regression/bootstrapped_regession_coefficients/bootstrap_regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bootstrapped Regression Coefficients\n",
    "\n",
    "Here we explore the theoretical coefficient distributions from a linear regression model. When fitting a regression model we can get estimates for the standard deviation of the coefficients. We use bootstrapping to get an empiracle distribution of the regression coefficients to compare against those distributions.\n",
    "\n",
    "The outline is as follows:\n",
    "* Collect some data\n",
    "* Fit a regression model\n",
    "* Fit many models on bootstrapped samples of the training data\n",
    "* Compare the distribution of bootstrapped coefficients to the theoretical distribution of coefficients\n",
    "\n",
    "\n",
    "The data used is weather data collect from kaggle:\n",
    "[https://www.kaggle.com/budincsevity/szeged-weather](https://www.kaggle.com/budincsevity/szeged-weather)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "                  Formatted Date        Summary Precip Type  Temperature (C)  \\\n0  2006-04-01 00:00:00.000 +0200  Partly Cloudy        rain         9.472222   \n1  2006-04-01 01:00:00.000 +0200  Partly Cloudy        rain         9.355556   \n2  2006-04-01 02:00:00.000 +0200  Mostly Cloudy        rain         9.377778   \n3  2006-04-01 03:00:00.000 +0200  Partly Cloudy        rain         8.288889   \n4  2006-04-01 04:00:00.000 +0200  Mostly Cloudy        rain         8.755556   \n\n   Apparent Temperature (C)  Humidity  Wind Speed (km/h)  \\\n0                  7.388889      0.89            14.1197   \n1                  7.227778      0.86            14.2646   \n2                  9.377778      0.89             3.9284   \n3                  5.944444      0.83            14.1036   \n4                  6.977778      0.83            11.0446   \n\n   Wind Bearing (degrees)  Visibility (km)  Loud Cover  Pressure (millibars)  \\\n0                   251.0          15.8263         0.0               1015.13   \n1                   259.0          15.8263         0.0               1015.63   \n2                   204.0          14.9569         0.0               1015.94   \n3                   269.0          15.8263         0.0               1016.41   \n4                   259.0          15.8263         0.0               1016.51   \n\n                       Daily Summary  \n0  Partly cloudy throughout the day.  \n1  Partly cloudy throughout the day.  \n2  Partly cloudy throughout the day.  \n3  Partly cloudy throughout the day.  \n4  Partly cloudy throughout the day.  ",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>Formatted Date</th>\n      <th>Summary</th>\n      <th>Precip Type</th>\n      <th>Temperature (C)</th>\n      <th>Apparent Temperature (C)</th>\n      <th>Humidity</th>\n      <th>Wind Speed (km/h)</th>\n      <th>Wind Bearing (degrees)</th>\n      <th>Visibility (km)</th>\n      <th>Loud Cover</th>\n      <th>Pressure (millibars)</th>\n      <th>Daily Summary</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>2006-04-01 00:00:00.000 +0200</td>\n      <td>Partly Cloudy</td>\n      <td>rain</td>\n      <td>9.472222</td>\n      <td>7.388889</td>\n      <td>0.89</td>\n      <td>14.1197</td>\n      <td>251.0</td>\n      <td>15.8263</td>\n      <td>0.0</td>\n      <td>1015.13</td>\n      <td>Partly cloudy throughout the day.</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>2006-04-01 01:00:00.000 +0200</td>\n      <td>Partly Cloudy</td>\n      <td>rain</td>\n      <td>9.355556</td>\n      <td>7.227778</td>\n      <td>0.86</td>\n      <td>14.2646</td>\n      <td>259.0</td>\n      <td>15.8263</td>\n      <td>0.0</td>\n      <td>1015.63</td>\n      <td>Partly cloudy throughout the day.</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>2006-04-01 02:00:00.000 +0200</td>\n      <td>Mostly Cloudy</td>\n      <td>rain</td>\n      <td>9.377778</td>\n      <td>9.377778</td>\n      <td>0.89</td>\n      <td>3.9284</td>\n      <td>204.0</td>\n      <td>14.9569</td>\n      <td>0.0</td>\n      <td>1015.94</td>\n      <td>Partly cloudy throughout the day.</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>2006-04-01 03:00:00.000 +0200</td>\n      <td>Partly Cloudy</td>\n      <td>rain</td>\n      <td>8.288889</td>\n      <td>5.944444</td>\n      <td>0.83</td>\n      <td>14.1036</td>\n      <td>269.0</td>\n      <td>15.8263</td>\n      <td>0.0</td>\n      <td>1016.41</td>\n      <td>Partly cloudy throughout the day.</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>2006-04-01 04:00:00.000 +0200</td>\n      <td>Mostly Cloudy</td>\n      <td>rain</td>\n      <td>8.755556</td>\n      <td>6.977778</td>\n      <td>0.83</td>\n      <td>11.0446</td>\n      <td>259.0</td>\n      <td>15.8263</td>\n      <td>0.0</td>\n      <td>1016.51</td>\n      <td>Partly cloudy throughout the day.</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 1
    }
   ],
   "source": [
    "import os\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "dir_path = os.getcwd()\n",
    "data = pd.read_csv(os.path.join(dir_path, \"data\", \"weatherHistory.csv\"))\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we do some data preparation. We create a model to predict apparent temperature using most of the remaining columns:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "   Temperature (C)  Humidity  Wind Speed (km/h)  Wind Bearing (degrees)  \\\n0         9.472222      0.89            14.1197                   251.0   \n1         9.355556      0.86            14.2646                   259.0   \n2         9.377778      0.89             3.9284                   204.0   \n3         8.288889      0.83            14.1036                   269.0   \n4         8.755556      0.83            11.0446                   259.0   \n\n   Visibility (km)  Loud Cover  Pressure (millibars)  rain  snow  Constant  \n0          15.8263         0.0               1015.13     1     0         1  \n1          15.8263         0.0               1015.63     1     0         1  \n2          14.9569         0.0               1015.94     1     0         1  \n3          15.8263         0.0               1016.41     1     0         1  \n4          15.8263         0.0               1016.51     1     0         1  ",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>Temperature (C)</th>\n      <th>Humidity</th>\n      <th>Wind Speed (km/h)</th>\n      <th>Wind Bearing (degrees)</th>\n      <th>Visibility (km)</th>\n      <th>Loud Cover</th>\n      <th>Pressure (millibars)</th>\n      <th>rain</th>\n      <th>snow</th>\n      <th>Constant</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>9.472222</td>\n      <td>0.89</td>\n      <td>14.1197</td>\n      <td>251.0</td>\n      <td>15.8263</td>\n      <td>0.0</td>\n      <td>1015.13</td>\n      <td>1</td>\n      <td>0</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>9.355556</td>\n      <td>0.86</td>\n      <td>14.2646</td>\n      <td>259.0</td>\n      <td>15.8263</td>\n      <td>0.0</td>\n      <td>1015.63</td>\n      <td>1</td>\n      <td>0</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>9.377778</td>\n      <td>0.89</td>\n      <td>3.9284</td>\n      <td>204.0</td>\n      <td>14.9569</td>\n      <td>0.0</td>\n      <td>1015.94</td>\n      <td>1</td>\n      <td>0</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>8.288889</td>\n      <td>0.83</td>\n      <td>14.1036</td>\n      <td>269.0</td>\n      <td>15.8263</td>\n      <td>0.0</td>\n      <td>1016.41</td>\n      <td>1</td>\n      <td>0</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>8.755556</td>\n      <td>0.83</td>\n      <td>11.0446</td>\n      <td>259.0</td>\n      <td>15.8263</td>\n      <td>0.0</td>\n      <td>1016.51</td>\n      <td>1</td>\n      <td>0</td>\n      <td>1</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 2
    }
   ],
   "source": [
    "# Calculate apprent temperature\n",
    "X = data.loc[\n",
    "    :,\n",
    "    [\n",
    "        \"Temperature (C)\",\n",
    "        \"Humidity\",\n",
    "        \"Wind Speed (km/h)\",\n",
    "        \"Wind Bearing (degrees)\",\n",
    "        \"Visibility (km)\",\n",
    "        \"Loud Cover\",\n",
    "        \"Pressure (millibars)\",\n",
    "    ],\n",
    "]\n",
    "X = X.join(pd.get_dummies(data[\"Precip Type\"]))\n",
    "\n",
    "# add constant column\n",
    "X[\"Constant\"] = 1\n",
    "\n",
    "y = data.loc[:, \"Apparent Temperature (C)\"]\n",
    "\n",
    "X.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We reduce the training data size just to enlarge the coefficient distributino for the purpose of this article."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(9645, 10)"
     },
     "metadata": {},
     "execution_count": 3
    }
   ],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.9)\n",
    "X_train.reset_index(inplace=True, drop=True)\n",
    "y_train.reset_index(inplace=True, drop=True)\n",
    "X_train.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Statsmodels approach\n",
    "\n",
    "With `statsmodels` we can apply the ordinary least squares solution to the above data to recover estimates of the model coefficients. When we fit a linear regression model the Hessian (2nd order derivatives) determines how sensitive the coefficients are to changes in the data. This in turn is used to calculate the standard deviation of the coefficients."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "OLS Regression Results                               \n====================================================================================\nDep. Variable:     Apparent Temperature (C)   R-squared:                       0.990\nModel:                                  OLS   Adj. R-squared:                  0.990\nMethod:                       Least Squares   F-statistic:                 1.175e+05\nDate:                      Thu, 11 Jun 2020   Prob (F-statistic):               0.00\nTime:                              00:00:29   Log-Likelihood:                -14401.\nNo. Observations:                      9645   AIC:                         2.882e+04\nDf Residuals:                          9636   BIC:                         2.888e+04\nDf Model:                                 8                                         \nCovariance Type:                  nonrobust                                         \n==========================================================================================\n                             coef    std err          t      P>|t|      [0.025      0.975]\n------------------------------------------------------------------------------------------\nTemperature (C)            1.1138      0.002    607.061      0.000       1.110       1.117\nHumidity                   0.9269      0.078     11.828      0.000       0.773       1.081\nWind Speed (km/h)         -0.0919      0.002    -54.661      0.000      -0.095      -0.089\nWind Bearing (degrees)     0.0006      0.000      5.584      0.000       0.000       0.001\nVisibility (km)           -0.0082      0.003     -2.805      0.005      -0.014      -0.002\nLoud Cover              2.722e-15   1.54e-15      1.764      0.078   -3.03e-16    5.75e-15\nPressure (millibars)       0.0002   9.24e-05      2.550      0.011    5.45e-05       0.000\nrain                      -0.3603      0.186     -1.942      0.052      -0.724       0.003\nsnow                      -0.8371      0.189     -4.432      0.000      -1.207      -0.467\nConstant                  -1.9649      0.224     -8.783      0.000      -2.403      -1.526\n==============================================================================\nOmnibus:                      240.963   Durbin-Watson:                   1.987\nProb(Omnibus):                  0.000   Jarque-Bera (JB):              262.505\nSkew:                           0.378   Prob(JB):                     9.95e-58\nKurtosis:                       3.287   Cond. No.                     3.57e+20\n==============================================================================\n\nWarnings:\n[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n[2] The smallest eigenvalue is 7.96e-32. This might indicate that there are\nstrong multicollinearity problems or that the design matrix is singular.\n"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "\n",
    "results = sm.OLS(y_train, X_train).fit()\n",
    "print(results.summary())\n",
    "# extract coefficient distributions\n",
    "w_sm_mu = results.params\n",
    "w_sm_std = np.sqrt(np.diag(results.normalized_cov_params))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above model coefficients suggest that the apparent temperature is mostly made up of the actual temperature. Humidity has a positive relationship and wind a negative relationship.\n",
    "\n",
    "## Bootstrapping approach\n",
    "\n",
    "To get an empirical idea of the distribution of the regression coefficients we can refit the model on many bootstrapped samples. A bootstrap sample is when we take random samples from our training set, with replacement. If we take 1000 bootstrap samples and fit a model on each we gain 1000 estimates of the regression coefficients.\n",
    "\n",
    "We do this as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "w_bs = []\n",
    "n = X_train.shape[0]\n",
    "for i in range(1000):\n",
    "    samp = np.random.randint(n, size=n)\n",
    "    results_bs = sm.OLS(y_train.loc[samp], X_train.loc[samp, :]).fit()\n",
    "    w_bs.append(results_bs.params)\n",
    "w_bs = np.array(w_bs)\n",
    "\n",
    "# summarise coefficient distributions\n",
    "w_bs_mu = np.mean(w_bs, axis=0)\n",
    "w_bs_std = np.std(w_bs, axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Results comparison\n",
    "We can now compare the coefficient distributions to the theoretical results from statsmodels.\n",
    "\n",
    "Below we plot the coefficient means and standard deviations from both statsmodels and the bootstrapped models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 720x432 with 2 Axes>",
      "image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Created with matplotlib (https://matplotlib.org/) -->\n<svg height=\"353.205312pt\" version=\"1.1\" viewBox=\"0 0 608.785937 353.205312\" width=\"608.785937pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n <defs>\n  <style type=\"text/css\">\n*{stroke-linecap:butt;stroke-linejoin:round;}\n  </style>\n </defs>\n <g id=\"figure_1\">\n  <g id=\"patch_1\">\n   <path d=\"M -0 353.205312 \nL 608.785937 353.205312 \nL 608.785937 0 \nL -0 0 \nz\n\" style=\"fill:#ffffff;\"/>\n  </g>\n  <g id=\"axes_1\">\n   <g id=\"patch_2\">\n    <path d=\"M 43.585938 333.36 \nL 297.222301 333.36 \nL 297.222301 7.2 \nL 43.585938 7.2 \nz\n\" style=\"fill:#ffffff;\"/>\n   </g>\n   <g id=\"matplotlib.axis_1\">\n    <g id=\"xtick_1\">\n     <g id=\"line2d_1\">\n      <path clip-path=\"url(#p1b256be9c1)\" d=\"M 55.114863 333.36 \nL 55.114863 7.2 \n\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_2\"/>\n     <g id=\"text_1\">\n      <!-- 0 -->\n      <defs>\n       <path d=\"M 4.15625 35.296875 \nQ 4.15625 48 6.765625 55.734375 \nQ 9.375 63.484375 14.515625 67.671875 \nQ 19.671875 71.875 27.484375 71.875 \nQ 33.25 71.875 37.59375 69.546875 \nQ 41.9375 67.234375 44.765625 62.859375 \nQ 47.609375 58.5 49.21875 52.21875 \nQ 50.828125 45.953125 50.828125 35.296875 \nQ 50.828125 22.703125 48.234375 14.96875 \nQ 45.65625 7.234375 40.5 3 \nQ 35.359375 -1.21875 27.484375 -1.21875 \nQ 17.140625 -1.21875 11.234375 6.203125 \nQ 4.15625 15.140625 4.15625 35.296875 \nz\nM 13.1875 35.296875 \nQ 13.1875 17.671875 17.3125 11.828125 \nQ 21.4375 6 27.484375 6 \nQ 33.546875 6 37.671875 11.859375 \nQ 41.796875 17.71875 41.796875 35.296875 \nQ 41.796875 52.984375 37.671875 58.78125 \nQ 33.546875 64.59375 27.390625 64.59375 \nQ 21.34375 64.59375 17.71875 59.46875 \nQ 13.1875 52.9375 13.1875 35.296875 \nz\n\" id=\"ArialMT-48\"/>\n      </defs>\n      <g style=\"fill:#262626;\" transform=\"translate(52.334394 344.017812)scale(0.1 -0.1)\">\n       <use xlink:href=\"#ArialMT-48\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_2\">\n     <g id=\"line2d_3\">\n      <path clip-path=\"url(#p1b256be9c1)\" d=\"M 106.354533 333.36 \nL 106.354533 7.2 \n\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_4\"/>\n     <g id=\"text_2\">\n      <!-- 2 -->\n      <defs>\n       <path d=\"M 50.34375 8.453125 \nL 50.34375 0 \nL 3.03125 0 \nQ 2.9375 3.171875 4.046875 6.109375 \nQ 5.859375 10.9375 9.828125 15.625 \nQ 13.8125 20.3125 21.34375 26.46875 \nQ 33.015625 36.03125 37.109375 41.625 \nQ 41.21875 47.21875 41.21875 52.203125 \nQ 41.21875 57.421875 37.46875 61 \nQ 33.734375 64.59375 27.734375 64.59375 \nQ 21.390625 64.59375 17.578125 60.78125 \nQ 13.765625 56.984375 13.71875 50.25 \nL 4.6875 51.171875 \nQ 5.609375 61.28125 11.65625 66.578125 \nQ 17.71875 71.875 27.9375 71.875 \nQ 38.234375 71.875 44.234375 66.15625 \nQ 50.25 60.453125 50.25 52 \nQ 50.25 47.703125 48.484375 43.546875 \nQ 46.734375 39.40625 42.65625 34.8125 \nQ 38.578125 30.21875 29.109375 22.21875 \nQ 21.1875 15.578125 18.9375 13.203125 \nQ 16.703125 10.84375 15.234375 8.453125 \nz\n\" id=\"ArialMT-50\"/>\n      </defs>\n      <g style=\"fill:#262626;\" transform=\"translate(103.574064 344.017812)scale(0.1 -0.1)\">\n       <use xlink:href=\"#ArialMT-50\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_3\">\n     <g id=\"line2d_5\">\n      <path clip-path=\"url(#p1b256be9c1)\" d=\"M 157.594202 333.36 \nL 157.594202 7.2 \n\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_6\"/>\n     <g id=\"text_3\">\n      <!-- 4 -->\n      <defs>\n       <path d=\"M 32.328125 0 \nL 32.328125 17.140625 \nL 1.265625 17.140625 \nL 1.265625 25.203125 \nL 33.9375 71.578125 \nL 41.109375 71.578125 \nL 41.109375 25.203125 \nL 50.78125 25.203125 \nL 50.78125 17.140625 \nL 41.109375 17.140625 \nL 41.109375 0 \nz\nM 32.328125 25.203125 \nL 32.328125 57.46875 \nL 9.90625 25.203125 \nz\n\" id=\"ArialMT-52\"/>\n      </defs>\n      <g style=\"fill:#262626;\" transform=\"translate(154.813733 344.017812)scale(0.1 -0.1)\">\n       <use xlink:href=\"#ArialMT-52\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_4\">\n     <g id=\"line2d_7\">\n      <path clip-path=\"url(#p1b256be9c1)\" d=\"M 208.833871 333.36 \nL 208.833871 7.2 \n\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_8\"/>\n     <g id=\"text_4\">\n      <!-- 6 -->\n      <defs>\n       <path d=\"M 49.75 54.046875 \nL 41.015625 53.375 \nQ 39.84375 58.546875 37.703125 60.890625 \nQ 34.125 64.65625 28.90625 64.65625 \nQ 24.703125 64.65625 21.53125 62.3125 \nQ 17.390625 59.28125 14.984375 53.46875 \nQ 12.59375 47.65625 12.5 36.921875 \nQ 15.671875 41.75 20.265625 44.09375 \nQ 24.859375 46.4375 29.890625 46.4375 \nQ 38.671875 46.4375 44.84375 39.96875 \nQ 51.03125 33.5 51.03125 23.25 \nQ 51.03125 16.5 48.125 10.71875 \nQ 45.21875 4.9375 40.140625 1.859375 \nQ 35.0625 -1.21875 28.609375 -1.21875 \nQ 17.625 -1.21875 10.6875 6.859375 \nQ 3.765625 14.9375 3.765625 33.5 \nQ 3.765625 54.25 11.421875 63.671875 \nQ 18.109375 71.875 29.4375 71.875 \nQ 37.890625 71.875 43.28125 67.140625 \nQ 48.6875 62.40625 49.75 54.046875 \nz\nM 13.875 23.1875 \nQ 13.875 18.65625 15.796875 14.5 \nQ 17.71875 10.359375 21.1875 8.171875 \nQ 24.65625 6 28.46875 6 \nQ 34.03125 6 38.03125 10.484375 \nQ 42.046875 14.984375 42.046875 22.703125 \nQ 42.046875 30.125 38.078125 34.390625 \nQ 34.125 38.671875 28.125 38.671875 \nQ 22.171875 38.671875 18.015625 34.390625 \nQ 13.875 30.125 13.875 23.1875 \nz\n\" id=\"ArialMT-54\"/>\n      </defs>\n      <g style=\"fill:#262626;\" transform=\"translate(206.053403 344.017812)scale(0.1 -0.1)\">\n       <use xlink:href=\"#ArialMT-54\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_5\">\n     <g id=\"line2d_9\">\n      <path clip-path=\"url(#p1b256be9c1)\" d=\"M 260.073541 333.36 \nL 260.073541 7.2 \n\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_10\"/>\n     <g id=\"text_5\">\n      <!-- 8 -->\n      <defs>\n       <path d=\"M 17.671875 38.8125 \nQ 12.203125 40.828125 9.5625 44.53125 \nQ 6.9375 48.25 6.9375 53.421875 \nQ 6.9375 61.234375 12.546875 66.546875 \nQ 18.171875 71.875 27.484375 71.875 \nQ 36.859375 71.875 42.578125 66.421875 \nQ 48.296875 60.984375 48.296875 53.171875 \nQ 48.296875 48.1875 45.671875 44.5 \nQ 43.0625 40.828125 37.75 38.8125 \nQ 44.34375 36.671875 47.78125 31.875 \nQ 51.21875 27.09375 51.21875 20.453125 \nQ 51.21875 11.28125 44.71875 5.03125 \nQ 38.234375 -1.21875 27.640625 -1.21875 \nQ 17.046875 -1.21875 10.546875 5.046875 \nQ 4.046875 11.328125 4.046875 20.703125 \nQ 4.046875 27.6875 7.59375 32.390625 \nQ 11.140625 37.109375 17.671875 38.8125 \nz\nM 15.921875 53.71875 \nQ 15.921875 48.640625 19.1875 45.40625 \nQ 22.46875 42.1875 27.6875 42.1875 \nQ 32.765625 42.1875 36.015625 45.375 \nQ 39.265625 48.578125 39.265625 53.21875 \nQ 39.265625 58.0625 35.90625 61.359375 \nQ 32.5625 64.65625 27.59375 64.65625 \nQ 22.5625 64.65625 19.234375 61.421875 \nQ 15.921875 58.203125 15.921875 53.71875 \nz\nM 13.09375 20.65625 \nQ 13.09375 16.890625 14.875 13.375 \nQ 16.65625 9.859375 20.171875 7.921875 \nQ 23.6875 6 27.734375 6 \nQ 34.03125 6 38.125 10.046875 \nQ 42.234375 14.109375 42.234375 20.359375 \nQ 42.234375 26.703125 38.015625 30.859375 \nQ 33.796875 35.015625 27.4375 35.015625 \nQ 21.234375 35.015625 17.15625 30.90625 \nQ 13.09375 26.8125 13.09375 20.65625 \nz\n\" id=\"ArialMT-56\"/>\n      </defs>\n      <g style=\"fill:#262626;\" transform=\"translate(257.293072 344.017812)scale(0.1 -0.1)\">\n       <use xlink:href=\"#ArialMT-56\"/>\n      </g>\n     </g>\n    </g>\n   </g>\n   <g id=\"matplotlib.axis_2\">\n    <g id=\"ytick_1\">\n     <g id=\"line2d_11\">\n      <path clip-path=\"url(#p1b256be9c1)\" d=\"M 43.585938 321.919733 \nL 297.222301 321.919733 \n\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_12\"/>\n     <g id=\"text_6\">\n      <!-- −2.0 -->\n      <defs>\n       <path d=\"M 52.828125 31.203125 \nL 5.5625 31.203125 \nL 5.5625 39.40625 \nL 52.828125 39.40625 \nz\n\" id=\"ArialMT-8722\"/>\n       <path d=\"M 9.078125 0 \nL 9.078125 10.015625 \nL 19.09375 10.015625 \nL 19.09375 0 \nz\n\" id=\"ArialMT-46\"/>\n      </defs>\n      <g style=\"fill:#262626;\" transform=\"translate(20.345312 325.498639)scale(0.1 -0.1)\">\n       <use xlink:href=\"#ArialMT-8722\"/>\n       <use x=\"58.398438\" xlink:href=\"#ArialMT-50\"/>\n       <use x=\"114.013672\" xlink:href=\"#ArialMT-46\"/>\n       <use x=\"141.796875\" xlink:href=\"#ArialMT-48\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_2\">\n     <g id=\"line2d_13\">\n      <path clip-path=\"url(#p1b256be9c1)\" d=\"M 43.585938 273.763533 \nL 297.222301 273.763533 \n\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_14\"/>\n     <g id=\"text_7\">\n      <!-- −1.5 -->\n      <defs>\n       <path d=\"M 37.25 0 \nL 28.46875 0 \nL 28.46875 56 \nQ 25.296875 52.984375 20.140625 49.953125 \nQ 14.984375 46.921875 10.890625 45.40625 \nL 10.890625 53.90625 \nQ 18.265625 57.375 23.78125 62.296875 \nQ 29.296875 67.234375 31.59375 71.875 \nL 37.25 71.875 \nz\n\" id=\"ArialMT-49\"/>\n       <path d=\"M 4.15625 18.75 \nL 13.375 19.53125 \nQ 14.40625 12.796875 18.140625 9.390625 \nQ 21.875 6 27.15625 6 \nQ 33.5 6 37.890625 10.78125 \nQ 42.28125 15.578125 42.28125 23.484375 \nQ 42.28125 31 38.0625 35.34375 \nQ 33.84375 39.703125 27 39.703125 \nQ 22.75 39.703125 19.328125 37.765625 \nQ 15.921875 35.84375 13.96875 32.765625 \nL 5.71875 33.84375 \nL 12.640625 70.609375 \nL 48.25 70.609375 \nL 48.25 62.203125 \nL 19.671875 62.203125 \nL 15.828125 42.96875 \nQ 22.265625 47.46875 29.34375 47.46875 \nQ 38.71875 47.46875 45.15625 40.96875 \nQ 51.609375 34.46875 51.609375 24.265625 \nQ 51.609375 14.546875 45.953125 7.46875 \nQ 39.0625 -1.21875 27.15625 -1.21875 \nQ 17.390625 -1.21875 11.203125 4.25 \nQ 5.03125 9.71875 4.15625 18.75 \nz\n\" id=\"ArialMT-53\"/>\n      </defs>\n      <g style=\"fill:#262626;\" transform=\"translate(20.345312 277.342439)scale(0.1 -0.1)\">\n       <use xlink:href=\"#ArialMT-8722\"/>\n       <use x=\"58.398438\" xlink:href=\"#ArialMT-49\"/>\n       <use x=\"114.013672\" xlink:href=\"#ArialMT-46\"/>\n       <use x=\"141.796875\" xlink:href=\"#ArialMT-53\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_3\">\n     <g id=\"line2d_15\">\n      <path clip-path=\"url(#p1b256be9c1)\" d=\"M 43.585938 225.607333 \nL 297.222301 225.607333 \n\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_16\"/>\n     <g id=\"text_8\">\n      <!-- −1.0 -->\n      <g style=\"fill:#262626;\" transform=\"translate(20.345312 229.186239)scale(0.1 -0.1)\">\n       <use xlink:href=\"#ArialMT-8722\"/>\n       <use x=\"58.398438\" xlink:href=\"#ArialMT-49\"/>\n       <use x=\"114.013672\" xlink:href=\"#ArialMT-46\"/>\n       <use x=\"141.796875\" xlink:href=\"#ArialMT-48\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_4\">\n     <g id=\"line2d_17\">\n      <path clip-path=\"url(#p1b256be9c1)\" d=\"M 43.585938 177.451133 \nL 297.222301 177.451133 \n\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_18\"/>\n     <g id=\"text_9\">\n      <!-- −0.5 -->\n      <g style=\"fill:#262626;\" transform=\"translate(20.345312 181.030039)scale(0.1 -0.1)\">\n       <use xlink:href=\"#ArialMT-8722\"/>\n       <use x=\"58.398438\" xlink:href=\"#ArialMT-48\"/>\n       <use x=\"114.013672\" xlink:href=\"#ArialMT-46\"/>\n       <use x=\"141.796875\" xlink:href=\"#ArialMT-53\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_5\">\n     <g id=\"line2d_19\">\n      <path clip-path=\"url(#p1b256be9c1)\" d=\"M 43.585938 129.294933 \nL 297.222301 129.294933 \n\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_20\"/>\n     <g id=\"text_10\">\n      <!-- 0.0 -->\n      <g style=\"fill:#262626;\" transform=\"translate(26.185938 132.87384)scale(0.1 -0.1)\">\n       <use xlink:href=\"#ArialMT-48\"/>\n       <use x=\"55.615234\" xlink:href=\"#ArialMT-46\"/>\n       <use x=\"83.398438\" xlink:href=\"#ArialMT-48\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_6\">\n     <g id=\"line2d_21\">\n      <path clip-path=\"url(#p1b256be9c1)\" d=\"M 43.585938 81.138733 \nL 297.222301 81.138733 \n\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_22\"/>\n     <g id=\"text_11\">\n      <!-- 0.5 -->\n      <g style=\"fill:#262626;\" transform=\"translate(26.185938 84.71764)scale(0.1 -0.1)\">\n       <use xlink:href=\"#ArialMT-48\"/>\n       <use x=\"55.615234\" xlink:href=\"#ArialMT-46\"/>\n       <use x=\"83.398438\" xlink:href=\"#ArialMT-53\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_7\">\n     <g id=\"line2d_23\">\n      <path clip-path=\"url(#p1b256be9c1)\" d=\"M 43.585938 32.982533 \nL 297.222301 32.982533 \n\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_24\"/>\n     <g id=\"text_12\">\n      <!-- 1.0 -->\n      <g style=\"fill:#262626;\" transform=\"translate(26.185938 36.56144)scale(0.1 -0.1)\">\n       <use xlink:href=\"#ArialMT-49\"/>\n       <use x=\"55.615234\" xlink:href=\"#ArialMT-46\"/>\n       <use x=\"83.398438\" xlink:href=\"#ArialMT-48\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"text_13\">\n     <!-- Mean -->\n     <defs>\n      <path d=\"M 7.421875 0 \nL 7.421875 71.578125 \nL 21.6875 71.578125 \nL 38.625 20.90625 \nQ 40.96875 13.8125 42.046875 10.296875 \nQ 43.265625 14.203125 45.84375 21.78125 \nL 62.984375 71.578125 \nL 75.734375 71.578125 \nL 75.734375 0 \nL 66.609375 0 \nL 66.609375 59.90625 \nL 45.796875 0 \nL 37.25 0 \nL 16.546875 60.9375 \nL 16.546875 0 \nz\n\" id=\"ArialMT-77\"/>\n      <path d=\"M 42.09375 16.703125 \nL 51.171875 15.578125 \nQ 49.03125 7.625 43.21875 3.21875 \nQ 37.40625 -1.171875 28.375 -1.171875 \nQ 17 -1.171875 10.328125 5.828125 \nQ 3.65625 12.84375 3.65625 25.484375 \nQ 3.65625 38.578125 10.390625 45.796875 \nQ 17.140625 53.03125 27.875 53.03125 \nQ 38.28125 53.03125 44.875 45.953125 \nQ 51.46875 38.875 51.46875 26.03125 \nQ 51.46875 25.25 51.421875 23.6875 \nL 12.75 23.6875 \nQ 13.234375 15.140625 17.578125 10.59375 \nQ 21.921875 6.0625 28.421875 6.0625 \nQ 33.25 6.0625 36.671875 8.59375 \nQ 40.09375 11.140625 42.09375 16.703125 \nz\nM 13.234375 30.90625 \nL 42.1875 30.90625 \nQ 41.609375 37.453125 38.875 40.71875 \nQ 34.671875 45.796875 27.984375 45.796875 \nQ 21.921875 45.796875 17.796875 41.75 \nQ 13.671875 37.703125 13.234375 30.90625 \nz\n\" id=\"ArialMT-101\"/>\n      <path d=\"M 40.4375 6.390625 \nQ 35.546875 2.25 31.03125 0.53125 \nQ 26.515625 -1.171875 21.34375 -1.171875 \nQ 12.796875 -1.171875 8.203125 3 \nQ 3.609375 7.171875 3.609375 13.671875 \nQ 3.609375 17.484375 5.34375 20.625 \nQ 7.078125 23.78125 9.890625 25.6875 \nQ 12.703125 27.59375 16.21875 28.5625 \nQ 18.796875 29.25 24.03125 29.890625 \nQ 34.671875 31.15625 39.703125 32.90625 \nQ 39.75 34.71875 39.75 35.203125 \nQ 39.75 40.578125 37.25 42.78125 \nQ 33.890625 45.75 27.25 45.75 \nQ 21.046875 45.75 18.09375 43.578125 \nQ 15.140625 41.40625 13.71875 35.890625 \nL 5.125 37.0625 \nQ 6.296875 42.578125 8.984375 45.96875 \nQ 11.671875 49.359375 16.75 51.1875 \nQ 21.828125 53.03125 28.515625 53.03125 \nQ 35.15625 53.03125 39.296875 51.46875 \nQ 43.453125 49.90625 45.40625 47.53125 \nQ 47.359375 45.171875 48.140625 41.546875 \nQ 48.578125 39.3125 48.578125 33.453125 \nL 48.578125 21.734375 \nQ 48.578125 9.46875 49.140625 6.21875 \nQ 49.703125 2.984375 51.375 0 \nL 42.1875 0 \nQ 40.828125 2.734375 40.4375 6.390625 \nz\nM 39.703125 26.03125 \nQ 34.90625 24.078125 25.34375 22.703125 \nQ 19.921875 21.921875 17.671875 20.9375 \nQ 15.4375 19.96875 14.203125 18.09375 \nQ 12.984375 16.21875 12.984375 13.921875 \nQ 12.984375 10.40625 15.640625 8.0625 \nQ 18.3125 5.71875 23.4375 5.71875 \nQ 28.515625 5.71875 32.46875 7.9375 \nQ 36.421875 10.15625 38.28125 14.015625 \nQ 39.703125 17 39.703125 22.796875 \nz\n\" id=\"ArialMT-97\"/>\n      <path d=\"M 6.59375 0 \nL 6.59375 51.859375 \nL 14.5 51.859375 \nL 14.5 44.484375 \nQ 20.21875 53.03125 31 53.03125 \nQ 35.6875 53.03125 39.625 51.34375 \nQ 43.5625 49.65625 45.515625 46.921875 \nQ 47.46875 44.1875 48.25 40.4375 \nQ 48.734375 37.984375 48.734375 31.890625 \nL 48.734375 0 \nL 39.9375 0 \nL 39.9375 31.546875 \nQ 39.9375 36.921875 38.90625 39.578125 \nQ 37.890625 42.234375 35.28125 43.8125 \nQ 32.671875 45.40625 29.15625 45.40625 \nQ 23.53125 45.40625 19.453125 41.84375 \nQ 15.375 38.28125 15.375 28.328125 \nL 15.375 0 \nz\n\" id=\"ArialMT-110\"/>\n     </defs>\n     <g style=\"fill:#262626;\" transform=\"translate(14.357812 182.78625)rotate(-90)scale(0.1 -0.1)\">\n      <use xlink:href=\"#ArialMT-77\"/>\n      <use x=\"83.300781\" xlink:href=\"#ArialMT-101\"/>\n      <use x=\"138.916016\" xlink:href=\"#ArialMT-97\"/>\n      <use x=\"194.53125\" xlink:href=\"#ArialMT-110\"/>\n     </g>\n    </g>\n   </g>\n   <g id=\"line2d_25\">\n    <path clip-path=\"url(#p1b256be9c1)\" d=\"M 55.114863 22.025455 \nL 80.734698 40.022625 \nL 106.354533 138.149391 \nL 131.974367 129.239192 \nL 157.594202 130.081057 \nL 183.214037 129.294933 \nL 208.833871 129.272249 \nL 234.453706 164.00061 \nL 260.073541 209.916031 \nL 285.693376 318.534545 \n\" style=\"fill:none;stroke:#1f77b4;stroke-linecap:round;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"line2d_26\">\n    <defs>\n     <path d=\"M -3 3 \nL 3 -3 \nM -3 -3 \nL 3 3 \n\" id=\"m03f1f09dee\" style=\"stroke:#ff7f0e;\"/>\n    </defs>\n    <g clip-path=\"url(#p1b256be9c1)\">\n     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"55.114863\" xlink:href=\"#m03f1f09dee\" y=\"22.029806\"/>\n     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"80.734698\" xlink:href=\"#m03f1f09dee\" y=\"40.155764\"/>\n     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"106.354533\" xlink:href=\"#m03f1f09dee\" y=\"138.162636\"/>\n     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"131.974367\" xlink:href=\"#m03f1f09dee\" y=\"129.239098\"/>\n     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"157.594202\" xlink:href=\"#m03f1f09dee\" y=\"130.074708\"/>\n     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"183.214037\" xlink:href=\"#m03f1f09dee\" y=\"129.294933\"/>\n     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"208.833871\" xlink:href=\"#m03f1f09dee\" y=\"129.272653\"/>\n     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"234.453706\" xlink:href=\"#m03f1f09dee\" y=\"164.404641\"/>\n     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"260.073541\" xlink:href=\"#m03f1f09dee\" y=\"210.320412\"/>\n     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"285.693376\" xlink:href=\"#m03f1f09dee\" y=\"317.56112\"/>\n    </g>\n   </g>\n   <g id=\"patch_3\">\n    <path d=\"M 43.585938 333.36 \nL 43.585938 7.2 \n\" style=\"fill:none;stroke:#cccccc;stroke-linecap:square;stroke-linejoin:miter;\"/>\n   </g>\n   <g id=\"patch_4\">\n    <path d=\"M 297.222301 333.36 \nL 297.222301 7.2 \n\" style=\"fill:none;stroke:#cccccc;stroke-linecap:square;stroke-linejoin:miter;\"/>\n   </g>\n   <g id=\"patch_5\">\n    <path d=\"M 43.585938 333.36 \nL 297.222301 333.36 \n\" style=\"fill:none;stroke:#cccccc;stroke-linecap:square;stroke-linejoin:miter;\"/>\n   </g>\n   <g id=\"patch_6\">\n    <path d=\"M 43.585938 7.2 \nL 297.222301 7.2 \n\" style=\"fill:none;stroke:#cccccc;stroke-linecap:square;stroke-linejoin:miter;\"/>\n   </g>\n  </g>\n  <g id=\"axes_2\">\n   <g id=\"patch_7\">\n    <path d=\"M 347.949574 333.36 \nL 601.585937 333.36 \nL 601.585937 7.2 \nL 347.949574 7.2 \nz\n\" style=\"fill:#ffffff;\"/>\n   </g>\n   <g id=\"matplotlib.axis_3\">\n    <g id=\"xtick_6\">\n     <g id=\"line2d_27\">\n      <path clip-path=\"url(#p274ced18a8)\" d=\"M 359.478499 333.36 \nL 359.478499 7.2 \n\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_28\"/>\n     <g id=\"text_14\">\n      <!-- 0 -->\n      <g style=\"fill:#262626;\" transform=\"translate(356.698031 344.017812)scale(0.1 -0.1)\">\n       <use xlink:href=\"#ArialMT-48\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_7\">\n     <g id=\"line2d_29\">\n      <path clip-path=\"url(#p274ced18a8)\" d=\"M 410.718169 333.36 \nL 410.718169 7.2 \n\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_30\"/>\n     <g id=\"text_15\">\n      <!-- 2 -->\n      <g style=\"fill:#262626;\" transform=\"translate(407.9377 344.017812)scale(0.1 -0.1)\">\n       <use xlink:href=\"#ArialMT-50\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_8\">\n     <g id=\"line2d_31\">\n      <path clip-path=\"url(#p274ced18a8)\" d=\"M 461.957838 333.36 \nL 461.957838 7.2 \n\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_32\"/>\n     <g id=\"text_16\">\n      <!-- 4 -->\n      <g style=\"fill:#262626;\" transform=\"translate(459.17737 344.017812)scale(0.1 -0.1)\">\n       <use xlink:href=\"#ArialMT-52\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_9\">\n     <g id=\"line2d_33\">\n      <path clip-path=\"url(#p274ced18a8)\" d=\"M 513.197508 333.36 \nL 513.197508 7.2 \n\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_34\"/>\n     <g id=\"text_17\">\n      <!-- 6 -->\n      <g style=\"fill:#262626;\" transform=\"translate(510.417039 344.017812)scale(0.1 -0.1)\">\n       <use xlink:href=\"#ArialMT-54\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_10\">\n     <g id=\"line2d_35\">\n      <path clip-path=\"url(#p274ced18a8)\" d=\"M 564.437177 333.36 \nL 564.437177 7.2 \n\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_36\"/>\n     <g id=\"text_18\">\n      <!-- 8 -->\n      <g style=\"fill:#262626;\" transform=\"translate(561.656708 344.017812)scale(0.1 -0.1)\">\n       <use xlink:href=\"#ArialMT-56\"/>\n      </g>\n     </g>\n    </g>\n   </g>\n   <g id=\"matplotlib.axis_4\">\n    <g id=\"ytick_8\">\n     <g id=\"line2d_37\">\n      <path clip-path=\"url(#p274ced18a8)\" d=\"M 347.949574 318.534545 \nL 601.585937 318.534545 \n\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_38\"/>\n     <g id=\"text_19\">\n      <!-- 0.00 -->\n      <g style=\"fill:#262626;\" transform=\"translate(324.988636 322.113452)scale(0.1 -0.1)\">\n       <use xlink:href=\"#ArialMT-48\"/>\n       <use x=\"55.615234\" xlink:href=\"#ArialMT-46\"/>\n       <use x=\"83.398438\" xlink:href=\"#ArialMT-48\"/>\n       <use x=\"139.013672\" xlink:href=\"#ArialMT-48\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_9\">\n     <g id=\"line2d_39\">\n      <path clip-path=\"url(#p274ced18a8)\" d=\"M 347.949574 247.131598 \nL 601.585937 247.131598 \n\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_40\"/>\n     <g id=\"text_20\">\n      <!-- 0.05 -->\n      <g style=\"fill:#262626;\" transform=\"translate(324.988636 250.710504)scale(0.1 -0.1)\">\n       <use xlink:href=\"#ArialMT-48\"/>\n       <use x=\"55.615234\" xlink:href=\"#ArialMT-46\"/>\n       <use x=\"83.398438\" xlink:href=\"#ArialMT-48\"/>\n       <use x=\"139.013672\" xlink:href=\"#ArialMT-53\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_10\">\n     <g id=\"line2d_41\">\n      <path clip-path=\"url(#p274ced18a8)\" d=\"M 347.949574 175.72865 \nL 601.585937 175.72865 \n\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_42\"/>\n     <g id=\"text_21\">\n      <!-- 0.10 -->\n      <g style=\"fill:#262626;\" transform=\"translate(324.988636 179.307556)scale(0.1 -0.1)\">\n       <use xlink:href=\"#ArialMT-48\"/>\n       <use x=\"55.615234\" xlink:href=\"#ArialMT-46\"/>\n       <use x=\"83.398438\" xlink:href=\"#ArialMT-49\"/>\n       <use x=\"139.013672\" xlink:href=\"#ArialMT-48\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_11\">\n     <g id=\"line2d_43\">\n      <path clip-path=\"url(#p274ced18a8)\" d=\"M 347.949574 104.325702 \nL 601.585937 104.325702 \n\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_44\"/>\n     <g id=\"text_22\">\n      <!-- 0.15 -->\n      <g style=\"fill:#262626;\" transform=\"translate(324.988636 107.904608)scale(0.1 -0.1)\">\n       <use xlink:href=\"#ArialMT-48\"/>\n       <use x=\"55.615234\" xlink:href=\"#ArialMT-46\"/>\n       <use x=\"83.398438\" xlink:href=\"#ArialMT-49\"/>\n       <use x=\"139.013672\" xlink:href=\"#ArialMT-53\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_12\">\n     <g id=\"line2d_45\">\n      <path clip-path=\"url(#p274ced18a8)\" d=\"M 347.949574 32.922754 \nL 601.585937 32.922754 \n\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_46\"/>\n     <g id=\"text_23\">\n      <!-- 0.20 -->\n      <g style=\"fill:#262626;\" transform=\"translate(324.988636 36.501661)scale(0.1 -0.1)\">\n       <use xlink:href=\"#ArialMT-48\"/>\n       <use x=\"55.615234\" xlink:href=\"#ArialMT-46\"/>\n       <use x=\"83.398438\" xlink:href=\"#ArialMT-50\"/>\n       <use x=\"139.013672\" xlink:href=\"#ArialMT-48\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"text_24\">\n     <!-- Standard deviation -->\n     <defs>\n      <path d=\"M 4.5 23 \nL 13.421875 23.78125 \nQ 14.0625 18.40625 16.375 14.96875 \nQ 18.703125 11.53125 23.578125 9.40625 \nQ 28.46875 7.28125 34.578125 7.28125 \nQ 39.984375 7.28125 44.140625 8.890625 \nQ 48.296875 10.5 50.3125 13.296875 \nQ 52.34375 16.109375 52.34375 19.4375 \nQ 52.34375 22.796875 50.390625 25.3125 \nQ 48.4375 27.828125 43.953125 29.546875 \nQ 41.0625 30.671875 31.203125 33.03125 \nQ 21.34375 35.40625 17.390625 37.5 \nQ 12.25 40.1875 9.734375 44.15625 \nQ 7.234375 48.140625 7.234375 53.078125 \nQ 7.234375 58.5 10.296875 63.203125 \nQ 13.375 67.921875 19.28125 70.359375 \nQ 25.203125 72.796875 32.421875 72.796875 \nQ 40.375 72.796875 46.453125 70.234375 \nQ 52.546875 67.671875 55.8125 62.6875 \nQ 59.078125 57.71875 59.328125 51.421875 \nL 50.25 50.734375 \nQ 49.515625 57.515625 45.28125 60.984375 \nQ 41.0625 64.453125 32.8125 64.453125 \nQ 24.21875 64.453125 20.28125 61.296875 \nQ 16.359375 58.15625 16.359375 53.71875 \nQ 16.359375 49.859375 19.140625 47.359375 \nQ 21.875 44.875 33.421875 42.265625 \nQ 44.96875 39.65625 49.265625 37.703125 \nQ 55.515625 34.8125 58.484375 30.390625 \nQ 61.46875 25.984375 61.46875 20.21875 \nQ 61.46875 14.5 58.203125 9.4375 \nQ 54.9375 4.390625 48.796875 1.578125 \nQ 42.671875 -1.21875 35.015625 -1.21875 \nQ 25.296875 -1.21875 18.71875 1.609375 \nQ 12.15625 4.4375 8.421875 10.125 \nQ 4.6875 15.828125 4.5 23 \nz\n\" id=\"ArialMT-83\"/>\n      <path d=\"M 25.78125 7.859375 \nL 27.046875 0.09375 \nQ 23.34375 -0.6875 20.40625 -0.6875 \nQ 15.625 -0.6875 12.984375 0.828125 \nQ 10.359375 2.34375 9.28125 4.8125 \nQ 8.203125 7.28125 8.203125 15.1875 \nL 8.203125 45.015625 \nL 1.765625 45.015625 \nL 1.765625 51.859375 \nL 8.203125 51.859375 \nL 8.203125 64.703125 \nL 16.9375 69.96875 \nL 16.9375 51.859375 \nL 25.78125 51.859375 \nL 25.78125 45.015625 \nL 16.9375 45.015625 \nL 16.9375 14.703125 \nQ 16.9375 10.9375 17.40625 9.859375 \nQ 17.875 8.796875 18.921875 8.15625 \nQ 19.96875 7.515625 21.921875 7.515625 \nQ 23.390625 7.515625 25.78125 7.859375 \nz\n\" id=\"ArialMT-116\"/>\n      <path d=\"M 40.234375 0 \nL 40.234375 6.546875 \nQ 35.296875 -1.171875 25.734375 -1.171875 \nQ 19.53125 -1.171875 14.328125 2.25 \nQ 9.125 5.671875 6.265625 11.796875 \nQ 3.421875 17.921875 3.421875 25.875 \nQ 3.421875 33.640625 6 39.96875 \nQ 8.59375 46.296875 13.765625 49.65625 \nQ 18.953125 53.03125 25.34375 53.03125 \nQ 30.03125 53.03125 33.6875 51.046875 \nQ 37.359375 49.078125 39.65625 45.90625 \nL 39.65625 71.578125 \nL 48.390625 71.578125 \nL 48.390625 0 \nz\nM 12.453125 25.875 \nQ 12.453125 15.921875 16.640625 10.984375 \nQ 20.84375 6.0625 26.5625 6.0625 \nQ 32.328125 6.0625 36.34375 10.765625 \nQ 40.375 15.484375 40.375 25.140625 \nQ 40.375 35.796875 36.265625 40.765625 \nQ 32.171875 45.75 26.171875 45.75 \nQ 20.3125 45.75 16.375 40.96875 \nQ 12.453125 36.1875 12.453125 25.875 \nz\n\" id=\"ArialMT-100\"/>\n      <path d=\"M 6.5 0 \nL 6.5 51.859375 \nL 14.40625 51.859375 \nL 14.40625 44 \nQ 17.4375 49.515625 20 51.265625 \nQ 22.5625 53.03125 25.640625 53.03125 \nQ 30.078125 53.03125 34.671875 50.203125 \nL 31.640625 42.046875 \nQ 28.421875 43.953125 25.203125 43.953125 \nQ 22.3125 43.953125 20.015625 42.21875 \nQ 17.71875 40.484375 16.75 37.40625 \nQ 15.28125 32.71875 15.28125 27.15625 \nL 15.28125 0 \nz\n\" id=\"ArialMT-114\"/>\n      <path id=\"ArialMT-32\"/>\n      <path d=\"M 21 0 \nL 1.265625 51.859375 \nL 10.546875 51.859375 \nL 21.6875 20.796875 \nQ 23.484375 15.765625 25 10.359375 \nQ 26.171875 14.453125 28.265625 20.21875 \nL 39.796875 51.859375 \nL 48.828125 51.859375 \nL 29.203125 0 \nz\n\" id=\"ArialMT-118\"/>\n      <path d=\"M 6.640625 61.46875 \nL 6.640625 71.578125 \nL 15.4375 71.578125 \nL 15.4375 61.46875 \nz\nM 6.640625 0 \nL 6.640625 51.859375 \nL 15.4375 51.859375 \nL 15.4375 0 \nz\n\" id=\"ArialMT-105\"/>\n      <path d=\"M 3.328125 25.921875 \nQ 3.328125 40.328125 11.328125 47.265625 \nQ 18.015625 53.03125 27.640625 53.03125 \nQ 38.328125 53.03125 45.109375 46.015625 \nQ 51.90625 39.015625 51.90625 26.65625 \nQ 51.90625 16.65625 48.90625 10.90625 \nQ 45.90625 5.171875 40.15625 2 \nQ 34.421875 -1.171875 27.640625 -1.171875 \nQ 16.75 -1.171875 10.03125 5.8125 \nQ 3.328125 12.796875 3.328125 25.921875 \nz\nM 12.359375 25.921875 \nQ 12.359375 15.96875 16.703125 11.015625 \nQ 21.046875 6.0625 27.640625 6.0625 \nQ 34.1875 6.0625 38.53125 11.03125 \nQ 42.875 16.015625 42.875 26.21875 \nQ 42.875 35.84375 38.5 40.796875 \nQ 34.125 45.75 27.640625 45.75 \nQ 21.046875 45.75 16.703125 40.8125 \nQ 12.359375 35.890625 12.359375 25.921875 \nz\n\" id=\"ArialMT-111\"/>\n     </defs>\n     <g style=\"fill:#262626;\" transform=\"translate(319.001136 211.97375)rotate(-90)scale(0.1 -0.1)\">\n      <use xlink:href=\"#ArialMT-83\"/>\n      <use x=\"66.699219\" xlink:href=\"#ArialMT-116\"/>\n      <use x=\"94.482422\" xlink:href=\"#ArialMT-97\"/>\n      <use x=\"150.097656\" xlink:href=\"#ArialMT-110\"/>\n      <use x=\"205.712891\" xlink:href=\"#ArialMT-100\"/>\n      <use x=\"261.328125\" xlink:href=\"#ArialMT-97\"/>\n      <use x=\"316.943359\" xlink:href=\"#ArialMT-114\"/>\n      <use x=\"350.244141\" xlink:href=\"#ArialMT-100\"/>\n      <use x=\"405.859375\" xlink:href=\"#ArialMT-32\"/>\n      <use x=\"433.642578\" xlink:href=\"#ArialMT-100\"/>\n      <use x=\"489.257812\" xlink:href=\"#ArialMT-101\"/>\n      <use x=\"544.873047\" xlink:href=\"#ArialMT-118\"/>\n      <use x=\"594.873047\" xlink:href=\"#ArialMT-105\"/>\n      <use x=\"617.089844\" xlink:href=\"#ArialMT-97\"/>\n      <use x=\"672.705078\" xlink:href=\"#ArialMT-116\"/>\n      <use x=\"700.488281\" xlink:href=\"#ArialMT-105\"/>\n      <use x=\"722.705078\" xlink:href=\"#ArialMT-111\"/>\n      <use x=\"778.320312\" xlink:href=\"#ArialMT-110\"/>\n     </g>\n    </g>\n   </g>\n   <g id=\"line2d_47\">\n    <path clip-path=\"url(#p274ced18a8)\" d=\"M 359.478499 316.102872 \nL 385.098334 214.671965 \nL 410.718169 316.305369 \nL 436.338004 318.397163 \nL 461.957838 314.677235 \nL 487.577673 318.534545 \nL 513.197508 318.412113 \nL 538.817342 72.660564 \nL 564.437177 68.189509 \nL 590.057012 22.025455 \n\" style=\"fill:none;stroke:#1f77b4;stroke-linecap:round;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"line2d_48\">\n    <g clip-path=\"url(#p274ced18a8)\">\n     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"359.478499\" xlink:href=\"#m03f1f09dee\" y=\"315.793219\"/>\n     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"385.098334\" xlink:href=\"#m03f1f09dee\" y=\"195.898193\"/>\n     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"410.718169\" xlink:href=\"#m03f1f09dee\" y=\"314.822166\"/>\n     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"436.338004\" xlink:href=\"#m03f1f09dee\" y=\"318.381034\"/>\n     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"461.957838\" xlink:href=\"#m03f1f09dee\" y=\"314.434427\"/>\n     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"487.577673\" xlink:href=\"#m03f1f09dee\" y=\"318.534545\"/>\n     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"513.197508\" xlink:href=\"#m03f1f09dee\" y=\"318.398228\"/>\n     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"538.817342\" xlink:href=\"#m03f1f09dee\" y=\"93.809289\"/>\n     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"564.437177\" xlink:href=\"#m03f1f09dee\" y=\"79.770694\"/>\n     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"590.057012\" xlink:href=\"#m03f1f09dee\" y=\"28.791296\"/>\n    </g>\n   </g>\n   <g id=\"patch_8\">\n    <path d=\"M 347.949574 333.36 \nL 347.949574 7.2 \n\" style=\"fill:none;stroke:#cccccc;stroke-linecap:square;stroke-linejoin:miter;\"/>\n   </g>\n   <g id=\"patch_9\">\n    <path d=\"M 601.585937 333.36 \nL 601.585937 7.2 \n\" style=\"fill:none;stroke:#cccccc;stroke-linecap:square;stroke-linejoin:miter;\"/>\n   </g>\n   <g id=\"patch_10\">\n    <path d=\"M 347.949574 333.36 \nL 601.585937 333.36 \n\" style=\"fill:none;stroke:#cccccc;stroke-linecap:square;stroke-linejoin:miter;\"/>\n   </g>\n   <g id=\"patch_11\">\n    <path d=\"M 347.949574 7.2 \nL 601.585937 7.2 \n\" style=\"fill:none;stroke:#cccccc;stroke-linecap:square;stroke-linejoin:miter;\"/>\n   </g>\n   <g id=\"legend_1\">\n    <g id=\"line2d_49\">\n     <path d=\"M 356.949574 19.857812 \nL 376.949574 19.857812 \n\" style=\"fill:none;stroke:#1f77b4;stroke-linecap:round;stroke-width:1.5;\"/>\n    </g>\n    <g id=\"line2d_50\"/>\n    <g id=\"text_25\">\n     <!-- statsmodels -->\n     <defs>\n      <path d=\"M 3.078125 15.484375 \nL 11.765625 16.84375 \nQ 12.5 11.625 15.84375 8.84375 \nQ 19.1875 6.0625 25.203125 6.0625 \nQ 31.25 6.0625 34.171875 8.515625 \nQ 37.109375 10.984375 37.109375 14.3125 \nQ 37.109375 17.28125 34.515625 19 \nQ 32.71875 20.171875 25.53125 21.96875 \nQ 15.875 24.421875 12.140625 26.203125 \nQ 8.40625 27.984375 6.46875 31.125 \nQ 4.546875 34.28125 4.546875 38.09375 \nQ 4.546875 41.546875 6.125 44.5 \nQ 7.71875 47.46875 10.453125 49.421875 \nQ 12.5 50.921875 16.03125 51.96875 \nQ 19.578125 53.03125 23.640625 53.03125 \nQ 29.734375 53.03125 34.34375 51.265625 \nQ 38.96875 49.515625 41.15625 46.5 \nQ 43.359375 43.5 44.1875 38.484375 \nL 35.59375 37.3125 \nQ 35.015625 41.3125 32.203125 43.546875 \nQ 29.390625 45.796875 24.265625 45.796875 \nQ 18.21875 45.796875 15.625 43.796875 \nQ 13.03125 41.796875 13.03125 39.109375 \nQ 13.03125 37.40625 14.109375 36.03125 \nQ 15.1875 34.625 17.484375 33.6875 \nQ 18.796875 33.203125 25.25 31.453125 \nQ 34.578125 28.953125 38.25 27.359375 \nQ 41.9375 25.78125 44.03125 22.75 \nQ 46.140625 19.734375 46.140625 15.234375 \nQ 46.140625 10.84375 43.578125 6.953125 \nQ 41.015625 3.078125 36.171875 0.953125 \nQ 31.34375 -1.171875 25.25 -1.171875 \nQ 15.140625 -1.171875 9.84375 3.03125 \nQ 4.546875 7.234375 3.078125 15.484375 \nz\n\" id=\"ArialMT-115\"/>\n      <path d=\"M 6.59375 0 \nL 6.59375 51.859375 \nL 14.453125 51.859375 \nL 14.453125 44.578125 \nQ 16.890625 48.390625 20.9375 50.703125 \nQ 25 53.03125 30.171875 53.03125 \nQ 35.9375 53.03125 39.625 50.640625 \nQ 43.3125 48.25 44.828125 43.953125 \nQ 50.984375 53.03125 60.84375 53.03125 \nQ 68.5625 53.03125 72.703125 48.75 \nQ 76.859375 44.484375 76.859375 35.59375 \nL 76.859375 0 \nL 68.109375 0 \nL 68.109375 32.671875 \nQ 68.109375 37.9375 67.25 40.25 \nQ 66.40625 42.578125 64.15625 43.984375 \nQ 61.921875 45.40625 58.890625 45.40625 \nQ 53.421875 45.40625 49.796875 41.765625 \nQ 46.1875 38.140625 46.1875 30.125 \nL 46.1875 0 \nL 37.40625 0 \nL 37.40625 33.6875 \nQ 37.40625 39.546875 35.25 42.46875 \nQ 33.109375 45.40625 28.21875 45.40625 \nQ 24.515625 45.40625 21.359375 43.453125 \nQ 18.21875 41.5 16.796875 37.734375 \nQ 15.375 33.984375 15.375 26.90625 \nL 15.375 0 \nz\n\" id=\"ArialMT-109\"/>\n      <path d=\"M 6.390625 0 \nL 6.390625 71.578125 \nL 15.1875 71.578125 \nL 15.1875 0 \nz\n\" id=\"ArialMT-108\"/>\n     </defs>\n     <g style=\"fill:#262626;\" transform=\"translate(384.949574 23.357812)scale(0.1 -0.1)\">\n      <use xlink:href=\"#ArialMT-115\"/>\n      <use x=\"50\" xlink:href=\"#ArialMT-116\"/>\n      <use x=\"77.783203\" xlink:href=\"#ArialMT-97\"/>\n      <use x=\"133.398438\" xlink:href=\"#ArialMT-116\"/>\n      <use x=\"161.181641\" xlink:href=\"#ArialMT-115\"/>\n      <use x=\"211.181641\" xlink:href=\"#ArialMT-109\"/>\n      <use x=\"294.482422\" xlink:href=\"#ArialMT-111\"/>\n      <use x=\"350.097656\" xlink:href=\"#ArialMT-100\"/>\n      <use x=\"405.712891\" xlink:href=\"#ArialMT-101\"/>\n      <use x=\"461.328125\" xlink:href=\"#ArialMT-108\"/>\n      <use x=\"483.544922\" xlink:href=\"#ArialMT-115\"/>\n     </g>\n    </g>\n    <g id=\"line2d_51\"/>\n    <g id=\"line2d_52\">\n     <g>\n      <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"366.949574\" xlink:href=\"#m03f1f09dee\" y=\"34.003125\"/>\n     </g>\n    </g>\n    <g id=\"text_26\">\n     <!-- boostrapped -->\n     <defs>\n      <path d=\"M 14.703125 0 \nL 6.546875 0 \nL 6.546875 71.578125 \nL 15.328125 71.578125 \nL 15.328125 46.046875 \nQ 20.90625 53.03125 29.546875 53.03125 \nQ 34.328125 53.03125 38.59375 51.09375 \nQ 42.875 49.171875 45.625 45.671875 \nQ 48.390625 42.1875 49.953125 37.25 \nQ 51.515625 32.328125 51.515625 26.703125 \nQ 51.515625 13.375 44.921875 6.09375 \nQ 38.328125 -1.171875 29.109375 -1.171875 \nQ 19.921875 -1.171875 14.703125 6.5 \nz\nM 14.59375 26.3125 \nQ 14.59375 17 17.140625 12.84375 \nQ 21.296875 6.0625 28.375 6.0625 \nQ 34.125 6.0625 38.328125 11.0625 \nQ 42.53125 16.0625 42.53125 25.984375 \nQ 42.53125 36.140625 38.5 40.96875 \nQ 34.46875 45.796875 28.765625 45.796875 \nQ 23 45.796875 18.796875 40.796875 \nQ 14.59375 35.796875 14.59375 26.3125 \nz\n\" id=\"ArialMT-98\"/>\n      <path d=\"M 6.59375 -19.875 \nL 6.59375 51.859375 \nL 14.59375 51.859375 \nL 14.59375 45.125 \nQ 17.4375 49.078125 21 51.046875 \nQ 24.5625 53.03125 29.640625 53.03125 \nQ 36.28125 53.03125 41.359375 49.609375 \nQ 46.4375 46.1875 49.015625 39.953125 \nQ 51.609375 33.734375 51.609375 26.3125 \nQ 51.609375 18.359375 48.75 11.984375 \nQ 45.90625 5.609375 40.453125 2.21875 \nQ 35.015625 -1.171875 29 -1.171875 \nQ 24.609375 -1.171875 21.109375 0.6875 \nQ 17.625 2.546875 15.375 5.375 \nL 15.375 -19.875 \nz\nM 14.546875 25.640625 \nQ 14.546875 15.625 18.59375 10.84375 \nQ 22.65625 6.0625 28.421875 6.0625 \nQ 34.28125 6.0625 38.453125 11.015625 \nQ 42.625 15.96875 42.625 26.375 \nQ 42.625 36.28125 38.546875 41.203125 \nQ 34.46875 46.140625 28.8125 46.140625 \nQ 23.1875 46.140625 18.859375 40.890625 \nQ 14.546875 35.640625 14.546875 25.640625 \nz\n\" id=\"ArialMT-112\"/>\n     </defs>\n     <g style=\"fill:#262626;\" transform=\"translate(384.949574 37.503125)scale(0.1 -0.1)\">\n      <use xlink:href=\"#ArialMT-98\"/>\n      <use x=\"55.615234\" xlink:href=\"#ArialMT-111\"/>\n      <use x=\"111.230469\" xlink:href=\"#ArialMT-111\"/>\n      <use x=\"166.845703\" xlink:href=\"#ArialMT-115\"/>\n      <use x=\"216.845703\" xlink:href=\"#ArialMT-116\"/>\n      <use x=\"244.628906\" xlink:href=\"#ArialMT-114\"/>\n      <use x=\"277.929688\" xlink:href=\"#ArialMT-97\"/>\n      <use x=\"333.544922\" xlink:href=\"#ArialMT-112\"/>\n      <use x=\"389.160156\" xlink:href=\"#ArialMT-112\"/>\n      <use x=\"444.775391\" xlink:href=\"#ArialMT-101\"/>\n      <use x=\"500.390625\" xlink:href=\"#ArialMT-100\"/>\n     </g>\n    </g>\n   </g>\n  </g>\n </g>\n <defs>\n  <clipPath id=\"p1b256be9c1\">\n   <rect height=\"326.16\" width=\"253.636364\" x=\"43.585938\" y=\"7.2\"/>\n  </clipPath>\n  <clipPath id=\"p274ced18a8\">\n   <rect height=\"326.16\" width=\"253.636364\" x=\"347.949574\" y=\"7.2\"/>\n  </clipPath>\n </defs>\n</svg>\n",
      "image/png": "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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.style.use(\"seaborn-whitegrid\")\n",
    "\n",
    "fig, ax = plt.subplots(ncols=2, figsize=(10, 6))\n",
    "ax[0].plot(range(X.shape[1]), w_sm_mu, label=\"statsmodels\")\n",
    "ax[0].plot(range(X.shape[1]), w_bs_mu, \"x\", label=\"boostrapped\")\n",
    "ax[0].set_ylabel(\"Mean\")\n",
    "\n",
    "ax[1].plot(range(X.shape[1]), w_sm_std, label=\"statsmodels\")\n",
    "ax[1].plot(range(X.shape[1]), w_bs_std, \"x\", label=\"boostrapped\")\n",
    "ax[1].set_ylabel(\"Standard deviation\")\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above figures show that both the means and standard deviations are close. This suggests the coefficient distribution from the theory are likely correct. The numbers should converge with more bootstrap samples.\n",
    "\n",
    "\n",
    "I would expect the bootstrapped coefficients to maybe over estimate the coefficient standard deviations - each bootstrap sample will have fewer unique data entries to fit the model, as such the coefficients may not be as tightly fit. It doesn't seem like we have enough evidence to clarify this.\n",
    "\n",
    "The raw result numbers are shown below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "                        statsmodels_mu  bootstrapped_mu  statsmodels_std  \\\nTemperature (C)           1.113766e+00     1.113721e+00     1.702782e-03   \nHumidity                  9.269036e-01     9.255212e-01     7.272990e-02   \nWind Speed (km/h)        -9.193476e-02    -9.207228e-02     1.560984e-03   \nWind Bearing (degrees)    5.787597e-04     5.797346e-04     9.620203e-05   \nVisibility (km)          -8.162228e-03    -8.096304e-03     2.701086e-03   \nLoud Cover                2.722203e-15     2.385971e-17     1.432384e-15   \nPressure (millibars)      2.355312e-04     2.313375e-04     8.573335e-05   \nrain                     -3.603448e-01    -3.645398e-01     1.721736e-01   \nsnow                     -8.370791e-01    -8.412777e-01     1.753044e-01   \nConstant                 -1.964852e+00    -1.954745e+00     2.076308e-01   \n\n                        bootstrapped_std  \nTemperature (C)             1.919617e-03  \nHumidity                    8.587625e-02  \nWind Speed (km/h)           2.599598e-03  \nWind Bearing (degrees)      1.074969e-04  \nVisibility (km)             2.871113e-03  \nLoud Cover                  2.841603e-15  \nPressure (millibars)        9.545615e-05  \nrain                        1.573641e-01  \nsnow                        1.671947e-01  \nConstant                    2.028931e-01  ",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>statsmodels_mu</th>\n      <th>bootstrapped_mu</th>\n      <th>statsmodels_std</th>\n      <th>bootstrapped_std</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>Temperature (C)</th>\n      <td>1.113766e+00</td>\n      <td>1.113721e+00</td>\n      <td>1.702782e-03</td>\n      <td>1.919617e-03</td>\n    </tr>\n    <tr>\n      <th>Humidity</th>\n      <td>9.269036e-01</td>\n      <td>9.255212e-01</td>\n      <td>7.272990e-02</td>\n      <td>8.587625e-02</td>\n    </tr>\n    <tr>\n      <th>Wind Speed (km/h)</th>\n      <td>-9.193476e-02</td>\n      <td>-9.207228e-02</td>\n      <td>1.560984e-03</td>\n      <td>2.599598e-03</td>\n    </tr>\n    <tr>\n      <th>Wind Bearing (degrees)</th>\n      <td>5.787597e-04</td>\n      <td>5.797346e-04</td>\n      <td>9.620203e-05</td>\n      <td>1.074969e-04</td>\n    </tr>\n    <tr>\n      <th>Visibility (km)</th>\n      <td>-8.162228e-03</td>\n      <td>-8.096304e-03</td>\n      <td>2.701086e-03</td>\n      <td>2.871113e-03</td>\n    </tr>\n    <tr>\n      <th>Loud Cover</th>\n      <td>2.722203e-15</td>\n      <td>2.385971e-17</td>\n      <td>1.432384e-15</td>\n      <td>2.841603e-15</td>\n    </tr>\n    <tr>\n      <th>Pressure (millibars)</th>\n      <td>2.355312e-04</td>\n      <td>2.313375e-04</td>\n      <td>8.573335e-05</td>\n      <td>9.545615e-05</td>\n    </tr>\n    <tr>\n      <th>rain</th>\n      <td>-3.603448e-01</td>\n      <td>-3.645398e-01</td>\n      <td>1.721736e-01</td>\n      <td>1.573641e-01</td>\n    </tr>\n    <tr>\n      <th>snow</th>\n      <td>-8.370791e-01</td>\n      <td>-8.412777e-01</td>\n      <td>1.753044e-01</td>\n      <td>1.671947e-01</td>\n    </tr>\n    <tr>\n      <th>Constant</th>\n      <td>-1.964852e+00</td>\n      <td>-1.954745e+00</td>\n      <td>2.076308e-01</td>\n      <td>2.028931e-01</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 7
    }
   ],
   "source": [
    "coefficients = pd.concat(\n",
    "    [\n",
    "        w_sm_mu,\n",
    "        pd.DataFrame(data=w_bs_mu, index=X_train.columns),\n",
    "        pd.DataFrame(data=w_sm_std, index=X_train.columns),\n",
    "        pd.DataFrame(data=w_bs_std, index=X_train.columns),\n",
    "    ],\n",
    "    axis=1,\n",
    ")\n",
    "\n",
    "coefficients.columns = [\n",
    "    \"statsmodels_mu\",\n",
    "    \"bootstrapped_mu\",\n",
    "    \"statsmodels_std\",\n",
    "    \"bootstrapped_std\",\n",
    "]\n",
    "coefficients"
   ]
  }
 ],
 "metadata": {
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6-final"
  },
  "orig_nbformat": 2,
  "kernelspec": {
   "name": "python37664bitdataanalysisenvvenv63b40a3c1a484f6297148098436bce1d",
   "display_name": "Python 3.7.6 64-bit ('dataAnalysisEnv': venv)"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}