linear-and-logistic-regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "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'] = 8, 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear and Logistic Regression"
   ]
  },
  {
   "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."
   ]
  },
  {
   "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": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "continent\tlatitude\twingsize\tsex\r\n",
      "1\t40.5\t941.111111111\t0\r\n",
      "1\t42.0\t924.444444444\t0\r\n",
      "1\t43.6\t924.204444444\t0\r\n",
      "1\t45.7\t915.217777778\t0\r\n",
      "1\t45.9\t905.471111111\t0\r\n",
      "1\t47.4\t896.004444444\t0\r\n",
      "1\t50.0\t913.0\t0\r\n",
      "1\t51.8\t916.44\t0\r\n",
      "1\t53.8\t933.417777778\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": true
   },
   "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": 35,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<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>40.5</td>\n",
       "      <td>941.111111</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>42.0</td>\n",
       "      <td>924.444444</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>43.6</td>\n",
       "      <td>924.204444</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>45.7</td>\n",
       "      <td>915.217778</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>45.9</td>\n",
       "      <td>905.471111</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   continent  latitude    wingsize  sex\n",
       "0          1      40.5  941.111111    0\n",
       "1          1      42.0  924.444444    0\n",
       "2          1      43.6  924.204444    0\n",
       "3          1      45.7  915.217778    0\n",
       "4          1      45.9  905.471111    0"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "insects.head()"
   ]
  },
  {
   "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": {},
   "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 float64\n",
      "sex          42 non-null int64\n",
      "dtypes: float64(2), int64(2)\n",
      "memory usage: 1.4 KB\n"
     ]
    }
   ],
   "source": [
    "insects.info()"
   ]
  },
  {
   "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": {},
   "outputs": [
    {
     "data": {
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W8PhDRLayeIlKoVBgwYIFWLt2LYQQuPfeexEWFuaIbER0k+Pxh4hspXzxxRdf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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e1e5b50>"
      ]
     },
     "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": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1123edf10>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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kDHXdeTyA578747fFKYflfP7lHDvAKZGJrMLc48ocp+7Z7GFIhOSNiQHRDTL3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\niQERERFJ/h/vMupDLBXSyAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112330a50>"
      ]
     },
     "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 first decrease, and then increase as latitude varies."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Regression"
   ]
  },
  {
   "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",
    "  \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": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1127d4e50>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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22yH+uvBXqtW4Mm+e6XEBlM+aZXEVukqlwqJFi7B06VJ8//33uHLlCq5du4bU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\nQY2BiIiIGP4DySDknl3OOUUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e1e5a50>"
      ]
     },
     "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": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1129b1bd0>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Tp6JVq1awtbXF/v370blzZ1haWsLBwaHWeIKDg/H6669Do9Fo/ZEKCgrC3LlzodFoGn17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\niVgYEBERkYiFAREREYlYGBAREZHo/wGMcBohvA95kAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112784490>"
      ]
     },
     "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": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              Linear Model Summary             \n",
      "===============================================\n",
      "Name         Parameter Estimate  Standard Error\n",
      "-----------------------------------------------\n",
      "Intercept                765.20           56.28\n",
      "latitude                   2.54            1.18\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",
    "$$ \\text{Wing Span} \\approx 765.20+ 2.54 \\times \\text{Latitude} $$\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": [
    "But is this really meaningful?  We need to make sure our model is representing the data honestly.\n",
    "\n",
    "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": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x11233ef90>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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QlNQ8CUhKUiIm5g4cHGolt+fjjz/WqjF45ZVX8PXXX+PQoUMA6ocaamtrMWLE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\njj0hcQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11294fe90>"
      ]
     },
     "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 two serious flaws in our model:\n",
    "\n",
    "  - It has no knowledge of the sex of the insect, so the fit line attemps to bisect the two clusters of data.\n",
    "  - It cannot account for the curvature in the data points.  The model attempts to fit a line to data that does not have a linear shape."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Accounting for the Sex of the Insect"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "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 now 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": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              Linear Model Summary             \n",
      "===============================================\n",
      "Name         Parameter Estimate  Standard Error\n",
      "-----------------------------------------------\n",
      "Intercept                948.25           31.66\n",
      "latitude                  -0.41            0.63\n",
      "sex                      -88.03            7.70\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": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x113638850>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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qegtSUkyTgJQUHeLjy+HlVaO4PR9++KFRjcELL7yAr7/+Grt37wZQN9RQU1OD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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11349ccd0>"
      ]
     },
     "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] \n",
    "             + insects_model_with_sex.params[1] * x,\n",
    "       linewidth=2, c=\"blue\")\n",
    "ax.plot(x, insects_model_with_sex.params[0] \n",
    "             + 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": [
    "### Accounting for the Curvature of the Data Points"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can account for the curvature of the data points by using a *poynomial regression*.  This means that we fit powers of latitude bigger than one:\n",
    "\n",
    "$$ \\text{Wing Span} \\approx a + b \\times \\text{Latitude} + c \\times \\text{Latitude}^2 +  d \\times \\text{Sex} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              Linear Model Summary             \n",
      "===============================================\n",
      "Name         Parameter Estimate  Standard Error\n",
      "-----------------------------------------------\n",
      "Intercept               1946.89           91.87\n",
      "latitude                 -43.21            3.89\n",
      "I(latitude ** 2)           0.45            0.04\n",
      "sex                      -89.46            3.81\n"
     ]
    }
   ],
   "source": [
    "linear_model = smf.ols(formula='wingsize ~ latitude + I(latitude**2) + sex', data=insects)\n",
    "insects_model_quad = linear_model.fit()\n",
    "linear_model_summary(insects_model_quad)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x113c19410>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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mAg+Pu/dO7M0336RFixZMnz6dl156iZCQkFw7it2vf//+tGnThjZt2uDt7U1YWBj//ve/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\ndvHFxDzxBLrSUuwXX8ypV16heP36gCUFrSWJgQiYuqWaz9T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zZIfTptPHyW7HcOiQL0kw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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1134b5a10>"
      ]
     },
     "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_quad.params[0] \n",
    "             + insects_model_quad.params[1] * x\n",
    "             + insects_model_quad.params[2] * x*x,\n",
    "       linewidth=2, c=\"blue\")\n",
    "ax.plot(x, insects_model_quad.params[0] \n",
    "             + insects_model_quad.params[1] * x\n",
    "             + insects_model_quad.params[2] * x*x\n",
    "             + insects_model_quad.params[3],\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": [
    "This now looks like a good model that represents the data honestly."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### How is the Line Determined?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have one question that remains unadressed: how did linear regression actually draw these lines and curves?  How were the fit coefficients determined?\n",
    "\n",
    "We can think of the fitted line as a *prediction*.  If we were to collect a new insect at a certain latitude, the y-coordinate of the line would be our best estiamte for the wing span of that insect.\n",
    "\n",
    "A good strategy for drawing the line would seem to be:\n",
    "\n",
    "> Try to draw the line that minimizes the dissimilarity between the predictions and the actual $y$ data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x113270b90>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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6duwIR0dH/PzzzwgJCYGtrS1cXFy0xhMdHY3XX38dKpVK7Y9UVFQU5syZA5VK1eLb4+p/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\nfwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112c15f90>"
      ]
     },
     "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",
    "# Draw a bunch of vertial lines to illistrate the difference between\n",
    "# predictions and actuals.\n",
    "for index, row in insects.iterrows():\n",
    "    t = row['latitude']\n",
    "    pred = insects_model.params[0] + insects_model.params[1] * t\n",
    "    ax.plot((t, t), (row['wingsize'], pred), color='grey')\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": [
    "In the picture above we have highlighted the vertical distance between each datapoint and its predicted value.\n",
    "\n",
    "A common numeric measure of the dissimilarity is the *sum of squared residuals*:\n",
    "\n",
    "$$ SSR = \\sum_{i=1}^N (y_i - \\text{pred}_i)^2 $$\n",
    "\n",
    "**The linear regression line is the line that minimizes that sum of squared residuals.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Logistic Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In linear regression we want to predict some quantity that has a continuous range of values.\n",
    "\n",
    "*Logistic Regression* solves a slightly different problem.  What if we flip our dataset around, and want to predict the sex of an insect from the other measurements?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1134cc710>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11349c150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "# Make a scatterplot of the data.\n",
    "ax.scatter(insects.latitude, insects.sex)\n",
    "ax.set_yticks([0, 1])\n",
    "ax.set_yticklabels(['Female', 'Male'])\n",
    "ax.set_xlabel(\"Latitude\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Logistic regression does *not* attempt to predict the exact value of $y$ (in this case, whether an insect is male or female).  Instead, it attempts to estiamte the probability that an insect is male or female.\n",
    "\n",
    "$$ P(\\text{Insect is Male} \\mid \\text{Latitude}) $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              Linear Model Summary             \n",
      "===============================================\n",
      "Name         Parameter Estimate  Standard Error\n",
      "-----------------------------------------------\n",
      "Intercept                  7.30            2.97\n",
      "latitude                  -0.16            0.06\n"
     ]
    }
   ],
   "source": [
    "logistic_model = smf.logit(formula='sex ~ latitude',\n",
    "                           data=insects)\n",
    "insects_model_logistic = logistic_model.fit(disp=0)\n",
    "linear_model_summary(insects_model_logistic)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Logistic regression attempts to draw a *curve* of predicted probabilities (not a line, as in linear regression).\n",
    "\n",
    "The above logistic regression results in the following curve:\n",
    "\n",
    "$$ P(\\text{Insect is Male} \\mid \\text{Latitude}) = \\frac{1}{1 + e^{-7.3 + 0.16 \\times \\text{Latitude}}} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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CixYtzvsWviIS2YwxmH5DsJn9gnsEzHwF++H72OWLMFd8BXPZtUBC2GGK1Bmh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\niGNU/EVERByj4i8iIuKY/w9PxHFwHtKIUwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113d425d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "# Make a scatterplot of the data.\n",
    "ax.scatter(insects.latitude, insects.sex)\n",
    "\n",
    "x = pd.DataFrame({'latitude': np.linspace(30, 65, num=250)})\n",
    "ax.plot(x, insects_model_logistic.predict(x), linewidth=2)\n",
    "\n",
    "ax.set_xlim([30, 65])\n",
    "ax.set_yticks([0, 1])\n",
    "ax.set_yticklabels(['Female', 'Male'])\n",
    "ax.set_xlabel(\"Latitude\")\n",
    "ax.set_ylabel(r\"$P \\ (Male)$\")\n",
    "ax.yaxis.set_label_coords(-0.02, 0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What if we need to make a binary decision, i.e. we need to use the estimated probabilities to acctually classify each insect as either male or female?\n",
    "\n",
    "We can accomplish this by thresholding probabilities:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Xy/m7nDtE0Zh/q1ataNmyJb169eKOO+5g3rx5YYQhIjWYSa0fLBB0/5PQPhMK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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115342990>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "# Make a scatterplot of the data.\n",
    "ax.scatter(insects.latitude, insects.sex)\n",
    "\n",
    "x = pd.DataFrame({'latitude': np.linspace(30, 65, num=250)})\n",
    "ax.plot((30, 65), (0.5, 0.5), color=\"black\", linestyle=\"--\")\n",
    "ax.plot((47.075, 47.075), (0, 1), color=\"black\", linestyle=\"--\")\n",
    "ax.plot(x, insects_model_logistic.predict(x), linewidth=2)\n",
    "\n",
    "ax.set_xlim([30, 65])\n",
    "ax.set_yticks([0, 1])\n",
    "ax.set_yticklabels(['Female', 'Male'])\n",
    "ax.set_xlabel(\"Latitude\")\n",
    "ax.set_ylabel(r\"$P \\ (Male)$\")\n",
    "ax.yaxis.set_label_coords(-0.02, 0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we threshold the probabilities at $0.5$, which divides the data into insects we predict are male and insects we predict are positive.\n",
    "\n",
    "Some datapoints are predicted incorrectly, these come in two types:\n",
    "\n",
    "  - **False Positives**: Insects we predict are in the positive class (Male in this case, an arbitrary decision), which we are incorrect about (they are actually female).\n",
    "  - **False Negatives**: Insects we predict are in the negative class (Female in this case), but incorrectly (they are actually Male)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Things to Futher Study\n",
    "\n",
    "#### Modeling in General\n",
    "\n",
    "  - Training sets, testing sets, and generalization.\n",
    "  - Cross validation.\n",
    "  \n",
    "#### Linear Regression\n",
    "\n",
    "  - The $R^2$ model fit statistic.\n",
    "  - Structural Assumptions (Homogeneity, Distribution of Errors).\n",
    "  - Hypothesis testing of parameter estimates.\n",
    "  \n",
    "#### Logistic Regression\n",
    "\n",
    "  - Log-Loss.\n",
    "  - Setting Thresholds."
   ]
  }
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