2021f_Lab04_kNN_SLR.ipynb

{
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   "cell_type": "markdown",
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   "source": [
    "<div class='heading'>\n",
    "    <div style='float:left;'><h1>CPSC 4300/6300: Applied Data Science</h1></div>\n",
    "    <img style=\"float: right; padding-right: 10px; width: 65px\" src=\"https://bsethwalker.github.io/assets/img/clemson_paw.png\"> </div>\n",
    "\n",
    "\n",
    "## Week 4: k-NN and Simple Linear Regression\n",
    "\n",
    "**Clemson University**<br>\n",
    "**Fall 2021**<br>\n",
    "**Instructor(s):** Nina Hubig <br>\n",
    "**Author(s):** Brandon Walker\n",
    "\n",
    "\n",
    "---\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
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       "    border-left: 5px solid #522D80; \n",
       "    padding: 0.5em;\n",
       "}\n",
       "\n",
       "div.exercise-r {\n",
       "    background-color: #fce8e8;\n",
       "    border-color: #E9967A; \t\n",
       "    border-left: 5px solid #800080; \n",
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       "\n",
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       "header {\n",
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     "execution_count": 1,
     "metadata": {},
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    }
   ],
   "source": [
    "## RUN THIS CELL TO GET THE RIGHT FORMATTING \n",
    "import requests\n",
    "from IPython.core.display import HTML\n",
    "styles = requests.get(\"https://bsethwalker.github.io/assets/css/cpsc6300.css\").text\n",
    "HTML(styles)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Learning Goals\n",
    "\n",
    "By the end of this lab, you should be able to:\n",
    "* Review `numpy` including 2-D arrays and understand array reshaping\n",
    "* Use `matplotlib` to make plots\n",
    "* Feel comfortable with simple linear regression\n",
    "* Feel comfortable with $k$ nearest neighbors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Table of Contents\n",
    "\n",
    "#### <font color='red'> HIGHLIGHTS FROM PRE-LAB </font>\n",
    "\n",
    "* [1 - Review of numpy](#first-bullet)\n",
    "* [2 - Intro to matplotlib plus more ](#second-bullet)\n",
    "\n",
    "#### <font color='red'> LAB 3 MATERIAL </font>\n",
    "\n",
    "* [3 - Simple Linear Regression](#third-bullet)\n",
    "* [4 - Building a model with `statsmodels` and `sklearn`](#fourth-bullet)\n",
    "* [5 - Example: Simple linear regression with automobile data](#fifth-bullet)\n",
    "* [6 - $k$Nearest Neighbors](#sixth-bullet)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "import matplotlib as mpl\n",
    "import matplotlib.cm as cm\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import time\n",
    "pd.set_option('display.width', 500)\n",
    "pd.set_option('display.max_columns', 100)\n",
    "pd.set_option('display.notebook_repr_html', True)\n",
    "#import seaborn as sns\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "# Displays the plots for us.\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a class=\"anchor\" id=\"first-bullet\"></a>\n",
    "## 1 - Review of  the  `numpy` Python library\n",
    "\n",
    "Earlier we learned about the `numpy` library [(documentation)](http://www.numpy.org/) and its fast array structure, called the `numpy array`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import numpy\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  4,  9, 16])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# make an array\n",
    "my_array = np.array([1,4,9,16])\n",
    "my_array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Size of my array: 4, or length of my array: 4\n",
      "Shape of my array: (4,)\n"
     ]
    }
   ],
   "source": [
    "print(f'Size of my array: {my_array.size}, or length of my array: {len(my_array)}')\n",
    "print (f'Shape of my array: {my_array.shape}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Notice the way the shape appears in numpy arrays\n",
    "\n",
    "- For a 1D array, .shape returns a tuple with 1 element (n,)\n",
    "- For a 2D array, .shape returns a tuple with 2 elements (n,m)\n",
    "- For a 3D array, .shape returns a tuple with 3 elements (n,m,p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  4],\n",
       "       [ 9, 16]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# How to reshape a 1D array to a 2D\n",
    "my_array.reshape(-1,2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Numpy arrays support the same operations as lists! Below we slice and iterate. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "array[2:4]: [ 9 16]\n",
      "element: 1\n",
      "element: 4\n",
      "element: 9\n",
      "element: 16\n"
     ]
    }
   ],
   "source": [
    "print(\"array[2:4]:\", my_array[2:4]) # A slice of the array\n",
    "\n",
    "# Iterate over the array\n",
    "for ele in my_array:\n",
    "    print(\"element:\", ele)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Remember `numpy` gains a lot of its efficiency from being **strongly typed** (all elements are of the same type, such as integer or floating point). If the elements of an array are of a different type, `numpy` will force them into the same type (the longest in terms of bytes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'int'> <class 'float'> <class 'str'> <class 'bool'>\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array(['1', '2.3', 'brandon', 'True'], dtype='<U32')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mixed = np.array([1, 2.3, 'brandon', True])\n",
    "print(type(1), type(2.3), type('brandon'), type(True))\n",
    "mixed # all elements will become strings"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we push ahead to two-dimensional arrays and begin to dive into some of the deeper aspects of `numpy`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  2,  3,  4],\n",
       "       [ 5,  6,  7,  8],\n",
       "       [ 9, 10, 11, 12]])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create a 2d-array by handing a list of lists\n",
    "my_array2d = np.array([ [1, 2, 3, 4], \n",
    "                        [5, 6, 7, 8], \n",
    "                        [9, 10, 11, 12] \n",
    "])\n",
    "\n",
    "my_array2d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pandas Slicing \n",
    "\n",
    "`.iloc` is by position (position is unique), `.loc` is by label (label is not unique)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "    .dataframe tbody tr th {\n",
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       "\n",
       "    .dataframe thead th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>title</th>\n",
       "      <th>year</th>\n",
       "      <th>name</th>\n",
       "      <th>type</th>\n",
       "      <th>character</th>\n",
       "      <th>n</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Closet Monster</td>\n",
       "      <td>2015</td>\n",
       "      <td>Buffy #1</td>\n",
       "      <td>actor</td>\n",
       "      <td>Buffy 4</td>\n",
       "      <td>31.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Suuri illusioni</td>\n",
       "      <td>1985</td>\n",
       "      <td>Homo $</td>\n",
       "      <td>actor</td>\n",
       "      <td>Guests</td>\n",
       "      <td>22.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Battle of the Sexes</td>\n",
       "      <td>2017</td>\n",
       "      <td>$hutter</td>\n",
       "      <td>actor</td>\n",
       "      <td>Bobby Riggs Fan</td>\n",
       "      <td>10.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Secret in Their Eyes</td>\n",
       "      <td>2015</td>\n",
       "      <td>$hutter</td>\n",
       "      <td>actor</td>\n",
       "      <td>2002 Dodger Fan</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Steve Jobs</td>\n",
       "      <td>2015</td>\n",
       "      <td>$hutter</td>\n",
       "      <td>actor</td>\n",
       "      <td>1988 Opera House Patron</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  title  year      name   type                character     n\n",
       "0        Closet Monster  2015  Buffy #1  actor                  Buffy 4  31.0\n",
       "1       Suuri illusioni  1985    Homo $  actor                   Guests  22.0\n",
       "2   Battle of the Sexes  2017   $hutter  actor          Bobby Riggs Fan  10.0\n",
       "3  Secret in Their Eyes  2015   $hutter  actor          2002 Dodger Fan   NaN\n",
       "4            Steve Jobs  2015   $hutter  actor  1988 Opera House Patron   NaN"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# import cast dataframe \n",
    "cast = pd.read_csv('data/cast.csv', encoding='utf_8')\n",
    "cast.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>title</th>\n",
       "      <th>year</th>\n",
       "      <th>name</th>\n",
       "      <th>type</th>\n",
       "      <th>character</th>\n",
       "      <th>n</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>When the Man Went South</td>\n",
       "      <td>2014</td>\n",
       "      <td>Taipaleti 'Atu'ake</td>\n",
       "      <td>actor</td>\n",
       "      <td>Two Palms - Ua'i Paame</td>\n",
       "      <td>8.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>Little Angel (Angelita)</td>\n",
       "      <td>2015</td>\n",
       "      <td>Michael 'babeepower' Viera</td>\n",
       "      <td>actor</td>\n",
       "      <td>Chico</td>\n",
       "      <td>9.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>Mixing Nia</td>\n",
       "      <td>1998</td>\n",
       "      <td>Michael 'babeepower' Viera</td>\n",
       "      <td>actor</td>\n",
       "      <td>Rapper</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                      title  year                        name   type               character    n\n",
       "10  When the Man Went South  2014          Taipaleti 'Atu'ake  actor  Two Palms - Ua'i Paame  8.0\n",
       "11  Little Angel (Angelita)  2015  Michael 'babeepower' Viera  actor                   Chico  9.0\n",
       "12               Mixing Nia  1998  Michael 'babeepower' Viera  actor                  Rapper  NaN"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get me rows 10 to 13 (python slicing style : exclusive of end) \n",
    "cast.iloc[10:13]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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>title</th>\n",
       "      <th>year</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Closet Monster</td>\n",
       "      <td>2015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Suuri illusioni</td>\n",
       "      <td>1985</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Battle of the Sexes</td>\n",
       "      <td>2017</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Secret in Their Eyes</td>\n",
       "      <td>2015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Steve Jobs</td>\n",
       "      <td>2015</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  title  year\n",
       "0        Closet Monster  2015\n",
       "1       Suuri illusioni  1985\n",
       "2   Battle of the Sexes  2017\n",
       "3  Secret in Their Eyes  2015\n",
       "4            Steve Jobs  2015"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get me columns 0 to 2 but all rows - use head()\n",
    "cast.iloc[:, 0:2].head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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>title</th>\n",
       "      <th>year</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>When the Man Went South</td>\n",
       "      <td>2014</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>Little Angel (Angelita)</td>\n",
       "      <td>2015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>Mixing Nia</td>\n",
       "      <td>1998</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                      title  year\n",
       "10  When the Man Went South  2014\n",
       "11  Little Angel (Angelita)  2015\n",
       "12               Mixing Nia  1998"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get me rows 10 to 13 AND only columns 0 to 2\n",
    "cast.iloc[10:13, 0:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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>title</th>\n",
       "      <th>year</th>\n",
       "      <th>name</th>\n",
       "      <th>type</th>\n",
       "      <th>character</th>\n",
       "      <th>n</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>When the Man Went South</td>\n",
       "      <td>2014</td>\n",
       "      <td>Taipaleti 'Atu'ake</td>\n",
       "      <td>actor</td>\n",
       "      <td>Two Palms - Ua'i Paame</td>\n",
       "      <td>8.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>Little Angel (Angelita)</td>\n",
       "      <td>2015</td>\n",
       "      <td>Michael 'babeepower' Viera</td>\n",
       "      <td>actor</td>\n",
       "      <td>Chico</td>\n",
       "      <td>9.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>Mixing Nia</td>\n",
       "      <td>1998</td>\n",
       "      <td>Michael 'babeepower' Viera</td>\n",
       "      <td>actor</td>\n",
       "      <td>Rapper</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>The Replacements</td>\n",
       "      <td>2000</td>\n",
       "      <td>Steven 'Bear'Boyd</td>\n",
       "      <td>actor</td>\n",
       "      <td>Defensive Tackle - Washington Sentinels</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                      title  year                        name   type                                character    n\n",
       "10  When the Man Went South  2014          Taipaleti 'Atu'ake  actor                   Two Palms - Ua'i Paame  8.0\n",
       "11  Little Angel (Angelita)  2015  Michael 'babeepower' Viera  actor                                    Chico  9.0\n",
       "12               Mixing Nia  1998  Michael 'babeepower' Viera  actor                                   Rapper  NaN\n",
       "13         The Replacements  2000           Steven 'Bear'Boyd  actor  Defensive Tackle - Washington Sentinels  NaN"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# COMPARE: get me rows 10 to 13 (pandas slicing style : inclusive of end)\n",
    "cast.loc[10:13]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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>year</th>\n",
       "      <th>type</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>2015</td>\n",
       "      <td>actor</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>2015</td>\n",
       "      <td>actor</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>2009</td>\n",
       "      <td>actor</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>2014</td>\n",
       "      <td>actor</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>2014</td>\n",
       "      <td>actor</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>2014</td>\n",
       "      <td>actor</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    year   type\n",
       "5   2015  actor\n",
       "6   2015  actor\n",
       "7   2009  actor\n",
       "8   2014  actor\n",
       "9   2014  actor\n",
       "10  2014  actor"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# give me columns 'year' and 'type' by label but only for rows 5 to 10\n",
    "cast.loc[5:10,['year','type']]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a class=\"anchor\" id=\"second-bullet\"></a>\n",
    "## 2 - Plotting with matplotlib and beyond\n",
    "<br>\n",
    "\n",
    "`matplotlib` is a very powerful `python` library for making scientific plots. \n",
    "\n",
    "We will not focus too much on the internal aspects of `matplotlib` in today's lab. There are many excellent tutorials out there for `matplotlib`.  For example,\n",
    "* [`matplotlib` homepage](https://matplotlib.org/)\n",
    "* [`matplotlib` tutorial](https://github.com/matplotlib/AnatomyOfMatplotlib)\n",
    "\n",
    "Conveying your findings convincingly is an absolutely crucial part of any analysis. Therefore, you must be able to write well and make compelling visuals.  Creating informative visuals is an involved process and we won't cover that in this lab.  However, part of creating informative data visualizations means generating *readable* figures.  If people can't read your figures or have a difficult time interpreting them, they won't understand the results of your work.  Here are some non-negotiable commandments for any plot:\n",
    "* Label $x$ and $y$ axes\n",
    "* Axes labels should be informative\n",
    "* Axes labels should be large enough to read\n",
    "* Make tick labels large enough\n",
    "* Include a legend if necessary\n",
    "* Include a title if necessary\n",
    "* Use appropriate line widths\n",
    "* Use different line styles for different lines on the plot\n",
    "* Use different markers for different lines\n",
    "\n",
    "There are other important elements, but that list should get you started on your way.\n",
    "\n",
    "We will work with `matplotlib` and `seaborn` for plotting in this class.  `matplotlib` is a very powerful `python` library for making scientific plots.  `seaborn` is a little more specialized in that it was developed for statistical data visualization.  We will cover some `seaborn` later in class. In the meantime you can look at the [seaborn documentation](https://seaborn.pydata.org)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let's generate some data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Let's plot some functions\n",
    "\n",
    "We will use the following three functions to make some plots:\n",
    "\n",
    "* Logistic function:\n",
    "  \\begin{align*}\n",
    "    f\\left(z\\right) = \\dfrac{1}{1 + be^{-az}}\n",
    "  \\end{align*}\n",
    "  where $a$ and $b$ are parameters.\n",
    "* Hyperbolic tangent:\n",
    "  \\begin{align*}\n",
    "    g\\left(z\\right) = b\\tanh\\left(az\\right) + c\n",
    "  \\end{align*}\n",
    "  where $a$, $b$, and $c$ are parameters.\n",
    "* Rectified Linear Unit:\n",
    "  \\begin{align*}\n",
    "    h\\left(z\\right) = \n",
    "    \\left\\{\n",
    "      \\begin{array}{lr}\n",
    "        z, \\quad z > 0 \\\\\n",
    "        \\epsilon z, \\quad z\\leq 0\n",
    "      \\end{array}\n",
    "    \\right.\n",
    "  \\end{align*}\n",
    "  where $\\epsilon < 0$ is a small, positive parameter.\n",
    "\n",
    "You are given the code for the first two functions.  Notice that $z$ is passed in as a `numpy` array and that the functions are returned as `numpy` arrays.  Parameters are passed in as floats.\n",
    "\n",
    "You should write a function to compute the rectified linear unit.  The input should be a `numpy` array for $z$ and a positive float for $\\epsilon$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def logistic(z: np.ndarray, a: float, b: float) -> np.ndarray:\n",
    "    \"\"\" Compute logistic function\n",
    "      Inputs:\n",
    "         a: exponential parameter\n",
    "         b: exponential prefactor\n",
    "         z: numpy array; domain\n",
    "      Outputs:\n",
    "         f: numpy array of floats, logistic function\n",
    "    \"\"\"\n",
    "    \n",
    "    den = 1.0 + b * np.exp(-a * z)\n",
    "    return 1.0 / den\n",
    "\n",
    "def stretch_tanh(z: np.ndarray, a: float, b: float, c: float) -> np.ndarray:\n",
    "    \"\"\" Compute stretched hyperbolic tangent\n",
    "      Inputs:\n",
    "         a: horizontal stretch parameter (a>1 implies a horizontal squish)\n",
    "         b: vertical stretch parameter\n",
    "         c: vertical shift parameter\n",
    "         z: numpy array; domain\n",
    "      Outputs:\n",
    "         g: numpy array of floats, stretched tanh\n",
    "    \"\"\"\n",
    "    return b * np.tanh(a * z) + c\n",
    "\n",
    "def relu(z: np.ndarray, eps: float = 0.01) -> np.ndarray:\n",
    "    \"\"\" Compute rectificed linear unit\n",
    "      Inputs:\n",
    "         eps: small positive parameter\n",
    "         z: numpy array; domain\n",
    "      Outputs:\n",
    "         h: numpy array; relu\n",
    "    \"\"\"\n",
    "    return np.fmax(z, eps * z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's make some plots.  First, let's just warm up and plot the logistic function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(-5.0, 5.0, 100) # Equally spaced grid of 100 pts between -5 and 5\n",
    "\n",
    "f = logistic(x, 1.0, 1.0) # Generate data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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, f)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f')\n",
    "plt.title('Logistic Function')\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Figures with subplots\n",
    "\n",
    "Let's start thinking about the plots as objects. We have the `figure` object which is like a matrix of smaller plots named `axes`. You can use array notation when handling it. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "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": [
    "fig, ax = plt.subplots(1,1) # Get figure and axes objects\n",
    "\n",
    "ax.plot(x, f) # Make a plot\n",
    "\n",
    "# Create some labels\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('f')\n",
    "ax.set_title('Logistic Function')\n",
    "\n",
    "# Grid\n",
    "ax.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wow, it's *exactly* the same plot!  Notice, however, the use of `ax.set_xlabel()` instead of `plt.xlabel()`.  The difference is tiny, but you should be aware of it.  I will use this plotting syntax from now on.\n",
    "\n",
    "What else do we need to do to make this figure better?  Here are some options:\n",
    "* Make labels bigger!\n",
    "* Make line fatter\n",
    "* Make tick mark labels bigger\n",
    "* Make the grid less pronounced\n",
    "* Make figure bigger\n",
    "\n",
    "Let's get to it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,1, figsize=(10,6)) # Make figure bigger\n",
    "\n",
    "# Make line plot\n",
    "ax.plot(x, f, lw=4)\n",
    "\n",
    "# Update ticklabel size\n",
    "ax.tick_params(labelsize=24)\n",
    "\n",
    "# Make labels\n",
    "ax.set_xlabel(r'$x$', fontsize=24) # Use TeX for mathematical rendering\n",
    "ax.set_ylabel(r'$f(x)$', fontsize=24) # Use TeX for mathematical rendering\n",
    "ax.set_title('Logistic Function', fontsize=24)\n",
    "\n",
    "ax.grid(True, lw=1.5, ls='--', alpha=0.75)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice:\n",
    "* `lw` stands for `linewidth`.  We could also write `ax.plot(x, f, linewidth=4)`\n",
    "* `ls` stands for `linestyle`.\n",
    "* `alpha` stands for transparency."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The only thing remaining to do is to change the $x$ limits.  Clearly these should go from $-5$ to $5$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "#fig.savefig('logistic.png')\n",
    "\n",
    "# Put this in a markdown cell and uncomment this to check what you saved.\n",
    "# ![](../images/logistic.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Resources\n",
    "If you want to see all the styles available, please take a look at the documentation.\n",
    "* [Line styles](https://matplotlib.org/2.0.1/api/lines_api.html#matplotlib.lines.Line2D.set_linestyle)\n",
    "* [Marker styles](https://matplotlib.org/2.0.1/api/markers_api.html#module-matplotlib.markers)\n",
    "* [Everything you could ever want](https://matplotlib.org/2.0.1/api/lines_api.html#matplotlib.lines.Line2D.set_marker)\n",
    "\n",
    "We haven't discussed it yet, but you can also put a legend on a figure.  You'll do that in the next exercise.  Here are some additional resources:\n",
    "* [Legend](https://matplotlib.org/api/_as_gen/matplotlib.pyplot.legend.html)\n",
    "* [Grid](https://matplotlib.org/api/_as_gen/matplotlib.pyplot.grid.html)\n",
    "\n",
    "`ax.legend(loc='best', fontsize=24);`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"exercise\"><b>Exercise</b></div>\n",
    "\n",
    "Do the following:\n",
    "* Make a figure with the logistic function, hyperbolic tangent, and rectified linear unit.\n",
    "* Use different line styles for each plot\n",
    "* Put a legend on your figure\n",
    "\n",
    "Here's an example of a figure:\n",
    "![](../images/nice_plots.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# your code here\n",
    "\n",
    "# First get the data\n",
    "f = logistic(x, 2.0, 1.0)\n",
    "g = stretch_tanh(x, 2.0, 0.5, 0.5)\n",
    "h = relu(x)\n",
    "\n",
    "fig, ax = plt.subplots(1,1, figsize=(10,6)) # Create figure object\n",
    "\n",
    "# Make actual plots\n",
    "# (Notice the label argument!)\n",
    "ax.plot(x, f, lw=4, ls='-', label=r'$L(x;1)$')\n",
    "ax.plot(x, g, lw=4, ls='--', label=r'$\\tanh(2x)$')\n",
    "ax.plot(x, h, lw=4, ls='-.', label=r'$relu(x; 0.01)$')\n",
    "\n",
    "# Make the tick labels readable\n",
    "ax.tick_params(labelsize=24)\n",
    "\n",
    "# Set axes limits to make the scale nice\n",
    "ax.set_xlim(x.min(), x.max())\n",
    "ax.set_ylim(h.min(), 1.1)\n",
    "\n",
    "# Make readable labels\n",
    "ax.set_xlabel(r'$x$', fontsize=24)\n",
    "ax.set_ylabel(r'$h(x)$', fontsize=24)\n",
    "ax.set_title('Activation Functions', fontsize=24)\n",
    "\n",
    "# Set up grid\n",
    "ax.grid(True, lw=1.75, ls='--', alpha=0.75)\n",
    "\n",
    "# Put legend on figure\n",
    "ax.legend(loc='best', fontsize=24);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"exercise\"><b>Exercise</b></div>\n",
    "\n",
    "These figures look nice in the plot and it makes sense for comparison. Now let's put the 3 different figures in separate plots.\n",
    "\n",
    "* Make a separate plot for each figure and line them up on the same row."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "# your code here\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x432 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# %load solutions/three_subplots.py"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"exercise\"><b>Exercise</b></div>\n",
    "\n",
    "* Make a grid of 2 x 3 separate plots, 3 will be empty. Just plot the functions and do not worry about cosmetics. We just want you ro see the functionality."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "# your code here\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x12fd23d60>]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x432 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# %load solutions/six_subplots.py"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a class=\"anchor\" id=\"third-bullet\"></a>\n",
    "## 3 - Simple Linear Regression\n",
    "\n",
    "Linear regression and its many extensions are a workhorse of the statistics and data science community, both in application and as a reference point for other models. Most of the major concepts in machine learning can be and often are discussed in terms of various linear regression models. Thus, this section will introduce you to building and fitting linear regression models and some of the process behind it, so that you can 1) fit models to data you encounter 2) experiment with different kinds of linear regression and observe their effects 3) see some of the technology that makes regression models work.\n",
    "\n",
    "\n",
    "### Linear regression with a toy dataset\n",
    "We first examine a toy problem, focusing our efforts on fitting a linear model to a small dataset with three observations.  Each observation consists of one predictor $x_i$ and one response $y_i$ for $i = 1, 2, 3$,\n",
    "\n",
    "\\begin{align*}\n",
    "(x , y) = \\{(x_1, y_1), (x_2, y_2), (x_3, y_3)\\}.\n",
    "\\end{align*}\n",
    "\n",
    "To be very concrete, let's set the values of the predictors and responses.\n",
    "\n",
    "\\begin{equation*}\n",
    "(x , y) = \\{(1, 2), (2, 2), (3, 4)\\}\n",
    "\\end{equation*}\n",
    "\n",
    "There is no line of the form $\\beta_0 + \\beta_1 x = y$ that passes through all three observations, since the data are not collinear. Thus our aim is to find the line that best fits these observations in the *least-squares sense*, as discussed in lecture."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"exercise\"><b>Exercise</b></div>\n",
    "\n",
    "* Make two numpy arrays out of this data, x_train and y_train\n",
    "* Check the dimentions of these arrays\n",
    "* Try to reshape them into a different shape\n",
    "* Make points into a very simple scatterplot\n",
    "* Make a better scatterplot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "# your code here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# solution\n",
    "x_train = np.array([1,2,3])\n",
    "y_train = np.array([2,3,6])\n",
    "type(x_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3,)"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 1)"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train = x_train.reshape(3,1)\n",
    "x_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3,) (3,)\n"
     ]
    },
    {
     "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": [
    "# %load solutions/simple_scatterplot.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:title={'center':'hello nice plot'}, xlabel='$x$', ylabel='$y$'>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# %load solutions/nice_scatterplot.py"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "#### Formulae\n",
    "Linear regression is special among the models we study because it can be solved explicitly. While most other models (and even some advanced versions of linear regression) must be solved itteratively, linear regression has a formula where you can simply plug in the data.\n",
    "\n",
    "For the single predictor case it is:\n",
    "    \\begin{align}\n",
    "      \\beta_1 &= \\frac{\\sum_{i=1}^n{(x_i-\\bar{x})(y_i-\\bar{y})}}{\\sum_{i=1}^n{(x_i-\\bar{x})^2}}\\\\\n",
    "      \\beta_0 &= \\bar{y} - \\beta_1\\bar{x}\\\n",
    "    \\end{align}\n",
    "    \n",
    "Where $\\bar{y}$ and $\\bar{x}$ are the mean of the y values and the mean of the x values, respectively."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Building a model from scratch\n",
    "In this part, we will solve the equations for simple linear regression and find the best fit solution to our toy problem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The snippets of code below implement the linear regression equations on the observed predictors and responses, which we'll call the training data set.  Let's walk through the code.\n",
    "\n",
    "We have to reshape our arrrays to 2D. We will see later why."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"exercise\"><b>Exercise</b></div>\n",
    "\n",
    "* make an array with shape (2,3)\n",
    "* reshape it to a size that you want"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "# your code here\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 2)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#solution\n",
    "xx = np.array([[1,2,3],[4,6,8]])\n",
    "xxx = xx.reshape(-1,2)\n",
    "xxx.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3, 1)\n"
     ]
    }
   ],
   "source": [
    "# Reshape to be a proper 2D array\n",
    "x_train = x_train.reshape(x_train.shape[0], 1)\n",
    "y_train = y_train.reshape(y_train.shape[0], 1)\n",
    "\n",
    "print(x_train.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "() ()\n"
     ]
    }
   ],
   "source": [
    "# first, compute means\n",
    "y_bar = np.mean(y_train)\n",
    "x_bar = np.mean(x_train)\n",
    "\n",
    "# build the two terms\n",
    "numerator = np.sum( (x_train - x_bar)*(y_train - y_bar) )\n",
    "denominator = np.sum((x_train - x_bar)**2)\n",
    "\n",
    "print(numerator.shape, denominator.shape) #check shapes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Why the empty brackets? (The numerator and denominator are scalars, as expected.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The best-fit line is 0.67 + 1.00 * x\n",
      "The best fit is 0.6666666666666665\n"
     ]
    }
   ],
   "source": [
    "#slope beta1\n",
    "beta_1 = numerator/denominator\n",
    "\n",
    "#intercept beta0\n",
    "beta_0 = y_bar - beta_1*x_bar\n",
    "\n",
    "print(\"The best-fit line is {0:3.2f} + {1:3.2f} * x\".format(beta_0, beta_1))\n",
    "print(f'The best fit is {beta_0}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"exercise\"><b>Exercise</b></div>\n",
    "\n",
    "Turn the code from the above cells into a function called `simple_linear_regression_fit`, that inputs the training data and returns `beta0` and `beta1`.\n",
    "\n",
    "To do this, copy and paste the code from the above cells below and adjust the code as needed, so that the training data becomes the input and the betas become the output.\n",
    "\n",
    "```python\n",
    "def simple_linear_regression_fit(x_train: np.ndarray, y_train: np.ndarray) -> np.ndarray:\n",
    "    \n",
    "    return\n",
    "```\n",
    "\n",
    "Check your function by calling it with the training data from above and printing out the beta values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your code here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "# %load solutions/simple_linear_regression_fit.py"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Let's run this function and see the coefficients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reshaping features array.\n",
      "Reshaping observations array.\n",
      "The best-fit line is 0.666667 + 1.000000 * x\n"
     ]
    }
   ],
   "source": [
    "x_train = np.array([1 ,2, 3])\n",
    "y_train = np.array([2, 2, 4])\n",
    "\n",
    "betas = simple_linear_regression_fit(x_train, y_train)\n",
    "\n",
    "beta_0 = betas[0]\n",
    "beta_1 = betas[1]\n",
    "\n",
    "print(\"The best-fit line is {0:8.6f} + {1:8.6f} * x\".format(beta_0, beta_1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"exercise\"><b>Exercise</b></div>\n",
    "\n",
    "* Do the values of `beta0` and `beta1` seem reasonable?\n",
    "* Plot the training data using a scatter plot.\n",
    "* Plot the best fit line with `beta0` and `beta1` together with the training data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your code here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# %load solutions/best_fit_scatterplot.py"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The values of `beta0` and `beta1` seem roughly reasonable.  They capture the positive correlation.  The line does appear to be trying to get as close as possible to all the points."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a class=\"anchor\" id=\"fourth-bullet\"></a>\n",
    "## 4 - Building a model with `statsmodels` and `sklearn`\n",
    "\n",
    "Now that we can concretely fit the training data from scratch, let's learn two `python` packages to do it all for us:\n",
    "* [statsmodels](http://www.statsmodels.org/stable/regression.html) and \n",
    "* [scikit-learn (sklearn)](http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html).\n",
    "\n",
    "Our goal  is to show how to implement simple linear regression with these packages.  For an important sanity check, we compare the $\\beta$ values from `statsmodels` and `sklearn` to the $\\beta$ values that we found from above with our own implementation.\n",
    "\n",
    "For the purposes of this lab, `statsmodels` and `sklearn` do the same thing.  More generally though, `statsmodels` tends to be easier for inference \\[finding the values of the slope and intercept and dicussing uncertainty in those values\\], whereas `sklearn` has machine-learning algorithms and is better for prediction \\[guessing y values for a given x value\\]. (Note that both packages make the same guesses, it's just a question of which activity they provide more support for.\n",
    "\n",
    "**Note:** `statsmodels` and `sklearn` are different packages!  Unless we specify otherwise, you can use either one."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below is the code for `statsmodels`.  `Statsmodels` does not by default include the column of ones in the $X$ matrix, so we include it manually with `sm.add_constant`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 1.]\n",
      " [1. 2.]\n",
      " [1. 3.]]\n",
      "The regression coef from statsmodels are: beta_0 = 0.666667 and beta_1 = 1.000000\n"
     ]
    }
   ],
   "source": [
    "# create the X matrix by appending a column of ones to x_train\n",
    "X = sm.add_constant(x_train)\n",
    "\n",
    "# this is the same matrix as in our scratch problem!\n",
    "print(X)\n",
    "\n",
    "# build the OLS model (ordinary least squares) from the training data\n",
    "toyregr_sm = sm.OLS(y_train, X)\n",
    "\n",
    "# do the fit and save regression info (parameters, etc) in results_sm\n",
    "results_sm = toyregr_sm.fit()\n",
    "\n",
    "# pull the beta parameters out from results_sm\n",
    "beta0_sm = results_sm.params[0]\n",
    "beta1_sm = results_sm.params[1]\n",
    "\n",
    "print(f'The regression coef from statsmodels are: beta_0 = {beta0_sm:8.6f} and beta_1 = {beta1_sm:8.6f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Besides the beta parameters, `results_sm` contains a ton of other potentially useful information."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.750\n",
      "Model:                            OLS   Adj. R-squared:                  0.500\n",
      "Method:                 Least Squares   F-statistic:                     3.000\n",
      "Date:                Thu, 05 Aug 2021   Prob (F-statistic):              0.333\n",
      "Time:                        14:37:51   Log-Likelihood:                -2.0007\n",
      "No. Observations:                   3   AIC:                             8.001\n",
      "Df Residuals:                       1   BIC:                             6.199\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          0.6667      1.247      0.535      0.687     -15.181      16.514\n",
      "x1             1.0000      0.577      1.732      0.333      -6.336       8.336\n",
      "==============================================================================\n",
      "Omnibus:                          nan   Durbin-Watson:                   3.000\n",
      "Prob(Omnibus):                    nan   Jarque-Bera (JB):                0.531\n",
      "Skew:                          -0.707   Prob(JB):                        0.767\n",
      "Kurtosis:                       1.500   Cond. No.                         6.79\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "print(results_sm.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's turn our attention to the `sklearn` library."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import linear_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The regression coefficients from the sklearn package are: beta_0 = 0.666667 and beta_1 = 1.000000\n"
     ]
    }
   ],
   "source": [
    "# build the least squares model\n",
    "toyregr = linear_model.LinearRegression()\n",
    "\n",
    "# save regression info (parameters, etc) in results_skl\n",
    "results = toyregr.fit(x_train, y_train)\n",
    "\n",
    "# pull the beta parameters out from results_skl\n",
    "beta0_skl = toyregr.intercept_\n",
    "beta1_skl = toyregr.coef_[0]\n",
    "\n",
    "print(\"The regression coefficients from the sklearn package are: beta_0 = {0:8.6f} and beta_1 = {1:8.6f}\".format(beta0_skl, beta1_skl))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The `scikit-learn` library and the shape of things"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before diving into a \"real\" problem, let's discuss more of the details of `sklearn`.\n",
    "\n",
    "`Scikit-learn` is the main `Python` machine learning library. It consists of many learners which can learn models from data, as well as a lot of utility functions such as `train_test_split()`. \n",
    "\n",
    "Use the following to add the library into your code:\n",
    "\n",
    "```python\n",
    "import sklearn \n",
    "```\n",
    "\n",
    "In `scikit-learn`, an **estimator** is a Python object that implements the methods `fit(X, y)` and `predict(T)`\n",
    "\n",
    "Let's see the structure of `scikit-learn` needed to make these fits. `fit()` always takes two arguments:\n",
    "```python\n",
    "estimator.fit(Xtrain, ytrain)\n",
    "```\n",
    "We will consider two estimators in this lab: `LinearRegression` and `KNeighborsRegressor`.\n",
    "\n",
    "It is very important to understand that `Xtrain` must be in the form of a **2x2 array** with each row corresponding to one sample, and each column corresponding to the feature values for that sample.\n",
    "\n",
    "`ytrain` on the other hand is a simple array of responses.  These are continuous for regression problems."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](../images/featurematrix.png)\n",
    "\n",
    "<!--![](../images/sklearn2.jpg)-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Practice with `sklearn` and a real dataset\n",
    "We begin by loading up the `mtcars` dataset. This data was extracted from the 1974 Motor Trend US magazine, and comprises of fuel consumption and 10 aspects of automobile design and performance for 32 automobiles (1973–74 models). We will load this data to a dataframe with 32 observations on 11 (numeric) variables. Here is an explanation of the features:\n",
    "\n",
    "- `mpg` is Miles/(US) gallon \n",
    "- `cyl` is Number of cylinders, \n",
    "- `disp` is\tDisplacement (cu.in.), \n",
    "- `hp` is\tGross horsepower, \n",
    "- `drat` is\tRear axle ratio, \n",
    "- `wt` is the Weight (1000 lbs), \n",
    "- `qsec` is 1/4 mile time,\n",
    "- `vs` is Engine (0 = V-shaped, 1 = straight), \n",
    "- `am` is Transmission (0 = automatic, 1 = manual), \n",
    "- `gear` is the Number of forward gears, \n",
    "- `carb` is\tNumber of carburetors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "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>Unnamed: 0</th>\n",
       "      <th>mpg</th>\n",
       "      <th>cyl</th>\n",
       "      <th>disp</th>\n",
       "      <th>hp</th>\n",
       "      <th>drat</th>\n",
       "      <th>wt</th>\n",
       "      <th>qsec</th>\n",
       "      <th>vs</th>\n",
       "      <th>am</th>\n",
       "      <th>gear</th>\n",
       "      <th>carb</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Mazda RX4</td>\n",
       "      <td>21.0</td>\n",
       "      <td>6</td>\n",
       "      <td>160.0</td>\n",
       "      <td>110</td>\n",
       "      <td>3.90</td>\n",
       "      <td>2.620</td>\n",
       "      <td>16.46</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Mazda RX4 Wag</td>\n",
       "      <td>21.0</td>\n",
       "      <td>6</td>\n",
       "      <td>160.0</td>\n",
       "      <td>110</td>\n",
       "      <td>3.90</td>\n",
       "      <td>2.875</td>\n",
       "      <td>17.02</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Datsun 710</td>\n",
       "      <td>22.8</td>\n",
       "      <td>4</td>\n",
       "      <td>108.0</td>\n",
       "      <td>93</td>\n",
       "      <td>3.85</td>\n",
       "      <td>2.320</td>\n",
       "      <td>18.61</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Hornet 4 Drive</td>\n",
       "      <td>21.4</td>\n",
       "      <td>6</td>\n",
       "      <td>258.0</td>\n",
       "      <td>110</td>\n",
       "      <td>3.08</td>\n",
       "      <td>3.215</td>\n",
       "      <td>19.44</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Hornet Sportabout</td>\n",
       "      <td>18.7</td>\n",
       "      <td>8</td>\n",
       "      <td>360.0</td>\n",
       "      <td>175</td>\n",
       "      <td>3.15</td>\n",
       "      <td>3.440</td>\n",
       "      <td>17.02</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Unnamed: 0   mpg  cyl   disp   hp  drat     wt   qsec  vs  am  gear  carb\n",
       "0          Mazda RX4  21.0    6  160.0  110  3.90  2.620  16.46   0   1     4     4\n",
       "1      Mazda RX4 Wag  21.0    6  160.0  110  3.90  2.875  17.02   0   1     4     4\n",
       "2         Datsun 710  22.8    4  108.0   93  3.85  2.320  18.61   1   1     4     1\n",
       "3     Hornet 4 Drive  21.4    6  258.0  110  3.08  3.215  19.44   1   0     3     1\n",
       "4  Hornet Sportabout  18.7    8  360.0  175  3.15  3.440  17.02   0   0     3     2"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "#load mtcars\n",
    "dfcars = pd.read_csv(\"data/mtcars.csv\")\n",
    "dfcars.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "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>car name</th>\n",
       "      <th>mpg</th>\n",
       "      <th>cyl</th>\n",
       "      <th>disp</th>\n",
       "      <th>hp</th>\n",
       "      <th>drat</th>\n",
       "      <th>wt</th>\n",
       "      <th>qsec</th>\n",
       "      <th>vs</th>\n",
       "      <th>am</th>\n",
       "      <th>gear</th>\n",
       "      <th>carb</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Mazda RX4</td>\n",
       "      <td>21.0</td>\n",
       "      <td>6</td>\n",
       "      <td>160.0</td>\n",
       "      <td>110</td>\n",
       "      <td>3.90</td>\n",
       "      <td>2.620</td>\n",
       "      <td>16.46</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Mazda RX4 Wag</td>\n",
       "      <td>21.0</td>\n",
       "      <td>6</td>\n",
       "      <td>160.0</td>\n",
       "      <td>110</td>\n",
       "      <td>3.90</td>\n",
       "      <td>2.875</td>\n",
       "      <td>17.02</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Datsun 710</td>\n",
       "      <td>22.8</td>\n",
       "      <td>4</td>\n",
       "      <td>108.0</td>\n",
       "      <td>93</td>\n",
       "      <td>3.85</td>\n",
       "      <td>2.320</td>\n",
       "      <td>18.61</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Hornet 4 Drive</td>\n",
       "      <td>21.4</td>\n",
       "      <td>6</td>\n",
       "      <td>258.0</td>\n",
       "      <td>110</td>\n",
       "      <td>3.08</td>\n",
       "      <td>3.215</td>\n",
       "      <td>19.44</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Hornet Sportabout</td>\n",
       "      <td>18.7</td>\n",
       "      <td>8</td>\n",
       "      <td>360.0</td>\n",
       "      <td>175</td>\n",
       "      <td>3.15</td>\n",
       "      <td>3.440</td>\n",
       "      <td>17.02</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            car name   mpg  cyl   disp   hp  drat     wt   qsec  vs  am  gear  carb\n",
       "0          Mazda RX4  21.0    6  160.0  110  3.90  2.620  16.46   0   1     4     4\n",
       "1      Mazda RX4 Wag  21.0    6  160.0  110  3.90  2.875  17.02   0   1     4     4\n",
       "2         Datsun 710  22.8    4  108.0   93  3.85  2.320  18.61   1   1     4     1\n",
       "3     Hornet 4 Drive  21.4    6  258.0  110  3.08  3.215  19.44   1   0     3     1\n",
       "4  Hornet Sportabout  18.7    8  360.0  175  3.15  3.440  17.02   0   0     3     2"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Fix the column title \n",
    "dfcars = dfcars.rename(columns={\"Unnamed: 0\":\"car name\"})\n",
    "dfcars.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(32, 12)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfcars.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Searching for values: how many cars have 4 gears?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(dfcars[dfcars.gear == 4].drop_duplicates(subset='car name', keep='first'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, let's split the dataset into a training set and test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "# split into training set and testing set\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "#set random_state to get the same split every time\n",
    "traindf, testdf = train_test_split(dfcars, test_size=0.2, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of full dataset is: (32, 12)\n",
      "Shape of training dataset is: (25, 12)\n",
      "Shape of test dataset is: (7, 12)\n"
     ]
    }
   ],
   "source": [
    "# testing set is around 20% of the total data; training set is around 80%\n",
    "print(\"Shape of full dataset is: {0}\".format(dfcars.shape))\n",
    "print(\"Shape of training dataset is: {0}\".format(traindf.shape))\n",
    "print(\"Shape of test dataset is: {0}\".format(testdf.shape))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we have training and test data.  We still need to select a predictor and a response from this dataset.  Keep in mind that we need to choose the predictor and response from both the training and test set.  You will do this in the exercises below.  However, we provide some starter code for you to get things going."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "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>car name</th>\n",
       "      <th>mpg</th>\n",
       "      <th>cyl</th>\n",
       "      <th>disp</th>\n",
       "      <th>hp</th>\n",
       "      <th>drat</th>\n",
       "      <th>wt</th>\n",
       "      <th>qsec</th>\n",
       "      <th>vs</th>\n",
       "      <th>am</th>\n",
       "      <th>gear</th>\n",
       "      <th>carb</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>Fiat X1-9</td>\n",
       "      <td>27.3</td>\n",
       "      <td>4</td>\n",
       "      <td>79.0</td>\n",
       "      <td>66</td>\n",
       "      <td>4.08</td>\n",
       "      <td>1.935</td>\n",
       "      <td>18.90</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>Merc 450SL</td>\n",
       "      <td>17.3</td>\n",
       "      <td>8</td>\n",
       "      <td>275.8</td>\n",
       "      <td>180</td>\n",
       "      <td>3.07</td>\n",
       "      <td>3.730</td>\n",
       "      <td>17.60</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Mazda RX4</td>\n",
       "      <td>21.0</td>\n",
       "      <td>6</td>\n",
       "      <td>160.0</td>\n",
       "      <td>110</td>\n",
       "      <td>3.90</td>\n",
       "      <td>2.620</td>\n",
       "      <td>16.46</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Hornet Sportabout</td>\n",
       "      <td>18.7</td>\n",
       "      <td>8</td>\n",
       "      <td>360.0</td>\n",
       "      <td>175</td>\n",
       "      <td>3.15</td>\n",
       "      <td>3.440</td>\n",
       "      <td>17.02</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>Chrysler Imperial</td>\n",
       "      <td>14.7</td>\n",
       "      <td>8</td>\n",
       "      <td>440.0</td>\n",
       "      <td>230</td>\n",
       "      <td>3.23</td>\n",
       "      <td>5.345</td>\n",
       "      <td>17.42</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             car name   mpg  cyl   disp   hp  drat     wt   qsec  vs  am  gear  carb\n",
       "25          Fiat X1-9  27.3    4   79.0   66  4.08  1.935  18.90   1   1     4     1\n",
       "12         Merc 450SL  17.3    8  275.8  180  3.07  3.730  17.60   0   0     3     3\n",
       "0           Mazda RX4  21.0    6  160.0  110  3.90  2.620  16.46   0   1     4     4\n",
       "4   Hornet Sportabout  18.7    8  360.0  175  3.15  3.440  17.02   0   0     3     2\n",
       "16  Chrysler Imperial  14.7    8  440.0  230  3.23  5.345  17.42   0   0     3     4"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "traindf.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "25    27.3\n",
       "12    17.3\n",
       "0     21.0\n",
       "4     18.7\n",
       "16    14.7\n",
       "5     18.1\n",
       "13    15.2\n",
       "11    16.4\n",
       "23    13.3\n",
       "1     21.0\n",
       "2     22.8\n",
       "26    26.0\n",
       "3     21.4\n",
       "21    15.5\n",
       "27    30.4\n",
       "22    15.2\n",
       "18    30.4\n",
       "31    21.4\n",
       "20    21.5\n",
       "7     24.4\n",
       "10    17.8\n",
       "14    10.4\n",
       "28    15.8\n",
       "19    33.9\n",
       "6     14.3\n",
       "Name: mpg, dtype: float64"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Extract the response variable that we're interested in\n",
    "y_train = traindf.mpg\n",
    "y_train"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, notice the shape of `y_train`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((25,), pandas.core.series.Series)"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train.shape, type(y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Array reshape\n",
    "This is a 1D array as should be the case with the **Y** array.  Remember, `sklearn` requires a 2D array only for the predictor array.  You will have to pay close attention to this in the exercises later. `Sklearn` doesn't care too much about the shape of `y_train`.\n",
    "\n",
    "The whole reason we went through that whole process was to show you how to reshape your data into the correct format.\n",
    "\n",
    "**IMPORTANT:** Remember that your response variable `ytrain` can be a vector but your predictor variable `xtrain` ***must*** be an array!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a class=\"anchor\" id=\"fifth-bullet\"></a>\n",
    "## 5 - Example: Simple linear regression with automobile data\n",
    "We will now use `sklearn` to predict automobile mileage per gallon (mpg) and evaluate these predictions. We already loaded the data and split them into a training set and a test set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to choose the variables that we think will be good predictors for the dependent variable `mpg`. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"exercise\"><b>Exercise</b></div>\n",
    "\n",
    "* Pick one variable to use as a predictor for simple linear regression.  Discuss your reasons with the person next to you.  \n",
    "* Justify your choice with some visualizations.  \n",
    "* Is there a second variable you'd like to use? For example, we're not doing multiple linear regression here, but if we were, is there another variable you'd like to include if we were using two predictors?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your code here\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Car MPG')"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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DMFB8EGqQJO1erzNevwV8fov2z1W3SSOtjlmSw1iDJGn3th1cHxF/lZlbbhUUESuZWWz/RgfXS5KkYdFrcH2vM14TPW5zAIkkSdIe9QpeSxHx42c2RsSPAcfqK0mSJKmZei0ncS3w1oj4AR4OWjPAVwAvqLkuSZKkxtk2eGXmZ4DLqpXqn1o1vy0zbytSmSRJUsPsuIBqZt4O3L7XJ46IJwBvAM6ju6n2jZn5qoh4PPBm4BDdfR//dWb+/V6fX5IkadjsZgHVR+oh4Bcy8yl093r8qYh4CnAd8K7MfDLwruq6JElS49UWvDLz/sy8o7r8BeBuYJLuSvg3VXe7CThcVw2SJEmDpM4zXqdExCFgGvggcF5m3l/d9Gm6XZGSJEmNV3vwqjbYvhm4NjNPWwk/u6u3brmCa0RcExFLEbF04sSJusuUJEmq3Y6D689GRIzTDV1vzMyjVfNnIuL8zLw/Is4HHtjqsZl5I3AjdFeur7NOaRAsLLeZX1zl+FqHgxMt5man3PpHkhqmtjNeERHAa4G7M/M3N910C/CS6vJLgD+pqwZpWCwstzlydIX2WocE2msdjhxdYWG53e/SJEn7qM6uxsuBHwKuiog7q5/vAW4Anh0RnwCeVV2XRtr84iqdk+untXVOrjO/uNqniiRJdaitqzEz3wvENjd/Z12vKw2j42udPbVLkoZTkVmNkno7OLH1vvPbtUuShpPBSxoAc7NTtMbHTmtrjY8xNzvVp4okSXWodVajpN3ZmL3orMZ6NHHGaBPfkzQKDF7SgDg8PekXZw02ZoxuTF7YmDEKDO3xbuJ7kkaFXY2SGq2JM0ab+J6kUWHwktRoTZwx2sT3JI0Kg5ekRmvijNEmvidpVBi8JDVaE2eMNvE9SaPC4CWp0Q5PT/LCSyYZi+56zmMRvPCS4Z7IcHh6kuuvvojJiRYBTE60uP7qi4b6PUmjwlmNkhptYbnNzcfarGcCsJ7JzcfazHz944c6qDgLVhpOnvGS1GjOAJQ0SAxekhrNGYCSBonBS1KjOQNQ0iAxeElqNGcAShokDq6X1GjugylpkBi8JDWeMwAlDQqDl6SRsrDc9uyXpL4xeEkaGQvLbY4cXTm1vER7rcORoysAhi9JRTi4XtLIcE0vSf1m8JI0MlzTS1K/2dUoqfE2xnXlNre7ppekUgxekhrtzHFdZ3JNL0klGbwkNdpW47o2TDqrUVJhBi9Jjbbd+K0A3nfdVWWLkTTyHFwvqdHcq1HSIDF4SWo092qUNEjsapTUaIO8V6Or6Eujx+AlqfEGca9GV9GXRpNdjZLUB66iL40mg5ck9YGr6EujyeAlSX3gbEtpNBm8JKkPnG0pjSYH10tSHwzybEtJ9TF4SVKfDOJsS0n1sqtRkiSpEIOXJElSIQYvSZKkQhzjJUnaFbc4ks6ewUuStCO3OJL2h12NkqQducWRtD8MXpKkHbnFkbQ/DF6SpB25xZG0PwxekqQducWRtD8cXC9J2pFbHEn7w+AlSdoVtziSzp7BS1ItXPNJkr6cwUvSvnPNJ0namoPrJe0713ySpK0ZvCTtO9d8kqSt2dUoad8dnGjR3iJkDcOaT45Nk1Qnz3hJ2nfDuubTxti09lqH5OGxaQvL7X6XJqkhDF6S9t3h6Umuv/oiJidaBDA50eL6qy8a+DNHjk2TVDe7GiXVYpDWfNpt9+GgjE2zu1NqLoOXpEbby9IWgzA2zaU4pGazq1FSo+2l+3AQxqbZ3Sk1W21nvCLidcBzgQcy86lV2y8DPw6cqO72ssx8e101SNJeug977UdYqvtvULo7JdWjzq7G1wOvBt5wRvsrM/PXa3xdSTplr92HW41NK9n9NwjdnZLqU1tXY2a+G/i7up5fknZjP7oPS3b/DUJ3p6T69GOM109HxF0R8bqI+Nrt7hQR10TEUkQsnThxYru7SVJP+7G0Rcnuv2FdikPS7kRm1vfkEYeAWzeN8ToP+FsggVcA52fmj+z0PDMzM7m0tFRbnZLUy+U33LZl99/kRIv3XXdVHyqSBIO79EpEHMvMma1uK3rGKzM/k5nrmfkl4DXApSVfX5IeCbv/pMEzrDtNFA1eEXH+pqsvAD5S8vUl6ZGw+08aPMO69Eqdy0n8EXAFcG5E3Af8EnBFRFxMt6vxHuAn6np9SdpPg7QSv6ThXXqltuCVmS/eovm1db2eJEkaHcO69Ior10vSLiwst7n8htv4huvexuU33Dbw40ikphvWsZfu1ShJO3D/RGnw9NppYpAZvCRpB70G8Q76H3mpyYZx7KVdjZK0g2EdxCtp8Bi8JGkH2w3WHfRBvJIGj8FLknYwrIN4JQ0ex3hJ0g6GdRCvpMFj8JKkXRjGQbySBo9djZIkSYUYvCRJkgoxeEmSJBVi8JIkSSrEwfWSNGQWltvOsJSGlMFLkoaI+0ZKw82uRkkaIr32jZQ0+AxekjRE3DdSGm4GL0kaIu4bKQ03g5ckDRH3jZSGm4PrJWmIuG+kNNwMXpI0ZNw3UhpedjVKkiQVYvCSJEkqxOAlSZJUiMFLkiSpEIOXJElSIQYvSZKkQgxekiRJhRi8JEmSCjF4SZIkFWLwkiRJKsTgJUmSVIjBS5IkqRCDlyRJUiEGL0mSpEIMXpIkSYUYvCRJkgoxeEmSJBVi8JIkSSrE4CVJklSIwUuSJKkQg5ckSVIhBi9JkqRCDF6SJEmFGLwkSZIKMXhJkiQVYvCSJEkqxOAlSZJUiMFLkiSpEIOXJElSIef0uwBJkiSAheU284urHF/rcHCixdzsFIenJwf+uffC4CVJkvpuYbnNkaMrdE6uA9Be63Dk6ArAWQekOp97r+xqlCRJfTe/uHoqGG3onFxnfnF1oJ97rwxekiSp746vdfbUPijPvVcGL0mS1HcHJ1p7ah+U596r2oJXRLwuIh6IiI9sant8RLwzIj5R/fu1db2+JEkaHnOzU7TGx05ra42PMTc7NdDPvVd1nvF6PfCcM9quA96VmU8G3lVdlyRJI+7w9CTXX30RkxMtApicaHH91Rfty+D3Op97ryIz63vyiEPArZn51Or6KnBFZt4fEecDf56ZO8bNmZmZXFpaqq1OSZKk/RIRxzJzZqvbSo/xOi8z768ufxo4b7s7RsQ1EbEUEUsnTpwoU50kSVKN+ja4Prun2rY93ZaZN2bmTGbOHDhwoGBlkiRJ9SgdvD5TdTFS/ftA4deXJEnqm9LB6xbgJdXllwB/Uvj1JUmS+qbO5ST+CHg/MBUR90XEjwI3AM+OiE8Az6quS5IkjYTa9mrMzBdvc9N31vWakiRJg8yV6yVJkgoxeEmSJBVi8JIkSSrE4CVJklRIrVsG7ZeIOAHcW+NLnAv8bY3PP+hG/f2DxwA8BuAxAI8BeAzAY3C27//rM3PL1d+HInjVLSKWtttTaRSM+vsHjwF4DMBjAB4D8BiAx6DO929XoyRJUiEGL0mSpEIMXl039ruAPhv19w8eA/AYgMcAPAbgMQCPQW3v3zFekiRJhXjGS5IkqZCRCV4R8bqIeCAiPrLN7VdExOci4s7q5xdL11iniHhCRNweER+LiI9GxM9tcZ+IiN+OiE9GxF0R8c39qLUuuzwGTf8cPDoiPhQRH66Owcu3uM9XRsSbq8/BByPiUB9Krc0uj8FLI+LEps/Bj/Wj1jpFxFhELEfErVvc1ujPwIYdjsEofAbuiYiV6v0tbXF7o78TYFfHYN+/E2rbJHsAvR54NfCGHvd5T2Y+t0w5xT0E/EJm3hERjwWORcQ7M/Njm+7z3cCTq59vBX6v+rcpdnMMoNmfgweBqzLzixExDrw3It6RmR/YdJ8fBf4+My+MiBcBvwb8m34UW5PdHAOAN2fmT/ehvlJ+DrgbeNwWtzX9M7Ch1zGA5n8GAK7MzO3Wq2r6d8KGXscA9vk7YWTOeGXmu4G/63cd/ZKZ92fmHdXlL9D9YzN5xt2eD7whuz4ATETE+YVLrc0uj0GjVb/bL1ZXx6ufMwd6Ph+4qbr8FuA7IyIKlVi7XR6DRouIC4DvBX5/m7s0+jMAuzoGavh3Qr+MTPDapWdW3Q/viIhv6ncxdam6DaaBD55x0yTwN5uu30dDg0mPYwAN/xxU3St3Ag8A78zMbT8HmfkQ8DngnxUtsma7OAYAL6y6V94SEU8oW2Htfgv4j8CXtrm98Z8Bdj4G0OzPAHT/w/FnEXEsIq7Z4vZR+E7Y6RjAPn8nGLwedgfdJf6fDvwXYKG/5dQjIh4D3Axcm5mf73c9/bDDMWj85yAz1zPzYuAC4NKIeGqfSypuF8fgfwKHMvNpwDt5+OzP0IuI5wIPZOaxftfSL7s8Bo39DGzybZn5zXS7FH8qIr6j3wX1wU7HYN+/Ewxelcz8/Eb3Q2a+HRiPiHP7XNa+qsaz3Ay8MTOPbnGXNrD5f3UXVG2NsdMxGIXPwYbMXANuB55zxk2nPgcRcQ7wNcBnixZXyHbHIDM/m5kPVld/H7ikcGl1uhx4XkTcA7wJuCoi/scZ92n6Z2DHY9DwzwAAmdmu/n0AeCtw6Rl3afx3wk7HoI7vBINXJSK+bmMMQ0RcSvfYNOYPTfXeXgvcnZm/uc3dbgF+uJrJ8gzgc5l5f7Eia7abYzACn4MDETFRXW4BzwY+fsbdbgFeUl3+fuC2bNCCf7s5BmeMY3ke3fGAjZCZRzLzgsw8BLyI7u/3B8+4W6M/A7s5Bk3+DABExFdXk4yIiK8Gvgs4c9Z/078TdjwGdXwnjMysxoj4I+AK4NyIuA/4JbqDasnM/0r3j8u/i4iHgA7woib9oaH7P7wfAlaqsS0ALwOeCKeOwduB7wE+Cfwj8G/Ll1mr3RyDpn8Ozgduiogxun9A/jgzb42IXwGWMvMWuuH0v0fEJ+lOSHlR/8qtxW6Owc9GxPPozoT9O+Clfau2kBH7DGxpxD4D5wFvrTLFOcAfZuafRsRPwsh8J+zmGOz7d4Ir10uSJBViV6MkSVIhBi9JkqRCDF6SJEmFGLwkSZIKMXhJkiQVYvCSNFCqdXPeFBGfqrbxeHtE/MtH+FzPj4iFTdePVEskbFz/voi4pcfjnxcR1+3wGldExK3b3HZtRHzVIyhdUkMZvCQNjGqhwrcCf56ZT8rMS4AjdNfb2dXjI2Lz37W/BJ6x6fozgc9HxD+vrl9W3WdLmXlLZt6wl/dwhmsBg5ekUwxekgbJlcDJauFCADLzw5n5noh4TES8KyLuiIiViHg+dDc8j4jViHgD3VWnn7DpsSfoBq0Lq6ZJultGXVZdvwx4X7Wa/c0R8VfVz+XVc780Il5dXX5SRHygeu1fjYgvbqr7MdHdSPnjEfHGKgD+LHAQuD0ibq/jYEkaPgYvSYPkqcB2Gxf/E/CCakPbK4Hf2NjKA3gy8LuZ+U2Zee8Zj3sfcFlETAGfAD5QXT8HeDrwV8CrgFdm5rcAL6S7N9+ZXgW8KjMvAu4747Zpume3ngL8C+DyzPxt4DhwZWZeuat3L6nxRmbLIElDL4D/HBHfAXyJ7tmrjS7IezPzA9s87i/pntkaA94PfAj4Rbph6eOZ+U8R8SzgKQ/nOB4XEY8543meCRyuLv8h8OubbvtQZt4HUG1HdQh4797foqSmM3hJGiQfpbs32lZ+ADgAXJKZJyPiHuDR1W3/0OM53wf8DN3g9ZrM/EJEPJru3q0b47seBTwjM/9p8wM3BbGdPLjp8jr+bZW0DbsaJQ2S24CvjIhrNhoi4mkR8e3A1wAPVKHrSuDrd/mcd9Mda/VtwHLVdifwk3RDGcCf0Q1nG6958RbP8wG63ZCw+02jvwA8dpf3lTQCDF6SBkZmJvAC4FnVchIfBa4HPg28EZiJiBXgh4GP7+E5Pwh8NjNPVs3vpzsWa+OM189Wz31XRHyMbig707XAf4iIu4ALgc/t4uVvBP7UwfWSNkT3b5IkqZdqPa5OZmZEvAh4cWY+v991SRoujkOQpN25BHh1NZNyDfiR/pYjaRh5xkuSJKkQx3hJkiQVYvCSJEkqxOAlSZJUiMFLkiSpEIOXJElSIQYvSZKkQv4/psBycJUgzbcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# %load solutions/cars_simple_EDA.py"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"exercise\"><b>Exercise</b></div>\n",
    "\n",
    "* Use `sklearn` to fit the training data using simple linear regression.\n",
    "* Use the model to make mpg predictions on the test set.  \n",
    "* Plot the data and the prediction.  \n",
    "* Print out the mean squared error for the training set and the test set and compare."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "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>name</th>\n",
       "      <th>mpg</th>\n",
       "      <th>cyl</th>\n",
       "      <th>disp</th>\n",
       "      <th>hp</th>\n",
       "      <th>drat</th>\n",
       "      <th>wt</th>\n",
       "      <th>qsec</th>\n",
       "      <th>vs</th>\n",
       "      <th>am</th>\n",
       "      <th>gear</th>\n",
       "      <th>carb</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Mazda RX4</td>\n",
       "      <td>21.0</td>\n",
       "      <td>6</td>\n",
       "      <td>160.0</td>\n",
       "      <td>110</td>\n",
       "      <td>3.90</td>\n",
       "      <td>2.620</td>\n",
       "      <td>16.46</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Mazda RX4 Wag</td>\n",
       "      <td>21.0</td>\n",
       "      <td>6</td>\n",
       "      <td>160.0</td>\n",
       "      <td>110</td>\n",
       "      <td>3.90</td>\n",
       "      <td>2.875</td>\n",
       "      <td>17.02</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Datsun 710</td>\n",
       "      <td>22.8</td>\n",
       "      <td>4</td>\n",
       "      <td>108.0</td>\n",
       "      <td>93</td>\n",
       "      <td>3.85</td>\n",
       "      <td>2.320</td>\n",
       "      <td>18.61</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Hornet 4 Drive</td>\n",
       "      <td>21.4</td>\n",
       "      <td>6</td>\n",
       "      <td>258.0</td>\n",
       "      <td>110</td>\n",
       "      <td>3.08</td>\n",
       "      <td>3.215</td>\n",
       "      <td>19.44</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Hornet Sportabout</td>\n",
       "      <td>18.7</td>\n",
       "      <td>8</td>\n",
       "      <td>360.0</td>\n",
       "      <td>175</td>\n",
       "      <td>3.15</td>\n",
       "      <td>3.440</td>\n",
       "      <td>17.02</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                name   mpg  cyl   disp   hp  drat     wt   qsec  vs  am  gear  carb\n",
       "0          Mazda RX4  21.0    6  160.0  110  3.90  2.620  16.46   0   1     4     4\n",
       "1      Mazda RX4 Wag  21.0    6  160.0  110  3.90  2.875  17.02   0   1     4     4\n",
       "2         Datsun 710  22.8    4  108.0   93  3.85  2.320  18.61   1   1     4     1\n",
       "3     Hornet 4 Drive  21.4    6  258.0  110  3.08  3.215  19.44   1   0     3     1\n",
       "4  Hornet Sportabout  18.7    8  360.0  175  3.15  3.440  17.02   0   0     3     2"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import mean_squared_error\n",
    "\n",
    "dfcars = pd.read_csv('data/mtcars.csv')\n",
    "dfcars = dfcars.rename(columns={\"Unnamed: 0\":\"name\"})\n",
    "\n",
    "dfcars.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "traindf, testdf = train_test_split(dfcars, test_size=0.2, random_state=42)\n",
    "\n",
    "y_train = np.array(traindf.mpg)\n",
    "X_train = np.array(traindf.wt)\n",
    "X_train = X_train.reshape(X_train.shape[0], 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_test = np.array(testdf.mpg)\n",
    "X_test = np.array(testdf.wt)\n",
    "X_test = X_test.reshape(X_test.shape[0], 1)"
   ]
  },
  {
   "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>name</th>\n",
       "      <th>mpg</th>\n",
       "      <th>cyl</th>\n",
       "      <th>disp</th>\n",
       "      <th>hp</th>\n",
       "      <th>drat</th>\n",
       "      <th>wt</th>\n",
       "      <th>qsec</th>\n",
       "      <th>vs</th>\n",
       "      <th>am</th>\n",
       "      <th>gear</th>\n",
       "      <th>carb</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Mazda RX4</td>\n",
       "      <td>21.0</td>\n",
       "      <td>6</td>\n",
       "      <td>160.0</td>\n",
       "      <td>110</td>\n",
       "      <td>3.90</td>\n",
       "      <td>2.620</td>\n",
       "      <td>16.46</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Mazda RX4 Wag</td>\n",
       "      <td>21.0</td>\n",
       "      <td>6</td>\n",
       "      <td>160.0</td>\n",
       "      <td>110</td>\n",
       "      <td>3.90</td>\n",
       "      <td>2.875</td>\n",
       "      <td>17.02</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Datsun 710</td>\n",
       "      <td>22.8</td>\n",
       "      <td>4</td>\n",
       "      <td>108.0</td>\n",
       "      <td>93</td>\n",
       "      <td>3.85</td>\n",
       "      <td>2.320</td>\n",
       "      <td>18.61</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Hornet 4 Drive</td>\n",
       "      <td>21.4</td>\n",
       "      <td>6</td>\n",
       "      <td>258.0</td>\n",
       "      <td>110</td>\n",
       "      <td>3.08</td>\n",
       "      <td>3.215</td>\n",
       "      <td>19.44</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Hornet Sportabout</td>\n",
       "      <td>18.7</td>\n",
       "      <td>8</td>\n",
       "      <td>360.0</td>\n",
       "      <td>175</td>\n",
       "      <td>3.15</td>\n",
       "      <td>3.440</td>\n",
       "      <td>17.02</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                name   mpg  cyl   disp   hp  drat     wt   qsec  vs  am  gear  carb\n",
       "0          Mazda RX4  21.0    6  160.0  110  3.90  2.620  16.46   0   1     4     4\n",
       "1      Mazda RX4 Wag  21.0    6  160.0  110  3.90  2.875  17.02   0   1     4     4\n",
       "2         Datsun 710  22.8    4  108.0   93  3.85  2.320  18.61   1   1     4     1\n",
       "3     Hornet 4 Drive  21.4    6  258.0  110  3.08  3.215  19.44   1   0     3     1\n",
       "4  Hornet Sportabout  18.7    8  360.0  175  3.15  3.440  17.02   0   0     3     2"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's take another look at our data\n",
    "dfcars.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((25,), (25, 1))"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# And out train and test sets \n",
    "y_train.shape, X_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((7,), (7, 1))"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_test.shape, X_test.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R^2 = 0.68798\n"
     ]
    }
   ],
   "source": [
    "#create linear model\n",
    "regression = LinearRegression()\n",
    "\n",
    "#fit linear model\n",
    "regression.fit(X_train, y_train)\n",
    "\n",
    "predicted_y = regression.predict(X_test)\n",
    "\n",
    "r2 = regression.score(X_test, y_test)\n",
    "print(f'R^2 = {r2:.5}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7701379909791616\n",
      "12.475985659918818\n",
      "7.7736977663875155\n",
      "Coefficients: \n",
      " -5.336941400557079 36.93731031351841\n"
     ]
    }
   ],
   "source": [
    "print(regression.score(X_train, y_train))\n",
    "\n",
    "print(mean_squared_error(predicted_y, y_test))\n",
    "print(mean_squared_error(y_train, regression.predict(X_train)))\n",
    "\n",
    "print('Coefficients: \\n', regression.coef_[0], regression.intercept_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x146db3250>]"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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frtobXroPFi9e/nMoUaNq5iwRngAaFi5iVM2chCqSpOQYoJRbqQrY5WdxL6l9/w7z34ObjoJLdoZnb7KXVB6bW9+Q0XFJKmYGKCWjPAXbnwRn1sKAK+JhvDtOgbHbwtTL7SWVhzpVpDI6LknFzAClZJW1he6Hw2lPwlE3wxobwv0jYEw3eGwUNHycdIVKG1FdRaq8bIljqfIyRlRXJVSRJCXHAKX8EAJU7QODHoAT7ofKbWHi2TC6GzzwG/js3aQrLHn9e1ZyzoBuVFakCEBlRcoJ5JJKlqvwlL/enRV3N3/+DmjTFnocDTsPgXU2S7oySVIJcBWeCtMG3eDQq+HM6dDjGJj5L7iwN9x6ArzzXNLVSZJKmAFK+W/t78EBY+KVezufCS8/CJftAtcfAm88Ee/FJ0lSDhmgVDhW3wD2/mPcS6rfb2DuTLhmX7i6Gubcby8pSVLOGKBUeFIVsOvP4yC179/jzYpvPBIu7QPP3gyLvk66QklSkTNAqXA19pIaMgMOvjweyrvjZLigJzx9BSy0waMkKTsMUCp8ZeWwzRHpXlI3wWobwH0/h9Fd4bG/Q0N90hVKkoqMAUrFo00bqPpR3Evq+PugUw+Y+Kc4SD3423hDY0mSWoEBSsUnBOjSB469HU55HLbYG568IO5ufvcw+Oi1pCuUJBU4A5SK24bd4bB/wuBp0OMomHkDXNALbhsUN+qUJGkFGKBUGtbZDA44P+4ltdNg+M+/4dK+cMNh8OaTSVcnSSowbuWinJlQW8eomjnMrW+gU0WKEdVVye2j1vAxPHMlTLkEvvgQNt4R+g6HLavjIUDl189LkhLQ3FYuBijlxITaOkaOn0XDwkXfHEuVlyW/Ge1XX0Dt9fDkWPjkLVhva+g7DLYeAGVtk6srYXn785KkHHIvPCVuVM2cJX4ZAzQsXMSomjkJVZS2yqqww8kwpBYOvgyiRTD+pJLvJZW3Py9JyhMGKOXE3Pqmg8iyjudcWTlscySc9hQceSOstn7cS2pMN3j8H/DlJ0lXmFN5//OSpIQZoJQTnSpSGR1PTJs28P19YdCDcPy9sEF3ePiPcS+ph35fMr2kCubnJUkJMUApJ0ZUV5EqL1viWKq8jBHVVQlVtBwhQJe+cNx4OOUx2HxPeOL8+IrUPT+Fj15PusKsKriflyTlWOnOklVONU48LshVXRtuA4ddAx++Goeo2utg+jXQdUC8cm/9rZOusNUV9M9LknLAVXhSpj59B6ZcBNP+CV/Nhy2qYZefQucdk65MktSKXIUntaY1NoQfng3DZ8Mev4a6aXB1NVy9D/znAcjhf0okSckwQEkrKrUW7DYi7m6+z1/hk7fhX4fFHc5n3QaLvk66QklSlhigpJW1SgfY8dS4l1T/S2DRQrh9EFywbdztfOGXSVcoSWplBiiptZSVQ4+j4fQpcMQN0GFduPdn6V5S55VcLylJKmYGKKm1tWkDP9gffvIwDLwbNugKD/8h3UvqDzD//aQrlCStJAOUlC0hwKa7wnF3wMmPwGb9YPLo+IrUvT+Dj99MukJJ0goyQEm50KknHD4OBk+D7ofD9HEwtifcfhK890LS1UmSMmQfKBWkCbV1hd3k8dO58FS6l9TCz2HLfaDvT6HzDklXJklKa64PlAFKBWdCbR0jx8+iYeGib46lyss4Z0C3wgpRAF98FK/Um3IJNHwEnXeOm3Juvlc8BChJSowBSkWlz7kTqatv+J/jlRUpnjirXwIVNS2jq2RffQ4zroUnL4BP62D9btB3GGzVH8ryc8elgr8KKEnLYSdyFZW5TYSn5o4nofEqWV19AxFQV9/AyPGzmFBb1/QDVukAO54GQ2bCQRfDogVxL6kLe8G0q/Oul1TGr0+SiowBSgWnU0Uqo+NJGFUzZ4khRoCGhYsYVTOn+Qe2XQV6HgOnT4XDr4PU2nDPcDi/O0weA19+mr2iM7DCr0+SioQBSgVnRHUVqfKyJY6lyssYUV2VUEX/a6WvkrVpA1sdCCdNhB/fBettBQ/9Lu4l9fAfYf68Vqw2c4VwFVCSsik/J1dIzWicZ9Oa829aez5Pp4pUk/O0mrtKtswavrdb/DG3Nu4j9fh58Qq+nsfBzmfCWpuscJ0rakVenyQVEyeRq+RlY1Vfps+Z0f0/eBmeOB+evQmixdDtUOg7HNb7wQrVuiKKaiWkJC2Dk8ilZmRjPk//npWcM6AblRUpAvEKwebCRUY1rLsFHHQhDH02nnj+4j1w8Y5w41Hw1tMrXHMmMn19klRsvAKlkrfpWffS1N+CALx+7n75X8MXH8HTl8PUS6HhY9ikb3xFavM97SUlSSvBK1BSM/JhVd9K1bDq2rD7WTD8eag+Bz5+HW44BC7bBWbfDosXLf85JEkZMUCp5OXDqr5WqWGVDrDT6XEvqQMvjHtH3XYiXNAr3jLm6wWtW7QklTADlEpePsznadUa2q4C2x4HZzT2kqqAe4bBmO7x5PMFn7Vy9ZJUepwDJRW7KILXH43bH7z+KLRfE7Y7KZ6A3mHdpKuTpLzlHCiplIUA39sdBt4VN+bcdDd4/B9xU877RkD9f5OuUJIKjgFKKiWVveCI6+CMp6HrIfE+e2N7wh2nwvsvJl2dJBUMA5RUijpuCf0vintJbX8yvHBnupfU0fDWM0lXJ0l5b7kBKoSwcQhhUgjhhRDC8yGEoenja4cQHgwhvJz+c63slyupVa25EexzTtwCYbez4M0n4Kq94Jr94ZWH4vlTkqT/0ZIrUF8DP4uiaCtgR+CMEMJWwFnAw1EUbQE8nP5aUiFadW3YY2S6l9Rf4MNX4fpD4LJdYfZ4e0lJ0lKWG6CiKHoniqIZ6c8/A14EKoGDgHHpu40D+mepRkm50m412OkMGDoz3UvqC7jtBLiwN0y/xl5SkpSW0RyoEEIXoCcwFVg/iqJ30je9C6zfuqVJSkzbduleUk/D4ddCuzXg7qFw/jbw5AX2kpJU8lrcByqEsBrwKPDnKIrGhxDqoyiq+M7tH0dR9D/zoEIIJwMnA3Tu3LnXm2++2SqFS/lqQm0do2rmMLe+gU4VKUZUVxX+JrtRBK9Ngsmj4fXHoH1FPPl8h1PsJSWpaDXXB6pFASqEUA7cA9REUXRe+tgcYPcoit4JIWwIPBJFUbP7TthIU8VuQm0dI8fPomHht3OGUuVlOe9snlVvT4fJ58FL90DbFPQaCDsNhoqNk65MklrVSjXSDCEE4CrgxcbwlHYXMDD9+UDgzpUtVCp0o2rmLBGeABoWLmJUzZyEKsqCjXrBkTeke0kNgGeuhLE94I7T4P2Xkq5OknKiJXOg+gDHAf1CCDPTH/sC5wJ7hxBeBvZKfy2VtLn1DRkdL2gdq6D/xfHmxdv9BJ6/Ay7eAW46Bt72SrOk4tZ2eXeIomgyEJZx856tW45U2DpVpKhrIix1qkglUE2OVGwMP/or7PoLePoymHpZPLzXZRfY5afwvT3i7WQkqYjYiVxqRSOqq0iVly1xLFVexojqZqcHFocO68Ae/wfDZ8MPz4YPX4HrDobLd4fnJ9hLSlJRafEqvNbgJHKVgqJchbcivl4Az90Mk8fAR6/COptDn6HQ/Yi4TcIKKMZzW4yvSSoWK70Kr7UYoKQStHgRvHh3vHLvnWdh9U5xs85ex8eNO1uoGFc4FuNrkorJSq3Ck6SV0qYMtu4PJz8Kx46HdTaDB34Fo7eGSX+Bzz9s0dMU4wrHYnxNUqkwQEnKjRBg8z3h+Htg0EOwSR949K8wpivcfxbUv9Xsw4txhWMxviapVBigJOXextvBUf+C06fCVgfBM1fEvaQmnA7zmr76sqyVjIW8wrEYX5NUKgxQkpKz3vfh4EthSC30HgSzx8NFjb2kpi9x1xHVVZSXLdkOobwsFPQKx5JetSkVOAOUpORVdIZ9/xa3QNj15/DG43BlPxh3ALw6Kd6LD2DpNS+5WwOTFf17VnLOgG5UVqQIQGVFygnkUoFwFZ6k/LPgM5j2T3jqIpj/LnTqya/m7c2/PutOtNT/+yorUjxxVr+ECpVUzFyFJ6mwtFsd+gyBYc/BAefDl5/w54V/46FVRnBY2SOU8/U3d3XCtaQkGKAk5a+27eJ+UYOn8evyn9NAO0aVX85j7YYxqOw+VuVLJ1xLSoQBSlL+a1NG731P5LDoXH781S95Y/EG/Kb8ep5sN4QrN3kIvvgo6QollZjlbiYsSfmgcWL1qJp2HF2/DXun/ssf1q7hB3MugtH/jK9U7TQY1nQCtqTscxK5pILUuIdch09eZnjqPqqjx2kT2sR77fUZCh23TLpESQXOSeSSikrjHnJ19Q38J9qI0744mb2/HsNrmxwGs2+Di7aHm4+FuhlJlyqpSBmgJBWcpvaQe3XhOhz3zmEwbDbs8jN47TG4Yg8YdyC89si3vaQkqRUYoCQVnGb3kFutI+z5m7gp595/ireGufYguKIfvHAXLF6c42olFSMDlKSCMaG2jj7nTlxmA/IlWhq0XyPuJTX0Wdh/DDR8DLccFw/v1V4PX3+Vi5IlFSkDlKSC8N15T01Z5h5y5e2h9wlw5nQ49Or46zvPgLE9Ycol8NXnWa5cUjEyQEkqCE3Ne2rUoj3k2pRB10PglMfhmNthrU3g32fB6K7wyLn2kpKUEftASSoIy5r3FCCzvfBCgC32ij/+OxUmj4ZHzoEnxqZ7SZ1hLylJy+UVKEkFYVlbtqzUVi6dd4Cjb4LTnoTv7wdTL4Xzt4E7B8MHL6/480oqegYoSQVhRHUVqfKyJY4tc95TptbfGg65AobMiK9CzboVLtwObj4O5tYu9+GNk9s3Pete+pw7kQm1dStfk6S8ZidySQWjsfv43PoGOlWkGFFd1fy8pxU1fx5MvQSevhIWfALf2wP6DodNd42HAJeqaeT4WUvMz0qVly1/TpakvNdcJ3IDlCQty5efwrSrYcrFMP89qOwVB6mq/aBNfAG/z7kTm1wZWFmRymxulqS841YukrQi2q8BfYfB0Odg/9HwxYfxFjEX7wi1N8Cihc039ZRUtAxQkrQ85e2h94kweDocchWUlcOdp8P5PRiy2sOk+PJ/HrJSk9sl5T0DlCS1VFlb6HYonDoZjr4VKjoz/OureLLdUIaUjWdN5gOtOLldUt5yDpQkrYz/TuHde//CBu89yvyoPXe1rWbtPYexz87bJl2ZpJXkJHJJyrZ3Z8MT58Ps2+Ou59scCTsPhXU3T7oySSvISeSSlG0bdI17SZ05Hbb9MTx7M1zYG24ZCHNnJl2dpFZmgJKk1rT2prDfP2D47LjlwasT4fLd4LqD4fXHIYdX/SVljwFKkrJhtfVgr9/FQWqv38dDfOP2hyv3gpfuhcWLk65Q0kpwDpQk5cLCBpj5r3ieVP2b0PH70GdYvKqvrDynpeSso7tU4JwDJUlJK0/BdoPgzBkw4EoIZTDhVBjbE6ZeBl99kZMyGreeqatvIALq6hsYOX6W+/dJGTJASVIulbWF7ofBaU/A0bfAGpVw/y9gTFd4dBQ0fJzVbz+qZs4S+/YBNCxcxKiaOVn9vlKxMUBJUhJCgC2rYVANnPBvqOwNk86G0V3hgV/Dp+9k5du69YzUOgxQkpS0TXaCY26BU5+Aqh/BUxfB+d3hriHw4aut+q2WtcWMW89ImTFASVK+2KArHHJlPE+q53Hw7E1xL6lbj4d3nm2VbzGiuopUedkSx9x6RsqcAUqS8s3am8L+58GwWbDzEHj5IbhsV7j+EHhj8kr1kurfs5JzBnSjsiJFACorUpwzoJur8KQM2cZAUrNc8p4HGuph2lUw5RL4fB5stH3cpHPLfaCN/w+WssU2BpJWiEve80SqAnb5WXxFat+/w/x34aaj4JKd42G+RQuTrlAqOQYoScvkkvc8U56C7U+CM2thwBXxSr47ToGx28LUy3PWS0qSAUpSMwp5yfuE2jr6nDuRTc+6lz7nTiyuq2ZlbaH74fGqvaNugjU2hPtHwJhu8NioeMhPUlYZoCQtU6EueS+Zocc2beK2ByfWwAn3Q+W2MLGxl9Rv4LN3k65QKloGKEnLVKhL3ktu6DEE2GRnOOZWOHUybPlDeOpCGNMd7h4GH72WdIVS0WmbdAGS8lfjart8WYXX0hWB+TL0mMgKxg26waFXQ79fw5MXQO0NMGMcbH1wvHnxht2z+/2lEmEbA0kFoXFY7rtXllLlZU32MOpz7kTqmghLlRUpnjirX9ZrhczqzarP3oUpF8MzV8NXn8Hme8ctEDbZOb5yJWmZVqqNQQjh6hDC+yGE2d859vsQQl0IYWb6Y9/WLFiSlpbJsFw+DD3mzTDi6hvA3n+E4bOh329gbi1csy9cXQ1z7ofFi3Nbj1QkWjIH6hpgnyaOj46iqEf6477WLUuSlpTJsFxz3bZztTovX4YRv5GqgF1//m0vqU/fgRuPhEv7wLM320tKytBy50BFUfRYCKFLDmqRpGXqVJFqclhuWSsC+/es/J+hsqWH1RpX5zXeP8l6c2aVVeNeUr2Oh9njYfJouONkmHR2vG1Mz2PjflOSmrUyq/AGhxCeSw/xrdVqFUlSE1pjWC6Xw2r5MIzYrLJy2OYIOO3JuJfUahvAfT+PWyA89nd7SUnLsaIB6hJgM6AH8A7wj2XdMYRwcghhWghh2rx581bw20kqda2xCW4uh9UKZtPexl5Sgx6A4++DTj1g4p/iIPXgb+Gz95KuUCWgEBvftmgVXnoI754oirpmctvSXIUnKUn5sDqvILzzXDy098IEaFMOPY+Jh/fW3jTpylSE8mbFahNafTPhEMKG3/nyYGD2su4rSfki74fV8sWG3eGwf8LgadDjKKi9Hi7YFm4bBO/6z71aV96sWM3QcieRhxBuBHYH1g0hvA38Dtg9hNADiIA3gFOyV6IktY58awya99bZDA44H3YfCU9dBNOuhtm3wRY/hL4/hU12SrpCFYG8W7HaQjbSlCS1TMPH8MyVMOUS+OJD2HjHuCnnltU25dQKy+eh9VYfwpOkQlWIk1XzRmot2HUEDJsNPxoFn9bBjUfAJX3guVtg0ddJV6gCVKhD6wYoSSWjcbJqXX0DEd/2gTJEZWiVVWGHk2FILRx8GUSLYPxJcEFPePoKWJjfQy/KLwWzYnUpDuFJKhn5PFRQ0BYvhv/8GyafB28/Ax3Wgx1Pg+0GQfs1k65OWmEO4UkShTtZNe+1aQPf3xcGPQgD74ENusHDf4h7ST30e5j/ftIVSq3OACWpZCxrG5XEt1cpFiHAprvAcePh5Edh8z1h8pg4SN3zU/jo9aQrlFqNAUpSySjUyaoFqVMPOOwaOHN6vGVM7XVwQS+4/Sfw3vNJVyetNAOUpJJRqJNVC9o6m8GBF8DQZ+N5UXPuh0t2hhsOhzefSro6aYU5iVySlDtffPRtL6mGj6DzTnFTzi32tpeU8o6TyCVJ+WHVtWG3X8Dw2bDPX6H+LfjXYXBpX5h1m72kVDAMUJKk3FulA+x4KgydCf0vgUUL4fZBcGEveOYqWPhl0hVKzTJASZKSU1YOPY6G06fAETfAquvCvT+FMd1g8mj48tOkK5Sa5BwoSUrIhNo6NzZeWhTBG4/D4+fBa5Og3ZpxQ84dT4PV1ku6OpWY5uZAGaAkKQGN28o0LFz0zbFUeZmrAr9rbm3cR+qFO6FtO+h5LOx8JqzVJenKVCKcRC5JeWZUzZwlwhNAw8JFjKqZk1BFeahTTzh8HAyeBt0Og+njYOy2cPtJ9pJS4gxQkpQAt5XJwLqbw0EXwrDn4qG8l+6Ne0n96wj479Skq1OJMkBJUgLcVmYFrNEJqv8ct0DY/f/grafh6h/C1T+Clx+M509JOWKAkqQEuK3MSlh1bdj9l+leUudC/Ztww6Fw6S72klLOGKAkKQFuK9MKVukQD+kNmZnuJbUg3UuqN0y72l5SyipX4UmSisPixTDn3rgFwtwZsNr6sNMZ0OsEaL9G0tWpALkKT5JU/Nq0gR8cACdNhB/fBev9AB78LYzpCg//CebPS7pCFREDlCSpuIQA39sNfnwnnDQJNt0NHv9HHKTu/Tl8/GbSFaoIGKAkScWrcls44jo442nodihMvwbG9oTxJ8N7LyRdnQqYAUqSVPw6bgkHXRRvXrzDKfDi3XDJTvCvI+N2CFKGDFCSpNKx5kawzzkw/HnYfSS8NQWu2hv+uR+8/JC9pNRiBihJUulZdW3Y/aw4SFWfAx+/DjccApftCrPHw+JFy38OlTQDlCSpdK3SAXY6Pe4lddBFsLABbjsh7iU1/Rr4ekHSFSpPGaAkSWq7CvQ8Fs6YCodfB+3XhLuHwpju8MRYWPBZ0hUqzxigJElq1KYMtjowbn9w3AToWAUP/gZGbw0Tz4bPP0i6QuUJA5QkSUsLATbbAwbeFTfm3HRXeOzvMLor3DcC6v+bdIVKmAFKkqTmVPaCI66Ph/e6Doj32Tu/B4w/Bd5/MenqlBADlCRJLdGxCvpfDEOfTfeSugsu3hFuPBreeibp6pRjBihJkjLR2Etq2GzY7Sx48wm4ai+4Zn94xV5SpcIAJUnSiuiwDuwxMt1L6i/w4atw/SFw+W7w/B32kipyBihJklZGu9VgpzPibWIOvBC++hxuPR4u3A6mj7OXVJEyQEmS1BratoNtj4s3Lj78Wmi3Otw9BM7fBp68wF5SRcYAJUlSa2pTBlsdBCc/AsfdAetuAQ/8Om6BMPHP9pIqEgYoSZKyIQTYrB8MvBt+8jB06QuP/S0OUvf/EurfSrpCrQQDlCRJ2bZRbzjyhnh4r+sAeOZKGNsD7jgN3n8p6eq0AgxQkiTlSmMvqSEzYbuT4IUJcPEOcNMx8Pa0pKtTBgxQkiTlWsXG8KNz415Su/4C3pgMV+4Z95J6daK9pAqAAUqSpKR0WAf6/QqGz4Yfng0fvgLXHQyX7w7PT7CXVB4zQEmSlLR2q8POZ8bbxBwwNm55cOtAuGh7mHGtvaTykAFKkqR80bYd9BoIg5+Bw66B8lXhrjPjzYufvBAWzE+6QqUZoCRJyjdtymDrg+GUx+DY8bDOZvDAr2D01jDpL/D5h0lXWPJClMOJar17946mTXOVgSRJGXvrGZg8GubcG1+Z2nYg7Dw43tw4z0yorWNUzRzm1jfQqSLFiOoq+veszPvnXloIYXoURb2bvM0AJUlSAXn/JXhiDMy6Nf66+xHQZxh03DLJqr4xobaOkeNn0bDw2wnwqfIyzhnQbaWDTjafuynNBSiH8CRJKiTrfR8OvhSG1ELvQTB7fDzZ/KZjoG560tUxqmbOEgEHoGHhIkbVzMnr586UAUqSpEJU0Rn2/VvcAmHXn8Mbj8MV/WDcAYn2kppb35DR8Xx57kwtN0CFEK4OIbwfQpj9nWNrhxAeDCG8nP5zreyWKUmSmtRhXej367gp595/gnn/SbSXVKeKVEbH8+W5M9WSK1DXAPssdews4OEoirYAHk5/LUmSktJ+DegzBIY9BwecDws+/U4vqevg669yUsaI6ipS5WVLHEuVlzGiuiqvnztTyw1QURQ9Bny01OGDgHHpz8cB/Vu3LEmStELatoNex8PgaXDoP6E8BXcNhvO3gacuynovqf49KzlnQDcqK1IEoLIi1WqTvLP53Jlq0Sq8EEIX4J4oirqmv66Poqgi/XkAPm78ujmuwpMkKceiCF59GB4fDW9OhtRasP0psMMpsOraSVeX17K6Ci+KE9gyU1gI4eQQwrQQwrR58+at7LeTJEmZCAE23wtOuBcGPQidd4JHz4XRXeHf/wef1CVdYUFa0QD1XghhQ4D0n+8v645RFF0eRVHvKIp6d+zYcQW/nSRJWmkbbw9H3QinT4GtDoSpl8ZDe3eeAR+8nHR1BWVFA9RdwMD05wOBO1unHEmSlHXr/SDuJTV0JvQ+AWbdBhduBzcfmxe9pArBcudAhRBuBHYH1gXeA34HTABuAToDbwKHR1G09ETz/+EcKEmS8tD8efHVqKevgAWfwKa7wS4/jf8MIenqEuNWLpIkafm+/BSmXQ1TLob570GnbaHvcPj+/tCm9Hpvu5WLJElavvZrQN9hMPQ52H80NHwEtxwX95KqvT5nvaQKgQFKkiQtqbw99D4RBk+HQ66Ctu3jieZje8BTF8NXnyddYeIMUJIkqWllbaHboXDq43DMbbBWF6gZGbdAeOSv8MVypz8XLQOUJElqXgiwxd5wwn1w4gOw8Q7wyF/iIFXzq5LsJWWAkiRJLdd5Bzj6JjjtKfjB/jDlknQvqcEl1UvKACVJkjK3/lYw4HIYMiPee2/WreleUsfB3Nqkq8s6A5QkSVpxa3WB/f4Ow2bHvaNeexQu3x2uPSj+PIftknLJACVJklbeah1hz9/C8Fmw1+/hvRfg2gPhyj3hxbth8eKkK2xVBihJktR62q8ZN98cNgv2Ow8+/yDeIubiHaD2Bli0MOkKW4UBSpIktb7y9rDdIDhzRtxLqmwVuPN0OL8HTLm04HtJGaAkSVL2fNNLajIcfStUdIZ//zJugfDo3wq2l5QBSpIkZV8IsOUP4cT74cQa2Hh7mPRnGNMt7iX16dykK8yIAUqSJOVW5x3h6JvhtCehat+4l9SY7uleUq8kXV2LGKAkSVIy1t8aDrkCzpwOvQbCc7fAhb3hloEwd2bS1TXLACVJkpK19qaw3z9g+GzoOwxenQiX7wbXHQyvP5aXvaQMUJIkKT+stl7cQ2r4bNjzd/DuLBh3AFy5F7x0b171kjJASZKk/NJ+zbir+bBZ8ZWpz+fBTUfDJTvBzBvzopeUAUqSJOWn8hRs95O4l9SAKyGUwYRTYWxPeOXhREszQEmSpPxW1ha6HwanPQFH3wJrbgSrb5BoSW0T/e6SJEktFQJsWR1/JMwrUJIkSRkyQEmSJGXIACVJkpQhA5QkSVKGDFCSJEkZMkBJkiRlyAAlSZKUIQOUJElShgxQkiRJGTJASZIkZcgAJUmSlCEDlCRJUoYMUJIkSRkKURTl7puFMA94M4vfYl3ggyw+f74r9dcPngPwHIDnADwH4DkAz8HKvv5Noijq2NQNOQ1Q2RZCmBZFUe+k60hKqb9+8ByA5wA8B+A5AM8BeA6y+fodwpMkScqQAUqSJClDxRagLk+6gISV+usHzwF4DsBzAJ4D8ByA5yBrr7+o5kBJkiTlQrFdgZIkScq6ggtQIYSrQwjvhxBmL+P23UMIn4QQZqY/fpvrGrMphLBxCGFSCOGFEMLzIYShTdwnhBDGhhBeCSE8F0LYNolas6WF56DY3wftQwhPhxCeTZ+DPzRxn3YhhJvT74OpIYQuCZSaNS08B8eHEOZ9533wkyRqzaYQQlkIoTaEcE8TtxX1e6DRcs5BKbwH3gghzEq/vmlN3F7UvxOgReeg1X8ntF3ZJ0jANcCFwLXN3OfxKIr2z005Ofc18LMoimaEEFYHpocQHoyi6IXv3OdHwBbpjx2AS9J/FouWnAMo7vfBAqBfFEXzQwjlwOQQwv1RFE35zn0GAR9HUbR5COFI4K/AEUkUmyUtOQcAN0dRNDiB+nJlKPAisEYTtxX7e6BRc+cAiv89ALBHFEXL6ndU7L8TGjV3DqCVfycU3BWoKIoeAz5Kuo6kRFH0ThRFM9Kff0b8j0blUnc7CLg2ik0BKkIIG+a41Kxp4Tkoaumf7fz0l+Xpj6UnNB4EjEt/fhuwZwgh5KjErGvhOShqIYSNgP2AK5dxl6J+D0CLzoGK/HdCUgouQLXQTunL+veHELZOuphsSV+O7wlMXeqmSuCt73z9NkUaMJo5B1Dk74P0sMVM4H3gwSiKlvk+iKLoa+ATYJ2cFpllLTgHAIekhy1uCyFsnNsKs24M8Atg8TJuL/r3AMs/B1Dc7wGI/+PwQAhhegjh5CZuL4XfCcs7B9DKvxOKMUDNIG69vg1wATAh2XKyI4SwGnA7MCyKok+TricJyzkHRf8+iKJoURRFPYCNgO1DCF0TLinnWnAO7ga6RFHUHXiQb6/GFLwQwv7A+1EUTU+6lqS08BwU7XvgO/pGUbQt8VDdGSGEXZMuKAHLOwet/juh6AJUFEWfNl7Wj6LoPqA8hLBuwmW1qvR8j9uBG6IoGt/EXeqA7/4va6P0saKxvHNQCu+DRlEU1QOTgH2Wuumb90EIoS2wJvBhTovLkWWdgyiKPoyiaEH6yyuBXjkuLZv6AAeGEN4AbgL6hRCuX+o+xf4eWO45KPL3AABRFNWl/3wfuAPYfqm7FP3vhOWdg2z8Tii6ABVC2KBxjD+EsD3xayyafzDSr+0q4MUois5bxt3uAn6cXnmxI/BJFEXv5KzILGvJOSiB90HHEEJF+vMUsDfw0lJ3uwsYmP78UGBiVESN31pyDpaa53Eg8Xy5ohBF0cgoijaKoqgLcCTxz/fYpe5W1O+BlpyDYn4PAIQQOqQX0xBC6AD8EFh6lXqx/05Y7jnIxu+EgluFF0K4EdgdWDeE8DbwO+LJo0RRdCnxPxKnhRC+BhqAI4vpHwzi/3EdB8xKz/0A+D+gM3xzDu4D9gVeAb4ATsh9mVnVknNQ7O+DDYFxIYQy4n8Ibomi6J4Qwh+BaVEU3UUcMq8LIbxCvPDiyOTKzYqWnIMhIYQDiVdufgQcn1i1OVJi74Emldh7YH3gjnQ2aAv8K4qif4cQToWS+Z3QknPQ6r8T7EQuSZKUoaIbwpMkSco2A5QkSVKGDFCSJEkZMkBJkiRlyAAlSZKUIQOUJElShgxQkiRJGTJASZIkZej/Ab1YsR4sAeymAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,1, figsize=(10,6))\n",
    "ax.plot(y_test, predicted_y, 'o')\n",
    "grid = np.linspace(np.min(dfcars.mpg), np.max(dfcars.mpg), 100)\n",
    "ax.plot(grid, grid, color=\"black\") # 45 degree line\n",
    "ax.set_xlabel(\"actual y\")\n",
    "ax.set_ylabel(\"predicted y\")\n",
    "\n",
    "fig1, ax1 = plt.subplots(1,1, figsize=(10,6))\n",
    "ax1.plot(dfcars.wt, dfcars.mpg, 'o')\n",
    "xgrid = np.linspace(np.min(dfcars.wt), np.max(dfcars.wt), 100)\n",
    "ax1.plot(xgrid, regression.predict(xgrid.reshape(100, 1)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a class=\"anchor\" id=\"sixth-bullet\"></a>\n",
    "## 6 - $k$-nearest neighbors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that you're familiar with `sklearn`, you're ready to do a KNN regression.  \n",
    "\n",
    "Sklearn's regressor is called `sklearn.neighbors.KNeighborsRegressor`. Its main parameter is the `number of nearest neighbors`. There are other parameters such as the distance metric (default for 2 order is the Euclidean distance). For a list of all the parameters see the [Sklearn kNN Regressor Documentation](https://scikit-learn.org/stable/modules/generated/sklearn.neighbors.KNeighborsRegressor.html).\n",
    "\n",
    "Let's use $5$ nearest neighbors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import the library\n",
    "from sklearn.neighbors import KNeighborsRegressor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set number of neighbors\n",
    "k = 5\n",
    "knnreg = KNeighborsRegressor(n_neighbors=k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "kNN model with 5 neighbors gives R^2 on the train set: 0.87181\n"
     ]
    }
   ],
   "source": [
    "# Fit the regressor - make sure your numpy arrays are the right shape\n",
    "knnreg.fit(X_train, y_train)\n",
    "\n",
    "# Evaluate the outcome on the train set using R^2\n",
    "r2_train = knnreg.score(X_train, y_train)\n",
    "\n",
    "# Print results\n",
    "print(f'kNN model with {k} neighbors gives R^2 on the train set: {r2_train:.5}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([20.14, 14.  , 15.3 , 26.3 , 19.56, 17.06, 16.88])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "knnreg.predict(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"exercise\"><b>Exercise</b></div>\n",
    "\n",
    "Calculate and print the $R^{2}$ score on the test set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your code here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not so good? Lets vary the number of neighbors and see what we get."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1: KNeighborsRegressor(n_neighbors=1),\n",
       " 2: KNeighborsRegressor(n_neighbors=2),\n",
       " 4: KNeighborsRegressor(n_neighbors=4),\n",
       " 15: KNeighborsRegressor(n_neighbors=15)}"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Make our lives easy by storing the different regressors in a dictionary\n",
    "regdict = {}\n",
    "\n",
    "# Make our lives easier by entering the k values from a list\n",
    "k_list = [1, 2, 4, 15]\n",
    "\n",
    "# Do a bunch of KNN regressions\n",
    "for k in k_list:\n",
    "    knnreg = KNeighborsRegressor(n_neighbors=k)\n",
    "    knnreg.fit(X_train, y_train)\n",
    "    # Store the regressors in a dictionary\n",
    "    regdict[k] = knnreg \n",
    "\n",
    "# Print the dictionary to see what we have\n",
    "regdict"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's plot all the k values in same plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,1, figsize=(10,6))\n",
    "\n",
    "ax.plot(dfcars.wt, dfcars.mpg, 'o', label=\"data\")\n",
    "\n",
    "xgrid = np.linspace(np.min(dfcars.wt), np.max(dfcars.wt), 100)\n",
    "\n",
    "# let's unpack the dictionary to its elements (items) which is the k and Regressor\n",
    "for k, regressor in regdict.items():\n",
    "    predictions = regressor.predict(xgrid.reshape(-1,1)) \n",
    "    ax.plot(xgrid, predictions, label=\"{}-NN\".format(k))\n",
    "\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"exercise\"><b>Exercise</b></div>\n",
    "\n",
    "Explain what you see in the graph. **Hint** Notice how the $1$-NN goes through every point on the training set but utterly fails elsewhere. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets look at the scores on the training set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$R^{2}$')"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ks = range(1, 15) # Grid of k's\n",
    "scores_train = [] # R2 scores\n",
    "for k in ks:\n",
    "    # Create KNN model\n",
    "    knnreg = KNeighborsRegressor(n_neighbors=k) \n",
    "    \n",
    "    # Fit the model to training data\n",
    "    knnreg.fit(X_train, y_train) \n",
    "    \n",
    "    # Calculate R^2 score\n",
    "    score_train = knnreg.score(X_train, y_train) \n",
    "    scores_train.append(score_train)\n",
    "\n",
    "# Plot\n",
    "fig, ax = plt.subplots(1,1, figsize=(12,8))\n",
    "ax.plot(ks, scores_train,'o-')\n",
    "ax.set_xlabel(r'$k$')\n",
    "ax.set_ylabel(r'$R^{2}$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"exercise\"><b>Exercise</b></div>\n",
    "\n",
    "* Why do we get a perfect $R^2$ at k=1 for the training set?\n",
    "* Make the same plot as above on the *test* set.\n",
    "* What is the best $k$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your code here\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$R^{2}$')"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# %load solutions/knn_regression.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "kNN model with 6 neighbors gives R^2 on the test set: 0.63189\n"
     ]
    }
   ],
   "source": [
    "# solution to previous exercise\n",
    "r2_test = knnreg.score(X_test, y_test)\n",
    "print(f'kNN model with {k} neighbors gives R^2 on the test set: {r2_test:.5}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "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": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}