Linear Regresion.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "third-highland",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from statistics import mean\n",
    "from matplotlib import style\n",
    "import random\n",
    "\n",
    "style.use('fivethirtyeight')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "large-outside",
   "metadata": {},
   "source": [
    "### Input values and plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "alpine-flush",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = [1, 2, 3, 4, 5, 6]\n",
    "y = [5, 4, 6, 5, 6, 7]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "governing-holmes",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2273d2b0a60>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "immune-nirvana",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array(x, dtype=np.float64)\n",
    "y = np.array(y, dtype=np.float64)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fundamental-treatment",
   "metadata": {},
   "source": [
    "### slope and y-intercept fn\n",
    "y = mx + c; m = slope and c = y-intercept"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "consecutive-weekly",
   "metadata": {},
   "outputs": [],
   "source": [
    "def slope(x, y):\n",
    "    m = (sum((x - mean(x)) * (y - mean(y)))) / sum((x - mean(x))**2)\n",
    "    \n",
    "#     m = ((mean(x) * mean(y)) - mean(x*y)) / ((mean(x)**2) - mean(x**2))\n",
    "    return m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "rocky-scene",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.42857142857142855"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = slope(x, y)\n",
    "m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "going-virtue",
   "metadata": {},
   "outputs": [],
   "source": [
    "def y_intercept(x, y, m):\n",
    "    return (mean(y) - m * mean(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "hourly-booking",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.0"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = y_intercept(x, y, m)\n",
    "c"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "canadian-employee",
   "metadata": {},
   "source": [
    "### Plotting the regression line or the line of best fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "original-request",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_regression_line(x, y, m, c):\n",
    "    regression_line = []\n",
    "    for i in x:\n",
    "        regression_line.append(m*i+c)\n",
    "    plt.scatter(x, y)\n",
    "    plt.plot(regression_line)\n",
    "    plt.show()\n",
    "    return regression_line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "accompanied-slave",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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2U3T7KKmaRgHvXDZi03kDKurFQ2ekrxtWx6rwiwEyDgRqB3s8j86qzU8QExMTcerUKWzcuBH5+fn47LPPkJGRgfnz5zftk5KSgocffrhp+bHHHoNcLkdiYiIuXbqEzMxMvPnmm0hMTOQLnHqtwUo3vPOAL/42qg7vPODbbW9YjWYBO65UIXZvCV45rRcNniFKKd4Z74NvHvbHQ0FsEu0IWz2Pzq7NK5+YmBjs3LkTqampSEtLQ1BQEFauXNksfEpKSlBQUNC07O3tjU8//RTLli3DhAkToFarkZSUhMWLF3fPWRARBEFAZlEt1mbrkacX79UJkLvgxdFKPDncC+69uFeH7K9dX6+TkJCAhIQEi9vT09NbrIuIiMAXX3zR+cqIqN3+VVyLlGw9ztwW79VRuUnw7Cglngn3gheHTFMPwO92I3JgOWX1SMnW4+ubdaLbZVJgYZgCfxylgK8H59WhnoPhQ+SAtJUNWJejx+eF4pO5uUiA32o8sTxKhQFeDB3qeRg+RA7khyoTNpzVY6e2GhZGTePhwXd7dYar+UE49VwMHyIHcKfOjD+fNyDjshG1JvF9xveTYU2sCjH+7rYtjqgTGD5EPVhVgxl/u1SFty4YoLfQqxPl54Y1cSr8vL+Hjasj6jyGD1EPVG8S8P7VKrx+zoDSGvHJ3Iap7k7m9vBg9umQ42H4EPUgZkHA3vwa/OmMHoUG8ftr/TxdsCJKhSc0nnB1YeiQY2L4EPUAgiDg8A91SMnW40K5eK+O2l2C5yKVWBCmgNyVoUOOjeFDZGcnS+uw5rQex27Vi26XSyV4JsILz45UQi1jgyg5B4YPkZ1cvtOAtTl6HPhevFfHVQL8boQXXhitRF9P9uqQc2H4ENnYzVoJNh25g7/nVcPSfMCPDpXj5RgVglX8EyXnxFc2kY3crjVh4zkD3r3sgQahWnSfXwyQYVWsCqP92KtDzo3hQ9TNDA1m/PWCEVsuGGFsFAC0HCzwE383vBLrjZ/142Ru1DswfIi6SZ1JwPbvqrDxnAG6OvFenVC1K1bFqDBlEHt1qHdh+BBZmcksYHd+DV49o8d1o3ivTpCXFC9FK/F4iCek7NWhXojhQ2QlgiDgi+t3J3O7XCE+mZuvzAW/61+L5fcPgQd7dagXY/gQWcG/S+qQclqPk2XivTperhIkjVRgcYQCt4quMXio12P4EHVBbnkDUk9X4ssfxCdzc3MBnhrhhWWjlfCX3+3VuWXLAol6KIYPUScU6Bvx6hk99uTXiG6XAJgVIsdL0SoMVvLPjOg/8a+CqANuVZuQds6A965UodFCh+jkgR5YFaNChC8ncyOyhOFD1A6V9Wb8JdeIrZeMqLaQOvcFumN1rArxgezVIWoLw4eoFTWNArZdNmJTrgF36sRDJ9zHFatjvTEpSMZeHaJ2YvgQiWg0C9iVV40NZwz4oVq8V2ewQoqXY1R4LFgOF4YOUYcwfIjuIQgCMotqsS5HD22leK+Ov4cLXoxS4nfDveAuZegQdUabk4OsX78earW62c/w4cMt7l9UVNRif7VajcOHD1u1cCJr+7q4FhP3leF3WeWiwaNyk+DlaCXOPBaIBWEKBg9RF7Trykej0WDfvn1Ny1Jp23OL7N27FyNHjmxa9vHx6UR5RN3v7O16pGTrkVUs3qsjkwILQhX4Y6QCfh6cV4fIGtoVPq6urggMDOzQL/b19e3wMUS2lFfZgHU5BnxWKN6r4yIB5gzzxIooJYIUvENNZE3t+osqLCxEaGgo3N3dERcXh1deeQVDhgxp9Zi5c+eitrYWISEhSExMxLRp06xRL1GXFVeZ8PpZPT7QVsNkoVfn14M9kByjwgg1e3WIukOb4RMXF4etW7dCo9Hg9u3bSEtLw6RJk3DixAn4+vq22F+hUGDt2rWIj4+Hq6srDhw4gHnz5iE9PR2zZs3qlpMgao87dWa8ed6Aty8bUSs+gA0/6+uO1XHeiPPnZG5E3UlSUVFhaSZfUUajEVFRUVi6dCkWL17crmOef/55HD9+HMeOHWt1P61W25FSiNqlxgT8vdgV799wg9EkPkgg1MuMpCH1GKs2g6OmiaxDo9FY3NbhG9kKhQKhoaHIz89v9zGxsbHYuXNnm/u1VmhbtFptl453BDzHjmkwC/jgajU2nNXjVo34ZG4hKimSY1SYNsR2vTp8Hp0Dz7FrOhw+tbW10Gq1+NnPftbuY3Jzczn4gGzGLAj4tKAG63L0KDCI31/rK3fBimgVntB4wo2TuRHZXJvhk5ycjMmTJyMoKKjpM5/q6mrMnj0bAJCSkoLs7GxkZmYCAHbt2gU3NzdERkbCxcUFBw8exLZt27BmzZpuPREiQRDwVfHdeXXOlzeI7uPtLsEfRymxMNwLnq5ttrkRUTdpM3yKi4sxf/586HQ69OnTB3Fxcfjyyy8xaNAgAEBJSQkKCgqaHbNx40Zcv34dUqkUISEh2LJlCwcbULc6VVqPlOxKHC0Rn8xNLpVgUbgX/jBKCbWMoUNkb22Gz/bt21vdnp6e3mx5zpw5mDNnTteqImqn7yoasDZbj/3f14pul0qAJ4d74sUoFfp5skGUqKdg5xw5pOvGRqw/Y8Dfr1XDbGG85iND5Xg5WoUQb77MiXoa/lWSQ9HVmvDGeQO2Xa5CvfgANkwcIMOqGBWi+rBXh6inYviQQzA2mPHXi0ZsuWCEoUH8Uie2jxtWx3ljfD9O5kbU0zF8qEerMwl470oV0s4ZcLtW/FJnuLcrVsWq8KtBHpzMjchBMHyoRzKZBezJr8GrZ/T43ijeqzPAU4oV0UrMHuYJV/bqEDkUhg/1KIIAHLxeg9RsPS7dEZ/MzVfmguciFZgfqoCHK0OHyBExfKjHOH6rDityZTinLxfd7uUqQWKEAotHKuDtzl4dIkfG8CG7u1DegLXZlTh0ow5Ay14cNxfg9yO88MJoJQLk7NUhcgYMH7KbQkMjXj2jx55rNRAbvyYBMDNEjpXRKgxR8qVK5Ez4F002V1pjQto5A967UoUGC706CUEyrIr1xkhfTuZG5IwYPmQzlfVm/OWCEekXjahqFO/ViVSa8Nr9gRjXl706RM6M4UPdrrZRwDvfGbHpvAF36sRDJ1ztilfiVAiuuYHhDB4ip8fwoW7TaBbw//Kq8doZA36oFu/VGaSQ4uUYFR4bKofURQJOZkvUOzB8yOoEQcA/imqxLkePq5XivTp9PFzwwmglfj/CCzIpe3WIehuGD1nVNzfrkHK6Etm3xSdzU7pJsGSkAs9EKKB0Y68OUW/F8CGrOHu7HqnZenxVXCe63d0FmB/mhecjlfDzYK8OUW/H8KEuuVbZiD+d0eOTghrR7S4SYPYwT6yIUmKggi83IrqL7wbUKTerTXj9rB7vX62GycJkbr8a5IHkWBVC1ezVIaLmGD7UIRV1ZryZa8Dbl6pQYyF17u/rjtWx3vhJACdzIyJxDB9ql+pGMzIuVeHPuQZU1ltoEPV1w+o4FR7sL+O8OkTUKoYPtarBLODDq9XYcFaPkhrx78IJVkqRHKPC9KFyuDB0iKgdGD4kyiwI+LywButy9LimF28QDZS7YHmUCnOHe8KNk7kRUQcwfKgZQRCQVVyHlGw9zunEe3VU7hL8cZQSC8O84MVeHSLqBIYPNTldVo+U05U4UlIvut1DCjwdpsDSSCV8ZAwdIuo8hg/hSkUD1mbrse/7WtHtUgkwV+OJF6NU6O/FBlEi6ro2//u6fv16qNXqZj/Dhw9v9ZiLFy9iypQp6Nu3L8LCwrBhwwYIgoVmELKbG8ZGLD56B/d9VmoxeGYMkePbGQF486c+DB4ispp2XfloNBrs27evaVkqtfwmpNfrMWPGDIwbNw5fffUVtFotkpKS4OnpiSVLlnS94l6oyNCAdTkG5N+WIbi4HMkxSgxWdr5xs7zWhDfOG7HtOyPqxMcSYEJ/GV6JVSG6D3t1qP2s/Vol59Wu8HF1dUVgYGC7fuGePXtQU1OD9PR0yOVyhIeH4+rVq9i6dSsWL17M/o8OKjI0YPohHQoMJgBSZOtrcLqsHp8l+HX4j9rYYEb6RSP+csEIfYP4lWhMHzesjlXhgf4eVqieehNrvlbJ+bXrU+PCwkKEhoYiMjISTz31FAoLCy3ue/LkSdx3332Qy+VN6yZOnIibN2+iqKioywX3NutyDP/7x/x/CgwmrMsxtPt31JsEZFwyIvrjW/jTGYNo8Gi8XbFjgi/+51f+DB7qFGu8Vqn3aPPKJy4uDlu3boVGo8Ht27eRlpaGSZMm4cSJE/D19W2xf2lpKfr3799snb+/f9O2IUOGWHwsbRdnEuvq8T1R/m0ZgJa3OfN1Rmi1ulaPNQvAwTIp3i5yQ3Gd+P8zAtzNWDioAVMDq+HaoEdenjWq7hpnfB7/kzOeY1deq47KGZ/H/9SVc9RoNBa3tRk+Dz30ULPluLg4REVFYdeuXVi8eHGnixLTWqFt0Wq1XTq+pwouLke2vuU3Rgf7KaDRDBI9RhAE/PNGHVKzK3Hxjvhkbj4yCZ6LVGJ+qAJy155zK9RZn8d7Oes5dua16sic9Xm8V3eeY4eHWisUCoSGhiI/P190e0BAAMrKypqt+3E5ICCgEyX2bskxSpwuq292O2OoUorkGKXo/idu3W0QPX5LvFfH01WCxHAFloxSwNudvTpkPR19rVLv1uF3n9raWmi1WosDEMaMGYPjx4+jtvb/hu5mZWWhX79+GDx4cOcr7aUGK93wWYIfZgbLEettwsxguegHuBfLG/D4YR0mH7gtGjyuEmBBqBfOPBqI5FgVg4esrr2vVSKgHVc+ycnJmDx5MoKCgpo+86mursbs2bMBACkpKcjOzkZmZiYA4LHHHsOGDRuQmJiIZcuWIS8vD2+++SZefPFFjnTrpMFKN7zzgC+0Wl2L2xeFhkasP6PH7ms1sNRJNTNYjpXRKgxVsaeYuldrr1Wie7X5blRcXIz58+dDp9OhT58+iIuLw5dffolBg+6+sEpKSlBQUNC0v7e3Nz799FMsW7YMEyZMgFqtRlJSktU/H+rtSmtM2HjOgP++UoUG8S+bxqQgGZJjVIj0Y68OEfUsbYbP9u3bW92enp7eYl1ERAS++OKLzldFFunrzdhy0Yi/XjCiqlH8WmdsgDteiVXhp31lNq6OiKh9eB/GQdQ2Ctj1gyt2nLqF8jrxS50wtSteiVVh8kAP3uIkoh6N4dPDmcwC/n6tGuvPGHCjyh1Ay+AZqJBiZbQKvwmWQ8p5dYjIATB8eihBELD/+1qsy9HjuwrxXp0+Hi5YNlqJeSO8IJMydIjIcTB8eqAjN+uQkl2J02Xik7kpXCVYPFKBpJEKKDmZGxE5IIZPD3JOV4/UbD3+54c60e1uEgHzwxR4frQSfTw4vQEROS6GTw+Qr2/En3L02FvQ8qtJAMBFAjwe4onH1TqMHxVk4+qIiKyP4WNHJdUmvH7WgPevVsHCqGlMGeSBVTEqhPm4Qau9bdsCiYi6CcPHDirqzNh8wYD0i1WoMYmnzrhAd6yJU2FMAHt1iMj5MHxsqLrRjHcuV+HP5w2oqBcPnZG+dydz+8UAGXt1iMhpMXxsoNEs4ENtNTac1eNmtXiD6BClFMkxKjwyVA4Xhg4ROTmGTzcyCwIyC+/26uTpxXt1AuUueDFKibkaL7izV4eIegmGTzcQBAH/Kr47r85ZnXivjspNgj+MUmJRuBe82KtDRL0Mw8fKssvqkZKtxzc3xXt1PKTAwjAFlo5SwJe9OkTUSzF8rORqRQPW5ujxj6Ja0e1SCfBbjSdejFJhgBdDh4h6N4ZPF90wNmLDWQN25lXDbKFXZ/oQOV6OUULjzRkdiYgAhk+nldeasOm8Ee98Z0SdSXyfn/eX4ZUYFWL8OZkbEdG9GD4dZGww42+XqrA51wB9g/ilTnSfu706P+/vYePqiIgcA8OnnepNAnZcrULaOQNKa8R7dTTerkiOUeHhwZzMjYioNQyfNpgFAR/n1+BPOXoUGcXvr/X3dMGKaBXmDPOEKydzIyJqE8PHAkEQ8OWNu/PqXLwj3iCqdpfg+Ugl5ocpIHdl6BARtRfDR8SJW3cbRI/fqhfd7ukqwTPhXlgyUgm1jA2iREQdxfC5x8Xyu706B6+L9+q4SoDfj/DCstFK9PVkrw4RUWcxfAAUGRqx/oweH12rgYVWHcwMlmNltApDVfwnIyLqql79TlpWY8LGcwZsv1KFBvEBbHhogAyrYlWI9GOvDhGRtXT4A4tNmzZBrVbjhRdesLhPUVER1Gp1i5/Dhw93qVhr0deb8eoZPaI/voW3L4sHzxh/d+z7ZR/smdSHwUNEZGUduvI5deoU3nvvPURERLRr/71792LkyJFNyz4+Ph2rzspqGwVsv1KFN84ZoKsTv9QJU7tiVawKvxzIXh0iou7S7vCprKzEggULsGXLFmzYsKFdx/j6+iIwMLDTxVmLySzg79eqsf6MATeqxHt1grykWBmtxKwQT0jZq0NE1K3afdtt6dKlmDZtGsaPH9/uXz537lwMGzYMCQkJ+PzzzztVYFcIgoD9RTX46eelSDpaIRo8fjIXrB/jjexHAzFH48XgISKyAUlFRYWlAV5NduzYge3bt+Pw4cNwc3PD1KlTER4ejrS0NNH9dToddu3ahfj4eLi6uuLAgQN44403kJ6ejlmzZll8HK1W2/kz+Q/ZlS74a6Ebcg3iQ6I9pQJ+O6ABc/o3wqtXD7sgIuoeGo3G4rY233a1Wi1SU1Nx8OBBuLm1b0oAPz8/LFmypGk5Ojoa5eXleOutt1oNn9YKbU+dGo0G53T1WJutx+EfxCdzc3cBngr1wvORSvjLHatX58dzdGY8R+fAc3QO3XmObYbPyZMnodPpEB8f37TOZDLh2LFj2L59O4qLiyGTydp8oNjYWOzcubNr1bbieo0Er/2rHHsLakS3SwA8PswTK6KUGKzkpQ4RkT21+S48depUREdHN1uXlJSEkJAQPPfcc3B3b98w5Nzc3G4bfLA2uxJv5nrAJIgHz5RBHkiOUSHch5O5ERH1BG2Gz489Ovfy9PSEj48PwsPDAQApKSnIzs5GZmYmAGDXrl1wc3NDZGQkXFxccPDgQWzbtg1r1qyx+gkAgI/MBSah5UCB+wLdsSZWhbGBbV+ZERGR7Vjl/lNJSQkKCgqardu4cSOuX78OqVSKkJAQbNmypdXPe7pifqgCm89VoLT+7uC9kb53J3P7xQAZe3WIiHqgToXP/v37my2np6c3W54zZw7mzJnT+ao6yMNVgqcHNeCDW55IjlHhkaFyuDB0iIh6LKf55H1qoAlLxgXCXcrQISLq6ZxmMhqpBAweIiIH4TThQ0REjoPhQ0RENsfwISIim2P4EBGRzTF8iIjI5hg+RERkcwwfIiKyOYYPERHZHMOHiIhsjuFDREQ2x/AhIiKbY/gQEZHNMXyIiMjmGD5ERGRzDB8iIrI5hg8REdkcw4eIiGyO4UNERDbH8CEiIptj+BARkc0xfIiIyOYYPkREZHMdDp9NmzZBrVbjhRdeaHW/ixcvYsqUKejbty/CwsKwYcMGCILQ6UKJiMh5uHZk51OnTuG9995DREREq/vp9XrMmDED48aNw1dffQWtVoukpCR4enpiyZIlXSqYiIgcX7uvfCorK7FgwQJs2bIFarW61X337NmDmpoapKenIzw8HNOmTcMf/vAHbN26lVc/JKrI0IAFX5dj0XkZFnxdjiJDg71LIqJu1O7wWbp0KaZNm4bx48e3ue/Jkydx3333QS6XN62bOHEibt68iaKios5VSk6ryNCA6Yd02JNfg2y9FHvyazD9kI4BROTE2hU+O3bsQH5+PpKTk9v1S0tLS+Hv799s3Y/LpaWlHSyRnN26HAMKDKZm6woMJqzLMdipIiLqbm1+5qPVapGamoqDBw/Czc2tW4vRarV2Pd4ROOM55t+WAZC2XK8zQqvV2b4gG3DG5/E/8RydQ1fOUaPRWNzWZvicPHkSOp0O8fHxTetMJhOOHTuG7du3o7i4GDKZrNkxAQEBKCsra7bux+WAgIBOFdoWrVbbpeMdgbOeY3BxObL1NS3X+ymg0QyyQ0Xdy1mfx3vxHJ1Dd55jm+EzdepUREdHN1uXlJSEkJAQPPfcc3B3d29xzJgxY7BmzRrU1tbCw8MDAJCVlYV+/fph8ODBViqdnEVyjBKny+qb3XobqpQiOUZpx6qIqDu1+ZmPWq1GeHh4sx9PT0/4+PggPDwcEokEKSkpePjhh5uOeeyxxyCXy5GYmIhLly4hMzMTb775JhITEyGRSLr1hMjxDFa64bMEP8wMliPW24SZwXJ8luCHwcruvc1LRPbToT4fS0pKSlBQUNC07O3tjU8//RTLli3DhAkToFarkZSUhMWLF1vj4cgJDVa64Z0HfKHV6pzyVhsRNdep8Nm/f3+z5fT09Bb7RERE4IsvvuhcVURE5NT43W5ERGRzDB8iIrI5hg8REdmcpKKigl+2RkRENsUrHyIisjmGDxER2RzDh4iIbI7hQ0RENsfwISIim3OK8Nm2bRsiIyMRGBiIBx54AMeOHbN3SVbz73//G48//jjCwsKgVquxc+dOe5dkVZs2bcKECRMwcOBAhISEYNasWbh06ZK9y7Kqd955B+PGjcPAgQMxcOBAPPTQQzh06JC9y+pWmzZtglqtxgsvvGDvUqxm/fr1UKvVzX6GDx9u77KsrqSkBIsWLUJISAgCAwMxduxYHD161OqP4/Dh88knn2DFihV4/vnn8c0332DMmDGYOXMmrl+/bu/SrKKqqgrh4eF47bXXms0M6yyOHj2K//qv/8KhQ4eQmZkJV1dXTJ8+HXfu3LF3aVbTv39/pKSk4Ouvv0ZWVhbGjx+PJ554AhcuXLB3ad3i1KlTeO+99xAREWHvUqxOo9HgypUrTT/O9B9dAKioqEBCQgIEQcDu3bvx7bff4vXXX28xOag1OHyfz8SJExEREYHNmzc3rYuJicG0adOwevVqO1ZmfQMGDMDrr7+OJ554wt6ldBuj0YhBgwZh586d+OUvf2nvcrrNkCFDsHr1asybN8/epVhVZWUlHnjgAWzevBkbNmxAeHg40tLS7F2WVaxfvx6ZmZk4fvy4vUvpNqmpqfj3v/9tkytzh77yqa+vx9mzZ/Hggw82W//ggw/i22+/tVNV1BVGoxFmsxlqtdrepXQLk8mEvXv3oqqqCmPGjLF3OVa3dOlSTJs2DePHj7d3Kd2isLAQoaGhiIyMxFNPPYXCwkJ7l2RV+/fvR2xsLObNm4dhw4bh/vvvR0ZGBgTB+tcoVplSwV50Oh1MJlOLS0J/f3+UlpbaqSrqihUrVmDUqFFO98Z88eJFTJo0CbW1tfDy8sKHH37odLelduzYgfz8fGRkZNi7lG4RFxeHrVu3QqPR4Pbt20hLS8OkSZNw4sQJ+Pr62rs8qygsLMS7776LxMRELF26FLm5uVi+fDkAYOHChVZ9LIcOH3IuK1euxIkTJ3Dw4EFIpVJ7l2NVGo0GR44cgV6vx+eff45nnnkG+/btQ3h4uL1LswqtVovU1FQcPHgQbm7OOQngQw891Gw5Li4OUVFR2LVrl9PMVWY2mxEdHd30kcXo0aORn5+Pbdu2MXzu5efnB6lUirKysmbry8rKEBAQYKeqqDNeeuklfPLJJ/jHP/6BIUOG2Lscq3N3d0dwcDAAICoqCjk5Odi6dSu2bNli58qs4+TJk9DpdIiPj29aZzKZcOzYMWzfvh3FxcWQyWR2rND6FAoFQkNDkZ+fb+9SrCYwMBAjRoxotm748OG4ceOG1R/LoT/zcXd3R1RUFLKyspqtz8rKwtixY+1UFXXU8uXLsXfvXmRmZjrl0FUxZrMZ9fX19i7DaqZOnYpjx47hyJEjTT/R0dF49NFHceTIEbi7u9u7RKurra2FVqtFYGCgvUuxmvj4eOTl5TVbl5eXh4EDB1r9sRz6ygcAkpKS8PTTTyM2NhZjx47F9u3bUVJS4jSjiIxGY9P/rMxmM27cuIHz58/Dx8enW14QtrZs2TJ89NFH+PDDD6FWq3Hr1i0AgJeXFxQKhZ2rs441a9Zg0qRJGDBgAIxGIz7++GMcPXoUu3fvtndpVvNj38u9PD094ePj4zS3FpOTkzF58mQEBQU1feZTXV2N2bNn27s0q0lMTMSkSZOwceNGPPLIIzh//jwyMjKwatUqqz+Www+1Bu42mb711lu4desWwsLC8Oqrr+KnP/2pvcuyiiNHjuDXv/51i/WzZ88Wnb7c0Vga1bZ8+XK89NJLti2mmzzzzDM4cuQISktLoVKpEBERgWeffRYTJ060d2ndaurUqU411Pqpp57CsWPHoNPp0KdPH8TFxeHll19GaGiovUuzqkOHDiE1NRV5eXkICgrCggUL8PTTT0MikVj1cZwifIiIyLE49Gc+RETkmBg+RERkcwwfIiKyOYYPERHZHMOHiIhsjuFDREQ2x/AhIiKbY/gQEZHNMXyIiMjm/j/0zyYfo4ALuQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4.428571428571429, 4.857142857142857, 5.285714285714286, 5.714285714285714, 6.142857142857142, 6.571428571428571]\n"
     ]
    }
   ],
   "source": [
    "regression_line = plot_regression_line(x, y, m, c)\n",
    "\n",
    "print(regression_line)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "parliamentary-geology",
   "metadata": {},
   "source": [
    "### Predicting for random value of x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "specific-stocks",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7.428571428571429\n"
     ]
    },
    {
     "data": {
      "image/png": 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a2tou30EJgmBK7Wbfn/Trr+NaccMVgO5nKxWKRgiCwmzHqW52QOb3LvhCqf9znF/7t+MP97XCz/EWvi837j7765gCfTeu5tafx9Sa9WZcw8LCul1vMIA6OjowceJEvPbaawCABx54ABUVFcjLy+sygHrKULHdEQShV/uTfv15XENqfkRpg+7lbUL8PBEWNrzX92+p7qT9eUwBy4+rJfT3MbVWlh5XgwEUGBiI0aNHay0bNWoUrl692uU+AQEBqKur01p273ZAQEBP6iTSkRrphS/rWrVOF93ndecD896y5+6klhxXop8zGEAxMTEoL9c+r1BeXo5hw4Z1uU90dDQ2bdqElpYWuLnd+e+wsLAQgwcPRnBwcC9LJroj2MsZh2L9kHFBBXmTGkFmmK2laFEj9XwD/mbH3UktMa5E+hgMoMTERMyePRvZ2dlYsGABLl68iNzcXGzcuLFzm7S0NJSWluLw4cMAgKeffhqZmZlITEzEqlWrUF5eju3bt2PNmjWcAUdmFezljN0zfHt9P4a6kw5yc0TGZPvpTmqucSXqjsEAioyMxL59+5Ceno6srCwMHToUGzZswLJlyzq3kcvlqKys7Lzt7e2NgwcPYtWqVZg5cyakUimSkpKQnJxsmUdB1AvsTkokDqMuxRMbG4vY2Ngu1+fk5Ogsi4iIwPHjx3teGZGFNbdrkP1NA3b8u5HdSYlEwGvBkV06dbUFq84pUaXSnd7G7qREfYMBRHZF3qTG+i/qcbCK3UmJxMbfMrILhrqTDvZwxJYp7E5K1JcYQGTzvlG04pUiJS7o7U4KJIwdgNTIgRjI7qREfYoBRDZL1daBzQa6k26fJsXEQS59XxwRMYDINhnbndTJkafbiMTCACKb8t/GdqztpjvpU3e7kw5hgzgi0TGAyCa0dWjw1qVGbP5ahaZ23fNtwzwlyI6RInaYaRcOJSLLYQCR1Ttf24qUopu4dFP3wqFODkCSlXcnJbJVDCCyWvbQnZTIljGAyOpoNBp8VNmMDSX1qG3WvYaOt4sD0id54/lRHnDkd3qI+i0GEFmVioZ2rCxWorDmtt71z4S64/XJ3vB35yQDov6OAURW4bZagzfLVNjaTXfSbVOlmGFid1IiEg8DiPq9M9duY2WxfXYnJbJlDCDqtwx1J50+2BVbp3rbdHdSIlvGAKJ+p0OjwT52JyWyeQwg6lfYnZTIfjCAqF9oau/A1m9UXXYnDb/bnTSG3UmJbAYDiER36moLVhYrIWvsujtp0v2ecOaFQ4lsCgOIRMPupET2zeCJ9M2bN0MqlWr9jBo1qsvtZTKZzvZSqRSnTp0ya+FkvdQdGuz+TyOiD1zXGz6DPRyxZ6YvPnjMj+FDZMOM+u0OCwvDkSNHOm9LJIa/Zf7RRx/h/vvv77zt4+PTg/LI1nTXndTRAVg2ht1JieyFUQHk5OSEwMBAk+7Y19fX5H3IdrE7KRH9klH/ZlZVVWHMmDEYP348XnjhBVRVVRnc5/nnn8fIkSMRGxuLjz/+uLd1khU7ImtGzIFa7LqkGz5ezg7YMsUbp/+PP8OHyM44KJVKfVey7/Tpp5+isbERYWFhuHHjBrKysiAIAs6dOwdfX1+d7RUKBQoKChATEwMnJyccO3YMW7duRU5ODuLj47stRhCE3j0a6leutTggu8IZn/+o/432o37tWBnShgDXbl+CRGSlwsLCul1vMIB+qbGxERMmTEBKSgqSk5ON2mflypUoLi5GUVGRKYcyiSAIBh8sma4n48rupN3ja9X8OKaWYelxNXmKkaenJ8aMGYOKigqj94mKisK+fftMPRRZIXYnJSJjmRxALS0tEAQBDz/8sNH7lJWVcUKCjWN3UiIylcEASk1NxZw5czB06NDOz4Camprw7LPPAgDS0tJQWlqKw4cPAwAKCgrg7OyM8ePHw9HRESdOnEBeXh42bdpk0QdC4mB3UiLqKYMBVFNTg2XLlkGhUGDQoEGYNGkSPv30UwwfPhwAIJfLUVlZqbVPdnY2qqurIZFIEBoaip07dxqcgEDWh91Jiag3DAZQfn5+t+tzcnK0bj/33HN47rnnelcV9WvsTkpE5sDrnJBJ2J2UiMyFAURGYXdSIjI3BhB1q0MD7L1yi91JicjsGEDUpW+VbfhdmSu+alDqXc/upETUGwwg0qHdnVR3Bhu7kxKROTCASAu7kxJRX2EAEQB2JyWivse/JnZO3aFB/ne38KfSBjS06Zlk4NKBrQ8OwlPBbpxkQERmxQCyY8Z0J33Wuw4TR7iLUB0R2ToGkB0ypTupINT1fYFEZBcYQHbmiKwZa8/V44cm3UkGXs4O+GPkQCSMGQAJJxkQkYUxgOzEfxvbsfZcPY5Xt+hd/1SwG7ZMkWLIAF44lIj6BgPIxrE7KRH1VwwgG8bupETUnzGAbBC7kxKRNWAA2RB2JyUia8IAshHsTkpE1oYBZOWM6U66daoUj7A7KRH1MwwgK3ZWfhsritidlIisEwPIChnqTvpwkAu2TZOyOykR9WtGzb/dvHkzpFKp1s+oUaO63efSpUt44oknEBQUhLFjxyIzMxMajb45WWQsjUaDvVduYdKB63rDZ5CbI9562AeH5wxi+BBRv2f0O6CwsDAcOXKk87ZE0vWH2Q0NDZg/fz6mTZuG06dPQxAEJCUlwcPDAy+//HLvKrZiMlUbMi6ocK1JjcEeEqRGeiHYy7ig+FbZhleKlCi+3qp3PbuT9n/3nv+KG64IqfnRpOefyBYZHUBOTk4IDAw0atv9+/ejubkZOTk5cHd3R3h4OK5cuYJdu3YhOTnZLi/rL1O1Ie6kApWqn2YKfFnXikOxft3+EWpu1yD7m4a73Ul117M7qXXQfv4lKG1oNur5J7JlRv+7XFVVhTFjxmD8+PF44YUXUFVV1eW2JSUlmDp1Ktzdf7qM/6xZs3Dt2jXIZLJeFWytMi6otMIHACpVamRcUHW5z6mrLZh66Dq2XtQNH3eJAzZFDcRn8wIYPlagJ88/ka0z6h3QpEmTsGvXLoSFheHGjRvIysrC7Nmzce7cOfj6+upsX1tbiyFDhmgt8/f371w3YsQIvccRBMHE8s27vyVV3HAFoHvaskLRCEFQaC270QpsrXDBqRv6n54HfdRYHdqKX7ndQtX3lqhWW38eV2thyvNPPcPXqWX0ZlzDwsK6XW9UAD3++ONatydNmoQJEyagoKAAycnJPS7ulwwV2x1BEHq1v6WF1PyI0gbddtchfp4ICxsO4GfdSb/S3510sIcjtkyR9ml30v4+rtbCmOefeo6vU8uw9Lj2aBq2p6cnxowZg4qKCr3rAwICUFen3cjs3u2AgICeHNLqpUZ64cu6Vq3TMPd53ZmIANzpTrqiSIlSPd1JHQAkjB2A1MiBGOjCSQbWyNDzT2SPevTXrKWlBYIgdDkpITo6GsXFxWhp+an3TGFhIQYPHozg4OCeVWrlgr2ccSjWD4tC3PFwkAsWhbjjUKwf/Nwk2FCixMxP6vSGzwN+zjj9pD/eiJEyfKzYz5//KG915/PPCQhkz4x6B5Samoo5c+Zg6NChnZ8BNTU14dlnnwUApKWlobS0FIcPHwYAPP3008jMzERiYiJWrVqF8vJybN++HWvWrLHLGXD3BHs5Y/eMnz4zu9OdVKG3O6mn093upGMHwIndSW3CvedfEBQ87UYEIwOopqYGy5Ytg0KhwKBBgzBp0iR8+umnGD78zi+RXC5HZWVl5/be3t44ePAgVq1ahZkzZ0IqlSIpKcmsnxdZs+rGdqxhd1IisnNGBVB+fn6363NycnSWRURE4Pjx4z2ryka1d2iQc7kRW75S4Ra7kxKRneO14PpId91JJQ5AMruTEpGdYQBZGLuTEhHpxwCyEGO6k6ZN8sZidiclIjvFALIAg91JQ9yREe2NAHYnJSI7xgAyo9tqDXaUqZDN7qRERAYxgMyE3UmJiEzDAOoldiclIuoZBlAPaTQavC804dUv63Hztu78Nj9XR7we7Y34UHe7vvoDEVFXGEA9wO6kRES9xwAygaHupGPvdiedygZxREQGMYCM9L8/tGBlsRJVKt3pbe4SB6yd4IXECE+4SHi6jYjIGAwgA+RNamwoqceBSt1mYgAwe6gr3oiRYoQXh5KIyBT8q9mFzu6kpf2nOykRkS1hAOnB7qRERJbHAPqZxrYO/PmrBrx1+RY69Fw59AE/Z2yfJsXEQS59XxwRkY1hAN11pztpPbuTEhH1EbsPIEPdSZ+82530V+xOSkRkVnYbQG0dGrx1qRGbv1ahqYvupFkx3pgzzF2E6oiIbJ9dBhC7kxIRic/kv7Dbtm2DVCrF6tWru9xGJpNBKpXq/Jw6dapXxfaW8nYHVhQpMftond7wifZ3wedPBSBtsjfDh4jIwkx6B3T+/Hm8++67iIiIMGr7jz76CPfff3/nbR8fH9OqMxN2JyUi6n+MDqD6+nokJCRg586dyMzMNGofX19fBAYG9rg4czDYnTTUHRmT2Z2UiKivGX2eKSUlBfPmzcP06dONvvPnn38eI0eORGxsLD7++OMeFdhTt9UaZH3dgKmHrusNn9CBEhyK9UPudF+GDxGRCIx6B7Rnzx5UVFQgNzfXqDv19PTEn/70J8TExMDJyQnHjh3D0qVLkZOTg/j4+F4VbAx2JyUi6v8clEqlnu/8/0QQBMyZMwcnTpxAWFgYAGDu3LkIDw9HVlaW0QdauXIliouLUVRU1O2xekPZBmyvdMHRWv25OslbjbWhrRjh0e1DJiIiM7iXGV0xGED79u1DUlISJJKfTlOp1Wo4ODjA0dERNTU1cHU13P+moKAAK1asgFwuN7J042k0Gmw7W4md1W7sTmpmgiAYfBGRaTim5scxtQxLj6vBU3Bz587FxIkTtZYlJSUhNDQUK1asgIuLcddFKysrs9iEhMSzSvyt3BWAbviwOykRUf9kMIDufYfn5zw8PODj44Pw8HAAQFpaGkpLS3H48GEAd97tODs7Y/z48XB0dMSJEyeQl5eHTZs2mf0BAMAzIe74W3mT1jJ2JyUi6t/MciUEuVyOyspKrWXZ2dmorq6GRCJBaGgodu7cabEJCDN/5YZY/3acrHNid1IiIith8DMga1F8ScDuOj+8GjWQ3UnNiOfWzY9jan4cU8sQ/TMgazHIBch/xFfsMoiIyEj8ZJ6IiETBACIiIlEwgIiISBQMICIiEgUDiIiIRMEAIiIiUTCAiIhIFAwgIiISBQOIiIhEwQAiIiJRMICIiEgUDCAiIhIFA4iIiETBACIiIlEwgIiISBQMICIiEgUDiIiIRMEAIiIiUTCAiIhIFCYH0LZt2yCVSrF69eput7t06RKeeOIJBAUFYezYscjMzIRGo+lxoUREZFucTNn4/PnzePfddxEREdHtdg0NDZg/fz6mTZuG06dPQxAEJCUlwcPDAy+//HKvCiYiIttg9Dug+vp6JCQkYOfOnZBKpd1uu3//fjQ3NyMnJwfh4eGYN28e/vCHP2DXrl18F2QlZKo2JHz2I5ZfdEXCZz9CpmoTuyQisjFGB1BKSgrmzZuH6dOnG9y2pKQEU6dOhbu7e+eyWbNm4dq1a5DJZD2rlPqMTNWGuJMK7K9oRmmDBPsrmhF3UsEQIiKzMiqA9uzZg4qKCqSmphp1p7W1tfD399dadu92bW2tiSVSX8u4oEKlSq21rFKlRsYFlUgVEZEtMvgZkCAISE9Px4kTJ+Ds7GzRYgRBEHV/uqPihisAie5yRSMEQdH3BdkgvlbNj2NqGb0Z17CwsG7XGwygkpISKBQKxMTEdC5Tq9UoKipCfn4+ampq4OrqqrVPQEAA6urqtJbdux0QENDjYrsjCEKv9qefhNT8iNKGZt3lfp4ICxsuQkW2ha9V8+OYWoalx9VgAM2dOxcTJ07UWpaUlITQ0FCsWLECLi4uOvtER0dj06ZNaGlpgZubGwCgsLAQgwcPRnBwsJlKJ0tJjfTCl3WtWqfh7vOSIDXSS8SqiMjWGPwMSCqVIjw8XOvHw8MDPj4+CA8Ph4ODA9LS0vDUU0917vP000/D3d0diYmJuHz5Mg4fPozt27cjMTERDg4OFn1A1HvBXs44FOuHRSHuiPJWY1GIOw7F+iHYy7KnYInIvpj0PaCuyOVyVFZWdt729vbGwYMHsWrVKsycORNSqRRJSUlITk42x+GoDwR7OWP3DF8IgoKn3YjIInoUQEePHtW6nZOTo7NNREQEjh8/3rOqiIjI5vFacEREJAoGEBERiYIBREREonBQKpW8OBsREfU5vgMiIiJRMICIiEgUDCAiIhIFA4iIiETBACIiIlHYRADl5eVh/PjxCAwMxIwZM1BUVCR2SVZr27ZtmDlzJoYNG4bQ0FDEx8fj8uXLYpdlU7Zt2wapVIrVq1eLXYrVk8vlWL58OUJDQxEYGIgpU6bg7NmzYpdltdRqNTIyMjr/no4fPx4ZGRlob2+3yPGsPoAOHDiAdevWYeXKlfj8888RHR2NRYsWobq6WuzSrNLZs2fx29/+FidPnsThw4fh5OSEuLg43Lx5U+zSbML58+fx7rvvIiIiQuxSrJ5SqURsbCw0Gg0+/PBDfPHFF3jjjTd0mmGS8bZv3468vDxkZmaipKQEW7Zswe7du7Ft2zaLHM/qvwc0a9YsREREYMeOHZ3LIiMjMW/ePLz22msiVmYbGhsbMXz4cOzbtw+//vWvxS7HqtXX12PGjBnYsWMHMjMzER4ejqysLLHLslrp6en417/+hZMnT4pdis2Ij4+Hj48P3nrrrc5ly5cvx82bN/HBBx+Y/XhW/Q6otbUVX3/9NR599FGt5Y8++ii++OILkaqyLY2Njejo6IBUKhW7FKuXkpKCefPmYfr06WKXYhOOHj2KqKgoLF26FCNHjsRDDz2E3NxcaDRW/T+1qGJiYnD27FlcuXIFAPDtt9/izJkzePzxxy1yPLO0YxCLQqGAWq3Wecvt7++P2tpakaqyLevWrcO4ceMQHR0tdilWbc+ePaioqEBubq7YpdiMqqoqvPPOO0hMTERKSgrKysqwdu1aAMCLL74ocnXWKSUlBY2NjZgyZQokEgna29uxatUqLFu2zCLHs+oAIsvasGEDzp07hxMnTkAikYhdjtUSBAHp6ek4ceIEnJ3Z1M9cOjo6MHHixM5T7Q888AAqKiqQl5fHAOqhAwcO4O9//zvy8vIwZswYlJWVYd26dRg+fDgWL15s9uNZdQD5+flBIpGgrq5Oa3ldXR0CAgJEqso2rF+/HgcOHMAnn3yCESNGiF2OVSspKYFCoUBMTEznMrVajaKiIuTn56Ompgaurq4iVmidAgMDMXr0aK1lo0aNwtWrV0WqyPq9+uqrSE5OxsKFCwHc6etWXV2Nv/zlLwygX3JxccGECRNQWFiIuLi4zuWFhYVaLcLJNGvXrsXBgwfxySefYNSoUWKXY/Xmzp2LiRMnai1LSkpCaGgoVqxYARcXF5Eqs24xMTEoLy/XWlZeXo5hw4aJVJH1a2pq0jnbIZFI0NHRYZHjWXUAAXd+kV966SVERUVhypQpyM/Ph1wux9KlS8UuzSqtWrUKH3zwAd5//31IpVJcv34dADBgwAB4enqKXJ11kkqlOpM4PDw84OPjg/DwcHGKsgGJiYmYPXs2srOzsWDBAly8eBG5ubnYuHGj2KVZrTlz5mD79u0IDg7GmDFjcPHiRfz1r3/Fb37zG4scz+qnYQN3voj65ptv4vr16xg7diz+/Oc/48EHHxS7LKvU1Wy3tWvXYv369X1bjA2bO3cup2GbwcmTJ5Geno7y8nIMHToUCQkJeOmll+Dg4CB2aVZJpVLh9ddfx5EjR3Djxg0EBgZi4cKFWLNmDdzc3Mx+PJsIICIisj5W/T0gIiKyXgwgIiISBQOIiIhEwQAiIiJRMICIiEgUDCAiIhIFA4iIiETBACIiIlEwgIiISBT/H+S3HQ2h1g+4AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "predict_x = 8\n",
    "predict_y = m*predict_x+c\n",
    "print(predict_y)\n",
    "\n",
    "plt.scatter(x, y)\n",
    "plt.scatter(predict_x, predict_y, color='green')\n",
    "plt.plot(regression_line)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "theoretical-lunch",
   "metadata": {},
   "source": [
    "### Figuring out the mean square error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "lonely-baker",
   "metadata": {},
   "outputs": [],
   "source": [
    "# returns r square value\n",
    "def coefficient_of_determination(y, reg_line):\n",
    "    return 1 - (sum((reg_line - y)**2) / sum([(mean(y) - i)**2 for i in y]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "binary-registration",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5844155844155845"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r_squared = coefficient_of_determination(y, regression_line)\n",
    "r_squared"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "spare-gender",
   "metadata": {},
   "source": [
    "### Working the fn on randomly generated dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "ordered-underwear",
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_dataset(n, variance, step=2, correlation=0):\n",
    "    y = []\n",
    "    val = 1\n",
    "    for i in range(n):\n",
    "        curr = val + random.randrange(-variance, variance)\n",
    "        y.append(curr)\n",
    "        if correlation and correlation == 1:\n",
    "            val += step\n",
    "        elif correlation and correlation == -1:\n",
    "            val -= step\n",
    "            \n",
    "    x = [i for i in range(n)]\n",
    "        \n",
    "    return np.array(x, dtype=np.float64), np.array(y, dtype=np.float64)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "sublime-approach",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.0772148859543815 -8.811764705882347\n",
      "0.6410450860761758\n",
      "[-8.811764705882347, -6.734549819927965, -4.6573349339735834, -2.580120048019202, -0.5029051620648204, 1.5743097238895611, 3.6515246098439427, 5.728739495798324, 7.805954381752706, 9.883169267707089, 11.960384153661469, 14.037599039615849, 16.114813925570232, 18.192028811524615, 20.269243697478995, 22.346458583433375, 24.423673469387758, 26.50088835534214, 28.578103241296525, 30.6553181272509, 32.732533013205284, 34.80974789915967, 36.886962785114044, 38.96417767106843, 41.04139255702281, 43.11860744297719, 45.19582232893158, 47.27303721488595, 49.350252100840336, 51.42746698679472, 53.504681872749096, 55.581896758703486, 57.65911164465786, 59.73632653061224, 61.81354141656663, 63.890756302521005, 65.96797118847539, 68.04518607442978, 70.12240096038414, 72.19961584633853, 74.27683073229292, 76.35404561824728, 78.43126050420167, 80.50847539015606, 82.58569027611043, 84.66290516206482, 86.74012004801921, 88.8173349339736, 90.89454981992796, 92.97176470588235]\n"
     ]
    }
   ],
   "source": [
    "x, y = create_dataset(n=50, variance=40, step=2, correlation=1)\n",
    "\n",
    "m = slope(x, y)\n",
    "\n",
    "c = y_intercept(x, y, m)\n",
    "\n",
    "line = plot_regression_line(x, y, m, c)\n",
    "\n",
    "r_sq = coefficient_of_determination(y, line)\n",
    "\n",
    "print(m, c)\n",
    "print(r_sq)\n",
    "print(line)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.6"
  }
 },
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