Gradiant descent implementation of Linear regression for single and multivariant variables.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Practical Work 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this practical work, the student will have to develop a Python program that is able to implement the gradient descent in order to achieve the linear regression of a set of datapoints."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Import numpy, matplotlib.pyplot and make it inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Read RegData csv file into numpy array  (check your data)\n",
    "##### Data source\n",
    "https://college.cengage.com/mathematics/brase/understandable_statistics/7e/students/datasets/slr/frames/frame.html\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "df= pd.read_csv('RegData.csv' ,header=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.9</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>6.7</td>\n",
       "      <td>7.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.9</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7.9</td>\n",
       "      <td>7.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>9.8</td>\n",
       "      <td>7.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6.9</td>\n",
       "      <td>6.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6.1</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>6.2</td>\n",
       "      <td>5.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>6.0</td>\n",
       "      <td>5.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>5.1</td>\n",
       "      <td>4.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>4.7</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>4.4</td>\n",
       "      <td>4.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>5.8</td>\n",
       "      <td>5.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      0    1\n",
       "0   2.9  4.0\n",
       "1   6.7  7.4\n",
       "2   4.9  5.0\n",
       "3   7.9  7.2\n",
       "4   9.8  7.9\n",
       "5   6.9  6.1\n",
       "6   6.1  6.0\n",
       "7   6.2  5.8\n",
       "8   6.0  5.2\n",
       "9   5.1  4.2\n",
       "10  4.7  4.0\n",
       "11  4.4  4.4\n",
       "12  5.8  5.2"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Explore your data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot.scatter(0,1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Define variables X and y. Assign first column data to X and second column to y\n",
    "<b>Note:</b> X is the independent variable (input to LR model) and y is the dependent variable (output)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "x=df.loc[: , 0].to_numpy()\n",
    "y=df.loc[:, 1].to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.9000001  6.69999981 4.9000001  7.9000001  9.80000019 6.9000001\n",
      " 6.0999999  6.19999981 6.         5.0999999  4.69999981 4.4000001\n",
      " 5.80000019]\n",
      "[4.         7.4000001  5.         7.19999981 7.9000001  6.0999999\n",
      " 6.         5.80000019 5.19999981 4.19999981 4.         4.4000001\n",
      " 5.19999981]\n"
     ]
    }
   ],
   "source": [
    "print(x)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Explore your data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.9000001 , 6.69999981, 4.9000001 , 7.9000001 , 9.80000019,\n",
       "       6.9000001 , 6.0999999 , 6.19999981, 6.        , 5.0999999 ,\n",
       "       4.69999981, 4.4000001 , 5.80000019])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4.        , 7.4000001 , 5.        , 7.19999981, 7.9000001 ,\n",
       "       6.0999999 , 6.        , 5.80000019, 5.19999981, 4.19999981,\n",
       "       4.        , 4.4000001 , 5.19999981])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot the original data (scatter plot of X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## LR Full Implementation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step1: Initialize parameters (theta_0 & theta_1) with random value or simply zero. Also choose the Learning rate. "
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_0= 0\n",
    "theta_1= 0\n",
    "r=0.001"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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QpU/TZo0cgh260FbJB735z/SP+VJ3tHHzEBPPSECMyzXYI4+5iPGC/HxbADObG0et65hvWzmU38pLHRDAw5fR/qf9mL4xX7vuUjcmI3ccpV1TZ2BvbZ+yUIc+gEGcU4jvQ1NcU217lD4yab19WZueQ4jislPGhh133HGJ+9aG+JbfTTfdtIS3r2mePp7fzRL5W2yxRUk20MuTOogHu3zmxqgPfehDpScQvdj0BVm854hhz26g7MTJHBXf30MuHkwrG8fDDz+8uOuuu0qyY5u0+P9HPeehDXJzRI5Pf/i62GSTTco2HbEAP/Rec801h/T++te/XpbR4+axHse5bz/0r76WnU4jFuNqg+Ool7ERRW/IpDqCNxr7Kpg31FN5co9JOmVIRR2Y3KKMKoOOycBPPJ6oeOOZyTYVmJBjfujKRGhP+3nCEuMgu02IMqrqAcMxZRxUpTFdxkkUKQN6gXkMVm8efx8HA42JK6Zl0Pf1B+5tg590mmBUKR8PohG/TJsZSm/fByRNMHqG4k3gwgxsa6vUScqYNAPd4oF/rt46qT2FWGIoWrmriEWu3LRfS2/GfC6u5UW9xHrw41bTsdHnA9lEvu87XGN4I4++al4o05djJHuMyYwZvg9RLtIiA3mWPpa3S58mX8YSxgQbZ618XMe2bP/ZEZ35+QeLufq0ekj97+fLFGnJld30aHJs2mZiPCsfYyL9k7HNl7fqoViXuqkrk+E5arumXIZrxNzypr9YHNp4KkS8Ypy++ojJnZTell+b45e+9KUBXoYbnizeFzzggAOKb3/72+VH6e0/O15yySXlpyTa5BXj8qkHT4zI98tf/nLWgwbJu/jii5fQF50OPfTQMh0bvPDO4UorrVR8/vOfL9s/G/KwEQxtI5IorlkyaeXi+LGPfWzwbiYbyfj/upzz+Y2qb1K+733vG8rroIMOKnd85R1ASIr/Icfr8vSnP71crgtxI17fweftz7/4xS+WeoDhd77znXJDIlua7OO11WlasRhHG+y7rpA3FqJIB0oRDN8QMQDGEeLE7vP053X5e8OHdLlJgjJgUPj4UTbGiM87krsUXuAXCa1NjF5WG0LCJO/TMuFUBXta69NgtDUJfjKrwq5KFuniBG4TN0Yo5zFwD6MvRTjsQUKOBPp6QkZbrxY6GVZVDxWizslrv0vnCiuwVrb655eejuBpTuowwk3K7fsCeFQZkuZNob3HfjFC9ukkU4il7x+RNKULMXy3zji12NQHdQC+pEkF6xfEo92n+lUqnb/nxwpID2Qu9h9P9siLfGPg4RT/mS4QDQvoTz5eruk+Sp9GDuUlr9w4GsdM0yUefflTRJC2TT65uvbtgXHEh6Z17dOkzpvK8fHQxXs5Ta61q6oydakbyyd3tPy7tGtft3Ge8flSRn65eczjFR9ieDm+jXTpI5PW25eh6hzjnY+4G1525HMRfLMPL9wtt9xSrLXWWkNx2GCF5ZjsDtqWAJg+pGPzFcuT40tf+tLiRz/6UfbTCqRhrHvSk540lI60eA4hTxCX1VZbrTj99NML3nFjzCBNJIimB8s6vQ6cH3HEEQOiCEm77rrryp08zzvvvGLUHxvzXH755aXtmdKFfCJhfc5znlOsv/76Q0tsbbkt/3m9eacU8t7nu5XgjaeWB8eQ79TP9KCvsQkPtnQqHt7O++67L1sPVh8cpxEL028cbdBk93kcC1FEQW80+wZo5zSWcQQGUSYPy6fqmNPBJiGfNheXQcOTU/L2hgxljAQP+T5gpPi8OE8Z11EO8erInuUTyWyTdEyAvh6ZBONTd5Mfj97wyU2wMU28Jl2cwP2knDI0kcHgQjvwgXqyp+C5MhDH10NOvpdr58j0adGzU8CI9h5FyF/Vz7+Dl3ny3UmfmsSUH9zBAMPSDHCuq4w5Iw+5/lWTbbO/pxBLM6KtzTQryOJYvh9UGac2NlXFQarFQ5/4oGtxrvkz39/Ji76UCj4fjOUYfLlSY6mP37VPW3tlXKgKfgzMxfP1mSKKVu7cuEu5Ge/AP+LiMamrx5x+3G8qx8dD71xdGi7UUwxd6ybKi9eGZx0eFi/VridNuPrqI5PWO2Kfu/bLBm1ce8YznlGceuqpJTliI5s77rhjyOtHPL43yCcQuryLxjJS701E7sEHH1zmm2u/lAOS9YY3vGFo7iYtm+F8/OMfLyAuF110UbkEEi9ibpmnYfLZz352CVknnXRScffdd5ckmE1Z/va3v5V2FHNmlx8kLrfJyyGHHLKEHlYnTY6k7/tTJt///vc76eT1hnCynDQu/bV68MdpxMLr13cb9LL7Oh8bUfRLiHwF23n0lvVVIORAxLyhanmmjpFQkB6jNcaN5M70hdD5uCkjywiKxWNw8IGn5vafHSPZJL4ZNhaHY+5JuJfPOZ5A4jOpN01DOowGMMqVP+Zj135S7JMoIt/qlrKkPAlgFzG2J/qkwbjI/Ty2rJFvGky+pW+aLhuP9/mMKOJRrAt+6emEPYqU3erE6sPXP5jkDDraBr+qybyu6LX/TyGW3tgDH/pZm+CN+Ry2vk2myIvPzz+sShn+Pm7q3Nd3VV6eUFHuWO9NymX5W/lG6dOMEaRDh/gwyuTbEXyJxy8XfH3G8jN2Wvq6cZQyxdAGk5jWXzeV0zSeEdsULl3qxuucOjfZ5BuxjvGr2rWvs6o2YHWXm8ea4tVXH5m03hHT3HVq2enb3/720jPFfIxBbEsLDVOOO+ywQ7maBM/PqGG33XYb9DFk8t1ANomhn+fIFHnh0YEQen04Z7dSPIl4/NgIB29nlRyTFT2qbNYDQbIlnOQHDl1/yOGXCtxn8x1fJsgSy34ZfyHu/ve5z31uKO66665bbrZz5513lnqm8hjl3ic/+cnSo8m7kBDw+Hv84x9f6gH22MzPfvazl4hjaSgHRLGOuE8rFh4/dOyrDXq5fZ7nZ76OuTB42hNH32A598uJOmaTTc7AZN6KmL+/ThE7PwESNzdBYOSYgWwyKRuTl/0i6SS+D+hpBovJyBl+US/ig3NdMByojzpDpU5W0//9pJjDr04W6VITuC1XNLx4aszAURXMYEAmE22TX5vNPUw+OsU6rtIr+x8eUSOKFQbqIL1fejrBdxQx2qyfU+c++Kf54BL/NwOauhhrmEIsvXEJNm37pU+fGy940GF9pM6g9ks+SdOm7VN3vr/X5eXHu0iMmpTL2or1uVH6tKWlrHX6diWKfslh6gGglSd3bINJTgb3m8ppGg/crX3FfA3fUeomyorXfbVrxh3TPzXPWL4Wh7KkQlO8+uojk9Y7VeZ4D2M3kiRwY8fRG2+8cbA7Zy4OGDbxDsV8uY4blZAvn4Gw9x7RrSqce+65g3Zgdc2RfstyWWy0OpKIfIhu9GqymQ4eSTypLMFlx1Rb7jnqcffddy+9kpDNVIh6QFb59AXLYiF/8Rd3acVmZVzG81mHXSr/3D3sZTYHAtPLLrts6MfnUvjmJLizay7vJzInxnhcswT4V7/6Vbkstk6/acUiYtRXG4xy+7oeG1FEQYyNaCzSCONT5L4Kk5KD59JPaH4g4Dy+c2fGq4+HzqkQvYkYzEYQc8doLPvJw/I0r4zP009GFi83cfl0RhKpB2RMKvhyYRiOEsAzNYEzcMd2BSbcy5EOMy5G1aVOf5OPHk3qpU5ewXcTPVFs83mMCe16Sv82khj7EeWL3iPimqHMGEB9QfrHHqYQS9qw9WOOuXabw8aPBzmiaH0f+XVkiPrw+rRd8eH7e11efoUFhMKHJuWy+NbnRunT/gFeHJNNvh27EkW/EmSUMbgNJqZz6thUTtN4fl6N+XWpmygrXvfVridNuPrqI5PWO+Kfuk4tO6Wf861Ell1Cali6GYlUjJOSbfcgBfazexzjRiX2SYymH7rHW+jHPjvff//9y3cq67xWpgseO0trx3322adc/sryU7vX9fie97ynJH05OzrqsfHGGxcXXHBBubSXejAMOUIG/buMeGJtE5km5NjK3uRI3uhMniyb9T/eXbW2gfeTjYmoFx/HzkmPnBxR9rpMKxZeR877aoNRbl/XYyWKpiTGYdsn5pa27ohRUmdk0ahSyzvpsNGjGL1VxMnpHr2JGL5tQ2qJrhnTXpZ/Km0DTdTdx+fcJlTKnhtUYpq+rv1khr6j5E+6HJFAHnXvvROGSyqNYUGcFL5dy+3rpxeiyDteEGwji5CdqsAmQxY3ePaqknX5z5Yzg2muj8R+xzWBugOnUdpFa52nFEtrr1X45craxJj3BCfVJ6JsP57Veehj2jZGsB/zIiFtUi7Lu0uf9m0XUlMVPI65eH68i0TZ94G6uSolvw0mqfR2r6mcpvGqiGKXujF9c0dfH13ata8z9M0F66e5cb0pXn31kUnrncPF30+9m8eyUzxAGPiQktzSVIvj5dk5XkaIyzrrrDMgWnymgh08jfRAbqyOOEI+We5pBNVk5Y7kwTJHL4Nz9GdDm6aEyb7/Z3LYpAeCiMfz5JNPLt71rncVb3rTm8pNd9h4Z9Qfu51CrHIeWN7NNB040keuvvrq8huOEYNIpPbcc8/ysyDs9kqdpQK433///aUHle9C2q6kqbhN7pGPLUlmYyHmBDywTYhgnfxxY2H5oyv1wS+Hm8VNHftqgynZfdybCFHsQ9GcDAaFppNvygsVnyZ7Y4lOlpsc4lIt4poRnNM13m+z7DSle1y2ZfIxvtEFEpXaFMfiUfZxGep+MgMbJtM2wTwu0eiKMiB93ighr1Rd2BNu/otejChzlGvvPcu1mdZy2ezDyF/d8kweUljcsFnSIN+zzy6K9dZbHG/ppYtihx1YMzOI0vSEtmdYc8y1I+on9im8ObTNpv22qU6V8frG0jI799wHNxkCy0susbu1R29cgl/bhxc+PYZzKmAgWB2lPL4xjTf8c8Q/prHrNkawJ06x3E3KZXl26dOeKNaRDU9MLO949ONdHLO89zK1WiTKitdtMIlp/XVTOU3j+fbi8+G8S91EWfG6r3bt62zaiGJVH5m03hH/eI1hHN+JY9xpuuzUlqZGuSwbfPGLX1yOYfRX3hf8wAc+MBjTvvrVr5aeNRvj7Mg7j1XkM+aDkc97eZbejmxowxJHdtesCymPqi1/ZRMfiBXElbKyBLTLD5IINjlC4scbysKYc/PNNy/xPh/l9t9OhHCzu2sqLuUnPstG2U3WMHr1q19d3HDDDSUJzelThx3pbEny61//+vKhM0S1jzAuLNANvSHJPMjgG5UsM+a7ljkCX1WePtpglfyu/800UTSy1tTg5EmFNXCOTHTewPUDsMWjoaWCN4zq4qbScy8lI2VIYLRZHnbMGX4QLHbNo2xVxh551xlIOb2b3McANF05VumSkmd1ET0b1BeGTAwQl0imaR8W7J0ZdGni+UX/VF2YvHj0dQQx6iXQ9oz8hSV6S8g372POq73XXg/KWnfdorjmmqK45Zai2HLLB++tuWZR3HXXEiKrbsRl174fxXSx31EHdd7wKKPzdZ9Yogz4bbHF4vppSRR9exll6WQTY97XEQ/U6oIRevSpqs+UHD+WRaIU4zM+0QZYihxDk3JZmi592hsQOaJt+XiimBp7iGfjFeWK5ffYNBl7GPP8w6w2mJjOqWNTOU3jVRHFLnWT0t3f66td+zqbNqJY1UcmrbfHPnXOjqO0e/+LS0pTu5LGOF42nqonP/nJpUw8e3zvkPmc9w5t0xNWJkAWfb6c873DHPn0eXCOsc9nGJZbbrkl5DzlKU8pP0HBUse6EDeEwZv4rW99q7RVzMsEqYAwdv0hD2KRCpQHr6XHBCIDgYlpvDeRDWQ+/elPlwQ75U1E5/e+972l3A9/+MNlvOOPP75Ydtlli9VXX71cKtqEUKd09u0HHPvabXVcWIA/S6o33XTTIZz33Xffst2BVZvQVxtsk2fbuDNNFJmQ6RBVXjMPiJ+8SBdJiH+XxDpajuBY3haPY468oQN5xafnfgmWyYlxSDTxKKcAABVASURBVBs9ZhhyngRZGZngGXyZwMmPCSX+0BvDBxmpvJBFGuSgE8ZcznNp+eaOZngip2kdmSzDF+LrA2XMeW4xbr1R5/OMHrBY9z4PzmkLcVlcjOOvzQNq9djW0PayBue8l2gE0H1PbvC/nfh38FKb+hxzzGJC4wnnokWL7zf8PqZlGftKrp/k4mMwx7q1uByR1wuGJrQvLG+7rSj22WcxbkbkWxJF2p+1Ffpa29DEmI9tnn5dFUyfXP+qSuvJEH23Kti4kCJoTcplsmP52vTpOBdUjXF+TEG/VABbwy+W3z8UIE6dnpAE3zfaYJLSze41ldM0XhVR7FI3pm/uGGWP2q69nKq52+qV8qZCU7z66iOT1jtVZn+vybLTujheHoTqla98ZdmfICHnnHNOAZnAi8Yyzhe84AXlfywXZamk1Q9HvGJnn312o2WnZqDTv1PLYnnXcdGiRbWf7UAO3yf0ekDWSEs/5v9JBfIy28n0SX2jEiz9u4l4avnmJBvdxKW2yHz3u99dlg/sWdZLm7/00ktLoviQhzykXDo66udNrG2sscYaJQHra7fVcWBB22QJ8Rvf+Mahhwu8X8m3HW+77bYl8Kuqe3TkQUXXNliVRx//zTRRNDLT1NDyS1ZSTxD9xEcn8xMDRqs3XP3SGuuQGEA+jlUQnqmYHyTN0tkxZThFI4O45B0D8WxjEZNXdcx5dJiEIJE+7SiGI/r5J79NnqRbmRiE0CE1edt/KZxJ7ydRJmYfvMEHVjmDjXT8n8vDy/Tn9hQY7NCjl7DHHg+SEghj5tt0hX0aI+VNfOCBxZ7DSGZuvLEoHv3oB+XH/2qU93VLeVN15UV4Q9raFm0i9cCDvkHfyz3I8HJbnfeB5bbbLl6u64l2S/wYEwwHHhi1DbRNS1/Vt6gXi1fVj32/qTO8U7p6I7hqpYLPJ9VHmhrdpsOofZq2ZYQVfKrar88D/VLBt+/UKhTqyOqh6uEbaWN7aFrXKb38vaZymtaBny9TY6XHre/xto927edgxu5U8PMvc1IqNMW1rz4yab1TZbZ7GLpNlp3WxTF5HD1pYzMYNqXBW0VevLv2xCc+sexLz3rWs4rXvva1g35F/9pyyy1L72Pd0kUz0HlPEC8lu25a//RHvJNswkP8XGCZq0+DN/GEE04ol2S29S7l8mh6Hz0hLF4fdtT0hJU4O+200yAOHlvIH+9jppZNfuELXyjjQggPPPDA0pvIctozzzxzIIN6sk+ANNWVeOhibYOlupBP3mntI4wDC/QCI/DccccdB+XnW6AXXnhhAS7k2yQQD5LYpQ32biNlFJ9ZooiB6TtDJAWxvP4JfiRtxPWDr8k144FGwbk3av2gb/E5MskTj8mDPEmXys8bipY+evmQ4Q0M4qWMPZ6OR3JnMlNHDCTKFAP5+cnf0lYZflGGv0aekXlkgQP3qgLYkYbypIwyM2JyRNdP7DG9N1J92cAPQw8Pohkgde0pVQb/JC9HQlPpKu/hCWOJHp6rQHzLdODJUlf+T3kTPRl8xCOGl5iSdpVVHkxLeu9trFTqwR2NDUM7ph5gUN/2UIW+EdszBiR1Sb0RqAPipdp5jUr1f3fFMubQgSj6ttJmibNXwXCnr1h/BkePHX3Ajw05Lzl9E3mpscrnmTv342ET4pobU6x/owvjVF3o0qfjGJwieOBJGzWsc/0aXC1OCsOoJzLpF8inzKSHrFBXfp6x8pvsqrq2uFXHJnJ8HUD2csHPFaSJIZaZvKn3PsZb8uujXfu6RV8faNP+4R/6xzgWvwmuffUR8pyk3lbG1JH306zsdmT+9rudNoljsiGFVranPe1ppZfLPFUY1pdffnnxyEc+ssyTfLbZZpuh/NkR9Lrrrqu0M/CmYaBvtdVW5Tt36AfJYSMVK4Mded+xakMbdIKcWnyOeDnZZZQxOS73tHKO80j5TR+8ooxzkF10QV8+Vm//M9fyvUmW6qaWjoKN1Qf9HQLMO4zM67vsskspBwJ5+OGH1xLqVJmpCz4ZstZaa5WvYqFHn+S6TyxMf3CEEPr2widL+N5mCkNL549d2yD429hEHY47zCxR9IaWNXq/1NCAo7NaXCaWlDFAXID3Ew8yuYY40EHiBOEryvJPHXP5+aetlhf5UPlMpGY4eJkpomVGuI9Xd57CCQwwWmJajLUuTy2Y0D05oFFDysDPB4wjjAgwZ2BCl1TwRkyqHGbw5nCPnrBYXq69oZ3SIXePMpg82lxvAQMGssgT7bPOWiwWDFmSCsnDW5YKftkp7yf6jWu8txEZLXVOtT0mb7Cn/NSFGZOGB/3RtwfDyx+p/5SxnCpe63tdsIyZdSCK1k7pX7EvxGxy1zZRgB1yaLfgHbHzZCfVt6xPMCYZ4czlmbvvjWD0sfr28RnX+I82khtTPOEibhx3vTw7N/2Jn/vl+jTjkU8DBsiDEPIAA12tDRMPnIlDeX2gzZsc0qTq1MexuPEIRqnQtK5Taf29JnJ8HVDeVJug/syApAykSYUudZOS5+/10a5pp74OqFvmIeqQcYqy+/+5TxzmMB+a4NpXHyHfSerty+nPMZjxAnl8ON96660H3zAkjvdeWdyc5w+D2+LQZ404QHBYEsl7dPY/3/9j8xO75njooYeW3+pjiWAMyIDAscSRuPQ1jHu8jxj49u6jl8d7inyqgXcmUyF6E1kyC0mu2pU0JafPexAtvIRWjqc+9anlLrEnnnji4L06yDZLKOm3bNgDcQGfGHx9UK/nn39++SkHiPWKK65Y5gFRPPLII8v7KRlRpr+mffAggDmLHwSMe32FPrHwOvnvHtqyU8bEOt37aoN+jKaec+Ov17nL+cwSRQZsSBxPS5jQmdAAjCP3GUgxApjMIB/EyRknBiADRySLyMqlg7T4ydI6JkcmjhzZQZ6PyzmDIkZRzJ//MFRST7LN2Iyyqq7BJ2XEgAGToi8PusQJ0bBqc0Quk6+XjY426Xp9KVM0dH1eniiaDOqaH/LQOUcSTQ5lsvbi8+Yc8tMl0F6QgzHRazCCA6FjiSmbs/BuG9dHHZXPaoxEkUwxBGO9ekzBIRr7tL+c0YyscQ96xahYRpQ7EEUjH3VtNWbpr+knHnvadA47+o3lSf3QV+hrvs/kxgWfZ+7cG8H0AeSiD/2evsn4Rr78lyIe9Eni+PIQn2v0rBuHuvRp5gbfZu2ctouuHLnH2EJ5/PjEuJwah5l76BsxMMfEMiIbvHJ1h4w2dR3z9NdVcnJ1QLsBI9oQfZlz9DWcOFIm7se+Tt5d6sbrnjrvo11b/fry+HZq9ykj/ZU8Y6jC1eJ27SMmx46T0tvy80c2SImfpTCc2BiF9854t/C5z33uUDvxcdgUhf5lxjVkbOWVV07Gt3T+iBfLvFp2nw1a4qcVMM55B4/3HS0eR3baREeWVsaNSXy8DTbYoPQ8RvKJXD4Ob3HZOZVdQ9mMhbK0JU0e3y7n4AkGsbymJ333iCOOKL21tGVIotWBz9d7EyFDfMIC0kx8xiqTx/jAjrSQvLYBjMAVvJh/Unq0lenj94WFl4nOu+2226D8TZadkqbPNki9Gf7MSzmO4vXucj6TRBFQmJRiYBLGKGGQNwOFSaoNiAz4pOGXmhBinlwTF4JhhCVHEC1tXPJEhaM7gTyZUExWiiCanHEcmejJm/K0wa2JLgwElN3KhjFl9dQ0P2SYMQLuVufIxDBrWmfI8fWGHOq+a0A36pPOSx69B55kQxL5UD1thuWUVaENUWy5oY1lSzuxesXYpy7ANkUILA1H8DHPDe2A+qtL49N3Pm+LZcxwRKJog3wfA7xhCI5N2htt3I8vfWHujWDq3/Syvk77qBsXI7xtr8lz1D5Nv7U2DCbIsUDZ+K+vtokcDC3DhvMmdWeYNq1r0z8e+5IT5VZdd6mbKrn2X9d2bfMedW/zi8mmnmgDdXVUh+s4+sgk9DYc/JGyskwUDx2kkTZpvzPOOKPs6yzZZKy76KKLyjinnnrqUBze6WJzGnsvDm+VGb8Y3yyJxGN31VVXlb+jjz568D9j57XXXlsSHkvDEW9efFcOsgCJIT76Qg7RkU1v+L4gO4LiVUMf3ruzcnBEZ+IbQfIYsOun5Y13je8bIo937PomPD7fJueQr5tuuqncqZTPNmy++eYFy3IhxbyPSLuh3HjccoTW3k2kjEaCqS/SeILO9yOrvK5N9B1nnD6w8PqxC27bZafjaIPMp4xNfditvnyp85kkiqmCzNI9v0yFTjg2UjFLoMwjXXlQQb0a+Z/TorUhii2Xns5puaYh8xGJIg9FaB9dvInTUHyvQzSC/X86FwJCYPhzWBh4sxxYBgoh4t03dqn0PwjIPffcU3qJMKpzcSB0EE4jVbazJmMjm9SwvA9jmM1mOPoP2vPuIOQPr9fSSy89IGykIW9PfjiHjLLEkW8Zoh/6co4MdGD5KXraf748Fs97FCFMtmsoS1ZZesmGODwEsvLMdf1SZjCG0F955ZUlUYY8Uh7qJe5u6vUl7Ste8YoBru985zsHu7jGZaef+tSnyvc4PT5e1jScd8Ei6h+XnWLn0V6q6n0cbTDqNc5rEcVxopuQbd4EBkP74YVRmD8I4GFj2R1LMpiE5jSIKI4P/hGIIu2BtsGysTlvGz0iI6LYI5gSNS8RmI99BAM497NKzP3PfQsY8ni+sIl4543v6fGeH6QP8gXBYdzkf5ZBQh7xbPGDNJothRcwEkXLI6dH3f+WzuKx9HKzzTYr8+R9x2OPPbbcaRUCVkW+LP0kj5AXMEJn5hvIXBWhMd2Ib8uAbdkpHlnu4+k1vPH8UhcQbl+fJmeajqNi4ctAGXm305efhxh1u+yaDGtL8Vj3v8W3eJM+iihOGHHzJlhD4zgVnqcJ4zDfs2PpGnU7514jT2Z63PV0vtdfo/J5bBt+HoP2wAOEvpd1N9J3jJHmoxE8RrgkegEioD6Sr3S/nA9iwvJIPJYYyBj49q095tS3vvWtpfeP+/xYNvrYxz62nG/322+/Wu9OXov6f9CHzxmgBxvXnHTSSeUyTrxs0+xRqy/ZcIzrr7++4DMflHOdddYpTjvttPJblmz6s/POO5f3IfRsHsQuqPOp7MNIDF/5dgo2bPbDO6mQ8fkcZo4oUjn6TScG87mjjFI23nehrVZtUjGK3FZp8GjaJzAimfH/RRLZKpMFGrklUaQdsMycJ5DzLcgInm81qvL0jYD6SB5RPDIrrbRSOV+yS+cVV1wx+NQARNBIC5/M4P06vxoDb+T+++9fpt1www0LSM44DHfIILu1QmT32muvgg/Z834Y3rRp8yTmkW72D7vBLrfcciWmvEpju53yLqLd59Mks+JNbFbq+lijLDutlzr9MUQURTzLwaAP8j39zX3yGkIK8CCxJGbOwl57pb+V6InOjL8zMyfYevwiCQ8KYdxU7YQcos/cJZu92BjCLqAKQkAIDCOgPjKMh79i10vbeRQixvcS8VJB+GxJKp+qYLOa+B4gXj7Imm2wwu6SkDq8jX0FNrlhl1fencSLyAY9LIdlKWaf+fSlb1c5EGAIIV7DAw44oNxMCG/aZz7zmXKcx6Y5+eSTy+XBC8WbSDuLy04vvvjixstOu9bJXKYXURRRHBh4ZuiNepzLhjzNeTOxYTzzRHlOAp5DPtfBpzTwHF5zTVH4byjG7yvOiZIzlulttxXF//3fYgIOtvvtN/ydyv8VieXmbF7hn4LPWGmz6lImlln7b2PyGYE59aJntdUfQmDyCKiP1GOOR45ljGZ77LvvvqVncKONNirvrbbaauXmNmwakiImpIccHnfccQWEEiLX13gL8WRXbmSyKQweTt5HhMRCHuZjADv77M+ee+5Z7l7Lw248u3xW5IQTTig3x4Eoz1cMYr2y+615tmmnm2yySdkWWI4738PMEcVZrBDeQcRQrPrNx+Vos1hX49R5TusYYrjPPkXx6EcvJjd8h/HYY8dZ5Pkn23sRIYe53/8+d8NDgjmt9zHXQNWYxn+UX0EILGQE1Efqax+ywSY022+//YAsYoyzDHWfffYpP13hP6WRkghZZAkrS0/Z6RMS00dgDCPvW2+9tSSjeD/noxfRYwUZx2O61VZbDeqD7y8eeOCB5UNACDO7yM53HKjr3PdC7aHG1772tXmPg4ii7x06FwJCQAgIASEgBISAEJgoAnhmbrzxxvLj7SwxZaXCokWLymWPfLaCdxHrAoQTTx8Gfl/vDSIHDxty5zsxMnzBkaWm7HRKPfAuIt+05BMgfJJkPr6XaWX3R+qbTZX4Jijf8zzvvPOK008/vXyViO9w8s4m3uWUl9vLmfVzEcVZr0HpLwSEgBAQAkJACAiBGUYAcgJZxPDm0xj8IIgQlr5I3wzDM3HVIUl4ZakPPKrUBV5E6mghEWZIIDjYdzjtG5vgAmFeCHiIKE68+ylDISAEhIAQEAJCQAgIgYgAJATjnN9CISQRg2m6tvrgCJlfqIGyp34LAQ8RxYVQyyqjEBACQkAICAEhIASEgBAQAkKgBQIiii3AUlQhIASEgBAQAkJACAgBISAEhMBCQEBEcSHUssooBISAEBACQkAICAEhIASEgBBogYCIYguwFFUICAEhIASEgBAQAkJACAgBIbAQEBBRXAi1rDIKASEgBISAEBACQkAICAEhIARaICCi2AIsRRUCQkAICAEhIASEgBAQAkJACCwEBEQUF0Itq4xCQAgIASEgBISAEBACQkAICIEWCIgotgBLUYWAEBACQkAICAEhIASEgBAQAgsBARHFhVDLKqMQEAJCQAgIASEgBISAEBACQqAFAiKKLcBSVCEgBISAEBACQkAICAEhIASEwEJAQERxIdSyyigEhIAQEAJCQAgIASEgBISAEGiBgIhiC7AUVQgIASEgBISAEBACQkAICAEhsBAQEFFcCLWsMgoBISAEhIAQEAJCQAgIASEgBFogIKLYAixFFQJCQAgIASEgBISAEBACQkAILAQERBQXQi2rjEJACAgBISAEhIAQEAJCQAgIgRYIiCi2AEtRhYAQEAJCQAgIASEgBISAEBACCwEBEcWFUMsqoxAQAkJACAgBISAEhIAQEAJCoAUCIootwFJUISAEhIAQEAJCQAgIASEgBITAQkBARHEh1LLKKASEgBAQAkJACAgBISAEhIAQaIGAiGILsBRVCAgBISAEhIAQEAJCQAgIASGwEBAQUVwItawyCgEhIASEgBAQAkJACAgBISAEWiAgotgCLEUVAkJACAgBISAEhIAQEAJCQAgsBAT+H+uDtLQI2juCAAAAAElFTkSuQmCC"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step2: Use (theta_0 & theta_1) to predict the output h(x)= theta_0 + theta_1 * x.![image.png](attachment:image.png)\n",
    "#### Note: you will need to iterate through all data points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "h_0 = theta_0 + (theta_1 *x )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n"
     ]
    }
   ],
   "source": [
    "print(h_0)"
   ]
  },
  {
   "attachments": {
    "image-2.png": {
     "image/png": 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"
    },
    "image.png": {
     "image/png": "iVBORw0KGgoAAAANSUhEUgAAAocAAABKCAYAAADJ/f6hAAAdn0lEQVR4Ae2dLYwlxxWFF0WWQtbMKDI0ibRKiKGhQSIZLolkuCTSKmiDDB1maBQZGhoaGgRYQY4US2axZGIpZJFlENDRN+vz9kxNVXf135vu3VPSU/Xrrp9bp27de+pWz5sHQ1IQCAJBIAgEgSAQBIJAEPgFgQdBIggEgSAQBIJAEAgCQSAICIGQQyGRPAgEgSAQBIJAEAgCQWAIOYwSBIEgEASCQBAIAkEgCFwQCDm8QJGLIBAEgkAQCAJBIAgEgZDD6EAQCAJBIAgEgSAQBILABYGQwwsUuQgCQSAIBIEgEASCQBAIOYwOBIEgEASCQBAIAkEgCFwQCDm8QJGLIBAEgkAQCAJBIAgEgZDD6EAQCAJBIAgEgSAQBILABYGQwwsUuQgCQSAIBIEgEASCQBAIOYwOBIEgEASCQBAIAkEgCFwQCDm8QJGLIBAEgkAQCAJBIAgEgZDD6EAQCAJBIAgEgSAQBILABYGQwwsUuQgCQSAIBIEgEASCQBAIOYwOBIEgEASCQBAIAkEgCFwQCDm8QJGLIBAEgkAQCAJBIAgEgZDD6EAQCAJBIAgEgSAQBILABYGQwwsUuQgCQSAIBIEgEAS+++674YsvvggQGyLw6aefDj/++OOGLe7bVMjhvvim9QMj8Pz58+H7778/sIQvRDuLnIcHMgIGgSAwisCXX345PHr0aHjw4MHwzjvvjJbNw34EIIVgyufx48cD5Pvo6bUhh5CAr776avjoo49uPp9//vkdYsAEfv3110efs1XyMUZw+OSTTwZ2MlxfO9Enu1LNRUsODNUe5I05/vDDD4c33njjRoZrj7+3v7PI2TueJeXuW1eWyHyNOqyLp0+f3uiwnA7OnLX0OibwePvtt4eHDx8On3322WsDwTfffHNjw1kntU+vP/v5559vSIt0Cd2ajHIRWXz8eBjeemsYHjwYhkePhuHZs2F4/vzY+N+T3MzV+++/f0MQ8T0ff/zxoXF65ckhi+O99967sPZ33333ZkekRfDBBx8MkBAWB9cssFcxoZgQIo3bc/AhOrVnwtCwGDDg6pu5oG/tVN96660bh8euivJ833I+cBo4UPVPDkE9WjqLnHvhdgRd2WtsW7SLTYME4cBZH2x0+S69xgG9bgnbovFjV16XhI3UuGt5jy7g+0RasMddUa1PPnlBCJ8+HQaiYJzAcO/hwxck8agnMgeQG74hP3hE/6O188qSQ98JYTiJlHFPCTL05MmTWwuLhTaVaAOjfKb07NmzW+OsGRGI8V6JaAY7JfrFcOPMaon7WjSSccv3XiDIGD4ZQvo44uI8i5y1OVx77yi6snYce9UnQsZawol7Qme0xtDr3oiRt3Hmax//0SMyW+KMPpQbXtlO7Nxk9G8g+Pf4xjbTjvvIppxsqIkUPnlytwhROZ69/fYwHO39ugPJjR/Sej1qpPuVJIcQP4wniwTCN7YTghxoMUEWxxILhwVHBO4MyXHQGFs5irp19BC8nID3kGrqyFgh6x4LhzaFwxHJoXTrmnLeNw5H1RXNxZp8S2zZxKG7tTbZSPGMDRZ4vkqpNt5yfNivMVtfln9VvtdOhPB7PTqgutj/Lux47Qry98Yb7eNjIreUOVIQ5YByu33fMgiylV6/cuSQBaFjSgxlK0olACmv0Dzh3lbC8BD1os2xcq36177PuJAXMgsG2kGihH4ExXj02VpGGR7anyLe3rdkpx4R360T86cx9zidrfvvbe9acqITZSSqV8atyh1VV9aOb0tssUHS29amSet8rdxHqr8lhkca11ay+GZa+tGzEccvqHxLn+7IyHuFEL+xVxc4GRKBPEr08KByy+7tEZy5M3czb7xy5BAyIYUnJ+w+lVhIECZISS1hlEU4x8rV6t7XPSIMLWIFIXKMuN76PR0Muvro3cU6Vjg5Fswe5I33tCTbHu37ONZcX0tOdPs+yeGRdWXN/FF3S2wXOfO1AzhA/S0xPMBwNhdBQQvZNHLW1FTS6RqR5q6k6BvEb+yPKfC5lOFzhOjhgeWGn2jeWv66a252KPRKkUOPAgrwnkUCQWD3VUu8u+PvdMD0j54gs2PvHHk4Wzjxzs5Wif4VjaX97l1pIQDRxjkRx6J68+u1SFdTgM4H15BTL/LfFzk8uq50TlW12NbY8j6m1uvSNVUV9MA3t8bwwENdJBo+j0209EI562oscYSssryT3pUoJ9I3RT75wxTKcvx839HDg8stcg/POFLanRwSAeJ4DMM2Rli2AMWNpxQfkjK1UCCH5fEzi672hxxzj5RZhDj5LRLt8Fl7dOTvAYJTj3GgT/qewpJxltHbnjo1fCCse5BxxiH9eJ0jhx6xuy9yeHRdqellz709sEVXpbdz7VCPzEcrsweGRxvjWnmwkdIJ5T2RQE7LVL7bL/NHUCKHU7/Tx7Gzyo68rrV2/F31Dy63NkDMx5HW9a7kEMJVvt8GS+456u2a9KJQSXqk/BBECEErIY8fKZfRQrVDjvw4Uj4tYkF9jnUZu0fQWlEwopZq03ORNpTH20GO3r9EK8fsxoQdJ21PJSfJjGnqxWUdwSMn41mTWrrCfIIx7SMTfYIJGwSfy1rfc8ghY2WeaZs5YP65LiPSkBzK+acsQ7/+nOuxo4ReOediUdv44FBctlYkmb5wLODO/II7+tvtYIoJuYau0CWbG/QYuTWPjIMI3NTmRXhJ18hZy+gaYwcTJZUFG316sVUbnqNDmhdhTrtsmnS/la/VP+w3uk6/SqwH+ibKwdyBae9mtXctLcGQOWQ+kAs8xtIaXdgakzE5e56Vmyvpxlhd8JU/6SGSl7Y4fhbhm4oGcsKmsvf9u5MHl9uPlvFpR0m7kUN3bDKSyjEqKOjWCaOlPmo5hnzKkDFRGEM/SlZb3OOZPqXxxUCJoEJY5DB9AbcIIm2qH+UYOd3XYtYzcp7NScgnZ8xYWgTA23TZ1fcYocQBqBy5CK63ueYavWEBafzMAXOGYwBz7uPQxvTLdXPMkUAcaBO9oR92dZrfsh/mmjIYW57xKaOeyEnfrqdjxnlKzqVYMH/ojo4zkJVxck+f2g6WuaQcObKBnY937lzvrSvSM3SDMTJe5hTZ0WvJzlpAllrCXlCOdUNdvpdzyHelpdiqfpmrPeZF8jIW5NFckSPbFvqHjjKPbm9onwQxqh1hIteUXZ2zljTmHv1k3bGeXK6xNb1EF/bCpJzrJd+xTeiDf9DtseQBgpY/qtbniFiEr1rAbvLLHyo7Qdat1j6XJ5Bbaxv7epS0Gzn0he2Kq2sMzdYJ46j2Wzng1xxfKQsGsmxDZK8sy3cMiCaYeu4wfDFixGoJA1z2h6wYM0U2RIq8XA/Boz/KuXw4l5ZDlHw8d6OrfsfmjmcqR478WyaRM+QqHZIT2TGiwtxIxpYj4T5las9dt0sCiBNU2+Uz4QCpUxnmpJWm5FyLBTorOUQAWrLghCAM1PEk8qR25sz33rqCnJpH9L3cMPiabdkF1hy6Vo6btmUjfK0LmznYqs5UrrGAda1P6q/VP2wjbbDB0pyKfKKrEDf6ppzbE6KwrSS5566lHgyRlY9v5mv9IJvkmKsLe2DSwmrufZ8DzdeUT3A/2cLqjhxECkX2Gj7sVh39piB17vM9/ZPI7f5f/v4WnvfwZRdyiBGukQopL/mYMVmDAwvf+2ldT/VfLjq+txKT6eXLtjEuLke5eGt4gR/1PMm4eVtjRA3HXRp6r4uzH1NE7bK9zlTYG+fh5el/y4QTp/0amWG86hs9aKUp0sX80E6rDcakfpDHk7fdIoeUV/0xvfK2akZ8LRY9zhdZ5UxaxM/1G50qSbvj49d76wqbOXBukTsfG+WQ3Qkk19wHZ7+vMXCPOsxTmXqxLeuNfff1X+uTuq4za/RPa0DjhyyWtsLLtPRYZZaspTkYuq2qrZW1ugC2GstaTMbmeM4zt3fIxAddn0q+iW6t6Ttt+F/88s8i0Pmxjx8rzzzhutP3mhsnkdsDP+jZEdIu5JCByXFJact8LLKzBhiM4xQxlSwtGWRIVI68VRYH4YSUvkvn6EadtsoIZBlBoUztaKBsh3Jj5KtWnjr+qRlS4Y9x9nmEkJUOQmWVQ4y9/ZYTU/m5Oc6Y9olk1ZL6bjkr6rgDrY1f89nCFly0GSCK6MnbXuOce+Rci0WP80W/FZVpzT1lhDs5ZLIn7a0rmsfaRsLlUzlk942d49MaE+VrOu51p/p3WcaufT3X+qTuVvrn8oNPK0kHwa6WhO2SteQyTGGoDQxyjK3pqXYkb6kLjM3lWYNJDacl93zMyMtnanz04+uupdd35NF/PmGeIaAQvrGPv+c3Eli508/WN04iN75Cc9g9J1tjVbRXX9FFoSVf/VhCg/a8jIot6aNVB/LlRsv7La9rRlbHRV62JHTq23dhlHfnojJyrmqvdLK190ZKgklbvqjV1ljkkDoYNB0/qo7nU5FA6oNRa/wao/JSxq3nGVkw/shVJnDV2JaSQ8apNqbGXNvhbeWcGZu3VXN4a7FwZ9dyKoqWsOmhTOsjzMiJCPakPXVFciNPDTuXzzdnZeRFdoT7tSgL67Rcz7Tdg63L0HPNOIQzc19LrjNrNie98vsrFqU8a9dSrwz06+Mu53srXeiVZwyTEqM138v1g260ghjej/ubKRt3qacftoYcdvyb2cGPle8zcngSuX1t1+zMZR6ueLEbOWQhedRJRo28FfXZctwYbGfj3r9fs8DKpKiQyrWIho6VVI6csTHR+pREE2fjCTlxPN5Gy1GXclEHnHtSKYf623ou/HiHPloRgx6Ze8tg4Jhr17fWnNHmmCNx+WsEfUomb3uNc56SsyXHHCx6nJ2IE3gytp7P1Luskt2x3lpX/Mi6JAvqXznyaj2Qu/zlxoqIUc/Ovgdb9d+buwNhHmppK/3rlR9bJexKeXx+l6ylXhno18ddzvdWutArzxgmJUZrvns/moMe3fR6jKkroW8QQ32mKvmxcuudw//9bxh4J/33v3/Z7q9+NQx/+tMwfPvtVA99z/eQ23v+4YcXEVRwWfGHN762S/317q55vRs5ZBAYWQ/To8CQFEjVtRKRqxqp0mIqI2e+21WZ1m6sjBpCTpjYsU9JlviufpRjVMvkhknlxghQWZ/vZQSTdmrH17W6vff8/TPa740i9bbv5TCE6Bc40M8WkUPfjXcbThPKndQ1yeESLFyncBi1JMdaRtRqZefe21NXfGM4ZWzLY3GPdqNTpQ1Dr7nXImjg0IPtXLwYh9Z+q++t9K9Xfica5XjWrqVeGejXx13O91a60CvPGCYlRku/o7NlUAHdQF+nkp/qdUcO+Wt+EUPyOT9lUyNNkKrf/OZFm3/4wzD89NMwQBb/+McX9yCJW/zR6tZyC1wR2zfffIlLbZwqP5H72t7TZ06IcevxruRQPbFr7FZCVerMAbVlKNUEC8lD6TKw5GXksIwUUKYlu46c1B4OY27yhap2arts34WrXCn7VN9urGkD41Lra6qdseduQOmjJN9jdXufMR9gjfzlQhI2Y8R5zJG4nkzpVU1eb/sa5HANFj5XLXLojvVMuuIOmjU9lXwtl9EX7Ad2puaMW233YDslU/ncHUhLN7fSv175HedS3rVrqVcG+vVxg5Mnl7E1X16+pQu98nh/3u6W135U3mPzvG/3caWue7lb1wR0eNdQBLHx00+XOvxen8qWf5RYksB//vNSbfjPf4ZBhAuC6M9eluq/2lJu9erRQo2RfAWZdTs79aqYxNg7vwo53HMQRMNahrLstxYBKCN5bhhYdC2SUR5FUXbuEe2cI+Wa7BiIOakkmHPJZW9fLisOFee6VWLh0CZR2tr4ewzlmCPx4/daBHdqHN723uRwLRY9zk6RQ3Ddw2jtpSvuAHs2KKxz6U5rMwg5diOu8rV134PtlC6Vz89GDteupTkY+roryeFWutArzzXIYXlqhS7W9LDUIb77mi79X6385R5/fCcy1Hit4VKWQInK8hfDnv7+95fPfve7F1FDPcdXKKJI/S1+FHoruSG1f/3rS9k1PuUryKFvpFr2RxBdKz81ORRB6yWH5TEWDsGJixsYGf7WkXLtOLhVtjWZtTZqhARlkTzKexxe2a9HDiHBW0eC1B+7UclJ3r07VQOWU1dzhHFW9KYVAVC/LVJP0z7PpSPxOYG4TCXkc9Lkbe9JDrfAosfZMTZh2oMHOlXT4RaOe+mKO082kFNJm0LfzKB3YFQmNiVOasHH31OkfA+2ZbtT389GDteupTkY+ror1/QWujBnTq9BDp1MaH32viLka7rEalQH/X8UTxEhRRlLG+pRwxb5+8tfXhKwX/96GP7731GxJh9uITedQGp/+1t+2+tFl05yGcsUJiOCus7s5ZdHuq8+OjU5lLFcsihYUCVpcfKkBddi8epb5cjHCBt9lZPee6RcRitwYKUzqs5ucdMV0AlNUeyGPOn9xFaErqxTfnfnWZLwsmzrO2QejJTcyOMMaknzsZQclkS81JGyT/4y0d/z8eOeMX1YK+cWWPQ4Xx8PMk/hwRryd/ZKvGrf99CVUu6WvkgezYdHX8DHv6ssOcTR11Npg3qw9fZ6rt3mtMbj416jf73yOwblGNaupV4Z6HeMHDomzHMLO8lf0wWe9cozhon6WJtj3ySncsbZkxyr1ia72g7vGYr0NX5K7Kaev+cnIqUG/dgYQlW8AnBTzMnhFkfLW8gt+T3fkBzK3zKXR0nHkWQBIgK0JzJA8368UIvqlAvOCQbOQBEs2vLQvBYn0QcvoyERSSn7gyiqnnKMSplKA0tZf8+O3Tnj5zNmHGQgIZbUaSXKKTonuVoOstUG9zFA3k45/rG6PEMOxuSE2klya8crmX3uyr7cONaivU5WxsgxdZ280o/Pa/kbiJLD5xSMWmlMzi2wQFeFF2NuJXd24NEiiOgVz2troNU29/fQFdqFHGl8YzqstUFZZFGCDDA/rfF4vXJN9WKrvnpyJ4dlf6q/lf4tIUI1nNaspTkYjq0VsFmrC7SxFSaaq6W5z7H0e0xPy37YzKpey0aVdS7f+XUPCAx2q/W6EISPMjWb8o9/vIwKtsjhBOnC/2GT+LRs0UVeXayVW+14PiGnFx279tfLxuyw2nCfqHt75KclhzpSlpK3jKVAQ4lUtkZUagtOO28mj2uP1tGf2vMcskA5DBt9Uq/WH4TR63HNAveJpw03rpRxJ+cGkWctIoP8tEP7Y1Ed+isJMu3O2l0K8F/+Fyv19QEbZJlK4IYc7qipAxlTWzxHXiUIl/++mEgKc1Hqhr9eUJsbd/r0R1sYJPrAQVCfvsDTdUKyUF5y0pYnZHE5KVeWUfkxObfCQnIyFs0N43Q9K/GgDjpB9Jk5Qk453xJrjWUq96Mu2l+rK/QncqcxImctiWiXuiAy0Ho310k+ZcukfsewLeuMffeTjbGj+y30T2NnDLVNq+T0jUMNg1J35q6lXgzH1gqyIhvzoPbm6oLaUP01mAi7pbn7sh55av1ovVK/Nm+1Ojf3iMLxX6EgdrUgAzaZn2vjeRk1pIENyKGvg1aQ4I78a+W+0+Avx8yMU5+Fx8rOJcoTCO8WfyffUQYlvNxW16clh76L1gKpAYvDU1mMQy1SBJgA78aDNvnOIoKIlA7cJ0r91/JWf25U1Rf9MPk4SoyXFEHt4rycEMmp6Tk5xhfjoUQ7ROAYRzkGlVHuzk5trn03kbHofS7JByZOgr1/SAk41EgX8vscUY65BSfGzVi5J9khxHxK4+fECmwcU8niZdRemTO2WpK+qTxzDZmiL+RBJ/WMnPuUGSPDpZxbYeE6xjy18PdjbJfdr51Q1nCZurelrqgvdFpkiZzvnjQu8Bc51nP0RuOr2Ratv9Ya78VW/Y3lyObraMw5bKF/zIXGDm4lNsjKGnaZWoRrzVrqxdD7KNeKcF2jC7SxJSaSaUnu5Ehz1NLBVvvMler6SVSr/K37bHghiEQPfcMFMeS4GbJU+f3gmzY2IIeu37MCF2vkvgXAL182ihyylpkLfFvNF6lrnzPKt9abyq/NT0sOMQAQHnbQLBYZKXLuo0CAjmEDdMrUCIkDyOJ38sEE0FarHs5DjkcLTTlGrXRE6ov2VE45jrV0+HoG4XHCp3ZQjlb/qttDCtUeDsDbA4uSsKjsnJx2WcTetuRjHkXomDuMXM0Rqb9axJV51hzRj7ftxBAM5dBVhpy5Ql/KftGHlsxTC7Mk//TDXKgP9U/7jHmJnGuwEJ6QcB8jc9AaG7qgdSb5lc92MBKgyLfUFTUNttIx5EXn0ANydBz8a0aZehqf6qEnfLyu+inzOdiWdfUdzJHP5ZdM3ONZjbgu1T/15zrhYwcT7BT2FAwkCzl1uM/zMi1dS1MYttY0NqGGyxJd2AuTEqPe77W5bfmasTalU9i/2UlECyLI8TF/9MEffvG98ju9l/Y3IIfomPSuNseXvmoXS+WutbUBOcTeiXMwrrHk9og68nljddY8OyU5BJQakBggDDdOGJLANQt7DogYI+rwYTJ6EmVxjnIcUwu15tSRnUSfhJnVVo0UukwoFwtE5clpC5lqDs/r1q4x7LTBeObgVmurdo/xSFaMHM6N7xCSXnmZI8YMjjVHRFu1+zV5pu6BL+1J5jlyCktkLeWhPea5d8wtObfAAhmYFz5T8vDc9R1dQ4Y90ha64nIhp68t5oX5bSXGqnljzLIvzB11e+zDHGxbciy9fw39myPb0rW0B4ZzdWHOOPcsC4YiEyJIkLwlCRuvNhavYd7RhRjyW6L4MI5vx9Jcclj5gxQCKZJ7ytc2RZkrd62hDcihz4FsTa0r3WO82J/F86WGOvJTksOOcR26iB+VoOQsdgxgUhAIAkEgCASBFgJsmESMlLPBXpIgmooeEgW+ig+a+9fKxU/ZIKNOL9a+xrIEs1t1VpJDiJ6IPicZR0shh1eeEQ8Na3Hfu5JfGYN0FwSCQBAIAvMR8KiZAgtrokhXJygEQaZ+5Np/yqb4kWz98Qakdo+TrVkzsoIcOjFnLHw/Wgo5vPKMeBhZ5FBHylcWJd0FgSAQBILASRDg1Qb5DOW8WrM2QbgUwcI/7Z5GyN+t/6/M+4v2O4iMHzmJcva80rH7OBaSQ4ggr74xh0RBe46Tdx9LpYPTkUMtiuQvfyLmKFhU9Cu3gkAQCAJBYCECeu+29gd9W5448S61/giJX1SAiO2W/Gi5fKfQnxVRQ0gVx6+HibKV5NCIbAs7yLyOxQ9DchvChhza7/AdhWSdVY6GjuV2EAgCQSAILEAAolb6A8jFHqdNHNP6rz3s+h6c/2GKSKD/az3+Td233y5A7ApVkPPf/759PE6UE5n/9a+qABBazSUknAjtVd7xrErTdzPkMOTwjvEpjVHv9z6VS6kgEASCQBDoQYA/NuFXHYgS8leqRBL3jpxxZEtffHZNP/wwDH/+8zC8+ebLH5Lm53D+9rdh+OmnXbte1Hj5viSEsPUp/pCG/jhK5gh/7/lbNLZKpdORw8oYDn/LfwJDi67MF/9J/uFHHwGDQBAIAkEgCASBMyEQcnim2YqsQSAIBIEgEASCQBDYGYGQw50BTvNBIAgEgSAQBIJAEDgTAiGHZ5qtyBoEgkAQCAJBIAgEgZ0RCDncGeA0HwSCQBAIAkEgCASBMyEQcnim2YqsQSAIBIEgEASCQBDYGYGQw50BTvNBIAgEgSAQBIJAEDgTAiGHZ5qtyBoEgkAQCAJBIAgEgZ0RCDncGeA0HwSCQBAIAkEgCASBMyEQcnim2YqsQSAIBIEgEASCQBDYGYGQw50BTvNBIAgEgSAQBIJAEDgTAiGHZ5qtyBoEgkAQCAJBIAgEgZ0RCDncGeA0HwSCQBAIAkEgCASBMyEQcnim2YqsQSAIBIEgEASCQBDYGYGQw50BTvNBIAgEgSAQBIJAEDgTAiGHZ5qtyBoEgkAQCAJBIAgEgZ0RCDncGeA0HwSCQBAIAkEgCASBMyEQcnim2YqsQSAIBIEgEASCQBDYGYGQw50BTvNBIAgEgSAQBIJAEDgTAiGHZ5qtyBoEgkAQCAJBIAgEgZ0RCDncGeA0HwSCQBAIAkEgCASBMyEQcnim2YqsQSAIBIEgEASCQBDYGYGQw50BTvNBIAgEgSAQBIJAEDgTAv8HfoX1d+lhKSYAAAAASUVORK5CYII="
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step3: Calculate Cost function 𝑱(theta_0,theta_1 ).![image.png](attachment:image.png)\n",
    "![image-2.png](attachment:image-2.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def J(theta_0,theta_1):\n",
    "    m=len(x)\n",
    "    h_0 = theta_0 + (theta_1 *x )\n",
    "    cost = (1/(2*m) *(h_0 - y)**2).sum()\n",
    "    return cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16.305384479692318"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "J(theta_0,theta_1)"
   ]
  },
  {
   "attachments": {
    "image-2.png": {
     "image/png": 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"
    },
    "image.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step4: Calculate the gradient.![image.png](attachment:image.png)\n",
    "![image-2.png](attachment:image-2.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradiant(h_0, y):\n",
    "    m=len(x)\n",
    "    theta0_grad= (1/m * (h_0 - y)).sum()\n",
    "    theta1_grad= (1/m * (h_0 - y) * x).sum()\n",
    "    return theta0_grad, theta1_grad\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-5.56923073976923, -35.04384604321538)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gradiant(h_0, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "#gradiant(h_0, y)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_0_grad , theta_1_grad = gradiant(h_0, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-5.56923073976923 -35.04384604321538\n"
     ]
    }
   ],
   "source": [
    "print(theta_0_grad , theta_1_grad)"
   ]
  },
  {
   "attachments": {
    "image-2.png": {
     "image/png": 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"
    },
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step5: Update the parameters (simultaneously).![image.png](attachment:image.png)\n",
    "![image-2.png](attachment:image-2.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_0 = theta_0 - r*theta_0_grad\n",
    "theta_1 = theta_1 - r*theta_1_grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00556923073976923"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.03504384604321538"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_1"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step6: Repeat from 2 to 5 until converge to the minimum or achieve maximum iterations.![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "it takes iterations =  120\n"
     ]
    }
   ],
   "source": [
    "iteration = 1000\n",
    "theta_0_list=[]\n",
    "theta_1_list=[]\n",
    "cost_list=[]\n",
    "hypothes_list=[]\n",
    "gradiant_0_list=[]\n",
    "gradiant_1_list=[]\n",
    "\n",
    "\n",
    "for i in range(iteration):\n",
    "    h_0 = theta_0 + (theta_1 *x )\n",
    "    hypothes_list.append(h_0)\n",
    "    #print(h_0)\n",
    "    \n",
    "    cost= J(theta_0,theta_1)\n",
    "    cost_list.append(cost)\n",
    "    \n",
    "    \n",
    "    theta_0_grad, theta_1_grad= gradiant(h_0, y)\n",
    "    gradiant_0_list.append(theta_0_grad)\n",
    "    gradiant_1_list.append(theta_1_grad)\n",
    "\n",
    "    \n",
    "    theta_0_list.append(theta_0)\n",
    "    theta_1_list.append(theta_1)\n",
    "    \n",
    "    theta_0 = theta_0 - r*theta_0_grad\n",
    "    theta_1 = theta_1 - r*theta_1_grad\n",
    "    \n",
    "    if i > 0:\n",
    "        if abs(cost_list[i-1] - cost_list[i] < 0.0001):\n",
    "            break\n",
    "            \n",
    "        if abs(np.linalg.norm([theta_0_list[i],theta_1_list[i]])-np.linalg.norm([theta_0_list[i-1],theta_1_list[i-1]]))< 0.0001:\n",
    "            break\n",
    "        \n",
    "        if abs(np.linalg.norm([gradiant_0_list[i],gradiant_1_list[i]])-np.linalg.norm([gradiant_0_list[i-1],gradiant_1_list[i-1]])) < 0.0001:\n",
    "            break\n",
    "    \n",
    "    \n",
    "print('it takes iterations = ', i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.1499960842169203\n",
      "0.8881463897205402\n"
     ]
    }
   ],
   "source": [
    "print(theta_0)\n",
    "print(theta_1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Predict y values using the LR equation\n",
    "##### h(x)= theta_0 + theta_1 * x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.7256207 , 6.10057673, 4.50191348, 7.16635265, 8.85383087,\n",
       "       6.27820626, 5.56768898, 5.65650353, 5.47887442, 4.67954259,\n",
       "       4.32428395, 4.05784028, 5.30124531])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_predict = theta_0 + theta_1 * x\n",
    "y_predict"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot  LR equation output (fitted line) with the original data (scatter plot of X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x19a724fddc8>]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x,y)\n",
    "plt.plot(x,y_predict)"
   ]
  },
  {
   "attachments": {
    "image-2.png": {
     "image/png": "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"
    },
    "image-3.png": {
     "image/png": "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"
    },
    "image.png": {
     "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIMAAAAvCAYAAADAQ3nzAAAGKklEQVR4Ae3ay60sNRAGYJMBLNnB5q6BFTseCQAR8Fix45EAjwSACC5EAEQARABEAFtWkAHok/qXSpZ7Tvc5M2ceuKSWPe7qcnXV76qye1qbNC0wLTAtMC3w+BZ4trX2cWvts6V9rrVm7O0VVdwf8b+xwj+Hr8QC77TW/mytfdJae7219n5r7bfW2k/LWP8a7uPXhv/n1tqvy1jPP39fiQVebq3921rTVhIRjPcr3e9/BvzvrcipMmf/wi1gRf840PGZxenaSmv8L67w12dn/4ItwNFW/w8rOvbj4f92wP9Sa200PmCdQ5dogax+gFA4Wt2HKGDYyn9I1rx3gRb4ZokOHOz6o7X2+QE9v97Jf0DUvHWJFrBFtHsIILRfHFB0L/8BUfPWpVrA2YHtJTD83VqTFg5R5Qemq6EXBtuhq1H+BIqqD2wHR2THABCVbD3XDqB+X3YSlf9i+3KgS76TE1W+/3eSBtacCwz9TkJt4YBpRA6bspNg27cWG7/bWrMIQ34rVOsYXmPaOp5njtpSjrKZiNL9ix51wisRxuEc3JOIISr0jmdDKaSnHFqFX+t0knyLT4s8D3z8IKVo1R4upI2MZej4jUkpFzCIEH0IPP6sly0xW0QnidUBWTg9SNQGbMaOI37H0pUAQOTxbYPdgcCz5nUBSaL196211xa++KjKurNPaZNFYFpj0NsfrVaBIkNCWh1/7P69XvxISjpSZgM6iJIcZeVasb5T9ISfA0WN8Eu3a/zAUOsR/jEH/+QCKmChB1AqWPl1NwUMJoBYigYc+oRDXE+e8wKUOAdZFYD6tITPc+jRz0mvPXQXPzDUCKLfR2NA7AFz7/RNIejk+J6yPfq03AAASp4LCFYXIGZl0eUWyYITZb7qVrr3tVCRtAEgIkZqBsBIf2Hb3qTQGX1k+WBBYpCWcBQgnDNNADHD3CoYODWpoK58nuVsAEjU0AJGBcV2BBRORYvQM6pwOdu9FDaQKjQb940+ICniHq1762B4NEPWiXKm3heL2epk9ctNQWraUZFUZZ+yP8FwAuta7Va/EOPi6OTjRISHTAtEkb213TLfBMMWK+3gyb5X3n1zueQnxWQiwg5xQ1b1RWTXViE4uvoINRS67LNvuWZYe++TjQvzo3pBdDD+yslmfrjgvZFBBR7w3NWmMFvT0kL564quD9depI6v1QsBg5V7DOK4rdfW+faCgdxj6fCktfbqFV3PbzGqekFKYKRKVo7IcAwwqBnuWon1/tYdyn3AUN9x9osFcr4wMj4gVDD0+9wiZlN364rsQXlI+ATDIetsvJfq3jEzhzsvkBaMhxIZHGQ4CcuJV+6fs43+Ptc6h3fpe4dJOy3AmAqkVPIqfP2cKhKnn4Lry53yT81Ot+jet6eee6t8C8iuKJGOztW+vZy9/P3z8/cFWiDfE6RexbkPgM5qnNqOdijA7LtQ+H1zwS9akzXpSi0gEkhZHFwpKTdRIvfwKd7ruYroAUCjoj7PzfYKLGCF939mobaPSr8M9Mc/qnOMjYr6gYg5dIkWsMoV46NUoAjvnX6I35H96KPhJb731GlggTjXDq0vFOX+ulPzeOXvxQFUz9/zzN8XbAEAkOdzPgMU0kMPjLyCM57wqzPwf3SAP8/N9kos4DtPHBxQcPQaIOwaen4nwmv8V2KGqWa1gLSgRoij+3qh8upLGZW/1gt708Ve/l6X+fuBFuCA0Wq2ZRQhbC0rrTksdYQCMqTfb0lzb9Qe628HI9lzbIMF/Hd0BAZOBIbqXOJ6cGSK8OfPrGTafo7AYKyfU+G5JjtzzPaEFuAUdYGCsCfOAYYaCeJwfyrqyRa08jtrSGSp34b0AQxoRAKgMJfTS6kJIB76YbHXbf7eYIGkgn71c7ZisDqRuKSCrP5Mgb8/hApwtCFFZ5VJTn7PyBArnalV7Fmd3y3O9/WUc3rHRj2FIl6pxfeH8DuCroVj+EWGSlZ9BR4AmAtNMCyGOFdTPyaJEraXQnSfz6Mfh4W28AODyJDngKHuTswFSKiCIfzLrdncggWAAbASDYBNRAmJSgFHBUPGwjfbG7AAECgka42R1FSB4FWBRuQwXiPWDZhhvsK0wLTA41ngP5YvqoC1obIFAAAAAElFTkSuQmCC"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Use R2 score to evaluate LR equation output\n",
    "![image.png](attachment:image.png)\n",
    "![image-2.png](attachment:image-2.png)\n",
    "![image-3.png](attachment:image-3.png)\n",
    "https://en.wikipedia.org/wiki/Coefficient_of_determination"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.251017173316544\n"
     ]
    }
   ],
   "source": [
    "SSot= ((y-y_predict)**2).sum()\n",
    "print(SSot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "SSret= ((y-y.mean())**2).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "r2=1-(SSot/SSret)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7466665893916266"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import r2_score\n",
    "score=r2_score(y,y_predict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7466665893916266"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## GD vectorize Implementation\n",
    "### Implement GD without iterate through data points i.e. use vector operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot the output and calculate R2 score\n",
    "##### Make sure that you obtained the same results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot loss function\n",
    "### Repeat your last vectorized implementaion version and save loss for each iteration (epoch)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot loss vs. iterations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "itertation=[]\n",
    "for i in range (len(cost_list)):\n",
    "    itertation.append(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Cost')"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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8AfwmeWWlv5rKIk4+ehi/XpgRs02IiBxwqLl6jjWzs9z9G8B/A9OBGcBfyKBTMJPlwuljWL65lRVbWsMuRURkwA61x38z0Arg7g+5+9+6+9eI7+3fnNzS0t8Hp48hx+Bx7fWLSAY5VPDXufui3gvdvQGoS0pFGWRkWSGnTxjB44s2ae4eEckYhwr+g90gpWgoC8lUF84Yy5vb9rBko+buEZHMcKjgf8XMPtd7oZldBcxLTkmZ5QPTRpOfm8OD8xvDLkVEZEBih1h/LfCwmV3OW0FfD+QDH0liXRmjsjif86aM5LEFG/nWB6eQlxvps1xFJAMc6kYsW9z9TOC7wJrg8V13PyOYxkGAj55Uy/Y97boRu4hkhEPt8QPg7n8A/pDkWjLWuydVM6IknwfnNXL+1FFhlyMiclAalxgCebk5XDSzht8v38LOPe1hlyMiclAK/iHysZNr6ehyHtM5/SKS5hT8Q2Tq2HKmjCnngXk6u0dE0puCfwhdWl/Laxt2sXjDrrBLERHpl4J/CH3kpFoK83KYM3dd2KWIiPQrlOA3s0oze8DMlpvZMjM7I4w6hlpFUR4XTB/LYws2sLutM+xyRET6FNYe/y3Ak+4+mfhsn8tCqmPIffK0o9jT3sWjCzaEXYqISJ9SHvxmVg68C/gZgLu3u3tzqutIlhPHVTJ5dBn3zV2nidtEJC2Fscc/AWgCfm5mr5rZHWZW0nsjM7vazBrMrKGpKXOuiDUzLj/tKJZsbGFhow7yikj6CSP4Y8BJwG3ufiKwB7i+90bufru717t7fXV1daprPCIXn1hDSX4ud/95TdiliIi8QxjB3wg0uvvc4P0DxH8IskZZYR5/XT+OxxdtZGvL/rDLERF5m5QHfzC523ozmxQsOg9Ymuo6ku3KM+vo7HbufWlt2KWIiLxNWGf1fBmYY2aLgJnAv4ZUR9LUVZVw3uSRzJm7jv0dXWGXIyJyQCjB7+4LgvH76e5+sbvvDKOOZPvMWePZvqdd8/eISFrRlbtJdMYxI5g0qow7/7Rap3aKSNpQ8CeRmfHZc8azfHMrz63InFNSRSS7KfiT7KKZNYytKOS2P7wRdikiIoCCP+nyYzl87l0TeHnNDhrW7Ai7HBERBX8qXHbKUQwvyefW57TXLyLhU/CnQFF+LleeWcezy7eydGNL2OWISMQp+FNk9hl1lBbE+I9nV4ZdiohEnII/RSqK8/jM2eP57eLNLNmoydtEJDwK/hS66uzxlBfG+PEzK8IuRUQiTMGfQhVFeXzunAn8btlWFqxvDrscEYkoBX+K/c3Z4xlWnMePtNcvIiFR8KdYaUGML7z7GJ5f0cSfV20LuxwRiSAFfwhmn1lHTWUR//KbZXR3aw4fEUktBX8ICvNyuW7WJJZsbOER3ZRdRFJMwR+SC6ePZXptBT946nXN1y8iKaXgD0lOjvGtD05h46793PHCm2GXIyIRouAP0ekTRvCBaaP5zz+sYkPzvrDLEZGICC34zSzXzF41s8fDqiEdfPuCqRjGP/866247LCJpKsw9/q8Cy0JsPy3UVBZxzbnH8uSSzfxRN2sRkRQIJfjNrBb4EHBHGO2nm8+eM57xVSV857ElOtArIkkX1h7/zcB1QHd/G5jZ1WbWYGYNTU3ZvSdcEMvlny46ntXb9mj2ThFJupQHv5ldAGx193kH287db3f3enevr66uTlF14TlnYjUfO7mWn/zxTRZv0OydIpI8YezxnwV82MzWAL8AzjWze0OoI+38/YemMrwkn+seWERHV79/DImIHJGUB7+73+Dute5eB1wGPOvuV6S6jnRUUZzHP190PEs3tfDff9RtGkUkOXQef5qZNW0MF0wfw82/W8lrjRryEZGhF2rwu/tz7n5BmDWko+9dPI2q0gK++stX2deus3xEZGhpjz8NVRbn88OPz+DNpj38628if6mDiAwxBX+aOuvYKj579njueWktTy7eHHY5IpJFFPxp7BuzJjGjtoJv/Goha7fvCbscEckSCv40VhDL5T8/eRI5OcYX752vq3pFZEgo+NPcuOHF/OjjM1i6qYW/f2Qx7rpjl4gcGQV/Bjhvyii+fO6x/GpeIz9/cU3Y5YhIhlPwZ4ivvfc43jd1FN97YinPaxZPETkCCv4MkZNj/PjSmRw3qoxr7pvPqq2tYZckIhlKwZ9BSgpi/PTT9RTk5TL7zlfY0rI/7JJEJAMp+DPMuOHF/PzKU2je287sO1+mZX9H2CWJSIZR8GegaTUV/ORTJ7Nq624+e3eDpnUQkcOi4M9Q50ys5seXzqRhzQ6uvqdB5/iLyIAp+DPYhTPG8n8/NoMXVm7j/8yZT1unwl9EDk3Bn+E+dnIt//KRaTy7fCtX/8887fmLyCEp+LPA5acdzU2XnMDzK5uYfefL7G7rDLskEUljCv4scdmpR3HzpTNpWLuTy3/6Ett2t4VdkoikKQV/FrloZg0/ueJkXt/SyiW3/pnV2zSjp4i8k4I/y5w/dRT3fe50drd1csmtL/LKmh1hlyQiaSblwW9m48zsD2a2zMyWmNlXU11DtjvpqGE89MUzGVaczyd/+hL3zV0XdkkikkbC2OPvBL7u7lOA04EvmdnUEOrIanVVJTz8pbM485gqvvXwa9z48Gs640dEgBCC3903ufv84HUrsAyoSXUdUVBRlMedV57C5989gTlz1/HR2/7MGo37i0ReqGP8ZlYHnAjM7WPd1WbWYGYNTU2ahniwcnOMGz4whZ9+up7Gnfu44D/+xCOvbtANXUQiLLTgN7NS4EHgWndv6b3e3W9393p3r6+urk59gVnm/KmjeOIrZzNpdBnX/nIBX77/VZr3toddloiEIJTgN7M84qE/x90fCqOGKKodVswvrz6db7x/Ek8u3sz7fvw8Ty7eHHZZIpJiYZzVY8DPgGXu/qNUtx91sdwcvvRXx/LIl86iqrSAL9w7j8/f08DmXZrbXyQqwtjjPwv4FHCumS0IHh8MoY5Im1ZTwaPXnMU3Z03mudebOPeHz3Hrc6s00ZtIBFgmHOSrr6/3hoaGsMvIWuu27+WfHl/K75ZtoW5EMd+cNZlZ00YT/+NMRDKVmc1z9/rey3XlrnDUiGLumF3PXX9zCnm5OXxxznw+etufeenN7WGXJiJJoOCXA94zaSS//eo53HTJCTTu3Mdlt7/EJ25/ibn6ARDJKhrqkT7t7+hiztx13PbcG2zb3Ub90cP4wruP4dzJI8nJ0RCQSCbob6hHwS8Hta+9i1++so6fvrCaDc37mFBdwpVn1vHRk2opKYiFXZ6IHISCX45IR1c3TyzaxJ0vrmZR4y7KCmJcfGINl506juPHVoRdnoj0QcEvQ8LdeXV9M/f8ZS1PvLaJ9s5uTqip4JKTarhwxliqSgvCLlFEAgp+GXLNe9t5+NUNPDi/kcUbWsjNMc48ZgQXTh/L+44fRWVxftglikSagl+SasWWVh5+dQNPLNrEuh17yc0xThs/nPdNHcV5U0Yxbnhx2CWKRI6CX1LC3Xltwy6eWrKZp5ZsYdXW3QBMqC7hPceN5OyJIzht/AgdGBZJAQW/hGL1tj089/pWnl2+lZdX76Cts5tYjjG9toLTJozg1PHDOWncMCqK88IuVSTrKPgldPs7upi3did/WrWNuW9uZ1HjLjq74//9HTeqlJnjKpleW8mM2kqOG11KQSw35IpFMlt/wa+/tyVlCvNyOevYKs46tgqAve2dLFjfzPy1O2lYu5Nnlm7h/zc0AhDLMSaOKmPqmHKmjClj0ugyjhtVxsiyAs0hJHKEFPwSmuL8GGceU8WZx8R/CNydxp37WNjYzJKNLSzZ2MILK5t4cH7jgc+UFcY4prqUCdUlHFNdytEjiqkbUcJRI4opL9RwkchAaKhH0t723W28vqWVVVt3s2JLK2827eHNpj1sbnn7PQQqivIYN7yImsoiaiqLGVtZyJiKIkZXFDK6opDq0gLyY5qeSqJDQz2SsUaUFnBmacGBvwx67GnrZN2OvazZtod1O/ayfude1u/YxxtNe3h+xTb2dbzz3gLDS/KpLi2guqyAqtJ8qkoLGF6az4iSfIaXFDCsOI/K4nyGFedRUZRHLFc/FJJ9FPySsUoKYkwZU86UMeXvWOfu7NrXwaZd+9m0ax9bW9rY3LKfptY2tra20dTaxprte9i2u439Hd39tlFaEKOiKI+ywhjlRXmUF8YoK8yjtCBGaWGM0oIYJfm5lBbmUZKfS1F+LiUFMYrycinOz6U4P/66MD+H/NwcHZ+QtKDgl6xkZlQW51NZnN/nD0Oive2d7NjTzo497ezc20Hz3nZ27mln175Omve107Kvk5b9HbTs62Bj835a21rZvb+T1v2dB85KGlhNUBjLpTAvh8K8XApibz3n9zxye17nBq+NvNycA4/8XCOWm0Ms18jLiT/HcnPIyzFyc+Lb5uYYseB9LNfIMSOWk0NODuRafHnPI8cSX3PgfY4ZOQnL4o+3XltO/LURPFu8f+9cph+6dBRK8JvZLOAWIBe4w91vCqMOEYgfZC7Oj1E77PCuLnZ32jq72dPWyZ62LvZ2BM/tnext72Jfexf7Ot563n/g0R1/7uymvbOLts5u2jq62d/RTcu+Tto7u+no6qYteG7v6qazy2nv6qa9s/+/TtKVGW//MeCtHwpIeE/8h8LiC99633tdwvcSfDb4yNu+M7Ft6PtHKHHR214nfP6tZX31zfpd19fCg31Hf/71Iydw6vjhB93mcKU8+M0sF/gv4HygEXjFzB5z96WprkXkSJgZhXm5FOblMqI0de12dTsdXfEfhc4up6O7m65up7PL6ex2urq76ejy+LLu+HO3x9d3e3xZd7C8y+Ovu50Dr3u2955lwXKH+HqP/+j1bONBTQTrHXAnvp74tvHt4u148Hmg13oObNdzzom7v215j8TtCZa/9ZngOfF7Ev75Ja5/a+E7Xyae+NLX33V9ffdb6965tM+/DQfwB2NJwdBfzxLGHv+pwCp3fxPAzH4BXAQo+EUGID40E//BERmMME5ZqAHWJ7xvDJaJiEgKhBH8fQ1oveMPHjO72swazKyhqakpBWWJiERDGMHfCIxLeF8LbOy9kbvf7u717l5fXV2dsuJERLJdGMH/CjDRzMabWT5wGfBYCHWIiERSyg/uununmV0DPEX8dM473X1JqusQEYmqUM7jd/ffAL8Jo20RkajTRCQiIhGj4BcRiZiMmJbZzJqAtYP8eBWwbQjLCZP6kn6ypR+gvqSrI+nL0e7+jtMiMyL4j4SZNfQ1H3UmUl/ST7b0A9SXdJWMvmioR0QkYhT8IiIRE4Xgvz3sAoaQ+pJ+sqUfoL6kqyHvS9aP8YuIyNtFYY9fREQSKPhFRCImq4PfzGaZ2etmtsrMrg+7noEys3Fm9gczW2ZmS8zsq8Hy4Wb2jJmtDJ6HhV3rQJlZrpm9amaPB+8zsi9mVmlmD5jZ8uDfzxmZ2Bcz+1rw39ZiM7vfzAozpR9mdqeZbTWzxQnL+q3dzG4IMuB1M3t/OFX3rZ++fD/472uRmT1sZpUJ64akL1kb/Am3ePwAMBX4hJlNDbeqAesEvu7uU4DTgS8FtV8P/N7dJwK/D95niq8CyxLeZ2pfbgGedPfJwAzifcqovphZDfAVoN7dpxGfLPEyMqcfdwGzei3rs/bg/5vLgOODz9waZEO6uIt39uUZYJq7TwdWADfA0PYla4OfhFs8uns70HOLx7Tn7pvcfX7wupV4uNQQr//uYLO7gYtDKfAwmVkt8CHgjoTFGdcXMysH3gX8DMDd2929mQzsC/EJGovMLAYUE78nRkb0w92fB3b0Wtxf7RcBv3D3NndfDawing1poa++uPvT7t4ZvH2J+D1LYAj7ks3BnxW3eDSzOuBEYC4wyt03QfzHARgZYmmH42bgOqA7YVkm9mUC0AT8PBi2usPMSsiwvrj7BuAHwDpgE7DL3Z8mw/rRS3+1Z3oOfAb4bfB6yPqSzcE/oFs8pjMzKwUeBK5195aw6xkMM7sA2Oru88KuZQjEgJOA29z9RGAP6Tsc0q9g/PsiYDwwFigxsyvCrSppMjYHzOxG4sO+c3oW9bHZoPqSzcE/oFs8piszyyMe+nPc/aFg8RYzGxOsHwNsDau+w3AW8GEzW0N8uO1cM7uXzOxLI9Do7nOD9w8Q/yHItL68F1jt7k3u3gE8BJxJ5vUjUX+1Z2QOmNls4ALgcn/rYqsh60s2B3/G3uLRzIz4OPIyd/9RwqrHgNnB69nAo6mu7XC5+w3uXuvudcT/HTzr7leQmX3ZDKw3s0nBovOApWReX9YBp5tZcfDf2nnEjyNlWj8S9Vf7Y8BlZlZgZuOBicDLIdQ3YGY2C/gm8GF335uwauj64u5Z+wA+SPyo+BvAjWHXcxh1n038T7hFwILg8UFgBPEzFlYGz8PDrvUw+/Ue4PHgdUb2BZgJNAT/bh4BhmViX4DvAsuBxcA9QEGm9AO4n/ixiQ7ie8FXHax24MYgA14HPhB2/QPoyyriY/k9/+//ZKj7oikbREQiJpuHekREpA8KfhGRiFHwi4hEjIJfRCRiFPwiIhGj4JdIMLM/B891ZvbJIf7ub/XVlki60umcEilm9h7g79z9gsP4TK67dx1k/W53Lx2C8kRSQnv8Eglmtjt4eRNwjpktCOakzw3mP38lmP/888H27wnuiXAf8Fqw7BEzmxfMY391sOwm4rNcLjCzOYltWdz3gznvXzOzSxO++zl7a17/OcEVtJjZTWa2NKjlB6n8ZyTREQu7AJEUu56EPf4gwHe5+ylmVgC8aGZPB9ueSnxe9NXB+8+4+w4zKwJeMbMH3f16M7vG3Wf20dYlxK/0nQFUBZ95Plh3IvF51TcCLwJnmdlS4CPAZHf3xBtwiAwl7fFL1L0P+LSZLSA+9fUI4nOgALycEPoAXzGzhcTnSB+XsF1/zgbud/cud98C/BE4JeG7G929m/hl+XVAC7AfuMPMLgH2vvMrRY6cgl+izoAvu/vM4DHe43PTQ3za5fhG8WMD7wXOcPcZwKtA4QC+uz9tCa+7gJjHb75xKvFZWS8GnjyMfogMmIJfoqYVKEt4/xTwxWAabMzsuODmKr1VADvdfa+ZTSZ+S8weHT2f7+V54NLgOEI18bt39TubYnD/hQp3/w1wLfFhIpEhpzF+iZpFQGcwZHMX8Xvo1gHzgwOsTfR9y8EngS+Y2SLiMyO+lLDudmCRmc1398sTlj8MnAEsJD7b6nXuvjn44ehLGfComRUS/2vha4Pqocgh6HROEZGI0VCPiEjEKPhFRCJGwS8iEjEKfhGRiFHwi4hEjIJfRCRiFPwiIhHzvxtf8lUftjlBAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(itertation, cost_list)\n",
    "plt.title('loss graph')\n",
    "plt.xlabel('iterations')\n",
    "plt.ylabel('Cost')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Cost')"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(theta_0_list, cost_list)\n",
    "plt.title('loss graph vs theta_0')\n",
    "plt.xlabel('theta_0')\n",
    "plt.ylabel('Cost')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Cost')"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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OZ8N2DeomIocmkmf8TwAj9lv2S+B9d+8GvB9+LIeoa4sMJl0+mO17Srlo4mcUFBUHXZKI1CERC353nwLsfxXyDGBS+PdJwJmR2n9916ddEx4bM4j12/Zy8cTpFO4qCbokEakjot3G39Ld1wOE/9siyvuvVwZ3asbE0bms2LKLSx6dzvbdGs5ZRA4uZi/umtlYM8szs7yCgoKgy4lZx3XN4qFLBrJ4YxGjH5+hsfxF5KCiHfwbzaw1QPi/Vd6N5O4Pu3uuu+dmZ2dHrcC66Ds9WjDhogHM/Wo7lz8xk90lZUGXJCIxLNrB/wowOvz7aODlKO+/3jqlVyvGjexH/qqtXDkpj72lmshFRCoXye6czwDTgB5mttbMrgDuAE42syXAyeHHUktO69OGv5zXl2nLt2gWLxGpUsQGaXP3C6t46sRI7VPg7AHtKC6r4JYX5vDjp2dx/6gBJCfG7KUcEQmAEqEeunBwB353ei/enb+RG5/9grLyiqBLEpEYomGZ66nRx+ZQUlbBH95YQGpSAned15fEBE3hKCIK/nrtquM7U1xWzl/eWUxCgnHnOX0U/iKi4K/vfvzdbpRVOOPeW4I7/Plchb9IvFPwx4EbT+qOYdzz3mLcXc0+InFOwR8nbjipGwkGf313MRXu/PX8fgp/kTil4I8j15/YjYQE4663F+HAX8/rS5K6eorEHQV/nLnuO10xgz+/tYgKh3vOV/iLxBsFfxy6dnhXDOPOtxZS4c74C/op/EXiiII/Tl0zvAsJBn96cyE4jBvZT3f4isQJBX8c+9EJXUgw4w9vLKDCnXsv7K/wF4kD+iuPc1cd35lbf3Akb87dwHVPfa6B3UTigIJfuHJYZ377w568M38jYyfns6dE4S9Snyn4BYDLjuvEHWcfxZQlBYx5fAY7izWZi0h9peCX/xg5uAPjLuhH3qqtXDxRc/iK1FcKfvmGM/q15f5RA5i/bgcjH/mMzTuLgy5JRGqZgl++5dRerXhkdC4rNu/kgoemsWH73qBLEpFapOCXSp3QPZtJlw1m445izntoKmsKdwddkojUkmoFv5n9vTrLqsvMbjKzeWY218yeMbO0mm5LIufozs158sqj2bGnjPMenMaygp1BlyQitaC6Z/y99n1gZonAwJrs0MzaAv8D5Lp7byARGFmTbUnk9WvfhGfHHkNZRQUXPDSNBet3BF2SiBymAwa/md1iZkVAHzPbEf4pAjYBLx/GfpOABmaWBDQE1h3GtiTCjmzdmOd+NISkhAQueGga+asKgy5JRA7DAYPf3f/k7hnAXe7eOPyT4e7N3f2WmuzQ3b8C/gKsBtYD2939nf3XM7OxZpZnZnkFBQU12ZXUoi7Z6fzz6iE0T09l1MTpfLBwU9AliUgNVbep5zUzawRgZheb2d1m1rEmOzSzpsAZQCegDdDIzC7efz13f9jdc909Nzs7uya7klrWvllD/nn1ELq2SOeqyXm8OGtt0CWJSA1UN/gfAHabWV/gF8AqYHIN93kSsMLdC9y9FHgBOLaG25Ioy0pP5ZmrjmFQTjNueu5LHv1kRdAlicghqm7wl7m7EzpTH+/u44GMGu5zNXCMmTU0MwNOBBbUcFsSgIy0ZB6/bBAjerXi/16bz11vLyT0z0NE6oLqBn+Rmd0CXAK8Hu7Vk1yTHbr7dOB54HNgTriGh2uyLQlOWnIiE0YN4MLB7ZnwwTJ+9eJcyisU/iJ1QXXH478AuAi43N03mFkH4K6a7tTdfwv8tqavl9iQmGD88ayjaNYohQkfLGPrrhLGjexHWnJi0KWJyAFU64zf3TcATwGZZnYasNfda9rGL/WImfHzU4/gN6f15K15G7js8ZkU7dXgbiKxrLp37p4PzADOA84HppvZuZEsTOqWK4Z24u7z+zJjZSEXPPQZG3dofB+RWFXdNv5fA4PcfbS7XwoMBn4TubKkLjp7QDseHZ3Lyi27OPv+qSzZWBR0SSJSieoGf4K773vHzpZDeK3EkeE9WvDc2CEUl1VwzgNTmb58S9Alich+qhveb5nZ22Y2xszGAK8Db0SuLKnLjmqXyYvXHktWRiqXPDqDV7/UiBwiseRgY/V0NbPj3P3nwENAH6AvMA11wZQDaN+sIS9ccyx922dy/TOzeGTKcvX1F4kRBzvjHwcUAbj7C+7+E3e/idDZ/rjIliZ1XZOGKfz9iqP5wVGt+cMbC/jdq/PV118kBhysH3+Ou8/ef6G755lZTmRKkvokLTmRv13Yn9aZaUz8ZAXrt+9h/Mj+6usvEqCDnfEfaIKUBrVZiNRfCQnGraf15LbTevLO/I1cpLl8RQJ1sOCfaWZX7b/QzK4A8iNTktRXlw/txP0XDWDeuh2cOeFTFqu7p0gg7EAX3MysJfAiUMJ/gz4XSAHOCt/RG3G5ubmel5cXjV1JFHy5ZhtXTs5jb0k5940awAndNey2SCSYWb675+6//GATsWx092OB3wErwz+/c/ch0Qp9qX/6tm/CS9cdR9umDbj8iZn8fdrKoEsSiSvVGqTN3T8APohwLRJH2jZpwPPXHMsNz8ziNy/PY1nBLm79wZEkJeq+QJFI01+ZBCY9NYmHL83liqGdeGLqSq6cnKcB3kSiQMEvgUpMMH5zWk/+cFZvPl6ymXMfmMbarbuDLkukXlPwS0wYdXRHJl02mHXb93DmhE/JW1kYdEki9ZaCX2LG0G5ZvHjtcaSnJnHhI5/xzIzVQZckUi8p+CWmdG2RzsvXDWVIlyxueWEOt708l9LyiqDLEqlXAgl+M2tiZs+b2UIzW2BmQ4KoQ2JTZsNkHh8ziB8d35nJ01Zx8cTpbNGdviK1Jqgz/vHAW+5+BKHRPhcEVIfEqMQE45bvH8k9F/Rl1pptnH7fp8xftyPoskTqhagHv5k1Bo4HHgVw9xJ33xbtOqRuOKt/O/75oyGUVzjnPDCV12evD7okkToviDP+zkAB8LiZzTKziWbWaP+VzGysmeWZWV5BQUH0q5SY0bd9E165/jiObJ3BdU9/zl1vL9TwziKHIYjgTwIGAA+4e39gF/DL/Vdy94fdPdfdc7OzNZZLvGuRkcYzY49h5KD2TPhgGWMen8HWXSVBlyVSJwUR/GuBte4+Pfz4eUIfBCIHlJqUyB3n9OFPZx/F9OWFnPa3T5izdnvQZYnUOVEP/vDgbmvMrEd40YnA/GjXIXXXhYM78M+rh+DunPPgVJ6bqf7+IociqF491wNPmdlsoB/wx4DqkDqqb/smvPY/wxic04yb/zWHW16Yzd7S8qDLEqkTqjU6Z21z9y8IjesvUmPNGqUw6fLB/PWdRdz/4TLmrdvB/aMG0K5pw6BLE4lpunNX6rTEBOMXI47goUsGsqJgFz/82yd8uGhT0GWJxDQFv9QLp/Zqxcs/Po6WjdMY8/hM7np7IWUa6kGkUgp+qTc6Z6fz4rXH/afL50WPTGfD9r1BlyUScxT8Uq80SAl1+bzngr7MXbed79/7MR8t1g2AIvtS8Eu9dFb/drzy46Fkp6cy+rEZavoR2YeCX+qtri3Seem647ggN9z0M1FNPyKg4Jd6rkFKInee24e7z+/L3K+2M2L8FN6ZtyHoskQCpeCXuHD2gHa8dv1Q2jVtwNi/53PrS3N0w5fELQW/xI3O2en865pjuWpYJ578bDWn3/cJCzdojH+JPwp+iSupSYn8+gc9mXz5YAp3lXL6fZ8yaepK3DXMs8QPBb/EpeO7Z/PWjcM4rktzfvvKPK6anMdmTe8ocULBL3ErKz2Vx8YM4rc/7MmUxZsZMW4K783fGHRZIhGn4Je4ZmZcdlwnXr1+KNkZaVw5OY9f/ms2O4vLgi5NJGIU/CJAj1YZvHTdsVwzvAvP5a3h++M/Jm9lYdBliUSEgl8kLDUpkZtHHME/fjQExzn/oWn8+a2FlJTpjl+pXxT8IvsZlNOMN284nvMGtuf+D5dx5oRPmb9O3T6l/lDwi1QiPTWJO8/twyOX5rKpqJjT7/uEce8tplTj/Ug9EFjwm1mimc0ys9eCqkHkYE7u2ZJ3bzqeH/Rpzbj3lnDGfZ8yb50meJe6Lcgz/huABQHuX6RamjZKYfzI/jx0yUA2FRVzxn2fMu69xWr7lzorkOA3s3bAD4CJQexfpCZO7dXqm2f/Ez5l7lc6+5e6J6gz/nHALwCdMkmdsu/Z/+adxZwx4VP+9MYC9pRowDepO6Ie/GZ2GrDJ3fMPst5YM8szs7yCAs2gJLHl1F6teO+mEzg/tx0PTVnOqeOm8OnSzUGXJVItFu3BqczsT8AlQBmQBjQGXnD3i6t6TW5urufl5UWpQpFDM3XZZn71whxWbtnNeQPb8esfHEmThilBlyWCmeW7e+63lgc5KqGZDQd+5u6nHWg9Bb/Eur2l5Yx/fwkPT1lO04bJ/Oa0npzetw1mFnRpEseqCn714xepBWnJobt+X/nxcbRp0oAbnv2Cix+dzvKCnUGXJvItgZ7xV5fO+KUuKa9wnp6+ij+/tYjisgquHt6Fa4d3IS05MejSJM7ojF8kShITjEuG5PD+z07ge0e14t73lzBi3BSmLFYnBYkNCn6RCGmRkcb4kf158oqjMTMufWwG1zyZz9qtu4MuTeKcgl8kwoZ2y+LNG4bx05O788GiTZx090fc+/4STfYugVHwi0RBWnIi15/Yjfd/OpwTj2jJ3e8u5uR7PuLd+Rs1369EnYJfJIraNmnAhFEDePrKo0lLSuSqyXmMfnwmSzYWBV2axBEFv0gAju2axRs3DOM3p/Vk1uqtjBj/Mbe9PJfCXSVBlyZxQMEvEpDkxASuGNqJj37+HUYd3YGnpq/mhLs+YOLHyzXyp0SUgl8kYM0apfC/Z/TmrRuGMaBDU37/+gJOuecj3pyzXu3/EhEKfpEY0a1lBpMuH8wTlw0iOTGBa576nHMemKpJ36XWKfhFYszwHi1484Zh3HnOUazduodzH5zG2Ml5LN2k4R+kdmjIBpEYtrukjMc+WcGDHy1nT2k55+e2439O7EbrzAZBlyZ1QEyOzlldCn6Jd5t3FnPfv5fy1PRVobuAj+nINcO70Dw9NejSJIYp+EXqgTWFuxn//hJe+HwtDZITuWJYZ64c1onGaclBlyYxSMEvUo8s3VTE3e8u5o05G8hskMyVQzsx5rgcMvQBIPtQ8IvUQ3O/2s649xbz3oJNNGmYzFXDOjP62BzSU5OCLk1igIJfpB6bvXYb495bwr8XbqJpw2SuGNqJS4/NURNQnFPwi8SBL9Zs4973Qx8AGWlJXHZsDpcd14mmjTQHcDxS8IvEkblfbee+fy/lrXkbaJiSyMXHdOSKoZ1o2Tgt6NIkimIm+M2sPTAZaAVUAA+7+/gDvUbBL1IzizcWMeGDpbz65ToSE4yz+7dj7Amd6ZKdHnRpEgWxFPytgdbu/rmZZQD5wJnuPr+q1yj4RQ7P6i27eeTj5fwjbw0l5RWc0rMlY4/vzMCOzYIuTSIoZoL/WwWYvQzc5+7vVrWOgl+kdmzeWcykqSuZPG0V2/eU0r9DE64c2plTe7UkKVEjuNQ3MRn8ZpYDTAF6u/uO/Z4bC4wF6NChw8BVq1ZFv0CRemp3SRnP56/l0U9WsGrLbto1bcCYY3M4L7c9mQ3UE6i+iLngN7N04CPgD+7+woHW1Rm/SGSUVzjvLdjIox+vYMbKQhqmJHLOgHaMPjaHri10HaCui6ngN7Nk4DXgbXe/+2DrK/hFIm/uV9t5YupKXvliHSXlFQztmsXFx3TkpCNbqBmojoqZ4DczAyYBhe5+Y3Veo+AXiZ7NO4t5dsZqnp6+mnXb99KqcRoXDu7AyMHt1R20joml4B8KfAzMIdSdE+BX7v5GVa9R8ItEX1l5Bf9euIknp69myuICEhOM7x7RgosGd+D47tkkJljQJcpBxEzw14SCXyRYKzfv4tmZa3g+fw2bd5bQJjONc3Pbc97AdrRv1jDo8qQKCn4ROWwlZRW8v2AjT89YzSdLN+MOQzo357zcdozo3YqGKRocLpYo+EWkVq3btod/5a/ln/lrWV24m4YpiYzo3YpzBrTjmM7N1RQUAxT8IhIRFRVO3qqtvPD5Wl6fvZ6i4jJaNk7lh33acGb/tvRq05hQnw6JNgW/iETc3tJy3p2/kZe/WMdHizdRWu50zmrED/q05rQ+bejRKiPoEuOKgl9Eomrb7hLemLOB12av47PlW6hw6Noine/3bsWI3q05snWGvglEmIJfRAKzqWgvb8/dwGuz1zNzZSEVDh2bN+TUXq04tVdL+rdvSoKuCdQ6Bb+IxITNO4t5Z95G3pq3gWnLNlNa7mSlp/LdI7I58ciWDOuWpd5BtUTBLyIxZ8feUj5cVMC78zfy4aJNFO0tIyUxgaM7N2N4jxYM75FN56xGahKqIQW/iMS00vIKZq4s5IOFm/hgUQFLN+0EoG2TBhzfPZth3bIY0rm5ppE8BAp+EalT1hTu5qPFBUxZXMDUZVvYWVyGGfRuk8mQLs0Z0qU5uR2bkqEJ5auk4BeROqusvIIv127j4yWbmbpsC7NWb6W03Ekw6N02k8E5zRjUqRm5HZvSPD016HJjhoJfROqNPSXl5K/ayvQVW5i+vJAv1m6jpCw05mPnrEYM6NiU/h2a0K99E3q0zIjbYaWrCn5dOheROqdBSiJDu2UxtFsWELpxbM5X28lftZX8VVv5YOEmns9fC0BacgK922RyVLtMjmqbSe+2mXTOahS3Hwag4BeReiAtOZFBOc0YlBOaPN7dWVO4h1lrtvLlmu18uXYbz8xYzeOloW8FqUkJHNEqgyNbN+aIVhn0aNWY7i3T46aZSE09IhIXysorWFawi3nrtjN/3Q7mrdvBwg072Lq79D/rNG+UQpcW6XTJTqdLdiM6Zzcip3kj2jVtSEpS3fuGoKYeEYlrSYkJ9GiVQY9WGZw9ILTM3SkoKmbRxiIWbShiycadLCvYyVtz13/jAyHBoE2TBrRv2pD2zRrQrmlD2jZpQJsmDWidmUarzDTSkhMDemeHTsEvInHLzGjROI0WjdMY1i37G88V7iphxeZdrNi8i9VbdrGqcDdrCnfz4aICNhUVf2tbmQ2SaZGRSnb4p1mjFJo3SqFpoxSaNkyhSYNkGjdIpnFaMulpSaSnJgX2LSKQ4DezEcB4IBGY6O53BFGHiEhVmjVKoVmjFAZ2bPqt5/aWlrNu2x7Wb9/L+u172bjjvz8FRcXMWr2NLTuL2VVSfsB9JCcaDZITaZiSRFpyAqlJiaQkJZCUaCQnJJCYYNz8vSPo175Jrb63qAe/mSUCE4CTgbXATDN7xd3nR7sWEZGaSEtOpHN2Op2z0w+43t7ScrbtLmXr7hK27S5lx95SduwpZWdxGbuKy9hZXM6ekjL2lJazt7SCkrIKisvKKS13yioqKKuoIBLXYYM44x8MLHX35QBm9ixwBqDgF5F6JS05kVaZibTKTAu6lG8IooGpLbBmn8drw8tERCQKggj+yobZ+9Z3GTMba2Z5ZpZXUFAQhbJEROJDEMG/Fmi/z+N2wLr9V3L3h909191zs7Oz939aRERqKIjgnwl0M7NOZpYCjAReCaAOEZG4FPWLu+5eZmY/Bt4m1J3zMXefF+06RETiVSD9+N39DeCNIPYtIhLv6t7gEyIiclgU/CIicaZOjM5pZgXAqvDDLGBzgOXEMh2bqunYHJiOT9Xq8rHp6O7f6hZZJ4J/X2aWV9kwo6JjcyA6Ngem41O1+nhs1NQjIhJnFPwiInGmLgb/w0EXEMN0bKqmY3NgOj5Vq3fHps618YuIyOGpi2f8IiJyGBT8IiJxJiaD38xGmNkiM1tqZr+s5Hkzs3vDz882swFB1BmUahyfUeHjMtvMpppZ3yDqDMLBjs0+6w0ys3IzOzea9QWpOsfGzIab2RdmNs/MPop2jUGqxt9Vppm9amZfho/PZUHUWSvcPaZ+CA3ctgzoDKQAXwI991vn+8CbhMb2PwaYHnTdMXZ8jgWahn//Xrwcn+ocm33W+zeh8aLODbruWDk2QBNCM+F1CD9uEXTdMXZ8fgXcGf49GygEUoKuvSY/sXjG/5+pGd29BPh6asZ9nQFM9pDPgCZm1jrahQbkoMfH3ae6+9bww88IzXkQD6rzbwfgeuBfwKZoFhew6hybi4AX3H01gLvr+HyTAxlmZkA6oeAvi26ZtSMWg786UzPG8/SNh/reryD07SgeHPTYmFlb4CzgwSjWFQuq8++mO9DUzD40s3wzuzRq1QWvOsfnPuBIQhNHzQFucPeK6JRXuwIZlvkgqjM1Y7Wmb6ynqv3ezew7hIJ/aEQrih3VOTbjgJvdvTx04hY3qnNskoCBwIlAA2CamX3m7osjXVwMqM7xORX4Avgu0AV418w+dvcdEa6t1sVi8FdnasZqTd9YT1XrvZtZH2Ai8D133xKl2oJWnWOTCzwbDv0s4PtmVubuL0WlwuBU9+9qs7vvAnaZ2RSgLxAPwV+d43MZcIeHGvmXmtkK4AhgRnRKrD2x2NRTnakZXwEuDffuOQbY7u7ro11oQA56fMysA/ACcEmcnK197aDHxt07uXuOu+cAzwPXxkHoQ/X+rl4GhplZkpk1BI4GFkS5zqBU5/isJvRtCDNrCfQAlke1yloSc2f8XsXUjGZ2dfj5Bwn1xvg+sBTYTeiTOC5U8/jcBjQH7g+f2ZZ5PRtdsDLVPDZxqTrHxt0XmNlbwGygApjo7nODqzp6qvlv5/+AJ8xsDqGmoZvdvU4O16whG0RE4kwsNvWIiEgEKfhFROKMgl9EJM4o+EVE4oyCX0Qkzij4RUTijIJf4pKZNTGza8O/Dzez1w7x9WPMrE0N931eeFjfCjOr9/dXSOxR8Eu8agJcexivHwPUKPiBucDZwJTD2L9IjcXcnbsiUXIH0MXMvgBKCY1N8zzQG8gHLnZ3N7OBwN2EhuHdTCjwjyM05s9TZrYHGAL8HPghocHNpgI/8irujnT3BQBxNkicxBCd8Uu8+iWwzN37EQrt/sCNQE9Ck3EcZ2bJwN8ITdYyEHgM+IO7Pw/kAaPcvZ+77wHuc/dB7t6bUPifFu03JFJdOuMXCZnh7msBwt8CcoBthL4BvBs+O08EqhoM8Dtm9gugIdAMmAe8GtGKRWpIwS8SUrzP7+WE/jYMmOfuQw70QjNLA+4Hct19jZndDqRFqlCRw6WmHolXRUDGQdZZBGSb2RAAM0s2s16VvP7rkN9sZulA3EzgLnWTzvglLrn7FjP71MzmAnuAjZWsU2Jm5wL3mlkmob+XcYSacZ4AHtzn4u4jhKbjW0lobPcqmdlZhK4dZAOvm9kX7n5qLb01kYPSsMwiInFGTT0iInFGTT0iEWJmEwj1+d/XeHd/PIh6RL6mph4RkTijph4RkTij4BcRiTMKfhGROKPgFxGJM/8PDl/yDGjcOc8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(theta_1_list, cost_list)\n",
    "plt.title('loss graph vs theta_1')\n",
    "plt.xlabel('theta_1')\n",
    "plt.ylabel('Cost')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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78mSc48ZbyxcWRx2WUB8jtGzt47V714IAl3x/EgXDju1dhnosRmzpUqIffED0gw9I1mwFQPT5cE+dSsbnPo976lSco0ZaO/EsjnqsT/AxwNblHbz17w14Mx1c9O0JBHKOvU0ShmGQ2r6dyLz5RN5bSHzZcgxFQXA4cE+Zgv/ii/HMPAHn6FHWMobFMYcl1Ec5a+c1seDJLeRX+LngGxNweuXDPaQDhpFKEVu+nPA77xKZNw+lsREAR3UVGddcg+ekE3FPmYLotPI2WhzbWEJ9lGIYBktermXZK3WUj8/m7BvHINuP/pmkHosRWbCQ8FtvEZk/Hz0cRnA48JxwAllfvgHvKacgFxYe7mFaWBxSLKE+CjF0g4VP17D23SZGzSrgtC+MQJSO3t1vejRK+N15hOfOJbJwIUYigZSRge/ss/CdeSaeE06wNpRYHDIMw0DXVDRVRVc1NFUx65pZ1zUNfaCtqRiahqZpGJqGIIqUT5h8wMdkCfVRhq7pvPvIJjYtamPi7BJmfabqqIwTrKdSRObNI/TKq0Tmz8dIJLDl5BD8zGfwnX027imTrZuAxxkDAqkkk6iplFmSiR11JW1TSVRFQVNSqCkFVUmZdUVBS6XQVAU1paRtCl1T0+cr6KqKqg6t66q6Q4zTAvxJcQeCfP3+Rw/gu2JifROOIjRN582HNrBtRQfTL6pg6vnlR5VIG4ZBfPly+l94gdDcN9BDIaSsLIKXX47//PNwTZ5sxcU4StBUlVQ8Rioe32ETcZREnFQisZPdqZ4060oyiZJMoCaTKKkkSiKBmkqiJJMYHwnzuj9INhuSbEeSZWyyHUm2IdlkJNksNpuM7PHglmUkm4woSelzZUTJhiSn+2y2HcdtNkTJhmiTdtsnSjZEUTKPSzZsBynIliXURwmaojP3wXXUru7ixCuqmDi79HAPaZ9RWlroe+45+p9/AaWxEcHtxn/WbPwXXoTnhJnWzPkQYxgGajJJIhohEY2QjER21KNRkrEBGzPrsRjJWHSHIMdiqMrHpO3aCUEUkR1O7E4nstOJzeFEdjhxuD14M7LMPrsd2eFEdjiw2R3Y7HZsdsdH2nZssn3wmM0uY7M7kGwyNrsdyWY7pv/JW9+QowBN0Xn9/rXUre3m5KuGM/704sM9pL1iKArhd96l7+mnib7/PhgG7pkzyfnWN/GddZYVZ/kAoiQSxEL9xEP9xML9xEMh4qF+4uFQuoRJRMLEwyFTkMMhtD2k6RrA7nLhcHtxuN3Y3R48wQwyC4uxu1zYXW4cbo9Zd7oGrexy76g7ndidLiRZPqp+9QHmDlZdAy0FugKaYtY1BXQ1bZUd7cE+FUQJKk874EPaJ6EWBCEIPAiMBQzgBsMwPjzgo7HYBU3Vef2BddSt7ebUq0cw9pSiwz2kj0VpbaX3ySfpe+YZtM4ubPn5ZH/96wQuvwx78ZH/D+ZIQVUUYn29RHp7iPb1EO3rI9rXS6yvl2h/H7G+XmKhPqL9fajJ5G4fQ5RsuHw+nF4fLp+fjIIiXD4fDo8Xl8+P0+PF4fHi9Hp31D1e7G4XongYPIh0HdQ4KOmiJj5ik+ZxNWn2DbHpupZK96VAS/drqbRVzL4B0R1iP1L/pHhy4KatB+49SbOvM+o7gNcNw7hCEAQ7YE2HDgGapvPGg+upW9PFKZ8bfsSKtGEYxBYvofd/jxJ++x0AvKecQvCqz+I95RRrA8pHSCXihLu6CHd3Eu7pItLdnbZdRHq6ifT2EA+Hdr1QEHD7A3gCQdzBDIIFhbj9AVz+AO5AALc/gNsfxOXz4/L7sbsOUkJaTYFkGFIRSEbSNgypaLpEdqpHQRmox0DZuaQFORVNi2viUwxKAJsDJAfY7GmbLpJ9h5WD6bYdRHlHvySbVrSl23aQ0nVR3rUuyuY1omzOogfqNseBepeHsFehFgTBD5wCXAdgGEYK+BT/ciz2BV03ePs/G9m+qpOTrqxm3GlH3mxUT6UIvfQyPQ8/THLzZqRgkKwv30Dwqs9hLz4y/6kcCpKxGP0dbfR3thPq6CDU2U5/Zwehrg7CnR0kopFdrnEHgngzs/Dl5FI4YhSejEw8wUy8mWmbkYnL50f8tP/0DMMUxngvJPog3geJ/l1LMrRTPWy2k2FTmNX43p4ljQB2D8husLtB9qStG1yZO+qyyyy2tJXdIDvT7Z3tzsVu9g9YSYajbYllP9iXGXUl0An8WxCECcBy4LuGYUR3PkkQhK8CXwUoLT16bnQdiRiGwfzHNlOztJ0TLhvGhDNLDveQhqD199P7xJP0PPoIWmcXjuHDKfh/v8d/4YXHzS7BeDhEb2szva0t9LW30tfWSl97K/3tbbvMhmWHE39OLv6cXAqrR+LLysafk4svKxtfVg7ezEwk2yfYUWoYppBGuyDWBbHunUqPWeIDttesx/vM9dWPw+4DZwCcfnD4zJ/zWcPAkW4PFLsXHF7zfLsnXffsaMuuY1o8DyWCYRgff4IgTAUWAScahrFYEIQ7gJBhGL/a0zVTp041li1bdmBHepxgGAYfPLOVVW81MuXcMmZeOuxwD2kQpaODnv/+l77Hn0CPxfCcdBJZN1yP+4QTjr4bRvuArmn0tbfR09xIT0sTPc1N9LQ20dvSTCISHjxPEER82TkE8wsI5uYTyMsnkJtPIDePQG4eTq9v398fwzBnrpF2CLeZdrB0QrQDIh2mOEc79yy6Nqc5a3Vngitjh3VlgDOYrgfT9WBamAOmGB+O9WkLBEFYbhjG1N0d25cZdRPQZBjG4nR7DvDTAzU4i6GsfKOBVW81Mu60YmZcUnm4hwOYNwi7H3iQvjlzMFQV/3nnkfWVG3GOHHm4h3ZAMHSdUFcHnfV1dDXW09VYT3dTA70tTUO8IzwZmWQWFjPihJPIKCgio6CIYH4Bgdy8fZsRG4Yprv1NEGqGUMsOG27bYZXorteKMnjzwJsDvgLIHw+ebHO268kGdzZ4skzrzjKXFSyOGfYq1IZhtAmC0CgIwgjDMDYDZwIbDv7Qjj82ftDCh89to3paHid/tvqwz1KV1la6/vlP+p55FoDgpZeS9ZUbsR/FS1tqKkVXQx0dddvpqK+ls247XY11pHbKHO7PySOruITyCZPJKi4lq7iEzMJiHO69xLHWdQi3Ql899DWkSz30NUJ/I/Q3m14HOyPZTeH1FUDBeBh+TrqdbwqzL98UY1eGtYxwHLOvXh/fBv6X9vjYDlx/8IZ0fFK3tot3H91M8cgMzrx21GHNyqJ2ddH1z/vpe+IJDCB4xWfI/spXjrpgSJqq0FlfR9u2Gtq319C+rYaupobB3W92l5ucsgpGn3IGOWUVZJeUk11Sit31MbNRTYHeeujZDj3b0rYWemtNYf6oa5c3H4IlUDARRl0EgRLwF4K/yCzuLDiGN2pYHBj2SagNw1gF7HbtxOLT01EfYu4D68gu9nLe18Yh2Q7PF1eLROh+6CF6/vswRjJJ8PLLyP7a15CLjnwPDsMwCHd10rJlI601m2mt2UxH3bbBpQuXz09eZRUVk6eRV1lFbvkwArl5e/7VEuuBri3Qudm03VuhqwZ668DYKRaE3QeZ5ZA7GkZeABnlECwzrb/I9FawsPiUWDsTDzOh7jiv3L0Gl9fOBd8cj9156P8khqLQ+9RTdN11N1pvL/7zzyP729/GUVFxyMeyr+i6RmddLc2b1tO8aQMtWzYS6e0BwOZwkF9ZzaTzLqagajj5w4bjy87ZvSgnQtCxETo27LCdm82bdgPYnJA5DPLHwpjLTA+IzGGmdWdZSxLHIIZhoGkauq4P2o+rDxRBEA6K15sl1IeRZFzl5bvWoKk6l3xvEp7AwXGW3xOGYRCZN4+OP/6JVF0d7unTyb3pJlzjxh7ScewLuq7RUbudhnWradq4juZNG0jFYwD4snMoHj2OwhGjKBw+ipzS8l39jQ3DXJpoXQNta83Svs5cQx7A7oWckVB9NuSMMOs5w83lCssT4qAxIIqKoqCqKqqqDqnvqWiatkt9ZztQPtreuQwI7kf79E8YHMrj8XDTTTcd4HfIEurDhq7pvPHAOvrbY1z83YlkFh7ahKvJbdtov/U2ou+9h72iguJ77sF7+mmH/QbmAIZh0NvaTP3aVTSsXUXj+rUkY6Y3REZhMSNnnULxqDEUjRqDPzv3oxebN/BaVkDLSrO0rjZ9iQEQIKsKiqbA5C9B3hhz6SJYas2O94BhGCiKQjKZJJVK7bUoioKiKEPqeyqqqrI3N+G9IYoiNpsNSZKQJGmPdVmWB+s7F1EUd6mLgogoiEiCiCAIpkVEEgQERERAREREQBAERATkT+IPvw9YQn2YeG/OVho29HD6F0dSNCLjkD2vFonSde899Pz3YUS3m7yf/4yMz38eQT78KbxS8Rj1a1dRt2oFtauXE+7qBEwvjOEzT6Rk7ARKRo/Dm5E59MJkGJpXQNNSaFoGzct3LF2INlOER10EBRMgfwLkjTY3ZBwnGIZBKpUikUgQj8dJJBK7lGQyOWh3V1Kp1H6Jqd1uR5blQTtQvF7vkLYsy9gkGzZJwibakAUJSZSQELEJEhISkiEgIZrFkLAZAqK+o0i6iKAZGKqOkbZoBoamY6gGaOn+xE79mrHbumkN0Hd+rQOz673HqRa9Mkzfv7/PvmAJ9WFg3YJm1r7bxITZJYw+8dB4UhiGQXjuG7TfeitqezuBKz5D7g9+gC0zc+8XH0R621rYvnwJ21csoWnjBnRNxe5yUTp2AjMuvZKy8ZMJ5uUPvSjUCg0fQMMis7SvAyP9Zcqqhqozzdly4WRztnwM3dDTNI14PE40GiUWiw2WeDy+ix0Q5Xg8vtef8rIs43A4cDqdOBwOHA4HPp9vsG6XZeySjCzK2AUbsmBDRkI2bMiGhKSL2HQRmyYiqWAoullSGkZKx1A0jJi+o67o6OlzUAfGZgBqunzMe8BuJFMSEGwigk0ASTTrkoAgiWAzrSAJYJcQRWHHeZIAorDj3LQ1JBBEA0PUQNIwRN20go4h6SBoGIIGkm72iRoIOqL08WP/pFhCfYhpqelj4RNbKB2TxazLqw7JcyrNzbT97vdE5s/HMWoUxXf8HdfEiYfkuT+KYRi0bdvC1qWL2Lp0ET3NZsLarOJSplxwCRWTplI4fBTSzjGq+5uhbmG6vGd6XoAZO6J4Cpz8IyiZAUWTzR14RxmaphGJRHYp0Wh00A6UeHzPcTZkWcbtduNyuXC5XAQCAZxOJy6HE4fNgUOScQgyDsOG3bBh123IqoSsSggpHSOhoic19ISK0auhpzSMhIaeVEEdmGEOyORQf3ADUNIFSUCwS4h2EcEumaJplxAcEqLXjiCLOxUJZAPDpmDYVAxZwZDSRVTTNt0WFHQxhSGo6KQwhHSfoWAYKXQ9hW6k0HUFQ0+hGwq6nsIwlHRf+lxdQTdSGIY6tN9Q0HUVw1AxDGXHC9sP7bXbcziZRft+wT5iCfUhJNKb4PX71+LLdnL2l0cjHmRfaUPT6H3scTpuvx2A3J/+hMxrrjnkgfoNXad58wa2LH6fmiUfEunuQhBFSkaPY8JZ5zNsyjQCuTvNmuO9sGUBbJ8H2+eb/spgbncuOxGmfxVKZ5rLGNKR+xE2DINkMkl/fz+hUGiwhMPhQTsgxLvD6XTi8XjweDzk5ubidrtx2124bE6cgh0XMg5DxqnasCsSQlxHj6voMRWjV0FvVtHjqjlrBXY3W1UARRQQnRKC04bokBCcElLAgc0pITokcEjgUNDtSbCn0G1JdFsCXUpbIY4uJtGFBDoJdCOBpsXQ9DialkDXYmh6Al1L7OgbtAkMQ/2I0u8/omhHEOyIYroIdgRRRhTldN2GKNixSU4EwZY+35Y+V0YQbQiCjCjYEETZPCaYfeYxyTxPkHb0IZrPMdAnSIjiwfn1duR+yo8xVEXjtfvWoio6l/5gPA73wV0TTm6vpfUXvyC+ciWeU06m4OabD+mGlYGZ86b3F7Bl0XtEerqRZJnyCZM56aovUjllOi6vzzxZ18y15a1vmaV5ubmUYfdC+Ukw7ctQcQrkjjmiNocYhkE0GqW3t5e+vj76+/t3sanUroEmPR4Pfr+fQCBAUVERXocbt82FR3Di1GXcmowjaUOM62iRFHpYQWtV0KNKeu1UBxLpYs5v45KA6LYhumVEtw0p04VcZENwCRiuFLozju6Io9tjaFIM3RZDE6JmMSKoWgRVjaCp4XQ9ijbQp0UBY5+FVJLciKITSXIjSS4k0YUouZDtmThEJ5LkNI+LTsTBugNRSveJjo8Uu3meYDfbkiNdt6cF9yhMTrCfWEJ9iFj4ZA0d9WHO+9o4MgsO3o0sQ9fpefhhOm//O6LTSeGf/oj/oosO2Qe5t62FDQveZdN78+hrb0Wy2SifOJVTvnA9w6ZM37HrL9EP656BLXNNcY51AwIUT4VTboLK0826dHhvcmqaRl9fHz09PfT09NDb2ztoe3t7UT+SKWVgySErK4uKsnJ8dg8e0YXHcOBR7TjjEkQ0tHAKvT6JFt5ZfE13QwNIyiKiV0by2pGCDuQiL3g1dHcUzRlBc0TQ5QiqFEYV+lGNEIrSh6r0o6h9KEo/qtqPqobNR0zy0dWKQSTJi83mTVsfNpsfp6MQyebFJnmQbB7TSt503Y0kedJCPFB3DQr0sSKauqGj6qpZDBVN11B1Fc3YYTVdG3JMFETGZI854GOxhPoQsPGDVja818Lkc8uonJhz0J5HaW6m5Sc/JbZsGd7TT6fgd7/FlnPwnm+AZCzK5g8Wsn7+27Rs2QiCQOmYcUy/7Eqqp8/C6fGaJ/Y3w5pHYdPLUP++mbrIlQnVZ5m+y8POOGxrzLFYjM7OTrq6uuju7h60vb29Q27EybJMRkYGmZmZVJZV4Je9+AUXXs2BJ2FHDOtofQm0LUn02ICI7wjhnnTZkPx2JL8dW04A/Cq6px/VFUZzhlClPhSxF0XrIaV0o6S6SSndpFLd6HrCXLmIpMsgIrIcwGYLIMsZ2O3ZeNzDsMkBZFsgbf3YBotvp7oHQTh8PuK6oZPSUiS15I6iJknqSVJaavDYznVFVwbtQL+qq6R0s67oilk006b0FKqmougKqq4OHh+o72x3Fmbd2H9f6mxXNu9+9t0D/j5ZQn2Q6WoKM//xzRSNyGDGRQdnp59hGIReeom23/0eDIOCP/yBwGWXHtSZjWEYNG/ewNq3XmfL4g9QU0kyi0o4+errGHXSafiyss0Te+tg1UOw4QVzSQMgezic8C0YcR4UTzukm0ni8Tjt7e10dHTQ0dFBZ2cnnZ2dxGKxwXMkSSIrK4vc3FxGVFQTlH34DRe+pANHCLTeJOrmBEZiwPfAXIZQ7BJShgNb0IFc4kILhFG9fajOXlS5h5TQRUrtIJlsJ5XsJJlqR9eTO5YU0mGsBUHGbs/CLmch2zNxuyux27OQ7VnY5QxkORNZDpp9cgY2mx9BODhLQrqhE1fjRJUoMSVGXI0TU2PElNigjavxwZJQE6bVEkPaSS05aBNqgoSWIKkmSemfPgeJJEjIoowsydhFOzbRhl2ym32ijF0y+2RRxmVzDdZtom1IGdInDG1LgjTE2kQboiAiizKSKGETbEiihFOy1qiPOlJxldf/uQ6n28bZXx6DKB34L5MWidD2298ReuklXJMnU/inPx7U3ISJaIQN899m9Vuv09PciN3lYvQppzP29LPIHzbc/OfQ3wwf3GUubbSsMC8smAhn/hpGXmTu9jvI6LpOT08PbW1ttLW10d7eTltbG+HwjjjSDoeDnJwcRlQNJ9MZIIiHgOLCFRLQu5MoaxNp1zEdiGJIMdRMJ1KGE0eZjBbsRfX2oDg6SUkdJNVWEslWEokWUqlOwBgy+5UkNw5HHnZ7Lv7ARBz2HOyOXBz2XOz2bBwO09psgQPyT1bRFPpT/YRT4aFFCRNJRQinwkSUCFElSiSVtun2QImrcQz23X/aZXMNFofkGLR+u59cd+6QPofNgVNyYpfsOKUBzxQHdsmOXbQPHrNLdhySA1mSzeskx6AA20U70nGwa9QS6oOEYRjM+98mQt0JLv3+JNx++wF/jvjadTT/8IcoTU1kf+fbZP/f/x20/ISd9bWsfP0lNr43HzWVpKBqBOd87buMOOFkZKfTzByy4mFY+7TpQodhivNZv4PRl5hBig4Suq7T3d1NS0sLLS0ttLa20traiqKYd75EUSQ7O5vy0jKyXRlkCj6CCSeOXtA642hbB2Z1SRBTaFlOpGwnjmoDJaMLxd1Byt5KUm8lnmgkHm9AUXrMu3j9pJ/DjtNZhNNRSFbWKTgdhTidBTgcBTic+Tgd+UiS9xMJsKZr9Kf66Uv00Zvs3WGTfYSSIfpT/fQn0yVdDyVDJLSPz0EoCiJe2YvP7sMje/DIHjKdmZT4SvDIHtyy2+y3mXW37MZtc+OyufDIHlw2F27ZPSjMTunYWZ8+0rCE+iCx8f1WapZ1MOOSSgqrgwf0sQ3DoPd/j9H+xz9iy8mm7NFHcE+efECfA8z4GtuWL2HFqy/QtGEdNruDUSedyoSzzievssr01tj+Lqx6DDa9YiYnzaqC034G464wgxYdBCKRCE1NTYOlpaVl0LtClmXy8/OZOHo82XKATMWLPySjtyfQGgaEK4kgKxi5buRKJ0JOFCXQRsLRQsJoIJ6oIxarR9MiOzlXiDidRbhcJeRkz8blKsXpKsblLMbpLMZuz9qv5QdFU+iKd+0oiS664910x7vpSfQMlt6EKch7mtXaRTsBR2CwlHhLGJs1Fr/dj9/hx2f34bcPtQPi7LK5LGE9SrCE+iDQ3RJhwZNbKBmVwZRzyg7oY2uRKK2/+iXh117He9ppFN52K1IweECfQ0kmWD/vbZa/+jx9ba34snM45QvXM/aMs02Xut56eOf/mQIdajaD2k/6Ikz8vLkb8AB++XVdp6uri/r6ehobG2lsbKS314zZIYoieXl5jBsxhlw5g+yUF2+3hNoYw6hJ38gTohjZLmzFMkztJ+VvIeloJKbVEo1tJZFoAoz0zFjA6SzG7S6noGAKblc5LncZblc5TmcRorh3DxTDMOhJ9NAea6c92k57rJ2OWAcdsQ464510xDroinfRl+zb7fU+u48sZxaZzkwqA5Vk5mWS4cwwiyODoDNIpjOToCNIwBHAZXMdkPfZ4sjGEuoDjKpovPnQeuxOidnXjzmgCQCS27fT9K1vk6qvJ+eHPyDry19GOIB+xYlIhFVzX2bFay8SD4fIrxrOhd/7EtXTZyFiwJbXYfm/YevbphgPOxPO+YN5U9B2YCL/6bpOe3s7dXV11NXV0dDQMLgbz+PxUFJUzMSyMeRofjJ6HRgtMfTatChLMYwCN7aJkMppJ+lpICZuJxrbTCxWB+gQAkGw43FXEPBPoLDgM7g9w/C4h+FylSNJH/86FF2hLdpGS6TFLFHTtkXbaI220h5t3+UGmSRIZLmyyHPnUeorZUreFLJd2WS7sslx5ZDtyibLZYqzXTrwS2QWRz+WUB9gPnxuG93NUS781oQDui4dfustWn7yUwSHg9KHHsIzc8YBe+xYfx/LXnmeVXNfQUnEqZw8jWkXf4aikWMQol3w/t9g2X8g1AS+Qjj1JzD5ixD49DctDcOgp6eHbdu2UVtbS11d3aAwZ2RkUF1eRZE9i5yYD1erjrYmvXwhJBHyRMSxOmpeMwlPLVFjM+HIenP9OO037HKW4vWOIC/3AjzeEXg9w3G5yhDFPX/0w6kwDeEGGsONNIYaaQw30hRpoincRHusfYjbliiI5LhyKPAUMDZrLLNLZ5PnySPfk0+eO488dx6Zzszj4oaXxcHDEuoDSP36bta808S404spG5t1QB7TMAy67r2Xrjv/gXPcOIrvvAO5oOCAPHasv48lLz7D6jdeRVVSjDjhZGZceiU5ZRVmvOYXvglr55h5/ipPg/Nug+Hnfept24lEgu3bt7N161a2bdtGf795Ry4QCFBdNowiOZu8sA97k4Lemr4h6E4hltlQJ3eRCGwjKm4iHF1LKtUFSRBSNjyearKzz8DnHY3PNwavdwQ2m2+3Y1B0haZwE7X9tdT211IfqqcuVEd9qJ6eRM+Qc7Nd2RR7i5mSN4Uib9FgKfQWkufJQ96HJRELi0+DJdQHiERE4Z3/biSz0MOsyw7MTTQ9Hqf1F78g9OprBC65mPzf/Q7R8emXGOKRMEtffIaVr7+EllIYedKpzLz8KjILisxljf9+F2rng+yGSdfAjP8zA+l/QgzDoKuriy1btlBTU0NDQwO6ruNwOCgvLmVa8XgKoj6cjRrGKnMZQwwoCMOTqEW1xNybCKXWEI1uYWA92e0eRmbmyfj9E/D7x+P1jNztsoWiKzSEGqjpq2Fb3za29W1je9926kP1qMaOXYXZrmzK/GWcXnI6pf5SSn2llPpLKfYW45atjN4WhxdLqA8AhmEw77HNJKIKF31nAjb7p/+Zq3Z20viNb5JYt47cH/2QzC9/+VPfoVcSCZa/8jxLX3qWVCLOyFmncMIVnyczLx/WPwfP3w4d680s2LN/C1OuNW8UfgJ0XaexsZFNmzaxefNmenrMWWpuTi7TR0yiWM0io8WGsd7c1yz4dISRMZKF24i61tEfX0Ey2QpJkFQvgcAkcnPPJeCfhN8/AVn27/KcfYk+NvZsZEvvFjb3bGZL7xa2929H0dOzckGk2FvMsOAwTis5jcpgJZWBSsr8Zfjsu595W1gcCVhCfQCoWdbOthUdzLy0kuziT/+FT2zZQuPXvobW20fx3XfhO+OMT/V4uqax7t03+eDp/xHt62XY1JmceNU15BQWwurH4Km/mSmpskfApffC2CvAtv/r65qmUVdXx4YNG9i0aRPRaBRJkigvKmVSziiKQn7sDQo0GgiygVgdJzF9KxHvGvoTS0km2yEJdiOHYHAaweBXCQam4fUO32Wbc3e8m/Xd69nQvYEN3RvY2LORtmjb4PFcVy7VmdXMKppFdbCa6oxqKgIVOPZys9DC4kjEEupPSbQvyYLHt5BX4WfSWZ8+qWV00WKavvUtRJeLskcewTX20wV4qVu1nHmPPER3UwOFw0dx0Q9+TtGwSlj5CMy53bxBWDgZzr3VXH/eTy8SXdepr69n3bp1bNiwgXg8jizLDCuuoFIqIL/dhbglPaPN1VBObCaavZaQvpRobCtoIMcyyciYSUbGCWQEZ+J2Vwz59ZBQE2zoXs2azjWs6VrDuq51tEZbARAQKPOXMSl3EqMzRzMicwQjM0eS4Tx0WXMsLA42llB/CgZ2H2qKzuzrRn/qLeL9r7xCy09/hqO8jJL77/9UNw17WpqY9/CD1K5cRjCvgIt/8HOqpkxDWP0Y/ONK6G+E4ulw8R2mm91+LKsYhkFraytr165l7dq1RCIRZFmmuqiSSjGfvEYHwkYNRBCqosSnbiLsXkpfdCm6nkCM2QkGplNQeAWZGSfi9Y4cslmkI9bByo6VrOxYyeqO1Wzq2TS4nlzkLWJCzgS+MOoLjMkaw6isUXjk4yetlsWhxTAMdEA1DFTDQDNI26H1gWMCUO058PE+LKH+FGxZ0k7d2m5OvKKKYN6nu+HU8/DDtP/hVtxTp1J8911IgcAnepxUPMaiZ59k+SsvYLPbOfWaG5h49gXYtr4K986E7q1mmqqL7jCj1e2HQIfDYdasWcOqVavo7OxEFEWGFVVQlT2R/CYn0iYDwyZgjOkiWrqWfukDIrFNoIFLKaWw8LNkZZ1KRnAGkrRjo0ZLpIWlbUtZ1r6M5e3LaQybWV+ckpOx2WO5bux1jM8ez7iccWS7sj/R+2Jx5GAYBkndIGUYJHWdpL7DJnSdlG6QSveljB11JX2dohso6X7T6kPaykesmj6mGun2Tv0DfZoBim7sJMgD5+zfa8u121hz4tgD/p5ZQv0JifYnWfjkFvIr/Yw/o+QTP45hGHTeeSfd996H76yzKPzLnz+RZ4dhGNQsfp93//sAkZ5uxpw2m5M/fy2e3nXw33PMTNy5o+Fzj5sbVPZRoDVNo6amhhUrVlBTU4NhGBTlFXBG+UxKWr3INQaGDYxx7YRKVtJrLCSRbIKkSCAwmaphPyE7+0zc7srB5YzueDdL2uaxqHURi1sX0xxpBiDgCDA5dzJXjbiKybmTGZk10nJ9O8QoukFE04hpOlFNT1uzHdN14um+uG4Q13Ti6b4Bm9B14popuHFdJ6GZIpvQdRL6QP3TZRzfGZsAsiBiFwVsgrDDCgKyKCALZnug7hJFbPLQfknArA/0CQKSIGATSNt0EQUkMK2wU50d57oOQuA1sIT6E7PwiS2oKZ0zvjTqE6fUMnSd9v/3/+h97HECV3yGgptv/kRpsvo72nj7oXupXbWcnPJKLvr+zyjMlODVr8OW18BfDJfeB+M/u88hRfv6+lixYgUrVqwgEong9XiYVjaeyr4svPUChmigj2mnv3w5vcY8kql2hKSdzMwTqaj4FtnZZ2C3m77kiqawtG0p77e8z4ctH7KxZyMAPtnH1PypXDPqGqblT6M6oxrxIIXrPJYxDIO4bhBSNfpVjbCqEUqXsKYRVnXC6XpE1QlrGlFVJ6JphNNCHFVNYU7tR6ZxAKdoip9TEk0rmmLlFEVyZBmnM31cFHGIAg5RxCkJOIS0FU2RdYoidkEYPMcumqLrSPcPtO1pUZbTfeJxEqvEEupPwPZVnWxb2cnMSyvJyP9k66OGptH6i1/S//zzZN5wA7k3/Wi/3e90XWPlay/x3pOPIAgip1/7FSaechLie3+BJ+43/aBn3wwzvgby3mNC6LpObW0tS5YsYcuWLRiGQWVhOad6J5DX6EDsFtAr+gmft5we27skko0IKTtZWadQlfsTsrPPGNxg0hnrZGH9syxoWsCi1kVElSg20cbEnIl8e9K3OaHgBEZljcL2MTsEjzcMwyCs6fQoarpo9CoqfYpGr2raPtXs61c1+hVTmEOqtleBFQCvJOKzSXjS1iuJ5NplPDYRj2T2eyURj2S23ZKIO912iyKudNudbjslEek4EErDMMxsLh/J6DLQ1g19sE8QzJvbBxrrW7KfpOIqC57YQlaRl4mf0MvDUBRafvJTQq++Sva3v0X2N76x3yLd1VjP3Hv/Ttu2GionT+PMG76Gv/ENuGcaxHpg8pfgjF+Bd+8ZXlKpFKtXr2bx4sV0dXXhdrmZVjSOqs4s3NtFjECS+MnL6fPPI5xYB5pIpn8WFZXfIif7bGTZj2EYbO3byjsNj/Fu47us714PQL4nn/MrzufkopOZXjD9uLvxF9d0OlMKXSmVjpRKp2LWu1Iq3coO250W5z2tiQpAwCYRlCXT2myUOO0EbBJ+m7SL9dskfDYJnyTit5mieyTMPg3DQNXVwWwuA9lakloSRVMGs7SktBQpPTUkU8vA8SF9H5OtRdEUVEMd7BtIl6XoypB0WgNZXQb70mI80Lc/mV6ynFnMu2reAX/fLKHeTxY9v41of5Lz/m8c0idYjzIUheYf/ojwG2+Q+6MfknXjjft1va5pLH3xGT6c8xh2l5sLvnMTIyqCCC98AZqWQskM+OKfoWDCXh8rHA6zZMkSli5dSiKRID8rj7PyZlDc6EbsBWVcI13lC+lJzccwFLy2UVRX/Zy8vItwOHIxDIP13et5s/5N3qp/i4ZwAwDjs8fznUnf4dSSU6kOVh+ToTRTuk57SqU1kaI1pdCWNEt7SqUtqdCRMktI3f2X3G8TyZJtZMsyZS47k/xusmQbmbKNLLtpM2wSGbJtUJwP5uzVMAwSWmIwc8vOWVviSnyXrC0JLTEke8vOfTun1EpoiSHptJJacr8SEeyNgSwuH83SMpDx5aOZWpw252AGF0mUdqkPZIuRBAlJlAYzuoiCOCTDiyiIuz3nYEUztIR6P2jb3s/aBc2MP62YvIpdd8btDUNRaP7RTYTfeIO8n/2UzGuv3a/re1ubee2uv9G6dTPDZ5zImV/8Eu4V98AD95q5Bi+9DyZ8bq83Cru6uvjggw9YvXo1mqZRnVfBGFshWc0OjECM2Knv0+2ZSyLVhE0LUlR0NYUFV+DzjcYwDDb0bGDu2kd5o/4NmiPN2AQbMwpmcO2Yazm95HRy3Ac/T+PBxDAMehSNpmSKxniK5mSK5oRCczJFUyJFa1KhM6XuIjcOUSDfLpPnkBnpcXJKho88u0yOw0aObCPHLpNjt5Ftt+E4QFEPFV0ZzNYykLklkooQVsK7ZG6JKBFiSmxI9paoEh1MqbW/AuqUnDht6SI5h2Rt8creIe3BzCySPJi5ZSCby87ZWgbOGWjvnGJLluRBYR4Q4WNxErA7LKHeR3RNZ/7jm/EEHMy4pHK/rzdUleYf/5jw3Lnk/vQn+yXShmGw5q3XmffIg0g2Gxd85yZG5qbg0XNMf+gp18Ps3+x1u3dbWxsLFy5k/fr12Gw2xuRUM6ojB2+9jFLZRPf0+fRo5uw5wz2TquqbyM4+C0ly0BBq4NFV9/Jq7avUheqwCTZOKDyBr0/4OqeVnEbA8cncCQ8XSV2nIZ6iLp6kPpGiPp6kPp6iIZGiMZEiqg2dCbtEkWKnTJHDzhivi0KHnUKHTL5DpiBtgzbpEwmHYRjE1fhg1pb+RL9pd8rcEkqFCCVDpk2XcCpMXI3v9fEdkmMwg4tX9uKW3eS4cwYzt+ycqWUwc4ttR+YWl+zCJe2UYistvseLSALouunWp+lpH2ot7T+t6+g6g1YQoCTzwMeGsYR6H1k7v5muxgjnfGUsduf+vW2GrtPy858Tfu11cn/8Y7Kuu26fr42HQ7zxzzvZunQRZeMncc511+Jb/Gd48wlzy/cNb0Dpx4c8bW1tZf78+WzatAm7bGdq7hiGt2ThrIfE5HU0579OVNmMDR/FxV+kqPDzeDyVhFNhntn6Ai9ue5HVnasREJiaP5Vrx1zLWWVnHfHirBsGzUmFmmiC7fEkW2NJamNJtseTNCdS7CzFbkmk1GmnzGXn5AwvJU47JU47xemyvyKc0lJ0x7vpinfRndiRtWUgg0tvopfeZC89iR76En0fm+TVbXMPZnDx2/2U+8uHZmyxe/Hb/XhlL167d0gWF7fsPmJcHA3DQNEMUppOUtHSViel6aRUnaRqWiXdTmk76opm7NKvDvTtVFc0UzwH2qo+0K+j6ebza+k+LS28iq6jaaYQq7qBmj42IMzqfrgTZnsdLPvl7AP+3llCvQ9E+5MseXE7paMzGTZ5/37WG4ZB282/JfTiS+R877tk3XD9Pl/buGEtr975Z2KhEKd96UYmV9oRHj8fYt1wyo/hlB99bMD+9vZ25s2bx8aNG3HYHUzPHsuIlkxsqRTRmQup87+ConbjsVczovL3FORfiiA6Wda2jGeW/5O3G94mqSWpClbxvcnf44LKC8j35O/X6z8UaIZBfTzFpmiczdEEW6IJamJJtsUSxHf6kvkkkUq3g6l+N1fkZVDpdlDuclDuspMt79vPaEVT6Ix3Ds3cEuukI95BV6yLzngnXfEuQqnQbq9329xkODPIcpqJBEZmjhzM3JLhyCDgCBB0BAk6gvgdfgKOwEEXWlXTiaY04imNWEolltKIK5ppU+pOdY2EopFQdOKKWY8rGklFN/tV81hSTfelbVJN96k6++n997FIounbbJdEbJKATRIH67IkYhMFs18UkdPWKQvpfnGIlUQBWRLSj7mjb+A5RNF8TFHY0ZYEkNKeLwN97gMQkG13WEK9D7w/ZyuqqnPyVcP3a1ZlGAYdf/wTfU89RdZXv0r21762T9fpusaS557mg6cfI5hfwNXf+wF5G/8JTz4GeWPhC3OgYPwer+/p6eHdd99l7dq1OOx2pmeOYURrFpIeJnTqK3Q75qLrcbL8p1BS+mUyM06kN9nLfzc+wZwtc2gMN+Kz+7i06lIuq7qM0Vmjj5ifuT2KyvpwnPWROBuicTZFEmyJJYZsoih2ygx3OzkxmE21x8kwt4Mqt2OvYjyQRqs12kpLpIXWaOtg5pa2aBvtsXa64927rOXaRTs57hxyXDlUBiqZnj99MGtLtiubLGfWYAYXp+3AbC/WdINIQiWUUAinbSShEkmqhBMK4aRKNKmm+zSznlSJpsz+aNIU5WhKI7WHG557QhTAJUs4B4s4WHfYRAIuGacs4rCZx+ySOHjMbjP7TWu2d+6zSyJ2m4BdMttyWnTNurijTxQ/8f6FoxFLqPdCS00vNUvbmXp++X5vE+9+4EF6/vMfMr7wBXK+/719uiYW6ufVf/yF+jUrGXniqZx1zlTsr37RDJ50yk3mTHoPke2i0Sjz589n2bJliILI5IyRjG7LRRR6CZ05hx7pbUAgP/ciSktvxOMZzurO1fxp4U95s/5NFF1hSt4UvjHxG8wunX3AROWT0pZUWBOOsTocY21anJuTyuDxXLuNUR4X1xZlM8rjZITHxXC3A49tz7OahJqgKdw0JGtLU6SJ5nAzLdGWXdZ8XTYXBZ4C8j35jMgcQb47n1x3LnmePHJcOeS58wg4Ap/4H1k8pdEbS9ETTdEXU+iLp+iNKfTHzHZ/fGgJJ1RCcVOI94YkCnjsEj6njMch4XHY8Dps5PoceBw2PHYbbodkWruEO21ddindlnDJZp9TNvtdsoQsCUfMP+7jBUuoPwZdN1jwZA3eDAeTz90/J/bep5+m829/w3/hheT94uf79MFu27qFF/92K7FQH2d9+euMk1YgPHE5BMvghrlQMn231ymKwuLFi1m4cCGpVIoxwWGMa8tDlvvoP/NxesR3EUUHxYXXUFr6ZSQ5h9frXufRjb9mQ/cGvLKXK4dfyWdHfJZhwYOTOXxvhFSNVaEYK0JRVoZjrA7FaUuZoiwAVW4HM4JexnpdjPG6GO11kmPf/ZKAqqs0R5qp66+jLmSWhlAD9aF62mPtQ871yl6KfcWUB8qZVTTLzNziKaTAW0CBpwC/3b9fopRQNLoiSboiKbrCSbqjZr07kqInmqQ7aopybzRFTyxFQtnzbNYlSwTdMgGXjN8lU5zhxu+ymW2n2edz2vA7bficMl6HDZ/Thtdpw+cwZ7WWoB4b7LNQC2ZA4GVAs2EYFx68IR05bHivhe4m8waivB9rT+F33qHtNzfjOflkCv9wyz4loF37zhu8/dA9uIMZfO5H3yd/2e+haQlMvMZMgeXYNc61YRhs2rSJuXPn0tfXR0WgiMnREjyRKP2nP02P7R0kyUVZ0VcoLf0ycUPmkc1P8fimx+mMd1IZqOSXM37JRcMuOqRZTAzDoD6RYnFflKX9UZaFomyOJgYXFIa5HJyU4WWCz80EnynMu5slK5pCbah2R+aW/u1m9pZwPaq+Y8YZdAQp9ZcyPX/6YPaWEl8JJb6SfZ4NJxSNjlCStlCCtlCCjlCC9lCC9lCSznCSjnCCznCSUGL3M123XSLLayfT4yDX52Bkvp9Mj0yGx06m207QbSfDbbYHxNnxMb8MLA4Dug66CoZmWl0DQ9+prgECBIoO+FPvz4z6u8BGYP8diI9CElGFRS9so2h4cL9uIMZXraL5Bz/EOXYsxXf8HcH+8QH4NVVl3sMPsmruy5SOm8gF503C/fo15ofiMw/BuCt2e11nZyevvvoqtbW1ZHkyOJ+p5PTr9M96iVrnm4iiTFnxVygt/QrdqSS3r3qIZ2qeIa7GmVU4i9+f+HtmFc46JDMu3TDYHE3wQV+ERX1RFvdH6EiZgua3iUzxe7gwJ8jUgJuJPjdBeejH0jAM2qJtg5lbanpr2NK7ZUg6LVEQKfGVUBGo4NSSUwczt1QEKvbqnaLrBh3hJM19MZr7ErT0xQdLa3+Ctv4E3dFdvTIcNpE8v5Ncn4MR+T5Oqsomx+cg25suPgfZXjtZHgeug3ST6ahB10BNgJoELbWrHawr6fZAfaCt7DhPV3fqU0BXdupX023FfM7Bujq0aB9p69ru2zuL8r74mXty4aaaA/727ZNQC4JQDFwA3AL84ICP4ghk6cu1pGIqJ312328gpurrafz6N7Dl5lJy7z2I7o+fpcYjYV6+/VYa1q1hyvkXc0pePeJLN5i7Cq/8D2Tu6q+dTCaZP38+ixYtQpZkTrKPYVi/l/Dkd6jLeAUDneKiL1Be9g1aE1F+t+RvvLL9FQDOqziPa8dcy4jMT57/cF8wDIPt8SQLeiO81xvmw74IPYoGQJFD5uQMHzMCHqYFPIzwOIdsbTYMg4ZQw2D2lo09G9ncs5m+ZN/gOUXeIqqD1ZxRegZVwSqGBYdREajALu35n2IoodDQHaOhZ0dpTJeWvgSpj/hN+5w2ioIuCgJOJpQEKfA7yQs4yfc7yQ84yfM78TuP4g0XhmEKZyoKSgxSMVCioMTT9ZhZH7RxUOOgJNJ2oC9pttXkTu0BQU7uaOt7X1PfPwSQ7CDJINrSVjYTL4vyrm1RMs+TXSBI6eNS+pgtXaSP9KXbws79onlssM8GgrjjPPvBCZGwrzPqvwM/BvaYZ0oQhK8CXwUoLf30mU4OJ71tUdbNb2b0yUVkF3v36Rq1t5eGr34VgNIH7seW9fFZyHtamnn+T78l1NnBuTd8mTHN98OiD2DajXD2LSDveiNv06ZNvPrqq4RCIUZ7y5nYXYAycgkNZc+h6iHycy+hsvJ7tKYUfrPkr7xW+xqyKPPZEZ/lujHXUeA9MNnLd0evorKgN8z8HrMM3PQrcsjMzvJzYtDHCUEPpa6h7oSdsU7WdK1hbeda1nWvY0PXBsJKGDC3B1dnmII8IsPM3FKdUb3H/IYJRaO2K8r2zii1XRG2d0Wp64pS1x2j5yMz4gy3TGmmmzFFAc4Zm09x0EVRhouioJvCoBOf88jwPR6CYUAyDMmQaROhdD3dHiwRSA3YiCnGAzaZtkrU/Nm+PwiSGehLdoLNZbqG7lz35priKbvA5jT7bE6zb7DtSLcdIDnMG+OSfWiflBbaXeq2HefuYxTIY4W9CrUgCBcCHYZhLBcE4bQ9nWcYxv3A/QBTp049gN6Sh54Pnt2GZBeZfmHFPp1vpFI0f+e7qK1tlP7nP9jLPv7GY+P6Nbz41z8giCJX/t81FC39GcT74PIHYfyVu5wfDod59dVX2bhxI1muIBepU/HKjXSedRsJGsgInEB11c/oNXz8dtndvFb7Gg7JwbWjr+VLY750UILtG4bBukicN7tDvNMdYkUoho4ZOOikDC/fyfBxSoaPcpd9cNap6irru9ezqmMVqztWs7pzNS3RFgBsgo3qjGrOrTiXMVljGJ01mqpgFbK0q2CGEwo1HRFq2sPUtEfY2hlhW2eEpt74ED/dfL+T8mw354zJoyzLQ3mWm5JMN6WZ7sMnxIZhzlJjPRDvSdveHSXRl673QaJ/aEmG9k1c7V6zOAasz0xYLLvNPtljzvwGiuwGuzvd7zaF1+42BVdOW5vrE+XRtDgw7MuM+kTgYkEQzgecgF8QhEcNw7jm4A7t8NC0uZe6NV3MvLQSt3/vH0zDMGj9zc3Eli6l8M9/xj150seev/H9+cy953YCeQVcduF4gvO+Zt58uPEtyB+aGcIwDFatWsXcuXNRFYXp8giGJyR6T3qUJvtS3O4KJlQ9gOIcxV/X/JPntz6PLMpcO/parht7HZnOzE/1XnyUpK7zXm+EuV39vNEVoi2lIAATfG6+V57HmZl+Jvrdg8GDUlqK5e3LB8uqzlWD7m957jwm5Ezg6lFXMyFnAiMzR+7iDqhqOjXtYTa2hdnYGmJzW5jNbWGa+3a40DlsIpU5XiaVZHDF5BIqczxU5nioyPbgth8ip6ZkBKIdEOmE6EDpMm2sy9ygFO02bazbXBLYEzYXuILgDIIzAP5CyB1l1p0BcPjB6d/JBkwhdvjSwuzb77yXFkc+e/0kG4bxM+BnAOkZ9Y+OVZE2dIP359Tgy3Qy4cx9y9rS869/0f/cc2R/85sELtqzM4xhGCx98RkWPvYfikeN4ZJJBs4FP4XK0+CKf5tBlXaiv7+fF198kW3btlHoymFWohR99EIaCl5ClOxUVfyUQO7l/Gv9f3ls44/RDZ2rRlzFV8Z/5YDOoKOqxts9YV7p7OOt7hBRTcctiZye6ePsrABnZPkG3eRUXWVt52oWty5madtSVnWuIpkWpeEZw7l42MVMzp3MpNxJuyzDJFWNNU19rG3uZ11ziA0t/WxqC5NMb8aQJYFhOV6mlmdwdV4pw/N8DM/zUpzhRjoYGx8Mw5zFhlvTpW0n2waRDoikrRLb/WM4AuDJAnc2BIqhcAK4Ms2/9UetM2jGatnNkpeFheVHvRNblrbT1RjhrBtGY5P3vgYWWbCAjr/8Fd+555L9rW/u8TxD15n38IOseO1FRsw4gXOzlmNb+bYZ0P/sW8y1t4FzDYPVq1fz2muvoasas4SRlNp66TrjjySFVvLyLqai8iaer3uXe5+/hFAyxIWVF/LNSd+kyHtg3IKimsabXSFe6uzj7e4QCd0gW7ZxeV4G52YHODHoxZkO8doYauSJ7e/zQcsHLG1bSkSJADAiYwRXDr+SafnTmJI3ZYjnha4bbGkPs6qhj9VNfaxp6mdTWwhFM9ct/E4bYwoDfHFmGaML/Ywq8DMsx4vddgBnikoc+pugr960/c2mDTVDqMUsSnTX6xwB8OWBNw+Kp5l3+b3p4sk14397csCd9bHb+y0s9of9EmrDMOYB8w7KSA4zmqKz+IXt5JT6qJ6at9fzk9traf7hj3CMHGn6Su/h7r+mqsy97w42LnyXyWeewWnKHIS6TXDh32Hq0LgfsViMl19+mQ0bNlDgyGaWkk9q0is0BxbgdlcwafgjrIup/Oz1/6MuVMeMghn8aOqPGJk58lO/fkU3mNcT4tn2XuZ2h4hpOnl2G1cXZHFhTpAZQQ+SIJDUkixr+5AFTQt4r/m9wRjURd4izq04l5kFM5meP50M545IfuGEwvwtnSyv72VlQy+rGvoGd9b5HDbGFQf48kmVjC8OMK4oQHGG69N7U+iaKby9tdBbly710NdglmjH0PMFEbz55jJU3mioPstcdvAVpG2+edx+6PzNLSwGsGbUadYtaCbck+D0L45E2MtPaS0Spelb30Kw2Si56x97dMNTUklevv02tq9YykkXnMX09rsR1ARc8wwMO33Iudu3b+e5554jGokynWrKvC10zfgDmhCjouw7kHkev1z2dxY2L6TcX87dZ97NyUUnfypBMwyDNZE4T7b28HxHLz2KRoZN4oq8DC7NzRgU555EDy9ufZN5jfP4sPVD4mocp+RkWv40rh51NScVnUSpr3RwLF2RJK+tbWVxbQ9LanvY1BZCN8wYESPy/Vw8sZBJpRlMLAlSme355DEbDMOcAXdvTZdtZunZZoqyvmO7OaINAiUQLIUR50Kg1KwHS8BfZIrxbm5cWlgcCVhCDSTjKsteraNkVAYloz7+BpxhGLT+/Oek6usp/de/kIt2v9yQSsR54c+/p2H9WmZffAYT6v9krkFe+yLk7pgBa5rGvHnzWLhwIRl2Pxfq1aiTX6DNtxS/fwIVVb/lse3v8u/3r8IhOfjR1B9x9cird+sNsa90p1TmtPfweGsPm6IJHKLAOdkBrsjL4LRMH3ZRpC3axuMbn+ethrdY2bES3dDJc+dx8bCLOaX4FKbnTx+8+dcfU5i7vp0PtnWxaHs3W9rN5Q+XLDG5LMh3zqxmalkmE0uDeB2f4COnqebMuHMTdGyCrs3QtQW6tg5dnpDdpu957mgYeSFkVkBGBWSUm2IsWR93i6MT65MLrHyjnkRU4YTLqvZ6bs+//m2m0frxj/HM2H3sjWQsyrO33kxrzWbOu2gWo7fdAjkjzah3/h030fr7+5kzZw6NjY2MFIsZ4+6jZ8af0MUEVcN+Rr1YzTVv30RzpJkLKy/kh1N/+IlvFBqGwft9ER5u6ea1zn4Uw2Cy382fhhdzSW6QgGwbFOc36t9gTecaAKqCVXx1/Fc5veR0RmWOQhAEFE1nRX0vC2vqWVjTydrmfnTDFOZpFZlcNqmYGZWZjCsKIO9vurJwO7Svhfb1ZunYAJ1bhnpKBEogezhMngXZ1WbJqjKXKY7WDSgWFh/DcS/UsVCK1e80UTUll5zSPe7nASC6eAkdf/0rvnPOIfP663Z7TiIa4Zk//JqO2u1ceMFEhtfcBuUnw+f+Z7pXpampqeHZZ59FS6mcpg/DO+YtOrLew+8bT17lL7hr3VO8VncHFYEK/nXOv5iWP+0Tvb5+ReXJth7+29zNtniSDJvE9UXZfL4gk1FeF32JPl7f9gyv1r7Kio4VAIzKHMV3J3+X2aWzKQ+UA9AeSvDE0kbmbe7g/a3dRJIqkigwqSTIt8+o5sSqbCaWBPf9hp9hmLPkllXQuhra1kDbWtOlbQBfIeSNMT1jckaZv0SyR5huaBYWxxHHvVCvmFuPltKYftHHb25Ru7po/tEPsZeVUXDL7m8eJiIR5tzyKzrra7lo9jCqtt0Boy4yY3akPQB0XWf+/PnMnz+fTJufk+1eIjPvISR1U17+XdbrZXz/ze8RU2J8Y+I3+PLYL3/s1ug9sTma4KGmTp5u6yWu60z1u/lHeSkX5QQRUZnfNJ97lrzIe83voeoqwwLD+NbEb3FuxbmU+cvMxLUtIW5fsoW3N7WzrtkMhF8YcHLRhEJOHZ7DrKos/Pu6cSTcBk3LoHk5tKyAlpWm+xuYW3NzR0L1OZA/zvQnzxuz19RiFhbHC8e1UEd6E6yb38yImflk5O95j76haTTfdBN6OELpgw8heXc9NxmLDor0xacVMqzhQZj0RdO7I702Go/HefbZZ6mpqWG4kM+oghp6Kl7E5SqmsOI+bl//LPObHmBizkR+e+JvqQzsX25GwzCY3xvmn42dvNsTxikKXJaXwfVF2Yz3udncs5nbl/2TV2pfoT/ZT44rhy+M/AIXDbuI4RnD0Q1YXt/Lf+dvYO76Npr74ggCTC7N4MfnjuCMkbmMyPPt/QampkDrGmhcbJamZWY8bTBv6uWOhjGXQeEkM65J7mjLlc3C4mM4roV62Wv1GIbBtAs+fjbdde99xD5cRMEt/w/niOG7HE8l4jx768101m/n4pNzGdbyP5jxdTj31sE1087OTh5//HH6enuZJRTim/gyPb715OddSq3jJG5691ektBQ/nvZjrh55NdJ+xDJQdIMXOnq5t7GD9ZEEuXYbP6nI50uF2biEFK/Wvsof5s9hffd6ZFHmjNIzuLTqUk4oOAEQWVrXw68XrOe1dW10RZLYbSKnVGfz3TOrOWNULtnevYhoKmaGZK17Hxo+NIV5IAB/oMSMo138TSieas6YZdc+vzYLC4vjWKhDXXE2vtfC6JMK8WfvWThiS5fSdc89BC65mMDll+9yXEkmeP6Pv6N162YunJXJsPan4KTvw5m/GRTpmpoa5syZg6jC2S4fyUn/JCEnKa68mQdr1/B63a8ZnzOeW068ZXBNeF9IaDpPtPVwd0MHjYkUw91Obh9ZwuV5GTSFarlvxUO8tP0lokqUqmAVP53+Uy6ouICAI8Da5n7+8OpmXl7TQnsoiVMWOWNkLueNLeD0kbkf752hJExhrl0AtQvN5QxdMX2R88fBlOvMhLslM0y3NwsLi0/FcSvUy1+vBxGmnLfnAEpafz/NN/0YuaSYvF/9epef/Jqq8NLtt9G4cR3nz8xiePdzcOpP4bSfgiBgGAaLFi3ijTfeIFPwMjO/hVDVi7jdFSj53+Cbi++iO97NdyZ9h+vHXo9N3Lc/R1zTeaSli7sbOmhPqUz2u/l/1UWckeFhYfMCvvnmYyxuW4xdtHNO+Tl8dsRnmZAzgZb+BI9+0MSzK1exvTOKXRI5dUQOF00oZPao3D3HxjAM0wNj2zuw/V2o/9CcMQsiFE6GE74J5SeZwuw8LsKVW1gcUo5LoQ51xdn0QStjTi7Em7H72AqGYdD6q1+jdndT/thju6xL67rGa3ffTu3KZcyelsmovrRIn/4zwPSPfv3111m6dCkVUpARIz4glL2c7JzzmZcs56H5v6bUX8qj5z/KmOwx+zTuhKbzaGs3d9a305FSmRX0cvfoPCZ5RJ7f9jyXLPgfjeFG8j35fHfyd/lM9WdwSX7mrm/jLy8u4f1tXRgGTK/I5CsnV3L+2AIC7j3cDEz0w/Z5UPMGbH3bjHMBpvfFlOtMT4yyWZYwW1gcAo5LoV4+15xNf1wexL45c0x/6Zt+hGvcrlHt3vn3/Wz+YAEnTcxiQuR5OPUngyKdTCaZM2cONTU1TJR9ZE96jqizlYyS7/K3rctZ0fEfLqu6jJ9O/+k+pcBSdYMn2nr4W10bLUmFWUEv943OZ7gzwWMb/81PNj9JKBViYs5Evjv5u5xZeibbO+Pc8UYDz61cSn9coTjDxXfPrOYzk4spydzDc/bUwubXYMtrUP+BGezdGYBhZ0DVbNNaSxkWFoec406oQ91xNr3fyuiPmU2nGhpov/U23DNnknn99bscX/zcU6x+4xWmjs1mRvI5c036NFOkI5EI//vf/2hrbeMkrw3bxP+i2+0oeT/mu8v/S1JLcuvJt3Jh5d7TThqGwatd/fxhWyvb4kmm+N3cOaqUSjnMv9fdwXe2PkdKS3Fm6ZlcN/Y6RmWM47V1rVz9+lKW1PVgl0TOHZvP56aVMLMya9et2gNLGhtfhE2vQPs6sz9nJJzwLRh+rhl4yNrRZ2FxWDnuvoEr5jaYs+lzdj+bNlSVlh//BEGSKLz1D7skpl037y3ef/IRRlVnc4r6HMz82uCNw+7ubh595FHC/SFOzw2jjHgBu2cYy22n88CiO6nKqOKvp/6VisDeExIs649y89ZmloViVLsd/HdcBaPs/Ty49s+8tO0lEOCSYZdw3ZjrcIv5PLqogS8vfoeuSJKyLDc/O28kV04tIdPzER9swzAFed2zsOF56NkOCFB6ghnJb+T5u00BZmFhcfg4roQ62pdk4wctjDqhAF/m7mfT3Q8+RHzVKgr//GfkgqExk+tWLeeNf95JWVk250jPI0z+Ipx7GwgCra2tPPLwI+iJFKeV1ZIsnY8rcAqP9thZ2PIoF1VexK9O+BUu28e7pjUlUvx+WwsvdPSRa7fx1xElnOSL8+Cav/CTbS8hCRKfHfFZrh97PT39bv4xt5YXV29A1Q1OG57DtbPKOaU6Z9fZc/c2WPs0rJ0D3TVmWqWKU2DWt824GN7cT/XeWlhYHDyOK6Fe+VYDhg6Tzt79bDqxaROdd9+N77xz8V94wZBjnQ11vPT328jODnCx40Wk0RfCRXeAIFBfX89j/3sMh6YyfeRKkjmrEbI+wx+2rac50sIvZvyCq0Zc9bEbReKazj0NHdzV0I4BfL8sj6tyBB5dfy9/qXkGEZHPj/w81425jpoWiZue2MbCmi7cdomrp5dy3YkVVGR/ZCNOrAfWPQOrHzdd6BCg7EQ44Rsw6mLwHPgUXRYWFgee40ao45EU6xc0Uz0tl0DOrrNaQ1Fo+dnPkQIB8n891BUv0tvDc7f9FrtN5LLAm9iHzTLzG4oSW7du5YnHn8Av6kwct4Ckv56+jC/w5/Vv4JAcPHjOg0zJm/KxY3ujq59f1DTTmEhxcW6QH5b6mVvzKFd+8AiqrnJ59eXcOO4rrK4zuPFfNaxt7ifH5+DH547gC9PLhnpuaCpsextWPmreGNQVyBsLZ/0exn7GjLdsYWFxVHHcCPWad5pQUzpTzinf7fGu++8nuXEjxXf9A1vGjhgTSjLB83/6PYlwP1eVrcZXXA2fewxkJ5s2beLpp54m264yetybqK4+Nns+y31rnmdk5kjuPONO8j35exxTUyLFL2qamNsVYrjbyVMTymlsf4UbX7mPvmQf51WcxzfGf4s19Ta+dP9majoilGW5ufXycVw+uQiHbafdi30NsOIRWPmI6UrnzobpX4WJnzc3oVhYWBy1HBdCnYqrrJ3XROXEHDILd43Tkdi0ia5778N/4YX4Zs8e7DcMg7n33kF77VYuGdZIXpYbvvA0OP2sX7+eZ+Y8Q6ErQdWE19EcOm9xBi9tepHZpbO55aRb9uh6pxkGDzV1clttG4YBv6wsYJSwiT/Pv8nM3JI/g+9N+T61zRnc+K8atnZEqM71csfnJnLBuAJsA6FDdc30cV76oOnvDKYb3Xl/Mj02rKzRFhbHBMeFUK9/r4VkTN2t37ShqrT+4pdIgQB5v/j5kGOLn32SzR8u5OTyMFW+XrjmDfDls379eubMmUOpJ0b5+FdRHF6ejFexuH0+N467kW9P+jaisPtwn5uicb6/sZGV4RhnZPr4VgE8vOY3/LP5fcr95fzj9H+QDI/kR49uYVNbHcPzvNx99WTOG5u/4wZhvA9W/Q+W3G+mmPLkwik/gslfMrOWWFhYHFMc80KtqTqr326kaESQvPJdd9H1PPwIifXrKfr77UOWPGqWfsj7Tz3KqEKY5l4Pn38RckawYcMG5syZQ5mvn9JxrxOzZ/Ovvgy29a/l5hNu5jPDP7PbcSi6wV0N7fytrh2fTeTvI/JpaXmcb859GKfk5KapN1HtOpc/v1zDioblVGR7uONzE7lofOEOge7ZDovuM9eflajpUnfmr2HkRdbs2cLiGOaYF+qape1E+5Kc/sVdE8CmGhvpvPNOvGecge+ccwb7u5sbef3uv5GXaeds3zsIl94HZbPYtGkTc56eQ3mgh5KxcwnZi7m3Q6Av2cZdZ97FSUUn7XYMm6MJvrOxntXhOJfkBjnPXcs9H/yQ1mgrlwy7hMvK/4/73mnn1xuWkud3cOvl47hySvGOJY6m5fD+32HjS2aY0HFXmBnMCycehHfMwsLiSOOYFmrDMFj5ZgNZRR5KR2fucqztN79BkCTyf/2rQS+PZCzGC3+5BQmNizMXYjvtRzDhc2zbto2nn3qKsmAHxWPeoNNWwV0tUURB4l/n/Gu38Tp0w+DBpk5u2d6KRxL5S1WQ5Vvv4FcNb1EVrOKu0/7Nu6tdXPXqWpyyxE3njOCGEytw2SVzY8q2d2HhX6FuobmV+6TvmzcI/QW7PJeFhcXhRdcNdMPYMcE6gBzTQl2/rpueliizrx+9iw9z6OWXiX7wIXm//hVyvumZYRgGr9/zN/ramrmyZA3+CefBaT+nvr6exx97nOJgG8Vj3qJZrODu5l4ynJn886x/Uubfde27Lanw3Y0NzO8Nc3aWn9Pk1dy98E8ousK3J34Xe/QMvvffrfTHFa6aVsoPzhpOjs9hCvTm12HBn6F5mZkH8Oz/ZwZCcnx8qjALi0OFYRhouoGiGSi6jqLqZl3TUTQdVTdIqaZVtR3HVF1H1QxUPd3WzMdRdWPwmKabj6mlzxs4run60LZmoKXHMaTsoU//iNX0HeI69Hj69aXPMXY6rhvmBExPnzdYN8z3JdvrYNkvZ3/8m/cJOKaFetWbDXgzHFRNHbrrTuvvp/22P+KcMJ6Mz31usH/ZS8+ydekiTi1soaSiBC69l9b2dh579H8UBFooHfMWdUIF9zZ3Uewt4f6z7yfXveuOvje6+vnepgbims7Py7ys3voHbm9dzPT86VxRehP/eKOTDa0bmVGRyW8uGsPoQr8p0FvegHl/MNNUBUvhwtth4hes7CcWu6DrBglVI57SSKi6aZWBopNQNJLqrjappq1i1lOqTlLV01YjpZn1wf608CqqseNYus8wDs1rFQWwSSKSIGCTBGyigDRQBAFJErCJonmeKCKK5jmiKCAJIIkCoiBgt4mD9R3WPC4I6cdK94sCphXNc8y+HdeIQvoaEQTM80SBj4/j/ik4ZoW6syFM85Y+Zl1ehfSRnyIdf/87Wm8vpQ/cPxjLo2nTehY+/l+qsxJMye+Dzz9PdzjBI/99hExvE+Wj32KzXsoDre0MzxzBfbPvI8M5NKdfSte5ZXsr/2zsZKzXyaXuzTzy4R8QBIEfTvoVm2pG8vX/biPf7+SuqydxwbgCc6ZfuxDe/p0ZjD9YChf/AyZ8HqR9zEdoccRiGAZJVSeSVIkkVNMmVaJJlWhKM21SJZrUiCkqsaRGNKUST2lEUxrxlEospRFXTFEesElV/8RjkiUBh03CYROx28RBa9Yl7JKI223b0SeJyJJZlyUR2SZgl0Rs4kCfYPZLIjbJPDZQl9MiOtAvicLgMZtoXjvQJ4kCsiimhXeHIO819dtxwDEr1KvfbsTmkBh90tD13Pjq1fQ98SSZX/oiztGjAYj19/HK3/9IwAXnZK9G+OyzhKUMHnnoQTzOeqrGvM0GvZiH2roYlz2Oe2bfg88+dBmiMZHiq+vqWBmO8fk8D7GWO/nnhnlMz5vBycHvcdeLrfTGmvjKyRV8d/Zw8z9v62p462YzIL+v0MyvOPELlgfHEYRhGERTGv1xhb5Yiv64QiiuEIqrZj2RbidUwokBqxJJKqZNqKj6vk09HTYRt13CbbelrYTLLpHnd+KyS7hls+2ySzhtO447bRIOWcQpS2ax7VRP9zvSIuywibvGgbE44jkmhTran6RmWTtjTinCsdP2akPTaPvd77Hl5JD97e+YfbrOa3f/jXioj6tLl+E49zckC6fz6AMPAdsZOeZd1ql5/Kujm0m5k7jnzHt22cjybneIb2yoRzEMvp8f5ZXV3yGmxvjamJ+xZE0VN8+rZ0JxgP/eMJ0xhQHoa4RX/h+seRJcQTNq3bQbQd59oCiLA8OA6PZEUnRFk/RGU3RHU/RGU/TETNsbMwXZtAr98RSKtmehHfi563PK+F0yfqeNoqATn9OX7rfhddrwOszicdjwpa3HIaWtDbcsHZSbUBbHBsekUK+d14SuG0w4o3hIf9+cZ0isX0/hX/4ymLFl2cvPUbd6BbPzt5E75Ry06V/jqUcfIxrfzKTx77JWDfLvzn6m5E3hrjPuGiLSumFwR307f6ptY4THwVT1dR5d8i+GB0dwauBn3PtSF5rew68vHM21s8qRlCi8/Xv48C5zTfrE75qeHK7goXx7jjmSqkZHKElHOElnOJG2SboipjXrKbqjSRLK7pcM7JJIhkcmw20n6JapzvUSTNeDLpmgWybgMsU4sFPx2G3WDNXioHPMCbWS0li/oIWK8dkEcnaIqtbXR+ftt+OeOhX/BecD0Lp1M+898TDVGSHGV/kwLrqTl196mea21UybMJ/1uov/dEaZlDtpF5GOqBrf2djAq139nJMhE2r4LXN713N5+Q1srZnJ3z5sY9awLG67fDylmS5Y8xS8+WuItMHYK2D2zRAsOdRvz1FHNKnS0henpT9BW3+clr4E7aEErf2mbQ8l6I0pu1wnCpDpcZDjc5DttTMsx0uW106W10GWx06W106mx6xneOx47JK1FmpxxHLMCXXNknYSUYUJZw4Vwc4770QLh8n71S8RBIFkLMYrf/8THlnl7ILtCFe9xcIlq1i34UOmT1jARt3gX90K47LHc/eZdw8R6fp4ki+trWVrLMHnMvp5f/1NOCUHXyj+O/97V0XV+vn9pWO5ZkYpQvs6+PdN0PChmQj2qkegZPqhfluOWEIJhcaeGI09cZp6YzT1xmnui9Octv3xoSIsCKYLVL7fSXGGm6nlGeT6nOT7neT4HeT6HOT6nGR67EjWTNfiGOGYEmrDMFjzbhNZRV4Kq4OD/YlNm+h94kkyrr4a54gRALz7n/sJdbVzVekanJf8mQ1dOu/Oe51p4xeyXYzy724nozJHcM/se/DIOwI5fdgX4cvratEMuMi+mLdX38X4zBl4+r/MfW/2MKUsg79eOYFynw5zfwGL7zOXNi7+B0y8BsTjax3SMAx6Ywq1XRHqumLUd0ep645R3xOjoTu6y2zYY5coznBTlOFiclmQoqCbwqCTgoCLgoCTPL8Tu+34eg8tLI4poW7d2kd3c4TTrxk5+DPWMAzab70Nyecj59vfAmDLovdYP/8tZmY3UHTixbTknsqzDz7AhFEf0mLv4sEeH6X+Uu6dfe8Q744nW3v40eZGihwiBX338X7HAs7O+xqLVo2kLdTLj84eztdPq0La8ho8/CMItZgbVWb/BlwZuxvyMYOq6dT3xNjaEWFbZ4RtHVG2d0XY3hkdMisWBSgMuijP8nDeuAJKM92UZropyXBTkuki4JKtJQgLi49wTAn1mnebcbhtVE/PG+yLvPMOscWLyfuVGSEv3NPFm/f/g3xPgpkjHIRP/jWPP/AwVZVLifgbeKgrg2xXNvefdT9BZxAwxf7PdW38ra6diR6DWP1PaUp2M9v/J55fYFAUFJnztROYlJGCOdeZuQhzx8CV/4WSaYflvThY6LpBU2+cTW0htrSH2dweoaY9zPbOKCltx426PL+DymwvF44voCLbQ0W2h/JsDyUZbmtGbGGxnxwzQh3pTbB9VScTzyxBtpsB9Y1UivY//Qn7sGFkXHUVhmHwxn13oiainFe5GeMzL/Hkky8QzFyKnLuJf3Zn4ZDdPHD2A+S4cwAz6t0PNjfwdFsvM91h6jZ/n1x7KbnRP/LcuhgXjC/g1svG4q95Hh67CZQYnPFLOPF7R/2GlYSisaktzIaWEBta+9nQEmJzW5hoShs8pzjDxYg8H6eNyKUq10tVrpdhOR58zqP7tVtYHEkcM0K9bkEzhmEw9tQdqaZ6/vcYSn0DJQ/cj2Czseat16lbvYIz87aSccHPeHFxHXF1EeVVK7inO4u4IfCf2fdS7DPd+qKqxo3r63i3J8wJ9q3UbPoto93n07D1LOoiCf7fpWP5whgnwgvXw6aXoXgaXHIP5Aw/XG/DJyapamxqDbOmqY81Tf2sbe6npiOClt6s4XPaGFXg58qpJYzM9zEi38fwPB+eg7Rl1sLCYgfHxLdMU3U2vNdC+bhs/NlmPkStr4+ue+/Fc9JJeE8+mf6OduY9/AClnn4mTBvDcmkaW7Y9wrgJH/BATwZtSor7Zt/HyEwzHGpXSuWaNdtZE44xWV9ATc0DTHJ+i0WrSsjzizzz9VmMCy+Ee78LybCZk/CEb4IofdxQjwgMw1y+WNHQy8qGPlY29LKxNTy4dJHlsTO2KMDsUXmMLfIzpjBAcYbLWju2sDhM7FWoBUEoAR4G8gEduN8wjDsO9sD2h+2rOomHlSGz6a77H0APh8m96UcYus7ce29HUBOcU91Oy8y7eevpx5k4YR5PhVxsSSS47eTbmFEwA4CWRIqrVm+jIZ5kVPxpmjteZ7T+exaukjl1eDZ3XF5NcP4vzPyE+ePh8gcgd9d410cKqqazsTXMkroeltb2sLyhl85wEgCXLDG+OMD1J5UzsTjIuOIARUFLlC0sjiT2ZUatAj80DGOFIAg+YLkgCG8ahrHhII9tn1k3vxl/tpPSUWbM6VRTM72PPELg0ktxjhjB6jdfpXHDOs7Kr0G68Daeeu41Ro2az1tJjaVRg+9M+g4XVF4AQG0syZWrt9KTUijqu4f+vq3k9N3CkjaNb54+jB+MjSM9Mhu6t8FJP4DTfnbExeZQNZ21zf18uL2bxdt7WF7fSySpAuaa8klV2Uwuy2ByaZAReT5r67KFxRHOXoXaMIxWoDVdDwuCsBEoAo4Ioe5pjdJS08cJlw1DSG9w6LzzDhBFcr7zbUJdnSx45CFKPX2MPfVMHl0eIqdgHhttXcztcXB59eXcOO5GALZEE1yxaisJTSGj4zaEKAjNP6E5YXDP1ZM4P/YiPPRL8OTAtS9BxcmH86UPYhgGWzsivLe1i/e3drFoe8+gMFflerlkYiEzKrOYXp5JfsCKJ2JhcbSxX2vUgiCUA5OAxbs59lXgqwClpYcuwer6Bc2IksDIE8woeYmNGwm99DJZN96ILT+ft2/7DbqS4OyRYd7zXEq042Hkoq082elmWv4UfjnT3Km4MRLnilXb0PQUrpbf4I2V0VF7AQGXjWeur2b0kpvMG4bDz4NL7wF35l5GdnAJJRTeq+li/uZOFtR00tqfAKAsy81FEwqZNSyLmZVZZjICCwuLo5p9FmpBELzAM8D3DMMIffS4YRj3A/cDTJ069ZCEFFeSGpsWtTFsci5uv7n80PH3vyP6/WR95UY2vT+f7atWcHrednpPvYWlH75M6dil/L3LS4G3gL+d+jdkUWZ9JM6Vq7ai60mkpl+QFZ1F3fapjC3y8Z9znWS+dBH0N5lR7k74prmP+RBjGAbbOqO8vbGddzZ1sKy+F0038DltnFSVzbfPyOHk6mxKMt17fzALC4ujin0SakEQZEyR/p9hGM8e3CHtO1uXd5CKq4w5uRCA2PLlROcvIOeHPyAlwLv/uocCV4jhp5zF/e+to2rsfO7rcaGJDu464y6CziAb0yKtaQnExp+S1X8x2xurOGt0HneN2YTjiR+auwqvexVKZxzS16frBisbe3ljfTtvbGintisKwMh8H/93SiVnjMxlYknQWmO2sDjG2RevDwF4CNhoGMbfDv6Q9p0N77UQzHNTWB3EMAw6br8dKSebzGuu4c3/3EcyFmX2mBDP906guOI/PBdTaVZs3HXmn6gMVrI5muCKVdtQtThSwy/I7P48DW0F3HBCMb+UH0V86X4oPxmu+Bd4d025dTDQdIMltT28tq6V19e10RFOIksCJwzL5oYTyzljVB5FQdchGYuFhcWRwb7MqE8EvgisFQRhVbrv54ZhvHrQRrUP9LREadvez6zLqxAEgcjChcSXLSfv17+ipXYb6+a9zbSsJmrH/ZBE9wtsdnSwvM/OtyZ+k1OKT2F7LMkVq7aSVGPYGm7G334tzd0Z3Dw7n2ubf4lQuwBmfhPO+h1IB9fdXNcNVjT08uLqFl5d20ZXJIlTFjl9RC7njs3n9JG5+K2dfhYWxy374vXxHnDEOdVueL8FURIYMTMfwzDo/PsdyEVF+C65hBd+9m38coLKGScwp3YxzhFrebHTwZmlZ/KV8V+hKZHiylVbiSpx7PW34Gm5lq6wj/vPdXP2qush3AaX3gcTP39QX8PWjjDPrGjmxVUtNPfFcdhEzhiZy4XjCzl9ZA5u+zGxH8nCwuJTclQqgabobF7URsWEbNx+O+F33iGxfj0Ft9zCirkv09PewcXDOnmp+0wKhj/Gnd1OSv0l3HLSLXQrGp9dtY2uZBxnw59xNn2RcNzD07PjTP7wa2bG7+tfheKpB2Xs/TGFF1Y388zyJlY39SOJAidVZfPDs4dz9pj8g5bF2MLC4ujlqFSF7as7SUQVRp9UaM6m/3EXcmkpwoknsOiHX6PK28W2qhvJ8D7N42GdlODi9tPuQBOcfG5VDY3xGO6GO7HXX4Wienj1pK1ULfw15IyEq5884JlXdN3gw+3dPLG0kbnr20ipOqMK/PzyglFcPLGQXJ/l22xhYbFnjkqh3vh+C75MJyUjMwm/9RbJjRspuO1W5j98H2gKw8ZV8r7yARtsHWyLy9x68s0U+yu5es12NkbieBv/ia3uEgTDw9uT3iN/0T+g6iy48t/g8O19APtITzTFU8saeXxJA/XdMQIumaunl3LFlGLGFgUO2PNYWFgc2xx1Qh3uSdC4qZdpF1QABl133Y29rIze0iJqHn+QGXntzNfHoRW+wDs9MlcOv4LzKi7g/9bX8UFfBG/TI0jbz8GFizernyZj9RyY/CW44PYDdtNwdWMf//2gjpfXtpJSdaaXZ/L92cM5d2w+TvnID9pkYWFxZHHUCfXmRa1gwMiZ+YTffpvk5s3k33Yrzz10J0E5TmfV5QRKn+WuPpnqYCU/nvYTfru1hZc7+3G3PoNt64kERTtvFD+Ar+YdOO3ncOqPP/UmFlXTeW1dG/96v5aVDX14HTY+N62Ea2aWMTzvwM3SLSwsjj+OKqE2DIONH7ZRNCKIL8tJ3b33YS8rY7ug0NvVy4yRPrYEPuSlRBwNF3857XYebQtzf1Mnrs53kDePJ0cQmJt3B+7GZXDh7TD1hk81pnBC4Ykljfzngzqa++KUZ7m5+aLRfGZKsRU838LC4oBwVAl169Z+Qp1xpl9QTnTBAhIbNhD81S95bc7/KPaGWJc5iVr/62wN2fndrF+yJZXFr2pqcfatwr6+iALB4LXMP+Hq3AZX/gfGXPqJx9IZTvLv92t5ZFE94YTK9IpMbr54DGeOzEW0sl9bWFgcQI4qod74YSuyU6JiYg4t134fW2EB63qbSKUUxDEzMMrm8nq/nbPLZjMs72wuXlmDPVKHfbVMERqvBv6CM9RienYMO+MTjaG1P84/52/n8SUNpDSdc8fk87VThzGhJHhgX6yFhYVFmqNGqFMJla3LO6iemouyahnx1auxf+/brH33VSryDHqLV/NUVCPHlc03pvyKy9dsQ4v14FzRT5EKrwb/jDPeB198Fspm7ffzt/bHufvdrTy1tAndMLhsUhFfP20YlTneA/9iLSwsLHbiqBHq7as6UZMaI08ooOv3f8SWk8PKxg3IkkrXsGEscb5Dd9TGvaf/ha9vaqczFse9rJbCpMSrGX/GqYbhSy9A8ZT9et6OcIK739nK40saMTC4cmoJXz91mBWlzsLC4pBx1Aj15kVt+LOdBKP11C9ejHL9F6lf8QFFw8tpLl3AopCN60dfy/96s1kT6sO9bA35MZnXMv6IS4uZIl04aZ+frz+u8M/52/j3+3Uoms6VU4v55ulVFGdYAm1hYXFoOSqEOtKbpGlzL1PPL6fnwb8j+P2sbFiHx2MjPLyWZyIGw3wluHI/x7PbOnGuWklev4PXM27FrQ+I9MR9eq6kqvHIh/Xc9e5W+uMKF08o5Puzh1Oe7Tm4L9LCwsJiDxwVQl2ztB0MqChQ6X7rLXovOZfO2i1kzSjhXcc8YnGZqybdwg+3d+LYtJmcTjuvBG/Dq0fg2hf3SaQNw+DVtW3c9vpGGnvinDI8h5+eO5LRhf6D/wItLCwsPoajQqg3L24jr8KP+vzD6A47a9tqycjPprXsA1ZGbHxpzFf4daOA1NBCZoPBS4E/k6H1wBef26fljnXN/fz2pfUsretlZL6Ph2+YzinDcw7BK7OwsLDYO0e8UHc1RehujnDi+QWEfvEi7SdPJdzXjXdiLy/FNKp9pbymnUK0rZ/MTRHm+P5KntaG8IU5e83I0htN8Zc3NvPYkgYy3Xb+cNk4rppWgmT5QVtYWBxBHPFCvXlxG6IokLVpLr2GwYb+TrJGljDPM4943EZu+U182JzCv7qNR9x3UqnVInzusY/NEK7rBk8vb+TW1zYRTqhcN6uc780eTsBl7SS0sLA48jiihVrXDWqWtFEyMkDs0cdpmjyKlGQnPHIJK+ISp1Z8njmdftzLarlH/icTtfUIlz8Aw8/Z42NuaQ/z82fXsqy+l+nlmfz+0rGMyLdicVhYWBy5HNFC3VrTR7Q/xYS8NuKxKFuUKN4ZNp5NxSl05vGScjr2FU38Tn+cM6VlcN6fYPyVu32spKpx9ztbuXf+NrwOG3++YjxXTClGOAwZxS0sLCz2hyNaqLcsa8dmF3G9/m82jSzDnlfMitz3CMVElMKvo28I853Iy1wjvwUnfg9m/N9uH2dFQy8/nrOGrR0RLp9UxC8vHE2mx35oX4yFhYXFJ+SIFWpN1dm2ooPiPJXYu/Vsz6pEn1LDBzGBwqwzWdtcyGdbXuIm+1Mw/nMw++ZdHiOhaNz+5hYeWLidfL+T/1w/jdNGHJps4hYWFhYHiiNWqBs39pCMqmR3vkVteQGe0fk8K72PW/CyJnUZJ298nz/ZH8AoPwXh4n/sEk96XXM/33tyFVs7Inx+egk/P3+UFXbUwsLiqOSIFeotS9qxOwTED16nYcJwmocvpSUhEg9ex4jlm7nf/nfErEqEqx4B245lDE03uG/+Nm5/cwuZHjv/vWE6p1o+0RYWFkcxR6RQKymN2jVdFBsN1BYGccwQeDep4HCOgY25/Fv4GR6nE+map8EVHLyupS/O955cxZLaHi4YX8Atl44l6LbWoi0sLI5ujkihrlvThZrUcG94nrrR5byfvQw1KdHfdwWPRP9GidyDdPUrkFE+eM3r69r4yTNrUDWdv145gcsnF1keHRYWFscER6RQb13egdOm0G7vpm9mmLVJgbh0Ab9pfJqTbevgonsGdx2mVJ0/vLqR/3xQx/jiAHd+bpIVQMnCwuKY4ogT6lRCpX5dNzntH9A5pZq35UUIei6XbE5yvW0u6oxvYJv0BQCaemN8838rWN3Uzw0nVvDT80Zit4mH+RVYWFhYHFiOOKGuX9uNpuhEoyvYPL6DTlUkt2smfxDvJ1by/9u7+9i66jqO4+9P2621wznY2GAdsVtSx+YemFRAhlMBs1GXTWMwJS7OgDWKhgcNyqySSPzDKEFJ5MEFcAviZoI4FgQdGcSZ4OYKM9vYKKuDsULXXiyle6JP+/rHOY2XrYVbdi/nd26/r6TpPee2N99P7u0nt7977zmLqFz8MwC2vJThhvU7ohcPV1zIkjnnJDy5c84VRnBF3fJcB2P62zm8cAJbBg5A/0we6l5PX+VkzrhmLaYS7nmmhTs2NTNzyoe5b8WFvtThnCtqQRV179v9HNiVofTwZrbN2EVvr7j9tYNMKjnM2K9t4FjZeG75ww7+squNZfOn8vMvz6VybFARnHMu74JquVd2vUF/33GOLOxkR+8A87um8KUT2+lZ+htaK2pouPefNB/q5kd159Pw6Rn+rg7n3KgQVFHv2/o6JQPPsmniAcp6KvhtVxOZj11N6+SlNNz9LD19Azzw9U/yOf8YuHNuFAmmqPt6Bnh1TzvtFz1PW38vt3Qepauimp2zGrlp9VYmjy9nXcPF1EzxQ5I650aXYN7LVja2hElvr+HJyv9S1SOWHznKP+b9im//cQ9zqj7ChusXekk750alYJ5R977ZydOf6eL4ieP85M0OHpt6M7f9/Rh1c8/hzq9cQMWY0qRHdM65RART1Ic697OVDJceO85bJ2q5bf9crrtsOo11syjxcxg650axYIr6SPl4ftzezcSBMq7vvpbGulk0LJqR9FjOOZe4nNaoJS2R1CypRdKthRhk2sRq2mwxvzj6LW6/+mIvaeeci73nM2pJpcDdwOeBVmC7pI1mtiefg4wrH8O+6m/wvXlTuXL2lHzetHPOpVouSx8XAS1mth9A0npgOZDXoi4rLeGu+gX5vEnnnCsKuSx9VAEHs7Zb433vIOmbkpokNWUymXzN55xzo14uRT3UWy7slB1mq82s1sxqzz7bT33lnHP5kktRtwLnZW1PA14vzDjOOedOlktRbwdqJE2XNBaoBzYWdiznnHOD3vPFRDPrl/Rd4G9AKfCgmb1Q8Mmcc84BOX7gxcyeAJ4o8CzOOeeGEMxBmZxzzg3Ni9o55wIns1PeaXf6NyplgAPv89cnAW/kcZwkFUuWYskBniVExZIDTi/LR81syPc2F6SoT4ekJjOrTXqOfCiWLMWSAzxLiIolBxQuiy99OOdc4LyonXMucCEW9eqkB8ijYslSLDnAs4SoWHJAgbIEt0btnHPunUJ8Ru2ccy6LF7VzzgUumKL+IE73VSiSzpP0jKS9kl6QdGO8/yxJT0naF38/M+lZcyGpVNIOSY/H22nNMUHSI5JejO+bT6U4y83xY2u3pHWSKtKSRdKDkjok7c7aN+zsklbFPdAsaXEyUw9tmCy/jB9jOyX9WdKErOvykiWIos463ddVwGzgGkmzk51qRPqB75vZLOAS4Dvx/LcCm82sBtgcb6fBjcDerO205rgL+KuZnQ/MJ8qUuiySqoAbgFozm0N0cLR60pNlDbDkpH1Dzh7/3dQDH49/5564H0KxhlOzPAXMMbN5wEvAKshvliCKmqzTfZlZLzB4uq9UMLM2M3s+vnyYqBCqiDKsjX9sLfDFRAYcAUnTgC8A92ftTmOO8cAi4AEAM+s1sy5SmCVWBnxIUhlQSXRM+FRkMbMtQOdJu4ebfTmw3sx6zOxloIWoH4IwVBYz22Rm/fHmVqJj9kMes4RS1Dmd7isNJFUDC4BtwBQza4OozIHJCY6Wq18DPwBOZO1LY44ZQAb4XbyMc7+kcaQwi5m9BtwBvAq0AW+Z2SZSmCXLcLOnvQuuBZ6ML+ctSyhFndPpvkIn6QzgT8BNZtad9DwjJWkp0GFmzyU9Sx6UAZ8A7jWzBcBRwl0aeFfx+u1yYDowFRgnaUWyUxVMartAUiPRMujDg7uG+LH3lSWUok796b4kjSEq6YfN7NF4d7ukc+PrzwU6kpovRwuBZZJeIVp+ulzS70lfDogeU61mti3efoSouNOY5UrgZTPLmFkf8ChwKenMMmi42VPZBZJWAkuBr9r/P5yStyyhFHWqT/clSURroXvN7M6sqzYCK+PLK4HHPujZRsLMVpnZNDOrJroPnjazFaQsB4CZHQIOSpoZ77oC2EMKsxAteVwiqTJ+rF1B9DpIGrMMGm72jUC9pHJJ04Ea4F8JzJczSUuAHwLLzOxY1lX5y2JmQXwBdUSvmP4HaEx6nhHOfhnRvzQ7gX/HX3XARKJXtPfF389KetYRZPos8Hh8OZU5gAuApvh+2QCcmeIsPwVeBHYDDwHlackCrCNaW+8jepZ53bvNDjTGPdAMXJX0/DlkaSFaix78278v31n8I+TOORe4UJY+nHPODcOL2jnnAudF7ZxzgfOids65wHlRO+dc4LyonXMucF7UzjkXuP8Bj0qFFKFxrOYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(hypothes_list);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x,y)\n",
    "for i in np.array(hypothes_list):\n",
    "    plt.plot(x,i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, hypothes_list[1])\n",
    "plt.title('hypothes_list vs x')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('hypothes_list');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- loss - epoch\n",
    "- loss - theta0\n",
    "- loss - theta1\n",
    "- x , y with plot\n",
    "- hypothis ,x "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multivariate LR"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Read MultipleLR csv file into numpy array  (check your data)\n",
    "##### Data source\n",
    "https://college.cengage.com/mathematics/brase/understandable_statistics/7e/students/datasets/slr/frames/frame.html\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>73</td>\n",
       "      <td>80</td>\n",
       "      <td>75</td>\n",
       "      <td>152</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>93</td>\n",
       "      <td>88</td>\n",
       "      <td>93</td>\n",
       "      <td>185</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>89</td>\n",
       "      <td>91</td>\n",
       "      <td>90</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>96</td>\n",
       "      <td>98</td>\n",
       "      <td>100</td>\n",
       "      <td>196</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>73</td>\n",
       "      <td>66</td>\n",
       "      <td>70</td>\n",
       "      <td>142</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>53</td>\n",
       "      <td>46</td>\n",
       "      <td>55</td>\n",
       "      <td>101</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>69</td>\n",
       "      <td>74</td>\n",
       "      <td>77</td>\n",
       "      <td>149</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>47</td>\n",
       "      <td>56</td>\n",
       "      <td>60</td>\n",
       "      <td>115</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>87</td>\n",
       "      <td>79</td>\n",
       "      <td>90</td>\n",
       "      <td>175</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>79</td>\n",
       "      <td>70</td>\n",
       "      <td>88</td>\n",
       "      <td>164</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>69</td>\n",
       "      <td>70</td>\n",
       "      <td>73</td>\n",
       "      <td>141</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>70</td>\n",
       "      <td>65</td>\n",
       "      <td>74</td>\n",
       "      <td>141</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>93</td>\n",
       "      <td>95</td>\n",
       "      <td>91</td>\n",
       "      <td>184</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>79</td>\n",
       "      <td>80</td>\n",
       "      <td>73</td>\n",
       "      <td>152</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>70</td>\n",
       "      <td>73</td>\n",
       "      <td>78</td>\n",
       "      <td>148</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>93</td>\n",
       "      <td>89</td>\n",
       "      <td>96</td>\n",
       "      <td>192</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>78</td>\n",
       "      <td>75</td>\n",
       "      <td>68</td>\n",
       "      <td>147</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>81</td>\n",
       "      <td>90</td>\n",
       "      <td>93</td>\n",
       "      <td>183</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>88</td>\n",
       "      <td>92</td>\n",
       "      <td>86</td>\n",
       "      <td>177</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>78</td>\n",
       "      <td>83</td>\n",
       "      <td>77</td>\n",
       "      <td>159</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>82</td>\n",
       "      <td>86</td>\n",
       "      <td>90</td>\n",
       "      <td>177</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>86</td>\n",
       "      <td>82</td>\n",
       "      <td>89</td>\n",
       "      <td>175</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>78</td>\n",
       "      <td>83</td>\n",
       "      <td>85</td>\n",
       "      <td>175</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>76</td>\n",
       "      <td>83</td>\n",
       "      <td>71</td>\n",
       "      <td>149</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>96</td>\n",
       "      <td>93</td>\n",
       "      <td>95</td>\n",
       "      <td>192</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     0   1    2    3\n",
       "0   73  80   75  152\n",
       "1   93  88   93  185\n",
       "2   89  91   90  180\n",
       "3   96  98  100  196\n",
       "4   73  66   70  142\n",
       "5   53  46   55  101\n",
       "6   69  74   77  149\n",
       "7   47  56   60  115\n",
       "8   87  79   90  175\n",
       "9   79  70   88  164\n",
       "10  69  70   73  141\n",
       "11  70  65   74  141\n",
       "12  93  95   91  184\n",
       "13  79  80   73  152\n",
       "14  70  73   78  148\n",
       "15  93  89   96  192\n",
       "16  78  75   68  147\n",
       "17  81  90   93  183\n",
       "18  88  92   86  177\n",
       "19  78  83   77  159\n",
       "20  82  86   90  177\n",
       "21  86  82   89  175\n",
       "22  78  83   85  175\n",
       "23  76  83   71  149\n",
       "24  96  93   95  192"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2=pd.read_csv('MultipleLR.csv', header=None)\n",
    "df2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "x=df2.iloc[:, :-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     0   1    2\n",
      "0   73  80   75\n",
      "1   93  88   93\n",
      "2   89  91   90\n",
      "3   96  98  100\n",
      "4   73  66   70\n",
      "5   53  46   55\n",
      "6   69  74   77\n",
      "7   47  56   60\n",
      "8   87  79   90\n",
      "9   79  70   88\n",
      "10  69  70   73\n",
      "11  70  65   74\n",
      "12  93  95   91\n",
      "13  79  80   73\n",
      "14  70  73   78\n",
      "15  93  89   96\n",
      "16  78  75   68\n",
      "17  81  90   93\n",
      "18  88  92   86\n",
      "19  78  83   77\n",
      "20  82  86   90\n",
      "21  86  82   89\n",
      "22  78  83   85\n",
      "23  76  83   71\n",
      "24  96  93   95\n"
     ]
    }
   ],
   "source": [
    "print (x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "y=df2.iloc[: , -1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[152 185 180 196 142 101 149 115 175 164 141 141 184 152 148 192 147 183\n",
      " 177 159 177 175 175 149 192]\n"
     ]
    }
   ],
   "source": [
    "y = np.array(y)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "25\n"
     ]
    }
   ],
   "source": [
    "print(len(y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ones</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>73</td>\n",
       "      <td>80</td>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>93</td>\n",
       "      <td>88</td>\n",
       "      <td>93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>89</td>\n",
       "      <td>91</td>\n",
       "      <td>90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>96</td>\n",
       "      <td>98</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>73</td>\n",
       "      <td>66</td>\n",
       "      <td>70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.0</td>\n",
       "      <td>53</td>\n",
       "      <td>46</td>\n",
       "      <td>55</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.0</td>\n",
       "      <td>69</td>\n",
       "      <td>74</td>\n",
       "      <td>77</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1.0</td>\n",
       "      <td>47</td>\n",
       "      <td>56</td>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1.0</td>\n",
       "      <td>87</td>\n",
       "      <td>79</td>\n",
       "      <td>90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1.0</td>\n",
       "      <td>79</td>\n",
       "      <td>70</td>\n",
       "      <td>88</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1.0</td>\n",
       "      <td>69</td>\n",
       "      <td>70</td>\n",
       "      <td>73</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1.0</td>\n",
       "      <td>70</td>\n",
       "      <td>65</td>\n",
       "      <td>74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1.0</td>\n",
       "      <td>93</td>\n",
       "      <td>95</td>\n",
       "      <td>91</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1.0</td>\n",
       "      <td>79</td>\n",
       "      <td>80</td>\n",
       "      <td>73</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1.0</td>\n",
       "      <td>70</td>\n",
       "      <td>73</td>\n",
       "      <td>78</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1.0</td>\n",
       "      <td>93</td>\n",
       "      <td>89</td>\n",
       "      <td>96</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1.0</td>\n",
       "      <td>78</td>\n",
       "      <td>75</td>\n",
       "      <td>68</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1.0</td>\n",
       "      <td>81</td>\n",
       "      <td>90</td>\n",
       "      <td>93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1.0</td>\n",
       "      <td>88</td>\n",
       "      <td>92</td>\n",
       "      <td>86</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>1.0</td>\n",
       "      <td>78</td>\n",
       "      <td>83</td>\n",
       "      <td>77</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1.0</td>\n",
       "      <td>82</td>\n",
       "      <td>86</td>\n",
       "      <td>90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>1.0</td>\n",
       "      <td>86</td>\n",
       "      <td>82</td>\n",
       "      <td>89</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1.0</td>\n",
       "      <td>78</td>\n",
       "      <td>83</td>\n",
       "      <td>85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1.0</td>\n",
       "      <td>76</td>\n",
       "      <td>83</td>\n",
       "      <td>71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1.0</td>\n",
       "      <td>96</td>\n",
       "      <td>93</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    ones   0   1    2\n",
       "0    1.0  73  80   75\n",
       "1    1.0  93  88   93\n",
       "2    1.0  89  91   90\n",
       "3    1.0  96  98  100\n",
       "4    1.0  73  66   70\n",
       "5    1.0  53  46   55\n",
       "6    1.0  69  74   77\n",
       "7    1.0  47  56   60\n",
       "8    1.0  87  79   90\n",
       "9    1.0  79  70   88\n",
       "10   1.0  69  70   73\n",
       "11   1.0  70  65   74\n",
       "12   1.0  93  95   91\n",
       "13   1.0  79  80   73\n",
       "14   1.0  70  73   78\n",
       "15   1.0  93  89   96\n",
       "16   1.0  78  75   68\n",
       "17   1.0  81  90   93\n",
       "18   1.0  88  92   86\n",
       "19   1.0  78  83   77\n",
       "20   1.0  82  86   90\n",
       "21   1.0  86  82   89\n",
       "22   1.0  78  83   85\n",
       "23   1.0  76  83   71\n",
       "24   1.0  96  93   95"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "one = np.ones(len(y))\n",
    "x.insert(0,\"ones\",one,True)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1.,  73.,  80.,  75.],\n",
       "       [  1.,  93.,  88.,  93.],\n",
       "       [  1.,  89.,  91.,  90.],\n",
       "       [  1.,  96.,  98., 100.],\n",
       "       [  1.,  73.,  66.,  70.],\n",
       "       [  1.,  53.,  46.,  55.],\n",
       "       [  1.,  69.,  74.,  77.],\n",
       "       [  1.,  47.,  56.,  60.],\n",
       "       [  1.,  87.,  79.,  90.],\n",
       "       [  1.,  79.,  70.,  88.],\n",
       "       [  1.,  69.,  70.,  73.],\n",
       "       [  1.,  70.,  65.,  74.],\n",
       "       [  1.,  93.,  95.,  91.],\n",
       "       [  1.,  79.,  80.,  73.],\n",
       "       [  1.,  70.,  73.,  78.],\n",
       "       [  1.,  93.,  89.,  96.],\n",
       "       [  1.,  78.,  75.,  68.],\n",
       "       [  1.,  81.,  90.,  93.],\n",
       "       [  1.,  88.,  92.,  86.],\n",
       "       [  1.,  78.,  83.,  77.],\n",
       "       [  1.,  82.,  86.,  90.],\n",
       "       [  1.,  86.,  82.,  89.],\n",
       "       [  1.,  78.,  83.,  85.],\n",
       "       [  1.,  76.,  83.,  71.],\n",
       "       [  1.,  96.,  93.,  95.]])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array(x)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.],\n",
       "       [0.],\n",
       "       [0.],\n",
       "       [0.]])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta = np.zeros((4,1))\n",
    "theta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Repeat your implementation but for more than one variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "theta =  [[0.00826966 0.01006505 0.00979302 0.01066351 0.0077256  0.00549497\n",
      "  0.00810644 0.00625665 0.00952099 0.00892253 0.0076712  0.0076712\n",
      "  0.01001064 0.00826966 0.00805204 0.01044589 0.00799763 0.00995623\n",
      "  0.0096298  0.0086505  0.0096298  0.00952099 0.00952099 0.00810644\n",
      "  0.01044589]\n",
      " [0.60614459 0.73774177 0.7178028  0.78160749 0.56626665 0.40276713\n",
      "  0.59418121 0.45859623 0.69786383 0.65399811 0.56227886 0.56227886\n",
      "  0.73375397 0.60614459 0.59019341 0.76565632 0.58620562 0.72976618\n",
      "  0.70583942 0.63405914 0.70583942 0.69786383 0.69786383 0.59418121\n",
      "  0.76565632]\n",
      " [0.60966766 0.74202972 0.72197486 0.7861504  0.56955795 0.40510812\n",
      "  0.59763475 0.46126172 0.70192    0.65779932 0.56554697 0.56554697\n",
      "  0.73801875 0.60966766 0.59362377 0.77010652 0.5896128  0.73400777\n",
      "  0.70994195 0.63774446 0.70994195 0.70192    0.70192    0.59763475\n",
      "  0.77010652]\n",
      " [0.62923873 0.76584977 0.74515113 0.81138678 0.58784144 0.41811258\n",
      "  0.61681954 0.47606877 0.72445248 0.67891547 0.58370171 0.58370171\n",
      "  0.76171004 0.62923873 0.61267981 0.79482787 0.60854009 0.75757031\n",
      "  0.73273194 0.65821683 0.73273194 0.72445248 0.72445248 0.61681954\n",
      "  0.79482787]]\n",
      "it takes iterations =  2413\n"
     ]
    }
   ],
   "source": [
    "iterations = 100000\n",
    "m= len(y)\n",
    "\n",
    "theta_list=[]\n",
    "cost_list=[]\n",
    "\n",
    "gradiant_list=[]\n",
    "\n",
    "r=0.0000001\n",
    "\n",
    "for i in range(iterations):\n",
    "    y_pred= x @ theta \n",
    "\n",
    "    cost_multiple =((y_pred - y)**2).sum()/(2*m)\n",
    "    \n",
    "    #print(cost_multiple)\n",
    "    cost_list.append(cost_multiple)\n",
    "    \n",
    "    gradiant= x.T @ (y_pred-y)/m\n",
    "    gradiant_list.append(gradiant)\n",
    "    \n",
    "    theta = theta - r* gradiant\n",
    "    theta_list.append(theta)\n",
    "    \n",
    "    #print('theta = ', theta)\n",
    "    \n",
    "    if i > 0:\n",
    "        if abs(cost_list[i-1] - cost_list[i] < 0.0001):\n",
    "            break\n",
    "            \n",
    "        if abs(np.linalg.norm([theta_list[i]])-np.linalg.norm([theta_list[i-1]]))< 0.0001:\n",
    "            break\n",
    "        \n",
    "        if abs(np.linalg.norm([gradiant_list[i]])-np.linalg.norm([gradiant_list[i-1]])) < 0.0001:\n",
    "            break\n",
    "    \n",
    "print('theta = ', theta)\n",
    "            \n",
    "print('it takes iterations = ', i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4, 25)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.00826966 0.01006505 0.00979302 0.01066351]\n",
      " [0.0077256  0.00549497 0.00810644 0.00625665]\n",
      " [0.00952099 0.00892253 0.0076712  0.0076712 ]\n",
      " [0.01001064 0.00826966 0.00805204 0.01044589]\n",
      " [0.00799763 0.00995623 0.0096298  0.0086505 ]\n",
      " [0.0096298  0.00952099 0.00952099 0.00810644]\n",
      " [0.01044589 0.60614459 0.73774177 0.7178028 ]\n",
      " [0.78160749 0.56626665 0.40276713 0.59418121]\n",
      " [0.45859623 0.69786383 0.65399811 0.56227886]\n",
      " [0.56227886 0.73375397 0.60614459 0.59019341]\n",
      " [0.76565632 0.58620562 0.72976618 0.70583942]\n",
      " [0.63405914 0.70583942 0.69786383 0.69786383]\n",
      " [0.59418121 0.76565632 0.60966766 0.74202972]\n",
      " [0.72197486 0.7861504  0.56955795 0.40510812]\n",
      " [0.59763475 0.46126172 0.70192    0.65779932]\n",
      " [0.56554697 0.56554697 0.73801875 0.60966766]\n",
      " [0.59362377 0.77010652 0.5896128  0.73400777]\n",
      " [0.70994195 0.63774446 0.70994195 0.70192   ]\n",
      " [0.70192    0.59763475 0.77010652 0.62923873]\n",
      " [0.76584977 0.74515113 0.81138678 0.58784144]\n",
      " [0.41811258 0.61681954 0.47606877 0.72445248]\n",
      " [0.67891547 0.58370171 0.58370171 0.76171004]\n",
      " [0.62923873 0.61267981 0.79482787 0.60854009]\n",
      " [0.75757031 0.73273194 0.65821683 0.73273194]\n",
      " [0.72445248 0.72445248 0.61681954 0.79482787]]\n"
     ]
    }
   ],
   "source": [
    "theta = theta.reshape(25,4)\n",
    "print(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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6764.042367430455, 6763.864953847857, 6763.688231074394, 6763.512196405124, 6763.336847145695, 6763.1621806123085, 6762.988194131675, 6762.814885040965, 6762.642250687786, 6762.470288430125, 6762.298995636317, 6762.128369684997, 6761.95840796507, 6761.789107875663, 6761.620466826085, 6761.452482235795, 6761.285151534348, 6761.118472161371, 6760.952441566513, 6760.787057209408, 6760.622316559644, 6760.45821709671, 6760.294756309965, 6760.1319316986055, 6759.969740771609, 6759.808181047718, 6759.6472500553855, 6759.486945332743, 6759.327264427558, 6759.168204897205, 6759.009764308623, 6758.851940238278, 6758.69473027212, 6758.538132005558, 6758.382143043413, 6758.226760999886, 6758.07198349852, 6757.917808172165, 6757.764232662934, 6757.611254622179, 6757.458871710447, 6757.3070815974415, 6757.155881961998, 6757.005270492032, 6756.855244884518, 6756.705802845448, 6756.556942089793, 6756.408660341478, 6756.260955333331, 6756.1138248070665, 6755.9672665132375, 6755.821278211204, 6755.675857669101, 6755.531002663803, 6755.386710980885, 6755.242980414601, 6755.099808767836, 6754.957193852081, 6754.815133487394, 6754.67362550237, 6754.532667734107, 6754.392258028169, 6754.252394238562, 6754.113074227691, 6753.97429586633, 6753.836057033593, 6753.698355616896, 6753.561189511929, 6753.424556622623, 6753.288454861111, 6753.152882147709, 6753.017836410867, 6752.883315587158, 6752.749317621223, 6752.615840465762, 6752.48288208148, 6752.350440437077, 6752.2185135092, 6752.087099282426, 6751.956195749214, 6751.825800909891, 6751.695912772612, 6751.566529353333, 6751.437648675775, 6751.309268771398, 6751.181387679377, 6751.054003446554, 6750.927114127426, 6750.80071778411, 6750.6748124863, 6750.549396311262, 6750.4244673437815, 6750.300023676145, 6750.176063408114, 6750.052584646884, 6749.929585507063, 6749.807064110647, 6749.68501858698, 6749.563447072732, 6749.442347711872, 6749.321718655632, 6749.201558062487, 6749.081864098117, 6748.962634935396, 6748.8438687543385, 6748.725563742095, 6748.6077180929105, 6748.4903300081005, 6748.3733976960275, 6748.256919372066, 6748.1408932585755, 6748.025317584884, 6747.910190587243, 6747.795510508821, 6747.681275599656, 6747.567484116644, 6747.454134323505, 6747.341224490758, 6747.22875289569, 6747.116717822341, 6747.005117561462, 6746.893950410504, 6746.783214673579, 6746.672908661443, 6746.563030691468, 6746.453579087605, 6746.34455218038, 6746.235948306849, 6746.12776581058, 6746.020003041631, 6745.912658356516, 6745.805730118183, 6745.699216696, 6745.593116465707, 6745.48742780941, 6745.382149115555, 6745.277278778889, 6745.172815200452, 6745.068756787539, 6744.965101953687, 6744.86184911864, 6744.758996708335, 6744.656543154867, 6744.554486896473, 6744.452826377506, 6744.35156004841, 6744.2506863656945]\n"
     ]
    }
   ],
   "source": [
    "print(cost_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(cost_list);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Predict y values using the LR equation\n",
    "##### h(x)= theta_0 + theta_1 * x1 + theta_2 * x2 + theta_3 * x3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[152 185 180 196 142 101 149 115 175 164 141 141 184 152 148 192 147 183\n",
      " 177 159 177 175 175 149 192]\n"
     ]
    }
   ],
   "source": [
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = x @ theta[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([162.56713711, 196.29764471, 192.8658098 , 210.20299264,\n",
       "       149.95752419, 111.20966568, 157.55806566, 117.00528554,\n",
       "       184.01507033, 171.07841885, 151.91147602, 150.34665866,\n",
       "       199.02572577, 165.32419627, 158.46052647, 199.29894785,\n",
       "       157.54150675, 188.837854  , 189.57886539, 169.62951389,\n",
       "       184.71054471, 184.34624861, 175.98813682, 163.41164172,\n",
       "       203.1447556 ])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot loss vs. iterations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title('Cost Function J')\n",
    "plt.xlabel('No. of iterations')\n",
    "plt.ylabel('Cost')\n",
    "plt.plot(cost_list)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Use R2 score to evaluate LR equation output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8089164450909526"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import r2_score\n",
    "r2_score(y, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bonus\n",
    "## LR Using sklearn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Single Variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "x=df.iloc[: , :-1].values\n",
    "y=df.iloc[: , -1].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(13, 1)"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2.9000001 ],\n",
       "       [6.69999981],\n",
       "       [4.9000001 ],\n",
       "       [7.9000001 ],\n",
       "       [9.80000019],\n",
       "       [6.9000001 ],\n",
       "       [6.0999999 ],\n",
       "       [6.19999981],\n",
       "       [6.        ],\n",
       "       [5.0999999 ],\n",
       "       [4.69999981],\n",
       "       [4.4000001 ],\n",
       "       [5.80000019]])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(13,)"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Build a LR model usin linearmodel.LinearRegression() from sklearn library"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import linear_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "regr = linear_model.LinearRegression()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Train the model (fit the model to the training data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "regr.fit(x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Predict y values using the trained model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = regr.predict(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3.44824549, 6.08745623, 4.83730388, 6.92089146, 8.240497  ,\n",
       "       6.22636227, 5.67073878, 5.74019163, 5.60128593, 4.97620959,\n",
       "       4.69839784, 4.49003928, 5.46238022])"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4.        , 7.4000001 , 5.        , 7.19999981, 7.9000001 ,\n",
       "       6.0999999 , 6.        , 5.80000019, 5.19999981, 4.19999981,\n",
       "       4.        , 4.4000001 , 5.19999981])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot model output (fitted line) with the original data (scatter plot of X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x19a725751c8>]"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x , y)\n",
    "plt.plot(x,y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Use R2 score to evaluate model output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8213156778363777"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2_score(y, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Repeat for Mulivariate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "x=df2.iloc[:, :-1].values\n",
    "y=df2.iloc[: , -1].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 73,  80,  75],\n",
       "       [ 93,  88,  93],\n",
       "       [ 89,  91,  90],\n",
       "       [ 96,  98, 100],\n",
       "       [ 73,  66,  70],\n",
       "       [ 53,  46,  55],\n",
       "       [ 69,  74,  77],\n",
       "       [ 47,  56,  60],\n",
       "       [ 87,  79,  90],\n",
       "       [ 79,  70,  88],\n",
       "       [ 69,  70,  73],\n",
       "       [ 70,  65,  74],\n",
       "       [ 93,  95,  91],\n",
       "       [ 79,  80,  73],\n",
       "       [ 70,  73,  78],\n",
       "       [ 93,  89,  96],\n",
       "       [ 78,  75,  68],\n",
       "       [ 81,  90,  93],\n",
       "       [ 88,  92,  86],\n",
       "       [ 78,  83,  77],\n",
       "       [ 82,  86,  90],\n",
       "       [ 86,  82,  89],\n",
       "       [ 78,  83,  85],\n",
       "       [ 76,  83,  71],\n",
       "       [ 96,  93,  95]], dtype=int64)"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([152, 185, 180, 196, 142, 101, 149, 115, 175, 164, 141, 141, 184,\n",
       "       152, 148, 192, 147, 183, 177, 159, 177, 175, 175, 149, 192],\n",
       "      dtype=int64)"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "regr.fit(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = regr.predict(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([152.60720439, 185.08011472, 181.78158547, 199.74522647,\n",
       "       139.1747207 , 103.69391793, 150.2632274 , 112.82069728,\n",
       "       174.55948394, 164.49442094, 143.42337551, 142.23416416,\n",
       "       186.54285759, 152.40794527, 151.24409108, 189.12496613,\n",
       "       143.50219218, 181.89389361, 177.29838914, 158.34934019,\n",
       "       176.57742415, 174.66365778, 167.68889392, 150.63279846,\n",
       "       191.1954116 ])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.98966157894484"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2_score(y, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ------------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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