhzIzM3Xs2DG/mpKSEk2ZMkW9e/dW3759NXv2bNXW1nbU2w1feXnSgAHS1VdL06d7fw4YwEbNAICQ12WC1bZt27Rs2TINGTLE7/iiRYu0ePFi5eTkaNu2bXI6nZo4caKOHz/uq8nOztaqVauUm5urgoICnThxQunp6fI02vR3+vTpKi4uVn5+vvLz81VcXKzMzEzfeY/Ho7S0NJ08eVIFBQXKzc3VypUr9cADD3T8m/8mHo/0zjvS8uXen115M+O8POmmm5rvLVhW5j1OuAIAhDLTBRw/ftwMGjTIrFmzxowfP97MmTPHGGNMfX29cTqd5oknnvDVVldXG4fDYZ5//nljjDHHjh0zPXv2NLm5ub6asrIyExERYfLz840xxuzZs8dIMps3b/bVFBYWGklm7969xhhj3nzzTRMREWHKysp8NcuXLzd2u9243e42vxe3220ktet3TmvlSmOSk43xbmXsfSQne493NadONX8vjR82mzEpKd46AAA6UVu/v7vEjNW9996rtLQ0ffe73/U7vm/fPlVUVGjSpEm+Y3a7XePHj9emTZskSUVFRaqrq/OrcblcSk1N9dUUFhbK4XBo1KhRvprRo0fL4XD41aSmpsrlcvlqJk+erJqaGhUVFbU69pqaGlVVVfk9LNPdZnc2bmz+XhozRiot9dYBABCCQj5Y5ebmqqioSAsXLmx2rqKiQpKUmJjodzwxMdF3rqKiQlFRUYqLizttTUJCQrPXT0hI8Ktp+nfi4uIUFRXlq2nJwoULfeu2HA6HUlJSvuktt43HI82Z4w0bTTUcy87uWpcFy8utrQMAoJOFdLAqLS3VnDlz9Morr+iss85qtc7WZP85Y0yzY001rWmpPpCaph555BG53W7fo7S09LTjarPuOLuTlGRtHQAAnSykg1VRUZEOHz6sESNGqEePHurRo4fWr1+v3/3ud+rRo4dvBqnpjNHhw4d955xOp2pra1VZWXnams8++6zZ3z9y5IhfTdO/U1lZqbq6umYzWY3Z7XbFxsb6PSzRHWd3xo3z7h3YWlC12aSUFG8dAAAhKKSD1bXXXqudO3equLjY9xg5cqRmzJih4uJinX/++XI6nVqzZo3vd2pra7V+/XqNHTtWkjRixAj17NnTr6a8vFy7du3y1YwZM0Zut1tbt2711WzZskVut9uvZteuXSpvFFRWr14tu92uESNGdOjn0KLuOLsTGSk984z3n5uGq4bnS5bQzwoAELo6YSG9pRrfFWiMMU888YRxOBwmLy/P7Ny500ybNs0kJSWZqqoqX83dd99tkpOTzdq1a8327dvNNddcY4YOHWpONbq77LrrrjNDhgwxhYWFprCw0AwePNikp6f7zp86dcqkpqaaa6+91mzfvt2sXbvWJCcnm6ysrHaN37K7AhvuoLPZrL2D7tQpY9atM+bVV70/g3EHXkt3OqakdM07HQEA3UJbv7+7fLCqr6838+bNM06n09jtdnPVVVeZnTt3+v3OV199ZbKyskx8fLyJjo426enppqSkxK/m6NGjZsaMGSYmJsbExMSYGTNmmMrKSr+aAwcOmLS0NBMdHW3i4+NNVlaWqa6ubtf4LW23sHKlN0A1DVcNx9obREKpdUMoBDwAAP6jrd/fNmNauq0MHaWqqkoOh0Nut9ua9VZ5ed67AxsvZE9J8V4yy8ho3+vcdFPzuwwbLsGtWNG+1wMAoBtp6/c3waqTWR6spDPfV8/j8W4Z09pdhjabd1H5vn2sbwIAhKW2fn+zCXN3EBkpTZgQ+O+3p3XDmfwdAAC6uZC+KxCdpDu2bgAAIAgIVuierRsAAAgCghVozAkAgEUIVqAxJwAAFiFYwSsjw9tSoV8//+PJybRaAACgjbgrEF/LyJCmTj2z1g0AAIQxghX8nWnrBgAAwhiXAgEAACxCsAIAALAIwQoAAMAiBCsAAACLEKwAAAAsQrACAACwCMEKAADAIgQrAAAAixCsAAAALELn9U5mjJEkVVVVBXkkAACgrRq+txu+x1tDsOpkx48flySlpKQEeSQAAKC9jh8/LofD0ep5m/mm6AVL1dfX69ChQ4qJiZHNZgv2cIKiqqpKKSkpKi0tVWxsbLCHE3b4/IOLzz+4+PyDqyt//sYYHT9+XC6XSxERra+kYsaqk0VERCg5OTnYwwgJsbGxXe5/WN0Jn39w8fkHF59/cHXVz/90M1UNWLwOAABgEYIVAACARQhW6HR2u13z5s2T3W4P9lDCEp9/cPH5Bxeff3CFw+fP4nUAAACLMGMFAABgEYIVAACARQhWAAAAFiFYAQAAWIRghU6zcOFCXXbZZYqJiVFCQoJuvPFGffjhh8EeVlhauHChbDabsrOzgz2UsFJWVqbbbrtNffr0Ua9evTRs2DAVFRUFe1hh4dSpU/rVr36lgQMHKjo6Wueff74ee+wx1dfXB3to3dKGDRs0ZcoUuVwu2Ww2vfbaa37njTF69NFH5XK5FB0drQkTJmj37t3BGazFCFboNOvXr9e9996rzZs3a82aNTp16pQmTZqkkydPBntoYWXbtm1atmyZhgwZEuyhhJXKykpdccUV6tmzp/75z39qz549+s1vfqNzzjkn2EMLC08++aSef/555eTk6IMPPtCiRYv01FNP6dlnnw320LqlkydPaujQocrJyWnx/KJFi7R48WLl5ORo27Ztcjqdmjhxom8/3a6MdgsImiNHjighIUHr16/XVVddFezhhIUTJ07oO9/5jpYuXarHH39cw4YN05IlS4I9rLDw8MMP69///rc2btwY7KGEpfT0dCUmJuqPf/yj79gPfvAD9erVS3/5y1+COLLuz2azadWqVbrxxhsleWerXC6XsrOzNXfuXElSTU2NEhMT9eSTT+pnP/tZEEd75pixQtC43W5JUnx8fJBHEj7uvfdepaWl6bvf/W6whxJ2Xn/9dY0cOVI//OEPlZCQoOHDh+uFF14I9rDCxpVXXql//etf+uijjyRJ7733ngoKCnT99dcHeWThZ9++faqoqNCkSZN8x+x2u8aPH69NmzYFcWTWYBNmBIUxRvfff7+uvPJKpaamBns4YSE3N1dFRUV69913gz2UsPTpp5/queee0/33369f/OIX2rp1q2bPni273a7bb7892MPr9ubOnSu3262LLrpIkZGR8ng8mj9/vqZNmxbsoYWdiooKSVJiYqLf8cTERB04cCAYQ7IUwQpBkZWVpffff18FBQXBHkpYKC0t1Zw5c7R69WqdddZZwR5OWKqvr9fIkSO1YMECSdLw4cO1e/duPffccwSrTvDXv/5VL7/8sl599VVdeumlKi4uVnZ2tlwul2bOnBns4YUlm83m99wY0+xYV0SwQqebNWuWXn/9dW3YsEHJycnBHk5YKCoq0uHDhzVixAjfMY/How0bNignJ0c1NTWKjIwM4gi7v6SkJF1yySV+xy6++GKtXLkySCMKLw899JAefvhh3XrrrZKkwYMH68CBA1q4cCHBqpM5nU5J3pmrpKQk3/HDhw83m8XqilhjhU5jjFFWVpby8vL09ttva+DAgcEeUti49tprtXPnThUXF/seI0eO1IwZM1RcXEyo6gRXXHFFs/YiH330kfr37x+kEYWXL7/8UhER/l95kZGRtFsIgoEDB8rpdGrNmjW+Y7W1tVq/fr3Gjh0bxJFZgxkrdJp7771Xr776qv7+978rJibGd53d4XAoOjo6yKPr3mJiYpqtZevdu7f69OnDGrdOct9992ns2LFasGCBbr75Zm3dulXLli3TsmXLgj20sDBlyhTNnz9f5513ni699FLt2LFDixcv1o9//ONgD61bOnHihD755BPf83379qm4uFjx8fE677zzlJ2drQULFmjQoEEaNGiQFixYoF69emn69OlBHLVFDNBJJLX4+NOf/hTsoYWl8ePHmzlz5gR7GGHljTfeMKmpqcZut5uLLrrILFu2LNhDChtVVVVmzpw55rzzzjNnnXWWOf/8880vf/lLU1NTE+yhdUvr1q1r8d/3M2fONMYYU19fb+bNm2ecTqex2+3mqquuMjt37gzuoC1CHysAAACLsMYKAADAIgQrAAAAixCsAAAALEKwAgAAsAjBCgAAwCIEKwAAAIsQrAAAACxCsAKAEHTq1KlgDwFAAAhWABACiouLNXPmTF144YWKi4tTbGysqqqqgj0sAO1EsAIQckpLS3XnnXfK5XIpKipK/fv315w5c3T06NFgD61DvPPOO7ryyivldDqVm5urbdu26eOPP1ZsbGywhwagndjSBkBI+fTTTzVmzBhdeOGFevzxxzVw4EDt3r1bDz30kGpra7V582bFx8cHe5iWMcbowgsv1Ny5c/WTn/wk2MMBcIaYsQIQUu69915FRUVp9erVGj9+vM477zx973vf09q1a1VWVqZf/vKXvtoBAwbIZrM1e9x4442+mgkTJig7O7vFv5Wdna0JEyZIku64444WX8tms+mOO+5o8fdffPFFnXPOOXrttdd04YUX6qyzztLEiRNVWlrqq/m///s/TZ06VYmJiTr77LN12WWXae3atb7ze/fu1YEDB/TJJ5+of//+OuusszR69GgVFBT4/a3169fr8ssvl91uV1JSkh5++GHfOqy2jL2tnwOAM0OwAhAyvvjiC7311lu65557FB0d7XfO6XRqxowZ+utf/6rGE+2PPfaYysvLfY+bb745oL/9zDPP+L3GzTff7Hv+zDPPtPp7X375pebPn6+XXnpJ//73v1VVVaVbb73Vd/7EiRO6/vrrtXbtWu3YsUOTJ0/WlClTVFJSIkk6cuSI6urq9NJLL2np0qXasWOHhg0bpuuuu07l5eWSpLKyMl1//fW67LLL9N577+m5557TH//4Rz3++ONnNHYA1usR7AEAQIOPP/5YxhhdfPHFLZ6/+OKLVVlZqSNHjighIUGSFBMTI6fT6auJjo5WTU1Nu/+2w+GQw+HwvYYkv9dtTV1dnXJycjRq1ChJ0ksvvaSLL75YW7du1eWXX66hQ4dq6NChvvrHH39cq1at0uuvv66srCzV19dLkp566imlpaVJkpYuXaq3335bv//97/X4449r6dKlSklJUU5Ojmw2my666CIdOnRIc+fO1a9//euAxw7AesxYAegyGmaqbDZbu35v6dKlOvvssxUfH6+RI0fqf//3fy0bU48ePTRy5Ejf84suukjnnHOOPvjgA0nSyZMn9fOf/1yXXHKJzjnnHJ199tnau3evb8aqwbhx43z/HBERobFjx2rPnj2SpA8++EBjxozxe99XXHGFTpw4oYMHD7Z5rB35OQDwIlgBCBkXXHCBbDabL1A0tXfvXsXFxalv377tet0ZM2aouLhYGzdu1PXXX69p06bpww8/tGLIkloOeg3HHnroIa1cuVLz58/Xxo0bVVxcrMGDB6u2tlaSFBcX942vYYxpdj6QkNnRnwMAghWAENKnTx9NnDhRS5cu1VdffeV3rqKiQq+88opuueWWds9YORwOXXDBBbr00kv13//934qIiNDOnTstGfOpU6f07rvv+p5/+OGHOnbsmC666CJJ0saNG3XHHXfo+9//vgYPHiyn06n9+/f76r/1rW+pR48efovV6+vrtWnTJl1yySWSpEsuuUSbNm3yW1u2adMmxcTEqF+/fm0ea0d+DgC8CFYAQkpOTo5qamo0efJkbdiwQaWlpcrPz9fEiRPVr18/zZ8/v92v6fF4VF1draqqKr3wwgvyeDy69NJLLRlvz549NWvWLG3ZskXbt2/Xj370I40ePVqXX365JO8sXF5enoqLi/Xee+9p+vTpvnVVknT22Wfrpz/9qR566CG9+eab+uCDD3TPPffo0KFDuueeeyRJ99xzj0pLSzVr1izt3btXf//73zVv3jzdf//9ioho+7/GO/JzAOBFsAIQUgYNGqR3331X3/rWt3TLLbfoW9/6lu666y5dffXVKiwsDKiHVU5OjqKjo3XuuedqyZIlevHFF1tdIN9evXr10ty5czV9+nSNGTNG0dHRys3N9Z3/7W9/q7i4OI0dO1ZTpkzR5MmT9Z3vfMfvNZ5++mndeOONmjlzpoYNG6b33ntPb731lpKSkiRJ/fr105tvvqmtW7dq6NChuvvuu3XnnXfqV7/6VbvG2pGfAwAvGoQCQIBefPFFZWdn69ixY8EeCoAQwYwVAACARQhWAAAAFuFSIAAAgEWYsQIAALAIwQoAAMAiBCsAAACLEKwAAAAsQrACAACwCMEKAADAIgQrAAAAixCsAAAALPL/ASmjI3H5R7u1AAAAAElFTkSuQmCC\n"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept: 27275.40097799508 Coef:  9183.592437483361\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "      Actual      Predicted\n0    37731.0   41050.789634\n1   122391.0  121866.403084\n2    57081.0   64928.129972\n3    63218.0   63091.411484\n4   116969.0  114519.529134\n5   109431.0  107172.655184\n6   112635.0  115437.888378\n7    55794.0   64009.770728\n8    83088.0   75948.440897\n9   101302.0   99825.781234\n10   56642.0   53907.819047\n11   66029.0   74111.722409\n12   64445.0   56662.896778\n13   61111.0   68601.566947\n14  113812.0  102580.858965",
      "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>Actual</th>\n      <th>Predicted</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>37731.0</td>\n      <td>41050.789634</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>122391.0</td>\n      <td>121866.403084</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>57081.0</td>\n      <td>64928.129972</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>63218.0</td>\n      <td>63091.411484</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>116969.0</td>\n      <td>114519.529134</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>109431.0</td>\n      <td>107172.655184</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>112635.0</td>\n      <td>115437.888378</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>55794.0</td>\n      <td>64009.770728</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>83088.0</td>\n      <td>75948.440897</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>101302.0</td>\n      <td>99825.781234</td>\n    </tr>\n    <tr>\n      <th>10</th>\n      <td>56642.0</td>\n      <td>53907.819047</td>\n    </tr>\n    <tr>\n      <th>11</th>\n      <td>66029.0</td>\n      <td>74111.722409</td>\n    </tr>\n    <tr>\n      <th>12</th>\n      <td>64445.0</td>\n      <td>56662.896778</td>\n    </tr>\n    <tr>\n      <th>13</th>\n      <td>61111.0</td>\n      <td>68601.566947</td>\n    </tr>\n    <tr>\n      <th>14</th>\n      <td>113812.0</td>\n      <td>102580.858965</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "url = 'https://raw.githubusercontent.com/AnnaShestova/salary-years-simple-linear-regression/master/Salary_Data.csv'\n",
    "df = pd.read_csv(url)\n",
    "\n",
    "years_experience = df['YearsExperience'].to_numpy()\n",
    "salary = df['Salary'].to_numpy()\n",
    "\n",
    "dictionary = {\n",
    "    'years_experience': years_experience,\n",
    "    'salary': salary\n",
    "}\n",
    "\n",
    "dataset = pd.DataFrame(dictionary)\n",
    "\n",
    "plt.scatter(dataset['years_experience'], dataset['salary'], color='r', label='данные з/п')\n",
    "plt.xlabel(\"Опыт работы\")\n",
    "plt.ylabel(\"Зарплата\")\n",
    "plt.show()\n",
    "\n",
    "x = dataset.iloc[:, :-1].values\n",
    "y = dataset.iloc[:, 1].values\n",
    "x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.5, random_state=0)\n",
    "regressor = LinearRegression()\n",
    "regressor.fit(x_train, y_train)\n",
    "\n",
    "# коэф\n",
    "print(f'Intercept: {regressor.intercept_} Coef:  {float(regressor.coef_)}')\n",
    "\n",
    "y_pred = regressor.predict(x_test)\n",
    "df = pd.DataFrame({'Actual': y_test, 'Predicted': y_pred})\n",
    "df.plot(kind='bar')\n",
    "plt.grid(which='major', linestyle='-', linewidth='0.5', color='green')\n",
    "plt.grid(which='minor', linestyle=':', linewidth='0.5', color='black')\n",
    "plt.show()\n",
    "plt.scatter(x_test, y_test, color='black')\n",
    "plt.plot(x_test, y_pred, color='green', linewidth=1)\n",
    "plt.show()\n",
    "df"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "1.3. Теоретический материал – Множественная регрессия\n",
    "\n",
    "В предыдущем примере мы проиллюстрировали линейную регрессию\n",
    "с двумя переменными. Однако, почти все реальные задачи имеют больше\n",
    "параметров. Линейная регрессия с участием нескольких переменных\n",
    "называется «множественной линейной регрессией» или многомерной\n",
    "линейной регрессией. Шаги для выполнения множественной линейной\n",
    "регрессии аналогичны шагам для простой . Разница заключается в оценке.\n",
    "Вы можете использовать множественную регрессию, чтобы узнать, какой\n",
    "фактор оказывает наибольшее влияние на прогнозируемый результат или\n",
    "как различные переменные связаны друг с другом.\n"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "1.3.1 Пример\n",
    "\n",
    "Для решения задачи множественной регрессии можно задействовать уже\n",
    "известный метод numpy.linalg.lstsq.\n"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.1338682   0.26840334 -0.02874936  1.5122571 ]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "y = [1, 2, 3, 4, 3, 4, 5, 3, 5, 5, 4, 5, 4, 5, 4, 5, 6, 0, 6, 3, 1, 3, 1]\n",
    "x = [[0, 2, 4, 1, 5, 4, 5, 9, 9, 9, 3, 7, 8, 8, 6, 6, 5, 5, 5, 6, 6, 5, 5],\n",
    "     [4, 1, 2, 3, 4, 5, 6, 7, 5, 8, 7, 8, 7, 8, 7, 8, 6, 8, 9, 2, 1, 5, 6],\n",
    "     [4, 1, 2, 5, 6, 7, 8, 9, 7, 8, 7, 8, 7, 4, 3, 1, 2, 3, 4, 1, 3, 9, 7]]\n",
    "x = np.transpose(x)\n",
    "x = np.c_[x, np.ones(x.shape[0])]\n",
    "linreg = np.linalg.lstsq(x, y, rcond=None)[0]\n",
    "print(linreg)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Кроме этого можно использовать возможности библиотеки sсikit-learn.\n",
    "Рассмотрим пример"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "1.3.2 Пример\n",
    "\n",
    "Для данных из предыдущей задачи построить модель множественной\n",
    "линейной регрессии с использованием средств библиотеки sсikit-learn.\n"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "outputs": [
    {
     "data": {
      "text/plain": "   y  x1  x2  x3\n0  1   0   4   4\n1  2   2   1   1\n2  3   4   2   2\n3  4   1   3   5\n4  3   5   4   6",
      "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>y</th>\n      <th>x1</th>\n      <th>x2</th>\n      <th>x3</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>1</td>\n      <td>0</td>\n      <td>4</td>\n      <td>4</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>2</td>\n      <td>2</td>\n      <td>1</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>3</td>\n      <td>4</td>\n      <td>2</td>\n      <td>2</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>4</td>\n      <td>1</td>\n      <td>3</td>\n      <td>5</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>3</td>\n      <td>5</td>\n      <td>4</td>\n      <td>6</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Импортируем необходимые библиотеки\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as seabornInstance\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn import metrics\n",
    "\n",
    "y = [1, 2, 3, 4, 3, 4, 5, 3, 5, 5, 4, 5, 4, 5, 4, 5, 6, 0, 6, 3, 1, 3, 1]\n",
    "x = [[0, 2, 4, 1, 5, 4, 5, 9, 9, 9, 3, 7, 8, 8, 6, 6, 5, 5, 5, 6, 6, 5, 5],\n",
    "     [4, 1, 2, 3, 4, 5, 6, 7, 5, 8, 7, 8, 7, 8, 7, 8, 6, 8, 9, 2, 1, 5, 6],\n",
    "     [4, 1, 2, 5, 6, 7, 8, 9, 7, 8, 7, 8, 7, 4, 3, 1, 2, 3, 4, 1, 3, 9, 7]]\n",
    "#формируем DataFrame из двух списков\n",
    "new_y = np.array(y)\n",
    "new_y = new_y.transpose()\n",
    "df1 = pd.DataFrame(new_y)\n",
    "new_x = np.array(x)\n",
    "new_x = new_x.transpose()\n",
    "df2 = pd.DataFrame(new_x)\n",
    "df1 = df1.rename(columns={0: 'y'}, inplace=False)\n",
    "df2 = df2.rename(columns={0: 'x1', 1: 'x2', 2: 'x3'}, inplace=False)\n",
    "\n",
    "frames = [df1, df2]\n",
    "dataset = pd.concat([df1, df2], axis=1, join=\"inner\")\n",
    "dataset.head()"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(23, 4)\n"
     ]
    },
    {
     "data": {
      "text/plain": "               y         x1         x2         x3\ncount  23.000000  23.000000  23.000000  23.000000\nmean    3.565217   5.347826   5.521739   5.043478\nstd     1.674029   2.404706   2.428422   2.704849\nmin     0.000000   0.000000   1.000000   1.000000\n25%     3.000000   4.500000   4.000000   3.000000\n50%     4.000000   5.000000   6.000000   5.000000\n75%     5.000000   6.500000   7.500000   7.000000\nmax     6.000000   9.000000   9.000000   9.000000",
      "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>y</th>\n      <th>x1</th>\n      <th>x2</th>\n      <th>x3</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>count</th>\n      <td>23.000000</td>\n      <td>23.000000</td>\n      <td>23.000000</td>\n      <td>23.000000</td>\n    </tr>\n    <tr>\n      <th>mean</th>\n      <td>3.565217</td>\n      <td>5.347826</td>\n      <td>5.521739</td>\n      <td>5.043478</td>\n    </tr>\n    <tr>\n      <th>std</th>\n      <td>1.674029</td>\n      <td>2.404706</td>\n      <td>2.428422</td>\n      <td>2.704849</td>\n    </tr>\n    <tr>\n      <th>min</th>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>1.000000</td>\n      <td>1.000000</td>\n    </tr>\n    <tr>\n      <th>25%</th>\n      <td>3.000000</td>\n      <td>4.500000</td>\n      <td>4.000000</td>\n      <td>3.000000</td>\n    </tr>\n    <tr>\n      <th>50%</th>\n      <td>4.000000</td>\n      <td>5.000000</td>\n      <td>6.000000</td>\n      <td>5.000000</td>\n    </tr>\n    <tr>\n      <th>75%</th>\n      <td>5.000000</td>\n      <td>6.500000</td>\n      <td>7.500000</td>\n      <td>7.000000</td>\n    </tr>\n    <tr>\n      <th>max</th>\n      <td>6.000000</td>\n      <td>9.000000</td>\n      <td>9.000000</td>\n      <td>9.000000</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(dataset.shape)\n",
    "dataset.describe()"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "outputs": [
    {
     "data": {
      "text/plain": "LinearRegression()"
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = dataset[['x1', 'x2', 'x3']]\n",
    "y = dataset['y']\n",
    "\n",
    "x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2, random_state=0)\n",
    "\n",
    "regressor = LinearRegression()\n",
    "regressor.fit(x_train, y_train)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "outputs": [
    {
     "data": {
      "text/plain": "    Coefficient\nx1     0.223219\nx2     0.136709\nx3    -0.063757",
      "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>Coefficient</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>x1</th>\n      <td>0.223219</td>\n    </tr>\n    <tr>\n      <th>x2</th>\n      <td>0.136709</td>\n    </tr>\n    <tr>\n      <th>x3</th>\n      <td>-0.063757</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coeff_df = pd.DataFrame(regressor.coef_, x.columns, columns=['Coefficient'])\n",
    "coeff_df"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "outputs": [
    {
     "data": {
      "text/plain": "    Actual   Predict\n11       5  4.119478\n10       4  3.153648\n21       3  3.199155\n14       4  4.078333\n20       1  3.258079",
      "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>Actual</th>\n      <th>Predict</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>11</th>\n      <td>5</td>\n      <td>4.119478</td>\n    </tr>\n    <tr>\n      <th>10</th>\n      <td>4</td>\n      <td>3.153648</td>\n    </tr>\n    <tr>\n      <th>21</th>\n      <td>3</td>\n      <td>3.199155</td>\n    </tr>\n    <tr>\n      <th>14</th>\n      <td>4</td>\n      <td>4.078333</td>\n    </tr>\n    <tr>\n      <th>20</th>\n      <td>1</td>\n      <td>3.258079</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = regressor.predict(x_test)\n",
    "df = pd.DataFrame({'Actual': y_test, 'Predict': y_pred})\n",
    "df"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean Squared Error: 1.3272699242343065\n"
     ]
    }
   ],
   "source": [
    "#Последний шаг - оценить производительность алгоритмов. Мы сделаем это, найдя значения для MSE\n",
    "print('Mean Squared Error:', metrics.mean_squared_error(y_test, y_pred))"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Задание\n",
    "\n",
    "Постройте модель множественной линейной регрессии для произвольных\n",
    "данных из нескольких столбцов. Для примера можно взять потребления\n",
    "газа (в миллионах галлонов) в 48 штатах США или набор данных о\n",
    "качестве красного вина (1) и (2) соответственно. Найдите коэффициенты\n",
    "множественной регрессии. Постройте прогноз.\n",
    "1.\n",
    "https://raw.githubusercontent.com/likarajo/petrol_consumption/master/data/petrol_consumption.csv\n",
    "2.\n",
    "https://raw.githubusercontent.com/aniruddhachoudhury/Red-WineQuality/master/winequality-red.csv"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "outputs": [
    {
     "data": {
      "text/plain": "    Petrol tax  Average income  Paved Highways  Population Driver licence  \\\n0         9.00            3571            1976                      0.525   \n1         9.00            4092            1250                      0.572   \n2         9.00            3865            1586                      0.580   \n3         7.50            4870            2351                      0.529   \n4         8.00            4399             431                      0.544   \n5        10.00            5342            1333                      0.571   \n6         8.00            5319           11868                      0.451   \n7         8.00            5126            2138                      0.553   \n8         8.00            4447            8577                      0.529   \n9         7.00            4512            8507                      0.552   \n10        8.00            4391            5939                      0.530   \n11        7.50            5126           14186                      0.525   \n12        7.00            4817            6930                      0.574   \n13        7.00            4207            6580                      0.545   \n14        7.00            4332            8159                      0.608   \n15        7.00            4318           10340                      0.586   \n16        7.00            4206            8508                      0.572   \n17        7.00            3718            4725                      0.540   \n18        7.00            4716            5915                      0.724   \n19        8.50            4341            6010                      0.677   \n20        7.00            4593            7834                      0.663   \n21        8.00            4983             602                      0.602   \n22        9.00            4897            2449                      0.511   \n23        9.00            4258            4686                      0.517   \n24        8.50            4574            2619                      0.551   \n25        9.00            3721            4746                      0.544   \n26        8.00            3448            5399                      0.548   \n27        7.50            3846            9061                      0.579   \n28        8.00            4188            5975                      0.563   \n29        9.00            3601            4650                      0.493   \n30        7.00            3640            6905                      0.518   \n31        7.00            3333            6594                      0.513   \n32        8.00            3063            6524                      0.578   \n33        7.50            3357            4121                      0.547   \n34        8.00            3528            3495                      0.487   \n35        6.58            3802            7834                      0.629   \n36        5.00            4045           17782                      0.566   \n37        7.00            3897            6385                      0.586   \n38        8.50            3635            3274                      0.663   \n39        7.00            4345            3905                      0.672   \n40        7.00            4449            4639                      0.626   \n41        7.00            3656            3985                      0.563   \n42        7.00            4300            3635                      0.603   \n43        7.00            3745            2611                      0.508   \n44        6.00            5215            2302                      0.672   \n45        9.00            4476            3942                      0.571   \n46        7.00            4296            4083                      0.623   \n47        7.00            5002            9794                      0.593   \n\n    Petrol Consumption  \n0                  541  \n1                  524  \n2                  561  \n3                  414  \n4                  410  \n5                  457  \n6                  344  \n7                  467  \n8                  464  \n9                  498  \n10                 580  \n11                 471  \n12                 525  \n13                 508  \n14                 566  \n15                 635  \n16                 603  \n17                 714  \n18                 865  \n19                 640  \n20                 649  \n21                 540  \n22                 464  \n23                 547  \n24                 460  \n25                 566  \n26                 577  \n27                 631  \n28                 574  \n29                 534  \n30                 571  \n31                 554  \n32                 577  \n33                 628  \n34                 487  \n35                 644  \n36                 640  \n37                 704  \n38                 648  \n39                 968  \n40                 587  \n41                 699  \n42                 632  \n43                 591  \n44                 782  \n45                 510  \n46                 610  \n47                 524  ",
      "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>Petrol tax</th>\n      <th>Average income</th>\n      <th>Paved Highways</th>\n      <th>Population Driver licence</th>\n      <th>Petrol Consumption</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>9.00</td>\n      <td>3571</td>\n      <td>1976</td>\n      <td>0.525</td>\n      <td>541</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>9.00</td>\n      <td>4092</td>\n      <td>1250</td>\n      <td>0.572</td>\n      <td>524</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>9.00</td>\n      <td>3865</td>\n      <td>1586</td>\n      <td>0.580</td>\n      <td>561</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>7.50</td>\n      <td>4870</td>\n      <td>2351</td>\n      <td>0.529</td>\n      <td>414</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>8.00</td>\n      <td>4399</td>\n      <td>431</td>\n      <td>0.544</td>\n      <td>410</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>10.00</td>\n      <td>5342</td>\n      <td>1333</td>\n      <td>0.571</td>\n      <td>457</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>8.00</td>\n      <td>5319</td>\n      <td>11868</td>\n      <td>0.451</td>\n      <td>344</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>8.00</td>\n      <td>5126</td>\n      <td>2138</td>\n      <td>0.553</td>\n      <td>467</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>8.00</td>\n      <td>4447</td>\n      <td>8577</td>\n      <td>0.529</td>\n      <td>464</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>7.00</td>\n      <td>4512</td>\n      <td>8507</td>\n      <td>0.552</td>\n      <td>498</td>\n    </tr>\n    <tr>\n      <th>10</th>\n      <td>8.00</td>\n      <td>4391</td>\n      <td>5939</td>\n      <td>0.530</td>\n      <td>580</td>\n    </tr>\n    <tr>\n      <th>11</th>\n      <td>7.50</td>\n      <td>5126</td>\n      <td>14186</td>\n      <td>0.525</td>\n      <td>471</td>\n    </tr>\n    <tr>\n      <th>12</th>\n      <td>7.00</td>\n      <td>4817</td>\n      <td>6930</td>\n      <td>0.574</td>\n      <td>525</td>\n    </tr>\n    <tr>\n      <th>13</th>\n      <td>7.00</td>\n      <td>4207</td>\n      <td>6580</td>\n      <td>0.545</td>\n      <td>508</td>\n    </tr>\n    <tr>\n      <th>14</th>\n      <td>7.00</td>\n      <td>4332</td>\n      <td>8159</td>\n      <td>0.608</td>\n      <td>566</td>\n    </tr>\n    <tr>\n      <th>15</th>\n      <td>7.00</td>\n      <td>4318</td>\n      <td>10340</td>\n      <td>0.586</td>\n      <td>635</td>\n    </tr>\n    <tr>\n      <th>16</th>\n      <td>7.00</td>\n      <td>4206</td>\n      <td>8508</td>\n      <td>0.572</td>\n      <td>603</td>\n    </tr>\n    <tr>\n      <th>17</th>\n      <td>7.00</td>\n      <td>3718</td>\n      <td>4725</td>\n      <td>0.540</td>\n      <td>714</td>\n    </tr>\n    <tr>\n      <th>18</th>\n      <td>7.00</td>\n      <td>4716</td>\n      <td>5915</td>\n      <td>0.724</td>\n      <td>865</td>\n    </tr>\n    <tr>\n      <th>19</th>\n      <td>8.50</td>\n      <td>4341</td>\n      <td>6010</td>\n      <td>0.677</td>\n      <td>640</td>\n    </tr>\n    <tr>\n      <th>20</th>\n      <td>7.00</td>\n      <td>4593</td>\n      <td>7834</td>\n      <td>0.663</td>\n      <td>649</td>\n    </tr>\n    <tr>\n      <th>21</th>\n      <td>8.00</td>\n      <td>4983</td>\n      <td>602</td>\n      <td>0.602</td>\n      <td>540</td>\n    </tr>\n    <tr>\n      <th>22</th>\n      <td>9.00</td>\n      <td>4897</td>\n      <td>2449</td>\n      <td>0.511</td>\n      <td>464</td>\n    </tr>\n    <tr>\n      <th>23</th>\n      <td>9.00</td>\n      <td>4258</td>\n      <td>4686</td>\n      <td>0.517</td>\n      <td>547</td>\n    </tr>\n    <tr>\n      <th>24</th>\n      <td>8.50</td>\n      <td>4574</td>\n      <td>2619</td>\n      <td>0.551</td>\n      <td>460</td>\n    </tr>\n    <tr>\n      <th>25</th>\n      <td>9.00</td>\n      <td>3721</td>\n      <td>4746</td>\n      <td>0.544</td>\n      <td>566</td>\n    </tr>\n    <tr>\n      <th>26</th>\n      <td>8.00</td>\n      <td>3448</td>\n      <td>5399</td>\n      <td>0.548</td>\n      <td>577</td>\n    </tr>\n    <tr>\n      <th>27</th>\n      <td>7.50</td>\n      <td>3846</td>\n      <td>9061</td>\n      <td>0.579</td>\n      <td>631</td>\n    </tr>\n    <tr>\n      <th>28</th>\n      <td>8.00</td>\n      <td>4188</td>\n      <td>5975</td>\n      <td>0.563</td>\n      <td>574</td>\n    </tr>\n    <tr>\n      <th>29</th>\n      <td>9.00</td>\n      <td>3601</td>\n      <td>4650</td>\n      <td>0.493</td>\n      <td>534</td>\n    </tr>\n    <tr>\n      <th>30</th>\n      <td>7.00</td>\n      <td>3640</td>\n      <td>6905</td>\n      <td>0.518</td>\n      <td>571</td>\n    </tr>\n    <tr>\n      <th>31</th>\n      <td>7.00</td>\n      <td>3333</td>\n      <td>6594</td>\n      <td>0.513</td>\n      <td>554</td>\n    </tr>\n    <tr>\n      <th>32</th>\n      <td>8.00</td>\n      <td>3063</td>\n      <td>6524</td>\n      <td>0.578</td>\n      <td>577</td>\n    </tr>\n    <tr>\n      <th>33</th>\n      <td>7.50</td>\n      <td>3357</td>\n      <td>4121</td>\n      <td>0.547</td>\n      <td>628</td>\n    </tr>\n    <tr>\n      <th>34</th>\n      <td>8.00</td>\n      <td>3528</td>\n      <td>3495</td>\n      <td>0.487</td>\n      <td>487</td>\n    </tr>\n    <tr>\n      <th>35</th>\n      <td>6.58</td>\n      <td>3802</td>\n      <td>7834</td>\n      <td>0.629</td>\n      <td>644</td>\n    </tr>\n    <tr>\n      <th>36</th>\n      <td>5.00</td>\n      <td>4045</td>\n      <td>17782</td>\n      <td>0.566</td>\n      <td>640</td>\n    </tr>\n    <tr>\n      <th>37</th>\n      <td>7.00</td>\n      <td>3897</td>\n      <td>6385</td>\n      <td>0.586</td>\n      <td>704</td>\n    </tr>\n    <tr>\n      <th>38</th>\n      <td>8.50</td>\n      <td>3635</td>\n      <td>3274</td>\n      <td>0.663</td>\n      <td>648</td>\n    </tr>\n    <tr>\n      <th>39</th>\n      <td>7.00</td>\n      <td>4345</td>\n      <td>3905</td>\n      <td>0.672</td>\n      <td>968</td>\n    </tr>\n    <tr>\n      <th>40</th>\n      <td>7.00</td>\n      <td>4449</td>\n      <td>4639</td>\n      <td>0.626</td>\n      <td>587</td>\n    </tr>\n    <tr>\n      <th>41</th>\n      <td>7.00</td>\n      <td>3656</td>\n      <td>3985</td>\n      <td>0.563</td>\n      <td>699</td>\n    </tr>\n    <tr>\n      <th>42</th>\n      <td>7.00</td>\n      <td>4300</td>\n      <td>3635</td>\n      <td>0.603</td>\n      <td>632</td>\n    </tr>\n    <tr>\n      <th>43</th>\n      <td>7.00</td>\n      <td>3745</td>\n      <td>2611</td>\n      <td>0.508</td>\n      <td>591</td>\n    </tr>\n    <tr>\n      <th>44</th>\n      <td>6.00</td>\n      <td>5215</td>\n      <td>2302</td>\n      <td>0.672</td>\n      <td>782</td>\n    </tr>\n    <tr>\n      <th>45</th>\n      <td>9.00</td>\n      <td>4476</td>\n      <td>3942</td>\n      <td>0.571</td>\n      <td>510</td>\n    </tr>\n    <tr>\n      <th>46</th>\n      <td>7.00</td>\n      <td>4296</td>\n      <td>4083</td>\n      <td>0.623</td>\n      <td>610</td>\n    </tr>\n    <tr>\n      <th>47</th>\n      <td>7.00</td>\n      <td>5002</td>\n      <td>9794</td>\n      <td>0.593</td>\n      <td>524</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn import metrics\n",
    "\n",
    "url = r\"https://raw.githubusercontent.com/likarajo/petrol_consumption/master/data/petrol_consumption.csv\"\n",
    "\n",
    "dataframe_raw = pd.read_csv(url, on_bad_lines='skip')\n",
    "\n",
    "petrol_tax = dataframe_raw.iloc[:, 0].values  # pt\n",
    "avg_income = dataframe_raw.iloc[:, 1].values  # ai\n",
    "paved_highways = dataframe_raw.iloc[:, 2].values  # ph\n",
    "pop_driver_license = dataframe_raw.iloc[:, 3].values  # pdl\n",
    "petrol_consumption = dataframe_raw.iloc[:, 4].values  # pc\n",
    "\n",
    "df_pt = pd.DataFrame(np.array(petrol_tax).transpose())\n",
    "df_ai = pd.DataFrame(np.array(avg_income).transpose())\n",
    "df_ph = pd.DataFrame(np.array(paved_highways).transpose())\n",
    "df_pdl = pd.DataFrame(np.array(pop_driver_license).transpose())\n",
    "df_pc = pd.DataFrame(np.array(petrol_consumption).transpose())\n",
    "\n",
    "df_pt = df_pt.rename(columns={0: 'Petrol tax'}, inplace=False)\n",
    "df_ai = df_ai.rename(columns={0: 'Average income'}, inplace=False)\n",
    "df_ph = df_ph.rename(columns={0: 'Paved Highways'}, inplace=False)\n",
    "df_pdl = df_pdl.rename(columns={0: 'Population Driver licence'}, inplace=False)\n",
    "df_pc = df_pc.rename(columns={0: 'Petrol Consumption'}, inplace=False)\n",
    "\n",
    "frames = [df_pt, df_ai, df_ph, df_pdl, df_pc]\n",
    "dataset = pd.concat(frames, axis=1, join=\"inner\")\n",
    "dataset"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean Squared Error:  3307.87066396728\n"
     ]
    }
   ],
   "source": [
    "x = dataset[['Petrol tax', 'Average income', 'Paved Highways', 'Population Driver licence']]\n",
    "y = dataset['Petrol Consumption']\n",
    "\n",
    "x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.5, random_state=0)\n",
    "\n",
    "regressor = LinearRegression()\n",
    "regressor.fit(x_train, y_train)\n",
    "\n",
    "coefficient_df = pd.DataFrame(regressor.coef_, x.columns, columns=['Coefficient'])\n",
    "y_pred = regressor.predict(x_test)\n",
    "df = pd.DataFrame({'Actual': y_test, 'Predict': y_pred})\n",
    "\n",
    "print('Mean Squared Error: ', metrics.mean_squared_error(y_test, y_pred))"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "outputs": [
    {
     "data": {
      "text/plain": "                           Coefficient\nPetrol tax                  -44.480205\nAverage income               -0.070439\nPaved Highways               -0.006585\nPopulation Driver licence  1293.646006",
      "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>Coefficient</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>Petrol tax</th>\n      <td>-44.480205</td>\n    </tr>\n    <tr>\n      <th>Average income</th>\n      <td>-0.070439</td>\n    </tr>\n    <tr>\n      <th>Paved Highways</th>\n      <td>-0.006585</td>\n    </tr>\n    <tr>\n      <th>Population Driver licence</th>\n      <td>1293.646006</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coefficient_df"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "outputs": [
    {
     "data": {
      "text/plain": "    Actual     Predict\n29     534  468.446949\n4      410  550.475773\n26     577  589.922533\n30     571  572.151628\n32     577  648.442611\n37     704  645.441003\n34     487  517.913312\n40     587  669.802235\n7      467  499.668226\n10     580  496.656659\n11     471  406.347089\n31     554  589.356261\n33     628  625.694916\n27     631  600.115638\n47     524  554.212026\n2      561  582.575412\n46     610  680.359903\n18     865  769.369480\n15     635  589.741398\n28     574  553.409075\n22     464  414.937462\n16     603  591.583736\n41     699  648.467615\n20     649  686.483997",
      "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>Actual</th>\n      <th>Predict</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>29</th>\n      <td>534</td>\n      <td>468.446949</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>410</td>\n      <td>550.475773</td>\n    </tr>\n    <tr>\n      <th>26</th>\n      <td>577</td>\n      <td>589.922533</td>\n    </tr>\n    <tr>\n      <th>30</th>\n      <td>571</td>\n      <td>572.151628</td>\n    </tr>\n    <tr>\n      <th>32</th>\n      <td>577</td>\n      <td>648.442611</td>\n    </tr>\n    <tr>\n      <th>37</th>\n      <td>704</td>\n      <td>645.441003</td>\n    </tr>\n    <tr>\n      <th>34</th>\n      <td>487</td>\n      <td>517.913312</td>\n    </tr>\n    <tr>\n      <th>40</th>\n      <td>587</td>\n      <td>669.802235</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>467</td>\n      <td>499.668226</td>\n    </tr>\n    <tr>\n      <th>10</th>\n      <td>580</td>\n      <td>496.656659</td>\n    </tr>\n    <tr>\n      <th>11</th>\n      <td>471</td>\n      <td>406.347089</td>\n    </tr>\n    <tr>\n      <th>31</th>\n      <td>554</td>\n      <td>589.356261</td>\n    </tr>\n    <tr>\n      <th>33</th>\n      <td>628</td>\n      <td>625.694916</td>\n    </tr>\n    <tr>\n      <th>27</th>\n      <td>631</td>\n      <td>600.115638</td>\n    </tr>\n    <tr>\n      <th>47</th>\n      <td>524</td>\n      <td>554.212026</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>561</td>\n      <td>582.575412</td>\n    </tr>\n    <tr>\n      <th>46</th>\n      <td>610</td>\n      <td>680.359903</td>\n    </tr>\n    <tr>\n      <th>18</th>\n      <td>865</td>\n      <td>769.369480</td>\n    </tr>\n    <tr>\n      <th>15</th>\n      <td>635</td>\n      <td>589.741398</td>\n    </tr>\n    <tr>\n      <th>28</th>\n      <td>574</td>\n      <td>553.409075</td>\n    </tr>\n    <tr>\n      <th>22</th>\n      <td>464</td>\n      <td>414.937462</td>\n    </tr>\n    <tr>\n      <th>16</th>\n      <td>603</td>\n      <td>591.583736</td>\n    </tr>\n    <tr>\n      <th>41</th>\n      <td>699</td>\n      <td>648.467615</td>\n    </tr>\n    <tr>\n      <th>20</th>\n      <td>649</td>\n      <td>686.483997</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "outputs": [
    {
     "data": {
      "text/plain": "    Actual   Predicted\n29     534  468.446949\n4      410  550.475773\n26     577  589.922533\n30     571  572.151628\n32     577  648.442611\n37     704  645.441003\n34     487  517.913312\n40     587  669.802235\n7      467  499.668226\n10     580  496.656659\n11     471  406.347089\n31     554  589.356261\n33     628  625.694916\n27     631  600.115638\n47     524  554.212026\n2      561  582.575412\n46     610  680.359903\n18     865  769.369480\n15     635  589.741398\n28     574  553.409075\n22     464  414.937462\n16     603  591.583736\n41     699  648.467615\n20     649  686.483997",
      "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>Actual</th>\n      <th>Predicted</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>29</th>\n      <td>534</td>\n      <td>468.446949</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>410</td>\n      <td>550.475773</td>\n    </tr>\n    <tr>\n      <th>26</th>\n      <td>577</td>\n      <td>589.922533</td>\n    </tr>\n    <tr>\n      <th>30</th>\n      <td>571</td>\n      <td>572.151628</td>\n    </tr>\n    <tr>\n      <th>32</th>\n      <td>577</td>\n      <td>648.442611</td>\n    </tr>\n    <tr>\n      <th>37</th>\n      <td>704</td>\n      <td>645.441003</td>\n    </tr>\n    <tr>\n      <th>34</th>\n      <td>487</td>\n      <td>517.913312</td>\n    </tr>\n    <tr>\n      <th>40</th>\n      <td>587</td>\n      <td>669.802235</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>467</td>\n      <td>499.668226</td>\n    </tr>\n    <tr>\n      <th>10</th>\n      <td>580</td>\n      <td>496.656659</td>\n    </tr>\n    <tr>\n      <th>11</th>\n      <td>471</td>\n      <td>406.347089</td>\n    </tr>\n    <tr>\n      <th>31</th>\n      <td>554</td>\n      <td>589.356261</td>\n    </tr>\n    <tr>\n      <th>33</th>\n      <td>628</td>\n      <td>625.694916</td>\n    </tr>\n    <tr>\n      <th>27</th>\n      <td>631</td>\n      <td>600.115638</td>\n    </tr>\n    <tr>\n      <th>47</th>\n      <td>524</td>\n      <td>554.212026</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>561</td>\n      <td>582.575412</td>\n    </tr>\n    <tr>\n      <th>46</th>\n      <td>610</td>\n      <td>680.359903</td>\n    </tr>\n    <tr>\n      <th>18</th>\n      <td>865</td>\n      <td>769.369480</td>\n    </tr>\n    <tr>\n      <th>15</th>\n      <td>635</td>\n      <td>589.741398</td>\n    </tr>\n    <tr>\n      <th>28</th>\n      <td>574</td>\n      <td>553.409075</td>\n    </tr>\n    <tr>\n      <th>22</th>\n      <td>464</td>\n      <td>414.937462</td>\n    </tr>\n    <tr>\n      <th>16</th>\n      <td>603</td>\n      <td>591.583736</td>\n    </tr>\n    <tr>\n      <th>41</th>\n      <td>699</td>\n      <td>648.467615</td>\n    </tr>\n    <tr>\n      <th>20</th>\n      <td>649</td>\n      <td>686.483997</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = pd.DataFrame({'Actual': y_test, 'Predicted': y_pred})\n",
    "df.plot(kind='bar')\n",
    "df"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Задание* вариант 8\n",
    "\n",
    "Экспериментально получены N − значений величины Y при\n",
    "различных значениях величины X. Построить полиномы первой и второй\n",
    "степени, аппроксимирующие результаты эксперимента, с применением\n",
    "метода наименьших квадратов. Результаты выводятся в виде таблиц\n",
    "значений и графиков, полученных полиномов.\n"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[5.  1. ]\n",
      " [5.2 1. ]\n",
      " [5.4 1. ]\n",
      " [5.6 1. ]\n",
      " [5.8 1. ]\n",
      " [6.  1. ]]\n",
      "-0.42857142857142483 5.190476190476168\n"
     ]
    }
   ],
   "source": [
    "x = np.array([5.0, 5.2, 5.4, 5.6, 5.8, 6.0])\n",
    "y = np.array([3.0, 2.0, 5.0, 2.0, 2.0, 3.0])\n",
    "#Переписываем линейное уравнение y = mx + c, как y = Ap, где A = [[x1]] и p = [[m], [c]]\n",
    "A = np.vstack([x, np.ones(len(x))]).T\n",
    "print(A)\n",
    "m, c = np.linalg.lstsq(A, y, rcond=None)[0]\n",
    "print(m, c)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.plot(x, y, 'o', label='Исходные данные', markersize=5)\n",
    "plt.plot(x, m * x + c, 'r', label='Линейная экстраполяция')\n",
    "plt.legend()\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ -0.89285714   9.39285714 -21.71428571]\n"
     ]
    }
   ],
   "source": [
    "m = np.vstack((x ** 2, x, np.ones(6))).T\n",
    "s = np.linalg.lstsq(m, y, rcond=None)[0]\n",
    "print(s)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_prec = np.linspace(3, 8, 10)\n",
    "plt.plot(x, y, 'D')\n",
    "plt.plot(x_prec, s[0] * x_prec ** 2 + s[1] * x_prec + s[2], '-', lw = 2)\n",
    "plt.grid()\n"
   ],
   "metadata": {
    "collapsed": false
   }
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}