{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": [
     "hide-input",
     "hide-output"
    ]
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import matplotlib_inline\n",
    "matplotlib_inline.backend_inline.set_matplotlib_formats('svg')\n",
    "import seaborn as sns\n",
    "sns.set_context(\"paper\")\n",
    "sns.set_style(\"ticks\")\n",
    "\n",
    "import scipy\n",
    "import scipy.stats as st\n",
    "import urllib.request\n",
    "import os\n",
    "\n",
    "def download(\n",
    "    url : str,\n",
    "    local_filename : str = None\n",
    "):\n",
    "    \"\"\"Download a file from a url.\n",
    "    \n",
    "    Arguments\n",
    "    url            -- The url we want to download.\n",
    "    local_filename -- The filemame to write on. If not\n",
    "                      specified \n",
    "    \"\"\"\n",
    "    if local_filename is None:\n",
    "        local_filename = os.path.basename(url)\n",
    "    urllib.request.urlretrieve(url, local_filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(logistic_regression_with_one_variable)=\n",
    "# Logistic regression with one variable (High melting explosives)\n",
    "\n",
    "\n",
    "[High Melting Explosives](https://en.wikipedia.org/wiki/HMX) (HMX) have applications as detonators of nuclear weapons and as solid rocket propellants.\n",
    "We will use logistic regression to build the probability that a specific HMX block explodes when dropped from a given height.\n",
    "To this end, we will use data from a 1987 Los Alamos Report\n",
    "(L. Smith, “Los Alamos National Laboratory explosives orientation course: Sensitivity and sensitivity tests to impact, friction, spark and shock,” Los Alamos National Lab, NM (USA), Tech. Rep., 1987).\n",
    "Let's download the raw data and load them.\n",
    "We will use the [Python Data Analysis Library](https://pandas.pydata.org/):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "url = \"https://github.com/PredictiveScienceLab/data-analytics-se/raw/master/lecturebook/data/hmx_data.csv\"\n",
    "download(url)\n",
    "\n",
    "import pandas as pd\n",
    "data = pd.read_csv('hmx_data.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each row of the data is a different experiment.\n",
    "There are two columns:\n",
    "\n",
    "+ The first column is **Height**: From what height (in cm) the specimen was dropped?\n",
    "+ The second column is **Result**: Did the specimen explode (E) or not (N)?\n",
    "\n",
    "Here is how to see the raw data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": [
     "hide-output"
    ]
   },
   "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>Height</th>\n",
       "      <th>Result</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>40.5</td>\n",
       "      <td>E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>40.5</td>\n",
       "      <td>E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>40.5</td>\n",
       "      <td>E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>40.5</td>\n",
       "      <td>E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>40.5</td>\n",
       "      <td>E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>40.5</td>\n",
       "      <td>E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>40.5</td>\n",
       "      <td>E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>40.5</td>\n",
       "      <td>E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>40.5</td>\n",
       "      <td>E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>40.5</td>\n",
       "      <td>E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>36.0</td>\n",
       "      <td>E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>36.0</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>36.0</td>\n",
       "      <td>E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>36.0</td>\n",
       "      <td>E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>36.0</td>\n",
       "      <td>E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>36.0</td>\n",
       "      <td>E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>36.0</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>36.0</td>\n",
       "      <td>E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>36.0</td>\n",
       "      <td>E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>36.0</td>\n",
       "      <td>E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>32.0</td>\n",
       "      <td>E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>32.0</td>\n",
       "      <td>E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>32.0</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>32.0</td>\n",
       "      <td>E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>32.0</td>\n",
       "      <td>E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>32.0</td>\n",
       "      <td>E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>32.0</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>32.0</td>\n",
       "      <td>E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>32.0</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>32.0</td>\n",
       "      <td>E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>28.5</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>28.5</td>\n",
       "      <td>E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>28.5</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>28.5</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>28.5</td>\n",
       "      <td>E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>28.5</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>28.5</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>28.5</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>28.5</td>\n",
       "      <td>E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>28.5</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>25.5</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>25.5</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>25.5</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>25.5</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>25.5</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>25.5</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>25.5</td>\n",
       "      <td>E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>25.5</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>25.5</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>25.5</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>22.5</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51</th>\n",
       "      <td>22.5</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>52</th>\n",
       "      <td>22.5</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>53</th>\n",
       "      <td>22.5</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54</th>\n",
       "      <td>22.5</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>55</th>\n",
       "      <td>22.5</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>56</th>\n",
       "      <td>22.5</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>57</th>\n",
       "      <td>22.5</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58</th>\n",
       "      <td>22.5</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>59</th>\n",
       "      <td>22.5</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Height Result\n",
       "0     40.5      E\n",
       "1     40.5      E\n",
       "2     40.5      E\n",
       "3     40.5      E\n",
       "4     40.5      E\n",
       "5     40.5      E\n",
       "6     40.5      E\n",
       "7     40.5      E\n",
       "8     40.5      E\n",
       "9     40.5      E\n",
       "10    36.0      E\n",
       "11    36.0      N\n",
       "12    36.0      E\n",
       "13    36.0      E\n",
       "14    36.0      E\n",
       "15    36.0      E\n",
       "16    36.0      N\n",
       "17    36.0      E\n",
       "18    36.0      E\n",
       "19    36.0      E\n",
       "20    32.0      E\n",
       "21    32.0      E\n",
       "22    32.0      N\n",
       "23    32.0      E\n",
       "24    32.0      E\n",
       "25    32.0      E\n",
       "26    32.0      N\n",
       "27    32.0      E\n",
       "28    32.0      N\n",
       "29    32.0      E\n",
       "30    28.5      N\n",
       "31    28.5      E\n",
       "32    28.5      N\n",
       "33    28.5      N\n",
       "34    28.5      E\n",
       "35    28.5      N\n",
       "36    28.5      N\n",
       "37    28.5      N\n",
       "38    28.5      E\n",
       "39    28.5      N\n",
       "40    25.5      N\n",
       "41    25.5      N\n",
       "42    25.5      N\n",
       "43    25.5      N\n",
       "44    25.5      N\n",
       "45    25.5      N\n",
       "46    25.5      E\n",
       "47    25.5      N\n",
       "48    25.5      N\n",
       "49    25.5      N\n",
       "50    22.5      N\n",
       "51    22.5      N\n",
       "52    22.5      N\n",
       "53    22.5      N\n",
       "54    22.5      N\n",
       "55    22.5      N\n",
       "56    22.5      N\n",
       "57    22.5      N\n",
       "58    22.5      N\n",
       "59    22.5      N"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's encode the labels as $1$ and $0$ instead of E and N.\n",
    "Let's do this below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": [
     "hide-output"
    ]
   },
   "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>Height</th>\n",
       "      <th>Result</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>40.5</td>\n",
       "      <td>E</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>40.5</td>\n",
       "      <td>E</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>40.5</td>\n",
       "      <td>E</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>40.5</td>\n",
       "      <td>E</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>40.5</td>\n",
       "      <td>E</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>40.5</td>\n",
       "      <td>E</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>40.5</td>\n",
       "      <td>E</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>40.5</td>\n",
       "      <td>E</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>40.5</td>\n",
       "      <td>E</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>40.5</td>\n",
       "      <td>E</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>36.0</td>\n",
       "      <td>E</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>36.0</td>\n",
       "      <td>N</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>36.0</td>\n",
       "      <td>E</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>36.0</td>\n",
       "      <td>E</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>36.0</td>\n",
       "      <td>E</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>36.0</td>\n",
       "      <td>E</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>36.0</td>\n",
       "      <td>N</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>36.0</td>\n",
       "      <td>E</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>36.0</td>\n",
       "      <td>E</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>36.0</td>\n",
       "      <td>E</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>32.0</td>\n",
       "      <td>E</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>32.0</td>\n",
       "      <td>E</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>32.0</td>\n",
       "      <td>N</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>32.0</td>\n",
       "      <td>E</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>32.0</td>\n",
       "      <td>E</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>32.0</td>\n",
       "      <td>E</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>32.0</td>\n",
       "      <td>N</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>32.0</td>\n",
       "      <td>E</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>32.0</td>\n",
       "      <td>N</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>32.0</td>\n",
       "      <td>E</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>28.5</td>\n",
       "      <td>N</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>28.5</td>\n",
       "      <td>E</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>28.5</td>\n",
       "      <td>N</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>28.5</td>\n",
       "      <td>N</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>28.5</td>\n",
       "      <td>E</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>28.5</td>\n",
       "      <td>N</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>28.5</td>\n",
       "      <td>N</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>28.5</td>\n",
       "      <td>N</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>28.5</td>\n",
       "      <td>E</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>28.5</td>\n",
       "      <td>N</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>25.5</td>\n",
       "      <td>N</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>25.5</td>\n",
       "      <td>N</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>25.5</td>\n",
       "      <td>N</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>25.5</td>\n",
       "      <td>N</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>25.5</td>\n",
       "      <td>N</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>25.5</td>\n",
       "      <td>N</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>25.5</td>\n",
       "      <td>E</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>25.5</td>\n",
       "      <td>N</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>25.5</td>\n",
       "      <td>N</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>25.5</td>\n",
       "      <td>N</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>22.5</td>\n",
       "      <td>N</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51</th>\n",
       "      <td>22.5</td>\n",
       "      <td>N</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>52</th>\n",
       "      <td>22.5</td>\n",
       "      <td>N</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>53</th>\n",
       "      <td>22.5</td>\n",
       "      <td>N</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54</th>\n",
       "      <td>22.5</td>\n",
       "      <td>N</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>55</th>\n",
       "      <td>22.5</td>\n",
       "      <td>N</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>56</th>\n",
       "      <td>22.5</td>\n",
       "      <td>N</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>57</th>\n",
       "      <td>22.5</td>\n",
       "      <td>N</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58</th>\n",
       "      <td>22.5</td>\n",
       "      <td>N</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>59</th>\n",
       "      <td>22.5</td>\n",
       "      <td>N</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Height Result  y\n",
       "0     40.5      E  1\n",
       "1     40.5      E  1\n",
       "2     40.5      E  1\n",
       "3     40.5      E  1\n",
       "4     40.5      E  1\n",
       "5     40.5      E  1\n",
       "6     40.5      E  1\n",
       "7     40.5      E  1\n",
       "8     40.5      E  1\n",
       "9     40.5      E  1\n",
       "10    36.0      E  1\n",
       "11    36.0      N  0\n",
       "12    36.0      E  1\n",
       "13    36.0      E  1\n",
       "14    36.0      E  1\n",
       "15    36.0      E  1\n",
       "16    36.0      N  0\n",
       "17    36.0      E  1\n",
       "18    36.0      E  1\n",
       "19    36.0      E  1\n",
       "20    32.0      E  1\n",
       "21    32.0      E  1\n",
       "22    32.0      N  0\n",
       "23    32.0      E  1\n",
       "24    32.0      E  1\n",
       "25    32.0      E  1\n",
       "26    32.0      N  0\n",
       "27    32.0      E  1\n",
       "28    32.0      N  0\n",
       "29    32.0      E  1\n",
       "30    28.5      N  0\n",
       "31    28.5      E  1\n",
       "32    28.5      N  0\n",
       "33    28.5      N  0\n",
       "34    28.5      E  1\n",
       "35    28.5      N  0\n",
       "36    28.5      N  0\n",
       "37    28.5      N  0\n",
       "38    28.5      E  1\n",
       "39    28.5      N  0\n",
       "40    25.5      N  0\n",
       "41    25.5      N  0\n",
       "42    25.5      N  0\n",
       "43    25.5      N  0\n",
       "44    25.5      N  0\n",
       "45    25.5      N  0\n",
       "46    25.5      E  1\n",
       "47    25.5      N  0\n",
       "48    25.5      N  0\n",
       "49    25.5      N  0\n",
       "50    22.5      N  0\n",
       "51    22.5      N  0\n",
       "52    22.5      N  0\n",
       "53    22.5      N  0\n",
       "54    22.5      N  0\n",
       "55    22.5      N  0\n",
       "56    22.5      N  0\n",
       "57    22.5      N  0\n",
       "58    22.5      N  0\n",
       "59    22.5      N  0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Extract data for classification in numpy array\n",
    "# Features\n",
    "x = data['Height'].values\n",
    "# Labels (must be integer)\n",
    "label_coding = {'E': 1, 'N': 0}\n",
    "y = np.array(\n",
    "    [\n",
    "        label_coding[r]\n",
    "        for r in data['Result']\n",
    "    ]\n",
    ")\n",
    "data['y'] = y\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's visualize the data.\n",
    "Notice that lots of observations fall on top of each other."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"405.364pt\" height=\"309.979875pt\" viewBox=\"0 0 405.364 309.979875\" xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n",
       " <metadata>\n",
       "  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
       "   <cc:Work>\n",
       "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
       "    <dc:date>2023-09-26T15:36:49.896817</dc:date>\n",
       "    <dc:format>image/svg+xml</dc:format>\n",
       "    <dc:creator>\n",
       "     <cc:Agent>\n",
       "      <dc:title>Matplotlib v3.7.1, https://matplotlib.org/</dc:title>\n",
       "     </cc:Agent>\n",
       "    </dc:creator>\n",
       "   </cc:Work>\n",
       "  </rdf:RDF>\n",
       " </metadata>\n",
       " <defs>\n",
       "  <style type=\"text/css\">*{stroke-linejoin: round; stroke-linecap: butt}</style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"M 0 309.979875 \n",
       "L 405.364 309.979875 \n",
       "L 405.364 0 \n",
       "L 0 0 \n",
       "z\n",
       "\" style=\"fill: #ffffff\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"patch_2\">\n",
       "    <path d=\"M 41.044 273.312 \n",
       "L 398.164 273.312 \n",
       "L 398.164 7.2 \n",
       "L 41.044 7.2 \n",
       "z\n",
       "\" style=\"fill: #ffffff\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_1\">\n",
       "    <g id=\"xtick_1\">\n",
       "     <g id=\"line2d_1\">\n",
       "      <defs>\n",
       "       <path id=\"m5ccc7c1a20\" d=\"M 0 0 \n",
       "L 0 4.8 \n",
       "\" style=\"stroke: #262626\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use xlink:href=\"#m5ccc7c1a20\" x=\"57.276727\" y=\"273.312\" style=\"fill: #262626; stroke: #262626\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_1\">\n",
       "      <!-- 22.5 -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(48.713915 287.910875) scale(0.088 -0.088)\">\n",
       "       <defs>\n",
       "        <path id=\"ArialMT-32\" d=\"M 3222 541 \n",
       "L 3222 0 \n",
       "L 194 0 \n",
       "Q 188 203 259 391 \n",
       "Q 375 700 629 1000 \n",
       "Q 884 1300 1366 1694 \n",
       "Q 2113 2306 2375 2664 \n",
       "Q 2638 3022 2638 3341 \n",
       "Q 2638 3675 2398 3904 \n",
       "Q 2159 4134 1775 4134 \n",
       "Q 1369 4134 1125 3890 \n",
       "Q 881 3647 878 3216 \n",
       "L 300 3275 \n",
       "Q 359 3922 746 4261 \n",
       "Q 1134 4600 1788 4600 \n",
       "Q 2447 4600 2831 4234 \n",
       "Q 3216 3869 3216 3328 \n",
       "Q 3216 3053 3103 2787 \n",
       "Q 2991 2522 2730 2228 \n",
       "Q 2469 1934 1863 1422 \n",
       "Q 1356 997 1212 845 \n",
       "Q 1069 694 975 541 \n",
       "L 3222 541 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "        <path id=\"ArialMT-2e\" d=\"M 581 0 \n",
       "L 581 641 \n",
       "L 1222 641 \n",
       "L 1222 0 \n",
       "L 581 0 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "        <path id=\"ArialMT-35\" d=\"M 266 1200 \n",
       "L 856 1250 \n",
       "Q 922 819 1161 601 \n",
       "Q 1400 384 1738 384 \n",
       "Q 2144 384 2425 690 \n",
       "Q 2706 997 2706 1503 \n",
       "Q 2706 1984 2436 2262 \n",
       "Q 2166 2541 1728 2541 \n",
       "Q 1456 2541 1237 2417 \n",
       "Q 1019 2294 894 2097 \n",
       "L 366 2166 \n",
       "L 809 4519 \n",
       "L 3088 4519 \n",
       "L 3088 3981 \n",
       "L 1259 3981 \n",
       "L 1013 2750 \n",
       "Q 1425 3038 1878 3038 \n",
       "Q 2478 3038 2890 2622 \n",
       "Q 3303 2206 3303 1553 \n",
       "Q 3303 931 2941 478 \n",
       "Q 2500 -78 1738 -78 \n",
       "Q 1113 -78 717 272 \n",
       "Q 322 622 266 1200 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#ArialMT-32\"/>\n",
       "       <use xlink:href=\"#ArialMT-32\" x=\"55.615234\"/>\n",
       "       <use xlink:href=\"#ArialMT-2e\" x=\"111.230469\"/>\n",
       "       <use xlink:href=\"#ArialMT-35\" x=\"139.013672\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_2\">\n",
       "     <g id=\"line2d_2\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#m5ccc7c1a20\" x=\"102.367636\" y=\"273.312\" style=\"fill: #262626; stroke: #262626\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_2\">\n",
       "      <!-- 25.0 -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(93.804824 287.910875) scale(0.088 -0.088)\">\n",
       "       <defs>\n",
       "        <path id=\"ArialMT-30\" d=\"M 266 2259 \n",
       "Q 266 3072 433 3567 \n",
       "Q 600 4063 929 4331 \n",
       "Q 1259 4600 1759 4600 \n",
       "Q 2128 4600 2406 4451 \n",
       "Q 2684 4303 2865 4023 \n",
       "Q 3047 3744 3150 3342 \n",
       "Q 3253 2941 3253 2259 \n",
       "Q 3253 1453 3087 958 \n",
       "Q 2922 463 2592 192 \n",
       "Q 2263 -78 1759 -78 \n",
       "Q 1097 -78 719 397 \n",
       "Q 266 969 266 2259 \n",
       "z\n",
       "M 844 2259 \n",
       "Q 844 1131 1108 757 \n",
       "Q 1372 384 1759 384 \n",
       "Q 2147 384 2411 759 \n",
       "Q 2675 1134 2675 2259 \n",
       "Q 2675 3391 2411 3762 \n",
       "Q 2147 4134 1753 4134 \n",
       "Q 1366 4134 1134 3806 \n",
       "Q 844 3388 844 2259 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#ArialMT-32\"/>\n",
       "       <use xlink:href=\"#ArialMT-35\" x=\"55.615234\"/>\n",
       "       <use xlink:href=\"#ArialMT-2e\" x=\"111.230469\"/>\n",
       "       <use xlink:href=\"#ArialMT-30\" x=\"139.013672\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_3\">\n",
       "     <g id=\"line2d_3\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#m5ccc7c1a20\" x=\"147.458545\" y=\"273.312\" style=\"fill: #262626; stroke: #262626\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_3\">\n",
       "      <!-- 27.5 -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(138.895733 287.910875) scale(0.088 -0.088)\">\n",
       "       <defs>\n",
       "        <path id=\"ArialMT-37\" d=\"M 303 3981 \n",
       "L 303 4522 \n",
       "L 3269 4522 \n",
       "L 3269 4084 \n",
       "Q 2831 3619 2401 2847 \n",
       "Q 1972 2075 1738 1259 \n",
       "Q 1569 684 1522 0 \n",
       "L 944 0 \n",
       "Q 953 541 1156 1306 \n",
       "Q 1359 2072 1739 2783 \n",
       "Q 2119 3494 2547 3981 \n",
       "L 303 3981 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#ArialMT-32\"/>\n",
       "       <use xlink:href=\"#ArialMT-37\" x=\"55.615234\"/>\n",
       "       <use xlink:href=\"#ArialMT-2e\" x=\"111.230469\"/>\n",
       "       <use xlink:href=\"#ArialMT-35\" x=\"139.013672\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_4\">\n",
       "     <g id=\"line2d_4\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#m5ccc7c1a20\" x=\"192.549455\" y=\"273.312\" style=\"fill: #262626; stroke: #262626\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_4\">\n",
       "      <!-- 30.0 -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(183.986642 287.910875) scale(0.088 -0.088)\">\n",
       "       <defs>\n",
       "        <path id=\"ArialMT-33\" d=\"M 269 1209 \n",
       "L 831 1284 \n",
       "Q 928 806 1161 595 \n",
       "Q 1394 384 1728 384 \n",
       "Q 2125 384 2398 659 \n",
       "Q 2672 934 2672 1341 \n",
       "Q 2672 1728 2419 1979 \n",
       "Q 2166 2231 1775 2231 \n",
       "Q 1616 2231 1378 2169 \n",
       "L 1441 2663 \n",
       "Q 1497 2656 1531 2656 \n",
       "Q 1891 2656 2178 2843 \n",
       "Q 2466 3031 2466 3422 \n",
       "Q 2466 3731 2256 3934 \n",
       "Q 2047 4138 1716 4138 \n",
       "Q 1388 4138 1169 3931 \n",
       "Q 950 3725 888 3313 \n",
       "L 325 3413 \n",
       "Q 428 3978 793 4289 \n",
       "Q 1159 4600 1703 4600 \n",
       "Q 2078 4600 2393 4439 \n",
       "Q 2709 4278 2876 4000 \n",
       "Q 3044 3722 3044 3409 \n",
       "Q 3044 3113 2884 2869 \n",
       "Q 2725 2625 2413 2481 \n",
       "Q 2819 2388 3044 2092 \n",
       "Q 3269 1797 3269 1353 \n",
       "Q 3269 753 2831 336 \n",
       "Q 2394 -81 1725 -81 \n",
       "Q 1122 -81 723 278 \n",
       "Q 325 638 269 1209 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#ArialMT-33\"/>\n",
       "       <use xlink:href=\"#ArialMT-30\" x=\"55.615234\"/>\n",
       "       <use xlink:href=\"#ArialMT-2e\" x=\"111.230469\"/>\n",
       "       <use xlink:href=\"#ArialMT-30\" x=\"139.013672\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_5\">\n",
       "     <g id=\"line2d_5\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#m5ccc7c1a20\" x=\"237.640364\" y=\"273.312\" style=\"fill: #262626; stroke: #262626\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_5\">\n",
       "      <!-- 32.5 -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(229.077551 287.910875) scale(0.088 -0.088)\">\n",
       "       <use xlink:href=\"#ArialMT-33\"/>\n",
       "       <use xlink:href=\"#ArialMT-32\" x=\"55.615234\"/>\n",
       "       <use xlink:href=\"#ArialMT-2e\" x=\"111.230469\"/>\n",
       "       <use xlink:href=\"#ArialMT-35\" x=\"139.013672\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_6\">\n",
       "     <g id=\"line2d_6\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#m5ccc7c1a20\" x=\"282.731273\" y=\"273.312\" style=\"fill: #262626; stroke: #262626\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_6\">\n",
       "      <!-- 35.0 -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(274.16846 287.910875) scale(0.088 -0.088)\">\n",
       "       <use xlink:href=\"#ArialMT-33\"/>\n",
       "       <use xlink:href=\"#ArialMT-35\" x=\"55.615234\"/>\n",
       "       <use xlink:href=\"#ArialMT-2e\" x=\"111.230469\"/>\n",
       "       <use xlink:href=\"#ArialMT-30\" x=\"139.013672\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_7\">\n",
       "     <g id=\"line2d_7\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#m5ccc7c1a20\" x=\"327.822182\" y=\"273.312\" style=\"fill: #262626; stroke: #262626\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_7\">\n",
       "      <!-- 37.5 -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(319.259369 287.910875) scale(0.088 -0.088)\">\n",
       "       <use xlink:href=\"#ArialMT-33\"/>\n",
       "       <use xlink:href=\"#ArialMT-37\" x=\"55.615234\"/>\n",
       "       <use xlink:href=\"#ArialMT-2e\" x=\"111.230469\"/>\n",
       "       <use xlink:href=\"#ArialMT-35\" x=\"139.013672\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_8\">\n",
       "     <g id=\"line2d_8\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#m5ccc7c1a20\" x=\"372.913091\" y=\"273.312\" style=\"fill: #262626; stroke: #262626\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_8\">\n",
       "      <!-- 40.0 -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(364.350278 287.910875) scale(0.088 -0.088)\">\n",
       "       <defs>\n",
       "        <path id=\"ArialMT-34\" d=\"M 2069 0 \n",
       "L 2069 1097 \n",
       "L 81 1097 \n",
       "L 81 1613 \n",
       "L 2172 4581 \n",
       "L 2631 4581 \n",
       "L 2631 1613 \n",
       "L 3250 1613 \n",
       "L 3250 1097 \n",
       "L 2631 1097 \n",
       "L 2631 0 \n",
       "L 2069 0 \n",
       "z\n",
       "M 2069 1613 \n",
       "L 2069 3678 \n",
       "L 634 1613 \n",
       "L 2069 1613 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#ArialMT-34\"/>\n",
       "       <use xlink:href=\"#ArialMT-30\" x=\"55.615234\"/>\n",
       "       <use xlink:href=\"#ArialMT-2e\" x=\"111.230469\"/>\n",
       "       <use xlink:href=\"#ArialMT-30\" x=\"139.013672\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_9\">\n",
       "     <!-- $x$ (Height in cm) -->\n",
       "     <g style=\"fill: #262626\" transform=\"translate(185.524 300.667875) scale(0.096 -0.096)\">\n",
       "      <defs>\n",
       "       <path id=\"DejaVuSans-Oblique-78\" d=\"M 3841 3500 \n",
       "L 2234 1784 \n",
       "L 3219 0 \n",
       "L 2559 0 \n",
       "L 1819 1388 \n",
       "L 531 0 \n",
       "L -166 0 \n",
       "L 1556 1844 \n",
       "L 641 3500 \n",
       "L 1300 3500 \n",
       "L 1972 2234 \n",
       "L 3144 3500 \n",
       "L 3841 3500 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"ArialMT-20\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"ArialMT-28\" d=\"M 1497 -1347 \n",
       "Q 1031 -759 709 28 \n",
       "Q 388 816 388 1659 \n",
       "Q 388 2403 628 3084 \n",
       "Q 909 3875 1497 4659 \n",
       "L 1900 4659 \n",
       "Q 1522 4009 1400 3731 \n",
       "Q 1209 3300 1100 2831 \n",
       "Q 966 2247 966 1656 \n",
       "Q 966 153 1900 -1347 \n",
       "L 1497 -1347 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"ArialMT-48\" d=\"M 513 0 \n",
       "L 513 4581 \n",
       "L 1119 4581 \n",
       "L 1119 2700 \n",
       "L 3500 2700 \n",
       "L 3500 4581 \n",
       "L 4106 4581 \n",
       "L 4106 0 \n",
       "L 3500 0 \n",
       "L 3500 2159 \n",
       "L 1119 2159 \n",
       "L 1119 0 \n",
       "L 513 0 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"ArialMT-65\" d=\"M 2694 1069 \n",
       "L 3275 997 \n",
       "Q 3138 488 2766 206 \n",
       "Q 2394 -75 1816 -75 \n",
       "Q 1088 -75 661 373 \n",
       "Q 234 822 234 1631 \n",
       "Q 234 2469 665 2931 \n",
       "Q 1097 3394 1784 3394 \n",
       "Q 2450 3394 2872 2941 \n",
       "Q 3294 2488 3294 1666 \n",
       "Q 3294 1616 3291 1516 \n",
       "L 816 1516 \n",
       "Q 847 969 1125 678 \n",
       "Q 1403 388 1819 388 \n",
       "Q 2128 388 2347 550 \n",
       "Q 2566 713 2694 1069 \n",
       "z\n",
       "M 847 1978 \n",
       "L 2700 1978 \n",
       "Q 2663 2397 2488 2606 \n",
       "Q 2219 2931 1791 2931 \n",
       "Q 1403 2931 1139 2672 \n",
       "Q 875 2413 847 1978 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"ArialMT-69\" d=\"M 425 3934 \n",
       "L 425 4581 \n",
       "L 988 4581 \n",
       "L 988 3934 \n",
       "L 425 3934 \n",
       "z\n",
       "M 425 0 \n",
       "L 425 3319 \n",
       "L 988 3319 \n",
       "L 988 0 \n",
       "L 425 0 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"ArialMT-67\" d=\"M 319 -275 \n",
       "L 866 -356 \n",
       "Q 900 -609 1056 -725 \n",
       "Q 1266 -881 1628 -881 \n",
       "Q 2019 -881 2231 -725 \n",
       "Q 2444 -569 2519 -288 \n",
       "Q 2563 -116 2559 434 \n",
       "Q 2191 0 1641 0 \n",
       "Q 956 0 581 494 \n",
       "Q 206 988 206 1678 \n",
       "Q 206 2153 378 2554 \n",
       "Q 550 2956 876 3175 \n",
       "Q 1203 3394 1644 3394 \n",
       "Q 2231 3394 2613 2919 \n",
       "L 2613 3319 \n",
       "L 3131 3319 \n",
       "L 3131 450 \n",
       "Q 3131 -325 2973 -648 \n",
       "Q 2816 -972 2473 -1159 \n",
       "Q 2131 -1347 1631 -1347 \n",
       "Q 1038 -1347 672 -1080 \n",
       "Q 306 -813 319 -275 \n",
       "z\n",
       "M 784 1719 \n",
       "Q 784 1066 1043 766 \n",
       "Q 1303 466 1694 466 \n",
       "Q 2081 466 2343 764 \n",
       "Q 2606 1063 2606 1700 \n",
       "Q 2606 2309 2336 2618 \n",
       "Q 2066 2928 1684 2928 \n",
       "Q 1309 2928 1046 2623 \n",
       "Q 784 2319 784 1719 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"ArialMT-68\" d=\"M 422 0 \n",
       "L 422 4581 \n",
       "L 984 4581 \n",
       "L 984 2938 \n",
       "Q 1378 3394 1978 3394 \n",
       "Q 2347 3394 2619 3248 \n",
       "Q 2891 3103 3008 2847 \n",
       "Q 3125 2591 3125 2103 \n",
       "L 3125 0 \n",
       "L 2563 0 \n",
       "L 2563 2103 \n",
       "Q 2563 2525 2380 2717 \n",
       "Q 2197 2909 1863 2909 \n",
       "Q 1613 2909 1392 2779 \n",
       "Q 1172 2650 1078 2428 \n",
       "Q 984 2206 984 1816 \n",
       "L 984 0 \n",
       "L 422 0 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"ArialMT-74\" d=\"M 1650 503 \n",
       "L 1731 6 \n",
       "Q 1494 -44 1306 -44 \n",
       "Q 1000 -44 831 53 \n",
       "Q 663 150 594 308 \n",
       "Q 525 466 525 972 \n",
       "L 525 2881 \n",
       "L 113 2881 \n",
       "L 113 3319 \n",
       "L 525 3319 \n",
       "L 525 4141 \n",
       "L 1084 4478 \n",
       "L 1084 3319 \n",
       "L 1650 3319 \n",
       "L 1650 2881 \n",
       "L 1084 2881 \n",
       "L 1084 941 \n",
       "Q 1084 700 1114 631 \n",
       "Q 1144 563 1211 522 \n",
       "Q 1278 481 1403 481 \n",
       "Q 1497 481 1650 503 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"ArialMT-6e\" d=\"M 422 0 \n",
       "L 422 3319 \n",
       "L 928 3319 \n",
       "L 928 2847 \n",
       "Q 1294 3394 1984 3394 \n",
       "Q 2284 3394 2536 3286 \n",
       "Q 2788 3178 2913 3003 \n",
       "Q 3038 2828 3088 2588 \n",
       "Q 3119 2431 3119 2041 \n",
       "L 3119 0 \n",
       "L 2556 0 \n",
       "L 2556 2019 \n",
       "Q 2556 2363 2490 2533 \n",
       "Q 2425 2703 2258 2804 \n",
       "Q 2091 2906 1866 2906 \n",
       "Q 1506 2906 1245 2678 \n",
       "Q 984 2450 984 1813 \n",
       "L 984 0 \n",
       "L 422 0 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"ArialMT-63\" d=\"M 2588 1216 \n",
       "L 3141 1144 \n",
       "Q 3050 572 2676 248 \n",
       "Q 2303 -75 1759 -75 \n",
       "Q 1078 -75 664 370 \n",
       "Q 250 816 250 1647 \n",
       "Q 250 2184 428 2587 \n",
       "Q 606 2991 970 3192 \n",
       "Q 1334 3394 1763 3394 \n",
       "Q 2303 3394 2647 3120 \n",
       "Q 2991 2847 3088 2344 \n",
       "L 2541 2259 \n",
       "Q 2463 2594 2264 2762 \n",
       "Q 2066 2931 1784 2931 \n",
       "Q 1359 2931 1093 2626 \n",
       "Q 828 2322 828 1663 \n",
       "Q 828 994 1084 691 \n",
       "Q 1341 388 1753 388 \n",
       "Q 2084 388 2306 591 \n",
       "Q 2528 794 2588 1216 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"ArialMT-6d\" d=\"M 422 0 \n",
       "L 422 3319 \n",
       "L 925 3319 \n",
       "L 925 2853 \n",
       "Q 1081 3097 1340 3245 \n",
       "Q 1600 3394 1931 3394 \n",
       "Q 2300 3394 2536 3241 \n",
       "Q 2772 3088 2869 2813 \n",
       "Q 3263 3394 3894 3394 \n",
       "Q 4388 3394 4653 3120 \n",
       "Q 4919 2847 4919 2278 \n",
       "L 4919 0 \n",
       "L 4359 0 \n",
       "L 4359 2091 \n",
       "Q 4359 2428 4304 2576 \n",
       "Q 4250 2725 4106 2815 \n",
       "Q 3963 2906 3769 2906 \n",
       "Q 3419 2906 3187 2673 \n",
       "Q 2956 2441 2956 1928 \n",
       "L 2956 0 \n",
       "L 2394 0 \n",
       "L 2394 2156 \n",
       "Q 2394 2531 2256 2718 \n",
       "Q 2119 2906 1806 2906 \n",
       "Q 1569 2906 1367 2781 \n",
       "Q 1166 2656 1075 2415 \n",
       "Q 984 2175 984 1722 \n",
       "L 984 0 \n",
       "L 422 0 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"ArialMT-29\" d=\"M 791 -1347 \n",
       "L 388 -1347 \n",
       "Q 1322 153 1322 1656 \n",
       "Q 1322 2244 1188 2822 \n",
       "Q 1081 3291 891 3722 \n",
       "Q 769 4003 388 4659 \n",
       "L 791 4659 \n",
       "Q 1378 3875 1659 3084 \n",
       "Q 1900 2403 1900 1659 \n",
       "Q 1900 816 1576 28 \n",
       "Q 1253 -759 791 -1347 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "      </defs>\n",
       "      <use xlink:href=\"#DejaVuSans-Oblique-78\" transform=\"translate(0 0.203125)\"/>\n",
       "      <use xlink:href=\"#ArialMT-20\" transform=\"translate(59.179688 0.203125)\"/>\n",
       "      <use xlink:href=\"#ArialMT-28\" transform=\"translate(86.962891 0.203125)\"/>\n",
       "      <use xlink:href=\"#ArialMT-48\" transform=\"translate(120.263672 0.203125)\"/>\n",
       "      <use xlink:href=\"#ArialMT-65\" transform=\"translate(192.480469 0.203125)\"/>\n",
       "      <use xlink:href=\"#ArialMT-69\" transform=\"translate(248.095703 0.203125)\"/>\n",
       "      <use xlink:href=\"#ArialMT-67\" transform=\"translate(270.3125 0.203125)\"/>\n",
       "      <use xlink:href=\"#ArialMT-68\" transform=\"translate(325.927734 0.203125)\"/>\n",
       "      <use xlink:href=\"#ArialMT-74\" transform=\"translate(381.542969 0.203125)\"/>\n",
       "      <use xlink:href=\"#ArialMT-20\" transform=\"translate(409.326172 0.203125)\"/>\n",
       "      <use xlink:href=\"#ArialMT-69\" transform=\"translate(437.109375 0.203125)\"/>\n",
       "      <use xlink:href=\"#ArialMT-6e\" transform=\"translate(459.326172 0.203125)\"/>\n",
       "      <use xlink:href=\"#ArialMT-20\" transform=\"translate(514.941406 0.203125)\"/>\n",
       "      <use xlink:href=\"#ArialMT-63\" transform=\"translate(542.724609 0.203125)\"/>\n",
       "      <use xlink:href=\"#ArialMT-6d\" transform=\"translate(592.724609 0.203125)\"/>\n",
       "      <use xlink:href=\"#ArialMT-29\" transform=\"translate(676.025391 0.203125)\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_2\">\n",
       "    <g id=\"ytick_1\">\n",
       "     <g id=\"line2d_9\">\n",
       "      <defs>\n",
       "       <path id=\"mc4d82b55e0\" d=\"M 0 0 \n",
       "L -4.8 0 \n",
       "\" style=\"stroke: #262626\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use xlink:href=\"#mc4d82b55e0\" x=\"41.044\" y=\"261.216\" style=\"fill: #262626; stroke: #262626\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_10\">\n",
       "      <!-- 0.0 -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(20.512 264.365437) scale(0.088 -0.088)\">\n",
       "       <use xlink:href=\"#ArialMT-30\"/>\n",
       "       <use xlink:href=\"#ArialMT-2e\" x=\"55.615234\"/>\n",
       "       <use xlink:href=\"#ArialMT-30\" x=\"83.398438\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_2\">\n",
       "     <g id=\"line2d_10\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mc4d82b55e0\" x=\"41.044\" y=\"212.832\" style=\"fill: #262626; stroke: #262626\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_11\">\n",
       "      <!-- 0.2 -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(20.512 215.981437) scale(0.088 -0.088)\">\n",
       "       <use xlink:href=\"#ArialMT-30\"/>\n",
       "       <use xlink:href=\"#ArialMT-2e\" x=\"55.615234\"/>\n",
       "       <use xlink:href=\"#ArialMT-32\" x=\"83.398438\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_3\">\n",
       "     <g id=\"line2d_11\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mc4d82b55e0\" x=\"41.044\" y=\"164.448\" style=\"fill: #262626; stroke: #262626\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_12\">\n",
       "      <!-- 0.4 -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(20.512 167.597437) scale(0.088 -0.088)\">\n",
       "       <use xlink:href=\"#ArialMT-30\"/>\n",
       "       <use xlink:href=\"#ArialMT-2e\" x=\"55.615234\"/>\n",
       "       <use xlink:href=\"#ArialMT-34\" x=\"83.398438\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_4\">\n",
       "     <g id=\"line2d_12\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mc4d82b55e0\" x=\"41.044\" y=\"116.064\" style=\"fill: #262626; stroke: #262626\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_13\">\n",
       "      <!-- 0.6 -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(20.512 119.213437) scale(0.088 -0.088)\">\n",
       "       <defs>\n",
       "        <path id=\"ArialMT-36\" d=\"M 3184 3459 \n",
       "L 2625 3416 \n",
       "Q 2550 3747 2413 3897 \n",
       "Q 2184 4138 1850 4138 \n",
       "Q 1581 4138 1378 3988 \n",
       "Q 1113 3794 959 3422 \n",
       "Q 806 3050 800 2363 \n",
       "Q 1003 2672 1297 2822 \n",
       "Q 1591 2972 1913 2972 \n",
       "Q 2475 2972 2870 2558 \n",
       "Q 3266 2144 3266 1488 \n",
       "Q 3266 1056 3080 686 \n",
       "Q 2894 316 2569 119 \n",
       "Q 2244 -78 1831 -78 \n",
       "Q 1128 -78 684 439 \n",
       "Q 241 956 241 2144 \n",
       "Q 241 3472 731 4075 \n",
       "Q 1159 4600 1884 4600 \n",
       "Q 2425 4600 2770 4297 \n",
       "Q 3116 3994 3184 3459 \n",
       "z\n",
       "M 888 1484 \n",
       "Q 888 1194 1011 928 \n",
       "Q 1134 663 1356 523 \n",
       "Q 1578 384 1822 384 \n",
       "Q 2178 384 2434 671 \n",
       "Q 2691 959 2691 1453 \n",
       "Q 2691 1928 2437 2201 \n",
       "Q 2184 2475 1800 2475 \n",
       "Q 1419 2475 1153 2201 \n",
       "Q 888 1928 888 1484 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#ArialMT-30\"/>\n",
       "       <use xlink:href=\"#ArialMT-2e\" x=\"55.615234\"/>\n",
       "       <use xlink:href=\"#ArialMT-36\" x=\"83.398438\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_5\">\n",
       "     <g id=\"line2d_13\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mc4d82b55e0\" x=\"41.044\" y=\"67.68\" style=\"fill: #262626; stroke: #262626\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_14\">\n",
       "      <!-- 0.8 -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(20.512 70.829437) scale(0.088 -0.088)\">\n",
       "       <defs>\n",
       "        <path id=\"ArialMT-38\" d=\"M 1131 2484 \n",
       "Q 781 2613 612 2850 \n",
       "Q 444 3088 444 3419 \n",
       "Q 444 3919 803 4259 \n",
       "Q 1163 4600 1759 4600 \n",
       "Q 2359 4600 2725 4251 \n",
       "Q 3091 3903 3091 3403 \n",
       "Q 3091 3084 2923 2848 \n",
       "Q 2756 2613 2416 2484 \n",
       "Q 2838 2347 3058 2040 \n",
       "Q 3278 1734 3278 1309 \n",
       "Q 3278 722 2862 322 \n",
       "Q 2447 -78 1769 -78 \n",
       "Q 1091 -78 675 323 \n",
       "Q 259 725 259 1325 \n",
       "Q 259 1772 486 2073 \n",
       "Q 713 2375 1131 2484 \n",
       "z\n",
       "M 1019 3438 \n",
       "Q 1019 3113 1228 2906 \n",
       "Q 1438 2700 1772 2700 \n",
       "Q 2097 2700 2305 2904 \n",
       "Q 2513 3109 2513 3406 \n",
       "Q 2513 3716 2298 3927 \n",
       "Q 2084 4138 1766 4138 \n",
       "Q 1444 4138 1231 3931 \n",
       "Q 1019 3725 1019 3438 \n",
       "z\n",
       "M 838 1322 \n",
       "Q 838 1081 952 856 \n",
       "Q 1066 631 1291 507 \n",
       "Q 1516 384 1775 384 \n",
       "Q 2178 384 2440 643 \n",
       "Q 2703 903 2703 1303 \n",
       "Q 2703 1709 2433 1975 \n",
       "Q 2163 2241 1756 2241 \n",
       "Q 1359 2241 1098 1978 \n",
       "Q 838 1716 838 1322 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#ArialMT-30\"/>\n",
       "       <use xlink:href=\"#ArialMT-2e\" x=\"55.615234\"/>\n",
       "       <use xlink:href=\"#ArialMT-38\" x=\"83.398438\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_6\">\n",
       "     <g id=\"line2d_14\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mc4d82b55e0\" x=\"41.044\" y=\"19.296\" style=\"fill: #262626; stroke: #262626\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_15\">\n",
       "      <!-- 1.0 -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(20.512 22.445437) scale(0.088 -0.088)\">\n",
       "       <defs>\n",
       "        <path id=\"ArialMT-31\" d=\"M 2384 0 \n",
       "L 1822 0 \n",
       "L 1822 3584 \n",
       "Q 1619 3391 1289 3197 \n",
       "Q 959 3003 697 2906 \n",
       "L 697 3450 \n",
       "Q 1169 3672 1522 3987 \n",
       "Q 1875 4303 2022 4600 \n",
       "L 2384 4600 \n",
       "L 2384 0 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#ArialMT-31\"/>\n",
       "       <use xlink:href=\"#ArialMT-2e\" x=\"55.615234\"/>\n",
       "       <use xlink:href=\"#ArialMT-30\" x=\"83.398438\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_16\">\n",
       "     <!-- Result ($0=N; 1=E$) -->\n",
       "     <g style=\"fill: #262626\" transform=\"translate(14.4 185.472) rotate(-90) scale(0.096 -0.096)\">\n",
       "      <defs>\n",
       "       <path id=\"ArialMT-52\" d=\"M 503 0 \n",
       "L 503 4581 \n",
       "L 2534 4581 \n",
       "Q 3147 4581 3465 4457 \n",
       "Q 3784 4334 3975 4021 \n",
       "Q 4166 3709 4166 3331 \n",
       "Q 4166 2844 3850 2509 \n",
       "Q 3534 2175 2875 2084 \n",
       "Q 3116 1969 3241 1856 \n",
       "Q 3506 1613 3744 1247 \n",
       "L 4541 0 \n",
       "L 3778 0 \n",
       "L 3172 953 \n",
       "Q 2906 1366 2734 1584 \n",
       "Q 2563 1803 2427 1890 \n",
       "Q 2291 1978 2150 2013 \n",
       "Q 2047 2034 1813 2034 \n",
       "L 1109 2034 \n",
       "L 1109 0 \n",
       "L 503 0 \n",
       "z\n",
       "M 1109 2559 \n",
       "L 2413 2559 \n",
       "Q 2828 2559 3062 2645 \n",
       "Q 3297 2731 3419 2920 \n",
       "Q 3541 3109 3541 3331 \n",
       "Q 3541 3656 3305 3865 \n",
       "Q 3069 4075 2559 4075 \n",
       "L 1109 4075 \n",
       "L 1109 2559 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"ArialMT-73\" d=\"M 197 991 \n",
       "L 753 1078 \n",
       "Q 800 744 1014 566 \n",
       "Q 1228 388 1613 388 \n",
       "Q 2000 388 2187 545 \n",
       "Q 2375 703 2375 916 \n",
       "Q 2375 1106 2209 1216 \n",
       "Q 2094 1291 1634 1406 \n",
       "Q 1016 1563 777 1677 \n",
       "Q 538 1791 414 1992 \n",
       "Q 291 2194 291 2438 \n",
       "Q 291 2659 392 2848 \n",
       "Q 494 3038 669 3163 \n",
       "Q 800 3259 1026 3326 \n",
       "Q 1253 3394 1513 3394 \n",
       "Q 1903 3394 2198 3281 \n",
       "Q 2494 3169 2634 2976 \n",
       "Q 2775 2784 2828 2463 \n",
       "L 2278 2388 \n",
       "Q 2241 2644 2061 2787 \n",
       "Q 1881 2931 1553 2931 \n",
       "Q 1166 2931 1000 2803 \n",
       "Q 834 2675 834 2503 \n",
       "Q 834 2394 903 2306 \n",
       "Q 972 2216 1119 2156 \n",
       "Q 1203 2125 1616 2013 \n",
       "Q 2213 1853 2448 1751 \n",
       "Q 2684 1650 2818 1456 \n",
       "Q 2953 1263 2953 975 \n",
       "Q 2953 694 2789 445 \n",
       "Q 2625 197 2315 61 \n",
       "Q 2006 -75 1616 -75 \n",
       "Q 969 -75 630 194 \n",
       "Q 291 463 197 991 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"ArialMT-75\" d=\"M 2597 0 \n",
       "L 2597 488 \n",
       "Q 2209 -75 1544 -75 \n",
       "Q 1250 -75 995 37 \n",
       "Q 741 150 617 320 \n",
       "Q 494 491 444 738 \n",
       "Q 409 903 409 1263 \n",
       "L 409 3319 \n",
       "L 972 3319 \n",
       "L 972 1478 \n",
       "Q 972 1038 1006 884 \n",
       "Q 1059 663 1231 536 \n",
       "Q 1403 409 1656 409 \n",
       "Q 1909 409 2131 539 \n",
       "Q 2353 669 2445 892 \n",
       "Q 2538 1116 2538 1541 \n",
       "L 2538 3319 \n",
       "L 3100 3319 \n",
       "L 3100 0 \n",
       "L 2597 0 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"ArialMT-6c\" d=\"M 409 0 \n",
       "L 409 4581 \n",
       "L 972 4581 \n",
       "L 972 0 \n",
       "L 409 0 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"DejaVuSans-30\" d=\"M 2034 4250 \n",
       "Q 1547 4250 1301 3770 \n",
       "Q 1056 3291 1056 2328 \n",
       "Q 1056 1369 1301 889 \n",
       "Q 1547 409 2034 409 \n",
       "Q 2525 409 2770 889 \n",
       "Q 3016 1369 3016 2328 \n",
       "Q 3016 3291 2770 3770 \n",
       "Q 2525 4250 2034 4250 \n",
       "z\n",
       "M 2034 4750 \n",
       "Q 2819 4750 3233 4129 \n",
       "Q 3647 3509 3647 2328 \n",
       "Q 3647 1150 3233 529 \n",
       "Q 2819 -91 2034 -91 \n",
       "Q 1250 -91 836 529 \n",
       "Q 422 1150 422 2328 \n",
       "Q 422 3509 836 4129 \n",
       "Q 1250 4750 2034 4750 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"DejaVuSans-3d\" d=\"M 678 2906 \n",
       "L 4684 2906 \n",
       "L 4684 2381 \n",
       "L 678 2381 \n",
       "L 678 2906 \n",
       "z\n",
       "M 678 1631 \n",
       "L 4684 1631 \n",
       "L 4684 1100 \n",
       "L 678 1100 \n",
       "L 678 1631 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"DejaVuSans-Oblique-4e\" d=\"M 1081 4666 \n",
       "L 1931 4666 \n",
       "L 3219 666 \n",
       "L 4000 4666 \n",
       "L 4616 4666 \n",
       "L 3706 0 \n",
       "L 2853 0 \n",
       "L 1569 4025 \n",
       "L 788 0 \n",
       "L 172 0 \n",
       "L 1081 4666 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"DejaVuSans-3b\" d=\"M 750 3309 \n",
       "L 1409 3309 \n",
       "L 1409 2516 \n",
       "L 750 2516 \n",
       "L 750 3309 \n",
       "z\n",
       "M 750 794 \n",
       "L 1409 794 \n",
       "L 1409 256 \n",
       "L 897 -744 \n",
       "L 494 -744 \n",
       "L 750 256 \n",
       "L 750 794 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"DejaVuSans-31\" d=\"M 794 531 \n",
       "L 1825 531 \n",
       "L 1825 4091 \n",
       "L 703 3866 \n",
       "L 703 4441 \n",
       "L 1819 4666 \n",
       "L 2450 4666 \n",
       "L 2450 531 \n",
       "L 3481 531 \n",
       "L 3481 0 \n",
       "L 794 0 \n",
       "L 794 531 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"DejaVuSans-Oblique-45\" d=\"M 1081 4666 \n",
       "L 4031 4666 \n",
       "L 3928 4134 \n",
       "L 1606 4134 \n",
       "L 1338 2753 \n",
       "L 3566 2753 \n",
       "L 3463 2222 \n",
       "L 1234 2222 \n",
       "L 909 531 \n",
       "L 3284 531 \n",
       "L 3181 0 \n",
       "L 172 0 \n",
       "L 1081 4666 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "      </defs>\n",
       "      <use xlink:href=\"#ArialMT-52\" transform=\"translate(0 0.78125)\"/>\n",
       "      <use xlink:href=\"#ArialMT-65\" transform=\"translate(72.216797 0.78125)\"/>\n",
       "      <use xlink:href=\"#ArialMT-73\" transform=\"translate(127.832031 0.78125)\"/>\n",
       "      <use xlink:href=\"#ArialMT-75\" transform=\"translate(177.832031 0.78125)\"/>\n",
       "      <use xlink:href=\"#ArialMT-6c\" transform=\"translate(233.447266 0.78125)\"/>\n",
       "      <use xlink:href=\"#ArialMT-74\" transform=\"translate(255.664062 0.78125)\"/>\n",
       "      <use xlink:href=\"#ArialMT-20\" transform=\"translate(283.447266 0.78125)\"/>\n",
       "      <use xlink:href=\"#ArialMT-28\" transform=\"translate(311.230469 0.78125)\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-30\" transform=\"translate(344.53125 0.78125)\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-3d\" transform=\"translate(427.636719 0.78125)\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-Oblique-4e\" transform=\"translate(530.908203 0.78125)\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-3b\" transform=\"translate(605.712891 0.78125)\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-31\" transform=\"translate(658.886719 0.78125)\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-3d\" transform=\"translate(741.992188 0.78125)\"/>\n",
       "      <use xlink:href=\"#DejaVuSans-Oblique-45\" transform=\"translate(845.263672 0.78125)\"/>\n",
       "      <use xlink:href=\"#ArialMT-29\" transform=\"translate(908.447266 0.78125)\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"line2d_15\">\n",
       "    <defs>\n",
       "     <path id=\"m555c3b53df\" d=\"M 0 2.4 \n",
       "C 0.636487 2.4 1.246992 2.147121 1.697056 1.697056 \n",
       "C 2.147121 1.246992 2.4 0.636487 2.4 0 \n",
       "C 2.4 -0.636487 2.147121 -1.246992 1.697056 -1.697056 \n",
       "C 1.246992 -2.147121 0.636487 -2.4 0 -2.4 \n",
       "C -0.636487 -2.4 -1.246992 -2.147121 -1.697056 -1.697056 \n",
       "C -2.147121 -1.246992 -2.4 -0.636487 -2.4 0 \n",
       "C -2.4 0.636487 -2.147121 1.246992 -1.697056 1.697056 \n",
       "C -1.246992 2.147121 -0.636487 2.4 0 2.4 \n",
       "z\n",
       "\" style=\"stroke: #1f77b4\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#p4910c91c6b)\">\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"381.931273\" y=\"19.296\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"381.931273\" y=\"19.296\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"381.931273\" y=\"19.296\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"381.931273\" y=\"19.296\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"381.931273\" y=\"19.296\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"381.931273\" y=\"19.296\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"381.931273\" y=\"19.296\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"381.931273\" y=\"19.296\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"381.931273\" y=\"19.296\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"381.931273\" y=\"19.296\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"300.767636\" y=\"19.296\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"300.767636\" y=\"261.216\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"300.767636\" y=\"19.296\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"300.767636\" y=\"19.296\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"300.767636\" y=\"19.296\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"300.767636\" y=\"19.296\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"300.767636\" y=\"261.216\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"300.767636\" y=\"19.296\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"300.767636\" y=\"19.296\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"300.767636\" y=\"19.296\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"228.622182\" y=\"19.296\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"228.622182\" y=\"19.296\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"228.622182\" y=\"261.216\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"228.622182\" y=\"19.296\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"228.622182\" y=\"19.296\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"228.622182\" y=\"19.296\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"228.622182\" y=\"261.216\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"228.622182\" y=\"19.296\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"228.622182\" y=\"261.216\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"228.622182\" y=\"19.296\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"165.494909\" y=\"261.216\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"165.494909\" y=\"19.296\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"165.494909\" y=\"261.216\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"165.494909\" y=\"261.216\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"165.494909\" y=\"19.296\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"165.494909\" y=\"261.216\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"165.494909\" y=\"261.216\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"165.494909\" y=\"261.216\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"165.494909\" y=\"19.296\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"165.494909\" y=\"261.216\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"111.385818\" y=\"261.216\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"111.385818\" y=\"261.216\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"111.385818\" y=\"261.216\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"111.385818\" y=\"261.216\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"111.385818\" y=\"261.216\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"111.385818\" y=\"261.216\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"111.385818\" y=\"19.296\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"111.385818\" y=\"261.216\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"111.385818\" y=\"261.216\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"111.385818\" y=\"261.216\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"57.276727\" y=\"261.216\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"57.276727\" y=\"261.216\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"57.276727\" y=\"261.216\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"57.276727\" y=\"261.216\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"57.276727\" y=\"261.216\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"57.276727\" y=\"261.216\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"57.276727\" y=\"261.216\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"57.276727\" y=\"261.216\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"57.276727\" y=\"261.216\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "     <use xlink:href=\"#m555c3b53df\" x=\"57.276727\" y=\"261.216\" style=\"fill: #1f77b4; stroke: #1f77b4\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path d=\"M 41.044 261.216 \n",
       "L 41.044 19.296 \n",
       "\" style=\"fill: none; stroke: #262626; stroke-linejoin: miter; stroke-linecap: square\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path d=\"M 57.276727 273.312 \n",
       "L 372.913091 273.312 \n",
       "\" style=\"fill: none; stroke: #262626; stroke-linejoin: miter; stroke-linecap: square\"/>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p4910c91c6b\">\n",
       "   <rect x=\"41.044\" y=\"7.2\" width=\"357.12\" height=\"266.112\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(x, y, 'o')\n",
    "ax.set_xlabel('$x$ (Height in cm)')\n",
    "ax.set_ylabel('Result ($0=N; 1=E$)')\n",
    "sns.despine(trim=True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's train a logistic regression model with just a linear feature using scikit-learn:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "# The design matrix\n",
    "X = np.hstack(\n",
    "    [\n",
    "        np.ones((x.shape[0], 1)),\n",
    "        x[:, None]]\n",
    ")\n",
    "\n",
    "# Train the model (penalty = 'none' means that we do not add a prior on the weights)\n",
    "# we are effectively just maximizing the likelihood of the data\n",
    "model = LogisticRegression(\n",
    "    penalty=None,\n",
    "    fit_intercept=False\n",
    ").fit(X, y);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is how you can get the trained weights of the model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-12.688,   0.411]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here is how you can make predictions at some arbitrary heights:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[9.99810986e-01, 1.89014081e-04],\n",
       "       [9.88560090e-01, 1.14399105e-02],\n",
       "       [5.85351787e-01, 4.14648213e-01],\n",
       "       [2.25419752e-02, 9.77458025e-01],\n",
       "       [3.76605766e-04, 9.99623394e-01]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_predict = np.array([10.0, 20.0, 30.0, 40.0, 50.0])\n",
    "X_predict = np.hstack(\n",
    "    [\n",
    "        np.ones((x_predict.shape[0], 1)),\n",
    "        x_predict[:, None]\n",
    "    ]\n",
    ")\n",
    "predictions = model.predict_proba(X_predict)\n",
    "predictions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the model gave us back the probability of each class.\n",
    "If you wanted, you could ask for the class of maximum probability for each prediction input:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 1, 1])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.predict(X_predict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To visualize the predictions of the model as a function of the height, we can do this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"404.944pt\" height=\"309.979875pt\" viewBox=\"0 0 404.944 309.979875\" xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n",
       " <metadata>\n",
       "  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
       "   <cc:Work>\n",
       "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
       "    <dc:date>2023-09-26T15:41:11.340911</dc:date>\n",
       "    <dc:format>image/svg+xml</dc:format>\n",
       "    <dc:creator>\n",
       "     <cc:Agent>\n",
       "      <dc:title>Matplotlib v3.7.1, https://matplotlib.org/</dc:title>\n",
       "     </cc:Agent>\n",
       "    </dc:creator>\n",
       "   </cc:Work>\n",
       "  </rdf:RDF>\n",
       " </metadata>\n",
       " <defs>\n",
       "  <style type=\"text/css\">*{stroke-linejoin: round; stroke-linecap: butt}</style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"M 0 309.979875 \n",
       "L 404.944 309.979875 \n",
       "L 404.944 0 \n",
       "L 0 0 \n",
       "z\n",
       "\" style=\"fill: #ffffff\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"patch_2\">\n",
       "    <path d=\"M 40.624 273.312 \n",
       "L 397.744 273.312 \n",
       "L 397.744 7.2 \n",
       "L 40.624 7.2 \n",
       "z\n",
       "\" style=\"fill: #ffffff\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_1\">\n",
       "    <g id=\"xtick_1\">\n",
       "     <g id=\"line2d_1\">\n",
       "      <defs>\n",
       "       <path id=\"m3a01524fb9\" d=\"M 0 0 \n",
       "L 0 4.8 \n",
       "\" style=\"stroke: #262626\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use xlink:href=\"#m3a01524fb9\" x=\"56.856727\" y=\"273.312\" style=\"fill: #262626; stroke: #262626\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_1\">\n",
       "      <!-- 20 -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(51.963102 287.910875) scale(0.088 -0.088)\">\n",
       "       <defs>\n",
       "        <path id=\"ArialMT-32\" d=\"M 3222 541 \n",
       "L 3222 0 \n",
       "L 194 0 \n",
       "Q 188 203 259 391 \n",
       "Q 375 700 629 1000 \n",
       "Q 884 1300 1366 1694 \n",
       "Q 2113 2306 2375 2664 \n",
       "Q 2638 3022 2638 3341 \n",
       "Q 2638 3675 2398 3904 \n",
       "Q 2159 4134 1775 4134 \n",
       "Q 1369 4134 1125 3890 \n",
       "Q 881 3647 878 3216 \n",
       "L 300 3275 \n",
       "Q 359 3922 746 4261 \n",
       "Q 1134 4600 1788 4600 \n",
       "Q 2447 4600 2831 4234 \n",
       "Q 3216 3869 3216 3328 \n",
       "Q 3216 3053 3103 2787 \n",
       "Q 2991 2522 2730 2228 \n",
       "Q 2469 1934 1863 1422 \n",
       "Q 1356 997 1212 845 \n",
       "Q 1069 694 975 541 \n",
       "L 3222 541 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "        <path id=\"ArialMT-30\" d=\"M 266 2259 \n",
       "Q 266 3072 433 3567 \n",
       "Q 600 4063 929 4331 \n",
       "Q 1259 4600 1759 4600 \n",
       "Q 2128 4600 2406 4451 \n",
       "Q 2684 4303 2865 4023 \n",
       "Q 3047 3744 3150 3342 \n",
       "Q 3253 2941 3253 2259 \n",
       "Q 3253 1453 3087 958 \n",
       "Q 2922 463 2592 192 \n",
       "Q 2263 -78 1759 -78 \n",
       "Q 1097 -78 719 397 \n",
       "Q 266 969 266 2259 \n",
       "z\n",
       "M 844 2259 \n",
       "Q 844 1131 1108 757 \n",
       "Q 1372 384 1759 384 \n",
       "Q 2147 384 2411 759 \n",
       "Q 2675 1134 2675 2259 \n",
       "Q 2675 3391 2411 3762 \n",
       "Q 2147 4134 1753 4134 \n",
       "Q 1366 4134 1134 3806 \n",
       "Q 844 3388 844 2259 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#ArialMT-32\"/>\n",
       "       <use xlink:href=\"#ArialMT-30\" x=\"55.615234\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_2\">\n",
       "     <g id=\"line2d_2\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#m3a01524fb9\" x=\"121.787636\" y=\"273.312\" style=\"fill: #262626; stroke: #262626\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_2\">\n",
       "      <!-- 25 -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(116.894011 287.910875) scale(0.088 -0.088)\">\n",
       "       <defs>\n",
       "        <path id=\"ArialMT-35\" d=\"M 266 1200 \n",
       "L 856 1250 \n",
       "Q 922 819 1161 601 \n",
       "Q 1400 384 1738 384 \n",
       "Q 2144 384 2425 690 \n",
       "Q 2706 997 2706 1503 \n",
       "Q 2706 1984 2436 2262 \n",
       "Q 2166 2541 1728 2541 \n",
       "Q 1456 2541 1237 2417 \n",
       "Q 1019 2294 894 2097 \n",
       "L 366 2166 \n",
       "L 809 4519 \n",
       "L 3088 4519 \n",
       "L 3088 3981 \n",
       "L 1259 3981 \n",
       "L 1013 2750 \n",
       "Q 1425 3038 1878 3038 \n",
       "Q 2478 3038 2890 2622 \n",
       "Q 3303 2206 3303 1553 \n",
       "Q 3303 931 2941 478 \n",
       "Q 2500 -78 1738 -78 \n",
       "Q 1113 -78 717 272 \n",
       "Q 322 622 266 1200 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#ArialMT-32\"/>\n",
       "       <use xlink:href=\"#ArialMT-35\" x=\"55.615234\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_3\">\n",
       "     <g id=\"line2d_3\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#m3a01524fb9\" x=\"186.718545\" y=\"273.312\" style=\"fill: #262626; stroke: #262626\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_3\">\n",
       "      <!-- 30 -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(181.82492 287.910875) scale(0.088 -0.088)\">\n",
       "       <defs>\n",
       "        <path id=\"ArialMT-33\" d=\"M 269 1209 \n",
       "L 831 1284 \n",
       "Q 928 806 1161 595 \n",
       "Q 1394 384 1728 384 \n",
       "Q 2125 384 2398 659 \n",
       "Q 2672 934 2672 1341 \n",
       "Q 2672 1728 2419 1979 \n",
       "Q 2166 2231 1775 2231 \n",
       "Q 1616 2231 1378 2169 \n",
       "L 1441 2663 \n",
       "Q 1497 2656 1531 2656 \n",
       "Q 1891 2656 2178 2843 \n",
       "Q 2466 3031 2466 3422 \n",
       "Q 2466 3731 2256 3934 \n",
       "Q 2047 4138 1716 4138 \n",
       "Q 1388 4138 1169 3931 \n",
       "Q 950 3725 888 3313 \n",
       "L 325 3413 \n",
       "Q 428 3978 793 4289 \n",
       "Q 1159 4600 1703 4600 \n",
       "Q 2078 4600 2393 4439 \n",
       "Q 2709 4278 2876 4000 \n",
       "Q 3044 3722 3044 3409 \n",
       "Q 3044 3113 2884 2869 \n",
       "Q 2725 2625 2413 2481 \n",
       "Q 2819 2388 3044 2092 \n",
       "Q 3269 1797 3269 1353 \n",
       "Q 3269 753 2831 336 \n",
       "Q 2394 -81 1725 -81 \n",
       "Q 1122 -81 723 278 \n",
       "Q 325 638 269 1209 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#ArialMT-33\"/>\n",
       "       <use xlink:href=\"#ArialMT-30\" x=\"55.615234\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_4\">\n",
       "     <g id=\"line2d_4\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#m3a01524fb9\" x=\"251.649455\" y=\"273.312\" style=\"fill: #262626; stroke: #262626\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_4\">\n",
       "      <!-- 35 -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(246.75583 287.910875) scale(0.088 -0.088)\">\n",
       "       <use xlink:href=\"#ArialMT-33\"/>\n",
       "       <use xlink:href=\"#ArialMT-35\" x=\"55.615234\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_5\">\n",
       "     <g id=\"line2d_5\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#m3a01524fb9\" x=\"316.580364\" y=\"273.312\" style=\"fill: #262626; stroke: #262626\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_5\">\n",
       "      <!-- 40 -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(311.686739 287.910875) scale(0.088 -0.088)\">\n",
       "       <defs>\n",
       "        <path id=\"ArialMT-34\" d=\"M 2069 0 \n",
       "L 2069 1097 \n",
       "L 81 1097 \n",
       "L 81 1613 \n",
       "L 2172 4581 \n",
       "L 2631 4581 \n",
       "L 2631 1613 \n",
       "L 3250 1613 \n",
       "L 3250 1097 \n",
       "L 2631 1097 \n",
       "L 2631 0 \n",
       "L 2069 0 \n",
       "z\n",
       "M 2069 1613 \n",
       "L 2069 3678 \n",
       "L 634 1613 \n",
       "L 2069 1613 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#ArialMT-34\"/>\n",
       "       <use xlink:href=\"#ArialMT-30\" x=\"55.615234\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_6\">\n",
       "     <g id=\"line2d_6\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#m3a01524fb9\" x=\"381.511273\" y=\"273.312\" style=\"fill: #262626; stroke: #262626\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_6\">\n",
       "      <!-- 45 -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(376.617648 287.910875) scale(0.088 -0.088)\">\n",
       "       <use xlink:href=\"#ArialMT-34\"/>\n",
       "       <use xlink:href=\"#ArialMT-35\" x=\"55.615234\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_7\">\n",
       "     <!-- $x$ (cm) -->\n",
       "     <g style=\"fill: #262626\" transform=\"translate(205.408 300.667875) scale(0.096 -0.096)\">\n",
       "      <defs>\n",
       "       <path id=\"DejaVuSans-Oblique-78\" d=\"M 3841 3500 \n",
       "L 2234 1784 \n",
       "L 3219 0 \n",
       "L 2559 0 \n",
       "L 1819 1388 \n",
       "L 531 0 \n",
       "L -166 0 \n",
       "L 1556 1844 \n",
       "L 641 3500 \n",
       "L 1300 3500 \n",
       "L 1972 2234 \n",
       "L 3144 3500 \n",
       "L 3841 3500 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"ArialMT-20\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"ArialMT-28\" d=\"M 1497 -1347 \n",
       "Q 1031 -759 709 28 \n",
       "Q 388 816 388 1659 \n",
       "Q 388 2403 628 3084 \n",
       "Q 909 3875 1497 4659 \n",
       "L 1900 4659 \n",
       "Q 1522 4009 1400 3731 \n",
       "Q 1209 3300 1100 2831 \n",
       "Q 966 2247 966 1656 \n",
       "Q 966 153 1900 -1347 \n",
       "L 1497 -1347 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"ArialMT-63\" d=\"M 2588 1216 \n",
       "L 3141 1144 \n",
       "Q 3050 572 2676 248 \n",
       "Q 2303 -75 1759 -75 \n",
       "Q 1078 -75 664 370 \n",
       "Q 250 816 250 1647 \n",
       "Q 250 2184 428 2587 \n",
       "Q 606 2991 970 3192 \n",
       "Q 1334 3394 1763 3394 \n",
       "Q 2303 3394 2647 3120 \n",
       "Q 2991 2847 3088 2344 \n",
       "L 2541 2259 \n",
       "Q 2463 2594 2264 2762 \n",
       "Q 2066 2931 1784 2931 \n",
       "Q 1359 2931 1093 2626 \n",
       "Q 828 2322 828 1663 \n",
       "Q 828 994 1084 691 \n",
       "Q 1341 388 1753 388 \n",
       "Q 2084 388 2306 591 \n",
       "Q 2528 794 2588 1216 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"ArialMT-6d\" d=\"M 422 0 \n",
       "L 422 3319 \n",
       "L 925 3319 \n",
       "L 925 2853 \n",
       "Q 1081 3097 1340 3245 \n",
       "Q 1600 3394 1931 3394 \n",
       "Q 2300 3394 2536 3241 \n",
       "Q 2772 3088 2869 2813 \n",
       "Q 3263 3394 3894 3394 \n",
       "Q 4388 3394 4653 3120 \n",
       "Q 4919 2847 4919 2278 \n",
       "L 4919 0 \n",
       "L 4359 0 \n",
       "L 4359 2091 \n",
       "Q 4359 2428 4304 2576 \n",
       "Q 4250 2725 4106 2815 \n",
       "Q 3963 2906 3769 2906 \n",
       "Q 3419 2906 3187 2673 \n",
       "Q 2956 2441 2956 1928 \n",
       "L 2956 0 \n",
       "L 2394 0 \n",
       "L 2394 2156 \n",
       "Q 2394 2531 2256 2718 \n",
       "Q 2119 2906 1806 2906 \n",
       "Q 1569 2906 1367 2781 \n",
       "Q 1166 2656 1075 2415 \n",
       "Q 984 2175 984 1722 \n",
       "L 984 0 \n",
       "L 422 0 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"ArialMT-29\" d=\"M 791 -1347 \n",
       "L 388 -1347 \n",
       "Q 1322 153 1322 1656 \n",
       "Q 1322 2244 1188 2822 \n",
       "Q 1081 3291 891 3722 \n",
       "Q 769 4003 388 4659 \n",
       "L 791 4659 \n",
       "Q 1378 3875 1659 3084 \n",
       "Q 1900 2403 1900 1659 \n",
       "Q 1900 816 1576 28 \n",
       "Q 1253 -759 791 -1347 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "      </defs>\n",
       "      <use xlink:href=\"#DejaVuSans-Oblique-78\" transform=\"translate(0 0.203125)\"/>\n",
       "      <use xlink:href=\"#ArialMT-20\" transform=\"translate(59.179688 0.203125)\"/>\n",
       "      <use xlink:href=\"#ArialMT-28\" transform=\"translate(86.962891 0.203125)\"/>\n",
       "      <use xlink:href=\"#ArialMT-63\" transform=\"translate(120.263672 0.203125)\"/>\n",
       "      <use xlink:href=\"#ArialMT-6d\" transform=\"translate(170.263672 0.203125)\"/>\n",
       "      <use xlink:href=\"#ArialMT-29\" transform=\"translate(253.564453 0.203125)\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_2\">\n",
       "    <g id=\"ytick_1\">\n",
       "     <g id=\"line2d_7\">\n",
       "      <defs>\n",
       "       <path id=\"m2b89f57211\" d=\"M 0 0 \n",
       "L -4.8 0 \n",
       "\" style=\"stroke: #262626\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use xlink:href=\"#m2b89f57211\" x=\"40.624\" y=\"261.931198\" style=\"fill: #262626; stroke: #262626\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_8\">\n",
       "      <!-- 0.0 -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(20.092 265.080635) scale(0.088 -0.088)\">\n",
       "       <defs>\n",
       "        <path id=\"ArialMT-2e\" d=\"M 581 0 \n",
       "L 581 641 \n",
       "L 1222 641 \n",
       "L 1222 0 \n",
       "L 581 0 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#ArialMT-30\"/>\n",
       "       <use xlink:href=\"#ArialMT-2e\" x=\"55.615234\"/>\n",
       "       <use xlink:href=\"#ArialMT-30\" x=\"83.398438\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_2\">\n",
       "     <g id=\"line2d_8\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#m2b89f57211\" x=\"40.624\" y=\"213.261119\" style=\"fill: #262626; stroke: #262626\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_9\">\n",
       "      <!-- 0.2 -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(20.092 216.410556) scale(0.088 -0.088)\">\n",
       "       <use xlink:href=\"#ArialMT-30\"/>\n",
       "       <use xlink:href=\"#ArialMT-2e\" x=\"55.615234\"/>\n",
       "       <use xlink:href=\"#ArialMT-32\" x=\"83.398438\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_3\">\n",
       "     <g id=\"line2d_9\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#m2b89f57211\" x=\"40.624\" y=\"164.59104\" style=\"fill: #262626; stroke: #262626\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_10\">\n",
       "      <!-- 0.4 -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(20.092 167.740477) scale(0.088 -0.088)\">\n",
       "       <use xlink:href=\"#ArialMT-30\"/>\n",
       "       <use xlink:href=\"#ArialMT-2e\" x=\"55.615234\"/>\n",
       "       <use xlink:href=\"#ArialMT-34\" x=\"83.398438\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_4\">\n",
       "     <g id=\"line2d_10\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#m2b89f57211\" x=\"40.624\" y=\"115.92096\" style=\"fill: #262626; stroke: #262626\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_11\">\n",
       "      <!-- 0.6 -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(20.092 119.070398) scale(0.088 -0.088)\">\n",
       "       <defs>\n",
       "        <path id=\"ArialMT-36\" d=\"M 3184 3459 \n",
       "L 2625 3416 \n",
       "Q 2550 3747 2413 3897 \n",
       "Q 2184 4138 1850 4138 \n",
       "Q 1581 4138 1378 3988 \n",
       "Q 1113 3794 959 3422 \n",
       "Q 806 3050 800 2363 \n",
       "Q 1003 2672 1297 2822 \n",
       "Q 1591 2972 1913 2972 \n",
       "Q 2475 2972 2870 2558 \n",
       "Q 3266 2144 3266 1488 \n",
       "Q 3266 1056 3080 686 \n",
       "Q 2894 316 2569 119 \n",
       "Q 2244 -78 1831 -78 \n",
       "Q 1128 -78 684 439 \n",
       "Q 241 956 241 2144 \n",
       "Q 241 3472 731 4075 \n",
       "Q 1159 4600 1884 4600 \n",
       "Q 2425 4600 2770 4297 \n",
       "Q 3116 3994 3184 3459 \n",
       "z\n",
       "M 888 1484 \n",
       "Q 888 1194 1011 928 \n",
       "Q 1134 663 1356 523 \n",
       "Q 1578 384 1822 384 \n",
       "Q 2178 384 2434 671 \n",
       "Q 2691 959 2691 1453 \n",
       "Q 2691 1928 2437 2201 \n",
       "Q 2184 2475 1800 2475 \n",
       "Q 1419 2475 1153 2201 \n",
       "Q 888 1928 888 1484 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#ArialMT-30\"/>\n",
       "       <use xlink:href=\"#ArialMT-2e\" x=\"55.615234\"/>\n",
       "       <use xlink:href=\"#ArialMT-36\" x=\"83.398438\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_5\">\n",
       "     <g id=\"line2d_11\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#m2b89f57211\" x=\"40.624\" y=\"67.250881\" style=\"fill: #262626; stroke: #262626\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_12\">\n",
       "      <!-- 0.8 -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(20.092 70.400319) scale(0.088 -0.088)\">\n",
       "       <defs>\n",
       "        <path id=\"ArialMT-38\" d=\"M 1131 2484 \n",
       "Q 781 2613 612 2850 \n",
       "Q 444 3088 444 3419 \n",
       "Q 444 3919 803 4259 \n",
       "Q 1163 4600 1759 4600 \n",
       "Q 2359 4600 2725 4251 \n",
       "Q 3091 3903 3091 3403 \n",
       "Q 3091 3084 2923 2848 \n",
       "Q 2756 2613 2416 2484 \n",
       "Q 2838 2347 3058 2040 \n",
       "Q 3278 1734 3278 1309 \n",
       "Q 3278 722 2862 322 \n",
       "Q 2447 -78 1769 -78 \n",
       "Q 1091 -78 675 323 \n",
       "Q 259 725 259 1325 \n",
       "Q 259 1772 486 2073 \n",
       "Q 713 2375 1131 2484 \n",
       "z\n",
       "M 1019 3438 \n",
       "Q 1019 3113 1228 2906 \n",
       "Q 1438 2700 1772 2700 \n",
       "Q 2097 2700 2305 2904 \n",
       "Q 2513 3109 2513 3406 \n",
       "Q 2513 3716 2298 3927 \n",
       "Q 2084 4138 1766 4138 \n",
       "Q 1444 4138 1231 3931 \n",
       "Q 1019 3725 1019 3438 \n",
       "z\n",
       "M 838 1322 \n",
       "Q 838 1081 952 856 \n",
       "Q 1066 631 1291 507 \n",
       "Q 1516 384 1775 384 \n",
       "Q 2178 384 2440 643 \n",
       "Q 2703 903 2703 1303 \n",
       "Q 2703 1709 2433 1975 \n",
       "Q 2163 2241 1756 2241 \n",
       "Q 1359 2241 1098 1978 \n",
       "Q 838 1716 838 1322 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#ArialMT-30\"/>\n",
       "       <use xlink:href=\"#ArialMT-2e\" x=\"55.615234\"/>\n",
       "       <use xlink:href=\"#ArialMT-38\" x=\"83.398438\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_6\">\n",
       "     <g id=\"line2d_12\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#m2b89f57211\" x=\"40.624\" y=\"18.580802\" style=\"fill: #262626; stroke: #262626\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_13\">\n",
       "      <!-- 1.0 -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(20.092 21.73024) scale(0.088 -0.088)\">\n",
       "       <defs>\n",
       "        <path id=\"ArialMT-31\" d=\"M 2384 0 \n",
       "L 1822 0 \n",
       "L 1822 3584 \n",
       "Q 1619 3391 1289 3197 \n",
       "Q 959 3003 697 2906 \n",
       "L 697 3450 \n",
       "Q 1169 3672 1522 3987 \n",
       "Q 1875 4303 2022 4600 \n",
       "L 2384 4600 \n",
       "L 2384 0 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#ArialMT-31\"/>\n",
       "       <use xlink:href=\"#ArialMT-2e\" x=\"55.615234\"/>\n",
       "       <use xlink:href=\"#ArialMT-30\" x=\"83.398438\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_14\">\n",
       "     <!-- Probability -->\n",
       "     <g style=\"fill: #262626\" transform=\"translate(14.0715 162.666) rotate(-90) scale(0.096 -0.096)\">\n",
       "      <defs>\n",
       "       <path id=\"ArialMT-50\" d=\"M 494 0 \n",
       "L 494 4581 \n",
       "L 2222 4581 \n",
       "Q 2678 4581 2919 4538 \n",
       "Q 3256 4481 3484 4323 \n",
       "Q 3713 4166 3852 3881 \n",
       "Q 3991 3597 3991 3256 \n",
       "Q 3991 2672 3619 2267 \n",
       "Q 3247 1863 2275 1863 \n",
       "L 1100 1863 \n",
       "L 1100 0 \n",
       "L 494 0 \n",
       "z\n",
       "M 1100 2403 \n",
       "L 2284 2403 \n",
       "Q 2872 2403 3119 2622 \n",
       "Q 3366 2841 3366 3238 \n",
       "Q 3366 3525 3220 3729 \n",
       "Q 3075 3934 2838 4000 \n",
       "Q 2684 4041 2272 4041 \n",
       "L 1100 4041 \n",
       "L 1100 2403 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"ArialMT-72\" d=\"M 416 0 \n",
       "L 416 3319 \n",
       "L 922 3319 \n",
       "L 922 2816 \n",
       "Q 1116 3169 1280 3281 \n",
       "Q 1444 3394 1641 3394 \n",
       "Q 1925 3394 2219 3213 \n",
       "L 2025 2691 \n",
       "Q 1819 2813 1613 2813 \n",
       "Q 1428 2813 1281 2702 \n",
       "Q 1134 2591 1072 2394 \n",
       "Q 978 2094 978 1738 \n",
       "L 978 0 \n",
       "L 416 0 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"ArialMT-6f\" d=\"M 213 1659 \n",
       "Q 213 2581 725 3025 \n",
       "Q 1153 3394 1769 3394 \n",
       "Q 2453 3394 2887 2945 \n",
       "Q 3322 2497 3322 1706 \n",
       "Q 3322 1066 3130 698 \n",
       "Q 2938 331 2570 128 \n",
       "Q 2203 -75 1769 -75 \n",
       "Q 1072 -75 642 372 \n",
       "Q 213 819 213 1659 \n",
       "z\n",
       "M 791 1659 \n",
       "Q 791 1022 1069 705 \n",
       "Q 1347 388 1769 388 \n",
       "Q 2188 388 2466 706 \n",
       "Q 2744 1025 2744 1678 \n",
       "Q 2744 2294 2464 2611 \n",
       "Q 2184 2928 1769 2928 \n",
       "Q 1347 2928 1069 2612 \n",
       "Q 791 2297 791 1659 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"ArialMT-62\" d=\"M 941 0 \n",
       "L 419 0 \n",
       "L 419 4581 \n",
       "L 981 4581 \n",
       "L 981 2947 \n",
       "Q 1338 3394 1891 3394 \n",
       "Q 2197 3394 2470 3270 \n",
       "Q 2744 3147 2920 2923 \n",
       "Q 3097 2700 3197 2384 \n",
       "Q 3297 2069 3297 1709 \n",
       "Q 3297 856 2875 390 \n",
       "Q 2453 -75 1863 -75 \n",
       "Q 1275 -75 941 416 \n",
       "L 941 0 \n",
       "z\n",
       "M 934 1684 \n",
       "Q 934 1088 1097 822 \n",
       "Q 1363 388 1816 388 \n",
       "Q 2184 388 2453 708 \n",
       "Q 2722 1028 2722 1663 \n",
       "Q 2722 2313 2464 2622 \n",
       "Q 2206 2931 1841 2931 \n",
       "Q 1472 2931 1203 2611 \n",
       "Q 934 2291 934 1684 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"ArialMT-61\" d=\"M 2588 409 \n",
       "Q 2275 144 1986 34 \n",
       "Q 1697 -75 1366 -75 \n",
       "Q 819 -75 525 192 \n",
       "Q 231 459 231 875 \n",
       "Q 231 1119 342 1320 \n",
       "Q 453 1522 633 1644 \n",
       "Q 813 1766 1038 1828 \n",
       "Q 1203 1872 1538 1913 \n",
       "Q 2219 1994 2541 2106 \n",
       "Q 2544 2222 2544 2253 \n",
       "Q 2544 2597 2384 2738 \n",
       "Q 2169 2928 1744 2928 \n",
       "Q 1347 2928 1158 2789 \n",
       "Q 969 2650 878 2297 \n",
       "L 328 2372 \n",
       "Q 403 2725 575 2942 \n",
       "Q 747 3159 1072 3276 \n",
       "Q 1397 3394 1825 3394 \n",
       "Q 2250 3394 2515 3294 \n",
       "Q 2781 3194 2906 3042 \n",
       "Q 3031 2891 3081 2659 \n",
       "Q 3109 2516 3109 2141 \n",
       "L 3109 1391 \n",
       "Q 3109 606 3145 398 \n",
       "Q 3181 191 3288 0 \n",
       "L 2700 0 \n",
       "Q 2613 175 2588 409 \n",
       "z\n",
       "M 2541 1666 \n",
       "Q 2234 1541 1622 1453 \n",
       "Q 1275 1403 1131 1340 \n",
       "Q 988 1278 909 1158 \n",
       "Q 831 1038 831 891 \n",
       "Q 831 666 1001 516 \n",
       "Q 1172 366 1500 366 \n",
       "Q 1825 366 2078 508 \n",
       "Q 2331 650 2450 897 \n",
       "Q 2541 1088 2541 1459 \n",
       "L 2541 1666 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"ArialMT-69\" d=\"M 425 3934 \n",
       "L 425 4581 \n",
       "L 988 4581 \n",
       "L 988 3934 \n",
       "L 425 3934 \n",
       "z\n",
       "M 425 0 \n",
       "L 425 3319 \n",
       "L 988 3319 \n",
       "L 988 0 \n",
       "L 425 0 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"ArialMT-6c\" d=\"M 409 0 \n",
       "L 409 4581 \n",
       "L 972 4581 \n",
       "L 972 0 \n",
       "L 409 0 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"ArialMT-74\" d=\"M 1650 503 \n",
       "L 1731 6 \n",
       "Q 1494 -44 1306 -44 \n",
       "Q 1000 -44 831 53 \n",
       "Q 663 150 594 308 \n",
       "Q 525 466 525 972 \n",
       "L 525 2881 \n",
       "L 113 2881 \n",
       "L 113 3319 \n",
       "L 525 3319 \n",
       "L 525 4141 \n",
       "L 1084 4478 \n",
       "L 1084 3319 \n",
       "L 1650 3319 \n",
       "L 1650 2881 \n",
       "L 1084 2881 \n",
       "L 1084 941 \n",
       "Q 1084 700 1114 631 \n",
       "Q 1144 563 1211 522 \n",
       "Q 1278 481 1403 481 \n",
       "Q 1497 481 1650 503 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"ArialMT-79\" d=\"M 397 -1278 \n",
       "L 334 -750 \n",
       "Q 519 -800 656 -800 \n",
       "Q 844 -800 956 -737 \n",
       "Q 1069 -675 1141 -563 \n",
       "Q 1194 -478 1313 -144 \n",
       "Q 1328 -97 1363 -6 \n",
       "L 103 3319 \n",
       "L 709 3319 \n",
       "L 1400 1397 \n",
       "Q 1534 1031 1641 628 \n",
       "Q 1738 1016 1872 1384 \n",
       "L 2581 3319 \n",
       "L 3144 3319 \n",
       "L 1881 -56 \n",
       "Q 1678 -603 1566 -809 \n",
       "Q 1416 -1088 1222 -1217 \n",
       "Q 1028 -1347 759 -1347 \n",
       "Q 597 -1347 397 -1278 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "      </defs>\n",
       "      <use xlink:href=\"#ArialMT-50\"/>\n",
       "      <use xlink:href=\"#ArialMT-72\" x=\"66.699219\"/>\n",
       "      <use xlink:href=\"#ArialMT-6f\" x=\"100\"/>\n",
       "      <use xlink:href=\"#ArialMT-62\" x=\"155.615234\"/>\n",
       "      <use xlink:href=\"#ArialMT-61\" x=\"211.230469\"/>\n",
       "      <use xlink:href=\"#ArialMT-62\" x=\"266.845703\"/>\n",
       "      <use xlink:href=\"#ArialMT-69\" x=\"322.460938\"/>\n",
       "      <use xlink:href=\"#ArialMT-6c\" x=\"344.677734\"/>\n",
       "      <use xlink:href=\"#ArialMT-69\" x=\"366.894531\"/>\n",
       "      <use xlink:href=\"#ArialMT-74\" x=\"389.111328\"/>\n",
       "      <use xlink:href=\"#ArialMT-79\" x=\"416.894531\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"line2d_13\">\n",
       "    <path d=\"M 56.856727 21.364709 \n",
       "L 60.136066 21.665648 \n",
       "L 63.415405 21.998655 \n",
       "L 66.694744 22.367044 \n",
       "L 69.974083 22.774445 \n",
       "L 73.253421 23.224833 \n",
       "L 76.53276 23.722552 \n",
       "L 79.812099 24.272341 \n",
       "L 83.091438 24.879363 \n",
       "L 86.370777 25.549228 \n",
       "L 89.650116 26.288018 \n",
       "L 92.929455 27.10231 \n",
       "L 96.208793 27.999196 \n",
       "L 99.488132 28.986297 \n",
       "L 102.767471 30.07177 \n",
       "L 106.04681 31.264311 \n",
       "L 109.326149 32.573145 \n",
       "L 112.605488 34.008008 \n",
       "L 115.884826 35.579105 \n",
       "L 119.164165 37.297064 \n",
       "L 122.443504 39.172855 \n",
       "L 125.722843 41.217698 \n",
       "L 129.002182 43.442935 \n",
       "L 132.281521 45.859881 \n",
       "L 135.56086 48.479635 \n",
       "L 138.840198 51.312864 \n",
       "L 142.119537 54.369557 \n",
       "L 145.398876 57.658739 \n",
       "L 148.678215 61.18816 \n",
       "L 151.957554 64.963968 \n",
       "L 155.236893 68.990359 \n",
       "L 158.516231 73.269225 \n",
       "L 161.79557 77.799813 \n",
       "L 165.074909 82.578413 \n",
       "L 168.354248 87.598081 \n",
       "L 171.633587 92.848435 \n",
       "L 174.912926 98.315521 \n",
       "L 178.192264 103.981785 \n",
       "L 181.471603 109.826158 \n",
       "L 184.750942 115.824248 \n",
       "L 188.030281 121.948676 \n",
       "L 191.30962 128.169512 \n",
       "L 194.588959 134.454824 \n",
       "L 197.868298 140.771321 \n",
       "L 201.147636 147.085042 \n",
       "L 204.426975 153.362085 \n",
       "L 207.706314 159.569334 \n",
       "L 210.985653 165.675143 \n",
       "L 214.264992 171.649964 \n",
       "L 217.544331 177.466874 \n",
       "L 220.823669 183.102009 \n",
       "L 224.103008 188.534858 \n",
       "L 227.382347 193.748454 \n",
       "L 230.661686 198.729431 \n",
       "L 233.941025 203.467977 \n",
       "L 237.220364 207.957692 \n",
       "L 240.499702 212.195368 \n",
       "L 243.779041 216.180706 \n",
       "L 247.05838 219.915998 \n",
       "L 250.337719 223.405781 \n",
       "L 253.617058 226.656488 \n",
       "L 256.896397 229.676099 \n",
       "L 260.175736 232.473818 \n",
       "L 263.455074 235.059761 \n",
       "L 266.734413 237.444682 \n",
       "L 270.013752 239.639731 \n",
       "L 273.293091 241.656236 \n",
       "L 276.57243 243.505532 \n",
       "L 279.851769 245.198804 \n",
       "L 283.131107 246.746973 \n",
       "L 286.410446 248.160602 \n",
       "L 289.689785 249.449823 \n",
       "L 292.969124 250.62429 \n",
       "L 296.248463 251.693144 \n",
       "L 299.527802 252.664992 \n",
       "L 302.80714 253.547905 \n",
       "L 306.086479 254.349417 \n",
       "L 309.365818 255.076533 \n",
       "L 312.645157 255.735748 \n",
       "L 315.924496 256.333068 \n",
       "L 319.203835 256.874026 \n",
       "L 322.483174 257.363714 \n",
       "L 325.762512 257.806807 \n",
       "L 329.041851 258.207585 \n",
       "L 332.32119 258.569966 \n",
       "L 335.600529 258.897527 \n",
       "L 338.879868 259.19353 \n",
       "L 342.159207 259.460948 \n",
       "L 345.438545 259.702486 \n",
       "L 348.717884 259.920604 \n",
       "L 351.997223 260.117536 \n",
       "L 355.276562 260.29531 \n",
       "L 358.555901 260.455765 \n",
       "L 361.83524 260.600569 \n",
       "L 365.114579 260.731231 \n",
       "L 368.393917 260.849121 \n",
       "L 371.673256 260.955475 \n",
       "L 374.952595 261.051414 \n",
       "L 378.231934 261.13795 \n",
       "L 381.511273 261.216 \n",
       "\" clip-path=\"url(#p0079a61c5e)\" style=\"fill: none; stroke: #1f77b4; stroke-width: 1.2; stroke-linecap: round\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_14\">\n",
       "    <path d=\"M 56.856727 259.147291 \n",
       "L 60.136066 258.846352 \n",
       "L 63.415405 258.513345 \n",
       "L 66.694744 258.144956 \n",
       "L 69.974083 257.737555 \n",
       "L 73.253421 257.287167 \n",
       "L 76.53276 256.789448 \n",
       "L 79.812099 256.239659 \n",
       "L 83.091438 255.632637 \n",
       "L 86.370777 254.962772 \n",
       "L 89.650116 254.223982 \n",
       "L 92.929455 253.40969 \n",
       "L 96.208793 252.512804 \n",
       "L 99.488132 251.525703 \n",
       "L 102.767471 250.44023 \n",
       "L 106.04681 249.247689 \n",
       "L 109.326149 247.938855 \n",
       "L 112.605488 246.503992 \n",
       "L 115.884826 244.932895 \n",
       "L 119.164165 243.214936 \n",
       "L 122.443504 241.339145 \n",
       "L 125.722843 239.294302 \n",
       "L 129.002182 237.069065 \n",
       "L 132.281521 234.652119 \n",
       "L 135.56086 232.032365 \n",
       "L 138.840198 229.199136 \n",
       "L 142.119537 226.142443 \n",
       "L 145.398876 222.853261 \n",
       "L 148.678215 219.32384 \n",
       "L 151.957554 215.548032 \n",
       "L 155.236893 211.521641 \n",
       "L 158.516231 207.242775 \n",
       "L 161.79557 202.712187 \n",
       "L 165.074909 197.933587 \n",
       "L 168.354248 192.913919 \n",
       "L 171.633587 187.663565 \n",
       "L 174.912926 182.196479 \n",
       "L 178.192264 176.530215 \n",
       "L 181.471603 170.685842 \n",
       "L 184.750942 164.687752 \n",
       "L 188.030281 158.563324 \n",
       "L 191.30962 152.342488 \n",
       "L 194.588959 146.057176 \n",
       "L 197.868298 139.740679 \n",
       "L 201.147636 133.426958 \n",
       "L 204.426975 127.149915 \n",
       "L 207.706314 120.942666 \n",
       "L 210.985653 114.836857 \n",
       "L 214.264992 108.862036 \n",
       "L 217.544331 103.045126 \n",
       "L 220.823669 97.409991 \n",
       "L 224.103008 91.977142 \n",
       "L 227.382347 86.763546 \n",
       "L 230.661686 81.782569 \n",
       "L 233.941025 77.044023 \n",
       "L 237.220364 72.554308 \n",
       "L 240.499702 68.316632 \n",
       "L 243.779041 64.331294 \n",
       "L 247.05838 60.596002 \n",
       "L 250.337719 57.106219 \n",
       "L 253.617058 53.855512 \n",
       "L 256.896397 50.835901 \n",
       "L 260.175736 48.038182 \n",
       "L 263.455074 45.452239 \n",
       "L 266.734413 43.067318 \n",
       "L 270.013752 40.872269 \n",
       "L 273.293091 38.855764 \n",
       "L 276.57243 37.006468 \n",
       "L 279.851769 35.313196 \n",
       "L 283.131107 33.765027 \n",
       "L 286.410446 32.351398 \n",
       "L 289.689785 31.062177 \n",
       "L 292.969124 29.88771 \n",
       "L 296.248463 28.818856 \n",
       "L 299.527802 27.847008 \n",
       "L 302.80714 26.964095 \n",
       "L 306.086479 26.162583 \n",
       "L 309.365818 25.435467 \n",
       "L 312.645157 24.776252 \n",
       "L 315.924496 24.178932 \n",
       "L 319.203835 23.637974 \n",
       "L 322.483174 23.148286 \n",
       "L 325.762512 22.705193 \n",
       "L 329.041851 22.304415 \n",
       "L 332.32119 21.942034 \n",
       "L 335.600529 21.614473 \n",
       "L 338.879868 21.31847 \n",
       "L 342.159207 21.051052 \n",
       "L 345.438545 20.809514 \n",
       "L 348.717884 20.591396 \n",
       "L 351.997223 20.394464 \n",
       "L 355.276562 20.21669 \n",
       "L 358.555901 20.056235 \n",
       "L 361.83524 19.911431 \n",
       "L 365.114579 19.780769 \n",
       "L 368.393917 19.662879 \n",
       "L 371.673256 19.556525 \n",
       "L 374.952595 19.460586 \n",
       "L 378.231934 19.37405 \n",
       "L 381.511273 19.296 \n",
       "\" clip-path=\"url(#p0079a61c5e)\" style=\"fill: none; stroke: #ff7f0e; stroke-width: 1.2; stroke-linecap: round\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path d=\"M 40.624 261.931198 \n",
       "L 40.624 18.580802 \n",
       "\" style=\"fill: none; stroke: #262626; stroke-linejoin: miter; stroke-linecap: square\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path d=\"M 56.856727 273.312 \n",
       "L 381.511273 273.312 \n",
       "\" style=\"fill: none; stroke: #262626; stroke-linejoin: miter; stroke-linecap: square\"/>\n",
       "   </g>\n",
       "   <g id=\"legend_1\">\n",
       "    <g id=\"line2d_15\">\n",
       "     <path d=\"M 305.515875 133.123875 \n",
       "L 314.315875 133.123875 \n",
       "L 323.115875 133.123875 \n",
       "\" style=\"fill: none; stroke: #1f77b4; stroke-width: 1.2; stroke-linecap: round\"/>\n",
       "    </g>\n",
       "    <g id=\"text_15\">\n",
       "     <!-- Probability of N -->\n",
       "     <g style=\"fill: #262626\" transform=\"translate(330.155875 136.203875) scale(0.088 -0.088)\">\n",
       "      <defs>\n",
       "       <path id=\"ArialMT-66\" d=\"M 556 0 \n",
       "L 556 2881 \n",
       "L 59 2881 \n",
       "L 59 3319 \n",
       "L 556 3319 \n",
       "L 556 3672 \n",
       "Q 556 4006 616 4169 \n",
       "Q 697 4388 901 4523 \n",
       "Q 1106 4659 1475 4659 \n",
       "Q 1713 4659 2000 4603 \n",
       "L 1916 4113 \n",
       "Q 1741 4144 1584 4144 \n",
       "Q 1328 4144 1222 4034 \n",
       "Q 1116 3925 1116 3625 \n",
       "L 1116 3319 \n",
       "L 1763 3319 \n",
       "L 1763 2881 \n",
       "L 1116 2881 \n",
       "L 1116 0 \n",
       "L 556 0 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       <path id=\"ArialMT-4e\" d=\"M 488 0 \n",
       "L 488 4581 \n",
       "L 1109 4581 \n",
       "L 3516 984 \n",
       "L 3516 4581 \n",
       "L 4097 4581 \n",
       "L 4097 0 \n",
       "L 3475 0 \n",
       "L 1069 3600 \n",
       "L 1069 0 \n",
       "L 488 0 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "      </defs>\n",
       "      <use xlink:href=\"#ArialMT-50\"/>\n",
       "      <use xlink:href=\"#ArialMT-72\" x=\"66.699219\"/>\n",
       "      <use xlink:href=\"#ArialMT-6f\" x=\"100\"/>\n",
       "      <use xlink:href=\"#ArialMT-62\" x=\"155.615234\"/>\n",
       "      <use xlink:href=\"#ArialMT-61\" x=\"211.230469\"/>\n",
       "      <use xlink:href=\"#ArialMT-62\" x=\"266.845703\"/>\n",
       "      <use xlink:href=\"#ArialMT-69\" x=\"322.460938\"/>\n",
       "      <use xlink:href=\"#ArialMT-6c\" x=\"344.677734\"/>\n",
       "      <use xlink:href=\"#ArialMT-69\" x=\"366.894531\"/>\n",
       "      <use xlink:href=\"#ArialMT-74\" x=\"389.111328\"/>\n",
       "      <use xlink:href=\"#ArialMT-79\" x=\"416.894531\"/>\n",
       "      <use xlink:href=\"#ArialMT-20\" x=\"466.894531\"/>\n",
       "      <use xlink:href=\"#ArialMT-6f\" x=\"494.677734\"/>\n",
       "      <use xlink:href=\"#ArialMT-66\" x=\"550.292969\"/>\n",
       "      <use xlink:href=\"#ArialMT-20\" x=\"578.076172\"/>\n",
       "      <use xlink:href=\"#ArialMT-4e\" x=\"605.859375\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"line2d_16\">\n",
       "     <path d=\"M 305.515875 145.782125 \n",
       "L 314.315875 145.782125 \n",
       "L 323.115875 145.782125 \n",
       "\" style=\"fill: none; stroke: #ff7f0e; stroke-width: 1.2; stroke-linecap: round\"/>\n",
       "    </g>\n",
       "    <g id=\"text_16\">\n",
       "     <!-- Probability of E -->\n",
       "     <g style=\"fill: #262626\" transform=\"translate(330.155875 148.862125) scale(0.088 -0.088)\">\n",
       "      <defs>\n",
       "       <path id=\"ArialMT-45\" d=\"M 506 0 \n",
       "L 506 4581 \n",
       "L 3819 4581 \n",
       "L 3819 4041 \n",
       "L 1113 4041 \n",
       "L 1113 2638 \n",
       "L 3647 2638 \n",
       "L 3647 2100 \n",
       "L 1113 2100 \n",
       "L 1113 541 \n",
       "L 3925 541 \n",
       "L 3925 0 \n",
       "L 506 0 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "      </defs>\n",
       "      <use xlink:href=\"#ArialMT-50\"/>\n",
       "      <use xlink:href=\"#ArialMT-72\" x=\"66.699219\"/>\n",
       "      <use xlink:href=\"#ArialMT-6f\" x=\"100\"/>\n",
       "      <use xlink:href=\"#ArialMT-62\" x=\"155.615234\"/>\n",
       "      <use xlink:href=\"#ArialMT-61\" x=\"211.230469\"/>\n",
       "      <use xlink:href=\"#ArialMT-62\" x=\"266.845703\"/>\n",
       "      <use xlink:href=\"#ArialMT-69\" x=\"322.460938\"/>\n",
       "      <use xlink:href=\"#ArialMT-6c\" x=\"344.677734\"/>\n",
       "      <use xlink:href=\"#ArialMT-69\" x=\"366.894531\"/>\n",
       "      <use xlink:href=\"#ArialMT-74\" x=\"389.111328\"/>\n",
       "      <use xlink:href=\"#ArialMT-79\" x=\"416.894531\"/>\n",
       "      <use xlink:href=\"#ArialMT-20\" x=\"466.894531\"/>\n",
       "      <use xlink:href=\"#ArialMT-6f\" x=\"494.677734\"/>\n",
       "      <use xlink:href=\"#ArialMT-66\" x=\"550.292969\"/>\n",
       "      <use xlink:href=\"#ArialMT-20\" x=\"578.076172\"/>\n",
       "      <use xlink:href=\"#ArialMT-45\" x=\"605.859375\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p0079a61c5e\">\n",
       "   <rect x=\"40.624\" y=\"7.2\" width=\"357.12\" height=\"266.112\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "xx = np.linspace(20.0, 45.0, 100)\n",
    "XX = np.hstack([np.ones((xx.shape[0], 1)), xx[:, None]])\n",
    "predictions_xx = model.predict_proba(XX)\n",
    "ax.plot(\n",
    "    xx,\n",
    "    predictions_xx[:, 0],\n",
    "    label='Probability of N'\n",
    ")\n",
    "ax.plot(\n",
    "    xx,\n",
    "    predictions_xx[:, 1],\n",
    "    label='Probability of E'\n",
    ")\n",
    "ax.set_xlabel('$x$ (cm)')\n",
    "ax.set_ylabel('Probability')\n",
    "plt.legend(loc='best', frameon=False)\n",
    "sns.despine(trim=True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Questions\n",
    "\n",
    "+ What is the probability of an explosion when the height becomes very small?\n",
    "+ What is the probability of an explosion when the height becomes very large?\n",
    "+ At what height is it particularly difficult to predict what will happen?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Tags",
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.11.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}