{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "42b9ccaa-fc57-446a-8168-5253839647e8",
   "metadata": {},
   "source": [
    "# Spearman's Rank Correlation\n",
    "\n",
    "In Chapter 1: Describing Data we looked at Spearman's Rank correlation coefficient, which is a robust correlation based on ranks.\n",
    "\n",
    "**If you are unsure about correlation coefficients, please revisit the page on correlation in Chapter 1: Describing Data**\n",
    "\n",
    "In this section on rank-based tests, we revisit Spearman's $r$ and see how to get a $p$-value for it using `scipy.stats`\n",
    "\n",
    "The reasons for using Spearman'srank correlation rather than Pearson's correlation are recapped there."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "be001071-90c6-462a-ba35-2e731a4096a3",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Set-up Python libraries - you need to run this but you don't need to change it\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as stats\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "sns.set_theme(style='white')\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6d7c73e-abbe-4d5a-9ce3-01bd155a993c",
   "metadata": {},
   "source": [
    "## Load the data\n",
    "\n",
    "Let's use the CO2 data discussed in the section on correlation in Chapter 1: Describing Data. The dataset contains GDP (weath) and carbon emissions per person for 164 countries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "dc0ce091-df7a-4796-bbc9-9b6a752189d8",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Country</th>\n",
       "      <th>CO2</th>\n",
       "      <th>GDP</th>\n",
       "      <th>population</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Afghanistan</td>\n",
       "      <td>0.2245</td>\n",
       "      <td>1934.555054</td>\n",
       "      <td>36686788</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Albania</td>\n",
       "      <td>1.6422</td>\n",
       "      <td>11104.166020</td>\n",
       "      <td>2877019</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Algeria</td>\n",
       "      <td>3.8241</td>\n",
       "      <td>14228.025390</td>\n",
       "      <td>41927008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Angola</td>\n",
       "      <td>0.7912</td>\n",
       "      <td>7771.441895</td>\n",
       "      <td>31273538</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Argentina</td>\n",
       "      <td>4.0824</td>\n",
       "      <td>18556.382810</td>\n",
       "      <td>44413592</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>159</th>\n",
       "      <td>Venezuela</td>\n",
       "      <td>4.1602</td>\n",
       "      <td>10709.950200</td>\n",
       "      <td>29825652</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>160</th>\n",
       "      <td>Vietnam</td>\n",
       "      <td>2.3415</td>\n",
       "      <td>6814.142090</td>\n",
       "      <td>94914328</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>161</th>\n",
       "      <td>Yemen</td>\n",
       "      <td>0.3503</td>\n",
       "      <td>2284.889893</td>\n",
       "      <td>30790514</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>162</th>\n",
       "      <td>Zambia</td>\n",
       "      <td>0.4215</td>\n",
       "      <td>3534.033691</td>\n",
       "      <td>17835898</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>163</th>\n",
       "      <td>Zimbabwe</td>\n",
       "      <td>0.8210</td>\n",
       "      <td>1611.405151</td>\n",
       "      <td>15052191</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>164 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         Country     CO2           GDP  population\n",
       "0    Afghanistan  0.2245   1934.555054    36686788\n",
       "1        Albania  1.6422  11104.166020     2877019\n",
       "2        Algeria  3.8241  14228.025390    41927008\n",
       "3         Angola  0.7912   7771.441895    31273538\n",
       "4      Argentina  4.0824  18556.382810    44413592\n",
       "..           ...     ...           ...         ...\n",
       "159    Venezuela  4.1602  10709.950200    29825652\n",
       "160      Vietnam  2.3415   6814.142090    94914328\n",
       "161        Yemen  0.3503   2284.889893    30790514\n",
       "162       Zambia  0.4215   3534.033691    17835898\n",
       "163     Zimbabwe  0.8210   1611.405151    15052191\n",
       "\n",
       "[164 rows x 4 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "carbon = pd.read_csv('https://raw.githubusercontent.com/jillxoreilly/StatsCourseBook_2024/main/data/CO2vGDP.csv')\n",
    "carbon"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "471a1535-7ec6-4f4c-8883-bdd3a493e459",
   "metadata": {},
   "source": [
    "## Plot the data\n",
    "\n",
    "From a scatter plot, we can see that the data are unsuitable for Pearson's correlation (please check the notes for Correlation in the section **Describing Data** if unsure why)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a0ebb0d3-3924-4836-9902-9d2e485e0f82",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
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OJrSfcfIgXDW7DDleZ4p6lv0YmIiIKCvFWqfgzCyYggtFdCxduw3vf16T0D4gz43r5lXgpFFFKepZ/8HAREREWeXQFJyOTK9DKYTAB1/U4C9rtiEcNdrbZUnC7K8Mx8VnjYbLyfPf+gIDExERZQ3TshEIadB0CxmelVDfFMELb2xBZVVjQvvIQTlYcOF4DB+Yk6Ke9U8MTERElBWimoFAWIdlZXZUsiwbqz/ci9fe2wnjsKKaLoeCS88djZmnD4csc1F3X2NgIiKijCaEQDCsIxIzMn4KrupAEItf34x9daGE9gljivCNCypQmOdOUc+IgYmIiDKWYdoIhjRoRmZPwcU0E6++uxNvfbQ34T5yfU5cM6ccp40rYamAFGNgIiKijBSJGQiGdVgZPqz02faDePHNSjQFtYT2sycOweUzx8LndqSoZ3Q4BiYiIsooti0QjMSn4DK5tlIgpOHl1VvxcWVdQvvAQi8WzKtA2YiCFPWMOsPAREREGcMwLQRCOjTD6vrJacoWAv/auB/L39qOqGa2tyuyhHnTSzFveikcKs9/SzcMTERElBHCMQMtGT4Fd+BgGC+s3Izt+wIJ7WOH5eG6eRUYMsCfop5RVxiYiIgorVm2QDCsIapl7vEmhmlj5foqrFxflRD4PC4VV8wci7MmDoHMRd1pLeWBqaGhAQ899BDeffddaJqGqVOn4q677sLYsWMBAJs3b8aDDz6Izz//HPn5+bj++utx8803p7jXRETUFzTDQjCkQTcz93iTbXub8MLKStQ0RBLaTxtXgmvmlCPP70pRz6gnUh6YvvOd70CWZTzzzDPwer14/PHHccMNN2DVqlWIxWK48cYbcf755+OBBx7Ap59+igceeAD5+fm48sorU911IiJKolBURyhiZOwUXDhm4K9vbcd7G/cntBfkuPCNC8bh1LLiFPWMjkdKA1NTUxOGDRuG73znOygrKwMA3Hbbbfja176Gbdu2Yf369XA6nbj//vuhqirGjBmD3bt345lnnmFgIiLKUpYtEAhpiOmZOQUnhMCGyjq8snorgmG9vV0CcN7pw/C1c8fA7Ur5eAX1UEr/ixUUFOCxxx5r//XBgwexaNEiDBo0CGPHjsVvf/tbTJ06Fap6qJvTpk3D73//ezQ0NKCoiKczExFlE003EQjpMKzMnIJrDMTw4ptbsGnHwYT2ocV+LLiwAqOG5KWoZ3Si0ibi/s///A9eeeUVOJ1OPP300/B6vaipqUF5eXnC80pKSgAA+/fvZ2AiIsoSQgiEIgZCUQN2Bg4r2bbAWxv24tV1OxNKHjhUGRefPQrnTx0BRWGpgEyWNoHpm9/8Jq655hq8+OKLuP3227FkyRLEYjE4nc6E57lc8cVxmqZ1dhkiIsowlmWjOaRDMzJzCm5vbQsWr6zE7gPBhPaKkQW4bl4FSgq8KeoZ9aa0CUxtu+J+9rOf4dNPP8XixYvhdruh63rC89qCktfLH0AiokwXa52CMzNwCk43LLz23i6s/s+ehFExn8eBq2aVYdopg3j+WxZJaWBqaGjA+vXrceGFF0JRFACALMsYM2YM6urqMGjQINTVJZaMb/v1wIED+7y/RETUO4QQaAkbCMd0ZOImuC93NWDJykocDMQS2s84eRCuml2GHK/zKK+kTJXSwFRXV4c777wTRUVFmD59OgDAMAx8+eWXmDVrFgYMGICXXnoJlmW1B6r169dj1KhRXL+UpWxbYGd1AMGwjlyfE6OH5kGW+Tc0omximDaCIQ2aYSHTslJLRMfSNdvwwRc1Ce0D8j24bu44nDSK303ZKqWBqaKiAmeffTYeeOAB/PznP0dubi4WLlyIYDCIG264AS6XC88++yzuu+8+3HLLLfjss8/w/PPP44EHHkhltylJNm6rx9K121BdF4Jp2VAVGUNL/LhqVhkmsl4JUVaIagYCYR2WlVlRSQiBDz6vwV/WbkM4arS3y5KE878yAhefPQpOh5LCHlKySUKkdoldS0sLHn30UaxevRotLS2YMmUKfvSjH7XXZfrss8/w4IMP4ssvv0RxcTFuuukmLFiw4Ljfb/bs2QCANWvW9Er/qXds3FaPJ5duRDRmIsfngEORYVg2WiIGPC4Vt181kaGJKIMJIRAM64jEjIybgqtrimDJykpU7m5KaB85OBcL5lVg+MCcFPUsPXndKgpy3L1+3VR/f6c8MPW1VP+GU0e2LfCTZ9ajan8QRXmuhEWSQgg0BDWUDs7FA7dO5/QcUQYyTAuBkA49w6bgLMvGqv/swT/+tQvGYUezuBwKLj13NGaePpyfSZ3I1sCUNrvkqP/aWR1AdV0IOT5Hhx0lkiQhx+NAdV0IO6sDGDs8PzWdJKLjEokZCIb1jDveZNf+ABa/Xonq+lBC+4QxA/CNC8ahMK/3AwGlNwYmSrlgOL6l2KE4On3cocoIRY2EIwaIKL3ZtkAwEp+Cy6R5jJhm4m/rduDtDfsSRsNyfU5cM6ccp40rYamAfoqBiVIu1+eE2rpmySV3XDRpmPEF4Lk+btMlygS6YSEQ0qCbmVVb6bNt9XjxzS1oakksjHzOpCG47Lyx8Lk7/0sd9Q8MTJRyo4fmYWiJH1UHgnDmyh3WMLVEDZQOzsXooTyDiSjdhaM6WiJGRk3BBUIaXl61FR9vSaz7N6jIi/nzKlA2vCBFPaN0wsBEKSfLEq6aVYYnl25EQ1BDjscBhyrDMG20RA14XSqumlXGxZVEacyyBYJhDVEtc443sYXAe59W469v70BUM9vbVUXCvOmlmDutFA6V579RHAMTpYWJZcW4/aqJ7XWYQlEDqiKjdHAu6zARpTlNNxEM6xk1Bbf/YAgvrKzEjn2BhPaxw/Iwf954DB7gS1HPMpssAYqUnSGTgYnSxsSyYkwYM4CVvokyhBACoYiBUNRIOEstnRmmhZXrd2Pl+qqEaUOPS8UVM8firIlDIHNRd4/JEuB0qPB7VLic2RktsvOuKGPJssTSAUQZwLRsBNqON8mMrISte5rwwspK1DZGEtpPqyjBNeeXI8/vSlHPMlc8KCnwexxZG5TaZPfdERFRr4vpJgIhDWaGHG8SjhlY/tZ2/Gvj/oT2glwXvjFnHE7llH+PSVK8gGd/CEpt+sddEhHRCcu0402EENhQWYdXVm9NqOMmAZg5ZTguPWc03C5+DfaEJAEuVYHP64C7nwSlNv3rbomI6LgYpo1g2xRcqjvTDQ2BKF58cws+39GQ0D6sxI/58yowagjLlPREfw5KbfrnXRMRUbdl0vEmlm3jrY/24dV3d0A3Du3ac6gyLj57NM6fOhyKkp27uJJBkgCnqsDnUeFx9e/CnQxMRETUqUw73mRPTQsWr9yMPTUtCe3jSwtx3dxxKC7wpqhnmYdBqSMGJiIi6iCTjjfRDQt/f28n1vxnb0J5A7/Hgatnl+ErJw/i+W/dxKB0dAxMRESUIBTVEcqQ402+3NWAJSsrcTAQS2ifdsogXDWrDH4vz6DsDkkCHIoMv9fBoHQUDExERAQgfrxJIKQhpqf/8SbBsI6la7fhP1/UJLQPyPdg/rwKjC8tTFHPMktbUPJ5HPC4VI7EHQMDExERQdNNBEI6DCu9p+CEEFi/6QCWrd2GcOzQ+W+yJGHOGSNw0Vmj4HQoKexhZmBQ6jkGJiKifq4lrGfE8SZ1TRG8sLISW3Y3JbSPHJyL6+dVYNjAnBT1LHO0BSWvxwEvg1KPMDAREfVTlmWjOaRDM9J7Cs6ybLz5wR7841+7YB42AuZyKrjs3DGYcdownjnZBQalE8fARETUD2XKFNzO6gAWr9yM/fXhhPZTxw7AtReMQ2GuO0U9ywySBKiyDJ9HhdftYFA6AQxMRET9TCZMwUU1Eyve2YF1H+9LqCye63PimjnlOG1cCb/8j0ECoCoMSr2JgYmIqJ/IlCm4T7fW46VVW9DcoiW0nzNpKC4/bwy8bm57P5q2oOT1qPC6HJyq7EUMTERE/UAmTME1t2h4edUWfLK1PqF9UJEXC+aNx9jh+anpWAaQAChtI0oMSknBwERElMWEEAhFjLSegrOFwHufVmP529sR06z2dlWRMG96KeZOK4VD5flvnYkHJQk+twNeN4NSMjEwERFlqfgUnAbNsNJ2Cm5/fQiLV1ZiZ3Ugob1seD7mz6vAoCJfinqW3iQAsiLBz6DUZxiYiIiyUKx1Cs5M0yk4w7Tw+r+r8Mb7uxOOYPG6VFwxayzOPHUIZC5U7pSiSPC5HPB6HFAYlPoMAxMRURYRQqAlbCAc05GuR8Ft3dOEF1ZWorYxktA+ZXwJrp5djjy/K0U9S28MSqnFwERElCUM00awbQou1Z3pRDhqYPlb2/Gvz/YntBfmuvGNC8ZhwtgBKepZelPk1jVKDEopxcBERJQFopqBQFiHZaVfVBJC4KPNtXhl9Va0RIz2dkkCZp4+HJeeOxpuJ7+OjsSglF74E0pElMGEEAiGdURiRlpOwR1sjuLFN7fgi50NCe3DSvxYcOF4lA7OTVHP0pciS/C6HPB5VCgKdwemi5QHpubmZjz22GN4++23EQqFMG7cONx5552YMmUKAOCee+7B8uXLE14zcOBArFu3LhXdJSJKG4ZpIRDSoafhFJxl23jro3149d0d0I1DC88dqoxLzhmN2VOGMwwcgUEpvaU8MH3/+99HQ0MDHnvsMRQWFmLJkiW4+eabsXz5cowZMwZbtmzBt7/9bSxYsKD9NYqipLDHRESpF4kZCIb1hB1m6WJPTRCLX6/EntqWhPbxpYW4bl4FivM9KepZelJkCR6XCr/HwaCUxlIamHbv3o1//etfePHFF3HaaacBAO677z6sW7cOr732Gv77v/8b27dvx2233Ybi4uJUdpWIKC3YtkAwEp+CS7faSppu4e/v7cSaD/ck9M3vceDq88vxlZMG8kyzw7QFJZ/HAZVBKe2lNDAVFBTgD3/4A0455ZT2NkmSIIRAIBBAVVUVNE3DmDFjUthLIqL0oBsWAiENupl+tZW+2NmAF1ZWojEYS2ifPmEwrpxVBr+H57+1kWUJXgaljJPSwJSbm4sZM2YktL3++uvYs2cPzj77bGzduhWSJOH555/HunXrIMsyZsyYgTvuuAM5OTkp6jURUd8LR3W0RIy0m4ILhnX8Zc1WfPhlbUJ7cb4H8+dVoKK0MEU9Sz+yJMHrVuF1O3jUSwZK+Rqmw23YsAH33nsvZs+ejVmzZuGJJ56ALMsYOnQoFi5ciN27d+Phhx/G1q1b8fzzz0OW+QNHRNnNsgWCYQ1RzUyrKTghBNZvOoBla7chHDPb22VZwgVnjMRXzyyF08H1pkA8KHncKnwMShktbQLT6tWr8YMf/AATJ07EY489BgD47ne/ixtuuAG5ufFtp+Xl5SguLsY111yDTZs2YeLEiansMhFRUmmGhWAaTsHVNkawZGUltuxpSmgfNSQXC+aNx9ASf4p6ll4YlLJLWgSmxYsX48EHH8ScOXPwyCOPwOl0AoivZ2oLS23Ky8sBADU1NQxMRJS1QpH4FJydRsNKpmXjzQ9245//qko4o87lVHDZjDGYMXkYD4FFPCi5XQr8HgccKkfZskXKA9OSJUvws5/9DNdffz3uvffehGm2O++8E83NzVi0aFF726ZNmwAAY8eO7fO+EhElm2XZCIR1xPT0moLbWR3A4pWbsb8+nNB+6tgB+MYF41CQ605Rz9IHg1J2S2lg2rVrF37xi19gzpw5+Na3voWGhkOVYN1uNy6++GJ85zvfwdNPP42LLroIu3btwk9/+lNcfPHF3DlHRFlH000EQjoMK32m4KIxEyvWbce6j6sTimPm+Z24ds44TCov7velAmQJcLviU29ct5W9UhqY3njjDRiGgVWrVmHVqlUJj11++eV46KGH8Pjjj2PhwoVYuHAhcnJycMkll+COO+5ITYeJiJJACIFQxEAoml5TcJ9urceLb25BIKQltJ87eSgunzEWHnfKJylSikGpf5GESKM/nX1g9uzZAIA1a9akuCdERPF1QYGQBk1Pn+NNmlpieHnVVny6tT6hffAAH+bPq8DYYfmp6ViakCXA5YzXUXIxKPWZVH9/9++/HhARpVBMNxEIaTCt9IhKthBY90k1Vry9HTHdam9XFQlfPXMULpg2sl8XWmRQ6t8YmIiI+pgQAsFw/HiTdKlDWV0fwgsrK7GzOpDQXjY8H/PnVWBQkS9FPUs9WQKcDhV+jwqXk1+b/RX/yxMR9SHDtBEMadCM9JiCM0wL//x3Fd54fzfsw9Kb163iypllOPPUwf12UXc8KMV3vTEoEX8CiIj6SFQzEAjpaXO8yZbdTXhh5WbUNUUT2qeMH4ivn1+GXJ8rRT1LLQYl6gx/EojouNm2wM7qAIJhHbk+J0YPzWPhwk7YtkBLJH2m4MJRA8ve2oZ/f3Ygob0w141vzB2HCWMGpKhnqSVJgItBiY6CPxFEdFw2bqvH0rXbUF0XgmnZUBUZQ0v8uGpWGSaWFae6e2nDMC0EQjo0w+r6yUkmhMBHm2vxyuqtaIkY7e2SBMyeMgIXnzMK7n4YFCQJcKkKfF5Hv7x/6h7+ZBBRj23cVo8nl25ENGYix+eAQ3HAsGxUHQjiyaUbcftVExmaAIRjBlrC6TEFd7A5ihff3IIvdjYktA8fmIMFF1Zg5KDco7wyezEoUU/wJ4SIesS2BZau3YZozERRnqt9QbBLVuDMldEQ1LB07TZMGDOg307PWbZAMKwhqqX+eBPLtrH2w734+3s7oRuHKog7VBmXnDMas6cOhyL3r1IBkgQ4VQU+jwqPy5Hq7lCGYGAioh7ZWR1AdV0IOT5Hh91TkiQhx+NAdV0IO6sDGDs8PzWdTCHdsBAIadDN1B9vsrsmiMWvV2JvbUtC+0mjCnHd3AoMyPekqGepwaBEJ4KBiYh6JBjWYVo2HErnXzgOVUYoaiAY1vu4Z6kXjupoiRgpn4KL6SZee3cX1ny0J2GEK8frwNWzyzH1pIH9qlQAgxL1BgYmIuqRXJ8TqiLDsGy45I7Vjg0zvgA81+dMQe9SI52m4D7fcRBL3tiCxmAsof3MCYNxxawy+D39JzBIEuBQZPi9DgYlOmEMTETUI6OH5mFoiR9VB4Jw5soJIxVCCLREDZQOzsXooXkp7GXf0QwLwTSYgguGNbyyehs+2lyb0F5c4MH8uRWoKC1MUc/6XltQ8nkc8LjUfjWaRsnDwEREPSLLEq6aVYYnl25EQ1BDjscBhyrDMG20RA14XSqumlXWLxZ8h1qn4OwUTsEJIfDvzw5g2dptiGhme7ssS5g7bSQunF4KZz8594xBiZKJgYmIemxiWTFuv2piex2mUNSAqsgoHZzbL+owWbZAIKQhpqd2Cq62MYLFr2/Gtr3NCe2jhuRiwbzxGFriT03H+lhbUPJ6HPAyKFGSMDAR0XGZWFaMCWMG9LtK35puIhjWUzoFZ1o23nx/N/757yqY1qF+uJ0KLjtvLM6dPBRyPwgNDErUlxiYiOi4ybLUb0oHCCEQihgIRQ3YKRxW2rGvGYtXVuLAwXBC+8SyYlx7QTkKctwp6lnfaQ9KbhVed8fyFkTJwMBERNQF07IRCGnQDCtlU3DRmIkV67Zj3cfVOLwLeX4Xrp1TjsnjSlLTsT4kAVAVGT4PgxL1PQYmIqJjiGpGa+2p1I0qfbKlDi+t2opASGtvkwCce9pQXHbuWHjc2f1R3haUvB4VPgYlSpHs/lNGRHSchBAIhnVEYgZStQmuKRjDS6u2YuO2+oT2wQN8WDCvAmOG5aemY31EAqC0jSi5HFm/Po7SW48D0xdffIE9e/agvLwcY8aM6fB4Y2Mj1q1bh8suu6w3+kdE1OcM00IgpEM3LKQiK9m2wLpP9mHFOzsQ0632dlWR8dWzSnHBGSOhKtl7/ls8KEnwuR3wuhmUKD10OzCFQiF873vfw/r16yGEgCRJmDNnDn7+858jN/fQKdd79+7FPffcw8BERBkpEotPwaXqeJPquhAWr9yMXfuDCe3lI/Ixf954DCz0pqRffUECICsS/AxKlIa6HZieeOIJbN68Gb/+9a9RWlqKN998E88++yzmz5+P5557DkVFRcnsJxFRUtm2QDASn4JLxcJu3bDwz39X4c0PdicUwvS6VVw5swxnnjo4a9futAUln8sBr8cBhUGJ0lC3A9PatWtxxx13YN68eQCAiooKnH322fjWt76FW265BX/+85/h9/ePImlElF10w0IghcebVFY14oU3KlHfFE1on3rSQFw9uzyrz+VTGJQoQ3Q7MDU0NGDEiBEJbaeddhqefvpp3HTTTbj99tuxaNGiXu8gUV+ybdHvCjH2d+HW401SMQUXihpYtnYb1m86kNBelOfGdXMrcPLo7B25V+TWNUoMSpQhuh2Yhg8fjvfffx/Tp09PaJ8yZQp++ctf4gc/+AHuvvtuXHfddb3eSaK+sHFbfftRH6ZlQ1VkDC3x94ujPvojyxYIhjVEtb4/3kQIgf98WYu/rN6KUNRob5ckYPaUEbjknNFwObPz/DcGJcpU3Q5M8+fPx09/+lOEw2FcdNFFmDx5cvtjF110EQ4cOIBHHnkEn376aTL6SZRUG7fV48mlGxGNmcjxOeBQHDAsG1UHgnhy6UbcftVEhqYsksrjTeqbo3jxjUp8uasxoX3EwBwsuLACIwblHuWVmU2RJXhdDvg8KpQs3uFH2avbgemaa65BMBjEM888AwAJgQkAbrnlFvj9fvzyl7/s3R4SJZltCyxduw3RmImiPFf7wlqXrMCZK6MhqGHp2m2YMGYAp+eyQCgSn4Lr6+NNLNvGmg/34u/v7oRxWFBzOmRces4YzJwyDIqcfUGCQYmyRY/qMN1666245ZZbEAqFOn382muvxfnnn4933nmnVzpH1Bd2VgdQXRdCjq9jBWFJkpDjcaC6LoSd1YF+c25aNrIsG80hHZrR91Nwu2uCWPzPzdhbl/jZefLoInzjgnEYkO/p2w71AUWW4HGp8HscDEqUFXpcuFKSJOTk5CAQCODAgQMQQmDw4MHIz88HAAwYMABXXnllb/eTKGnix17YcCiOTh93qDJC0XhtHspMmm4iENJhWH07BRfTTfz93Z1Y+9HehJCW43Xg6+eXY8r4gVlXKoBBibJVjwPT+vXr8dRTT2HDhg0Qh30CnH766fj2t7+Ns88+u1c7SJRsuT4nVEWGYdlwyR0X2hpmfAF4Nm/tzlZCCIQiBkLRvp+C27TjIF58Ywsag7GE9jNPHYwrZ5bB5+k8oGeqtqDk8ziyugo59V89CkzPPfccHn74YQwePBgLFizAyJEjoSgK9uzZgzVr1uDWW2/FD3/4Q9x0003dvmZzczMee+wxvP322wiFQhg3bhzuvPNOTJkyBQCwefNmPPjgg/j888+Rn5+P66+/HjfffHPP7pLoGEYPzcPQEj+qDgThzJUT/sYvhEBL1EDp4FyMHpqXwl5ST5mWjUBIg6b37fEmwbCGV1ZvxUeb6xLaSwo8mD+vAuNGFvZhb5JPliV4GZSoH+h2YPrss8/wq1/9Ctdffz1++MMfwuFI/NvRD37wAzz66KN49NFHMWXKFJx66qnduu73v/99NDQ04LHHHkNhYSGWLFmCm2++GcuXL0dhYSFuvPFGnH/++XjggQfw6aef4oEHHkB+fj6n/ajXyLKEq2aV4cmlG9EQ1JDjccChyjBMGy1RA16XiqtmlXHBdwaJakbrVGvfRSVbCPz7s/1YvnY7IprZ3i7LEuZNG4kLzyyFQ82eUgEcUaL+RhKie+PUd955JxoaGvDcc88d83m33nor8vLy8Mgjj3R5zd27d+OCCy7Aiy++iNNOOw1A/G/0c+fOxUUXXQS3240XXngBa9euharGs91jjz2GN998EytXruxOtzuYPXs2AGDNmjXH9XrKXqzDlPmEEAiG48eb9GUdypqGMF5YWYlte5sT2kcPzcP8eRUYWpw9pyAwKFGqpPr7u9sjTB9//DHuvPPOLp93xRVX4H//93+7dc2CggL84Q9/wCmnnNLeJkkShBAIBAL4/PPPMXXq1PawBADTpk3D73//ezQ0NPD8OupVE8uKMWHMAFb6zlCGaSMY0qAZfTcFZ5g23ny/Cq+vr0oYzXK7FFw2YyzOnTwUcpYs6mZQov6u24Hp4MGDGDRoUJfPKy4uRmNjY5fPA4Dc3FzMmDEjoe3111/Hnj17cPbZZ+PXv/41ysvLEx4vKSkBAOzfv5+BiXqdLEssHZCBIrH4FFxfHm+yfW8zFq/cjJqGSEL75PJifH1OOQpy3H3Wl2RiHSWiuG7/9BcWFmLfvn1dPq+6uhrFxcc3fbFhwwbce++9mD17NmbNmoVYLAanM3FnksvlAgBomnZc70FE2cO2BZpDGppDWp+FpUjMwAsrK/HICxsSwlJ+jgvfvuJUfOuKU7MiLCmyhFyvE8X5HuT6nQxL1O91e4TpjDPOwIsvvoivfe1rR60bIoTAiy++iDPPPLPHHVm9ejV+8IMfYOLEiXjssccAAG63G7qeWPumLSh5vd4evwcRZQ/DtNDcovXZ8SZCCHyypR4vr96CQOjQ55IEYMZpw/C1GWPgcfW4UkvaURQJPhfPeiM6Urf/ynDzzTfjiy++wI9//GPEYrEOj8diMdxzzz2orKzEN7/5zR51YvHixfjud7+Lc889F8888wzc7vjfzgYNGoS6usStuW2/HjhwYI/eg4iyRziqoyEQ67Ow1BiM4elln+EPKzYlhKUhxT788PopuPaCcRkdliTEg1J8RMmLHJ+TYYnoCN3+Ez5u3Dg8+OCDuO+++7B69WpMnz4dw4YNg6qqqK6uxrvvvotIJIKHHnoIY8aM6XYHlixZgp/97Ge4/vrrce+990I+7CylqVOn4qWXXoJlWVCU+Hbc9evXY9SoUVy/RNQPWbZAMKwhqvXN8Sa2LfDOx/uwYt0OaLrV3q4qMi4+exTmfGVERk9VSQBkjigRdUuP/kr0ta99DWVlZVi4cCHee++99jPlPB4PZs2ahW9961sdFmkfy65du/CLX/wCc+bMwbe+9S00NDS0P+Z2u3HllVfi2WefxX333YdbbrkFn332GZ5//nk88MADPek2EWWBvj7eZF9dC15YWYld+4MJ7eNGFOC6eRUYWJi5ywLaRpR8bge8bgd3ghJ1Q4/HkE866ST88pe/hNfrRXNzM4QQKCwsxMaNG3sUlgDgjTfegGEYWLVqFVatWpXw2OWXX46HHnoIzz77LB588EFcfvnlKC4uxl133YXLL7+8p90mogzV18eb6IaFf/57F978YA/swxaS+9wqrpxVhukTBmfs+W/xoCTD51HhdTEoEfVEtwtXAvFjSu655x5ccMEFuO2229rbA4EApk+fjlGjRuGJJ57o0ZRcX0t14Ssi6r6+rq1UWdWIF1ZWor45mtA+9aSBuHp2ecaeJyghPo3oZVCiDJbq7+9uT77v3bsXN9xwAwKBAMaOHZvwmNPpxL333otwOIzrrrsONTU1vd5RIupfwjEDDYEoYn0QlkIRHc+99iV+89InCWGpKM+N7359Em6+9JSMDEuSBDgUGXl+Jwbke+D3OBmWiI5Tt6fk/vCHP6CgoAAvvfQS8vPzEx7zeDxYsGABLrzwQlx11VVYuHAh7r///l7uKlH2s23R7yuN9+XCbiEE/vNFDf6yZhtCUaO9XZYkzJ46HBefPRouZ+ad/9YWlLxuFV63I2OnEInSSbcD0/r16/Htb3+7Q1g6XFFREW688Ua88MILvdE3on6FZ9nFF3YHw3qflAuob45iycpKbK5KPJlgxMAcLLhwPEYMykl6H3obgxJR8nQ7MNXX12PkyJFdPq+8vJxTckQ9tHFbPZ5cuhHRmIkcnwMOxQHDslF1IIgnl27E7VdNzPrQFIroaIkkf2G3ZdlY/eFevPbeThiHBTOnQ8al54zBzCnDoMiZVSqAQYko+bodmAoLCzsUkexMY2PjMUehiCiRbQssXbsN0ZiJojxX+5edS1bgzJXRENSwdO02TBgzICun5yzLRnNIh2Ykfwqu6kAQi1/fjH11oYT2k0cX4bq541CU50luB3pZ22Jun4dBiSjZuh2Ypk6diuXLl+Oiiy465vNWrFiB8ePHn3DHiPqLndUBVNeFkOPr+IUnSRJyPA5U14WwszqQdQcD91VtpZhu4tV1O/HWhr0JoSzH68A1c8bh9IqSjAob3PVG1Pe6Pe58/fXX44MPPsBDDz3U6cG3uq7j4Ycfxrvvvov58+f3aieJslkwrMO0bDiOUjHaocowLRvBsN7p45mqJayjMaglPSxt2n4QP332A6z9KDEsnTVxCO7/r+mYMn5gxoSleFCSkOvjrjeivtbtEaYJEybgnnvuwS9+8Qv87W9/az8axbIs7N+/Hx988AGamprwf//v/8U555yTzD4TZZVcnxOqIsOwbLjkjjuyDDO+ADwTt7V3pq+m4AIhDa+s3ooNlYlLCQYWejF/XgXKRxQk7817WdsRJn5W5iZKmR5V+p4/fz4qKiqwaNEirFmzpn2kyefz4eyzz8ZNN92EiRMnJqWjRNlq9NA8DC3xo+pAEM5cOWG0QwiBlqiB0sG5GD00L4W97B19MQVnC4F/bdyPv761HRHNbG9XZAlzp43EhWeWwqFmTqkAhWe9EaWFHh+Ncvrpp+P0008HADQ1NUGWZeTlZf4HOVGqyLKEq2aV4cmlG9EQ1JDjccChyjBMGy1RA16XiqtmlWX0qEJfHW9S0xDG4tcrsX1fc0L7mGF5mD+vAkMG+JP23r1NkVvPemNQIkoLPQ5MhysoyJwhbUotFmQ8tollxbj9qontdZhCUQOqIqN0cG7G12EyLRuBtuNNkpSVDNPGG+9XYeX6KpjWoTdxuxRccd5YnD1pKOQMWaekyBK8Lgd8HhXKUda1EVHfO6HARNQdLMjYPRPLijFhzICsCpYx3UQgpCWEmN62fW8zFq/cjJqGSEL75PJiXDNnHPJzXEl7796kyBI8LhV+j4NBiSgNMTBRUrEgY8/IspQVpQOEEGgJGwjHdNhJykqRmIG/vr0d7366P6E9P8eFa+eMw6TyzPi5kmUJXpcKn8cBlUGJKG0xMFHS9PeCjP2VYdoItk3BJeH6Qgh8vKUOL6/amlBqQQJw3unDcOm5Y+Bxpf9HmyxJ8LhV+NzxNWtElN7S/1OFMlZ/LsjYX0U1A4GwDitJU3CNwRheenMLPtt+MKF9aLEf8+dVZMROQgYloszEwERJc6ggo6PTxx2qjFDUyLqCjMcj0xfFCyEQDOuIxIykTMHZtsDbH+/D39btgKZb7e0OVcZFZ43CnK+MSPt1P7Ikwe1S4Pc4MqqsARHFMTBR0vS3gozHK9MXxRtmfBecnqQpuH21LfjzykrsPhBMaK8YWYDr5lWgpMCbhHftPbIEuF3xESWng0GJKFMxMFHS9KeCjMcr0xfFR2LxEUIrCcNKumHhH//ahVUf7Emo3eTzOHDVrDJMO2VQWh9pIkuAyxlfzO1iUCLKeAxMlDT9oSDjiejNRfF9PaVn2wItER3hmJGU2kqbqxqxZGUl6pujCe1nnDwIV80uQ443fUclZQlwOlT4PSpcTn7EEmUL/mmmpMrmgownqrcWxff1lJ5hWgiEdGiG1fWTeygU0fGXNdvwwRc1Ce0D8j24bu44nDSqqNffs7dIEuByxNcoMSgRZR/+qaaky8aCjL2hNxbF9/WUXrKm4IQQ+OCLGvxlzTaEo0Z7uyxJOP8rI3Dx2aPSdv2PJAEuVYHfy6BElM34p5v6RLYUZOxNJ7oovi/rXNm2QDAS3wXX21Nw9U0RvPDGFlRWNSa0jxyUgwUXjsfwgTnH7Nfe2haEIgb8XgeGD8zpsyDeFpR8XgfcDEpEWY9/yolS5EQXxfdVnSvDtNDcokE37eO+Rmcsy8bqD/fgtfd2wTjs2i6HgkvPHY2Zpw8/ZviprGrEyverUNsQgWXbUGQZA4u8mDetFBWlhb3a18NJEuBUFfg8KjyuzkcHiSj7MDARpciJLorv7pRec0jD9r3NxzUdGo4ZaEnCFNyu/QEsfr0S1fWhhPYJY4pw7QXjUJTnOebrK6sa8cIblYhpZuuRIipMS6C6PoQX3qjE/LkVvR6aJAlwKDL8XgeDElE/xMBE1It6ulvtRBbFd2dKzxYCL75Ziaag1qMF4bYtEAhriGpmr07BxTQTf1u3A29v2JdQsynX58TXzy/H6RUlXZYKsG2Ble9XIaaZyPc725/vVCU4fE40h3WsfL8K5SMKemV6ri0o+TwOeFxqWpcyIKLkYWAi6iXHu1vteBfFdzWl19SiQTct1DZEkOt3dntBuG5Y8UKUvTwF99m2erz45hY0tWgJ7WdNHIIrZo6Fz929UZu9tS2obYjA5+l8KtLncqC2IYK9tS0YOTj3uPvbFpS8Hge8DEpE/R4DE1EvONHdasezKP6YU3oRA7ppwaEoGJDv7vaC8HBUR0vE6NUpuEBIw8urtuLjLXUJ7QMLvVgwrwJlIwp6dL1QxIBl21CVzj++VFVCRLMRihidPt4VCYCqyPB5VHjdHUMZEfVPDExEJ6gvd6sd6WhTeiWFXtQ2hJF72JRVm84WhFu2QLCXp+BsIfDep9X469s7ENXM9nZFljBveinmTS89rsNn/V4HFFmGaQk41Y6/n6YpoMjxtUY9waBERMfCwER0gvpqt9rRdDal1xzS8MTLn8BxlANp2xaEh6IGNMNCsJen4A4cDOOFlZuxfV8goX3MsDwsmDcegwf4jvvawwfmYGCRF9X1ITh8zg5TkWHNwNBi/zHLERxOAqC0BSWXo9/XByOizqVVYHrqqaewfv16/PnPf25vu+eee7B8+fKE5w0cOBDr1q3r6+4Rdao3ClCeqCOn9LbvbT7mgnDTtFGY64bLqaAxEEs4q+1EGKaNleursHJ9VcK0nsel4oqZY3HWxCGQT3DkRpYlzJtWihfeqERzWIfP5YCqSjDNeFjyOFXMm1baZfCRAMiKBL/bAa+bQYmIji1tAtNzzz2HJ554AlOnTk1o37JlC7797W9jwYIF7W2Kkp4Vf9NNX58v1l+daAHKZDjWgnBZBhxOBUMG+JDjdfRaWNq2pwkvvFGJmoZIQvtp40pwzZxy5PldvfI+AFBRWoj5cyva6zBFtHgdpqHF/m7VYVKU+OJwr8cBhX8miKgbUh6Yamtrcd9992HDhg0YNWpUwmOWZWH79u247bbbUFzcf88cOx59fb5Yf3aiBSiT4WgLwuPhQIJTlTBl/MBeWacTiRlY/tZ2vLdxf0J7QY4L114wLmk/bxWlhSgfUdCjSt+KLMHnZlAiop7r+YrLXvbFF18gLy8Pr776KiZOnJjwWFVVFTRNw5gxY1LUu8zUtmOran8QbpeCghwX3C6lfcfWxm31qe5iVmkLJx6XioagBk23YNsCmm6hIah1WYAyWdoWhJcOzoWmW7BsAYeqINfnxNxppRg38sQKOwoh8NHmWtz/zPsJYUkCMPP0YfjJLdOSHs5lWcLIwbk4eUwRRg7OPervsSJLyPE4UZzvQY7PybBERD2W8hGmWbNmYdasWZ0+tnXrVkiShOeffx7r1q2DLMuYMWMG7rjjDuTkdG9BZ3+Tyh1b/dmJFKBMdr8mjBmAqv0B1DZFIUnA0GL/Cf+3bwzE8OKbldi0oyGhfWixHwsurMCoIX03mnYssiTB61Zbq4Gn/O+HRJTBUh6YjmXbtm2QZRlDhw7FwoULsXv3bjz88MPYunUrnn/+ecgyPwCPlOodW/3Z8RagTDbdtODzOjHCdeJ/3G1b4K0Ne/Hqup3QDKu93aHKuOisUZjzlRFQ0iCYyJIEt0uB3+M8rtIFRERHSuvA9N3vfhc33HADcnPj1XrLy8tRXFyMa665Bps2beowhUfpsWOrPzueApTJIoRAS9hAOKajN+pQ7q1tweLXN2N3TUtCe3wB9jgUF3hP/E1OkCwBbpcKn9sBp4ObQ4io96R1YJIkqT0stSkvLwcA1NTUMDB1Ih13bFHfM0wbwZAGzbBwollJNyy89t4urP7PnoQddT6PA1fPLsMZJw9KeZFHWQKcDhV+rwMuBiUiSoK0Dkx33nknmpubsWjRova2TZs2AQDGjh2bqm6ltXTcsUV9K6oZCIR1WNaJDyt9uasBS1ZW4mAgltB+xsmDcNXsMuR4Uxu840FJgd/jgMuZ1h9nRJTh0voT5uKLL8Z3vvMdPP3007jooouwa9cu/PSnP8XFF1/MnXNHcczzxaJGynZsUfLZtkBLREckZpzwFFxLRMfSNdvwwRc1Ce0D8j2YP68C47uoc5RskgS4GJSIqA+l9SfNzJkz8fjjj2PhwoVYuHAhcnJycMkll+COO+5IddfSWrru2KLkMUwLgZAO/QSn4IQQeP/zGixdsxXh2KHz32RJwpwzRuCis0aldG2QJAEuVYHP64CbQYmI+pAkRG8dtZkZZs+eDQBYs2ZNinuSfKz03T+EYwZawnrCUSTHo64pgiUrK1G5uymhfeTgXFw/rwLDunk2WzIwKBFRqr+/+cmTxdJpxxb1PtsWCIQ1RDUTJ/LXHsuyseo/e/CPf+2CcdgBvC6Hgq/NGIPzThuWsqAtSYBTVeDzqPC4Ot/5SUTUFxiYKKU4CnZ8dMNCIKRBPyzgHI9d+wNY/HolqutDCe0TxgzANy4Yh8I89wld/3gxKBFRumFgopTheXfHJxzV0RIxTmgKLqaZ+Nu6HXh7w76ENU+5Pie+fn45Tq8oSUmpAAYlIkpXDEyUEm3n3UVjJnJ8DjgUBwzLbj/v7varJjI0HcGyBYK9MAW3cVs9XnpzC5patIT2cyYNwWXnjYXP3fdBRZIAhyLD73UwKBFRWmJgoj6XLufdZdJ0oKabCIb1E5qCa27R8PLqLfhkS+Lhy4OKvJg/rwJlwwtOtJs91haUfB4HPC415QUwiYiOhoGJ+lw6nHeXSdOBoUh8Cs4+zmElWwi892k1lr+9HTHt0PlvqiJh3vRSzJ1W2ufnrTEoEVGmYWCiPpfq8+4yZTrQsmw0h3RoxvFPwe0/GMILKyuxY18goX3ssHzMn1eBwQN8vdDT7msLSl6PA14GJSLKIAxM1OdSed5dukwHdkXTTQRCOgzr+KbgDNPCyvW7sXJ9VcLicI9LxRUzx+KsiUMg92FYkQCoigyfR4XX3XFkkYgo3TEwUZ9L5Xl36TAdeCxCCIQiBkLR45+C27qnCS+srERtYySh/fSKEnz9/HLk+V290dVuUxQJfrcDXrcjbdeIERF1hYGJ+lyqzruzbYHKqkZENRMOhwyB+MjH4ZI9HXgspmUjENKg6cd3vEk4ZmD5W9vxr437E9oLcl34xgUVOHXsgN7paDcpsgSf2wGvxwGFQYmIMhwDE6VEX59317bIu2p/EOGYgahmwOlQUZDrgtd16I9BMqcDjyWqGQiEdVhWz6OSEAIbKuvwyuqtCUFPkoCZpw/HpeeO7tPjRBRZgselwu9xQFH6djE5EVGyMDBRykwsK8aEMQOSvrX/8EXefq8KTTehGRY03UR9k43iAg+8LjXp04GdEUIgGNYRiRk4njqUDYEoXnpzCzbtaEhoH1bix4ILx6N0cG4v9bRrsiTB444HJZVBiYiyDAMTpVSyz7vrbJF3Qa4b9U1R2MKGZdloDMQg53sQSuJ0YGcM00IgpEM3ej4FZ9sCb23Yi1fX7YRmHCoV4FBlXHz2aJw/dXifje7IkgS3S4Hf44BD7biIn4goGzAwUZ/ry4KRnS3y9rpVFBd40NQSg27Y0A0LodaRpb6qwxSOGWgJ68d1vMmemhYsXrkZe2paEtrHlxbiurnjUFzg7a1uHpMsAS5nfETJ6WBQIqLsxsBEfaqvC0YereaT163C4/IhplkIhHVcM7scXz1r1AkFt+4EwRM53kTTLbz2r51Y85+9CTvo/B4Hrp5dhq+cPKhPtutLEuByxEeUXH24NoqIKJX4aUd9JhUFI49V80mSJMitC5QrSgtPKCx1JwhqhoVgSDuu402+2NmAJW9UoiEQS2ifdsogXDWrDH5v8heptx2M6/c6+nQRORFROuCnHvWJVBWM7IuaT10Fwf97zSSMHJyLUMTo8RRcMKzjL2u24sMvaxPai/M9uG5eBcaXFh53v7uLB+MSETEwUZK1TVNVVjWi6kAQ/j4uGJnsmk/HCoKefAWmLfCPf+3CdXMrejRdJoTA+k0HsGztNoRj5qH7kSTMOWMELjprVNLXDUmILyLnMSZERAxMlESHT1NFNRPhmIGYZqIwz51Q+whIbsHIZNZ8OlrlcJdTgc/tQCRmoLKqEXtqWjCym1v8axsjWPJGJbbsbkpoLx2ciwUXVmBYSc5x97c7JABK6zEmPh5jQkQEgIGJkuTIaSqnKiOqmdANC/VN0fbaR22SXTAyWTWfjlxULgHwe51wqBIiMSNeuduwEIoYXV7Lsmy8+cEe/ONfu2Aedoacy6ngsnPHYMZpw5Je7kBRJPhcDvg8PMaEiOhwDEzU6zqbphKqgNMhQzcsWJaNpqAGT7EKCck/P65NMmo+Hb6o3OtQket1QgiguUVDTLdgmAKKHF//cyw7qwNYvHIz9teHE9pPHTsA114wDoW57l7t95EUWYLX5YDPy2NMiIg6w8BEva6zaSpJklCQEy8YaQkbumEiqplQJCmp58clW9ui8trGCPK8TuiWjUCLBssWEEIgrBkYWuzH8IGdT6NFNRMr3tmBdR/vSyhemed34przx2HyuOKkTonJkgSvW4WP1bmJiI6JgYl63bFqHxUXeNAUjCFmWAiGdHhcap8WjOxtsizhmvPLseTNLahuCMMyBVRVgmnGw5LHqWLetNJOg+CnW+vx0qotaG7REtrPnTwUl80YA687eTvS2o4x8bnji+CJiOjYGJio1x2r9pHXrUKW3AhFTVxzfjkqSguTWuk7mWxboGp/AC0RA5PLivGfL2tQ2xhBRLOhyDKGFvsxb1opKo7Y+t/UEsMrq7bik631Ce2DirxYMG98Uo+KYVAiIjo+DEzU67qqfRSKmSgdknvClbVT6fMdB/HGB7uxr7YFDYEoAAkDC72YN70UA/I88HsdGD4wJ+H+bCHw7ifV+Os72xHTDp3/pioS5k0vxdxppUkLMTzvjYjoxDAwUa9Ldu2jVPti50EseXMLGpqjsIWAz+OAaQlUHwyhIRjD/LkVHUoI7K8PYfHKSuysDiS0lw3Px/x5FRhU5EtKXxmUiIh6BwMTJUUyax+lkqZbeO29XThQH4LHpUCV4iNCTlWCw+dEc1jHyverUD6iALIswTAtvP7vKrzx/u6EKt9el4orZo3FmacOgZyERd0MSkREvYuBiZImWbWPUiUSM7B5VwM2VzXCocqdViz3uRyobYhgb20LYrqFJW9UorYxkvC8KeNLcPXscuT5Xb3eR1kC3K74GqVkVwInIupPGJgoqZJR+6iv2bZAMKIjEjPQENBgmBY8rs7DiKpKCMcs/G3dDny5qzHhscJcN75xwThMGDug1/soS4DLqcLvYVAiIkoGBiaiY9AMC8GQBt2MV972ex1QZBmmJeBUE0eYhBBoCRsIRc2EsCRJwKwpw3HJOaPhdvbuH7m2oOTzOOBiUCIiSpq02lf81FNP4frrr09o27x5MxYsWIBJkybhvPPOw6JFi1LUO+pvQhEdjYFYe1gCgOEDczCwyItwzIAQh9YkmZaN+uYYAmEdhzVjeIkfP/o/U3H17PJeDUuyBHhcKgrzPCjMdTMsERElWdoEpueeew5PPPFEQltTUxNuvPFGlJaWYtmyZfjud7+Lxx9/HMuWLUtRLylVbFtg+95mfFxZh+17m2HbousXHSfTstEQiCEY0WGLxPeRZQnzppXC7VTRHNah6RYCYR0HDkYQ0w+VCnCoMq6YORY/+ubUbh+62x2yBLidKgpz3QxKRER9KOVTcrW1tbjvvvuwYcMGjBo1KuGxV155BU6nE/fffz9UVcWYMWOwe/duPPPMM7jyyitT1GPqaxu31bfvtjOt+CG9Q0v8SdltF9WM1krlRw9kFaWFmD+3Aive2Y69taGE3W8AML60ENfNq0BxvqfX+iVLgNMR3/Xm6uVpPSIi6lrKR5i++OIL5OXl4dVXX8XEiRMTHvvoo48wdepUqOqhL4hp06Zh165daGho6OuuUgps3FaPJ5duRNX+INwuBQU5LrhdCqoOBPHk0o3YuK2+64t0gxACgZCG5hbtmGEJiJcW+HxnA3bXtCSEJb/HgRsvORnfu2ZSr4Wl+IiSgsJcN4ryPAxLREQpkvJP31mzZmHWrFmdPlZTU4Py8vKEtpKSEgDA/v37UVRUlPT+UerYtsDStdsQjZkoynO1b+N3yQqcuTIaghqWrt2GCWMGnFCpAsO0EAjp0A0LXU30fbGzAUveqERDIJbQPn3CYFw5qwx+T++c/yZJgIsjSkREaSOtP4ljsRicTmdCm8sVr12jaVpnL6EssrM6gOq6EHJ8jk5rHuV4HKiuC2FndeC4SxeEYwZawnqHabUjBcM6/rJmKz78sjahvbjAg/lzKzqcF3e8JAlwqQp8Xkev76gjIqLjl9afyG63G7quJ7S1BSWv15uKLlEfiq8lsuFQOh+1cagyQtH4mqOesmyBYFhDVDMhjpGVhBBYv+kAlq7dhkjMbG+XZQkXnDECXz1zVLfrHtm2wN7aFoQiRoez5hiUiIjSW1p/Mg8aNAh1dXUJbW2/HjhwYCq6RH0o1+eEqsgwLBsuuWMoMcz4AvBcn7OTVx+dppsIhvWEcgGdqW2M4IWVm7F1T3NC+6ghuVgwbzyGlvi7/Z6VVY1Y+X4VahsisGwbiixjYJEXF581CiePHgCfR4XH1TvTeURE1PvSOjBNnToVL730EizLgqLEvzDXr1+PUaNGcf1SPzB6aB6GlvhRdSAIZ27iUSRCCLREDZQOzsXooXndup4QAqGIgVDU6FAu4HCmZePND3bjn/+qgmkdClVup4LLZozBuZOHdWvNVNuI0uZdjXjnk30wLRs+jwOqosKhKjBMG29+sAcD8j04eXTvV/8mIqLek9aB6corr8Szzz6L++67D7fccgs+++wzPP/883jggQdS3TXqA7Is4apZZXhy6UY0BDXkeBxwqDIM00ZL1IDXpeKqWWXdCi+mZSMQ0qDpHRd2Hz5V1hzSsPrDPThwMJzwnIllA3DtnHEoyHV3q+/tI0oHwwhGdFg24HTIrbvd3HCoMjTdwt66EF5atRUP3FqUsWfsERH1B2kdmIqKivDss8/iwQcfxOWXX47i4mLcdddduPzyy1PdNeolti2OeTjvxLJi3H7VxPY6TKGoAVWRUTo4t9t1mKKagUBYh9VJuYC2YFNzMIxwzIRxxDRdnt+Ja+eMw+RxJd2+p8qqRrzwRiVimgmnQ4YAkONV4fc4IYRARDMhogKWLeB1qSe8cJ2IiJIvrQLTQw891KHt1FNPxcsvv5yC3lCydbcg5cSyYkwYM+CYwaozQggEw/FDczvbBNcWbFrCOnTD7jBNN2pwLi47bwzKhhd0+55sW2Dl+1WIaSby/U5IsgSHqsCpyojpJhobY5BlGUOKfZBwYgvXiYio76RVYKLU6Wqkp7evvWnHQTy5dCOiMRM5PgccigO6ZWPHvmY8tuRjXDunHHOnlbb3QZalHo3AdFVbybYF/v7eTjQFYx0KVUoABIA9tUE89/cvMHCAD/OmlXardMDe2hbUNkRQlBc/usQWwL7aIAIhDbYN2AKwTAuabsHtVI574ToREfUtBiZK6tEjnV17SLEPoaiRUJAyoploCmrQDRO2beCZv32Of322H1fPLu9xH8JRHS0R46i1lWwhsOKdHdixL9DhMVkChAAUOR6aZEVCdX0IL7xR2a16S1HNREGuG0W5LpiWjUjMQDhmQjdsKLIESUI8ONniuBauExFRaqT8aBRKrWQePXK0a++oDmDX/iAcDrk9LNU3RaEbFmRZhqJKsG2BHdWBHvXBsgWaWmLx9UpHCUvV9SE8sngD3vxgd0K7yyFDVaV4WFIkyK3DTLIsId/nREw3sfL9qqMe+itJgFOVMazYDxnAwUAULREDtg0U5LghSxIsW7S+XsC0bTQEtR4tXKe+15eHPhNReuMIUz+WzKNHjnXtHI8D4Wi8wnau14mmoAbbFlAVCUA8tFgQyPE4ENXMbvVB000EQjoMq/PaSoZp4Z//rsIb7+9O+NKTpPgZcFHdhGnG29um6GQJkKV4qPO5HKhtiGBvbQtGDs5NeL1DkeH1OOB1qSjK88Dvc6LqQBBFufH79rpVFBd40NQSQ0y3oMgybBs9WrhOfa8vD30movTHwNSPJfPokWNdW1FkyJIEw7QQihowTKs1DMWfJxAPIooiI8cjH7MPQgi0hA2EY0evrbRldyNeWFmJuqZoQnuOzwHTiE+b2Z3kLFsAtm0DiI8+RTQboYgR//0BoCoyfB4VXvehe5QkdFoKQZElOB0KfB4HLjprFCaVlfTqOrG+lsw1b+mgbXT08DV2hmW3j7zeftVEhiaifoaBKYt050vs8Ofsrw/BMC3keHv/6JFjHWvicsitu8as+KJsAcitk8NCxKetnA4ZLocMIXDUPhimjWBIg3aUhd2hqIHla7fh35sOJLQX5rrxjbnjoMoSnlq2EZYdX7N05OCU1HofbqcC0xRQZBm5ficcnQSlwx2tFMKoIXlZMTrR05GXTAtXfXXoMxFlFgamLNGdL7EjnyMAhGMmHA4deT5Xh2ueyA6uYx1rIkkS/F4HNNOGZlgABGwbrQuiBWRJQkGOG5IkQTesTvsQicVDVGdrlYQQ+PDLWvxlzVa0tI4Ixd8XmD1lBC4+ZxTcThW7DwThcqiAZME+Ii2psgRI8YKXumHDEgIVpYU4eVQRfB5Hl1+Ux1sKId31dOQlE6e1+uLQZyLKPAxMWaA7X2IAOt3GH4roaGiOxaeX3IdGg050B1dXx5oYlsCoIbnwexz4clcjTMuGIserYRfkuOF1q532oatDcw82R7HkjUp8uasxoX34wBwsuLACIwcdWn8UihiQZWBgvgeGJRDTDYRaF2rHZwcFHA4FDoeCQbluXHruaOT0IDz2tBRCuuvpyEumTmsl89BnIspcDEwZrltfYmu2QUB0eI5bVlBc4EFtQwT1TVEohfF1Nsdz9MiRunOsyY0Xn4wJYwZg5ftVeHnVFuimjXyfE06HAk23OvThWIfmWraNNR/uxd/f3ZlQrduhyrjknNGYPXU4FDlxU6jf64AiyzBtAZdDhsvhgsuhIhDSIcuA3+OEU5UxuMiLy84bi1P6+XlvPRl5GT00L2OntZJ16DMRZTYGpgzXnS+xqpogINDpc3xuB4ryPWhu0RCKmpBiZo+PHjma7h5r8tUzR2Fosb/9eeEj+nDq2AFoCetHPTR3d00Qi1+vxN7aloT2k0YV4to54xDVTFTuaoLf68DwgTntX9DDB+ZgYJEX1fUhOHzO+O+X14FBA7yQIKExGEOez4V7bzgDqpoYtjJtXU5v6MnISyZPa/X2oc9ElB0YmDJcd77EzNYRF4fSedmtHI8Dpmnj67PLMaTY36sBoLtreY72PFsINAZj8YXdR2SlmG7itXd3Yc1HexIey/E6cPXscuR4HVjyZiVqGyKwbBuKLGNgkbe9arcsS5g3rRQvvFGJsGZiYL4Xfo+KmGGhtikKRZZw7QXjOoSlTFyX0xt6MvKSydNavXnoMxFlDwamDNetLzE1Xra6qy+6itLCpPxtv7treY583rEOzf18x0EseWMLGoOxhPbpEwbjylll2Ffb0n4Ars/jgKqoMC3RoWp3RWkhbr7kZLz/+QEcOBjGnrowbFscNQBl6rqc3tCTkZed1YGMntbqjUOfiSi7MDBluKN9iQkAMc1Ec0jH0GIfPE4Vu2tbMmKKwbYFgpH4oblHjioFwxpeWb0NH22uTWiXJcDrdqCpJYY9NUG8+cHuQwfgtt6vU5Xg8DnRHNax6j+7Mb60EDleJ6ZNGILpE4Z0qyRDpq7L6Q09GXnJhmmtbN3pSETHh4Epw3X2JWbYNpoCGnTTggSgtiGCAQUeyLKU9lMMumEhENI6LOwWQuDfnx3AsrXbENHMhMd8HhX5ficsO370yZ//+SUMS8Dv6bh+RlVkDCnyQ9hAVLMwpPjQCEdXo2CZvC6nt3R35CVbprWybacjER0/BqYscPiX2K79AbSEDQgIOB0KCnNcUFUZDYEYZElCUZ4bwZCellMMoYiOlqgBu/XMtb21LQhFDGiGhbc27MW2vc0Jz5dlCcX5brgc8SkfRQYcPicOBuKH+Ob7nQnP9Xsc8LhV2LbA/oNhBEJaj/qXyetyelNP1qVxWouIsgUDU5aYWFaMk0cV4e4n34VphlGQ44TLqRyajmqdMvJ7HLjtyokIRYykTTH0dAeZZdloDunQjHhtpcqqRqx8vwo1B8OIaiY0I3G0yemQ41W3fY72sNRGkiR4XQpimomoZiLH44TXo8LndkCSgIhmIdCiwTRFj9fPcLv5Id0deeG0FhFlCwamDNVZKKk6EERTUENhnqvTIJHjcWB/fRiyJOG0ipKk9KunO8hirYfmmq2VtiurGuO71iLxekvmEQu+xwzNw7mTh2LZW9vgUDvf9edxqVAVDYqiYEC+G5IsQdMsRDUT9gmsn8mGdTmpwGktIsoGDEwZ6GihZGLZgJROGfVkB5kQAoGQhq17mtHcosHvdWBosR//+PcuNLdoCcUnAUCRJTgcMhwOGQMLvfGCk5aAUz1yLRHgdqoYOSgPDoeCmqYoZAGovbB+JlvW5RARUc8xMGWYY4WSfXUtsIXotSmjnkyt9WQHmWULbNhcg1ff24l9tSFYtg1ZkuBQZRwMxDrsjPN7HMj3O2FaArUNEQDoUHBSAuB1xw/EbYkaGJDvwYXTS7Hsre3xYNlL62e4LoeIqH9iYMogXYWSg4EYbFugJWzAmXdiU0Y9nVrrzg6yYEjDtr1NqG+K4k//+ALRWLxGEiCjKaijOZQ48uVQZBTmuuByxsOfKgERzUY4arYXnGwO6yjO8yDP7wIgUNcchW0L/J+vnoSJZcU4dWxxr6+f4bocIqL+h4Epg3QVSnK98QrLqiqf0JTRxm31+N1fPkUoYsDtUuB1qZBkHLM447F2kCmyhOICD0IRA/vqQlj5fhWiMRN5PgdCMROBFh1HlqbM8zmRe8R9mqaAIsvwex0YOTgX/+er4/H+5zVoCsbQGIwhplkYXOzrsL09lcU4iYgoOzAwZZDubGuXZQkXnTkKG7fXH9eUkW0L/Om1L3CwOQoAiGomJCl+7fwcF6Ka2WlxxqPtIHO7VPhcKsIxA00tMQRaNNQ2ROB0KKhpjHZY1N3m8B1+QHyELKwZGFrsx4hBOXCqMr5y0iCcM3Eodu0Ppu1IT388c46IKBsxMGWQ7m5rn1RejCtmjj2uL+o33q/Crv1BQAgoigxZilcN1w0bB5tiyM9xdlqc8cgdZLIcP8hWUWQEIxr21YcxtNgPl0tBOGZAP6JUABCv1m235qfmkIbCHDdUVYJpxsNSns+Fy2eMRUGOC173odGndB3p6a9nzhERZaPO92VTWmoLJS0RA+KIldFta5SGlvjbw9HY4fk4raIEY4fndyss2bbAyvd3Q9gCiiJBliRIUvzfiizBFgKhiAHDtDrstGvbQeZxqQhFTfjcDgghobYhgn31YXicKk4qLcJLq7Z2CEuSBKiKBEWRobbmQBkSNCP+PrYQOHlUEf7rslMw7ZTB8HmcHaYk003b4vyq/UG4XQoKclxwu5T2ac2N2+qP+lrbFti+txkfV9Zh+95m2Hbno3BERNR3OMKUQZK9rX1ndQCNwRhkGQA6rpGSZUA3bbicaqc77SaWFeN710zCG+ursKe2BY3BGCRIGFTohaooWP729g6vUWTpUH+FgG3Hp/9cThnnTh4Gr0vFkAE+TD91CFxOpT1MdHXmW0929/X2lNmJnDnHUSkiovTEwJRhkrmtPRjWIQFwqAoM00Z81u/QF7oEAVsIFOa5O91pZ9kCQ4v9uGbOOOypaUFLWMfu2ha89dFehKJGh+dLiI8uQQgIxIOGLEnI8aiQZAlf7moAhEBMt7Bmw15MHleCT7bUHTNM9CRwJCucHO+Zcz2pY0VERH2LgSkDdbWt/XhHTdrWSOX4nGhu0WBaArIcDzVCAJYVDzRzp43scD1NNxEMx6tzS5IEr8eBv63bgS93NSY8b8TAHMyeOhx/WbMNmmnBtmzYIv4eLoeM4nwvbAgYpoBhWpAlCZCAbXubsWn7QbhdKgpzXZ2GCQDdDhzJDCfHc+bciYxKERFR8jEwZaijbWs/kVGTwxduD8h3o7lFh2FasG0AEJBlCSMH52LetNL21wgRr/sUjhmwhYBl21jz4V78/d2dCdW6nQ4Zl5w9GrOmDocECes/P4B9dSH4/C4ICPg9ThTkONEQjKGpWYdp2/B7/ZAAOCUZtm3DtgUsy4bToUDCEWFizTYIiG4FDgBJDSfHc+bc8Y5KERFR3+Ci7wxzrAXBJ7LQGEhcuB3VLBTluVFS6EVhrhtetwPFBV7cePHJ7SFCNyw0BGIIReMLs3cfCOKh5z7E8re2J4Slk0cX4f/dPA1zzhgJRY7voJs3rRQelwohAQMLfSjKdaM5pGNvbQhR3URBrrt9MlAzbBimDUWRYFo2NN1qv3ZbmKiqCWL3gZZuBY6ehJPj0ZPF+W0OjUp1/kfSocowLTtpx9oQEdGxcYQpgxxr9GjCmAG9Mmpy5Bopw7QASCgu8GLutJHtIzShiI5Q1IBlC8R0E6+u24m3NuxNONYkx+vA188vx5TxAyFJEmxbYG9tC0IRA7l+J26+9GS8vyk+0nTgYBhG63TegAIPvK5DP5qWbUMIQJYB20aHXWMOVYbZGtCOFTgOnwZL5pl7x7M4/3hGpYiIqO9kRGCqrq7GrFmzOrT//Oc/x9VXX52CHvW9rtbcXD5jzFFHTQDApcrYVR3AOx/vw4zThnUZmiaMGYA33q/Cyvd3ozEYQ1Mwhr+9swObdzXg7ElDMXxgDoQANu04iBff2ILGYCzhGmeeOhhXzixrPfoEqKxqxMr3q9AYiMHnccDjVFGY58KpYwdg3IhCAIDHrWLxysoOoUeR5fZ1VJKEDn03TBuqKgMC3Q4ch4cTAUDTrfii89Zrn2g46eni/CPrWJ3IsTZERNT7MiIwbdmyBS6XC6tXr074IsnJyUlhr/pOdxYEr3x/NwzTQo43cdQkEjPR1BKDbsbXAC169XOs3bC3yzVNm3YcxF/f2dEe0PL9LqiKjF0HWlC5+3NccvZofLK1Dh9trkt43cBCL66bW4FxIwva2yqrGvHy6i1wKDKGFPshS0BtYxhb9zbh35tq4HIocKoySgq9yPPF1zEdHhpcDhkOVUZMs+ByKu1nywGHhYlBuRAQ2F3T0q3A0RZOTJfdvlYrPjomIEnxtVonGk56cuZcsktGEBHRicmIwLR161aMGjUKJSUlqe5KSnRnzU18hEdKGGGJxEzUN0VhCxEfmZGQsKbpaDvBDg9oxQVu5PqckGUJobAOyzTR1KJh0d+/SJgaU+T47rkLzyyFQ1USrvWvz6qR44mfDRfVLDS1aKhvih8UbIv48SuaDgQjOhRZgtft6BAaZFmGLMdHiXTd6hgmZpcBQLcDx1WzyvDYix+jtiECIB5YJBmwrXjAagpq2LTj4Alv4+/JmXPJLBlBREQnJiMC05YtWzB27NhUdyNlurNNXQJQkOdGY+voDAA0tcRgCwFFBiwbcDpU+L1O+IU45pqmtoBWXOBGQa4bpmmjoTmGqGaiMRiDdkSl7tFD87BgXgWGFPsT2mUJaGzREIoYgAQ0h/R4GGmJwbJtHL4USVFkCCFgWQKRmIGRg3IRDOvtoaFseH5CHaajhYnuBo4JYwagIMeFYEgD0Drdh/gZdvEz86yUbOPvyagUERH1nYwITFu3bkVxcTGuu+46VFVVYeTIkbjttttwzjnnpLprfaK7C4LnThuJFe/sQENQg0uVW2sixcOSLEsoyHXFd551sU09GNbh86jI9zsRiRoIhjQEwgYCRyyCdqoyrpxVhrMmDkF1XQhf7GiA3+vAiEE58LhU+D0O1DVGUdsYQb7fBVmW2ne8tYUlCfGz6oC2tUp2e/2nH31zanyB+GGh4bJzxxwzTHQ3cOysDiAY0jGoyAtAgmXbUGQZLkd8Ok+V5ZRt4+/JqBQREfWNtA9Muq6jqqoKHo8Hd911F7xeL1599VXceuut+NOf/oTp06enuotJ190FwfOmlWJosR9L127DrupAa+Xs+MhSQa4rYefZsXaC5fudcDtV1DfHEI2ZaAxqMKzEUSWHKuO/LpsAVZXxu798itqGCJwOGfl+FwYX+zBvWilOHj0APo8Dinwo7B0+stTZmIkECZIE1DVGIUsSTqtInIbtTpjoznPaRu1yVEdrmEoMoie6U46IiLJL2gcmp9OJDz/8EKqqwumM71o65ZRTsGPHDixatKhfBKbuLggGAJ/bga+dOwbb9zbj7+/thMelwO91dggnR9umHokZ8LpVCAhU14cT6ikB8bVKDkd8mktWJCxeuRmGYaO4wA2f2wnDsrBpRwO27G7G7VdNxIQxAxLCniIn7oATaN351hoC235tC5HUsJLsbfzJOKOuL2Rqv4mIki3tAxMAeL3eDm3l5eV47733UtCb1OhsQbAiSygp8GD6hMGorg/hL2u2Yn99GKZlQ5ElCCEQjprwexyth7bFdbZrzLJsBCM6IjEDH1fWY19tqENY8rpUyArgdTkw94yRWLFuBwAg1+dAMGxgf30YAmhdA2S2rwE6POz53SocigTNjp8fJyG+hb+tX7YtoCoyXA4lqTWHkrmNP1MP0M3UfhMR9YW0r/RdWVmJyZMn46OPPkpo//zzz/vdQvCJZcV44NbpuPeGr+DSc8agMM+DxqCGZWu34/d/3YQvdjYAkkBBjgset9q+A622MdpeZ0jTLTQEtYRdY1HNwMFAFPvqQnhq6Wf4w4pNCMfM9veVJcDrjm/nH1aSg+vmViAY0uOjMLKMQNhAc4sGwxLQDRsHm2JwKBL21bbgnY/3wbIELpsxBiMH5UAz7PaABACKIkECWo9Vie/mU1UZwwbmJLXm0OFVzRuC2jF/f3riRKutp0qm9puIqK+k/QhTeXk5ysrK8MADD+AnP/kJCgoK8Morr+DTTz/F0qVLU929PifLEsIxA2/+ZzeiMRN+nwOhiA6I+IhNU1CDEPE1OAV+J5paSwpEdSth19jVs8tw8ugBaAzEsHVPI979dD/e//wA9CNGlZwOGU5VRn6OG2dPHIKxw/Jg2cBbG/aiJawjppuQpfgIjQRAkgHLFgiE4selLHr1c8iyFB+tKPbj6tllGFjow4bKWqx8vyq+AFyKD4CpigxVlZHnc/ZJzaHe3safqQfoZmq/iYj6UtoHJlmWsXDhQjzyyCO44447EAwGcdJJJ+FPf/oTxo0bl+ru9bkjv9w0w45PwbVuyzctgYPNMcitFbEVWYZTljD3jJGQJQnFBR6cM2koTNvGB58fwCurt6DqQAusI44bUVp31bmdCgzTRiiiY90n+/DhlzWI6RZqGsKw7PjzDl8CFP+yFfEdeojXffK5W6uS1wRR2xTB7VdNxK2XTcCUkwZi8eubUdsQgS0EXA4Fwwbm9OkUUG9u48/UA3Qztd9ERH0p7QMTABQWFuIXv/hFqruRFo78crNt0V5DyLIOhR5ZliBJEgzTgmZYWPHOdnhcKgpz3dhQWYuSQi9e+9cuRA+bejtcQa4TXld8Wk9R4sUkI63Te7IswW4diLJsAVmKF5YEDq1DAuJTa20LzjsbrZhcXoKJY4tTvsi4t7bxd6deVjruvMvUfhMR9aWMCEx0yJFfbm3hwrRsHD5GJLXui2sbOHKoMkYOzoFmWNiwpS5eTPIYojELhTluRGMmNN1GIBR/3/g1RftuNiEAwxJQYceDVOtjAJDvdyXszutstCKbag5l6gG6mdpvIqK+lPaLvinR4V9uEc1EQyAGyxYQRz5RiocoWQIKc93I8TrQFNSwqzp4zLAkyxLy/S7k57gQjhk4GIyhIRBrD0sAWs9ci/9bllqLT7ZW6W4bXXKqMnL9Hb9gHaoM07JPeLTCtgW2723Gx5V12L63OeGYllRp23nXEjEgRGJ/2nbeDS3xp90BupnabyKivsQRpgzT9uW2fW8zYroJIeLriI5cg2SaNtwuFXl+JyQI1DREYLZO3x2N3+NAjtcJAYHmFg1R3WwfqTrc4dW5bREfacrLcUGRZIRjBmK6hbwcV6eFKXtjtCJdt79n6gG6mdpvIqK+xBGmDCPLEq6cORa6acFqPULkiHW6rceguFHQWg/pQEMUhnX0sOR2KhhY6EWOz4lwzEBdYwThmAlhA5LUyYukxCrdQgC6bgEAyobnY9SQXBimnZTRinTf/t628650cC5ievyg4ZhuoXRwLm47ymHH6SBT+01E1Fc4wpSB/B4nPE4VkmTBsuz2Rd8CgN+rIsfjgmXbqGuKwLSOPqSkKjLyc5xwqgpiuoVgWEt4vgA6hKwjxxgkKT7Cdd0FFRg/qgijh+Zh046DSRmtyJTt75l6gG6m9puIqC8wMGWgYFiHLEsYUuSFYYn4+Wy2gLAFVFVBMKwjFD32OqVcX3wXnGnZaAjGoLWOEB35vCOn+kT7/8QpsgS3U8XQkpz2xdu9Xd+oTSZtf8/UxeyZ2m8iomRjYMpAuT4nFEVGRDOhyDJyvU7k+V1oDMSw60CwQ8gB4ouzAcDnccDvdUIIgeaQhshRygo4VBmXnjMaq/6zBy1hHZIMCDshK8HpiBeZBKQOa5KSMVrB7e9ERJQqDExp4vBDT/3eeCAIRYxOg0ZLVIemm9ANC/n++G62AwfDaIkaHabQ3E6l9Xw2CTk+F2RZgq6baIkYHap6t5EAjBiUg//z1ZMwqbwY//vnjxCKGq2H5AJK66LtXK8DjS06Sgd3foxJb49WcPs7ERGlCgNTGjh811dUM6EZ8ekxl0OBx6Um7ADbuK0eC5d9Br/HCdUPRDQL9fVhHDmopMgSivJc8Lod8HsdUBQFwZCGfXUtKMh1Y0C+B7WNkU5Ho3J9Ttx48cmQZQmTykvww+un4ImXP0FUs+B3q/C6VZiWQGOL3r4mCQC2721O6tqXZB6YS0REdCwMTCnWtusrGjPhcMiI6WZ7TaGYEPC4D+0A+86Vp+Lv7+6E160iz+dAVU0LGgJah2vGay+5UJDrRq7HCUmOj1Y1BTW4nSo03UJOngMDC71oaolBN+I72gTipQV+sOD0hHVGk8tLcMe1p7WHuuaQnrAmCQB+8sz6pG/z5/Z3IiJKFQamFDp811dhngsHDkZg2wKKIkHY8cdbwjqGDPChKaTjb+9sRyRmwbYFPt/V1OlCbSC++02SJMQ0C5atQdMsNIc0OFQF50wejg+/rMHBQAxuh4JcrxOGaSNmWPC6VXzvmsmYVF7S4ZpHW5PUtiMuGjOR43PAobSeG9ca8m7v5S3pyVpQTkREdCwMTCl0+K4v3bChGfFClIZ5aJosptvQTRsjBubgYHMMtY0RxI4SlCQAeX4XvG4Vhmmjuj4My7ahtJ4rJwTw/qYDUFUZumGhJWxAQECCBJ9HxcVnj0aOx4mPK+s6nVY7ck1Sqrb5c/s7ERH1NQamFDp811cgpLcfaNtGkSXk57ggBLC7JojmlqPv/vK0V/WWOux+s2yBIQM8cDlUtER11DaEAcTDlcupQAiBUMTEkjcq8de3t0OWpG5Nq6Vymz+3vxMRUV9ipe8Uatv1pZsWgpHEMOT3OFBS6IUsSTjQEDlqWFIVCUV58areMd1CbWO4Y6kAET+MV5Lia5nask1Mt+DzOKDIMjTDhGHYiGkW8rtZPftQ4Ov8x6i3zo0jIiJKNY4wpVDp4FwU5LpRdSAAo3WLv9upxOssyVL8PDet8zpJAJDjjddUsm2BhkCsfXfdkQTi4QiSBMO0IcvxgGOYFmKaiaaWWPxMOkWCZdswTBtuZ8dpNQAJ02B+r4Pb/ImIqF9gYOoDh9dYOnyx9NK121DTEIZuxINFnt8Jl0NBRDMRaNFwtENNnKqM/BwXFEVGuJuFGk3Lbj9GRZYASIBtA5phtYao+AiUZYn2XXqHT6u98X4V/r3pQOJOuGI/cv1ONARi3OZPRERZjYEpyQ6vsdQWNHL9TjQFNdi2gM+tQpEleFwqDNNCbVME1jHOf8vzO+FzO2CYNuq7OCvucMGwjkjMgBAiXrNJtB7aK9AeokRr2+GLpx2qjKYWDS+t2grbFok74WqCkGUJsiRxmz8REWU1BqYkOrzGUlvQ0C0buw8EYdsCo4flwetyoL4pgsZg7Ki73wDA5VSQ73dBliQEQhrCRznS5GiEAPTW3Xd2a8iSZQmQ4iFJQMC2AadDgct5aHpNNyxohgVJAkoKPJ3uhCvKc8PvcWB/fZjb/ImIKCsxMCXJ0bbcw4yHnxyPE6ZpI2hpqGmIHHX6TZKAfL8LHpeKmB6vp2R3Up27K529QtgCTcEYZFmGadpQFAkFuS60jQcJIdDcOt2Xl+M66k64YEjHbVdOhCxJ3OZPRERZiYEpSTrbcq8qMvJ8CiAEYqaFfbURCEhHDUvxit4uCAg0dbEA/GhkCR2OTQHiU21CiPjRKLaAwyHDqSpQJAm2Ldqn1ZyqDAjAeYydcKGogVDEwGkVHQteEhERZQMGpiRp23KvKg5ohgWvywG3S4WuWzgYiELT7dag1DHNqEq8/pJTVRCJmQiGtU5DT3coigy7dQeeIkuQ5XggGpDnhqLIiGkmTEvg2gvK8f7nNR2qZ0+fMBhL12zjTjgiIurXGJiSJNfnhC0EAiEdHpeCloiG/fVBRHX7mAu120oFWJZ9zFIB3aEcMSXWNkUmSfEg5XYqcLYu6h5c5McDt07vsJsPANZvOsADb4mIqF9jYEqScMyA3+OAEEA0ZiAU1WGYna8lAuJTW/k5LjiU+BRXT4o9Hm3aDYiHGiB+bIoEAeuIhd2HjxAdrXo2D7wlIqL+jpW+e5ltC2zf14y/vbMdlg3UN0XQ1KJDP0ZYyvU5UZzvAQDUNUV7XBm7rRzAkSxbwLJE+yJu0xKQ5UMLu9tGiIaW+I85QtR24G3p4FzEdAtNLRpiuoXSwbm4rZcP1yUiIkpHHGHqRZ/vqMcb63dj5/4AahujXU6nOVUZBbluyHJ8d1koahzX+woAausIT2fTfU6HDMMSkCXEjz1xKNB0q0cjRDzwloiI+jMGpl6ycVs9/r9/fomDzVE0BrUun99WgFI3LTQEtG4XoDxca91JAPGq3bIcP4TX3zptZto2dN3GNeeXQ1Ek/PuzA6iuD6GpRTuuWkk88JaIiPorBqZeYNsCf3rtC4QjBqJdFJQ8fFQpENYRPs5RJVWWYB+2Pqkwzw23M742qW3Mx7YFmgwNQ4r9OK2iBHOnlXKEiIiI6DgwMPWC7fuasftAEKoiH7Nad67PCb8nPqp0sFmL10A6XocNLzlUBXl+J46MPkdu+ecIERER0fFhYOoFm7YfhGkJmFbnYUlVZBTkuqAq8gmNKh3OsuNrklRFhkOVO6z85pZ/IiKi3sNdcr1g+97moz7m8zhQXOCBBKC+KdorYQmIH0tSOiQP8+eNR47PiYagBk23YNsCmm6hIahxyz8REVEvyYgRJtu28bvf/Q5/+ctfEAwGcfrpp+MnP/kJRo4cmequ4XdLP8V7n+0HEB/tURQJmm7Ft+/nuOByKD2uq9SVwUVeXHbeWMybVgpZljBmaB6Wrt3WoUo3D78lIiLqHRkRmJ566im89NJL+OUvf4mBAwfiV7/6FW699Va89tprcDpTdyTHsre24Y31u9t/XZTnRiRmQJYk5PmdEAInXK1bav+feOXuC88chVsuPSVh1Ihb/omIiJIr7QOTruv44x//iB/+8IeYMWMGAODXv/41zjnnHKxatQoXXXRRSvplmjZeerOyQ7vX7YAiS4hqJgKh4z8DTpYARZbhcspQZBkDi7xYcOF4TC7v/IBbLugmIiJKnrQPTJWVlQiHw5g2bVp7W25uLk466SR8+OGHKQtM735ajZhud2iXJQlNLRqi2rHLCxyL26mgINeNy2eMwcBCH0eMiIiIUiztA1NNTQ0AYPDgwQntJSUlOHDgQCq6BCC+gPtIjcEYLFvA7uGwktRaIkCWJfg8Dowemsf1R0RERGkk7QNTNBoPJkeuVXK5XAgEAqnoEgCguMDToc0wO444Hcspowtww0WnoCVqoCWsI8fnRL7fxdEkIiKiNJP2gcntdgOIr2Vq+/8AoGkaPJ6OoaWvnDNpKH7/140Ix3q+oFuWgf9z4XhcOas8CT0jIiKi3pb2dZjapuLq6uoS2uvq6jBo0KBUdAkAoKoyvj6nokN17WO+RpFQPiIfD9w6nWGJiIgog6T9CFNFRQX8fj8++OADjBgxAgAQDAbx5ZdfYsGCBSnt2xXnjQUAvLByM3Tj6NNxEoDTKkqwYN54TrcRERFloLQPTE6nEwsWLMAjjzyCwsJCDB06FL/61a8waNAgzJkzJ9XdwxXnjcWlZ4/GOx/vxX++qEFL1EC+34lwzIQkyxg3PB9XziyD06mkuqtERER0nNI+MAHA9773PZimiR//+MeIxWKYOnUqFi1alNKilYdTVRmzvzISs7+S+srjRERE1PsyIjApioIf/vCH+OEPf5jqrhAREVE/lPaLvomIiIhSjYGJiIiIqAsMTERERERdYGAiIiIi6gIDExEREVEXGJiIiIiIusDARERERNQFBiYiIiKiLmRE4creVFdXB8uyMHv27FR3hYiIiLrpwIEDUJTUHTPW70aYXC4XVLXf5UQiIqKMpqoqXC5Xyt5fEkKIlL07ERERUQbodyNMRERERD3FwERERETUBQYmIiIioi4wMBERERF1gYGJiIiIqAsMTERERERdYGAiIiIi6gIDExEREVEXGJiIiIiIusDARERERNQFBiYiIiKiLjAwEREREXWBgekE2LaNJ554Aueccw4mTpyIm266Cbt37051tzpobm7G//t//w/nnnsuTjvtNHzjG9/ARx991P745s2bsWDBAkyaNAnnnXceFi1alPD67txnb1yjN+3atQuTJ0/G8uXLs/Y+V6xYga9+9auYMGECLrroIrz++utZea+GYeDXv/41zjvvPEyePBnXXXcdPv7446y716eeegrXX399r/erL67RG/e6du1aXHnllZg8eTJmzZqFhx9+GLFYLCvv9XA//vGPMWvWrF7vZ7rca11dHb7//e9jypQpOOOMM3DnnXeisbExM+9V0HH77W9/K6ZPny7efvttsXnzZnHTTTeJOXPmCE3TUt21BDfeeKO49NJLxYcffih27Nghfvazn4lTTz1VbN++XTQ2NoozzjhD3HfffWL79u1i6dKlYsKECWLp0qXtr+/qPnvjGr1J13VxxRVXiPLycrFs2bJe62M63eeKFSvE+PHjxXPPPSeqqqrE7373O1FRUSE+/vjjrLvXxx9/XJx11lni3XffFVVVVeK+++4Tp512mqipqcmae/3Tn/4kxo0bJxYsWNDeli731p1rnOi9fvjhh2L8+PHi97//vaiqqhLvvPOOmDFjhvjRj36Udfd6uFWrVony8nIxc+bMhPZsuVdN08RFF10krrrqKvHZZ5+JTz75RMybN0/ccsstGXmvDEzHSdM0MXnyZLFkyZL2tkAgIE499VTx2muvpbBniaqqqkR5ebnYsGFDe5tt22LOnDniN7/5jVi4cKE455xzhGEY7Y8/+uijYu7cuUKI7t1nb1yjNz366KPi+uuvTwhM2XSftm2LmTNnioceeiih/aabbhILFy7MqnsVQohLL71U/PKXv2z/dUtLiygvLxcrV67M+HutqakRN998s5g0aZKYN29ewpdNutxbV9fojXu98847xY033pjw/BUrVoiTTjpJaJqWVffapra2VkybNk0sWLAgITBl070uW7ZMTJo0SdTX17e3rVu3TsyePVu0tLRk3L1ySu44VVZWIhwOY9q0ae1tubm5OOmkk/Dhhx+msGeJCgoK8Ic//AGnnHJKe5skSRBCIBAI4KOPPsLUqVOhqmr749OmTcOuXbvQ0NDQrfvsjWv0lg8//BAvv/wyHn744YT2bLrPnTt3orq6GpdccklC+6JFi/Ctb30rq+4VAPLz8/HWW29h3759sCwLL7/8MpxOJ8aPH5/x9/rFF18gLy8Pr776KiZOnJjwWLrcW1fX6I17vemmm3DXXXd1eI1pmgiFQll1rwAghMCPfvQjfO1rX8NXvvKVhMey6V7fffddTJs2DQMGDGhvO+ecc7B69Wr4/f6Mu1cGpuNUU1MDABg8eHBCe0lJCQ4cOJCKLnUqNzcXM2bMgNPpbG97/fXXsWfPHpx99tmoqanBoEGDEl5TUlICANi/f3+37rM3rtEbgsEg7rrrLvz4xz/u8F7ZdJ9VVVUAgEgkgptvvhnTp0/H1VdfjbVr1/ZaP9PlXgHgvvvug6qqmD17NiZMmIBf//rX+M1vfoMRI0Zk/L3OmjULjz76KIYPH97hsXS5t66u0V3HuteTTjoJFRUV7b/WdR1/+tOfcPLJJ6OwsDCr7hUAnnvuOdTX1+P73/9+h8ey6V6rqqowbNgwPPnkk5gzZw5mzpyJ//mf/0EwGMzIe2VgOk7RaBQAEoIIALhcLmialooudcuGDRtw7733Yvbs2Zg1axZisVin9wAAmqZ16z574xq94f7778ekSZM6jLz0Vh/T5T5DoRAA4O6778bFF1+MP/7xjzjrrLNw2223Yf369Vl1rwCwY8cO5Obm4sknn8TLL7+MK664AnfffTcqKyuz7l4Ply731tU1eptpmrjrrruwfft2/OQnPwHQvc/bTLnXyspK/O53v8OvfvWrDu8FZNe9hkIhrFixAlu2bMGjjz6Kn/70p9iwYQNuu+02CCEy7l7Vrp9CnXG73QDifxNq+/9A/Dff4/GkqlvHtHr1avzgBz/AxIkT8dhjjwGI34eu6wnPa/sB8nq93brP3rjGiVqxYgU++ugj/P3vf+/08Wy5TwBwOBwAgJtvvhmXX345AGD8+PH48ssv8ac//Smr7rW6uho//OEP8dxzz2HKlCkAgAkTJmD79u347W9/m1X3eqR0ubeurtGbQqEQ7rjjDnzwwQd44okn2qd4suVeNU3DD37wA3znO99JGFE7XLbcKxD/rPJ6vXj00UfbP7fy8vJw9dVXY9OmTRl3rxxhOk5tw391dXUJ7XV1dR2G/tLB4sWL8d3vfhfnnnsunnnmmfYfrEGDBnV6DwAwcODAbt1nb1zjRC1btgwNDQ3tW88nT54MAPjJT36Ciy66KGvus60fAFBeXp7QPnbsWOzbty+r7vWzzz6DYRiYMGFCQvvEiRNRVVWVVfd6pHS5t66u0Vvq6uowf/58fPLJJ3jmmWcSttpny71u3LgR27Ztw+9+97v2z6nf//732L9/PyZPnoxXX301a+617T1GjRrVHpYAoKysDACwb9++jLtXBqbjVFFRAb/fjw8++KC9LRgM4ssvv2z/m3C6WLJkCX72s59h/vz5+M1vfpMwNDl16lRs2LABlmW1t61fvx6jRo1CUVFRt+6zN65xoh555BH885//xIoVK9r/AYDvfe97+MMf/pA19wnE13v4fD5s3LgxoX3r1q0YMWJEVt1r24fhli1bOtzryJEjs+pej5Qu99bVNXpDIBDAN7/5TTQ2NmLJkiUJC3iB7n3eZsK9nnrqqXjzzTfxt7/9rf1z6tprr0VJSQlWrFiBWbNmZc29AsCUKVPap87bbN26FQAwcuTIzLvXHu2powSPPfaY+MpXviJWr17dXvvhggsuSKs6TDt37hQnn3yyuP3220VdXV3CP8FgUBw8eFBMnTpV3H333WLbtm1i2bJlYsKECWL58uXt1+jqPnvjGslweFmBbLvPJ598UkyePFn8/e9/F7t37xZPPfWUqKioEO+//35W3atlWeK6664T8+bNE+vXrxe7du0Sv/71r8X48ePFJ598klX3evfddydsyU6Xe+vONU70Xu+++25x8skni/Xr13f4nDJNM6vu9UhPPPFEhzpM2XKvDQ0N4swzzxS33Xab2LJli/joo4/ExRdfLK6//vqMvFcGphNgmqb43//9XzFt2jQxadIkceutt4q9e/emulsJnn76aVFeXt7pP3fffbcQQoiNGzeKr3/96+KUU04RM2fOFH/+858TrtGd++yNa/S2wwNTb/Uxne7zj3/8o5g1a5Y4+eSTxaWXXipWrVqVlffa3Nws7r//fnHeeeeJyZMni2uuuUZ88MEHWXevnX2xpsu9dXWNE7lXy7LEhAkTjvo51daXbLjXznQWmLLpXnft2iX+67/+S0ycOFFMnTpV3HPPPSIYDGbkvUpCCNGzQTYiIiKi/oVrmIiIiIi6wMBERERE1AUGJiIiIqIuMDARERERdYGBiYiIiKgLDExEREREXWBgIiIiIuoCD98lorS0Y8cOLFmyBO+99x5qamqgqirGjh2LSy+9FF//+tfbz6eaNWsWqqur218nyzJ8Ph/Kyspw7bXX4mtf+1rCdY98PhA/6XzQoEGYN28e/vu//7v9JHMiojYMTESUdv75z3/innvuwejRo3HjjTdi1KhRiMVieOedd/DLX/4S69atw8KFCyFJEgBgxowZuO222wAApmmiqakJ//znP3HXXXehsrISd999d8L1D38+ED+5/IMPPsBTTz2F6upqPPbYY313s0SUERiYiCit7NixA/fccw/OPPNM/Pa3v4WqHvqYmjFjBs444wx873vfwz/+8Q9cfPHFAIDCwkJMmjQp4Tpz5sxBUVER/vjHP+L888/H6aef3v5YZ88/44wzUFNTg+XLl+NHP/oRSkpKknaPRJR5uIaJiNLKs88+C1mW8fOf/zwhLLWZO3cuLrvsMshy1x9f3/ve9+B0OvHSSy91671POeUUCCFw4MCBHvebiLIbR5iIKK2sWbMG06ZNQ1FR0VGf8/DDD3frWrm5uTj11FOxYcOGbj1/165dAIDhw4d36/lE1H8wMBFR2ggEAggEAigtLe3wmGmaCb+WJAmKonR5zQEDBuDzzz9PaBNCJFyvoaEB69atw0svvYQLL7wQhYWFx3cDRJS1GJiIKG3Ytt1p++7du3HBBRcktA0dOhRr1649rvdZsWIFVqxYkdCmqirmzJmD+++//7iuSUTZjYGJiNJGQUEBvF5vh23/gwcPxtKlS9t//eSTT2Lr1q3dumZtbS0GDRqU0DZz5kzcfvvtAOIjVR6PB0OHDoXb7T7BOyCibMXARERpZfbs2Vi7di1CoRD8fj+AeJ2kCRMmtD8nPz+/W9cKBAL44osvOtRiys/PT7geEVFXuEuOiNLKt771LViWhXvvvRe6rnd4PBaLYe/evd261sKFC2EYBq655pre7iYR9TMcYSKitFJWVoZHH30Ud999Ny677DJ8/etfx7hx42CaJj755BMsXboUBw8exC233NL+msbGRnz66acAAMuy0NDQgDfeeAOvvfYavv3tb3M0iYhOGAMTEaWd888/H6+++ipefPFFLF26FNXV1RBCYPjw4fjqV7+Ka6+9NmEn3TvvvIN33nkHQHzx9oABA1BeXo6FCxdi5syZKboLIsomkhBCpLoTREREROmMa5iIiIiIusDARERERNQFBiYiIiKiLjAwEREREXWBgYmIiIioCwxMRERERF1gYCIiIiLqAgMTERERURcYmIiIiIi6wMBERERE1AUGJiIiIqIuMDARERERdeH/Byrg6Vqvg3MYAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(data=carbon, x='GDP', y='CO2')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af1276d2-8515-4bf6-80f4-305a510240d0",
   "metadata": {},
   "source": [
    "## Calculating correlation\n",
    "\n",
    "We have seen that we can get the correlation ($r$-value) between all pairs of columns using a `pandas` function `df.corr()` as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3b5c78e4-6e93-40f9-a38e-928bcfbfadba",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CO2</th>\n",
       "      <th>GDP</th>\n",
       "      <th>population</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>CO2</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.914369</td>\n",
       "      <td>-0.098554</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GDP</th>\n",
       "      <td>0.914369</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.122920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>population</th>\n",
       "      <td>-0.098554</td>\n",
       "      <td>-0.122920</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 CO2       GDP  population\n",
       "CO2         1.000000  0.914369   -0.098554\n",
       "GDP         0.914369  1.000000   -0.122920\n",
       "population -0.098554 -0.122920    1.000000"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "carbon.corr(numeric_only=True, method='spearman')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ca28233-2a51-459c-9587-84068b22e720",
   "metadata": {},
   "source": [
    "Or between two particular columns like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ed788a1e-bef9-469b-9fa0-78a6a34dfb7d",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9143688871356085"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "carbon.GDP.corr(carbon.CO2, method='spearman')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "572cec75-c862-41c8-ae21-3d70966ced6e",
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   "source": [
    "However, the `pandas` function `df.corr()` doesn't calculate the significance of the correlation. We could calculate it using a permutation test (as last week) but we can also use a built in function from `scipy.stats`, called `stats.spearmanr`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d959c076-88e5-4720-bb72-8a84ec0db59b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SignificanceResult(statistic=0.9143688871356085, pvalue=1.6676605949335523e-65)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.spearmanr(carbon.GDP, carbon.CO2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fda80ee3-31d0-47d1-8258-03e564950553",
   "metadata": {
    "tags": []
   },
   "source": [
    "This gives us the correlation coefficient $r=0.79$ (which is a very strong correlation) and the $p$-value $4.9 \\times 10^{-37}$ (it is highliy significant)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a59e0754-28e8-425f-9102-51e5ee8a8c88",
   "metadata": {},
   "source": [
    "### Note on Hypotheses\n",
    "\n",
    "For Pearson's correlation (the 'standard' correlation coefficient, calculated on actual data values rather than ranks) we might express our null and alternative hypotheses as follows:\n",
    "\n",
    "$\\mathcal{H_o}$ There is no linear relationship between GDP and CO2 emissions per capita\n",
    "\n",
    "$\\mathcal{H_a}$ There is a positive linear relationship between GDP and CO2 emissions per capita\n",
    "* in plain English, CO2 emissions are proportional to GDP\n",
    "\n",
    "(remember from the section on correlation in **Describing Data** that Pearson's correlation assumes that the relationship, if there is one, is a straight line)\n",
    "\n",
    "For Spearman's rank correlation coefficient, our null and alternative hypotheses are slightly different:\n",
    "\n",
    "$\\mathcal{H_o}$ There is no relationship between GDP and CO2 emissions per capita\n",
    "\n",
    "$\\mathcal{H_a}$ There is a relationship between CO2 and GDP rank\n",
    "* in plain English, richer a country is, the higher its carbon emissions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1c5874c1-e95f-4495-bf8c-52f578a9a1c0",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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