Linear_Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "\n",
    "\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## First, let's get the files (Dataset for linear regression from Kaggle) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_train = pd.read_csv('data/random-linear-regression/train.csv')\n",
    "data_test = pd.read_csv('data/random-linear-regression/test.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### It is always a good idea to check the contents of the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "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>x</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>24.0</td>\n",
       "      <td>21.549452</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>50.0</td>\n",
       "      <td>47.464463</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>15.0</td>\n",
       "      <td>17.218656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>38.0</td>\n",
       "      <td>36.586398</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>87.0</td>\n",
       "      <td>87.288984</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      x          y\n",
       "0  24.0  21.549452\n",
       "1  50.0  47.464463\n",
       "2  15.0  17.218656\n",
       "3  38.0  36.586398\n",
       "4  87.0  87.288984"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                 x           y\n",
      "count   700.000000  699.000000\n",
      "mean     54.985939   49.939869\n",
      "std     134.681703   29.109217\n",
      "min       0.000000   -3.839981\n",
      "25%      25.000000   24.929968\n",
      "50%      49.000000   48.973020\n",
      "75%      75.000000   74.929911\n",
      "max    3530.157369  108.871618\n"
     ]
    }
   ],
   "source": [
    "print(data_train.describe())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11cde7ba8>"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a8b8cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_train.boxplot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Seems we have a missing value on y row, and a big outlier on x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x11a8b89b0>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x11d36ba20>]],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ce5a1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_train.hist()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### and our missing value ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "x    0\n",
       "y    1\n",
       "dtype: int64"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_train.isna().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kinda hard to see anything with this big guy there. Let's get rid of him..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_train=data_train[data_train.x<3500]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                x           y\n",
      "count  699.000000  699.000000\n",
      "mean    50.014306   49.939869\n",
      "std     28.954560   29.109217\n",
      "min      0.000000   -3.839981\n",
      "25%     25.000000   24.929968\n",
      "50%     49.000000   48.973020\n",
      "75%     75.000000   74.929911\n",
      "max    100.000000  108.871618\n"
     ]
    }
   ],
   "source": [
    "print(data_train.describe())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11c97ae80>"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d797e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_train.boxplot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x11c95a4a8>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x11d3961d0>]],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d583748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_train.hist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "x    0\n",
       "y    0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_train.isna().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Seems that our outlier didn't have a y value either, so we are better now.  Let's check the correlation between the X and Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9953399077212528"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_train['x'].corr(data_train['y'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_____________"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                x           y\n",
      "count  300.000000  300.000000\n",
      "mean    50.936667   51.205051\n",
      "std     28.504286   29.071481\n",
      "min      0.000000   -3.467884\n",
      "25%     27.000000   25.676502\n",
      "50%     53.000000   52.170557\n",
      "75%     73.000000   74.303007\n",
      "max    100.000000  105.591837\n"
     ]
    }
   ],
   "source": [
    "print(data_test.describe())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x11e352b70>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x11d760588>]],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAEICAYAAABPgw/pAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAAE3VJREFUeJzt3X+sZOV93/H3x/wQaJ0GE5zbLbhdt0aNkFdeW1eEyKl0TepobUeFSK5bl8SgoGwaxWrSbNIQR2rtOpHgD0IdZLlaBNlNtTV27aC1cNqGUkYIqcGFGrxgnILpumW7ZmPxw778QbPk2z/mrLVcz+ydmXvnztxn3i9pdGfOnHPne8597kdnnnOec1JVSJK2vzfMugBJ0uYw0CWpEQa6JDXCQJekRhjoktQIA12SGmGgS1IjDHRJaoSBLkmNMNDnQJK/k+SFJO/qXv+NJH+RZGXGpUlTkeQ3k3xxzbQ/SPKpWdXUgjj0fz4k+UXgnwPLwD3A0ar6jdlWJU1Hkp3AM8ClVfVSknOB/wu8r6oenW1125d76HOiqu6g38AfBnYCvzPbiqTpqaoTwIPAP+wm7QW+Y5hvjIE+X+4A3g7cXlWvzroYacoOAT/XPf854N/NsJYm2OUyJ5K8EXgceAB4H7C7ql6YbVXS9CS5ADgB/D3gz4Arqup/z7aq7c1AnxNJ7gTeWFX/KMkB4KKq+tCs65KmKckdwI/T7265etb1bHd2ucyBJNfQ70P85W7SrwPvSnLd7KqStsQhYDd2t2wK99AlzUySvwl8A/jrVfXdWdez3bmHLmkmkryB/rfRuw3zzXHurAuQtHiS7ACeB75Fv7tRm8AuF0lqhF0uktSILe1yueSSS2rXrl0D33vllVfYsWPHVpYzl9wOfWfbDo8++uh3qurNW1zSRM7W5tdaxL/9oq3zpOs7apvf0kDftWsXjzzyyMD3er0eKysrW1nOXHI79J1tOyT51tZWM7mztfm1FvFvv2jrPOn6jtrm7XKRpEYY6JLUCANdkhphoEtSIwx0SWqEgS5JjTDQJakRBrokNcJAl6RGeLVFTd2um7489jIH9y7OcPBFN0n7OHbzB6ZQyfbnHrokNcJAl6RGGOiS1AgDXZIaYaBLUiMMdElqhIEuSY0w0CWpEQa6JDXCQJekRjj0f84cPf4yN4w5FNph0JLAPXRJasa6gZ7kgiRfSfJ4kieTfKKbfjDJ/0ryWPfYM/1yJUnDjNLl8ipwdVWtJjkPeCjJf+ze+82q+sL0ypMkjWrdPfTqW+1entc9aqpVSXMgyTlJvprk3u71W5M8nOSZJJ9Lcv6sa5TONNJB0STnAI8CbwM+XVUPJ/ll4PeS/EvgfuCmqnp1wLL7gH0AS0tL9Hq9gZ+xuro69L1FsnQh7N99aqxlbj98ZOzP2X3pD4+9zKTGXR+Ym/bwq8BTwF/rXt8C3FZVdyf5t8CNwGdmVZy01kiBXlWvAXuSXATck+TtwG8D3wbOBw4AvwX86wHLHujeZ3l5uVZWVgZ+Rq/XY9h7i+T2w0e49ej0Tz46dt3K1D/jtHHP2oH+DS5m2R6SXAZ8APg94NeTBLga+CfdLIeAj2Oga46MdZZLVb0EPADsraoTXXfMq8AfAldOo0BpRv4N8C+Av+pe/wjwUlWd/rrxHHDpLAqThll3VzDJm4G/rKqXklwIvBe4JcnOqjrR7blcCzwx5VqlLZHkZ4CTVfVokpUJlh+pm3GtUbqZjh5/edxytrR7bVyrq6vs3/3a2MvNQXfcRKbdlTjKd/udwKGuH/0NwOer6t4k/7UL+wCPAf90alVKW+vdwD9I8n7gAvp96J8CLkpybreXfhlwfNDCo3YzrjVKt+Mk3Vdb2b02rl6vx60PvTL2cvO8Tmcz7a7ldQO9qr4GvHPA9KunUpE0Y1X12/SPEdHtof9GVV2X5D8AHwTuBq4Hxj8aLU2RI0Wl0f0W/QOkz9DvU79zxvVIr+O1XKSzqKoe0OueP4sH/zXH3EOXpEYY6JLUCANdkhphoEtSIwx0SWqEgS5JjTDQJakRBrokNcJAl6RGGOiS1AgDXZIaYaBLUiMMdElqhIEuSY3Y1pfP3TXJ3Vtu/sAUKpGk2XMPXZIasW6gJ7kgyVeSPJ7kySSf6Ka/NcnDSZ5J8rkk50+/XEnSMKPsob8KXF1V7wD2AHuTXAXcAtxWVW8DXgRunF6ZkqT1rBvo1bfavTyvexRwNfCFbvoh4NqpVChJGslIB0WTnAM8CrwN+DTwTeClqjrVzfIccOmQZfcB+wCWlpbo9XoDP2N1dXXoe8Ps331q/ZnWuP3w+Ddq333pD4+9zNHjL4+9DMDShZOt17jG3dYbMcn6TNIepEU3UqBX1WvAniQXAfcAPzbqB1TVAeAAwPLycq2srAycr9frMey9YW6Y4CyXSRy7bmXsZSatbf/uU9x6dPonH02yTpOaZFsc3Ltj7PYgLbqxznKpqpeAB4CfAC5Kcjp5LgOOb3JtkqQxjHKWy5u7PXOSXAi8F3iKfrB/sJvtemD8vgxJ0qYZ5bv9TuBQ14/+BuDzVXVvkq8Ddyf5XeCrwJ1TrFOSvs9BhYOtG+hV9TXgnQOmPwtcOY2iJEnj29ZD/zU593Ck9jj0X5Ia4R66pIH8Frf9uIcuSY0w0CWpEXa5jGCSr56StNXcQ5ekRhjoktQIA12SGmGgS1IjDHRJaoSBLkmNMNAlqREGurRGkguSfCXJ40meTPKJbvpbkzyc5Jkkn0ty/qxrlc5koEs/6FXg6qp6B7AH2JvkKuAW4LaqehvwInDjDGuUfoCBLq1Rfavdy/O6RwFXA1/oph8Crp1BedJQBro0QJJzkjwGnATuA74JvFRVp7pZngMunVV90iBey0UaoKpeA/Z099O9B/ixUZdNsg/YB7C0tESv1xtpudXV1XXn3b/71FnfH2TUz5/FZ62urrJ/92tjf84kJt0Om2mUv/FGrBvoSd4C/BGwRP9r54Gq+lSSjwO/CPxFN+vHqupPplWoNAtV9VKSB4CfAC5Kcm63l34ZcHzIMgeAAwDLy8u1srIy0mf1ej3Wm/eGSa5Rft1onz+Lz+r1etz60Ctjf84kJt0Om2mUv/FGjNLlcgrYX1VXAFcBv5Lkiu6926pqT/cwzNWEJG/u9sxJciHwXuAp4AHgg91s1wNHZlOhNNgoN4k+AZzonn8vyVPYd6i27QQOJTmH/k7P56vq3iRfB+5O8rvAV4E7Z1mktNZYfehJdgHvBB4G3g18NMlHgEfo78W/uNkFSlutqr5Gv52vnf4scOXWVySNZuRAT/JG4IvAr1XVd5N8Bvgk/X71TwK3Ar8wYLmRDhBNcrBgkoM2827pwvldr608uDbtg0dSi0YK9CTn0Q/zw1X1xwBV9fwZ798B3Dto2VEPEE1ysGCSgzbzbv/uU9x6dD5PPtrKg2sH9+6Y6sEjqUXrHhRNEvp9hU9V1e+fMX3nGbP9LPDE5pcnSRrVKLuC7wZ+HjjaDbQA+Bjw4SR76He5HAN+aSoVSpJGMspZLg8BGfCWpylKep1xb6jeP76yNV2Mk97s/djNH9i0z9q/+9TQLshJPmcth/5LUiMMdElqhIEuSY0w0CWpEfN5wrOkTTPpwUBtP3MT6EePv9zkQCFJ2ip2uUhSIwx0SWqEgS5JjTDQJakRBrokNcJAl6RGGOiS1AgDXZIaYaBLUiMMdElqhIEuSY0w0CWpEQa6JDVi3UBP8pYkDyT5epInk/xqN/3iJPclebr7+abplytJGmaUPfRTwP6qugK4CviVJFcANwH3V9XlwP3da0nSjKwb6FV1oqr+R/f8e8BTwKXANcChbrZDwLXTKlKStL6xbnCRZBfwTuBhYKmqTnRvfRtYGrLMPmAfwNLSEr1eb+DvXroQ9u8+NU45TZrn7XD74SMTLbd/9/jLrK6uDm0rkgYbOdCTvBH4IvBrVfXdJN9/r6oqSQ1arqoOAAcAlpeXa2VlZeDvv/3wEW49Ojc3UJqZ/btPuR2Ag3t3MKytSFtpO93Cb6SzXJKcRz/MD1fVH3eTn0+ys3t/J3ByOiVKkkYxylkuAe4Enqqq3z/jrS8B13fPrwcm+z4uSdoUo3y3fzfw88DRJI910z4G3Ax8PsmNwLeAD02nREnSKNYN9Kp6CMiQt39qc8uRJE3KkaKS1AgDXZIaYaBLUiMMdElqhIEuSY0w0CWpEQa6tIaXjNZ2ZaBLP8hLRmtbMtClNbxktLYrL+snncU0Lxm91iiXDJ7XSytPap4vFz0NZ1vfzbhctIEuDTHtS0av1ev11r1k8A3b6FKuo1i0y0WfbX2PXbey4d9vl4s0gJeM1nZkoEtreMlobVeL811HGp2XjNa2ZKBLa3jJaG1XdrlIUiMMdElqhIEuSY0Y5SbRdyU5meSJM6Z9PMnxJI91j/dPt0xJ0npG2UM/COwdMP22qtrTPf5kc8uSJI1r3UCvqgeBF7agFknSBmzktMWPJvkI8Aj9K9O9OGimUa9rsWjXdBjG7dA3ynVNJL3epIH+GeCTQHU/bwV+YdCMo17X4vbDRxbqmg7DLNq1LYY5uHfHutc1kfR6E53lUlXPV9VrVfVXwB3AlZtbliRpXBMF+ukLFHV+Fnhi2LySpK2x7nf7JJ8FVoBLkjwH/CtgJcke+l0ux4BfmmKNkqQRrBvoVfXhAZPvnEItkqQNcKSoJDXCQJekRhjoktQIA12SGmGgS1IjHJIozcium778utf7d5/ihjXTpHG4hy5JjTDQJakRBrokNcJAl6RGGOiS1AgDXZIaYaBLUiMMdElqhIEuSY0w0CWpEQa6JDXCQJekRqwb6EnuSnIyyRNnTLs4yX1Jnu5+vmm6ZUqS1jPKHvpBYO+aaTcB91fV5cD93WtJ0gytG+hV9SDwwprJ1wCHuueHgGs3uS5J0pgmvR76UlWd6J5/G1gaNmOSfcA+gKWlJXq93uBfeGH/etCLzu3Qt7q6OrStSBpswze4qKpKUmd5/wBwAGB5eblWVlYGznf74SPcetT7bezffcrtABzcu4NhbUXSYJOe5fJ8kp0A3c+Tm1eSJGkSkwb6l4Dru+fXA0c2pxxJ0qRGOW3xs8B/A/5ukueS3AjcDLw3ydPA3+9eS5JmaN3O2qr68JC3fmqTa5HmRpK7gJ8BTlbV27tpFwOfA3YBx4APVdWLs6pRWsuRotJgB3H8hbYZA10awPEX2o48P04a3UjjL0Yde7F2vMEijkFYtHU+2/puxrgLA12awNnGX4w69uKGm778uteLOAZh0db5bOt77LqVDf9+u1yk0Tn+QnPNQJdG5/gLzTUDXRrA8Rfajhan80oag+MvtB25hy5JjTDQJakRBrokNcJAl6RGGOiS1AgDXZIaYaBLUiMMdElqhIEuSY0w0CWpERsa+p/kGPA94DXgVFUtb0ZRkqTxbca1XN5TVd/ZhN8jSdoAu1wkqREbDfQC/jTJo91ttyRJM7LRLpefrKrjSX4UuC/JN7qb637fqPdXXLR7Cw7jduhbXV3dlHssSotkQ4FeVce7nyeT3ANcCTy4Zp6R7q94++EjC3VvwWEW7R6Lwxzcu4NhbUXSYBN3uSTZkeSHTj8Hfhp4YrMKkySNZyO7gkvAPUlO/55/X1X/aVOqkiSNbeJAr6pngXdsYi2SpA3wtEVJaoSBLkmNMNAlqREGuiQ1wkCXpEYY6JLUCANdkhphoEtSIwx0SWqEgS5JjTDQJakRBrokNcJAl6RGGOiS1AgDXZIaYaBLUiMMdElqhIEuSY0w0CWpERsK9CR7k/x5kmeS3LRZRUnzzHaveTVxoCc5B/g08D7gCuDDSa7YrMKkeWS71zzbyB76lcAzVfVsVf0/4G7gms0pS5pbtnvNrXM3sOylwP854/VzwI+vnSnJPmBf93I1yZ8P+X2XAN/ZQD1N+GduBwDec8tZt8Pf2spa1li33Y/R5l9nEf/2i7bOZ1vf3HLWRUdq8xsJ9JFU1QHgwHrzJXmkqpanXc+8czv0beftMGqbX2s7r/OkFm2dp72+G+lyOQ685YzXl3XTpJbZ7jW3NhLo/x24PMlbk5wP/GPgS5tTljS3bPeaWxN3uVTVqSQfBf4zcA5wV1U9uYFaxv6K2ii3Q99cbocptPszzeU6T9mirfNU1zdVNc3fL0naIo4UlaRGGOiS1IiZB/oiD6NOcizJ0SSPJXmkm3ZxkvuSPN39fNOs65yGJHclOZnkiTOmDVz39P1B10a+luRds6t8Ohbh/2AR2vus2/VMA91h1AC8p6r2nHFu6k3A/VV1OXB/97pFB4G9a6YNW/f3AZd3j33AZ7aoxi2xYP8Hrbf3g8ywXc96D91h1D/oGuBQ9/wQcO0Ma5maqnoQeGHN5GHrfg3wR9X3Z8BFSXZuTaVbYpH/D5pq77Nu17MO9EHDqC+dUS2zUMCfJnm0Gy4OsFRVJ7rn3waWZlPaTAxb99bbSevrd9qitvcta9dTH/qvs/rJqjqe5EeB+5J848w3q6qSLOR5pYu87g1b+PY+7XWc9R76Qg+jrqrj3c+TwD30v3o/f/prV/fz5Owq3HLD1r31dtL6+gEL3d63rF3POtAXdhh1kh1Jfuj0c+CngSfor//13WzXA0dmU+FMDFv3LwEf6c4KuAp4+YyvsC1o/v9gwdv71rXrqprpA3g/8D+BbwK/M+t6tnC9/zbwePd48vS6Az9C/0j408B/AS6eda1TWv/PAieAv6Tfd3jjsHUHQv8skG8CR4HlWdc/he3R9P/BorT3Wbdrh/5LUiNm3eUiSdokBrokNcJAl6RGGOiS1AgDXZIaYaBLUiMMdElqxP8HSqtT44LeDDYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11e370b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_test.hist()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The objective is to 'guess' the value of a dependent variable Y based on values of the independent variable X.\n",
    "\n",
    "\n",
    "\n",
    "The Linear Regression Formula is:\n",
    "\n",
    "$\n",
    "\\begin{equation*}\n",
    "Y = \\hat{\\alpha }+ \\hat{\\beta} X\n",
    "\\end{equation*}\n",
    "$\n",
    "\n",
    "where,\n",
    "\n",
    "$X$ = Independent Variable\n",
    "\n",
    "$Y$ = Dependent Variable\n",
    "\n",
    "$\\hat{\\alpha}$ = the intercept \n",
    "\n",
    "$\\hat{\\beta}$ = The slope of the line \n",
    "\n",
    "\n",
    "\n",
    "\n",
    "**Formulas:**\n",
    "\n",
    "\n",
    "\n",
    "$\n",
    "\\begin{equation*}\n",
    "\\hat{\\alpha} = \\overline{y} -\\hat{\\beta} \\, \\overline{x}\n",
    "\\end{equation*}\n",
    "$\n",
    "\n",
    "\n",
    "$\n",
    "\\begin{align}\n",
    "    \\hat{\\beta} = \\frac{ \\sum_{i=1}^{n}(x_i - \\overline{x})(y_i - \\overline{y})}{\\sum_{i=1}^{n}(x_i- \\overline{x})^2}\n",
    "\\end{align}\n",
    "$\n",
    "\n",
    "\n",
    "where $n$ is the number of rows of data on data_train\n",
    "\n",
    "\n",
    "$\\overline{x}$ = average $x$\n",
    "\n",
    "\n",
    "\n",
    "$\\overline{y}$   = average $y$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [],
   "source": [
    "def beta(x,y,avg_x,avg_y):\n",
    "\n",
    "    num=sum((x-avg_x)*(y-avg_y))\n",
    "    den=sum((x-avg_x)**2)\n",
    "    return float(num)/float(den)\n",
    "\n",
    "def alfa(x,y,avg_x,avg_y):\n",
    "    \n",
    "    \n",
    "    return avg_y - (beta(x,y,avg_x,avg_y)*avg_x)\n",
    "    \n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "50.01430615164521"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_train['x'].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [],
   "source": [
    "x=data_train['x']\n",
    "y=data_train['y']\n",
    "avg_x=data_train['x'].mean()\n",
    "avg_y=data_train['y'].mean()\n",
    "\n",
    "\n",
    "x_test=data_test['x']\n",
    "y_test=data_test['y']\n",
    "\n",
    "\n",
    "y_predicted= alfa(x,y,avg_x,avg_y) + beta(x,y,avg_x,avg_y)*x_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    76.943276\n",
       "1    20.906519\n",
       "2    21.907175\n",
       "3    19.905862\n",
       "4    35.916364\n",
       "Name: x, dtype: float64"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_predicted.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    79.775152\n",
       "1    23.177279\n",
       "2    25.609262\n",
       "3    17.857388\n",
       "4    41.849864\n",
       "Name: y, dtype: float64"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_test.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### They seem close enough. Let's plot the points along with the predicted points and the line ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d9d6b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "\n",
    "plt.figure(figsize=(20,10))\n",
    "# vamos mostrar os pontos atuais de nossa tabela\n",
    "plt.scatter(x, y, color='blue')\n",
    "\n",
    "# vamos mostrar os pontos previstos\n",
    "plt.scatter(x_test, y_predicted, color='green')\n",
    "\n",
    "# vamos mostrar a reta\n",
    "plt.plot(x_test, y_predicted, color='red')\n",
    "\n",
    "\n",
    "plt.title('Linear Regression', fontsize=16)\n",
    "plt.xlabel('x', fontsize=13)\n",
    "plt.ylabel('y', fontsize=13)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median Absolute Error: 2.074114513023469\n",
      "R2 Score: 0.9888014444327563\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import median_absolute_error, r2_score\n",
    "\n",
    "print(\"Median Absolute Error: \"+str(median_absolute_error(y_test, y_predicted)))\n",
    "print(\"R2 Score: \"+str(r2_score(y_test, y_predicted)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Let's compare with the sklearn implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import linear_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "regr = linear_model.LinearRegression()\n",
    "\n",
    "regr.fit(x.values.reshape(-1, 1), y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_sklearn_predicted= regr.predict(x_test.values.reshape(-1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median Absolute Error: 2.074114513023501\n",
      "R2 Score: 0.9888014444327563\n"
     ]
    }
   ],
   "source": [
    "print(\"Median Absolute Error: \"+str(median_absolute_error(y_test, y_sklearn_predicted)))\n",
    "print(\"R2 Score: \"+str(r2_score(y_test, y_sklearn_predicted)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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