intro-to-data-science.ipynb

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   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import statsmodels.formula.api as smf\n",
    "from helper_functions import linear_model_summary\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('ggplot')\n",
    "\n",
    "# This is not good practice, but is appropriate here for a beginners class.\n",
    "# This allows us to not fuss with image sizes later in the presentation.\n",
    "from pylab import rcParams\n",
    "rcParams['figure.figsize'] = 10, 6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A Short Introduction to Data Science"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Data Science** is the practice of asking and answering questions using data.  It is a cross disciplinary pursuit combining skill in:\n",
    "\n",
    "  - Data Analysis.\n",
    "  - Statistics.\n",
    "  - Programming and Software Development.\n",
    "  - Mathematics.\n",
    "  \n",
    "![](wills-twitter-quote.png)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A data scientist must at a minimum have the two skills:\n",
    "\n",
    "  1. Can use data to generate interesting questions.\n",
    "  2. Can use data to answer those interesting questions.\n",
    "  \n",
    "Today we will be looking at a simple dataset, and use it to ask and answer some interesting questions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Objectives for Today"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "  - Gain exposure to the some standard tools of the Data Scientist working in python:\n",
    "    - Pandas\n",
    "    - Matplotlib\n",
    "    - Statsmodels\n",
    "    - Sklearn\n",
    "  - Discuss some basic visualizations of data, and how they lead to questions and answers:\n",
    "    - Histograms\n",
    "    - Scatterplots\n",
    "    - Colored Scatterplots\n",
    "  - Use a Linear Model to address some questions in a simple data set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loading and Inspecting the Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For our example we will use a dataset dataset about various specimens of single species of insect collected across two continents.  The data was acquired from this question on CrossValidated, a statistics/data science question and answer site:\n",
    "\n",
    "[Multiple regression, full and restricted model](http://stats.stackexchange.com/q/267034/74500)\n",
    "\n",
    "We chose this dataset because it is small enough to be accesable, but has some interesting features for us to discover!\n",
    "\n",
    "We will be interested in explaining how the insects wing span varies, as influenced by the other measurements in our dataset.\n",
    "\n",
    "![](dragonfly.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'd like to load the `insects` data into python.  Our first step is to take a quick look at the raw data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "continent\tlatitude\twingsize\tsex\r\n",
      "1\t35.5\t901\t0\r\n",
      "1\t37\t896\t0\r\n",
      "1\t38.6\t906\t0\r\n",
      "1\t40.7\t907\t0\r\n",
      "1\t40.9\t898\t0\r\n",
      "1\t42.4\t893\t0\r\n",
      "1\t45\t913\t0\r\n",
      "1\t46.8\t915\t0\r\n",
      "1\t48.8\t927\t0\r\n"
     ]
    }
   ],
   "source": [
    "!head ./insects.csv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`head` is actually a small command line program that displays the first 10 lines of a file.  We're using it here to inform our strategy for reading the data into python.\n",
    "\n",
    "**Discussion:** How would you describe this dataset?  How many varaibles are they?  How would you describe these varaibles?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It looks like there are four columns in our dataset:\n",
    "\n",
    "```\n",
    "continent, latitude, wingsize, and sex\n",
    "```\n",
    "\n",
    "Each data element is separated from the next by a tab character, this type of format is often called \"tab separated data\".  Tab separated data can be read into python using the `read_csv` function in the `pandas` library."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "insects = pd.read_csv('./insects.csv', sep='\\t')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we have the data in a python object:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
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       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>continent</th>\n",
       "      <th>latitude</th>\n",
       "      <th>wingsize</th>\n",
       "      <th>sex</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>35.5</td>\n",
       "      <td>901</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>37.0</td>\n",
       "      <td>896</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>38.6</td>\n",
       "      <td>906</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>40.7</td>\n",
       "      <td>907</td>\n",
       "      <td>0</td>\n",
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       "      <th>4</th>\n",
       "      <td>1</td>\n",
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       "      <td>0</td>\n",
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       "      <th>5</th>\n",
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       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1</td>\n",
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       "      <td>913</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1</td>\n",
       "      <td>46.8</td>\n",
       "      <td>915</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1</td>\n",
       "      <td>48.8</td>\n",
       "      <td>927</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1</td>\n",
       "      <td>49.8</td>\n",
       "      <td>924</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1</td>\n",
       "      <td>50.8</td>\n",
       "      <td>930</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0</td>\n",
       "      <td>36.4</td>\n",
       "      <td>905</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0</td>\n",
       "      <td>39.3</td>\n",
       "      <td>889</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0</td>\n",
       "      <td>41.3</td>\n",
       "      <td>915</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0</td>\n",
       "      <td>43.4</td>\n",
       "      <td>930</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0</td>\n",
       "      <td>45.5</td>\n",
       "      <td>895</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0</td>\n",
       "      <td>47.3</td>\n",
       "      <td>926</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0</td>\n",
       "      <td>48.5</td>\n",
       "      <td>944</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0</td>\n",
       "      <td>50.4</td>\n",
       "      <td>925</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0</td>\n",
       "      <td>52.1</td>\n",
       "      <td>920</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0</td>\n",
       "      <td>56.1</td>\n",
       "      <td>934</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>1</td>\n",
       "      <td>35.5</td>\n",
       "      <td>797</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1</td>\n",
       "      <td>37.0</td>\n",
       "      <td>806</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1</td>\n",
       "      <td>38.6</td>\n",
       "      <td>812</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1</td>\n",
       "      <td>40.7</td>\n",
       "      <td>807</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>1</td>\n",
       "      <td>40.9</td>\n",
       "      <td>818</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>1</td>\n",
       "      <td>42.4</td>\n",
       "      <td>809</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>1</td>\n",
       "      <td>45.0</td>\n",
       "      <td>810</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>1</td>\n",
       "      <td>46.8</td>\n",
       "      <td>819</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>1</td>\n",
       "      <td>48.8</td>\n",
       "      <td>800</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>1</td>\n",
       "      <td>49.8</td>\n",
       "      <td>823</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>1</td>\n",
       "      <td>50.8</td>\n",
       "      <td>814</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>0</td>\n",
       "      <td>36.4</td>\n",
       "      <td>789</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>0</td>\n",
       "      <td>39.3</td>\n",
       "      <td>803</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>0</td>\n",
       "      <td>41.3</td>\n",
       "      <td>812</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>0</td>\n",
       "      <td>43.4</td>\n",
       "      <td>820</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>0</td>\n",
       "      <td>45.5</td>\n",
       "      <td>808</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>0</td>\n",
       "      <td>47.3</td>\n",
       "      <td>815</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>0</td>\n",
       "      <td>48.5</td>\n",
       "      <td>855</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>0</td>\n",
       "      <td>50.4</td>\n",
       "      <td>842</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>0</td>\n",
       "      <td>52.1</td>\n",
       "      <td>819</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>0</td>\n",
       "      <td>56.1</td>\n",
       "      <td>839</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "    continent  latitude  wingsize  sex\n",
       "0           1      35.5       901    0\n",
       "1           1      37.0       896    0\n",
       "2           1      38.6       906    0\n",
       "3           1      40.7       907    0\n",
       "4           1      40.9       898    0\n",
       "5           1      42.4       893    0\n",
       "6           1      45.0       913    0\n",
       "7           1      46.8       915    0\n",
       "8           1      48.8       927    0\n",
       "9           1      49.8       924    0\n",
       "10          1      50.8       930    0\n",
       "11          0      36.4       905    0\n",
       "12          0      39.3       889    0\n",
       "13          0      41.3       915    0\n",
       "14          0      43.4       930    0\n",
       "15          0      45.5       895    0\n",
       "16          0      47.3       926    0\n",
       "17          0      48.5       944    0\n",
       "18          0      50.4       925    0\n",
       "19          0      52.1       920    0\n",
       "20          0      56.1       934    0\n",
       "21          1      35.5       797    1\n",
       "22          1      37.0       806    1\n",
       "23          1      38.6       812    1\n",
       "24          1      40.7       807    1\n",
       "25          1      40.9       818    1\n",
       "26          1      42.4       809    1\n",
       "27          1      45.0       810    1\n",
       "28          1      46.8       819    1\n",
       "29          1      48.8       800    1\n",
       "30          1      49.8       823    1\n",
       "31          1      50.8       814    1\n",
       "32          0      36.4       789    1\n",
       "33          0      39.3       803    1\n",
       "34          0      41.3       812    1\n",
       "35          0      43.4       820    1\n",
       "36          0      45.5       808    1\n",
       "37          0      47.3       815    1\n",
       "38          0      48.5       855    1\n",
       "39          0      50.4       842    1\n",
       "40          0      52.1       819    1\n",
       "41          0      56.1       839    1"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "insects"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We've got our four columns `continent, latitude, wingsize, and sex`.  \n",
    "\n",
    "We can see some short descriptions of their qualities using `info`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 42 entries, 0 to 41\n",
      "Data columns (total 4 columns):\n",
      "continent    42 non-null int64\n",
      "latitude     42 non-null float64\n",
      "wingsize     42 non-null int64\n",
      "sex          42 non-null int64\n",
      "dtypes: float64(1), int64(3)\n",
      "memory usage: 1.4 KB\n"
     ]
    }
   ],
   "source": [
    "insects.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exploratory Visualizations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is always a good idea to start making visualizations when confronted with a new set of data.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Looking at the Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can get a first feel for how the quantities in our data are spread out using **histograms**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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AtEQEZAAAACBIk92t/fTp05o3b55qa2vl8/k0dOhQ3XTTTVq7dq02btyolJQU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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10eb8ef90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "column_names = {\n",
    "    \"continent\": \"Continent\",\n",
    "    \"latitude\": \"Latitude\",\n",
    "    \"wingsize\": \"Wing Span\",\n",
    "    \"sex\": \"Sex\"\n",
    "}\n",
    "\n",
    "fig, axs = plt.subplots(2, 2)\n",
    "for ax, (column, name) in zip(axs.flatten(), column_names.iteritems()):\n",
    "    ax.hist(insects[column])\n",
    "    ax.set_title(name)\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Discussion:** What have you learned form the data from these histograms?  How do they help you describe the data?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some observations:\n",
    "\n",
    "  - `continent` and `sex` take only two values.  There are two continents represented in the data, labeled zero and one, and there are two sexes (probably Male and Female), also labeled zero and one.\n",
    "  \n",
    "These zero/one columns are called **binary** or **indicator variables**, they measure a specific yes/no condition.\n",
    "\n",
    "  - The values of `wingspan` cluster into two distinct groups.  This is very interesting, and worthy of investigation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scatterplots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Histograms are useful, but limited, as they do not reveal anything about the *relationships between the columns in our data*.  To rectify this we turn to uncountably the most effective and flexible visualization, the **scatterplot**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x11266f2d0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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DeXl5+PnnnzFz5kyMGjUKw4YNwzPPPIMlS5agf//+KC4uxqlTp/Diiy/Cz88PXl5e2LFj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\nBhouAm0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10eb8ecd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.scatter(insects.latitude, insects.wingsize, s=40)\n",
    "ax.set_xlabel(\"Latitude\")\n",
    "ax.set_ylabel(\"Wing Size\")\n",
    "ax.set_title(\"Insect Wing Sizes at Various Latitudes\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we have a scatterplot of `wingsize` against `latitude`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Discussion:** What patterns do you see in the scatterplot.  Can you form any hypothesis about the data?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are some thoughts:\n",
    "    \n",
    "  - The most prominent feature of this data is the two bands.  There seem to be two very well defined elongated clusters of data, with the average wingsize in one cluster much greater than in the other.\n",
    "  - Within each cluster there is noticeable tendency for wingsize to increase as latitude increases."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exploratory Data Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This leads to a few questions we may wish to answer with the data.\n",
    "\n",
    "  1. Are the two clusters associated with one of the other two variables in the dataset, continent or sex?\n",
    "  2. Is the increase of wing size as latitude increases real or illusory?\n",
    "  3. Does continent have any effect on wingsize?\n",
    "  4. If the increase in wing size is real, does the *rate* of increase differ in the two clusters?\n",
    "  \n",
    "Let's answer each of these questions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Are The Two Clusters Associated With Either Continent or Sex?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can discover if the two clusters in the data are associated with either `continent` or `sex` through a well chosen visualization.  Let's make the same scatterplot from before, but color each point either red or blue, according to the value of `continent` or `sex`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1126cbe10>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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//vpri/aXut9cc1h32UlERETNUt6tG67HxBgtuzFoECpDQgyPrwcFoWTbNlzd\nsAGl8fEoSUrCtQEDDOt1gYEQ9vZGxxAqFW727GlyHCqVCosWLcLixYvx008/4fr167h58yZSUlKw\nfPlyAMCkSZMQFxcHjUYDjUaD1atX4+GHHzbp+F5eXjh79qzJ8QC3Lp8OHDgQLi4uWLt2LcrLy6HT\n6ZCVlYUjNfodNrSvqeeurKxEeXm54eeKiopmxdpSLOyIiIhsiHBwQNnMmbiSkICyt97C1Y0bcWX9\nelTWagkr794dZePHo/S++3BdrTZeFxCA0s8/h87fHwBws3dvXP3yS1T8+dhUzzzzDJYsWYK4uDgM\nGDAAQ4cOxcaNGxEREQEAmD9/PkJDQzF27FiMGzcOoaGhmDdvXoPHq9lSNnXqVGRlZSE4OBizZs2q\ns76x/eVyOTZu3IiMjAyMGDECoaGhiImJQWlpqUnn/tvf/obVq1cjODgY69atq3f7e+65B7169UJR\nURGmT5+OwMBA5OXlNRpfa5AJa+39Zyb5+fmWDqFdUalUjf6iUOtjzqXHnEuPOa9i7jw4aDSQX70K\nXceOuOHmZrbztHcNvY5+f14+bw72sSMiIqJ6VXp4AB4elg6DmoGXYomIiIhsBAs7IiIiIhvBwo6I\niIjIRrCwIyIiIrIRLOyIiIiIbAQLOyIiIiIbwcKOiIiIyEawsCMiIiKbEBYWhn379lk6DItiYUdE\nRERmk5CQgIkTJ6J3794YPHgwZsyYgQMHDtz2cRcsWIDY2FijZSkpKRg+fPhtH7spw4cPx65duxrd\n5tdff8WoUaPQq1cvTJkyRZLbiQEs7IiIiNqly5ftcfCgEgcOKHHpkoNZzrFu3TosXboU8+fPx5Ej\nR7B//35ERUVh+/btZjmftdBoNIiOjsaLL76IjIwMhIaGYvbs2ZKcm4UdERGRDcrPd0RamhLZ2c6o\nrJQZrTt3zgnTp3fE/fe7Y/Jkd0ya5I7cXOd6jyOXt6xUKC0txTvvvIPly5cjIiICzs7OUCgUCA8P\nxyuvvAIAqKysxGuvvYbBgwdj8ODBWLJkCW7cuAEA2Lt3L4YMGYJ169ZhwIABGDx4MDZv3gwA+Oyz\nz5CQkID3338fQUFBmDlzJgDjlrSVK1di9uzZmD9/PoKCghAeHo6jR48a4isqKsLTTz+N0NBQjBw5\nEh999JFhXWP7zps3D3l5eYiKikJQUBA++OCDOs9927ZtCAoKwsSJE+Hg4IBFixbh2LFjyMnJaVEu\nm4OFHRFB4RDwAAAgAElEQVQRkY3ZvdsF4eEdMWmSO8LC3LFunRvKyqpvDy/Dl1864ciRW7eLP33a\nDitXKnHjxq2y4OxZJ6xf74aZMz3w+eeuKChwbFYMv//+OyorKzF+/PgGt4mLi8Phw4exfft2bN++\nHYcPH0ZcXJxh/cWLF3Ht2jUcPHgQsbGxWLx4Ma5evYrp06fjwQcfxJw5c5CVlYWPP/643uNv374d\nDz74IDIzMzF27FhDQSmEQFRUFPr3749Dhw5h8+bN2LBhA3bu3NnkvmvWrEGXLl2wceNGZGVl1dsS\nl5WVhX79+hkeOzs7o2fPnjhx4kSzctgSLOyIiIhsSH6+I2bNcsHVq1Uf8TqdDG+/rcSxY1WFWVmZ\nAlu31i3Sfv7ZASUlVcVeUZEDZsxwxZIlHZCY6ICYGBf83/+pUFJib3Icly9fhoeHR6Mtflu2bMHC\nhQvh4eEBDw8PLFy4EN98841hvb29PZ577jkoFAqEhYWhQ4cOzWr1Gjp0KEaPHg2ZTIa//OUvOH78\nOADg0KFD0Gg0mD9/PhQKBbp27Ypp06bhu+++a3LfakKIBs+r1WqhUqmMlrm4uKCsrMzk2FvKrulN\niIiIqK3Iz1cYirqaMjMVGDoUcHbWYdCgGzh5UmG0vn//m+jQQffntvbIzjYuEfbudUB2tj2GDLlh\nUhwdO3aERqOBXq9vsLgrLCxEly5dDI+7dOmCoqIio2PU3NfZ2RnXrl0z6fwA4OXlZbRvRUUF9Ho9\n8vLyUFhYiODgYABVRZper8ewYcOa3NeUS9NKpbJOEVdaWgoXFxeTY28pttgRERHZEHd3AYWibmuS\nn58eAKBQCDzzzHW4uekN65ycBF59VQulsqqwu35dVmf/xpbXZ/DgwXBwcEBiYmKD2/j4+OD8+fOG\nx3l5eejcubNJx5fJTI+lNj8/P3Tr1g0ZGRnIyMjAsWPHkJmZiY0bN7bKuYOCgpCRkWF4rNVqcfr0\nafTu3bvFMZuKhR0REZEN6datHDEx142WDRp0AyEhlYbHQUHXsW1bCTZsuIr4+FIkJZVgwIBbLWGB\ngTrY2xsXhyqVQM+eN02OQ6VSYdGiRVi8eDF++uknXL9+HTdv3kRKSgqWL18OAJg0aRLi4uKg0Wig\n0WiwevVqPPzwwyYd38vLC2fPnjU5HuDW5dOBAwfCxcUFa9euRXl5OXQ6HbKysnDkyJEm9zXl3BMm\nTMCJEyewbds2VFRUYOXKlQgODoZarW5WvC3Bwo6IiMiGODgIzJxZhoSEK3jrrTJs3HgV69dfQefO\nlUbbde9ejvHjy3DffaVQq40LwYCAcnz+eSn8/ata8Hr3vokvv7wKf/+KZsXyzDPPYMmSJYiLi8OA\nAQMwdOhQbNy4EREREQCA+fPnIzQ0FGPHjsW4ceMQGhqKefPmNXi8mi1lU6dORVZWFoKDgzFr1qw6\n6xvbXy6XY+PGjcjIyMCIESMQGhqKmJgYlJaWmnTuv/3tb1i9ejWCg4Oxbt26Ott6eHggPj4eb7/9\nNoKDg3HkyBG8//77jcbWWmSisd5/Nig/P9/SIbQrKpWq0V8Uan3MufSYc+kx51XMnQeNxgFXr8rR\nsaMObm6m9a2j5mvodfTz82v2sTh4goiIiOrl4VEJDw9LR0HNwUuxRERERDaChR0RERGRjWBhR0RE\nRGQjWNgRERER2QgWdkREREQ2goUdERERkY3gdCdERERtlBCizs3mzUWhUECn00lyrvamNacUZmFH\nRETURtW+0bw5cVLotoGXYomIiIhsBAs7IiIiIhvBwo6IiIjIRrCwIyIiIrIRLOyIiIiIbAQLOyIi\nIiIbwcKOiIiIyEawsCMiIiKyESzsiIiIiGwECzsiIiIiG8HCjoiIiMhGsLAjIiIishF2lg4AAH78\n8UckJycDAMLDwzFx4kR8/fXXSE5OhpubGwBg2rRpuOOOOwAACQkJSE1NhUKhQFRUFAYMGGCx2ImI\niIishcULu3PnziElJQVvv/02FAoFli9fjkGDBgEAIiMjERkZabT9+fPnsXfvXqxatQrFxcV44403\nsGbNGshkMkuET0RERGQ1LH4pNi8vD4GBgbC3t4dcLkffvn2xf/9+AIAQos72aWlpGDlyJBQKBby9\nveHr64vs7GypwyYiIiKyOhYv7Lp27YrMzEyUlZWhoqIChw4dQnFxMWQyGRITExETE4MPPvgAWq0W\nAKDRaNCpUyfD/h4eHtBoNJYKn4iIiMhqWPxSbJcuXTBp0iS8+eabcHJyQo8ePSCXy3Hvvffi4Ycf\nhkwmw5dffolNmzZh9uzZlg6XiIiIyGpZvLADgDFjxmDMmDEAgC+++AKenp5wdXU1rA8PD8eKFSsA\nVLXQXbp0ybCuuLgYHh4e9R43IyMDGRkZhsdTpkyBSqUyx1OgBjg4ODDnEmPOpcecS485lx5zbhlf\nffWV4efg4GAEBwc3ur1VFHZXr16Fq6srLl26hP3792PZsmUoKSmBu7s7AOC3335D165dAQBDhgzB\nmjVrEBkZCY1Gg8LCQgQGBtZ73PoSUFpaat4nQ0ZUKhVzLjHmXHrMufSYc+kx59JTqVSYMmVKs/ax\nisLunXfeQVlZGRQKBWbNmgWlUomPPvoIp0+fhkwmg5eXF6KjowEA/v7+GDFiBBYsWAA7OzvMmjWL\nI2KJiIiIAMhEfUNPbVh+fr6lQ2hX+A1Pesy59Jhz6THn0mPOpefn59fsfSw+KpaIiIiIWodVXIol\nIqK2SatVIDfXEfn5cvj56REQUAGlUmfpsIjaLRZ2RETUIlqtAvHxKsTGOgOQARCIibmO6OhSFndE\nFsJLsURE1CI5OY41ijoAkCE21hk5OY6WDIuoXWNhR0RELVJQIMetoq6aDIWF/GghshT+9hERUYv4\n+uoB1J5YQcDHR2+JcIgILOyIiKiF1OoKxMRcx63irqqPnVpdYcmwiNo1Dp4gIqIWUSp1iI4uRXh4\nJQoL5fDx0UOt5qhYIktiYUdERC2mVOoQEqJFSIilIyEigJdiiYiIiGwGCzsiIiIiG8HCjoiIiMhG\nsLAjIiIishEs7IiIiIhsBEfFEhERkWS0WgVycx2Rny+Hn58eAQGcIqc1sbAjIiIiSWi1CsTHq2rc\nY7hqUuvo6FIWd62El2KJiIhIEjk5jjWKOgCQITbWGTk5jpYMy6awsCMiIiJJFBTIcauoqyZDYSHL\nkdbCTBIREZEkfH31uHVv4WoCPj56S4Rjk1jYERERkSTU6grExFzHreKuqo+dWl1hybBsCgdPEFGb\nx1F2ZAqFVgvH3FzI8/Oh9/NDRUAAdEqlpcNqV5RKHaKjSxEeXonCQjl8fPRQq/n72ppY2BFRm8ZR\ndmQKhVYLVXw8nGNj/3yXANdjYlAaHc3iTmJKpQ4hIVqEhFg6EtvES7FE1KZxlB2ZwjEnx1DUAVXv\nFufYWDjm5FgyLKJWx8KOiNo0jrIjU8gLCup5lwDywkJLhENkNrwUS0Rt2q1RdjU/tjnKzpKssS+b\n3te3nncJoPfxsVBERObBr7RE1KZxlF3TtFoF0tOVSEpyQXq6Elqtwmznqu7L5hYRAdeZM+EWEQFV\nfDwUWq3ZzmmKCrUa12NiarxLqvrYVajVlgyLqNXJhBC1J5Sxafn5+ZYOoV1RqVQoLS21dBjtSnvM\nuVarQE6Oo8VG2VlzzqUeXKI8ehRu48fXaRm7kpgIbSv2lq8v502NjlZotXDMyYG8sBB6Hx9UqNUW\nb0lsS6z5fW6r/Pz8mr0PL8USUZvHUXYNa2hwSXh4JUJCWr8VrdG+bGZ8gUwpYHVKZVVxyTcK2TBe\niiUismFSDy6p7stW0+30ZVNotVCmp8MlKQnK9PQGL+lydDRRFRZ2REQ2TOpbOLVmX7bm9Nfj6Gii\nKrwUS0Rkw6oHl9S+RGmuwSU6pRKl0dGoDA+/7b5sDc09VxkeDnTubLQtR0cTVWFhR0RkwyxxC6fW\n6svWnLnnpC5giawVCzsiIhvXVgeXNDb3XO0JW3gPUqIqLOyIiMgqVffXq31/1wq1GvVd2LV0AdvU\ndCtEUmBhR0REVqk1++uZm9TzBRI1hIUdERFZrbYy95zU8wUSNYTjwImIiG4Tp1sha8F3HBER0W2S\ner5AooawsCMiIrpN1dOtoMbUzJxuhSyBfeyIiIhuE6dbIWvBwo6ITMKpHKyTQquFY24u5Pn50Pv5\noSIgwCpHjbYHlp5uhQhgYUdEJuBUDtap+l6qted5K42OZnFH1E6xjx0RNamhqRxychwtGVa719C9\nVB1zciwZFhFZEAs7ImoSp3Kon0KrhTI9HbKEBCjT06HQSjtfWXPupUpE7QMvxRJRk25N5WB81872\nPJWDNVwGbexeqkTUPrXvr9tEZBJO5VCXNVwGrb6X6q1X5da9VImofWKLHRE1iVM51NXoZVCJhkW2\npXupEpE0WNgRkUk4lYMxa7kM2lbupUpE0uClWCKiFuBlUCKyRmyxIyJqgZqXQe0uXMBNb29eBiUi\ni2NhR0TUQtWXQVUqFbSlpZYOh4iIhR1Re8bbURER2RYWdkRmZq3FkzXMw0ZERK2LgyeoTdNqFUhP\nVyIpyQXp6UpotQpLh2Skunhyi4iA68yZcIuIgCo+XvI7FNTHGuZhIyKi1sXCjtqs6hvTR0S4YeZM\nV0REuCE+XmVVxZ01F0+8HRURke1hYUdtVlu4Mb01F0/V87DVxNtRERG1bSzsqM1qCzemt+biifOw\nERHZHg6eoDarLdyYvrp4qj1AwRqKJ96OiojI9lhFYffjjz8iOTkZABAeHo6JEyeirKwMq1evxsWL\nF+Ht7Y0FCxZA+ecHTkJCAlJTU6FQKBAVFYUBAwZYMnyykOob09+6HGt9N6a39uKJt6MiIrItFi/s\nzp07h5SUFLz99ttQKBRYvnw5Bg0ahJ9//hkhISGYNGkStmzZgoSEBEyfPh3nz5/H3r17sWrVKhQX\nF+ONN97AmjVrIJPVviRH1u52pwFpKzemZ/FERERSsXhnpLy8PAQGBsLe3h5yuRx9+/bF/v378fvv\nv2PUqFEAgNGjR+PAgQMAgLS0NIwcORIKhQLe3t7w9fVFdna2JZ8CtUBrTQNSfWP6cePKEBKitbqi\njoiISEoWL+y6du2KzMxMlJWVoaKiAocOHcKlS5dQUlICd3d3AIC7uzuuXLkCANBoNOjUqZNhfw8P\nD2g0GovETi1nzdOAEBERtVUWvxTbpUsXTJo0CW+++SacnJzQo0cPyOV1601earUtjU4DwkuWRERE\nLWLxwg4AxowZgzFjxgAAvvjiC3h6esLd3d3QaldSUgI3NzcAVS10ly5dMuxbXFwMDw+Peo+bkZGB\njIwMw+MpU6ZApVKZ8ZlQbQ4ODvXn3N+/nvGsgKxLF75Gt6nBnDdBf/Uq5JmZkOXlQXTpAn2fPpC7\nupohQtvT0pxTyzHn0mPOLeOrr74y/BwcHIzg4OBGt7eKwu7q1atwdXXFpUuXsH//fixbtgwXLlzA\njh07MHnyZOzYsQNDhgwBAAwZMgRr1qxBZGQkNBoNCgsLERgYWO9x60tAaWmp2Z8P3aJSqerNuaJH\nDyjqmQZE26MHdHyNbktDOW8M7xt7e1qSc7o9zLn0mHPpqVQqTJkypVn7yIQQtedPldySJUtQVlYG\nhUKBJ554AsHBwSgrK8OqVatw6dIleHl5YcGCBejQoQOAqulOUlJSYGdn1+zpTvLz8831NKgejf0h\nUGi1cMzJkWwakNsdhdtWtOSPr/LoUbiNH1+nBfVKYmLViF5qFD/wpMecS485l56fn1+z97GKwk5K\nLOykZS1/CNpTi1RLcu6SlATXmTPrLL/6n/+gbNy41grNZlnL+7w9Yc6lx5xLryWFncVHxRJJgaNw\nG2fNtz5r67RaBdLTlUhKckF6uhJarcLSIRGRDWtWYXfp0iWcOHHCXLEQmU2jo3CJ9401E61Wgfh4\nFSIi3DBzpisiItwQH69icUdEZmPS4IlLly4hLi4Op0+fBgB88skn2LdvHw4fPozZs2ebMz6iVlHd\nIlW7DxlbpKpY4tZn7aHPY06OY41b3gGADLGxzggPr0RISPMm4yYiMoVJLXbx8fEYOHAgNm7cCDu7\nqlowNDQUf/zxh1mDI2otbJFqWvWtz8rGjYM2JMTsRV1r3HnE2hUUyIF62ooLC9kLhojMw6QWu+zs\nbLz00ktGEwcrlUpobeyPMNkuS7RIUcMa6vNYGR5uU6NwfX31QD1txT4+egtFRES2zqSvjW5ubiis\n1Rfp/PnzRrf2IrJ2UrZIUePaS59HtboCMTHXgRptxTEx16FWV1gyLCKyYSa12N1///1YsWIFJk+e\nDL1ej127diEhIQGTJ082d3xEZIPaS59HpVKH6OhShIdXorBQDh8fPdTqCiiVOkuHRkQ2yqTCLiws\nDCqVCj///DM8PT2xc+dO/PWvf8XQoUPNHR8R2aDqPo+15xW0xT6PSqUOISFa3gKZiCTBCYrJrDih\nZctotQrk5joiP18OPz89AgJMb+VpKzmX+s4j5tRWcm5LmHPpMefSM9sExX/961+xZs0a3Lx502j5\nE0880ewTElHj2svcZ+zzSETU+kwq7BwcHAAAr776KjQajWF5O2vsI5JEQ3Of5eQ4WjIsIiJqA0wq\n7ORyOebNm4dhw4bhlVdeMdx9QiarPa6NiG4X5z4jIqKWMmnwRLXJkyeje/fuiI2NxbRp08wVE1G7\nxrnPiIiopUxqAqh5yXXgwIFYunQpvv/+e5SXl5stMKL2inOfERFRS5k0Kvby5cvo2LGj0bLr16/j\n1KlT6Nevn9mCMweOipUWR1G1jFarQE6OY4vmPmPOpcecS485lx5zLr2WjIpt8FLshQsX4O3tDQCo\nrKxEUVFRnW08PT2bfUIiahrnPiMiopZosLB7/vnnsWnTJgDAvHnzGjzA5s2bWz8qIiIiImq2Bgu7\n6qIOYPFGRERE1BY0e/6Ea9eu4dSpU6ioYEduIiIiImvS6HQn3333HXx8fDBs2DAAwOHDh7Fy5UpU\nVFSgQ4cOeOmll9C7d29JAiUiIiKixjXaYpeamoquXbsaHn/88ceYMGECNm7ciMjISHzxxRdmD5CI\niIiITNNoYXf58mXDUNvCwkJcvHgRDz74IJycnHD//ffj7NmzkgRJRERERE1rtLBzdHSEVqsFAGRm\nZqJ79+5wcnICUHU7MZ3OtHm1iIiIiMj8Gi3sBg4ciPj4eKSlpeH777839LUDgDNnznAeOyIiIiIr\n0mhh98QTT8DBwQFffPEFevXqhfvuu8+w7vDhw7jzzjvNHiARERERmcakW4rZEt5STFq8BY30mHPp\nMefSY86lx5xLryW3FGv2PHZEREREZJ1Y2BERERHZCBZ2RERERDaChR0RERGRjWj0lmLVUlJS6l1u\nb28PT09P9OrVC/b29q0aGBERERE1j0mF3c6dO3HixAm4ubnB09MTxcXFuHLlCtRqNS5cuAAAeOGF\nF6BWq80aLBERERE1zKTCzt/fH0OHDsXEiRMNyxITE5GXl4fXX38d3377LT766CMsW7bMbIESERER\nUeNM6mO3e/dujB8/3mjZvffei127dkEmk+GBBx7A+fPnzRIgEREREZnGpMLOzc0Nv//+u9GygwcP\nwtXVFQBw48YN2NmZ1PhHRERERGZiUjU2c+ZMrFy5Et26dTP0sTt79iwWLlwIADh58mSdFj0iIiIi\nkpbJtxQrLS3FoUOHoNFo0LFjRwwaNAgqlcrc8bU63lJMWrwFjfSYc+kx59JjzqXHnEuvJbcUM/n6\nqUqlwj333NPsExARERGRNEwq7C5cuIAvvvgCp0+fRnl5udG6999/3yyBEREREVHzmFTYxcXFoXPn\nznj88cfh6Oho7piIiIiIqAVMKuzOnz+PN954A3I570BGREREZK1MqtT69u2L06dPmzkUIiIiIrod\nJrXYeXl5YdmyZRg6dCjc3d2N1v31r381S2BERERE1DwmFXYVFRUYPHgwdDodiouLzR0TEREREbWA\nSYXd3LlzzR0HEREREd2mBgu7CxcuwNvbGwBQVFTU4AE6d+7c+lERERERUbM1WNg9//zz2LRpEwBg\n3rx5DR5g8+bNrR8VERERETVbg4VddVEHsHgjIiIiagsane5kz549KCkpkSoWIiIiIroNjQ6e2Lx5\nMwoLC+Hj44O+ffuiX79+6Nu3L7y8vKSKj4iIiIhMJBNCiMY2KCkpwfHjxw3/zp07Bw8PD0OhFx4e\nLlWsrSI/P9/SIbQrKpUKpaWllg6jXWHOpcecS485lx5zLj0/P79m79PkdCfu7u4YMWIERowYAQAo\nKytDcnIyfvjhB+zatavNFXZEREREtqrJwk4IgdOnT+P48eM4duwYTpw4gY4dO2LEiBHo27evFDES\nERERkQkaLezeeustnD59Gn5+fggKCsLYsWPx7LPPwtnZWar4iIjIimm1CuTmOiI/Xw4/Pz0CAiqg\nVOosHRZRu9VoYVdQUAA7Ozt4eXnBx8cHPj4+LOqIiAhAVVEXH69CbKwzABkAgZiY64iOLmVxR2Qh\nzR48UVpaiqCgIPTt2xd9+vRBjx49JAq1dXDwhLTY2VZ6zLn02mvOjx5VYvx4N1QVddUEEhOvICRE\na9Zzt9ecWxJzLj1JB0988803uHr1KicvJiJqpwoK5DAu6gBAhsJCOUJCLBERETV78ERWVhauXbsG\ntVqNMWPGSBEjERFZIV9fPQCB2i12Pj56C0VERE0Onjhx4gRu3ryJwMBA9OvXD+PHj0fv3r3h4ODQ\nakH88MMPSE1NhUwmQ7du3TBnzhxs2bIFycnJcHNzAwBMmzYNd9xxBwAgISEBqampUCgUiIqKwoAB\nA1otFiIiMo1aXYGYmOt1+tip1RWWDo2o3Wq0sOvbty8eeughqNVq2Nk12bjXIhqNBomJiVi9ejXs\n7OywatUq7N69GwAQGRmJyMhIo+3Pnz+PvXv3YtWqVSguLsYbb7yBNWvWQCarfTmAiIjMSanUITq6\nFOHhlSgslMPHRw+1mqNiiSyp0Wpt8uTJkgSh1+tRXl4OZ2dnVFRUwMPDAxcvXkR94zrS0tIwcuRI\nKBQKeHt7w9fXF9nZ2ejVq5cksRIR0S1KpQ4hIVr2qSOyEuZphmsGDw8PREZGYu7cuXB0dERoaChC\nQ0ORlZWFxMRE7Ny5E2q1Go8//jiUSiU0Gg169+5ttL9Go7HgMyAiIiKyDnJLB3Dt2jWkpaVh7dq1\nWLduHcrLy7Fr1y5ERETg3//+N2JjY+Hu7o5NmzZZOlQiIiIiq2bxFrujR4/C29sbLi4uAIBhw4Yh\nKysLd911l2Gb8PBwrFixAkBVC92lS5cM64qLi+Hh4VHvsTMyMpCRkWF4PGXKFKhUKnM8DWqAg4MD\ncy4x5lx6zLn0mHPpMeeW8dVXXxl+Dg4ORnBwcKPbW7yw69SpE06ePInKykrY29vj6NGjUKvVKCkp\ngbu7OwDgt99+Q9euXQEAQ4YMwZo1axAZGQmNRoPCwkIEBgbWe+z6EsDJFaXFCS2lx5xLjzmXHnMu\nPeZceiqVClOmTGnWPhYv7AIDAzF8+HC8+OKLUCgU6NmzJ8aOHYsPPvgAp0+fhkwmg5eXF6KjowEA\n/v7+GDFiBBYsWAA7OzvMmjWLI2KJiIiIYMItxWwNbykmLX7Dkx5zLj3mXHrMufSYc+m15JZiFh88\nQUREREStg4UdERERkY1gYUdERERkI1jYEREREdkIi4+KJSIiag1arQK5uY7Iz5fDz0+PgADet5ba\nHxZ2RETU5mm1CsTHqxAb6wxABkAgJuY6oqNLWdxRu8JLsURE1Obl5DjWKOoAQIbYWGfk5DhaMiwi\nybGwIyKiNq+gQI5bRV01GQoL+TFH7QsvxRIRUZvn66sHIGBc3An4+OgtFBE1hH0hzYtfZYiIqM1T\nqysQE3MdVcUdUN3HTq2usGRYVEt1X8iICDfMnOmKiAg3xMeroNUqLB2azeAtxciseAsa6THn0mPO\npVdfzrVaBXJyHFFYKIePjx5qNVuCWlNrvM+PHlVi/Hg31G5ZTUy8gpAQ7W0d2xa15JZivBRLREQ2\nQanUISREi5AQS0dCDWmsLyRft9bBS7FEREQkiVt9IWtiX8jWxMKOiIiIJMG+kObHS7FEREQkCaVS\nh+joUoSHV7IvpJmwsCMiIiLJsC+kefFSLBEREZGNYGFHREREZCNY2BERERHZCBZ2RERERDaChR0R\nERGRjWBhR0RERGQjWNgRERER2QgWdkREREQ2goUdERERkY1gYUdERERkI1jYEREREdkIFnZERERE\nNoKFHREREZGNsLN0AERERA1RaLVwzM2FPD8fej8/VAQEQKdUWjosIqvFwo6IiKySQquFKj4ezrGx\nkAEQAK7HxKA0OhpQqSwdHpFV4qVYIiKySo45OYaiDgBkAJxjY+GYk2PJsIisGgs7IiKySvKCAkNR\nV00GQF5YaIlwiNoEXoolojZPq1UgN9cR+fly+PnpERBQAaVSZ+mw6DbpfX0hAKPiTgDQ+/hAYaGY\niKwdW+yIqE3TahWIj1chIsINM2e6IiLCDfHxKmi17eOjX6HVQpmeDpekJCjT06HQai0dUqupUKtx\nPSYG4s/H1X3sKtRqS4bVIK1WgfR0JZKSXJCermw370GyLjIhhGh6M9uRn59v6RDaFZVKhdLSUkuH\n0a60t5wfParE+PFuqN2uk5h4BSEh0hQ5lsp5Y4MLbGXkqEKrhWNODuSFhdD7+KBCrYZOqbS693n1\nF4zYWGfgz1cjJuY6oqNLbab12Npy3h74+fk1ex+22BERgLbb8lNQIAfq6YlVWGj7f97aw+ACnVIJ\nbUgIysaNgzYkxGoL1pwcxxpFHQDIEBvrjJwcR0uGRe2Q7f/lI6ImVbf8uEVEwHXmTLhFREAVH98m\nijtfXz2A2hceBHx89JYIR1IcXGA92vMXDLIufMcRUZtu+VGrKxATcx2o0RMrJuY61OoKS4YlierB\nBS5D5ZAAABK1SURBVDVVDy4gabXnLxhkXVjYEVGbbvlRKnWIji5FYuIV/Oc/V5GYeMWm+jU1pq0N\nLrBl7fkLBlkXTndCRI1OK9EWKJU6hIRoERJi6UikpVMqURodjcrw8DqDC2ridDDmV/0FIzy8EoWF\ncvj46KFWM88kPRZ2RGRo+ak9upItP9avenBBQ1VtexitaSpz33e2vX7BIOvC6U7IrDg8XnotzXlD\n00pQ06z5fW4N08GYQ3Nz3h6mhjE3a36f2ypOd0JELdZWppWg5uFozSpteYAQUXPwUiyRmZn78o9U\n2E+rbbo1WtO4xa69jdZsdIAQr52SDWlfX9mIJNaW54erqb3ftqst42jNKpwahtoL9rEjs2rvfTKU\nR4/Cbfz4OqNNryQmVnV4NwNz5NxW+2ndrurWWLvCQtz08bHa1litVoGcHEebGq3JPnbSa+9/zy2h\nJX3seCmWyIxs5fJPY/202tDTaFVtqVDgaE3Tp4YhautY2BGZUVufH66aOfpptfW+hw11xq8MDzdb\nayzdnqamhiGyBexjR2RGtnJngNbup2ULfQ9NvVuHVqtAeroSSUkuSE9Xsl8iEZkVW+yIzMjaL/+Y\n2mrW2rPq20JrlymtsZwcmIikxhY7IjOz1vnhmttqVt1Pa9y4MoSEaG+rMGnL96atZkprbE6OY42i\nDgBkiI11Rk6Oo8TRElF7wRY7ajfaep+u1mbJVjNb6HtYszXW7sIF3PT2rtMay0EnRCQ1tthRu2AL\nfbpamyVbzWyl72F1a6yYPLne1thbg05qan+TAxORdNhiR+2CLfTpam2WbDWz9r6HraV60EntPnbt\nbXJgIpIOCztqF2xlPrnWVN1qVnseNqlazdrD1BOtPeiEiKgpLOyoXWhrfbqkuC9re2k1szRODkxE\nUmIfO2oX2lKfLinvy2qtI3aJiKhlrOJesT/88ANSU1Mhk8nQrVs3zJ07F+Xl5Vi9ejUuXrwIb29v\nLFiwAMo/P3QSEhKQmpoKhUKBqKgoDBgwwORz8V6x0rKmewsqtFo45uRYfevU7d6X1Zpy3l4w59Jj\nzqXHnEuvJfeKtXiLnUajQWJiIlasWIF//etf0Ol02LVrF7Zs2YKQkBDExcUhODgYCQkJAIDz589j\n7969WLVqFV5++WWsX78eVlCbUhvQVlqnGpsig4iIqDFW8Umh1+tRXl4OnU6HyspKeHh4IC0tDaNG\njQIAjB49GgcOHAAApKWlYeTIkVAoFPD29oavry+ys7MtGT5Rq+IUGdTWKbRaKNPT4ZKUBGV6erue\nVohIahYv7Dw8PBAZGYm5c+di9uzZUCqVCA0NxZUrV+Du7g4AcHd3x5UrVwBUtfB16tTJaH+NRmOR\n2InMobXvy0okJc4ZSWRZFh8Ve+3aNaSlpWHt2rVQKpVYuXIlfv311zrbyWS1L00R2SZOkUFtGeeM\nJLIsixd2R48ehbe3N1xcXAAAQ4cORVZWFtzd3VFSUmL4383NDUBVC92lS5cM+xcXF8PDw6PeY2dk\nZCAjI8PweMqUKVCpVGZ8NlSbg4MDc94CKhXQuXP1IwUA0/sDMufSY85vkRUV1TtnpN2FC62aI+Zc\nesy5ZXz11VeGn4ODgxEcHNzo9hYv7Dp16oSTJ0+isrIS9vb2OHr0KNRqNZycnLBjxw5MnjwZO3bs\nwJAhQwAAQ4YMwZo1axAZGQmNRoPCwkIEBgbWe+z6EsARPdJqbBQV791qHhy5Jj3m/BZl5871zhl5\n09sb2lbMEXMuPeZceiqVClOmTGnWPhYv7AIDAzF8+HC8+OKLUCgU6NGjB8aOHYvy8nKsWrUKqamp\n8PLywoIFCwAA/v7+GDFiBBYsWAA7OzvMmjWLl2nboOp+OLXvelAaHc3ijqgNs/QdTYj+f3t3H1Nl\n3cdx/HNBgp4JHA+BSdjK4/xDarpSpjTz4bC859iSLUV6MMxGI2mLlVFr1Qo3S5wagrp7c1PHmokr\nV9asjTAjHxYLDE0rVJrMB3wIUNAD5+H+o7tzQ2IP3pxz4Hfer815znVdHH7nu+/0c67fda5fpBsU\n97ELJe5jF1o3+4Rna2xUwr/+dcOn+vY9e7gO5//Ep+rQo+Z9heKekdQ89Kh56N3KfezCfsYOkYm1\nWwFzRcI6wMBgFfbbnSAy/b52a2+Dee1WAACGAoIdwmIord0KAMBQwVQswsJrs+lKfr66Xa5Bv3Yr\nAABDBcEOYcN1OAAADCymYgEAAAxBsAMAADAEwQ4AAMAQXGOHIa2rK1onT8bqzJkopaT4NG6cWzab\nN9zDAgAgLAh2GLK6uqL173/HqbR0hPTfxYuWL7+m/PwrhDsAQERiKhZD1okTsb1CnSRZKi0doRMn\nYsM5LAAAwoZghyHr7NkoqZ+Fyc6do60BAJGJ/wExZI0Z45P6WZjsjjt84RgOAABhR7DDkOV0urV8\n+TWp18Jky5dfk9PpDuewAAAIG748gSHLZvMqP/+KXK5unTsXpTvu8Mnp5FuxAIDIRbDDkGazeXXf\nfV2sSgYAgJiKBQAAMAbBDgAAwBAEOwAAAEMQ7AAAAAxBsAMAADAEwQ4AAMAQBDsAAABDEOwAAAAM\nQbADAAAwBMEOAADAEAQ7AAAAQxDsAAAADEGwAwAAMATBDgAAwBAEOwAAAEMQ7AAAAAxBsAMAADAE\nwQ4AAMAQBDsAAABDEOwAAAAMQbADAAAwBMEOAADAEAQ7AAAAQxDsAAAADEGwAwAAMATBDgAAwBAE\nOwAAAEMQ7AAAAAxBsAMAADAEwQ4AAMAQBDsAAABDEOwAAAAMQbADAAAwBMEOAADAEAQ7AAAAQxDs\nAAAADEGwAwAAMATBDgAAwBAEOwAAAEMQ7AAAAAxBsAMAADAEwQ4AAMAQt4V7AGfOnNG6detkWZb8\nfr/Onz+vnJwcdXZ2qrq6WgkJCZKk3NxcTZ48WZL00UcfqaamRtHR0crLy9OkSZPC+RYAAAAGhbAH\nu5SUFK1atUqS5PP5VFBQoPT0dNXU1CgrK0tZWVl9jm9padGBAwe0du1aXbp0SSUlJSorK5NlWeEY\nPgAAwKAxqKZiGxsbNXr0aN1+++2SJL/ff8MxdXV1ysjIUHR0tJKTkzVmzBg1NTWFeqgAAACDTtjP\n2PW2f/9+Pfjgg4Hne/bs0b59++R0OrV48WLZbDZdvnxZEyZMCBzjcDh0+fLlcAwXAABgUBk0Z+w8\nHo/q6uo0ffp0SdLcuXNVXl6u0tJS2e12bdu2LcwjBAAAGNwGzRm7hoYGjRs3TvHx8ZIU+FuSXC6X\n3n33XUm/naG7ePFiYN+lS5fkcDj6fc2jR4/q6NGjgecLFy5USkpKMIaPPxEXFxfuIUQcah561Dz0\nqHnoUfPQ27FjR+BxWlqa0tLS/vT4QXPGrra2ts80bFtbW+DxoUOHNHbsWEnSlClTtH//fnk8HrW2\nturcuXMaP358v6+ZlpamhQsXBv70Lg5Cg5qHHjUPPWoeetQ89Kh56O3YsaNPjvmrUCcNkjN2brdb\njY2NevbZZwPbKisr1dzcLMuylJSUpPz8fElSamqqpk+frqKiIt1222165pln+EYsAACABkmwi42N\n1ebNm/tsKywsvOnx2dnZys7ODvawAAAAhpRBMxUbCn/nFCYGFjUPPWoeetQ89Kh56FHz0LuVmlv+\n/m4WBwAAgCEnos7YAQAAmIxgBwAAYIhB8eWJgdbT06M333xTHo9HXq9X06ZN04IFC3T16lWtW7dO\nFy5cUHJysoqKimSz2cI9XCPcrOZVVVWqrq5WQkKCJCk3N1eTJ08O82jN4vP59Oqrr8rhcKi4uJg+\nDwGfz6dXXnlFiYmJKi4ups+DbNmyZbLZbLIsS9HR0Vq5ciV9HmT91Zw+D66uri5t2rRJp0+flmVZ\nKigo0JgxY/5xnxt7jZ3b7VZsbKx8Pp9ef/11LVmyRAcPHlRcXJweeeQR7dq1S52dnXr88cfDPVRj\n9Ffz+vp6jRgxQllZWeEenrF2796tkydP6tq1ayouLlZlZSV9HmR/rHlVVRV9HkSFhYV65513NHLk\nyMA2+jy4+qs5fR5cFRUVmjhxombPni2v1yu3260PP/zwH/e5sVOxsbGxkn47k+T1eiVJdXV1mjlz\npiRp1qxZ+vbbb8M2PhP1V3NJMvSzw6Bw6dIl1dfXy+VyBbbR58HVX80l+jyY/H7/DfWlz4Orv5r/\nvh0Dr6urS8ePH9fs2bMlSdHR0bLZbLfU50ZOxUr/myo5f/685s6dq/Hjx6u9vV12u12SZLfb1d7e\nHuZRmqW/mtfX12vPnj3at2+fnE6nFi9ezHTJANq6dauefPJJdXV1BbbR58HVX80l0edBZFmWVqxY\noaioKGVmZsrlctHnQda75i6XS5mZmZLo82BpbW1VXFycNmzYoF9++UXjxo1TXl7eLfW5scEuKipK\nq1atUldXl1avXq3Tp0/fcAwrVgysP9a8paVFc+fO1aOPPirLsrR9+3Zt3bpVBQUF4R6qEb777jsl\nJCTo7rvv7rMm8h/R5wPnZjWnz4OrpKREo0aNUkdHh1asWNHvmt/0+cDqXfOSkhKlpqbS50Hk8/l0\n6tQpLV26VE6nU1u2bNGuXbtuOO7v9LmxU7G/s9lsmjhxohoaGmS32wNr0La1tQUuAMXA6l3z+Pj4\nQCO6XC6dOHEizKMzx/Hjx1VXV6fCwkK99957OnLkiNavX0+fB1F/NS8vL6fPg2zUqFGSpPj4eE2d\nOlVNTU30eZD1rnl6erqampro8yByOBxKTEyU0+mUJE2bNk2nTp26pT43Mth1dHQEpkm6u7vV2Nio\nO++8Uw888ID27t0rSdq7d6+mTJkSxlGapb+ap6SkBBpSkg4dOqSxY8eGa4jGeeyxx7Rx40aVl5fr\nhRde0L333qvnn3+ePg+i/mpeWFhInweR2+3W9evXJUnXr1/X999/r7vuuos+D6L+aj527Fj6PIjs\ndrsSExN15swZSVJjY6NSU1Nvqc+NnIpta2tTRUWFfD6f/H6/MjIydP/992vChAlau3atampqlJSU\npKKionAP1Rg3q3l5ebmam5tlWZaSkpKUn58f7qEab/78+fR5iFVWVtLnQdLe3q7S0lJZliWv16sZ\nM2Zo0qRJcjqd9HmQ3Kzm/HseXEuWLNH69evl8Xg0evRoPffcc/L5fP+4z4293QkAAECkMXIqFgAA\nIBIR7AAAAAxBsAMAADAEwQ4AAMAQBDsAAABDEOwAAAAMQbADgL9p8eLFam1tHbDXy8nJ0fnz5wfs\n9QCAYAfAeMuWLdORI0f+0c+89dZb+vLLL/ts27Ztm5KTkyVJGzZs0AcffDBgYwSAgUCwAwAAMISR\nS4oBwF/p7OzU+vXr1dTUJJ/PpwkTJig/P18Oh0Pbt2/XsWPH9PPPP2vr1q2aOXOmnn76aeXk5Kis\nrEyNjY36+uuvFRUVpc8++0xpaWl6+eWXA/tHjx4t6bezeomJicrJyZEkffzxx/r0009lWVZg2+88\nHo/ef/99HTx4UB6PR+np6Xrqqac0bNiwkNcGwNBFsAMQkfx+v+bMmaMXX3xRXq9XGzdu1ObNm7V8\n+XItWrRIP/74o2bMmKE5c+bc8LOZmZn66aef+oS2v9LQ0KDdu3frjTfeUHJysjZt2tRnf2VlpVpb\nW7V69WpFRUWprKxMO3fuVG5u7oC8XwCRgalYABFp5MiRSk9P17BhwzR8+HBlZ2fr2LFjQft9Bw4c\n0KxZs5SamqqYmBgtWLCgz/7q6mrl5eXJZrNp+PDhmj9/vr755pugjQeAmThjByAidXd3a8uWLTp8\n+LA6Ozvl9/t1/fp1+f1+WZY14L/v119/ldPpDDxPSkoKPO7o6FB3d7eKi4sD2/x+v/x+/4CPA4DZ\nCHYAItInn3yis2fPauXKlYqPj1dzc7OKi4v/r2AXExMjt9sdeN7W1qbExERJkt1u18WLFwP7Lly4\nEHgcFxenmJgYrVmzRqNGjbrFdwQATMUCiBAej0c9PT3q6elRd3e3Ojs7FRMToxEjRujq1auqqqrq\nc3xCQsKf3rPObrffcA+6e+65R7W1tfL5fGpoaNAPP/wQ2JeRkaGvvvpKLS0tcrvd2rlzZ2CfZVly\nuVzasmWLOjo6JEmXL1/W4cOHB+KtA4ggnLEDEBFWrlzZ5/ns2bPV3d2tpUuXyuFwKCsrS3V1dYH9\n8+bNU0VFhb744gs99NBDysvL6/Pzc+bM0Zo1a7RkyRKlpaXppZdeUl5enioqKvT5559r6tSpSk9P\nDxw/efJkzZs3T2+//baioqK0aNEi1dbWBvY/8cQTqqqq0muvvaYrV67I4XDo4Ycf1qRJk4JTEABG\nsvxcxAEAAGAEpmIBAAAMQbADAAAwBMEOAADAEAQ7AAAAQxDsAAAADEGwAwAAMATBDgAAwBAEOwAA\nAEMQ7AAAAAzxH9tr7oBAioMXAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10eb8e550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "continent_boolean = insects.continent.astype(bool)\n",
    "ax.scatter(insects.latitude[continent_boolean], \n",
    "           insects.wingsize[continent_boolean], \n",
    "           s=40, c=\"red\", label=\"Continent 1\")\n",
    "ax.scatter(insects.latitude[~continent_boolean], \n",
    "           insects.wingsize[~continent_boolean],\n",
    "           s=40, c=\"blue\", label=\"Continent 0\")\n",
    "ax.set_xlabel(\"Latitude\")\n",
    "ax.set_ylabel(\"Wing Size\")\n",
    "ax.set_title(\"Are The Two Clusters Associated With Continent?\")\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The values of continent seem scattered randomly across the two clusters, so it does **not** seem like continent is associated with the clusters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x112a68b90>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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AzpxxxvLl7njuOS3+9S9XXLvWOQ//9Ho9Zs2ahYULF+L06dN47bXX8Oyzz8Jg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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112896350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "sex_boolean = insects.sex.astype(bool)\n",
    "ax.scatter(insects.latitude[sex_boolean], \n",
    "           insects.wingsize[sex_boolean],\n",
    "           s=40, c=\"red\", label=\"Male\")\n",
    "ax.scatter(insects.latitude[~sex_boolean], \n",
    "           insects.wingsize[~sex_boolean],\n",
    "           s=40, c=\"blue\", label=\"Female\")\n",
    "ax.set_xlabel(\"Latitude\")\n",
    "ax.set_ylabel(\"Wing Size\")\n",
    "ax.set_title(\"Insect Wing Sizes at Various Latitudes\")\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There we go!\n",
    "\n",
    "This is pretty definitive, the cluster of the larger insects are all female, and the cluster of smaller insects are all male.  This seems like enough evidence to conclude that the sex of the insect causes the data to cluster into two groups."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Is An Increasing Latitude Associated With an Increasing Wing Size?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This question is a little more sophisticated, and we need some new technology to answer it.\n",
    "\n",
    "The idea is to create an equation:\n",
    "\n",
    "$$ \\text{Wing Span} \\approx a + b \\times \\text{Latitude} $$\n",
    "\n",
    "Then we can look at the number $b$, which tells us how we should expect `wingspan` to change as `latitude` changes.  If we find that $b > 0$, that's evidence that an increasing latitude is associated with an increasing wingspan.\n",
    "\n",
    "I'll skip the technicalities, but the basic tool for creating equations like this is called **linear regression**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              Linear Model Summary             \n",
      "===============================================\n",
      "Name         Parameter Estimate  Standard Error\n",
      "-----------------------------------------------\n",
      "Intercept                780.53           64.53\n",
      "latitude                   1.88            1.44\n"
     ]
    }
   ],
   "source": [
    "linear_model = smf.ols(formula='wingsize ~ latitude', data=insects)\n",
    "insects_model = linear_model.fit()\n",
    "linear_model_summary(insects_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The linear regression has attempted to estimate the equation we are after, and it has returned:\n",
    "\n",
    "$$ \\text{Wing Span} \\approx 780.53 + 1.88 \\times \\text{Latitude} $$\n",
    "\n",
    "So we can expect an on average increase of 1.88 wingspan for every increase in one latitude."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One way we can visualize this is to look at the equation as the equation for a line. If we *know* the latitude that we find an insect, we can *predict* the wing span using the equation.  If we plot the latitudes verses the predictions, we get a line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x112a68790>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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fuGHv3stJnhBATo4HFi/2xZNP+uO///XChQsd0/lXWlqKqVOnYt68ecjOzsbC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\njujQSwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112a8a150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "# Make a scatterplot of the data.\n",
    "sex_boolean = insects.sex.astype(bool)\n",
    "ax.scatter(insects.latitude[sex_boolean], \n",
    "           insects.wingsize[sex_boolean],\n",
    "           s=40, c=\"red\", label=\"Male\")\n",
    "ax.scatter(insects.latitude[~sex_boolean], \n",
    "           insects.wingsize[~sex_boolean],\n",
    "           s=40, c=\"blue\", label=\"Female\")\n",
    "\n",
    "# Make a linea graph of the predictions.\n",
    "x = np.linspace(30, 60, num=250)\n",
    "ax.plot(x, insects_model.params[0] + insects_model.params[1] * x,\n",
    "       linewidth=2, c=\"black\")\n",
    "\n",
    "ax.set_xlim(30, 60)\n",
    "ax.set_xlabel(\"Latitude\")\n",
    "ax.set_ylabel(\"Wing Size\")\n",
    "ax.set_title(\"Insect Wing Sizes at Various Latitudes\")\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This plot elucidates a serious flaw in our model, it has no knowledge of the sex of the insect, so its predictions bisect the two clusters in the data.\n",
    "\n",
    "It would much better to take account of the sex of the index and fit two lines, we make one line of prediction of the wing size given the latitude for males, and another for females.\n",
    "\n",
    "The easiest way to do this is to modify our equation:\n",
    "\n",
    "$$ \\text{Wing Span} \\approx a + b \\times \\text{Latitude} + c \\times \\text{Sex} $$\n",
    "\n",
    "There is not another term: if the insect is male we *add $c$* to the prediction, otherwise we add nothing.\n",
    "\n",
    "Again, linear regression can find an equation of this shape describing the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              Linear Model Summary             \n",
      "===============================================\n",
      "Name         Parameter Estimate  Standard Error\n",
      "-----------------------------------------------\n",
      "Intercept                829.96           13.94\n",
      "latitude                   1.88            0.31\n",
      "sex                      -98.86            3.43\n"
     ]
    }
   ],
   "source": [
    "linear_model = smf.ols(formula='wingsize ~ latitude + sex', data=insects)\n",
    "insects_model_with_sex = linear_model.fit()\n",
    "linear_model_summary(insects_model_with_sex)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now have an estimate for the number $c$ of $-98.86$.  This means, that on average, being male costs an insect about $-98.86$ in wingspan.\n",
    "\n",
    "The predictions from this model now depend on whether an insect is male or female.  We have two lines of predictions, and the sex of the insect chooses which line to use:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x113cd6fd0>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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mfO4f/vAH+Pv7Qy6XY/bs2WhoaMCZM2fatCMrK6vD17UlrrEjIiKiTispUSIv\nr22M2L1bhQkTZDAYDLjlluttwp1Wa4CvrwEAkJfngW+/NX08P1+J48c9EBZW36n2fPzxxyZr7F5+\n+WV888032LlzJ4CmqdrGxkbcfvvtxueEhIQYv/fy8mpzu7q62nh79erV2LhxI0pKSgAAVVVVZkfh\nCgsLzb6uVOv/GOyIiIio0zQaA/z8DLh2zXTyLyWl0bjeLT29Hp984oXCwqa1d3K5wJIlVejVq2kK\ns67O/E7S2trO7zBtvcZOq9Xi3nvvxeLFizt9rtYOHTqEDz74AF9++SUSExMBACkpKWbX9fXk63YF\np2KJiIio07TaBrzzTjWAG+EmMlKP1NQb68769KlDVlYF1q+/hg8+qMSOHRUYNerGKFhMTCMCAgwm\n51UoBBISGrvdvilTpmDnzp349ttvYTAYUFdXhwMHDkCn03X6XNXV1VAqlQgMDERDQwOWLVuGqqoq\nm79uVzDYERERUacJIZCeXo1t267ivfeqsHZtJb76qgLR0XUmz9Nq65GWVoV77qlEcnItFAph8tiG\nDdeQlNQU5CIiDPjii0okJJieoyPmashptVp8/PHH+N///V8MGDAAw4YNw+rVq2EwGNo9pj2pqalI\nTU3FqFGjMGLECHh7e0Or1Zp9bkeva2syYW4c0YUVFRXZuwluRaPRoLKy0t7NcCvsc+mxz6XHPpeW\nrfv76lUPXLmigEZjQHBwz9e5c3Tt9W974dESrrEjIiIiu/L3vw5//+v2boZL4FQsERERkYtgsCMi\nIiJyEQx2RERERC6CwY6IiIjIRTDYEREREbkIBjsiIiIiF8FyJ0RERGSREAIBAQHQ6/X2bopL6smS\nwgx2REREZFFVVRWLQjsJTsUSERERuQgGOyIiIiIXwWBHRERE5CIY7IiIiIhcBIMdERERkYtgsCMi\nIiJyEQx2RERERC6CwY6IiIjIRTDYEREREbkIBjsiIiIiF8FgR0REROQiGOyIiIiIXITS3g0AgG3b\ntmHXrl0AgLS0NEycOBFffvkldu3aBX9/fwDAQw89hEGDBgEAsrKykJ2dDYVCgenTp2PgwIF2azsR\nERGRo7B7sLtw4QJ2796Nd999FwqFAm+//TaGDBkCAMjIyEBGRobJ8wsLC3HgwAEsW7YMZWVlePPN\nN7Fy5UrIZDJ7NJ+IiIjIYdh9KvbixYtISEiAh4cH5HI5kpOT8cMPPwAAhBBtnn/48GGMHDkSCoUC\noaGhCA+zT1ZzAAAgAElEQVQPR15entTNJiIiInI4dg92UVFROHnyJKqqqlBfX4+ffvoJZWVlkMlk\n2L59O+bNm4fVq1ejpqYGAFBeXo5evXoZjw8KCkJ5ebm9mk9ERETkMOw+FRsREYFJkybhrbfegpeX\nF2JiYiCXyzFu3Djce++9kMlk2LhxI9avX48//elP9m4uERERkcOye7ADgDFjxmDMmDEAgA0bNiA4\nOBh+fn7Gx9PS0vDee+8BaBqhKy0tNT5WVlaGoKAgs+fNzc1Fbm6u8fbUqVOh0Whs8RaoHSqVin0u\nMfa59Njn0mOfS499bh+bN282fp+SkoKUlBSLz3eIYHft2jX4+fmhtLQUP/zwAxYtWoSKigoEBAQA\nAA4dOoSoqCgAwNChQ7Fy5UpkZGSgvLwcOp0OCQkJZs9rrgMqKytt+2bIhEajYZ9LjH0uPfa59Njn\n0mOfS0+j0WDq1KmdOsYhgt3777+PqqoqKBQKzJo1C2q1Gh9//DHy8/Mhk8kQEhKC2bNnAwAiIyMx\nYsQIZGZmQqlUYtasWdwRS0RERARAJsxtPXVhRUVF9m6CW+FveNJjn0uPfS499rn02OfS02q1nT7G\n7rtiiYiIiKhnOMRULBEROaeaGgXOnvVEUZEcWq0BcXH1UKv19m4WkdtisCMioi6pqVFgzRoNlizx\nBiADIDBvXi1mz65kuCOyE07FEhFRl5w549ki1AGADEuWeOPMGU97NovIrXHEjoiIuqS4WI4boa6Z\nDDqdHAMG2KNFRM6rulqGggIFCgqUxq/r1nX+PAx2RETUJeHhBgACpuFOICzMYKcWETkuIYCSEjnO\nn1ciP980wBUUKFBaqmhzDIMdERFJJj6+HvPm1bZZYxcfX2/vphHZRUMDcOGCAufPN4W1/Pymr823\na2vbXwHn6SkQHd2I6Gg9YmIa0aePHoB/p9vAYEdERF2iVusxe3Yl0tIaoNPJERZmQHw8d8WSa7t6\nVdZmtC0/X4nz5xUoKlLAYGj/ogmBgXrExOgRHd0U3JoDXHR0I8LCDJC3yX0MdkREJCG1Wo8BA2q4\npo5chsHQtH60oKAprDWNut0IchUV7Y+6yeUCUVFNYa1PnxtfY2KaRuL8/Gx/TQgGOyIiInIrtbXA\nhQtNa91aT5teuKBEQ0P7o27e3gbExNwIbtHRjcbbERF6qFQSvhEzGOyIiIjIpQgBXLkiN25SaBng\nCgqU0OnablRoKSRE32a0rel7PXr1MsCRL1HPYEdEREROp7ERKCpStNhheiO4nT+vQGVl+1OmSqVA\nZOSNNW4tp0379NFDrbb9lKmtMNgRERGRQ2pd2615k0JBgRKFhQo0NrY/dKbRGIxBreUmhZgYPbRa\nPRSWB+2cFoMdERER2UVXaru1FB5ufpNCnz6NCAwUDj1laisMdkRERGQzrWu75eV54MQJFS5ckKO0\nVI76+vbTl7nabs1BLiqqEV5eEr4RJ8FgR0RERN3Sndpu3t4Cffs2Ijb2upW13cgSBjsiIiKyyGAA\nCgtlyM1Vdau2m0YD/N//qdDyMnS1tcDixdUYMKBGgnfi+hjsiIiIyMrabr5mj7W2ttuOHb74v//z\nbHW0DDqdnEWuewiDHRERkRvobm230FDDb5fC6nptt/BwAwCBliN2gEBYmKE7b41aYLAjIiJyEbas\n7da7ty8qKyu71b74+HrMm1eLJUu80RTuBObNq0V8fH23zks3MNgRkdOrqVHg7FlPFBXJodUaEBfH\nC9FTW67yc+LMtd3Uaj1mz65EWloDdDo5wsIMiI93zs/BUTHYEZFTq6lRYM0aTZsRgNmzK/mfBRk5\n089Jc2231rtMXaW2m1qtx4ABNVxTZyMyIYTzXjejC4qKiuzdBLei0Wi6PXRPneNufZ6To8aECf5o\nvWZn+/arku2yc7c+dwSd7XNH+Dlpqbm2W/MUafMmheY1b7W17U+Z2qu2G3/OpafVajt9DEfsiMip\nFRfLYfqfNcBddtSaPX5Ommu7td5lak1tt8BAPWJi9L9tVmBtN7Iegx0ROTXusnM8jriWzRY/JwZD\nU2BsvUmhs7XdzE2b+vm51WQa9SAGOyJyatxl1zEpg5ajrmXr6s9Jy9puradNb9R2M8/a2m5EPYlr\n7MimuCZDeu7Y5zU1Cpw542m3XXaO3OdSBy2p1rKZ6/OOAqy5nxNvbz3Ky+XGUbbO1nYLCdGb3aTQ\nmdpuzsKRf85dFdfYEZFb4i679p0549ki1AGADEuWeCMtrcEmmwbstebRUoBVqfS4eFHxW1gDCgrk\nKCjwQEGBDwoKFKiq6nptN7XarcZGyAkw2BERuTCpg1ZPr2Wzdhr52DHzAfbvf/fE5ctyh67tRtST\nGOyIiFyY1JtLenLNo7lRuIceqsfgwfUoK1Ph118DOqjtJkNxcdP9jl7bjaincI0d2RTXZEiPfS49\nR+5ze2xm6Oqax9a13Q4f9kJWlifajji25eEhcP060DrArllTibS0KpvVdnMnjvxz7qq4xo6IiEzY\n4xJOltY8dqe2W7Nhw65j1CgDtNoa47Spn58MH37YNsCOGVPLUEduhSN2ZFP8DU967HPpsc9v6G5t\nt4iIG7tMPT3l+PhjL5jbYTtypMLsrlh77o52dfw5lx5H7IiIyOakqu1WU6NAcLBoZ72eus257b07\n2hELM5P7YbAjIiITQsAharvZYxq5qxy1MDO5HwY7IiI31NiIFrXd2k6bOkptN3uPwllL6nqBRO1h\nsCMiclHV1TKzmxQKCpQoLFSwtlsPsldhZqLWGOyIiJyUEEBJidzsJoX2a7vdwNpuPUfqeoFE7WGw\nIyJyYK1ruzVvUmgehautbX/K1NNTIDq6Kay1njaNimpkGZAe1JOFmYm6g8GOiMjOulPbLTBQj5iY\npmnS1tOmYWEGyNvPfdSDnGmjB7k2BjsisgpLOXRdd2u7RUW13aTQPG2qVMpbfS4N/FzsxFk2epBr\nY7Ajog6xlEPHpKrt1hI/FyJqjVeeIJtipXLp2aLPc3LUmDDBH+auAOAupRws1XY7f97jt12R7eup\n2m4tufPnwn9bpMc+lx6vPEFENuEupRy6U9tNoWiq7RYba/vabs3c5XMhIusx2BFRh1yplENP1XaL\niDAgP1+JHTtUAGTQ64GpUxsknQZ1pc+FiHoGgx0RdciZSjlIVdutaRpUDXteacCZPhcikgaDHRF1\nyNFKOThCbTdHmAZ1tM+FiOyPwY6IrCJ1KYeeqO3Wp49pgOvJ2m6OMg3KEhtE1BKDHRHZhS1ru/n5\n2X6zP6dBicgRMdgRkc10p7abWm0wCW4ta7tFRurh4SHhGzHbvhvToCUlSoSGNnIalIjsjsGOiLrM\nUm23ggIldDrLGxVCQ/Ut6rn1TG03KTVPgzbV93LtunFE5BwY7IjcmDWXCetObTcPj6babq1rutmy\nthsRkTtjsCOyMUe9xqq5y1FNmtSApKQGFBXJra7t5udnMLtJISZGD61WD4XlQTsiIupBDHbk1Bw1\nNDVzlGt5mqvt9vPPnsjO9kDLOmxff+2Jr7/2bHN8eLi+1VSp+dpuRERkXwx25LQcJTRZcuaMZ4v2\nAbYsYttc262kRIFTp9Sdqu3W0tix9Rg1qq5Ltd2IiMi+GOzIaUkZmrqqp4vYWl/bTd3m2Na13ZRK\nBZYubdl/ACDw3HO1DtN/RETUOQx25LQcofJ/RzpbxLYnarvFxwMREfUd1narqVFAoQDrsBERuRAG\nO3JajlL53xJzRWyfeaYWBkMjduzwtEltt6bSG5Udto2XoyIicj0OEey2bduGXbt2AQDS0tIwceJE\nVFVVYfny5bh8+TJCQ0ORmZkJtbppeikrKwvZ2dlQKBSYPn06Bg4caM/mk504auX/1rXdGhoMGDu2\nAQUFCpSVybF8uRrLl7edKm0mZW03Xo6KiMi12D3YXbhwAbt378a7774LhUKBt99+G0OGDMHOnTsx\nYMAATJo0CVu2bEFWVhYefvhhFBYW4sCBA1i2bBnKysrw5ptvYuXKlZBxW57T6e6OVnuOOLG2GxER\nOSK7B7uLFy8iISEBHr9dHyg5ORk//PADjhw5gjfeeAMAkJqaigULFuDhhx/G4cOHMXLkSCgUCoSG\nhiI8PBx5eXno27evPd8GdVJP7Wi15YhTdbXM7CYF1nYjIiJHZfdgFxUVhY0bN6KqqgoeHh746aef\nEBcXh4qKCgQEBAAAAgICcPXqVQBAeXk5EhMTjccHBQWhvLzcLm2nrnOEHa3maru1/Fpaajl9sbYb\nERE5GrsHu4iICEyaNAlvvfUWvLy8EBMTA7m87TQWp1pdi1Q7Wptru7XepGBNbTdPT4HoaPPTpazt\nRkREjsjuwQ4AxowZgzFjxgAANmzYgODgYAQEBBhH7SoqKuDv7w+gaYSutLTUeGxZWRmCgoLMnjc3\nNxe5ubnG21OnToVGo7HhO6HWVCqV2T6PjATM7WiNiJB1+jOqqADOnZPj3Dk58vPlOHdOZvy+sFDW\norZbW0FBBsTGCsTGGhATY0BcXNPtmBgDwsMFTH/HkANQdapt9tBen3fk2jUDTp6U4+JFGSIiBJKS\nDPDzs66osbvrap9T17HPpcc+t4/Nmzcbv09JSUFKSorF5ztEsLt27Rr8/PxQWlqKH374AYsWLUJJ\nSQn27NmDyZMnY8+ePRg6dCgAYOjQoVi5ciUyMjJQXl4OnU6HhIQEs+c11wHWlIGgntNe6Y2YGAXm\nzVO0WWMXE1ODykrTNXY9Udut9ahbe7XdWqqu7uq7ti9ry5205AxX8XBkXelz6h72ufTY59LTaDSY\nOnVqp46RCSHsvgXvjTfeQFVVFRQKBaZNm4aUlBRUVVVh2bJlKC0tRUhICDIzM+Hj4wOgqdzJ7t27\noVQqO13upKioyFZvg8yw9A9BTY0CZ854QqeTIzDQAA+PRly6JLNJbbfm13Pk68r2lK7845uTo8aE\nCf5oPYK6fftVXoXCCvwPT3rsc+mxz6Wn1Wo7fYxDBDspMdhJq/kfgta13VruNi0oUEKns7xRobu1\n3dxpRKor//ju2OGLGTP82tz/6afXMHZsVU81zWXxPzzpsc+lxz6XXleCnUNMxZJrMFfbrajIE3l5\nXnav7eYIu3AdmTNcxcNZuctIMRE5hk4Fu9LS0jblRsi9OGttN2e4rqw9OepVPJydO40UE5FjsCrY\nlZaWYsWKFcjPzwcAfPbZZzh48CB+/vln/OlPf7Jl+0hi7dV2aw5wna3tlpTkgdDQKrvXduOIlGX2\nuIqHO4xkcaSYiKRmVbBbs2YNBg8ejIULF2LmzJkAgJtuugnr16+3aePINtqr7dYc4urqeq62W9Oa\njOs2fkcd44hUx6S8bqy7jGRxpJiIpGZVsMvLy8OLL75oUjhYrVajpoa/cTqqq1dlbTYpNAe44mKF\nxdpugYF6467S1tOmYWEGmKkf7fDseV1ZastdRrI4UkxEUrMq2Pn7+0On05nszigsLESvXr1s1jCy\nzF613ZyZlCNSZJm7jGRxpJiIpGZVsLv77rvx3nvvYfLkyTAYDNi/fz+ysrIwefJkW7fPrdXWAhcu\nNI262aq2G5E9uMtIFkeKiUhqVgW7O+64AxqNBjt37kRwcDD27t2LBx54ALfeequt2+fS7F3bjche\n3GkkiyPFRCQlFii2MXO13VpOm9qztpsUWNCya7qzY9RZ+rzllUecfSTLWfrclbDPpcc+l57NChQ/\n8MADuO222/DUU09BqbxxyLRp07Bu3bpOv6irMVfbraCg6bYj13Yjx+QuO0Y5kkVE1POsCnYqlQoA\n8Nprr2HevHkICgoCALjLYF9P13Zr+b09a7uRY3KXHaNERNTzrAp2crkcc+fOxZYtW/Dyyy/j2Wef\nRWJiImQulEikrO1GZIm77BglIqKe16lLik2ePBl9+vTBkiVL8NBDD9mqTTb1yy8erO1GDs1ddowS\nEVHPsyrYtZxybb4CxZIlS1BXV2ezhtlKenqI2fvdtbYbOR532jFKREQ9y6pdsVeuXEFgYKDJfbW1\ntTh37hz69+9vs8bZQv/+11nbTULcRdU13dkxyj6XHvtceuxz6bHPpdeju2JLSkoQGhoKAGhoaMCl\nS5faPCc4OLjTL2hvO3detncTiDrEHaNERNQV7Qa7559/HuvXrwcAzJ07t90TbNq0qedbRURERESd\n1m6waw51AMMbERERkTPo9F7O6upqnDt3DvX1XMhNRERE5Egs7or9+uuvERYWhmHDhgEAfv75Zyxd\nuhT19fXw8fHBiy++iMTEREkaSkRERESWWRyxy87ORlRUlPH2J598gvT0dKxbtw4ZGRnYsGGDzRtI\nRERERNaxGOyuXLli3Gqr0+lw+fJl/OEPf4CXlxfuvvtunD9/XpJGEhEREVHHLAY7T09P1NQ0XZvy\n5MmT6NOnD7x+uz6WTCaDXu86FyQnIiIicnYWg93gwYOxZs0aHD58GP/617+Ma+0AoKCgwCnr2BER\nERG5KovBbtq0aVCpVNiwYQP69u2Lu+66y/jYzz//jNtuu83mDSQiIiIi61h1STFXUlRUZO8muBVe\ngkZ67HPpsc+lxz6XHvtcel25pFin69gRERERkWNisCMiIiJyEQx2RERERC6CwY6IiIjIRVi8pFiz\n3bt3m73fw8MDwcHB6Nu3Lzw8PHq0YURERETUOVYFu7179+L06dPw9/dHcHAwysrKcPXqVcTHx6Ok\npAQA8MILLyA+Pt6mjSUiIiKi9lkV7CIjI3Hrrbdi4sSJxvu2b9+Oixcv4s9//jO++uorfPzxx1i0\naJHNGkpEREREllm1xu67777DhAkTTO4bN24c9u/fD5lMhnvuuQeFhYU2aSARERERWceqYOfv748j\nR46Y3Hf06FH4+fkBAK5fvw6l0qrBPyIiIiKyEavS2IwZM7B06VJER0cb19idP38ezz77LADg119/\nbTOiR0RERETSsvqSYpWVlfjpp59QXl6OwMBADBkyBBqNxtbt63G8pJi0eAka6bHPpcc+lx77XHrs\nc+l15ZJiVs+fajQajB49utMvQERERETSsCrYlZSUYMOGDcjPz0ddXZ3JYx988IFNGkZEREREnWNV\nsFuxYgV69+6Nxx57DJ6enrZuExERERF1gVXBrrCwEG+++Sbkcl6BjIiIiMhRWZXUkpOTkZ+fb+Om\nEBEREVF3WDViFxISgkWLFuHWW29FQECAyWMPPPCATRpGRERERJ1jVbCrr6/HzTffDL1ej7KyMlu3\niYiIiIi6wKpg99RTT9m6HURERETUTe0Gu5KSEoSGhgIALl261O4Jevfu3fOtIiIiIqJOazfYPf/8\n81i/fj0AYO7cue2eYNOmTT3fKiIiIiLqtHaDXXOoAxjeiIiIiJyBxXIn33//PSoqKqRqCxERERF1\ng8XNE5s2bYJOp0NYWBiSk5PRv39/JCcnIyQkRKr2EREREZGVZEIIYekJFRUVOHHihPHPhQsXEBQU\nZAx6aWlpUrW1RxQVFdm7CW5Fo9GgsrLS3s1wK+xz6bHPpcc+lx77XHparbbTx3RY7iQgIAAjRozA\niBEjAABVVVXYtWsXvvnmG+zfv9/pgh0RERGRq+ow2AkhkJ+fjxMnTuD48eM4ffo0AgMDMWLECCQn\nJ0vRRiIiIiKygsVg98477yA/Px9arRb9+vXDnXfeiTlz5sDb21uq9hERkQNT1NTA8+xZyIuKYNBq\nUR8XB71abe9mEbkti8GuuLgYSqUSISEhCAsLQ1hYGEMdEREBaAp1mjVr4L1kCWQABIDaefNQOXs2\nwx2RnXR680RlZSX69euH5ORkJCUlISYmRqKm9gxunpAWF9tKj30uPXftc3VODvwnTICsxX0CwNXt\n21EzYIBNX9td+9ye2OfSk3TzxD//+U9cu3aNxYuJiNyUvLjYJNQBgAyAXKcDbBzsiMi8Tm+eOHXq\nFKqrqxEfH48xY8ZI0UYiInJAhvBwCKDNiJ0hLMxOLSKiDjdPnD59Go2NjUhISED//v0xYcIEJCYm\nQqVS9VgjvvnmG2RnZ0MmkyE6OhpPPvkktmzZgl27dsHf3x8A8NBDD2HQoEEAgKysLGRnZ0OhUGD6\n9OkYOHBgj7WFiIisUx8fj9p589qssauPj7d304jclsVgl5ycjClTpiA+Ph5KZYeDe11SXl6O7du3\nY/ny5VAqlVi2bBm+++47AEBGRgYyMjJMnl9YWIgDBw5g2bJlKCsrw5tvvomVK1dCJms9IUBERLak\nV6tROXs2GtLSINfpYAgLQ318PDdOENmRxbQ2efJkSRphMBhQV1cHb29v1NfXIygoCJcvX4a5fR2H\nDx/GyJEjoVAoEBoaivDwcOTl5aFv376StJWIiG7Qq9VNGyW4po7IIdhmGK4TgoKCkJGRgaeeegqe\nnp646aabcNNNN+HUqVPYvn079u7di/j4eDz22GNQq9UoLy9HYmKiyfHl5eV2fAdEREREjkFu7wZU\nV1fj8OHDWLVqFf7f//t/qKurw/79+zF+/Hj89a9/xZIlSxAQEID169fbu6lEREREDs3uI3Y5OTkI\nDQ2Fr68vAGDYsGE4deoUbr/9duNz0tLS8N577wFoGqErLS01PlZWVoagoCCz587NzUVubq7x9tSp\nU6HRaGzxNqgdKpWKfS4x9rn02OfSY59Lj31uH5s3bzZ+n5KSgpSUFIvPt3uw69WrF3799Vc0NDTA\nw8MDOTk5iI+PR0VFBQICAgAAhw4dQlRUFABg6NChWLlyJTIyMlBeXg6dToeEhASz5zbXASyuKC0W\ntJQe+1x67HPpsc+lxz6XnkajwdSpUzt1jN2DXUJCAoYPH4758+dDoVAgNjYWd955J1avXo38/HzI\nZDKEhIRg9uzZAIDIyEiMGDECmZmZUCqVmDVrFnfEEhEREcGKS4q5Gl5STFr8DU967HPpsc+lxz6X\nHvtcel25pJjdN08QERERUc9gsCMiIiJyEQx2RERERA5EVlEBj19+6dKxdt88QURERORW9HoodDoo\n8vOhPH++6WtBARTnz0NZUAB5RUXT87qwDYLBjoiIXIKipgaeZ89CXlQEg1aL+rg4XreW7Ke2tim0\nFRQ0hbaWXy9cgKyhod1DDd7e0MfEwKMLL8tgR0RETk9RUwPNmjXwXrIEMgACQO28eaicPZvhjmxD\nCMjLy2+MtrUMbufPQ6HTWTxcHxICfZ8+aOzTx/i1+XtDSAggk6Hze2IZ7IiIyAV4njljDHUAIAPg\nvWQJGtLSUDNggD2bRs6ssRGKixebAlvztGlBAZT5+VCcPw95VVW7hwqlEvrISDTGxDQFt+ho6GNi\nmsJbdDSEj49NmsxgR0RETk9eXIzWpeplAOQ6HcBgRxbIqqrMT5cWFEBRWAiZXt/usQaN5saIW0wM\n9NHRTbdjYqAPDweU0scsBjsiInJ6hvBwCMAk3AkAhrAwO7WI2iP5WkghIL90qe0mhfx8KAoKoCgr\ns3i4Pizsxqhbq2lTERgIONjVrxjsiIjI6dXHx6N23rw2a+zq4+Pt3TRqwWZrIevrobhwoc1UafPo\nm7yurt1DhacnGqOiboy6tZw2jYoCvLy63i474CXFyKZ4CRrpsc+lxz6Xnrk+V9TUwPPMGch1OhjC\nwlAfH8+NEz2oJ37O1Tk58J8woc3I6tXt2ztcCymrqDA/XVpQAEVREWQW4ow+MLApqEVHt5k2NYSF\nAXLHLOvblUuKccSOiIhcgl6tbgoHXFPnsCyuhezf37rabmYIuRyNkZFtpkubvwo/P5u+L0fCYEdE\nRESSMAQFmV0L6fPqq9CUlFhV2615V2nzJoXG6GjoIyMBlcrWzXcKDHZERETUM7pQ200GQFFYCMC6\n2m5kGYMdERERWa+7td0iIiB69YLw94c+Ph71gwejITHRprXd3AmDHREREZkwV9vNs7AQ3mfPOmVt\nN3fC3iUiInI3blbbzZ0w2BEREbmiHq7t5tGvH6p693bK2m7uhMGOiIjISUlZ202j0aCR9RodHoMd\nERGRo9LrWduNOoXBjoiIyJ5qa29Ml7YefbtwgbXdqFMY7IiIiGypC7XdWmJtN+oMBjsiIqLu6m5t\nt8jItheg/20UjrXdqDMY7IiIiKxgrrab8Stru5GD4E8SERER0P3abuHhZjcpsLYbSYnBjoiI3Ed3\na7tFRzeNtrWeNmVtN3IQDHZERORSpKztRuRoGOyIiMi56PWQXbgAVW6u6bTpb7tMu1LbrTnAsbYb\nOTsGOyIicjzt1HZT5uc3bVRoaIBvO4e2W9utTx/oIyJY241cGoMdERFJz1Jtt4ICKC5dsni4ITQU\njc2hrWVtt5gYGHr14kYFclsMdkREZBvdre0WEQGZTAZ5fj5kAASAuunTcS0zE+rYWFTyuqVEbTDY\nERFRl9mytpv6xAn4T5iA5rE3GQCvTz9F/YMPArGxkrw/ImfDYEdERO0zV9ut5S5TG9Z2kxcXo/Wj\nMgDyDi7BReTOGOyIyOkpamrgefYs5EVFMGi1qI+Lg16ttneznIeZ2m7NxXntWdvNEB4OAZiEOwHA\nEBYGRZfPSuTaGOyIyKkpamqgWbMG3kuWGNdh1c6bh8rZs90i3Fkbas3WdvttrZuj1narj49H7bx5\nbT7b+vh4OOIny18wyBHIhLDwt9kFFRUV2bsJbkWj0XCBs8Tcrc/VOTkm67CApgBwdft21AwYIEkb\n7NXn5kJt/QMPoH7gQMiLijpV200fEeGQtd0UNTXwPHMGcp0OhrAw1MfHQ69WO9zPuTv8guFofe4O\ntFptp4/hiB0RAXDe0QaL67AkCnaSaVXbzevoUai2bjXdXLBpE7w2bWpzqLPWdtOr1U0B3cE/S88z\nZ4yhDmj6LLyXLEFDWppkv2AQAQx2RATnHm2wtA7L6XSztluzhpEjUT98OGu7ScitfsEgh8ZgR0RO\nPdpgaR2WQ+pubbfISOMmBblKBa+1a9uE2prXX3f4z83VuNQvGOTUGOyIyKlHG/RqNSpnz0ZDWlqb\ndU61JJ0AABSaSURBVFj2YsvablDe+GdbUVMDERDgPKHWhTndLxjkshjsiMjpRxskX4fVqrabqrgY\nAb/+KkltN5PzWBlqnXX9pDNxxF8wyD0x2BERRxvMcdDabq11FGqdef1kT7N1wHWWjR7k2ljuhGyK\n2+Ol19U+b6+shCvrqdpuir59UaPVSlLbrbMcoRyMLXT255wBt/v477n0WO6EiLrMJUcb9HoodLob\nmxRa7ja1orZbY2SkVbXdNBoNah30PzxnXj/Zk5x5gxBRZzDYEdmYq6xvctj30aq2W/NXZX5+00aF\nhoZ2D3XW2m6d4ezrJ3sKAy65CwY7Ihtylekfu76PbtZ204eEmN2k4C613bh+sgkDLrkLrrEjm3L3\nNRn2WN9kiz63+fvowdpuxk0KvwU5YcPg2TyKqdTp0BgW5jijmK244vpJrrGTnrv/e24PXGNH5GBc\nZfqnJ96HVLXdpOJMQcEl1092EsuRkLtgsCOyIVeZ/rHqfbSq7dY6wHVY2y0s7MaoWzdqu0mFi/Gd\nDwMuuQMGOyIbcpX1Tebex/W0NHhs3Iig99/vdG03Q0QElIWF8Ni923i++kcfdcjRrvZYO4rpsJtO\niMglMdgR2ZCjT/+YCx2Ghgaztd2UBQVNo2ZCQAZAtWsXWu8ZbVnbrfW0acvabuqcHHi3WLPnjKNd\n1oxiOtN0LRG5BgY7IhtzuOmf32q7eZw6BZ+//x2qf//bGDrg5QWZpVG3TtR2s8QV1h5aMxrL6Voi\nkhqDHbkNt5oS60JtNxkA1NU1TZnGxdm0tpsrrD1sORqrLClBY2hom9FYVwiwRORcGOzILbjclJiF\n2m4e589Do9NZPFwfEgLh7w9lXl6bxypXr0bVuHG2ajkA11l72Dwaq9FoUGOmDIQrBFgici4MduQW\nnHJKzMa13dqrTWcID7f5W3P0tYc9xVUCLBE5DwY7cguOOiVmi9puXikpuObn12FtN3uHDodbe2gD\n7hJgichxMNiRW7DblFg3a7sZAgNhiIzE9cREXI+Pt6q2m6dGA1hRHZ6hQxruEGCJyHEw2JFbsOno\nVH09FBcumEyVKgsKOl3brXna1NC7N7wOHYLXxx9DfuUKZFeuoGHCBNQ+/niPhy6GDiIi1+IQ14r9\n5ptvkJ2dDZlMhujoaDz11FOoq6vD8uXLcfnyZYSGhiIzMxPq3/5Ty8rKQnZ2NhQKBaZPn46BAwda\n/Vq8Vqy0HOnagt25XqasosJsbTfF+fNQFBVBZuGvkbW13Zp197qsjtTn7oJ9Lj32ufTY59JzymvF\nlpeXY/v27Vi+fDmUSiWWLVuG/fv3o7CwEAMGDMCkSZOwZcsWZGVl4eGHH0ZhYSEOHDiAZcuWoays\nDG+++SZWrlwJmYNdbogcj8XRqd9quxk3KbScNj1/HvKKinbP21O13Zo56npAIiJyfHYPdgBgMBhQ\nV1cHb29vNDQ0ICgoCFu2bMGCBQsAAKmpqViwYAEefvhhHD58GCNHjoRCoUBoaCjCw8ORl5eHvn37\n2vdNkOPrQm23ZgZv7xu7Sm1U2834WiyRQU7OrWpGEjkYuwe7oKAgZGRk4KmnnoKnpyduuukm3HTT\nTbh69SoCAgIAAAEBAbh69SqAphG+xMREk+PLy8vt0nZyMBZquykLCqC4dMni4fqQELMXoNfHxMDQ\nq5dkF6G3925Vou5wuZqRRE7G7sGuuroahw8fxqpVq6BWq7F06VLs27evzfM41UoAbF7bzRFwtyo5\nM6esGUnkQuwe7HJychAaGgpfX18AwK233opTp04hICAAFRUVxq/+/v4AmkboSktLjceXlZUhKCjI\n7Llzc3ORm5trvD116lRoNBobvhtqTaVSdb7PKyshz8+H/Nw5yM6da/r+7Nmm2xcuWKztJvz8YIiN\nNf4RMTE3vo+IMKntJv/tj0fX3pptaTRA794AAAWAzkS6LvU5dQv7/AbZpUtm14gqS0p6tI/Y59Jj\nn9vH5s2bjd+npKQgJSXF4vPtHux69eqFX3/9FQ0NDfDw8EBOTg7i4+Ph5eWFPXv2YPLkydizZw+G\nDh0KABg6dChWrlyJjIwMlJeXQ6fTISEhwey5zXUAd/RIy+wuqt9qu6lOn4bnkSNQnj4NWWUlcOUK\nFBcudFjbTR8ebjJdak1tNwBAbW0PvSvHxp1r0mOf36Du3dvsGtHG0FCzl13rKva59Njn0tNoNJg6\ndWqnjrF7sEtISMDw4cMxf/58KBQKxMTE4M4770RdXR2WLVuG7OxshISEIDMzEwAQGRmJESNGIDMz\nE0qlErNmzeI0rSP6rbab4vJlqE+e7HZtN+O0aVQU4OUl4Rshos7gGlEi+3KIOnZSYh27ntOd2m4G\nPz/Irl1r81v9tc8+Q3VqapvabmQ9/lYtPfa5qe7UjLQW+1x67HPpOWUdO3JgPVDbDfHxqI+IaFPb\nzefgQfjNmGFyjAxoWj/HUEfk1HhFEyL7YbBzdzau7dbeb3is1UZERNTzGOxcXQ/Wdmt5Kazu1nbj\nOhwiIqKex2DnCnqytlur3aa2qu3GWm1EREQ9j8HOSciqqtqOtjV/LSy0WNvNoNHcCGytdpnqtVpA\noZDwndzAdThEREQ9i8HOUfxW263NJoXfvna2tlvLaVOLtd2IiIjIZTDYSem32m7N9dy6XdutOcix\nttv/b+/eY6qu/ziOv76QoEzgcAj8SeDK4/hD2uBXytRmCodyc2zpliJdCLPRTNpiXai1aoWbpU6N\ni7o2N3SsmbhyZc3aSDPzslhgeKvw0nRe8BKSEAcO5/z+8Nf5gWKpv3Ohz3k+Nuc53++Xw+e89557\n+fmc8/kCAAAR7PzOt7fbIJ91+7u93foSEq5+q3TMmOuWTT3/+hfbgAAAgL9EsLtV/fd2u/bzbje5\nt9t1t8L677KpNy4uiG/EDJFdXYo+dkwRp0/Lk5Ii19ixfAEDABC2CHaD6b+3239n225rb7f+t8Lq\nt7cb/COyq0uxH3xw3ZYpv5eUEO4AAGEpPIPdEN3bDbcm+uhRX6iTrm52PGLZMvU4nVe/bQsAQJgJ\nu2CX9NBDQ3ZvN9yaiDNndG2EtiRFnD3LFioAgLAUdsFu2KFDkobu3m64edyWDACAgcIu2J3fupW9\n3QzBbckAABgo7IJd77//HeohwE+4LRkAAAOFXbCDWbgtGQAA/8OOtwAAAIYg2AEAABiCYAcAAGAI\ngh0AAIAhCHYAAACGINgBAAAYgmAHAABgCIIdAACAIQh2AAAAhiDYAQAAGIJgBwAAYAiCHQAAgCEI\ndgAAAIYg2AEAABiCYAcAAGAIgh0AAIAhCHYAAACGINgBAAAYgmAHAABgCIIdAACAIQh2AAAAhiDY\nAQAAGIJgBwAAYAiCHQAAgCEIdgAAAIYg2AEAABiCYAcAAGAIgh0AAIAhCHYAAACGINgBAAAYgmAH\nAABgCIIdAACAIQh2AAAAhiDYAQAAGIJgBwAAYAiCHQAAgCEIdgAAAIYg2AEAABiCYAcAAGAIgh0A\nAIAhCHYAAACGINgBAAAY4o5QD+D06dNatWqVLMuS1+vVuXPnVFBQoM7OTjU0NCg+Pl6SVFhYqKys\nLEnSJ598ou3btysyMlLFxcXKzMwM5VsAAAAYEkIe7FJSUrR06VJJksfj0cKFC5Wdna3t27crPz9f\n+fn5A64/deqU9uzZo5UrV+rixYuqqKhQZWWlLMsKxfABAACGjCG1FNvS0qJRo0bpzjvvlCR5vd7r\nrmlsbNSUKVMUGRmp5ORkjR49Wq2trcEeKgAAwJAT8hm7/nbv3q0HHnjA93zbtm3auXOnHA6HioqK\nFBMTo0uXLik9Pd13jd1u16VLl0IxXAAAgCFlyMzYud1uNTY2avLkyZKkGTNmqLq6WsuWLZPNZtOG\nDRtCPEIAAIChbcjM2DU3N2vs2LGKi4uTJN/fkuR0OvXee+9JujpDd+HCBd+5ixcvym63D/qaBw8e\n1MGDB33P586dq5SUlEAMH38hNjY21EMIO9Q8+Kh58FHz4KPmwbdp0ybf44yMDGVkZPzl9UNmxm7X\nrl0DlmHb29t9j/ft26e0tDRJ0oQJE7R792653W61tbXp7NmzGjdu3KCvmZGRoblz5/r+9C8OgoOa\nBx81Dz5qHnzUPPioefBt2rRpQI75u1AnDZEZO5fLpZaWFj377LO+Y3V1dTpx4oQsy1JSUpJKSkok\nSampqZo8ebLKysp0xx136JlnnuEbsQAAABoiwS46Olrr1q0bcKy0tPSG18+ePVuzZ88O9LAAAAD+\nUYbMUmww3MwUJvyLmgcfNQ8+ah581Dz4qHnw3U7NLe9gm8UBAADgHyesZuwAAABMRrADAAAwxJD4\n8oS/9fb26q233pLb7VZfX58mTZqkOXPm6MqVK1q1apXOnz+v5ORklZWVKSYmJtTDNcKNal5fX6+G\nhgbFx8dLkgoLC5WVlRXi0ZrF4/Hotddek91uV3l5OX0eBB6PR6+++qoSExNVXl5OnwfYokWLFBMT\nI8uyFBkZqSVLltDnATZYzenzwOrq6tLatWt18uRJWZalhQsXavTo0bfc58Z+xs7lcik6Oloej0dv\nvPGG5s+fr7179yo2NlaPPPKItmzZos7OTj3++OOhHqoxBqt5U1OTRowYofz8/FAPz1hbt27VsWPH\n9Mcff6i8vFx1dXX0eYBdW/P6+nr6PIBKS0v17rvvauTIkb5j9HlgDVZz+jywampqNH78eOXk5Kiv\nr08ul0sff/zxLfe5sUux0dHRkq7OJPX19UmSGhsbNW3aNEnS9OnT9f3334dsfCYarOaSZOj/HYaE\nixcvqqmpSU6n03eMPg+swWou0eeB5PV6r6svfR5Yg9X8z+Pwv66uLh05ckQ5OTmSpMjISMXExNxW\nnxu5FCv9b6nk3LlzmjFjhsaNG6fLly/LZrNJkmw2my5fvhziUZplsJo3NTVp27Zt2rlzpxwOh4qK\nilgu8aP169frySefVFdXl+8YfR5Yg9VcEn0eQJZlafHixYqIiFBeXp6cTid9HmD9a+50OpWXlyeJ\nPg+UtrY2xcbGavXq1fr11181duxYFRcX31afGxvsIiIitHTpUnV1dWn58uU6efLkdddwxwr/urbm\np06d0owZM/Too4/Ksixt3LhR69ev18KFC0M9VCP88MMPio+P19133z3gnsjXos/950Y1p88Dq6Ki\nQgkJCero6NDixYsHvec3fe5f/WteUVGh1NRU+jyAPB6Pjh8/rgULFsjhcKi2tlZbtmy57rqb6XNj\nl2L/FBMTo/Hjx6u5uVk2m813D9r29nbfB0DhX/1rHhcX52tEp9Opo0ePhnh05jhy5IgaGxtVWlqq\n999/XwcOHFBVVRV9HkCD1by6upo+D7CEhARJUlxcnCZOnKjW1lb6PMD61zw7O1utra30eQDZ7XYl\nJibK4XBIkiZNmqTjx4/fVp8bGew6Ojp8yyQ9PT1qaWnRXXfdpfvvv187duyQJO3YsUMTJkwI4SjN\nMljNU1JSfA0pSfv27VNaWlqohmicxx57TGvWrFF1dbVeeOEF3XvvvXr++efp8wAarOalpaX0eQC5\nXC51d3dLkrq7u/Xjjz9qzJgx9HkADVbztLQ0+jyAbDabEhMTdfr0aUlSS0uLUlNTb6vPjVyKbW9v\nV01NjTwej7xer6ZMmaL77rtP6enpWrlypbZv366kpCSVlZWFeqjGuFHNq6urdeLECVmWpaSkJJWU\nlIR6qMabNWsWfR5kdXV19HmAXL58WcuWLZNlWerr69PUqVOVmZkph8NBnwfIjWrOv+eBNX/+fFVV\nVcntdmvUqFF67rnn5PF4brnPjd3uBAAAINwYuRQLAAAQjgh2AAAAhiDYAQAAGIJgBwAAYAiCHQAA\ngCEIdgAAAIYg2AHATSoqKlJbW5vfXq+goEDnzp3z2+sBAMEOgPEWLVqkAwcO3NLPvP322/r6668H\nHNuwYYOSk5MlSatXr9ZHH33ktzECgD8Q7AAAAAxh5C3FAODvdHZ2qqqqSq2trfJ4PEpPT1dJSYns\ndrs2btyow4cP65dfftH69es1bdo0Pf300yooKFBlZaVaWlr07bffKiIiQl988YUyMjL0yiuv+M6P\nGjVK0tVZvcTERBUUFEiSPv30U33++eeyLMt37E9ut1sffvih9u7dK7fbrezsbD311FMaNmxY0GsD\n4J+LYAcgLHm9XuXm5urFF19UX1+f1qxZo3Xr1unll1/WvHnz9NNPP2nq1KnKzc297mfz8vL0888/\nDwhtf6e5uVlbt27Vm2++qeTkZK1du3bA+bq6OrW1tWn58uWKiIhQZWWlNm/erMLCQr+8XwDhgaVY\nAGFp5MiRys7O1rBhwzR8+HDNnj1bhw8fDtjv27Nnj6ZPn67U1FRFRUVpzpw5A843NDSouLhYMTEx\nGj58uGbNmqXvvvsuYOMBYCZm7ACEpZ6eHtXW1mr//v3q7OyU1+tVd3e3vF6vLMvy++/77bff5HA4\nfM+TkpJ8jzs6OtTT06Py8nLfMa/XK6/X6/dxADAbwQ5AWPrss8905swZLVmyRHFxcTpx4oTKy8v/\nr2AXFRUll8vle97e3q7ExERJks1m04ULF3znzp8/73scGxurqKgorVixQgkJCbf5jgCApVgAYcLt\ndqu3t1e9vb3q6elRZ2enoqKiNGLECF25ckX19fUDro+Pj//LPetsNtt1e9Ddc8892rVrlzwej5qb\nm3Xo0CHfuSlTpuibb77RqVOn5HK5tHnzZt85y7LkdDpVW1urjo4OSdKlS5e0f/9+f7x1AGGEGTsA\nYWHJkiUDnufk5Kinp0cLFiyQ3W5Xfn6+GhsbfednzpypmpoaffXVV3rwwQdVXFw84Odzc3O1YsUK\nzZ8/XxkZGXrppZdUXFysmpoaffnll5o4caKys7N912dlZWnmzJl65513FBERoXnz5mnXrl2+8088\n8YTq6+v1+uuv6/fff5fdbtfDDz+szMzMwBQEgJEsLx/iAAAAMAJLsQAAAIYg2AEAABiCYAcAAGAI\ngh0AAIAhCHYAAACGINgBAAAYgmAHAABgCIIdAACAIQh2AAAAhvgPTHOasJj7LsQAAAAASUVORK5C\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112afb6d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "# Make a scatterplot of the data.\n",
    "sex_boolean = insects.sex.astype(bool)\n",
    "ax.scatter(insects.latitude[sex_boolean], \n",
    "           insects.wingsize[sex_boolean],\n",
    "           s=40, c=\"red\", label=\"Male\")\n",
    "ax.scatter(insects.latitude[~sex_boolean], \n",
    "           insects.wingsize[~sex_boolean],\n",
    "           s=40, c=\"blue\", label=\"Female\")\n",
    "\n",
    "# Make a linea graph of the predictions.\n",
    "x = np.linspace(30, 60, num=250)\n",
    "ax.plot(x, insects_model_with_sex.params[0] + insects_model_with_sex.params[1] * x,\n",
    "       linewidth=2, c=\"blue\")\n",
    "ax.plot(x, insects_model_with_sex.params[0] + insects_model_with_sex.params[1] * x + insects_model_with_sex.params[2],\n",
    "       linewidth=2, c=\"red\")\n",
    "\n",
    "ax.set_xlim(30, 60)\n",
    "ax.set_xlabel(\"Latitude\")\n",
    "ax.set_ylabel(\"Wing Size\")\n",
    "ax.set_title(\"Insect Wing Sizes at Various Latitudes\")\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Does Continent Have Any Effect on Wing Size?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have a model that seems to fit the data, we can use it as a jumping off point to answer other questions about the data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let's see if continent has any effect on wing size.  To accomplish this, we need to modify our model from this:\n",
    "\n",
    "$$ \\text{Wing Span} \\approx a + b \\times \\text{Latitude} + c \\times \\text{Sex} $$\n",
    "\n",
    "to the slightly more complicated\n",
    "\n",
    "$$ \\text{Wing Span} \\approx a + b \\times \\text{Latitude} + c \\times \\text{Sex} + d \\times \\text{Continent} $$\n",
    "\n",
    "Then the new number $d$ captures the effect of the insect being found on the continent labeled $1$.  If $d$ is zero, or close to zero, then continent has no effect on wing span.\n",
    "\n",
    "Let's estimate the model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              Linear Model Summary             \n",
      "===============================================\n",
      "Name         Parameter Estimate  Standard Error\n",
      "-----------------------------------------------\n",
      "Intercept                836.16           14.84\n",
      "latitude                   1.79            0.32\n",
      "sex                      -98.86            3.41\n",
      "continent                 -4.13            3.52\n"
     ]
    }
   ],
   "source": [
    "linear_model = smf.ols(formula='wingsize ~ latitude + sex + continent', data=insects)\n",
    "insects_model_full = linear_model.fit()\n",
    "linear_model_summary(insects_model_full)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The continent estimate is **not** zero.\n",
    "\n",
    "On the other hand, look at the **Standard Error** column.  This number is a rough measure of how certain the model is in its estimate of a parameter, the larger, the more uncertain.\n",
    "\n",
    "A common (though not always appropriate) rule of thumb is that if the parameter estimate divided by the standard error is between -2 and 2, then the variable is called **insignificant**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.1721742732074607"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "insects_model_full.params[3] / insects_model_full.bse[3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So the continent parameter is insignificant.  This is often interpreted as \"having no effect\"."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Is The Effect of Latitude Different for Males vs. Females?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above we have drawn a separate line for each cluster, but these lines are restricted to have the **same slope**.  It's possible that this is not a correct description of the data, we may want the slope to be different for males and females.\n",
    "\n",
    "A model like this contains an **interaction**, and the shape of the equation we want to create is\n",
    "\n",
    "$$ \\text{Wing Span} \\approx a + b \\times \\text{Latitude} + c \\times \\text{Sex} + d \\times \\text{Sex} \\times \\text{Latitude} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The final part of this model\n",
    "\n",
    "$$ d \\times \\text{Sex} \\times \\text{Latitude} $$\n",
    "\n",
    "is called an interaction term, it allows us to change the slope of the latitude line based on the sex of the insect."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot both of these lines to inspect if the difference of slopes in noticeable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1143477d0>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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qFeRyOaKionD48GEAwIYNGzBz5kyL/VNTUzF27FgoFAp4e3vD19cX+fn5UjWX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\nS1dXFwwGA7Zu3YqTJ09ixowZqKqqGvd1HvPhTafTYcOGDRgYGMBLL72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      "text/plain": [
       "<matplotlib.figure.Figure at 0x113c25a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "# Make a scatterplot of the data.\n",
    "sex_boolean = insects.sex.astype(bool)\n",
    "ax.scatter(insects.latitude[sex_boolean], \n",
    "           insects.wingsize[sex_boolean],\n",
    "           s=40, c=\"red\", label=\"Male\")\n",
    "ax.scatter(insects.latitude[~sex_boolean], \n",
    "           insects.wingsize[~sex_boolean],\n",
    "           s=40, c=\"blue\", label=\"Female\")\n",
    "\n",
    "# Make a linea graph of the predictions.\n",
    "model_params = insects_model_with_interaction.params\n",
    "x = np.linspace(30, 60, num=250)\n",
    "ax.plot(x, model_params[0] + model_params[1] * x,\n",
    "       linewidth=2, c=\"blue\")\n",
    "ax.plot(x, model_params[0] + model_params[1] * x + model_params[2] + model_params[3] * x,\n",
    "       linewidth=2, c=\"red\")\n",
    "\n",
    "ax.set_xlim(30, 60)\n",
    "ax.set_xlabel(\"Latitude\")\n",
    "ax.set_ylabel(\"Wing Size\")\n",
    "ax.set_title(\"Insect Wing Sizes at Various Latitudes\")\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These two lines have different slopes, but the change is almost imperceptible.\n",
    "\n",
    "To investigate a bit more, we can look at the parameter estimates from the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              Linear Model Summary             \n",
      "===============================================\n",
      "Name         Parameter Estimate  Standard Error\n",
      "-----------------------------------------------\n",
      "Intercept                825.08           19.78\n",
      "latitude                   1.99            0.44\n",
      "sex                      -89.10           27.98\n",
      "sex:latitude              -0.22            0.62\n"
     ]
    }
   ],
   "source": [
    "linear_model = smf.ols(formula='wingsize ~ latitude + sex + sex*latitude', data=insects)\n",
    "insects_model_with_interaction = linear_model.fit()\n",
    "linear_model_summary(insects_model_with_interaction)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `sex:latitude` parameter is the $d$ from the equation above.  It encodes that the *difference* in slopes between males and females is $-0.22$.  A few observations:\n",
    "\n",
    "  - This is tiny compared to the overall slope of $1.99$, so we have only made a small adjustment between the two clusters.\n",
    "  - The estimated standard error of the difference is $0.62$, much larger than the estimated difference.  This makes the difference *insignificant*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Altogether, changing the slopes based on the sex of the insect seems pointless, so we should conclude that the relationship between latitude and wing span does not depend on the sex of the insect."
   ]
  }
 ],
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