Statistical_Thinking_in_Python_Part_2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Statistical Thinking in Python (Part 2)\n",
    "## Parameter estimation by optimization\n",
    "How we can know the mean  and standart deviation calculated from the data where the appropricate values for out model?\n",
    "What if the standart deviation differs by 50% ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Optimal Paremeters\n",
    "Paremeter values that bring the model in cloest agreement with the data, the parameters are only optimal for the model you chose for your data. We will using hacker statatistic with numpy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "#loading the libraies\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "nohitter_times =np.array([ 843, 1613, 1101,  215,  684,  814,  278,  324,  161,  219,  545,\n",
    "        715,  966,  624,   29,  450,  107,   20,   91, 1325,  124, 1468,\n",
    "        104, 1309,  429,   62, 1878, 1104,  123,  251,   93,  188,  983,\n",
    "        166,   96,  702,   23,  524,   26,  299,   59,   39,   12,    2,\n",
    "        308, 1114,  813,  887,  645, 2088,   42, 2090,   11,  886, 1665,\n",
    "       1084, 2900, 2432,  750, 4021, 1070, 1765, 1322,   26,  548, 1525,\n",
    "         77, 2181, 2752,  127, 2147,  211,   41, 1575,  151,  479,  697,\n",
    "        557, 2267,  542,  392,   73,  603,  233,  255,  528,  397, 1529,\n",
    "       1023, 1194,  462,  583,   37,  943,  996,  480, 1497,  717,  224,\n",
    "        219, 1531,  498,   44,  288,  267,  600,   52,  269, 1086,  386,\n",
    "        176, 2199,  216,   54,  675, 1243,  463,  650,  171,  327,  110,\n",
    "        774,  509,    8,  197,  136,   12, 1124,   64,  380,  811,  232,\n",
    "        192,  731,  715,  226,  605,  539, 1491,  323,  240,  179,  702,\n",
    "        156,   82, 1397,  354,  778,  603, 1001,  385,  986,  203,  149,\n",
    "        576,  445,  180, 1403,  252,  675, 1351, 2983, 1568,   45,  899,\n",
    "       3260, 1025,   31,  100, 2055, 4043,   79,  238, 3931, 2351,  595,\n",
    "        110,  215,    0,  563,  206,  660,  242,  577,  179,  157,  192,\n",
    "        192, 1848,  792, 1693,   55,  388,  225, 1134, 1172, 1555,   31,\n",
    "       1582, 1044,  378, 1687, 2915,  280,  765, 2819,  511, 1521,  745,\n",
    "       2491,  580, 2072, 6450,  578,  745, 1075, 1103, 1549, 1520,  138,\n",
    "       1202,  296,  277,  351,  391,  950,  459,   62, 1056, 1128,  139,\n",
    "        420,   87,   71,  814,  603, 1349,  162, 1027,  783,  326,  101,\n",
    "        876,  381,  905,  156,  419,  239,  119,  129,  467])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### How often do we get no-hitters?\n",
    "\n",
    "The number of games played between each no-hitter in the modern era (1901-2015) of Major League Baseball is stored in the array `nohitter_times`. \n",
    "\n",
    "If you assume that no-hitters are described as a `Poisson process`, then the time between no-hitters is `Exponentially distributed`. As you have seen, the Exponential distribution has a single parameter, which we will call τ, the typical interval time. The value of the parameter τ that makes the exponential distribution best match the data is the `mean` interval time (where time is in units of number of games) between no-hitters.\n",
    "\n",
    "Compute the value of this parameter from the data. Then, use `np.random.exponential()` to \"repeat\" the history of Major League Baseball by drawing inter-no-hitter times from an exponential distribution with the τ you found and plot the histogram as an approximation to the PDF."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Seed the random number generator with 42\n",
    "np.random.seed(42)\n",
    "#Compute the mean time (in units of number of games) between no-hitters\n",
    "tau = np.mean(nohitter_times)\n",
    "#Draw 100,000 samples from an Exponential distribution\n",
    "inter_no_hitter = np.random.exponential(tau, size=100000)\n",
    "\n",
    "#Plot the theoretical PDF using plt.hist()\n",
    "_ = plt.hist(inter_no_hitter, bins=50)\n",
    "_ = plt.xlabel('Games between no-hitters')\n",
    "_ = plt.ylabel('P D F')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ecdf(data):\n",
    "    \"\"\"Compute ECDF for a one-dimensional array of measurements.\"\"\"\n",
    "    # Number of data points: n\n",
    "    n = len(data)\n",
    "    # x-data for the ECDF: x\n",
    "    x = np.sort(data)\n",
    "    # y-data for the ECDF: y\n",
    "    y = np.arange(1, n + 1) / n\n",
    "    return x, y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Do the data follow our story?   \n",
    "You have modeled no-hitters using an Exponential distribution. Create an ECDF of the real data. Overlay the theoretical CDF with the ECDF from the data. This helps you to verify that the Exponential distribution describes the observed data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Compute an ECDF from the actual time between no-hitters\n",
    "x, y =ecdf(nohitter_times)\n",
    "#Compute an ECDF from the theoretical samples\n",
    "x_theor, y_theor = ecdf(inter_no_hitter)\n",
    "\n",
    "#Plot the actual ECDF and theoretical ECDF\n",
    "_ = plt.plot(x, y, marker = '.', linestyle='none')\n",
    "_ = plt.plot(x_theor, y_theor)\n",
    "\n",
    "\n",
    "plt.margins(0.02)\n",
    "plt.xlabel('Games between no-hitters')\n",
    "plt.ylabel('C D F')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### How is this parameter optimal?\n",
    "Now sample out of an exponential distribution with τ being twice as large as the optimal τ. Do it again for τ half as large. Make CDFs of these samples and overlay them with your data. You can see that they do not reproduce the data as well. Thus, the τ you computed from the mean inter-no-hitter times is optimal in that it best reproduces the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#implement the original sample\n",
    "x, y = ecdf(nohitter_times)\n",
    "x_theor, y_theor = ecdf(inter_no_hitter)\n",
    "\n",
    "_ = plt.plot(x_theor, y_theor)\n",
    "_ = plt.plot(x, y, marker = '.', linestyle='none')\n",
    "\n",
    "#Take 10000 samples out of an Exponential distribution with parameter τ1/2 = tau/2\n",
    "half   = np.random.exponential(tau/2, size=100000)\n",
    "#Take 10000 samples out of an Exponential distribution with parameter τ2 = 2*tau.\n",
    "double = np.random.exponential(tau*2, size=100000)\n",
    "\n",
    "#Generate CDFs from these two sets of samples\n",
    "x_half, y_half = ecdf(half)\n",
    "x_double, y_double =ecdf(double)\n",
    "\n",
    "#Add these two CDFs as lines to your plot\n",
    "_ = plt.plot(x_half, y_half)\n",
    "_ = plt.plot(x_double, y_double)\n",
    "_ = plt.legend(('sample', 'original', 'half sample', 'double sample'))\n",
    "\n",
    "plt.margins(0.02)\n",
    "plt.xlabel('Games between no-hitters')\n",
    "plt.ylabel('C D F')\n",
    "plt.show()\n",
    "#Notice how the value of tau given by the mean matches the data best. \n",
    "#In this way, tau is an optimal parameter."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Regressian by least squarest\n",
    "\n",
    "Linar function has two parameter, the slope and intercept. **The slope** sets the how steep the line is, and **The intercept** sets the where the line crosses the y-axis.\n",
    "\n",
    "*How do we figure out the which slope and intercept best describe the data?*\n",
    "\n",
    "**Residual:** The vertical distance between the data and the line.<br>\n",
    "**Least Squarest:** We define the line that is closest to the data to better line. for which the sum of the squares of all residual is minimal. \n",
    "\n",
    "*Use the **polfit()** functions which perform least squares analysis and return the slope and intercept.ee can use it becasue a linear fuctions is  a first degree polynominal.*\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "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>Continent</th>\n",
       "      <th>female literacy</th>\n",
       "      <th>fertility</th>\n",
       "      <th>population</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Chine</td>\n",
       "      <td>ASI</td>\n",
       "      <td>90.5</td>\n",
       "      <td>1.769</td>\n",
       "      <td>1,324,655,000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Inde</td>\n",
       "      <td>ASI</td>\n",
       "      <td>50.8</td>\n",
       "      <td>2.682</td>\n",
       "      <td>1,139,964,932</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>USA</td>\n",
       "      <td>NAM</td>\n",
       "      <td>99.0</td>\n",
       "      <td>2.077</td>\n",
       "      <td>304,060,000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Indonésie</td>\n",
       "      <td>ASI</td>\n",
       "      <td>88.8</td>\n",
       "      <td>2.132</td>\n",
       "      <td>227,345,082</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Brésil</td>\n",
       "      <td>LAT</td>\n",
       "      <td>90.2</td>\n",
       "      <td>1.827</td>\n",
       "      <td>191,971,506</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Country  Continent  female literacy  fertility     population\n",
       "0      Chine       ASI             90.5      1.769  1,324,655,000\n",
       "1       Inde       ASI             50.8      2.682  1,139,964,932\n",
       "2        USA       NAM             99.0      2.077    304,060,000\n",
       "3  Indonésie       ASI             88.8      2.132    227,345,082\n",
       "4     Brésil       LAT             90.2      1.827    191,971,506"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "female_literacy_fertility = pd.read_csv('data/female_literacy_fertility.csv')\n",
    "female_literacy_fertility.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "illiteracy = np.array(female_literacy_fertility['female literacy'])\n",
    "fertility = np.array(female_literacy_fertility['fertility'])\n",
    "population = np.array(female_literacy_fertility['population']) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### EDA of literacy/fertility data\n",
    "We will look at the correlation between `female literacy` and `fertility` (defined as the average number of children born per woman) throughout the world. For ease of analysis and interpretation, we will work with the illiteracy rate.\n",
    "\n",
    "Plot the `fertility versus illiteracy` and compute the `Pearson correlation coefficient`. \n",
    "\n",
    "Here, it may be useful to refer back to the function you wrote in the previous course to compute the Pearson correlation coefficient.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.set()\n",
    "#Plot fertility (y-axis) versus illiteracy (x-axis)\n",
    "_ = plt.plot(illiteracy,fertility, marker='.', linestyle='none')\n",
    "_ = plt.xlabel('percent illiterate')\n",
    "_ =plt.ylabel('fertility')\n",
    "#Set a 2% margin\n",
    "plt.margins(0.02)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pearson_r(x, y):\n",
    "    \"\"\"Compute Pearson correlation coefficient between two arrays.\"\"\"\n",
    "    # Compute correlation matrix: corr_mat\n",
    "    corr_mat = np.corrcoef(x,y)\n",
    "    # Return entry [0,1]\n",
    "    return corr_mat[0,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.8041324026815341\n"
     ]
    }
   ],
   "source": [
    "print(pearson_r(illiteracy, fertility))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear regression\n",
    "We will assume that fertility is a linear function of the female illiteracy rate. That is, $f = ai + b $, where a is the slope and b is the intercept. We can think of the `intercept as the minimal fertility rate`, probably somewhere between one and two. The slope tells us how the fertility rate varies with illiteracy. We can find the best fit line using np.polyfit().\n",
    "\n",
    "Plot the data and the best fit line. Print out the slope and intercept. (Think: what are their units?)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "slope =  -0.049798548090634234  children per women/ percent illiterate \n",
      "intercept =  6.8679054196999765  children per women\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#implemet the plot \n",
    "_ = plt.plot(illiteracy, fertility, marker='.', linestyle='none')\n",
    "plt.margins(0.02)\n",
    "_ = plt.xlabel('percent illiterate')\n",
    "_ = plt.ylabel('fertility')\n",
    "\n",
    "#Compute the slope and intercept of the regression line using np.polyfit()\n",
    "a, b = np.polyfit(illiteracy, fertility, 1)\n",
    "#Print out the slope and intercept from the linear regression\n",
    "print('slope = ', a, ' children per women/ percent illiterate ')\n",
    "print('intercept = ',b, ' children per women')\n",
    "\n",
    "#To plot the best fit line, create an array x that consists of 0 and 100 using np.array()\n",
    "x = np.array([0,100])\n",
    "y = a*x + b\n",
    "\n",
    "#Plot the data and the regression line on the same plot\n",
    "_ = plt.plot(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### How is it optimal?\n",
    "The function np.polyfit() that you used to get your regression parameters finds the optimal slope and intercept. It is optimizing the sum of the squares of the residuals, also known as RSS (for residual sum of squares). In this exercise, you will plot the function that is being optimized, the RSS, versus the slope parameter a. To do this, fix the intercept to be what you found in the optimization. Then, plot the RSS vs. the slope. Where is it minimal?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Specify slopes to consider: a_vals\n",
    "a_vals = np.linspace(0, 0.1, 200)\n",
    "\n",
    "#Initialize sum of square of residuals: rss\n",
    "#empty_like() function returns a new array with the same shape and type as a given array\n",
    "rss = np.empty_like(a_vals)\n",
    "\n",
    "# Compute sum of square of residuals for each value of a_vals\n",
    "for i, a in enumerate(a_vals):\n",
    "    rss[i] = np.sum((fertility - a * illiteracy -b) **2)\n",
    "    \n",
    "#-Plot the RSS (rss) versus slope (a_vals)   \n",
    "_ = plt.plot(a_vals, rss, '-')\n",
    "plt.xlabel('slope (children per woman / percent illiterate)')\n",
    "plt.ylabel('sum of square of residuals')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The importance of EDA: Anscombe's quartet\n",
    "We are goint to use the  Anscombe's quartet data to make a point. That point becomes clean if we blindly go about doing parameter estimation on these dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Edward Tufte uses this example from Anscombe to show 4 datasets of x\\nand y that have the same mean, standard deviation, and regression\\nline, but which are qualitatively different.'"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "anscombe = pd.read_csv('data/anscombe.csv', skiprows=1)\n",
    "anscombe\n",
    "\"\"\"Edward Tufte uses this example from Anscombe to show 4 datasets of x\n",
    "and y that have the same mean, standard deviation, and regression\n",
    "line, but which are qualitatively different.\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'Average value on x and y are same, Linear regression is same but data totaly different \\n   Before dive into analysis Explorer your data first'"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_1 = np.array(anscombe.iloc[:,0])\n",
    "y_1 = np.array(anscombe.iloc[:,1])\n",
    "\n",
    "x_2 = np.array(anscombe.iloc[:,2])\n",
    "y_2 = np.array(anscombe.iloc[:,3])\n",
    "\n",
    "x_3 = np.array(anscombe.iloc[:,4])\n",
    "y_3 = np.array(anscombe.iloc[:,5])\n",
    "\n",
    "x_4 = np.array(anscombe.iloc[:,6])\n",
    "y_4 = np.array(anscombe.iloc[:,7])\n",
    "\n",
    "#Let's calculate the slope and intercep for this array\n",
    "a_1, b_1 = np.polyfit(x_1,y_1,1)\n",
    "a_2, b_2 = np.polyfit(x_2,y_2,1)\n",
    "a_3, b_3 = np.polyfit(x_3,y_3,1)\n",
    "a_4, b_4 = np.polyfit(x_4,y_4,1)\n",
    "\n",
    "x_theor = np.array([3,15])\n",
    "y_theor_1 = x_theor * a_1 + b_1\n",
    "y_theor_2 = x_theor * a_2 + b_2 \n",
    "y_theor_3 = x_theor * a_3 + b_3 \n",
    "y_theor_4 = x_theor * a_4 + b_4\n",
    "#PLOT TIME\n",
    "plt.figure(figsize=(10,10))\n",
    "ax1= plt.subplot(221)\n",
    "plt.plot(x_1, y_1 , marker='.', linestyle='none')\n",
    "plt.plot(x_theor, y_theor_1)\n",
    "plt.vlines(x=np.mean(x_1),ymin=min(y_1), ymax=max(y_1),color='g' )\n",
    "plt.text(6,10, 'mean:' +str(np.mean(x_1)), color='g')\n",
    "plt.hlines(y=np.mean(y_1),xmin=min(x_theor), xmax=max(x_theor),color='b' )\n",
    "plt.text(3,8, 'mean:' +str(round(np.mean(y_1),2)), color='b')\n",
    "\n",
    "\n",
    "ax2= plt.subplot(222)\n",
    "plt.plot(x_2, y_2 , marker='.', linestyle='none')\n",
    "plt.plot(x_theor, y_theor_2)\n",
    "plt.vlines(x=np.mean(x_2),ymin=min(y_2), ymax=max(y_2),color='g' )\n",
    "plt.text(6,10, 'mean:' +str(np.mean(x_2)), color='g')\n",
    "plt.hlines(y=np.mean(y_2),xmin=min(x_theor), xmax=max(x_theor),color='b' )\n",
    "plt.text(3,8, 'mean:' +str(round(np.mean(y_1),2)), color='b')\n",
    "\n",
    "ax3 = plt.subplot(223)\n",
    "plt.plot(x_3, y_3 , marker='.', linestyle='none')\n",
    "plt.plot(x_theor, y_theor_3)\n",
    "plt.vlines(x=np.mean(x_3),ymin=min(y_3), ymax=max(y_3),color='g' )\n",
    "plt.text(6,10, 'mean:' +str(np.mean(x_3)), color='g')\n",
    "plt.hlines(y=np.mean(y_3),xmin=min(x_theor), xmax=max(x_theor),color='b' )\n",
    "plt.text(3,8, 'mean:' +str(round(np.mean(y_3),2)), color='b')\n",
    "\n",
    "ax4 = plt.subplot(224)\n",
    "plt.plot(x_4, y_4 , marker='.', linestyle='none')\n",
    "plt.plot(x_theor, y_theor_4)\n",
    "plt.vlines(x=np.mean(x_4),ymin=min(y_4), ymax=max(y_4),color='g' )\n",
    "plt.text(5,10, 'mean:' +str(np.mean(x_4)), color='g')\n",
    "plt.hlines(y=np.mean(y_4),xmin=min(x_theor), xmax=max(x_theor),color='b' )\n",
    "plt.text(3,8, 'mean:' +str(round(np.mean(y_4),2)), color='b')\n",
    "plt.show()\n",
    "\n",
    "\"\"\"Average value on x and y are same, Linear regression is same but data totaly different \n",
    "   Before dive into analysis Explorer your data first\"\"\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generating bootstrap replicates\n",
    "\n",
    "We can simulate the getting the data again and again. The idea of resampling the data is recompute the summary statistic of interest. To resample an array of measurment, we randonly select one entry and store it. Importantly. we replace the entry in the original array, and equivalently, we just don't delete it. This is called **sampling with replacement.** Then, we randonly select anaother one and store it. We do this *n* times, where *n* is the total number of measurement. We then then have a resmapled array of the data. This process is an example of bootstrapping , whic is more generally is the use of resampled data to perform statistical inference.\n",
    "\n",
    "Each resampled array is called a **bootstrap sample.**\n",
    "\n",
    "**A bootstrap replicate** is teh value of the summary statisticcomputed from the bootstrap data acquired by bootstrapping. \n",
    "\n",
    "For resampling the data `np.random.choice()` function can be used. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.4799999999999995 4.2\n"
     ]
    }
   ],
   "source": [
    "#Let's create an array size of 5\n",
    "sample = np.array([4., 5., 6.2, 4.2, 3.])\n",
    "#print the mean and median\n",
    "print(np.mean(sample), np.median(sample))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4.2 4.  6.2 4.2 3. ]\n",
      "4.319999999999999 4.2\n"
     ]
    }
   ],
   "source": [
    "#resample the array of interest\n",
    "resample = np.random.choice(sample, size=5)\n",
    "#look at the resampling array\n",
    "print(resample)\n",
    "#print the mean and median of the resampled array\n",
    "print(np.mean(resample), np.median(resample))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing bootstrap samples\n",
    "\n",
    "We will generate bootstrap samples from the set of annual rainfall data measured at the Sheffield Weather Station in the UK from 1883 to 2015. The data are stored in the NumPy array rainfall in units of millimeters (mm). By graphically displaying the bootstrap samples with an ECDF, you can get a feel for how bootstrap sampling allows probabilistic descriptions of data.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   yyyy  mm  tmax  tmin  af   rain  sun\n",
      "0  1883   1   6.3   1.7   6  122.1  ---\n",
      "1  1883   2   8.0   2.8   2   69.8  ---\n",
      "2  1883   3   4.8  -1.6  23   29.6  ---\n",
      "3  1883   4  12.2   3.8   2   74.0  ---\n",
      "4  1883   5  14.7   6.2   0   31.2  ---\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Index(['yyyy', 'mm', 'tmax', 'tmin', 'af', 'rain', 'sun'], dtype='object')"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rainfall_df = pd.read_csv('data/sheffield_weather_station.csv', skiprows=8,delim_whitespace=True)\n",
    "print(rainfall_df.head())\n",
    "rainfall_df.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "66.75024968789013 60.1\n"
     ]
    }
   ],
   "source": [
    "#the rain data comes from the Sheffield Weather Station dataset\n",
    "rain_mm = np.array(rainfall_df['rain'])\n",
    "rain_mm\n",
    "print(np.mean(rain_mm), np.median(rain_mm))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "800.0917293233083 788.1\n"
     ]
    }
   ],
   "source": [
    "#this data comes from the datacamp example\n",
    "rainfall =np.array([  875.5,   648.2,   788.1,   940.3,   491.1,   743.5,   730.1,\n",
    "         686.5,   878.8,   865.6,   654.9,   831.5,   798.1,   681.8,\n",
    "         743.8,   689.1,   752.1,   837.2,   710.6,   749.2,   967.1,\n",
    "         701.2,   619. ,   747.6,   803.4,   645.6,   804.1,   787.4,\n",
    "         646.8,   997.1,   774. ,   734.5,   835. ,   840.7,   659.6,\n",
    "         828.3,   909.7,   856.9,   578.3,   904.2,   883.9,   740.1,\n",
    "         773.9,   741.4,   866.8,   871.1,   712.5,   919.2,   927.9,\n",
    "         809.4,   633.8,   626.8,   871.3,   774.3,   898.8,   789.6,\n",
    "         936.3,   765.4,   882.1,   681.1,   661.3,   847.9,   683.9,\n",
    "         985.7,   771.1,   736.6,   713.2,   774.5,   937.7,   694.5,\n",
    "         598.2,   983.8,   700.2,   901.3,   733.5,   964.4,   609.3,\n",
    "        1035.2,   718. ,   688.6,   736.8,   643.3,  1038.5,   969. ,\n",
    "         802.7,   876.6,   944.7,   786.6,   770.4,   808.6,   761.3,\n",
    "         774.2,   559.3,   674.2,   883.6,   823.9,   960.4,   877.8,\n",
    "         940.6,   831.8,   906.2,   866.5,   674.1,   998.1,   789.3,\n",
    "         915. ,   737.1,   763. ,   666.7,   824.5,   913.8,   905.1,\n",
    "         667.8,   747.4,   784.7,   925.4,   880.2,  1086.9,   764.4,\n",
    "        1050.1,   595.2,   855.2,   726.9,   785.2,   948.8,   970.6,\n",
    "         896. ,   618.4,   572.4,  1146.4,   728.2,   864.2,   793. ])\n",
    "print(np.mean(rainfall), np.median(rainfall))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Write a for loop to acquire 50 bootstrap samples of the rainfall data\n",
    "for _ in range(50):\n",
    "    bs_sample = np.random.choice(rainfall, size = len(rainfall))\n",
    "    #generate the x and y values for the ECDF of the bootstrap sample\n",
    "    x, y = ecdf(bs_sample)\n",
    "    _ = plt.plot(x, y, marker= '.', linestyle='none', color='gray', alpha=0.1)\n",
    "\n",
    "    #Use ecdf() to generate x and y values for the ECDF of the original rainfall\n",
    "x, y = ecdf(rainfall)\n",
    "#Plot the ECDF values of the original data\n",
    "_ = plt.plot(x, y, marker='.')\n",
    "_ = plt.xlabel('yearly rainfall (mm)')\n",
    "_ = plt.ylabel('ECDF')\n",
    "plt.margins(0.02)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Let's produce the same plot with rain_mm from original dataset\n",
    "plt.figure(figsize=(10,7))\n",
    "for _ in range(50):\n",
    "    sample_rain = np.random.choice(rain_mm, size=len(rain_mm))\n",
    "    x_rain, y_rain = ecdf(sample_rain)\n",
    "    \n",
    "    _ = plt.plot(x_rain, y_rain, marker='.', linestyle='none', color='gray', alpha=0.1)\n",
    "\n",
    "x, y =ecdf(rain_mm)\n",
    "_ = plt.plot(x,y, marker='.', linestyle='none') \n",
    "_ = plt.xlabel('Yearly Rainfall (mm)')\n",
    "_ = plt.ylabel('ECDF')\n",
    "plt.margins(0.02)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bootstrap Replicates\n",
    "\n",
    "We can write a function to genrate a boot strap replicate.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bootstrap_replicate_1d(data, func):\n",
    "    \"\"\"Generate a bootstrap replica of 1D data and compute teh statistic with desired function\"\"\"\n",
    "    bs_sample = np.random.choice(data, len(data))\n",
    "    return func(bs_sample)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generating many bootstrap replicates\n",
    "\n",
    "We will write another function, draw_bs_reps(data, func, size=1), which generates many bootstrap replicates from the data set. This function will come in handy for you again and again as you compute confidence intervals and later when you do hypothesis tests.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Define a function with call signature draw_bs_reps(data, func, size=1)\n",
    "def draw_bs_reps(data, func, size=1):\n",
    "    \"\"\"Genrate bootstrap replicate over and over again taking the size argument and loop\"\"\"\n",
    "    #initialize an empty array\n",
    "    bs_replicates = np.empty(size)\n",
    "    #Write a for loop that ranges over size and computes a replicate using bootstrap_replicate_1d()\n",
    "    for i in range(size):\n",
    "       bs_replicates[i] = bootstrap_replicate_1d(data, func)\n",
    "    #Return the array of replicates bs_replicates\n",
    "    return bs_replicates"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can make a histogram to see what might expect to get for the mean of the repeated measurment of the speed of light. When plotting, set the density=True to normalize the histogram, which means the total area under the bars is equel to one. Then, histogram could approximetly a probablitiy density function. Rememeber that under the are of the PDF gives the probablity.So, we here compute the approximate PDF of the mean seed of light. We could expected to get if we perform the measurment again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Let's use the michelson speed of light data to explore the PDF\n",
    "speed_of_light = pd.read_csv('data/michelson_speed_of_light.csv')\n",
    "#Making a list from velocity of light in air (km/s)\n",
    "speed = np.array(speed_of_light['velocity of light in air (km/s)'])\n",
    "\n",
    "bs_replicate_sample = draw_bs_reps(speed, np.mean, size=10000)\n",
    "_ = plt.hist(bs_replicate_sample, bins=50, density=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bootstrap confidence intervals\n",
    "if we repeated measurment over and over again , p% of the observed value, lie witin the p% caonfidence intervals.\n",
    "\n",
    "In our case, if we repeat the 100 times the measurement over again, 95% of the sample means would lie within the 95% confidence interval. \n",
    "\n",
    "We could use the `np.percentile([2.5, 97.5]` to find 95% Confidence Interval. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95% Conficende Intervel for replicated speed of light measurement is  [299837.  299867.7]\n"
     ]
    }
   ],
   "source": [
    "print('95% Conficende Intervel for replicated speed of light measurement is ', np.percentile(bs_replicate_sample, \n",
    "                                                                                             [2.5, 97.5]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Bootstrap replicates of the mean and the SEM\n",
    "\n",
    "We will compute a bootstrap estimate of the probability density function of the mean annual rainfall at the Sheffield Weather Station. Remember, we are estimating `the mean annual rainfall` we would get if the Sheffield Weather Station could repeat all of the measurements from 1883 to 2015 over and over again. This is a probabilistic estimate of the mean. You will plot the PDF as a histogram, and you will see that it is Normal.\n",
    "\n",
    "In fact, it can be shown theoretically that under not-too-restrictive conditions, the value of the mean will always be Normally distributed. (`This does not hold in general, just for the mean and a few other statistics.`) The standard deviation of this distribution, called the standard error of the mean, or SEM, is given by the standard deviation of the data divided by the square root of the number of data points. I.e., for a data set, `sem = np.std(data) / np.sqrt(len(data))`. Using hacker statistics, you get this same result without the need to derive it, but you will verify this result from your bootstrap replicates.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Standard error of the mean (sem):  10.510549150506188\n",
      "Standard deviation for bootstrap replicates:  10.636065875635353\n"
     ]
    }
   ],
   "source": [
    "#Draw 10000 bootstrap replicates of the mean annual rainfall using your draw_bs_reps() \n",
    "bs_replicating = draw_bs_reps(rainfall, np.mean , size=10000)\n",
    "#Compute and print the standard error of the mean of rainfall.\n",
    "sem = np.std(rainfall) / np.sqrt(len(rainfall))\n",
    "print('Standard error of the mean (sem): ', sem)\n",
    "#Compute and print the standard deviation of your bootstrap replicates \n",
    "bs_sem = np.std(bs_replicating)\n",
    "print('Standard deviation for bootstrap replicates: ', bs_sem)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot the replicated sample for rainfall\n",
    "_ = plt.hist(bs_replicating, bins=50, density=True)\n",
    "_ = plt.xlabel('mean annual rain (mm)')\n",
    "_ = plt.ylabel('P D F')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Confidence intervals of rainfall data\n",
    "A confidence interval gives upper and lower bounds on the range of parameter values you might expect to get if we repeat our measurements. For named distributions, you can compute them analytically or look them up, but one of the many beautiful properties of the bootstrap method is that you can take percentiles of your bootstrap replicates to get your confidence interval. Conveniently, you can use the `np.percentile()` function.\n",
    "\n",
    "Use the bootstrap replicates you just generated to compute the 95% confidence interval. That is, give the 2.5th and 97.5th percentile of your bootstrap replicates stored as `bs_replicates`. `What is the 95% confidence interval?`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[779.50364662 820.93800752]\n"
     ]
    }
   ],
   "source": [
    "percentile = np.percentile(bs_replicating, [2.5, 97.5])\n",
    "print(percentile)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bootstrap replicates of other statistics\n",
    "We saw that the `mean is Normally distributed`. This does not necessarily hold for other statistics, but no worry: as hackers, we can always take bootstrap replicates! In this exercise, you'll generate bootstrap replicates for `the variance of the annual rainfall` at the Sheffield Weather Station and plot the histogram of the replicates.\n",
    "\n",
    "```python\n",
    "def draw_bs_reps(data, func, size=1):\n",
    "    return np.array([bootstrap_replicate_1d(data, func) for _ in range(size)])\n",
    "```\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Draw 10000 bootstrap replicates of the variance in annual rainfall, \n",
    "bs_var = draw_bs_reps(rainfall, np.var, size=10000)\n",
    "\n",
    "#Divide bs_var by 100 to put the variance in units of square centimeters\n",
    "bs_var = bs_var /100\n",
    "#Make a histogram of bs_replicates using the density=True\n",
    "_ = plt.hist(bs_var, bins=50, density=True)\n",
    "_ = plt.xlabel('variance of annual rainfall (sq. cm)')\n",
    "_ =plt.ylabel('PDF')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pairs bootstrap\n",
    "\n",
    "We would like to get new optimal paremert if we acquired the data again.We can perform bootstrap estimates to get canfidence intervels at the slope and intercept.\n",
    "\n",
    "We do not assume the any model underlying the data; the estimates were done using the data alone. When we perform the a linear least squres regression, however, we were using a linear model, which has two parameter, slope and intercept.`This was a parametric estimate`. The optimal parameter values we compute for our parametric model are like others statistic. in that we would get differetn values if we acquired the data again. We can perform bootstrap replicates to get confidence intervals on the slope and intercept as well.Let's consider the swing data election data from prequel to this course. What if we had the election again, under the identical conditions? How would the slope and intercept change?   \n",
    "`We will do the method that makes the least assumptions, called paris bootstrap`. Since we can not resample indivudial data beacuse each county has two varibales assosiated with it, the vote share for Obama and total number number of votes,intervals from many bootstrap replicates of the slope and intercept \n",
    "* We resmaple pairs: for the election data we could randomly select  a given county, and keep it total votes and democratic share as pair.So our bootstrap sample consist of set (x,y) pairs.\n",
    "* We then select the slope and intercept from this pairs bootsatrap sample to get bootstrap replicates.\n",
    "* Each slope and intercept is a bootstrap replicate\n",
    "* Then we can get \n",
    "\n",
    "`Let's see in practice !!!`\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A function to do pairs bootstrap\n",
    "Pairs bootstrap involves resampling pairs of data. Each collection of pairs fit with a line, in this case using np.polyfit(). We do this again and again, getting bootstrap eplicates of the parameter values. To have a useful tool for doing pairs bootstrap, you will write a function to perform pairs bootstrap on a set of x,y data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw_bs_pairs_linreg(x, y, size=1):\n",
    "    \"\"\"Perform pairs bootstrap for linear regression.\"\"\"\n",
    "    \"\"\"Compute the slope and intercept from resampled data to get bootstrap replicated \"\"\"\n",
    "    #Use np.arange() to set up an array of indices going from 0 to len(x). \n",
    "    #These are what you will resample and use them to pick values out of the x and y arrays\n",
    "    #Becasue np.random.choice() must sample 1D array. We will sample the indices of the data points\n",
    "    inds = np.arange(len(x))\n",
    "    #initialize an empty slope and an empty intercept replicate arrays to be of size\n",
    "    bs_slope_rep = np.empty(size)\n",
    "    bs_intercept_rep =np.empty(size)\n",
    "    \n",
    "    for i in range(size):\n",
    "        #Resample the indices inds\n",
    "        #Sample the array with replacement\n",
    "        bs_inds = np.random.choice(inds, len(inds))\n",
    "        #Rhe bootstrap sample is generated by the slicing out the respective values from original data frame\n",
    "        bs_x, bs_y = x[bs_inds], y[bs_inds]\n",
    "        #Use np.polyfit() on the new x and y arrays and store the computed slope and intercept\n",
    "        bs_slope_rep[i], bs_intercept_rep[i] = np.polyfit(bs_x, bs_y,1)\n",
    "    #Return the pair bootstrap replicates of the slope and intercept\n",
    "    return bs_slope_rep, bs_intercept_rep\n",
    "        \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pairs bootstrap of literacy/fertility data\n",
    "Using the function you just wrote, perform pairs bootstrap to plot a histogram describing the estimate of the slope from the illiteracy/fertility data. Also report the 95% confidence interval of the slope. The data is available to you in the NumPy arrays illiteracy and fertility.\n",
    "\n",
    "As a reminder, draw_bs_pairs_linreg() has a function signature of draw_bs_pairs_linreg(x, y, size=1), and it returns two values: bs_slope_reps and bs_intercept_reps.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95% confidence level for slop =  [-0.05573801 -0.04431356]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Use your draw_bs_pairs_linreg() function to take 1000 bootstrap replicates of the slope and intercept\n",
    "bs_slop_reps, bs_intercept_reps = draw_bs_pairs_linreg(illiteracy, fertility, size=1000)\n",
    "#Compute and print the 95% bootstrap confidence interval\n",
    "print('95% confidence level for slop = ', np.percentile(bs_slop_reps, [2.5, 97.5]))\n",
    "#Plot and show a histogram of the slope replicates\n",
    "_ = plt.hist(bs_slop_reps, bins=50, density=True)\n",
    "_ =plt.xlabel('slope')\n",
    "_ = plt.ylabel('PDF')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting bootstrap regressions\n",
    "A nice way to visualize the variability we might expect in a linear regression is to plot the line you would get from each bootstrap replicate of the slope and intercept. Do this for the first 100 of your bootstrap replicates of the slope and intercept (stored as bs_slope_reps and bs_intercept_reps).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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6etGZLKJSRl27gpESAyjXtXmIbPY97eJv/oO9fvBt4K//oDqATILN5fythqwtG48PBCCVQmdzVpOn0UDN3YRi0TZjNeqIYgmaTVuXr411BIsLiNKudQK1OuRyeN19yNIOotZAJxKIchG5uYnZLeGsLIKSNM9+GHI91rH09UMggJyaRM7OImpVTCaD15lFNBuYWNwOlUkmEc0mYnfHSk8AenAIOpKwtYWanMBEooh6HSIhWh/7PvgeQ3T8zX+w1w++Dfz1H1QHIJtsbZVssldrxNoqcmMNXA1OAJPssMNbIhFwXeT8HHJ7Gx2JINyWTRbXara0UynE5hZyfs46gmYDUala3Z/+AWRxB1Gt4cUTyEoJubaOKZUJrCxiHEXr2ecx3T3WCfX2WbmJyQnE4jyyXsfN9UI6CfU6JtGG6emGRBumWkNWStBoglS2czkWg5VlnJkZ3EQCp7SL192Hd/bD35Uo9jf/wV4/+Dbw13+QHcDCBkKACQQx6TRIidjaRK6uIKo1TDCAaW//9jhHz0MsLqLym+hgEBDInQJUqpjUrc/nC8j5GVtW2mwgyhX7Jj80iqzsIkplvFgCWS4iNzYw5QqBlSWMkrSeP4vJdYMQ6J4+cFuoqQnE4jKi2cTr6YVUh21ia09ienow4TBUa4h6DZpNRMDBHR5DBAOImRnU2io6HkcWd3HHj6HPPP5tG/ib/0CvH3wb+OvfOwewv6qAOjuouCCaDWi1kJUyolrFdCQxvX2YtjZEtWrF3rYLiFIJAgEr4tbVDdqgirvocBSTTCLLJcTuNrS34Q0MQjKJrDdACszboSTXwxsYRpgWslbDy+UQ8RgmHEI7IYJXL9mqoY4kwmhErYYePYTp67WnkPUV5PoaxOLgBJErizY81NYB0TBCCDDC/rtSEW90DNPVDcUdZKOBqVYInD+HjsYgmfIrIA74+mHvbTC9vMurV9eQUpBqC+/Zde8VB30PHNwqoO/0fK0WolBAuC1bxSOl1QOKxaBaRa4sIbbygLAlnl3dmJSd5CU21pFrq4DBBMPIzQ3rSBIJdCyG3NlGTU3A9i7GbSJLFUxbO96Ro4h6DZnfwotGkfUqcn3dngiWFjFOgNbZ5+yJIBjCy3VbJzN9A7WyCp5rS0LbEshSCS/Xjcl1IYyHabasWF21atVNh0cQ5TJy8jqy1UQbkED7v/0Um+bgzh846G9/sLc2mF7e5ff+6jyup3GU5D/8uzOM9bbvybXvFQd9DxzcE8B3ej6lIB63zV2uZ2P89RqiXAalbHw+l0NgkDvbVqytYB2CyWSsLEMohNzZhmDI9g7Uaqh8HkIhvOFR6Oq2w+XRGNdF3ZxF1qt4w2MIx0FWquhUGhJxTDSKVorglSvIyUl0WxxpDEJr9NgRTDYDzRZidRWxvm47l10XtbSAcYK2O1hIjAogXA+1tABS2iE1sThyawsjJZHZGVpTN99JQB80DvrbH+ytDV69usbVuYJ91owh0xHhcH/Hnlz7XnHQ98DBbQR7t4ULAdEo5pa8gmg2odFAlkvgeZiuLnR3DziOrcLZ2kAWCgjtYZIp6yii9q0fR6EzGag3kNvbIAV6aATd1Yts1gAP0/JQC7PI8g7e0BgiEkWWi9aBJBIQjqAdxzqCG5OYRAKhQSiFHhvDpFPIZhO5sojcyuPlcshmA7mwiImEb8lIGwgEEY06cnkBE42jx4+CkkSrJaoNl8ClC7CzYxPQd9BItt856A8/7K0NpBS8dnUdjEEpyY+eHX7ow0AHfQ/4IaD3o1pF7u5gPG0Txk7Ahn8cB5HfQi4v2kRvMITJZm3lUDhsewkW5mzlTjiM3N2BnR37492RglYTNXEdsb4GrSaiVsOEw3hHTyCUQi4voQMBRKOB2lxHF0sEVlbRwQDuh561eYpYDJNK2TDUzDQivwVSoceOICRQKdt5xG3ttoQViXFd27w2NEx6pI/CGxdRqyt4KoCsVXCPn8KcOnUgHMFBP/7D3ttgenmXyYVtjgwkH/rwD/h74OBWAd3pf/hmE7ldANe1eQKl0B1JiEQQxV3k0qKdJ6AC6GzGJopjMdtLsLgA5bKVe9jdsdPIpMC0J0Fr5MQ1xOqK/Y5qDRMK4h09jojFEAvzgMC4TZyNdXS5RGB5BR0K4z7zIVsJ1NZmG9ZWlm0PQT5v5xMcGUc2mlCv4Y0dRoSDtmQ0FMTU66RiQbY6exGBAOLGDdRugRsVh4l6gENPHGb0iXF7KnpEOegPP/g28Ne/TxzA1772Nf7oj/6IWq3G888/z2c/+9nb/uyeOIC38TybMG42MFojlLI/wPEE1GrIpQXk2jooYSeJ9fTYN/BWC7m0iNzdRQcDiGoNsb0JWtimMimRE1cRS8u2nLNahWAQ7/hxSLQjZ2dBuza5u7FhO4vXV9DBIO4zz2L6+jHxdkx7G2JxETk/jyhsQiSCd/QYslSCZss6AilAeyS7OyksriMFtA4f5eZaif/0jXWrQioM/0t/meFPPGf1kR5BDvrDD74N/PXvgyTw4uIiv/qrv8qf/dmf8Qu/8At88YtfpLOzk6Ghodv6/G3nAG4HKSEWs/F4YxCtFqJWtWWi2EYu3d0DUiHX1+3Er2IRQiE7/jGbhWYL2WzYUFA4ZB1KpYTp7sMcHrcloA3rYNTSImJlCd3bjx4cQu4WMZEopqMNwhFQAQKXLyOnJjDRMMIAySR6ZAQTCiMqVdTMNLgtvP4h1OoyYruATnUSEZq6azDRGM7iIq8sN7iyK6wKKZCRLY4uXUUtL6Fz3bY7+hHioMd/wbeBv/59kAT+8pe/TE9PD5/85CdRSnH27Fl6e3sJh28vwbSnDuBthLDzAxJtGKlsP0GjaRPGrdatoe999kc4v4lcXUbsbNsu464udC4Hroeo1+wJIBJDbBcQxR1Mtsu++RuQtTpoD7WyglyYR/f0oEdGkeUSJhK2J49oFJS0juDGJCYYQggJmQx6aMj+cO+UCNycwmDw+vtQi/OEm3VqkRii3sCEQ8hgkFfXXQwCR0k+fTJJullG12oErl+DUgmTy+35aMoHxUF/+MG3gb/+feAA/v7v/x4hBH/5l3/JF7/4RUqlEi+88IJtfLoN7okD+E6CQUyiDUKhbzeWlUv2xz3diRkYtCeGnR3k4iIiv2nLNHM526gFiGoF094B8QSitGtF39Ip3FOPgXKQtQoYjVpbQ87NYbI59OFxZLWKCTqYRAdEIyAVgSuXkFM3bBJZ2jJWPTCAUQq5s4MzPYUJhAgPD9KcmIR6A9PeRqdb5Wg2TCYq+bFkhdFsFH3sBNIYqJQR2wXUxBUw2DnJ+zxRfNAffvBt4K9/H1QBffazn+X8+fN86UtfIhqN8ku/9Ev8yI/8CD/+4z9+L77u7nFdyOetOJwxts8gmbRJ4WIRZmZgY8NWCw0MQG8vBINQKMCCrdnH82BrC0ol+4afzcLkJExMQLkMzaa99tGjcPiw/fvOjv3cxob93PKy/ezZs/Z7cjn7mclJWFqy9zIwAMPDMDsL6TT090OtBqmU/bf5vP032Sxcu2av3Wzae3/mGRgd3feOwMfH5+65Zw7gD/7gDyiXy+8kfv/iL/6CqakpbvfAsadJ4DvBGBvWqdVAe6AcW7rZ3mETxovzyOUVq/3T14fu7ft2VdHyEmhtheq2t2F3x4acMhnEwhxqchJRKkKrBZ7GGx3DGz+KMz1lHYnrorY2oFZFrq5iojFaTz4Ng4OYTA7TbJJam6c4PYeoVNBDI3jd3ThzN/G6eiDTaZVMMxloNWy38fAYhILIyQmrgdRqYVJp3CeexnR17buKoUcpAfhByy8fJRt8EPz174MkcCQS4U/+5E/40R/9URzH4Qtf+ALPPPMMx48fv63P3/MQ0PdCCIjcaiyT0jaW1es2T6CNTRj394Oj7PD4hTmr9d/Rge7ts1271SoEQ5hkGmG0rTAKhfCOn0QnO5CVMrLlIgtbqBvXMe0duKfPIFwPHIGOJBDRCEhwrl5GzkyjlUKEQ4RPHqfSkUZ4BrG+gpqdRff2IqJx1I1JdCyC0BrZaKAzOcR2HrW+hntkHJPrgmoFWdpFzU4jNrdu5TIi99ame8ijcvx/W4Lh6lyB166uc3QwedsNWI+KDT4o/vr3QQ6gq6uLcDjM5z73Ob70pS9x/PhxfvEXf/HhyQHcDqGQzRMEg4hGw9b8l2/NFsjm0ANDmEgMtbpiB8OUypBIWEfQ1o6oVe1JIZVCSInYWEUKhXv0OCabs6cB7SLzBdTENYgncE8/fqueB3Q0johEAIO6dhk1M0VQCOqBMGZsDDI5ppoBXt4QOEvzJAe7ECqAmpnCi0YQjSbCGEy2C7W8iCwW8U6exMQSVjKjkEdNT307l7EPKoYelYf/biQYHhUbfFD89e+DHMDd8sBCQO9Fq2X1hFq3BOgcB51M2UTydgE5M4PYLmBSKfTgsB1b2WpZqerdXXTAQZXKsL6OUAIvlUKUK6hLFxCFPMLzoNFED4/injyJWl6y4aZGHbmdh1KJ+G6BcjCM99TT3Mge4v9YTOBqg4PhN6rf4oi7TevkaQQgV1fw+gcRwQAmGsN0diLX1iASxT10CLW4gFhYgFrFSlgcO4536IjNFTykPPA9sEe8fQLwPI26QxG2R8UGHxR//fsgBHS3PBQngP8/SmHicUw8YWcNt5pQLiOrFYhG0cMjmGzWDoqfmUKurVm5iZ5emwdotax6aboTEQgiCnlkvYEZG0UPjd4aVdlElouoa1chGMQ98zgiEACjMdEIoXiMZsPFmZjgpUqEK7EeNLYPoLMnzWFVRc7eRG5u4I0fRVQrqKUlvGDIahbF26wa6c2bNix14pR1PMUianHe5jECQUwi8V3DaB4GHvge2CNSbWGODibJdET40bPDd5QDeFRs8EHx178PQkB3y0PpAN7mbQG6RBtCYH/Yq5V3lEj14BC6tx9aDdT0FHJpCRyF6erBZHM2Sdxq2oE0kTBydxeqVczAoJWc3tlB1BuI4q4NDQUU3mNPQDRGOKCoywAEA8iWy8vxYYwQOMLwY5km7afGEfG4lbOYnkIWd3CPnUAWd1GrqxBwEOUyJtmBCYZxZqYw6U704XFEs2HLRm/OIAp5TDBkxekeooqhh2YP7AGptjCH+zvuWHztbRvsNx3/veJR2gMfBD8E9DBSqSCLu5iWazWDQmErQKc1YnkJNTsDnoceHEb3D9i8Qj6PXF/DCIFo1BGFbaiWEJEYXjiCc/4Ne4rAQK2J6eul/SPPsbOwipy9CbslpquGaybJic1JxiiizzyJHjuMl+tCzd5EzN1EbRcwsTitM0+gVpaQlRJuTz8iFEJ39wIGmc/j9Q9ahzR5Hbm5hXAE3uAo3pFxTDb7UFQMPdR74D6RySR49cLSvtPx3ysO+h7wQ0API8FbYZNw2L5JtxqIUgnxdsJ4ZBQTjaPmZ5FTUzaRnMlienutSmmjAfGYnRvstlA725DJ4p4+jSxVkfUaVEqEJq7TqDXwHjsD6TRpt8oRvUPaq0HLQ01NIqcnEc0GurcX7/hJCCgo7uJMTCCA1qkzqKUlVGHLlq3WG+juLkSlglpZxjt8BNOdQxRLiOVF5OKCHVgfjT7wiqGHeg/cJ2KxEF/91vy+0/HfKw76HvBDQA8zjoOJJzCxuB0A02pCqWS7fzs67LjIdBq1uoKauIYolzCZrA0ZhcOIRhNCYXRbGxhQm1uQ7sQ9eRpVrRPSLZrbRdTkBDTqeCdPQa4Lg4CgA44C10NN3UBNTSKaTXTfIN6xU+BIyG8TuH4VEw7hHjuJmptFbedtI9ytMle5tYHc3qZ1/BSyrQ2xu227odeWbalqLAbBvakYutMwxr7YA/eYWCxErdbadzr+e8VB3wO+A9gPvCNA12aF4lotRKVkFUNDIfTYIXR3LzKfR129gtzaxCRT6L5+TCyGaDWtfHXSzjFQWxuYVAfhDz1NvVS2JablMmriBtSqeKdO2TnESFAOKKDlomamkFOTyGYTPTiMd+oUAo3Y2MCZtLOM3WPHbDlo3iqm4jiYnh5bJdRo4p46jXAUbOVRC3N2hgFWkO5uppJ9kFr4fbUH7oA7cYSxWIiwEh84ibzfeVT3wO3iO4D9hBAQidjGMqUQjQaiVrNKpEKDl0AfAAAgAElEQVSih4fRg0N2HOXVK8iVJUyi3UpFt7Vbx2EMOplEhMJEyrvUnRD6+AmEp21oqFxCTU1BuYR39DhmYACkA1KBARp11OwMcuoGsllHjx7GO34S4bUQK8uoyUlMthvv8CHUjUlEPo9o1DHxBLozgzM3B4Eg3slTCK0Rq6uohXlEaRektI7gA1QMfZBa+H25B96HO3WEb9vggyaR9zuP4h64E3wHsF8J2sYyEwp/u8O4VLQDa/r7bZ5ACNTENeTsjE0k9w9gUmk7wtL1iHZnqMqgVSmNROwQGims8FyphJqegeIuevw4ZnjI6hVJBZ655QhuWkmKZgN99Bj66AlEw0pcqNlZzNAwuq8fNTmJ3FhHuk1MRxLd1m4T2e0ddlZBrYZcWEAuLUKjZgXsYrE7qhj6IOMI9/0eeBfu1BE+ija4E/z1+w5gf3MrT0AsZgfJtJpQLCIbdZswPnQYE4mipiZRNybscPi+AUwmSywapFasQjxhk86lEiLg4B05CqEIqlqEcgV1cxpRKGDGj6KHhhDhiA0NtVzrCOZmkRPXEa0G+vgpvPFjiEoZOTWNWllCHzqC7spaDaHNDdAG0p3ocBhnfg7dayWuKRVRc3PI9VV7baXsum6jYuiD1MI/MnvgO7hTR/go2uBO8Nfvl4E+WtwSjxO1qq3KcRw7sSwWRxTyqGtXEdvbeINDpJ9/ks2dOmJrC5nfupW89WB7G7W9jReLItfXcG7OYEpl20DW1o5+7Iydczw7Y9/cV5YxzQay5aJjCfSJk7hPPAlK4bzxOqyuIIJB3MefspLW169hEm3o4WFMdx9Ig9zK4w4NIRt15C2hO53twoyM2rkKqfSem+pR3QN3Igy3lzbYb/OA4dHdA7fLvhkJeTccKAfwHYjirm0oc1tWiTQaxXQkoVzGmbhGsrLNdqQd99gJiMVsL0F+084NNhp2dmxCORKF/BaBqRuYShkEmFgb+tRpTCSMXJhHzs8hl5YwjRrS0+hEG/r4CdwnnwJtcM69ActLiEQ7rSefRhZLqJkJvI4UjBxC93RBvYGsVHCHR1D5PGLyGsLTeL19MDRsHUGibc/scxD2wPuxVzZ4O/ew33oJDvoe8PsAHmVCYZsnCARtRU7tlhIpoEdGiZ0+TnVtC+fCOeT6qp1i9nZj2a0QjEmlEUIgWi283n50KoUq1zClXeTiHHJjEz08ih4bxSRTVjeoUoV6FbW4iLx+HeG5uE8+jRkdRW6s41y+gmhUaT39LLLVQl29iNjKIxIJTCaHyG8h61W8U4+BFMi5ecTK4i1ZbY0Jh++qYuhtDsQeeB/2wgbTy7v8l5duslao2T/so16Cg74H/BzAI8708i6v3sgj2tpI5ZKIZtM2l5VKRB1BJZ1DHz6C8TzUhfPIhTlMMo0eHLTNWm4LwIZgwiFko46Xy2E6s6hKFUplO9dgfQM9OGhnEWezdsh9qQTVCmp52ToC7eE++zx6eAi5vIxz+QLCQOuZ55CVMuriJczONqTT6M5O5OoKSIl3/CSy2bTVR2s2PyCMZ08md6ExdFD2wHtxtzZ4+81//daPvwAcZ//0Ehz0PeA7gEeY7yoJHOkk2d1pG8taLlEHaut5mzDOZNFHj2HCYdSVS7fmASQwQ8OQSNjcgtvCJFMQjyPdBqYzg5exjkBUiojFReT6Grp/wIrZ5bq4EUjzcrgPWauQnZtEXruK0Ab37Edt78LiPIFLlzCRCO7Zs8jNTQIX34Jy2Sax25OolSVItOMePYrc3kHNziA2bcOZwFhH8AE0hg7CHng/7tYG71QdYXP1x4aT/I8/dGxfhH/A3wO+A3iE+Z4lgbcay2LdGarVhj0VlEuIagXa2tDHT2JSKdTkJOrqRVCO/UHvSCKMhqaLaG9Hd3Qg3BZ0tONlc8h63Q6JmV9Abm4w2TnC/+4d4XKin5cyxzlZWiK9u4FaW0FevYKUgtYLH8fLZHBmbqAuX4RUktbTz6EWF3EunrfjJ7t60JEIamUZurvxBoeRqyuoxVnY3bX3gBXVuxONoYOwB96Pu7XBd1YdOUruqx9/8PeA7wAeYd6vJDAWC1HR0lYJOY4NDVUqiHIJAkH00aPo3n7Uwhzq3FsIz0UPj2IyGftDW28g4nG8zjTTZcnLIoPJZel0K8hyiZfKYa4EMmghMUKQHuzmSKxlJSmqVeT6KvLKJWQgQOvj34dOpnCuXkFNXMPr68d94gnU9BTOpYt2PnFvL1oq1MY63ugopNKIxXnE0iKiWrVS1FJCOHJbjuAg7IH3425t8Hb5rRSCgWyc/lxiX4R+3uag7wHfATzCvF9t/L+yQTBoE8aRiE0Y1+vI4i4Ygz50GD06htzawnnzdeTuNt7gMKa7G6RkeqXEf7ricbkW4tV6nGO9cZLdGVS1zMsyiwEcDD/WVqR9uA8zOGQlKTY3oVpGrq0hL1+EUAT3Ez+AjscJXjyPvDmNHjmEe+IkauIKzuXL9j67u+1Etd1d3PFjiFAIOTuDWF6GW3MScBwIHbxGsDtlL2xQKDX4669NM7tavOORlA+a+70HHjbZ7b10AM5e3ZTP3jHW235nR/JQCN3VbXsCCgVEvQbLy4hQEO/oMbyTp5DTUwS++s+YtgTeqce4HkjT0iUM4GrB1bYBRtN1RoNB/tfyOtc3GhwvLnFobR0iMbzxY7QeexxvdAx1cwbn2lVEYYvAm6+jrlzEO3mKxk/8NHJqAufN1zHhCN6ZJ3E7kjgvv4y4fAHviafQ/QPIQh7RbNF69sM487M4165ilhfxRsZsVVM2Z5vJfO4ZkwvbuJ7GGPA8zeTC9r4KA90v9mup7O3iO4BHCcfBZLN2XOV24VbIZg0CAUxfH63DRxCLizivv8LxaoB/UBE7TlIKjuYimKBEHz3GSKXMWNs8VHsxSxq5s4O68AYqEkOPHcI7dRpvZAwxP0vw8iVkeRPx+uuoS5fxTp6k+Zl/j5q8jvPNF9GJdrxnnsYIQeC11xAXzuE98yw6m0NurGHCYVrPncWZuI5z4S10KgOjo5DJonNd+2JO8X7kyEASR8l3RlIeGUg+6Ft6KHnUHaUfAtpnvJ8N3j6uiliMZF8WlLQJ49ItJdJ4HO/kYyQz7RwvL5GVLT71ZDcjTx+HaMzOMWg2MV296GQa4QTQbXGUC9TKiJUV5E4e2pOY3j68oVF0LIazsoIo7yI3NlFXLmOSbbg/+EOIRh3n1VcQO7t4zz2HTqUIvfQiYn4B3d0DHR2o/CamvQNvaBi5sopaWoDSLnga4Xn/qmLI3wN7Y4O7GUn5oLmfe+CD6FXda3wpiAPMe9ngPY+rtRpyZxvTaCKUxIQjdmJZuYxz8TxiawtvdAx91GoCiXyemZvrXC9Jxtslh0tLiK1NnNUVzO4utFoQjdkEczwG1SpiaZHghXPoZhNicUwkgnfqFN4TT+Ocews1cRW3dwD9xFOIzQ0CF87hdXXhPvE0JBKI0g7EE2gPnKlJjADT22sF6lKdmM5OMrn2+7oHHkaphIP+HNzv9T9se8DvBD7AvJcN3lNVMhCw4nGxmB1U06ghdosIDN7bCePlZZw3X4dmkxvxHn7vG2tc2XJ5ba3F0dEsHaMDtlonGLKDYeoVxNoKcruA6OjA5LrxRobR8XYCK0uInSJyYx119So6m6H5fT+IWl8h8MpLmIDC/fCHoV4n+Oo3YWcbMzCIUcoOrx8chFAIOT+H2Fi3eQ2tiUaCVI26L+MpP8i8gvvBQX8O7vf6HzbZbb8K6ADzXja4reOqUhCPW30ez0M06laJ1G2hBwbRx44jSkVee/EqVysOBoEBMuk4R0INSCZxB4ehLQGBgC3jrNdvOYJdREc7JpNDj4zgtbcTWFlB7BaQm5uoq9fQ3T00P/4J1OI8wddeQbd14J79KHJnh8BLL0K9hhkYRHjaTjMbOYRoNGzn8tYW4YCkXq6BFBD+7gdyLys2Psi8gvvBQX8O/PX7DuDA8l42uKO4rrBNWKatDSGFHVRTKiLqNSsLMTDAa1fXMcbgCPiRJ7tJHhm1chE724h4HHfkkM0FSIlsedCowNoGqrhj/57JooeGba/AyhKiUEBtbtiO5f5BWi98jMCNSQJvvo6XyeE+8yxybQ3n9ZcxCHRPH6JuZw24g8Oo4g7h5UVa61t2CY0GxgnYmQfs/Rv7wxj/Bf858Ne/T3IAP/uzP0uhUMBxbLHR7/zO73D69Onb+qyfA3h37qkNKhXbR9BogFJMlWBix2M85jG+fB1cD+/0aXRXDzK/hVhdRRiNDoeRm1uIG9dRKytQLmE8FxmK4I2MYJyAPWmsrRO88CamWoNEAt3WhnfqMbyxwwS/+SJip0DriScxvX04588h8pu0Tp2Bw+OYehUhBMlcit3zV6DVwqQ78UZG7JyCzgz/9fwa/++LNzHGHhB+7CMj/NCzQ3dlkoct/gv+c+Cvf+9yAPesDNQYw9zcHF//+tffcQA+DzmxGDoWg0YDuV3gULzJoZjEhKO0jn8SSiWcc2+gzr2JN34M78RJ5M62FXuLRdHPn8Vs7yAnJqxAXbmEuHIFJxahNTgKA/00MxnYWCd4+QJyeQVZ3MW5eBH39Gm8Z54h+Mo3ERfO4T79PPrkSZxzbyIuX8J9/AnM8AhUKujefgwaNT+P2tnF5DpheIyj0dCelzbecU8GD6fT8PF5N+7ZCWBmZoaf//mfZ3h4mJ2dHX7iJ36Cn/mZn7ntz/sngHfnvtrA8xCFAqJWxWiDCIfQHUl4W4V0dRlveNRWDpXLyPVVRLWGjkWRpRJicgI1dQNqZUxLI6Mx3OFhhBJQqcPWOoHLF6FShVgU057EPXMGr6uH4MvfBM/Dfe4sxnFwLrwFnibxwofZjqcR1ZKdRVwsIdfXMNEw5LqZjPVwvSw4cqSHsYHU/bHTd3A/GocO+nPgr38fnACKxSLPPvssn/vc52i1Wvzcz/0cw8PDPP/88/fqK332GqUwmYxtLNvZtiGi1RUIhfBOP4b31NPIK5cI/uM/4HX34p06bXMJG+sgJN7jT6FPnGDmwjSTS0WOVlY4dO0KMhKxjqB/gFY6B1trBK5cQawsE9gp4LSncB8/g06mCb30TbxwCO9Dz0OjzsTr13lTdnJ4pJND/REQ4I0dQuY3EXOzHIlucGhgAONGMFsak07fl4qht3nUG4d8Hi3uWx/An/7pn7KyssJv/MZv3I+v87lXlEqws2MVPwMBKzvd1gbXr8Ply9DRAc88Y4Xg1teZmFrjN18u43oGRxh+t/km45VVO/oyFoOREftvGw1YW4NLl6BSsR3AnZ3w1FMQj8NLLzHROcJvxp7FNeAYze9yifEnD0N7u72faBSWlqBatfdx6BBks5BM2v/dBybmCvzm//0yrqtxHMnv/uLzjA/d/5OIj8/tcM9OAG+++SatVotnn30WsDmBO8kF+CGgd+ehsEG4A6jbxrK1HdtYFoliPvZJ5MoSN//iv3G95nD4zCEm6nFa3i3NISN4/fhH6WrNoS6cg/VtTP6cPREMjUBnN/LpOGJ9HXnzBnJuAVbW0OkM7uOP8y2vC7dp0ELiCsm3Al30/uN/t6WpJ05DuI5QYUwygVxbxay9Col2vEOHoCOJSaUw8cQ9NU06FuB/+qkz7+QA0rHAnv/3eij2wAPEX/8+CAGVSiX+8A//kL/+67+m1Wrxd3/3d/z2b//2vfo6n/tNOPxtAbp8HlGrIhYrTJc0/+dSAtfTBP77PP8+VyWg4t/WHIq20NlDeMePIW/cQL35LSjuoK5dRkTjuMOjEIthOjPozQ3kzWnE2hLBf1rnZP8J/svwj+CicbTmWHER79mzMD9H4F++js7l8MaPgwaTy6IbLVQhj3PxAiaZwhsZQbR3oFNpiETumWk+SOLYZ+/wk/C3zz1zAB/72Me4ePEin/70p9Fa89M//dOcOXPmXn2dz4PCcTC5HEZrxPY2E9cXcV1t3/iFoDh4mP85vcTEWpUjR3oYPjWK2Skg1tYxg8O0jowjb86gXn8V8nnk5QvIRAJ3cBiRaMOkUojCFnJuliOzF/jd0i5v5sY52hPnsFdB/eM/0Bw7hPvMhxBzswS++XU7B3l0FCkddHcXlMqIjXXU7jamMwvDo5CIo9Od7/QQ+DwaPOrqnXuNrwW0z3jYbTC9vMv/9VfnbMxfCv7jJ/oYHcligiHkhXM4i0t4AwN4h48gS0XE+hoIhQkHkQsLyNdeQW5sABrR3o43OAxGILa3EJubJNZXqBa2EULgdXehj59G7hRRq4s0x49huntRM1OI3SJ6eAjd2w9KYEJh5PY2otFER0Lo7l50Xz8iHkd3Zu5qTvH95mHfA/ea91r/f311bs97QR42fC2gA8zDboNUW5jxwZTtRn6yh0NJB1EsIup1TFe3rRQq7hB46w1oNPCOjCPCIdjZhVgcffoMemDQzgwo5BEb68haDd3Ti+lIE86mqTtBRKuF2NxCzd3E6Bbe0ROojS2cyat4/YN4AwOo5SXUwizGCUEoaCemxRPIag2xs4PcWAdtEMZYcbvI7U0le9A87HvgXnPXcij7nH3TCXw3+CeAd2df2qDZRG4XoFYDITHhMCaVQs7P4ly5io6G8U6eBoNtKvM8TDiM2NrC+ebXUUvLGCWhrY34iaPslht2zsHmBmpjDYq7CANeVzf6yDhqYwsqZVqnH4NgEDU7CxK8oWFEewcmFMJ4Glkuo6VChoN4Y4cx6TQmkcAkH+6qnX25B/aQ91v/o54D2MsTgO8A9hn72gb/qrFMI8JhdDKFyG+hzp9DGG2reYJB5MYaotlCh0KIYgnnX76GWpwnFg5QDkZxh0aZdkNM7BqO5ac5sjyJKO5YR9DdhT48jlpZBe3ROn0GoT3E3DxEQ5j+IUwsfkvVtIlp1EAoSLThHjqCaEtgOjqsYN5DyL7eA3uAv37fARxYHgkbGIPY3UGUy7Z+PxRCt3dAo45z7hyiVMQ9egw6ksjNdag3IByCaoXUG69QvXSdiXCa3+35BK5QOBh+o/I6RzamENvbiJ1bJ4JcDj08itxYgUAI9/TjyNKuzTsk2tBdPZhIGBMKIuoNe19CYtJpO8A+FkcnU7a/4CHikdgDd4G//n1QBurj8z0RAtORxHQkoVxG7u7YxG8wgPfUUxipcC6dQ167ijcygh7ot2JzUsGnPkX9mQ9z7RsTuJ5EI3CN4WpyhLGuBHJhEfIbiFIRtbGOWl9Fd3Xh9aZxXnsZk2jDO3HCTi67MYGX7kSkUphQGMIhdL2GyG+itguQy8LQKESjtnTUH0/p84jhOwCfB0s8jo7H3xGgE9vbCCnxjhzHfTyGmrhK4JWX0V3deEPDIFsI4NDTx3G+VbL9BUZzYuYNVNjDHRmBwUHk/E1MJIKs15Gbm8jVdXQ2h+lIEnj5m3iZDO6hcdTqMtycRmdykIhDMAxSIJoNzNoGamMTPTCIaDQRkbAtHd3n4oaPeozc5/Z53yqgL33pS4yOjhK8z/XSfhXQu/PI2sBxMPGEnVrmuraxrFKGVBr35Gmo1ghcvkhYGiq5XjpDcCzWIhMP8OmRIIcpIpeXUYsLyHoVr38IPTCEwHYOm4CD2skjVtcw0QioIM7MDbxwDDM4jNxYR2zlMaEA0vMwKgCA8JpW6G5tBaSyFUONxgOtGLqbPfCwTjm7Ex7ZZ+A22csqoPd9lZmcnOQHfuAHeOGFF/ipn/opTp48eUdf4ONzRzgOJpu1AnTbBUSlglxdhlSS5id+ALwKzouvYpwAI2OHGHNdKJVwP/Ix3Oc/gnr1JZzLVwicfxOTTOEOD2OGR3CmpnBDYUSjjtrcwKyvobM5ZH4LubyIOzwC/QOolQWbEO7tQ2mDGw4jdQOjXOSNG7C4gDd2yJ4QolFbMbQPSkff5nbE6vwTwsHhfU8AH//4x/nJn/xJdnZ2+MIXvsDf/M3foJRidHT0nur8+yeAd+fA2EAIiEQx7e3gOIh6HbGzQzSZoNw3jEl3oq5fQ2xtoHPdEAzaCWFDI3iPPQ5C2j6ApXmmmxFe7DoJQ4Nk3ArGGEwojCpsIQoFCIWhUsFZmsft6oJUGrUwB60GRKPIWh2EQHiunUOwsQnbBdtc1qjb+w2991v0Xo6qvJs98H518vvhhHBgnoHvwX0fCRkMBunr68MYw7e+9S2mpqb44z/+YwYGBhgeHr6jL7xdfAfw7hxIG4RCmLY2TCRCTBlqa1sIY9DDw5j+AdTMNGp5CZ1OQySMbDXRA4N4Zx5nysT53zjOVZ3g1UYb4x2K5OFhZLOJ8Qw6EkRtbyOLO5hA4P9r786j46jOxO9/b1W19l1q7ZJt7bItL+w2BhsCZjEE4iGJTWbIJG+SYYaEGeaEJYRkMmEZyDCHJDDvO7/kxyzJEEg4ARIgZscEbxjvlqzVkqyttUutXeqquu8fbcmyLWFZ7tbW95OTc3Cru+veq1I9VXd5LlpXF4arGSsjAxkVhVZbA5pAhoWj9fchTdu7DzI2WpMLMejNXCoGB5G6PmFqCV9fVC/kHDjXtqFzdR/k8QLyb2CcGe0C2r17N7/97W/ZvXs3N9xwA//+7/9OQUEBdXV13HnnnVx77bXndUBFmbbQUHAmYotQ73qCnh5AYC0rwgwOxjhWglZTjZ2Sgh0Whj4wQElSPmbPEDZgSih39VLQ2IiVkY6dX4ijtARbOLClhd7dhWaDHR2FceAQIjwEz9Ii0DT0shLs5FQIC0f0uGF4yFue9g709g5ITUUuWoxwB3kHisfNGPLVHgGjXTNXrEgjPtwx7Wb8rGR1+ZmxPt9VTZm7zhkA/vmf/5k777yTRx99lMjIU6l0MzMz+dKXvuTXwinKhByOUwnoOjsR/X2Ivl7sJUswlxehV1XiqKzAjo2jwBmBcXwI0wZD18jPS0UU16IfLUaPjsZKy0AWLscoPuK9QNs2utuNQCKtCIy9uyEyEnN5EWLEg1FajJWZhQxyINrbEKF9EBmBbKzHaHF5B55NCxHk8OYYMgyfXFTHJzl7fVct393inyRnOWnR3L91tRoDCBDn7AISQvBXf/VXBI+7o/nFL37BxRdfzOWXX+63gqkuoIkFehucVn8hIOzkOIGueccJet0QHY2Zl48EEptqKIzRccaFcXt2ENk5ydirL8YODUN3NaE1NqD19mClpWMVFnrzBFkm0hGE6O1DGxkE0+J4h4cdehKkZ5DQ34HeUIeVmgqGA721BTFieoNCj9u7RaXhQAAMDRGXFEvh4rhJu12mYnzXjPRz10xcVAh5GTFzru9/lPobmIEuoBdffJGhoSH++7//m5GRUwfzeDy89NJLfOtb3zqvAymK3wiBjI5BRsd4t610d6O1tUNoGObaq8hyu8ktL4VhsKUTbIlcuZKRVavQDh/B2P8JetkxiI7GzszAs6wIvfQoWnML0vJQKaJ4dOmXMDUdY9DikebjLCnMxWhsgoEBzGXL0fsH0KprIC4eKzYKo7QE2XACKysHYXrIDQkh54pF054xNP4pwjBU14ziG5MGAMMwqKioYGhoiIqKirHXdV3noYcempHCKcp5Cw/HDg8fS0An3N3e/YkvvhRME720BDE4gO1MBCGwioqwV65EO3oE/cBe9NIyREwMdmoGVl4hevkxikUGpqaf3IlMcswMI/9Pf8ROy8BcuRqjshJhefAsX4He3oFeVeXdd8CWaMVHIDoGOzsXMTyEDA/3BqrzNL5r5kLHABRl1DlzAb333ntcd911M1WeMSoX0MQCvQ3Ou/6jCegG+r37EIeFIYVALy9Hc3dhxcZ7E8eHhoGuoZUUo3+yB63bjR0bg52YRIUjjieHszGFhmFb/ODA/5DX0wSGQNhgLVqMufoijOrjoBt4lq9AczUi3N3YKWne/Yl1DZyJmDm5CMPhzX0UcX55W6bdBguMqv8M5AL65S9/yTe/+U12797Nnj17zvr5I488cl4HUpRZoetIpxMpExDdXYjeXoTpwc7JwXQ40Gtr0ZubsKKiELqBnb8Ua3kRemkJ+u5d6BWlFMTG8T3nCMf0OIoaj5Gj9yNDghFDg0hhIGpqCa6pxsrJYWT5SoL2fwIRUXiWLkevOY5orMfOXIxtg6O9DTstHbloCaLH7c0xFDI3+9qVhW/SADA64yc2VvU1KguAEMjYOGRsHKKvF+F2o3W7kcnJeBYtRmtuRNTXw+CQdwZPdh7msiKMkhKMPTspqPiU/Ph4ZEoSZvpaHNVV2O0daAN9J9cAaGgVFYRVVDCydClWUjKOPbuwExMxly5Hr6jEUX8CM3MJQtbjaG7GWrQYYUuEoXunjjpUt44ys1Q66Hkm0NvAp/UfGkLr7oL+fu/U0pBQRFeHd/EXwjsTKCIcKyICo6wMY+efEd3d2PEJ3s1jbBu9oQ7aO9F63TA4gHA4kCMeNE1jZEURVlYuQRXlWBmZWCkpGGXlSAH2kixEWDh2WAj24iykM8mbBiMh4aztKc9MzaDOAVV/v3cBrV69GvEZMxYOHDhwXgdSlDknJAQ7OcWbfK6jw5t8LjjEm0qirx/9RDV0dqJ3u5GpqQx9426MijKMP29HqyjDTkjEWpQFqWnQUA+dXWjdbhAWUtcwDh7CcfgInlUXYRsOgvZ+gpmVix0ThaOsDNsRjFiShT5YCo0NWFnZ3imoQcHI+HgQYsJNzp3OyHPXTVGmYNIA8MYbb8xkORRl9hjGqYVlXV2Ivl4QErtwGdLjQa+tgc5OjO5uZHwCw9/8W7TKchzbP8QoO4blTMTKyYXePmhxQXc3WnsnFbEpHIvPZunxCvIP7cNzyeVgDhO0bx8j+QUIhwOjrBg7PBx70WK0vl5ETBxWbt5YsrnyOvdZq4jXrEqf7RZTFohJA0BdXR1r1qzhnXfemfDnaWlpfiuUoswKzbsbmIyPR/S4vZvZe0aws3OQUqI1NKB1d6K7u5GRkQx/8260mhocH7yDKC7GSkzCyslHuLupcFo8nnwtJjpG1oUhBl0AACAASURBVNX8cN//kLN7J5rDYOTyNRh9vQhXE56ly9BGPBglxd7NahYtQXN3IxIS8OTkURjqwaELTEuq1AyKz00aAN58803WrFnDr3/967N+JoRg48aNfi2YoswmGRWNjIqGgQG07i7EwCAyLQ0zPR2tuRnR0YZWVQlBQQx/7RtoDfU43n0bcfQwdnIyJZmrMT0n1w5Ig+L4JeR2VIPQcHz8ZzRHECNr1mG0tiK62rHylsLQMMaRQ8iYOKzFi3B0dJKXlsr916VR3jJEXm6ySs2g+NSkAeCxxx4D4P7772fFihWn/WzXrl3+LZWizBVhYdhhYacWlvX3IRMSsFNS0DraEc3NaFVV4DAY/quvQXsrQW//ieVV+3ht0SZMJAaSpSHDyPRFiFYXQhPYQmB88B5aWChDV65DdzXDQA9mbh6irw/j4EFkfBz20CAF4S60qEyOVbag9fbivHrpbLeKskBMGgCOHTuGlJIHH3yQf/u3f2N0spBpmvzoRz+atGvoTE899RRdXV08+eSTvimxosyGoCDspGTvwrKuLm8giIhELo2H3h40lwvtRDVCwsjWu8h0u3n43Y8p63dQEG6yZNlirFogNASGh9Aam0AH27YJfvdtCI9g+Kp16HV1CNPEysqCvl70g/uoiF3MU0FxmLKf1zXB4zFhOEOEN9ncGTOGFOV8fGYuoJ07d9La2sq3v/3tUx8wDK6//vopffnu3bt59dVX2bBhwwUXVFHmBF1HJningQp3tzcldVAQdm4esq8fva0FrbEeMeJhya3Xs9gcxvHmG+i7irHT0hm59Aqq69spS7qEwt4GCisPIATYHpPgP22D6GhGrrgKraEeDTAzF1MyEItpgy0Epi05uquEay9KR7NtpOHwzhjSNL9UV+0OtrBNGgAeffRRAL7//e/z+OOPn/cXd3d388wzz3D33XdTVlY2/RIqylwkBDImFhkTC3193oFbh4G9JMu7vqC9DdHegjY0jLXpVjxCw7HtdWr3H+OJrNswIzWMhNU8ounk9Lsw6uu8KSmGhgh663VkfCwjl63FaKhjefAAr0VmYkobA5ui5kr0w+0QHYOZl4/mGUGGhnq3p/ShsSmopo2mCb6yMY8Nq9Tkj4XknPsB7N+/f1pf/MMf/pD77rsPl8s1rc9PtqBBzYFWbTDn6u+MBFK8m8V3dEBfH6TEwcgS77/b2qCnBzbfTlWdxCwdxEZgIqi66GpWN30CYcHeXEW1tWCOwOAgYW+/CUlJrL7iCh4f+ISjjgSK4nQKhrphXzksWQIMQ1ISFBTAUDdER0NUlE+qtf2IyzsFFbBsyQvvVFCUm0jBYt8GmumYc+eAH5XVdnL0eDtF2Qljbe+r+p8zAKSlpXHgwAFWrVqFNsXHzJdffpmUlBTWrFnDK6+8Mq2CqZXAEwv0Npjz9XdEQuTJHcv6h8AIRyaHogV1IVrbWdzdjyFiMSUYSHI//YDeaA1z7dUYZWVowyPIVIF+4gRYNrK9A+33r5KZnERK0Sq0bg+Eh+BOSoN2N0bxm5j5eciaOuzEFOysLITdiB0bB2FhF1SV9PgwNCGwTo7/2bZkz5HGWc9EOufPAR+aaCHgmlXpPlsJfM5UEBs2bKC5uRnDMAgKCkJKiRDiM1cCf+1rX6OtrQ1d13G73QwMDHD77bfz8MMPT7lgKgBMLJDboKrRTUPHAOnxYfOjP1pKRFcnorcXTA9oOqKzk6qGLsqa+ymMNVicHkvw9vcwjh7FSk3Ds3I1RnkZRl0tli4wqquhtw9pGAjLxE7PJPyilfS6e0EzsDMywN2Do7WZkYKlkJ7uTTyXmurdN/mM7SmnYny/f0NbH//7TgXSlhiG9wI0G20/vkyTXQAXojd31/LKn6uR0ttD+IWrs/jrzxfNXABobGyc8PWpLgR75ZVX2Lt373nPAlIBYGKB2gajd0Kj2yrO1oVoukRvD6K7G4YGwREE7m607m60FhfSEYTlTMKxewfGgU+xktLwXLQK4/hx9Jrj2JwKBBiCUE2jLy0TmZuH9HjQkFhLliDaO9A72vEUrYS0dKzsbGRcgnfaaXwCGOd84J/wjhOY1YHgM8v0xN9eOetPITNl+6FGXninAltKvzwBnLNPJy0tjaNHj/K73/2OuLg4Dh48qFYBKzNudGN1e1xKhPlERkZhZ2Rip2dCUBCERWAvWoxVsBSZ4ERvbsResoTBv/k2Mj2N4G3bEN1dDF9/AzInFzs7C3P5MggJBdtGr63G8f476HW1SMOBXlmN5nbjyV+KVleL4+1t6Lt3YhzY552m2t6GaG31jjN8hsk2sN+0ZvGsBdwzy3T0ePuslGOmVTW6efG9Sizb2+uy9bpcn/8OznlL8Itf/IKdO3fS3NzMX//1X/Pcc89x4sQJ7rnnnikdYPPmzWzevPmCC6oENl9srD4nhIZih6aBx4Po7ATbQkZGQUwMWm8vWrMLOyMTz4rVOIoPE7ztT9ixcYxcez16wwlsh+HtCyitQPb3oVVWoNWeQGYtxspcglFeBoaGZ+ky9PIyxOFD0N6GTE3Fyiv07lccHOydMTRBsse52M5nlqkoO2G2izQjRgMfAFLSP+jx+THO2QV022238fLLL/OlL32J1157jZ6eHr785S+zbds2nxdmPNUFNLFAboN5NwYwFbbtHTDu6wXL8k4h7e0BVzPa8CBWVAx6RSn6p59AVBSeSy8ntreL/oNHkCOD6DUnvLOOkBAcjL0kG7loMaKnBzssFCuvEEdFKba0MS+5HNIzMPML0aSNjIz0prs4w1yc+x+IYwCTdXvOSDrosTecHPwdFRUVhTGFvkRF8bWctOiF98evaacWlvW4EW43dpADYmKQ3W609lZITsbz5a8gao/j+OA9iI9lZO1VaN0dEBaO6B9Cq62Cvn600hKoqcZasgSiFuPYvxc7KhIzt5Cg/Z8gD+5HNDViZ2Ujs7LQenuxY2IhPHysSDlp0XPmwj9qOmWai4HsfIzfB9pfdTjnlTwlJYXt27cjhGBkZITnn39ejQEoiq8JgYyO8W4Y39+P1t2F1HSsmFiEuxutsxMSk/F84YvQ3Ypj+4doISEMX3QZWv8AemQEoqsL7UQt9PehlxyF6mrsrCyIjSd47x6sOCdmTg6O3Tvh0AHMiy/FLihE6Lp3/+JpzBiaqyYazJ6vQcCf5Z40APz0pz/lH/7hH/jqV7/Kc889R3l5OatWrWLlypU8/fTTfiuQogS88HDs8PCxBHQYOlZsrDcHkdsNYQaeW25Ha3bh2L0TzQhi5KKLEeYIeoIT0d6GVncCetxoxUfRaqqxs3KRGgTv2omVmoKZkoHjo+3Yhw5gX3IZ9tLlCE1HIBfE9pSTDWYrp/vMDWG2bt3Ko48+yq9+9SsGBgYQQhAaGjqT5VOUwDWagC7B6R0wNgxkXBwwDHUubCGQm25BtLRg7N+HpoGnaAXk5aM7E6HFhV5fDz3daEcOotVUYefkwvAIwft3Y6UvwnI6cbz/LvLwQaxLLsNcsQqtox0pNKTT6bccQ/42Fwez56JJA8CVV17Jhg0bkFKyZs2asddHF4KVlpbOSAEVJeDpOtLpRCYkILq7wLCwpQMREwvd3UjDAc5ELJcL48hhhGXjKSqCvDyoroamevSaWuhxo+//FC0qGjs3H9nfS3BDHVZ6JnZEFI5tf0I/eADz8jVYRSu8M4aCgr1B5zO2h52LZqL/fCE45yygr3zlK7zwwgszVZ4xahbQxAK9DQK9/uBtg/aaJkRXFwwMIAb6Ed3diK4OxNAw0uXCKDmCZpqYhUuRIeHodbWIulq0muPez9i2d21CQQFWdBxGrxsrNRM7Mgy9qcm7+c2adViFyxDSRoaHe8cn5oBAPwd8OQvonAFgtqgAMLFAb4NArz+c0QZDQ95xgt4+xOAAWns79LgRgwPQ2IAoPYZjxIOnIBcZGYPW0IBeVYGoqYGBfu93REYi8/KwomLQBgexUlMhLAy9tRUrLQ1zw+ews3MQHg92dAxEnN9FxtcC/RyY0WmgiqLMYSEh2Cmp4DQRHR3IiHAYHERraYWwUER6OiP1dehlZejDw5g5eXjWX4vIa0Qvr/A+EfT2ou3bj4iKQubmITo70JqbsJJSkUPDBP3m19gZGZgbb0Y4HIgeN3ZcPISEzHbtlQukAoCiLASGgUxKQjqdiK4u7PAIxOAgtDQjQyOwMxZhnTiBXllOUFUZ5uIcPNdsQM/PRysrRauphl432qefIGJisbNz0Dpa0UwbM8GJcPcQ9D//FztjEZ6bb/XOGJK2d1eyeT5jKJCpAKAoC4mmIePjTy0si4jw3uG3tWKHhSGzsrFqjqOXlRJ8vAorewnmtdehuZrQS49BzXFwd6Pv34uMjsXOyUbr1r2BID4BOtoJ+j//L3ZWFp5bbkO0t48tZptP21PO90VivqICgKIsQKdd4JY4ISbGmxSurQ2CHHgWLcGqP4F+rARHdTV2ZiYj116L7lqKfqwYamug141+YD8yKgY7KwtdCIS0sOPi0ZqaCHn2GcyCZZibbkFrbUE6grzbU87xGUMLZZGYL6gAoCgLzMQXuHQYGYHYOIQ7GdrbIDgIM2MRoqEOveQowbU1WOmZjKy/Bm3pcoziI1B/AtHjRjt0EKJjsBcvQQgNIQQyOg69uhzj345hrV6N57ob0VxNftme0pfUIrFTVABQlAVm0gvc6MIyZyIiLh6ZlIzo6EAPDsaTkYnZ1IDjyBGC6+sw0zMZueYa9LZO9OJDiPoGRHcX2oFOiI3FXpwFHhPNEYSMiUEUHyH40CGsK9biuWo9WmMDMjoaGTH3tm4cXSRmWjZCCMJDJx/DmImuoqkeY/R9V6xI89l+CPqPfvSjH/nkm3xscHCEMyeohocHMzAwMjsFmiMCvQ0Cvf5w7jbQNMGekhaQEl3X+Py6JcRFjZuxIwSEhSFjYyEiHBkXiwwJQRMaduZirLg4jJrjGDU1yNBQzOXLkclpCGkjRoYRfT2Ipgb03h5kSBDSNNEGByE0FNnYSPCunciQUGRiIlp3N9Lh8OlA8YWeA3FRIUSGOTha3YltS47VdlG4KPb0NuLUk1RJbSd7SlomfM+Fmuoxxr9v+4EGCiZ4nxCCsLCgsz77WdQTgKIsMFNeBSsEMiYWGRML8U5ITIaOdvSwcDwJTuhox3H4IPqn9VipqXiuvBrR0YJRXo6ob/TmGjp0EC0uHjvV28VkhAQjY2LRt7+HY8d2Rm64BbHUgeju8uYYCjq/C5S/9A96GF0CdWY30Oiddod7yO9dRVPtjhr/PtP0XVlUAFCUBei8s0hGRGBHREBiEpzsGhI11Xji4qGzC+PIARz7P8VKTcFzxTpEbhtGZSWiqQHR2YXW2YGIi8dOTEIODiJDw5BxcQS9/nvke28xcuvtJ8cO8E4dneUZQ5PlCho/fqJrAk0TSFv6NJ/Q+C6fqeYsGv8+w/BdWdRK4Hkm0Nsg0OsPM9QGpundqMbdhVZRgdbeht3dhVF8FKOjHSspGTsxCdHVgX68GtFYj+hxI4WAWO8ThR0bhwyPQMbFelcRx8Th+fznISUNaTi8M4amkWxuKvWfSr/6RO85cxP2q1emEh8d4rMxgAvZc/lcYwBqJbCiKL5hGMjERG8SuvgE7O5utMoK7OhYhru70EtLMI4ewXYmYF50ESIjE72xDnHiBKKzC9ndjRYZBfEJyJ4e7JhYRFAfwb/6L+zEFDy33orwjCBDQibdnnK6pjrNc6KnpDPvyNcWpfi022eiLp+p7rc8Wl5f3gCoAKAoyuSEQMbFe//vdGJ3dSEqKxDR0didnWjlpTiOFWPFOzGXrUCkpKE3NSLqasHdDf19iI529Lh4ZHwsdkwCdHcS/H9/ibVoEZ4bb0YbHERGRVHZI30y42b8RdZj2uw66pry9/k7i+hcS1OtAoCiKFMiI6O8G9g7E5EFhVBzHCMujpG2NrTq4zjKSrHi4717DienoLlciBM14HbDQD+iswM9uh2R4B0rEC0thPyf/w8rL5eyVet5elc3Hlte8OKs/MxYdE1gWt4u5I+Pus7rTt6fu3DNtTTVKgAoinJ+QkOx09IhMQlPbgHaiRpvd5GrCVFXi6OmGismFnPJErTkJLSWFkRtDfT0eBPVdXWitbRgJyZhJyehNdRR2bQDM3IpEuHtGqlun/bFMSctmnVFKWw/1ASAtOWcWuw1l/ZcVgFAUZTpcTiQSUlYTid2Vg6isQH90AFkYz2ivg7D5cKOjsJOToeERERbC1ptDfT1wcgwWnc3WrMLOzmFwsxgjIgCTAQGUCh6vD9LcIJx/peptUUp7CxunjNdLXOVX2cB/exnP+Ptt99GCMEdd9zB1772tSl/Vs0Cmligt0Gg1x/mdhsIdzeiqcm781hNLcJVj97a6p1iKjSwJVqbC626BukxITQYbAlRUZTnXkJx+lIK9QEKzA48S5djXbbGO/6QkDA2Y6ij38OeI41TnjUzF7pafGle7Aewd+9e9uzZwx//+EdM0+Tmm29m/fr1ZGVl+euQiqLMMhkdg4yOwc5chNbiQv90D7KiAq2+Ea27w5uRND4JKzEZXE3oNbVIbOjvI3/fe+RX7kOmpGKlpqGXl6NVlCMLlmJeehkyIZHKQZ2nf3sIj3nuRG6+6mq50EAylwOR3wLAZZddxq9+9SsMw6ClpQXLsggLC/PX4RRFmUvCw7GzcrDTM9FamtE+3YNeXIxWV4sY7MUOCUHEJ2AlJiEaGxENdaAb3u0qS49hNDQgU9Ow0tOgvBRHTRV2dh4V4fmY5qkVsX/YUc1t67L8mqdnuplDqxrd7Drq4uOjLmwfDG77g1/HABwOBz//+c/5z//8T2688UaSkpL8eThFUeaaoCDsjEzs1DSsNVeh7f8U48A+9JrjCNvCdjgQiUneO/76EwiXC+kIQgwPQlkpRmM9pKdjpqSjWzbLQzr4oyjCg0ACx2q6qKg/6LcL63Qzh44GDo9pj702FzOPzshK4MHBQe6++25uvvlmvvzlL/v7cIqizFVSQns77N8P27dDZSUMDnoHej0eb4qIykrve8LDve8fGIDISMjMhIwMytKX8hsyOWRGIhFoAv7ypkK++Lk8nxe3rLaT7//HTkzTm4Lh8buvpGDxuVNdv/x+Bf+7rZTRYUwBOBxT//xM8dsTwPHjxxkZGaGwsJDQ0FA2btxIeXn5lD+vBoEnFuhtEOj1h4XQBiFw8ZWI3OVoR4/g2P4+WmkZYngYOzgEkbYY0hehVVYg+tzelNLDw4ijJdjVtRQsquW2RSspSb4OU2gYSDL72mhrSvD59pTx4Q6+u+XUvP34cMeU2j49Pgxd18Cy0TTBuqIU1halTPnzn2VeDAI3NDTw85//nBdffBGA999/n7/4i7/w1+EURZlhFzq4KaOisa68CuuiS9CLj+B4/x20w8Vgm8jgYOzCQkT/AKKmGoaGkZERCI8HystZWlfPD7KbKF6yikJnMLkHi7FrDmNechkyN3daOYYmM53B5Lm24Gsyfu0CevbZZ9m2bRu6rrNx40a+853vTPmz6glgYoHeBoFef5gbbeCXbRU9HrSSEhzvvY1+YB8MDSDDIkAIb7bRujrwjBAaE81gXz94RiA8HJmQiL0kG6twGSI0GDsqCvPSNcjs7Dm/PeV0+PIJQGUDnWcCvQ18Uf+5PC0Pzl2+uXAOnJk18wtXZ7FpzWLffLlloVWW43jrLfRPdyN6eyAiEjs0DK2xnrDGBgYtGzs8HG1gECwTERqKjI/DysrzJqfTdSoc8ZQ4s8lflTMnf8/TNS+6gBRlLprrG4LP9fKN8mtSM13HLljKcMFStOPH0d/ehrHzI/RmF3ZMPORkw7EyNFcTCA07MhJtaAhczegdXejlZZSuWseTKbmYzd0Yxfu4/9oUsi9d6rsyLhC+6yhTlHlgoml9c8lcL9+o0T7uL1yd5dcgZWdn4/m7bzP05NMM334HUtegthY7MQnPhmsgMRGtrw8hbWRwMGJkCNnVRVnbCKYtsRGYEio+KcHxu5cQtbWctdfsLKlqdPPm7lqqGt2zVgb1BKAElLmWjvdMc718481kUjOZsQjPN/8Gz623EbHrA+zX/oijshI7MQlzaSFBR48h2pq9i8kcGssaSjCW3ogJGNJiedV+ZFQBxkcfQngY5uVrkOkZszZGMFee9NSm8PNMoLeBLzYEL1wUizMmlM+vWzLtP7qqRje7S5rRNOHTjcKnUr6Ffg58ZttGRBB+9Vp6LlmLjIpGO1GLo7oG6UzAXLYczd2D1uMmfqSXZe1VJHU388Wydyk4tgfj4H4EYDmTMGprECdqkOHhEBHh01lDU7G7pJmS2k7vNU5KnDGh5GXETOmzk/3+1abwijIFF3rn6u+7t7mULnimTda24wfGnc5IiE/Ac+dfUrp6PVV/PsCyQ9spLPsUOzkRa/lyjOJiChqOke8qB80B1ggEBaF//BHavk+8SeYuvgTHRx9ix8ZjrVyJTE6ZVubR6ZgrT3oqACjKeZpuegDl3CYbAxkfFJ6ICSM+3OENFm8ex7QieTX783zvyqsp/OgPOMrLkc4ERvLycVSUIjo7kMKAwX6Q3i4fx0cfoH+yC+uKtbD6IrQ/d2InOLELl2EnJUNQkF9ni82VdQIqACjKeZord28L0URte2ZQOHq8nQ0rUs54XVKSvZrFn/8cjg/fwfjTNhyVZRCXgGdJFnpNNVpnBxKB6O3zDiYbDoztH8AnezAvuxy5ciVGeztWWhqVEWn864cuv/bRz4UnPRUAlDlrrs7Xnyt3bwvRZG07PigUZScAkwTiqCg8t92B59obcLz/DsY772CUH4PYGDwZi9CbGhBtrWAKhKcDgoKRDh3Hn7ej7d+LfdHlsHwp5fRimZFIFvZTnloINs8EShtM1hccKPX/LIHYBuNvBtasSh+r/zlvEnp7cbz3DvqH71Lt6qM4ZjGFw23k1x5Ba2sGy/auZAsLQ4ZGoPX1YEVFUXbZ9TzhvMa7Q5kmeOBzaWTlp3kHjGfYmXVUC8GUBU/1syvjTdZdMvra6FjBWe+JjMTzhb+gdPlann7lGKYtMWyLH/b3kRMfC51daK0t0NuL6B9ARkSgSRvjyCGuzglHxsVzVZxF9olOLH2AKiuU0h7Iz5t8k/nPCkrn+1Q70Y2Q0xk5lSabEhUAlDlJ9bMrUzHVGVnl7cPePQSEwNQFRwouJ6dkG5rDgczOQfb2oLW2QrebitAkfrz+O5iajmFbrN/5PxgVoVQtWclPxHI8UuDY5+L+W3LILkg/bS3BZ5VnOrPHJroRWrMq3WftpwKAMiepfnZlKqb6pHj6DYVOzl1/gbUvFuvgPozq42hGEPaixdA/QElyAaamY2s6JlAankrBgfcot1Mxs6Q3iFg2ZZXN5EZIZFg4MjYWNO0zyzOdp9rRcpumDUIQHurbdNcqAChz1lyYJaHMbVN9UpzohmI4/6/g5lvgjT/C0SPoNVUIy2SZ3Y0hLUwbDMtkWe0hkDbLG47yyqJ13icDJEUHP0DXCzALl6MNDiCDQ8hPixorj6YJOtxDVDW6yUmLntZTbU5aNFuvy+WFdyqwbcmL71VSlJtIfLhvAoFaCTzPBHobBHr9QbXB+Pqfz8ruuKgQ8jJiTl9dHBqKtXIV1srVaEIgg4KI72tjeWMpumWzuKeRxW21xLfUEd/bwfKuWhIHu/hi5XvktR1Hr6pCr6pEBgUjY6JJcEgKUyPRQkM50dpHbXMve0paKFzkDTrTWYVeUtPJsRNdSAApSY4PZ3HS2eMAaiWwopxhrk4lnSmBUH+fPCkmJjL81/8PNDUR9NYbWDXtfBS6ClPofJRxMT/c8Qvyjx8gr/IgDA9Rkr6cupEBerVYCl3d5L/0a8yUDKz168kpWkm5y8S25FnTSKdT1jOfHEanwfqCCgDKgjVXEm7NlkCv/7SkpjLy9W9x9E8HMY90YiPwaAa/K7qZLwYbiKEhfrzub/FoDqQQCGnjsC1+cOBX5DTUYvy2AevD9ym85DoceoR31pEmyE8Kn3aRzuy+Klgc57NpwCoAKAuWr6eSzre76UCYSuuv30n+yiz0Y26kaSOF4EjsEkou/yYXdVZhagZS00BK5OhAcVA8+WUfQkICwoZlb/wv308toDjvMvIuzScnQiKaGrFjYiEs7LzLM34gOfZkKgxfUAFAWbB8OZV0Pt5NL/SptP78nYzedf9hRzUlNV0gwEJjf1wumpRIaXvTStgWhm2ytOEYDA8hGhrQ29shNZU8vZL8pnJkcTzm2qswr1qPGBxEdHcho6K8m91PsZ67jrrYcdSFZUte31XLd7f4pq4qACgLli+nks7Hu+mFPpXW37+TnLRobluXRdmJA1i2BAS2EGwI7sLZ00ZkXyd9Qx6W15WQ110PQ4PgCPJuUVlVgdbQiFiUiRnswPHGaxg7/oy59krMq68B00RrakRGRCCjJl8sBt5EeB7THvu5afqurioAKAuar6aSzte76YU8lXYmfic5adFsvDSDbZ/Ujb2Wvu4iPqe3o3+6F9HYiPBEYgUtRW9rQba1QU8vMjQEISSi9BhGeDhkLcEMCcPx9pvoe3ZhXXwx5rUbvRveNzUiQ0ORMbFUNfWc9lRz5fJkTMs+rUyG4bu6qgCgKFOw0O+m56OZ+p2EhRgIQOJd9NtvCazLLsXOyUUrPUbNp6Ucc1ssaztOnqsSrdVFpRXOsYRslnbXktdVhzhajBFeg8zOg+BQHNu3o+/bi7ViNebGG5GOIDRXE+Vl7tOeaoBxC8FgVU4Cd95YqMYAFGWmLeS76fnK37+TqkY3He4hdF1g2/K0Jw0ZHUN5+lKe/ngY05C8lpLFw/EJ0NHOE0nXYqJh2CY/fPNJckUrAtCOHECEhyNz8iEkDOOT3RhHDmMVLsWz8SbylyTgONCCefJYa4tSyEyOHFsIVlzT6dP6qQCgKMq85c+ZWeMHmTVNp/7FIgAAEbNJREFUcPXKVNYWnZ4Erry+G4/tne9vCo3irNVokW2YQwa2EJhCUFy4lrwdv0F4PNjR0QghEIcOokeEIXPysYJC0Q4dIrislKXZudx/5TWUWREURoPs7OTjQ20nxyBO3w/BF1QAUBRlXvL3zKzxg8zSlsRHh5z1/WeOQ+RdtRKtox3j3QZMKTGEZGmkhXXJ5YgWF1ptDcK2vdNBsdEOH0ALDcfOy8dOS0VUlLG8uorCzMWUX7Sef9nbh2WdSokgNDF/FoI999xzbNu2DYD169fzwAMP+PNwiqIEEH/PAppskPnMp46zxiEWxfPdmDh276tBdHViRS3FSo/DqCrHSkpBa2tFq64Ey8aOi0XY0hsIKsqxc3OwMxYhTtRS0RmCFV4InMo2ujI1nIKUcNp6fJMKxG8BYNeuXezYsYNXX30VIQTf+MY3ePfdd7n++uv9dUhFUQKIv2cBTXRxn+yp46zAExzEjroBTCuIHSKTBxfFkx+fgOhsh4pybGciorUZveY4Eg0ZFYlmS7SjR9Gqq7EXLSaicAlCeruXRlNOR8X6dkMavwUAp9PJQw89RFCQNzlRdnY2TU1N/jqcoigBZiZmAZ15cZ/qU8f495nAMWcO2Usz0auPYyUlo7e3IcpKwelEuFxoTQ3eJ4LoGKqi0/go+iK2hy9Hjt79n8yMmV28G0qDIS3bJ/XzWwDIzc0d++/a2lq2bdvGiy++OOXPT7a1mS93w5mvAr0NAr3+oNpgtP5OZ6RPN0g5lytWpPH6rlpM08YwNK5YkTbh7+Ks912eQ3xmDCzLhRMnoLYWcpdQVtfN0YZeitqqKKg9QtlQED/+3D+M5RpCCO/FXwiElN4FYeXlOFet8kl9/D4IXFlZyd/8zd/wwAMPsHjx4il/Tu0JPLFAb4NArz+oNpjN+seHO/jullNPHfHhjgnLMuH7OvpBC4OMXLSQaI4fOc5TvbGYUWBELeeR4DCOyYjTcg2N5cQ/2RUUVFkOKydOBjfn9gTev38/9957Lw8//DCbNm3y56EURVFmxJndQpNNRZ10jYJhYKekcqxyAI+s804hRePoqqtZ1nUCwyMxpYWwJbYQSKGdfBKwOaFF8PJeF+mr3HM7FYTL5eKee+7hmWeeYc2aNf46jKIoyqy5kKmo+dlOjL0NWJaNoWkUJIeTlZnDg+0DlNe76egd4P3I3FPdQAjez1qLrekYvznAA3dedMFBwG8B4Pnnn2d4eJgnn3xy7LUtW7awdetWfx1SUZQZNN/SY59puuUf/7nyui5M0/bexZ/nVNQzB7Gzwixks4vc4FZyk8L5sH4Imk+NASAltqaDEJiWZNdR19wNAI888giPPPKIv75eUZRZ5I9FWP4OKBNl2Tzf8p9Z7+suTmd0pFJKznvT9vHdRBKwomMQ8U5Ei4velk7AHpsCeiZ3/4WvBVArgRVFOW/+2GzHn6t6z/z+0Syb51v+8fX2mDZldV1jPxNA/6DnwgqqacjERGRcHAWe42h1jXhTwsnx68EAiA4/v/1/JzzcBX+DoigBZ3QRlibwySKsiQKKL535/cC0yp+fGYuunboSn2jpxdAFmvBtmuaqln5Kh4NZmRV38hUBiJP/A0MXrC268HxA6glAUZTz5utFWP5e1Xvm968tSmFtUcp5lz8nLZp1RSlsP3RyUauEdStSiI8O8VnX1WlJ6Cbo/slNCuOK1RlzexaQoigLmy9TMft7Ve9k3z+d46wtSmFncfNpwcRfSegsefpaKAlUtAxQ814l6c6IuTsIrCiKcj78ndvfV9/v72A1+rRiWvbYRjRnxAGfJb9TYwCKoijnKSctmk1rFvtk5tObu2upanSf9t1br8tFCIEtQdcEq3MTWJ2bMDbe4KtuMvUEoCiKMgs+a+ZT/6AHefK237IlI6bFxfmJRIcHERoaxOqceDUGoCiKMl991lTa8d1AUkJJTRclNV0IwOHQWJ0T75MyqC4gRVGUWTB+Kq3QBB3uobGuoNFxhqWLT+/mkYDHY7PrqMsnZVABQFEUZRaMXuSvXpmKAD463MS/vniQ7YcaeXN3LQC3rcvCYWinrQGTwMdHXaeNG0yXCgCKoiizJCctmvjoECxLejePMW3+950KXvlzNf/64kEArrs4HWdsCBnO8LHPSVv6ZLGcGgNQFEWZYePzEoWHOk7lE8J7cQdvqolfv11OfWvf2OfEyXmhQhNqFpCiKMp8Mzb7x7TRNMGK7NMHdMeyP8NpF3849frE6eHOn+oCUhRF8bGJ5vePGp9C2rIlh6va0U/O73cYGslxYef8fstSXUCKoihzzrkym+ZnxqJpAutkV4+UsDIrfmyuP8Cv3ir/7IMIfNIFpJ4AFEVRfOhcmU1z0qL5ysY8NM2b2VPXBUeqOzhW28WLJ3P83HVjPktSzt5sflRyXJhaCKYoijLbztzIZiqZTTesSiPdGUF5XRcd7iE+Otx0WsDYtGYxG1al8ezvj3Cwsv2sz19/aYZPyq4CgKIoyjRN1t1z/9bV51ysNZqcrqrRfVp20fEBoyg7/qwAoGuQ7ozwSflVAFAURZmmz0rnsLO4GdOy2VncPOEOZ6NPDuGhDq5cngxwVmrpiXYYs218kgkUVABQFEWZtsm6e861Zeb4qaCjawAchnbWLl/5mbHousCyTuWD9uXOYyoAKIqiTNNkewOcaxxgLECMe22iQJGTFs2Dd17ErqMu3P0jRIcHsemqbOLDz2/z+cmoAKAoinIBJtpo5lybxpyZ7dM7G2jiO/szv9/pjKStrdcnZVcBQFEUxQ8+awey8QEiPNRB/6DHL7uLnYvfA0BfXx9btmzhP/7jP0hPT/f34RRFUeYFf2+BORV+XQh2+PBhtm7dSm1trT8PoyiKokyDXwPA7373O/7pn/6JxMREfx5GURRFmQa/dgE9/vjj/vx6RVGUWXHm6t/5as4OAsfHT7zSzemcPD9GoAj0Ngj0+oNqg9msf1ltJ0+/5J3Dbxgaj999JQWL42a0DL6q/5wNAB0dfdi2PO01X05/mq8CvQ0Cvf6g2mC267/nSCMe0x7bwWvPkUafzcufisnqr2li0hvnyahsoIqiKOdh/Gbuk83dny/m7BOAoijKXHSuRV7zyYwEgA8++OC8P6NpE296NtnrgSTQ2yDQ6w+qDWa7/nkZMeRlxMza8Seq/3TaREgp5bnfpiiKoiw0agxAURQlQKkAoCiKEqBUAFAURQlQKgAoiqIEKBUAFEVRApQKAIqiKAFKBQBFUZQApQKAoihKgFIBQFEUJUDNmwDw+uuvc/PNN7Nx40ZeeOGF2S7OjHjuuefYtGkTmzZt4ic/+QkAu3bt4tZbb2Xjxo0888wzs1zCmfHUU0/x0EMPAVBaWsrmzZu54YYb+P73v49pmrNcOv/64IMP2Lx5MzfddBOPPfYYEFjnwB/+8Iexv4GnnnoKCIxzoK+vj1tuuYWGhgZg8t/5BbeFnAeam5vlNddcI7u6umR/f7+89dZbZWVl5WwXy6927twpv/zlL8vh4WE5MjIi77rrLvn666/L9evXy7q6OunxeOTXv/51uX379tkuql/t2rVLXn755fLBBx+UUkq5adMmefDgQSmllN/73vfkCy+8MJvF86u6ujq5bt066XK55MjIiNy6davcvn17wJwDAwMD8tJLL5UdHR3S4/HIO+64Q+7cuXPBnwOHDh2St9xyi1y2bJmsr6+Xg4ODk/7OL7Qt5sUTwK5du7jiiiuIiYkhLCyMG264gbfeemu2i+VXTqeThx56iKCgIBwOB9nZ2dTW1rJo0SIyMjIwDINbb711QbdDd3c3zzzzDHfffTcAjY2NDA0NsWrVKgA2b968oOv/7rvvcvPNN5OcnIzD4eCZZ54hNDQ0YM4By7KwbZvBwUFM08Q0TQzDWPDnwJlb6R45cmTC37kv/h7mRTro1tZWnE7n2L8TExM5cuTILJbI/3Jzc8f+u7a2lm3btvGXf/mXZ7VDS0vLbBRvRvzwhz/kvvvuw+VyAWefB06nc0HX/8SJEzgcDu6++25cLhcbNmwgNzc3YM6BiIgI/v7v/56bbrqJ0NBQLr30UhwOx4I/B87cSnei619LS4tP/h7mxROAbdsIcSrVqZTytH8vZJWVlXz961/ngQceICMjI2Da4eWXXyYlJYU1a9aMvRZo54FlWezevZsnnniC3/72txw5coT6+vqAaYOysjJ+//vf8+GHH/Lxxx+jaRo7d+4MmPqPmuy898Xfw7x4AkhOTmbfvn1j/25raxt7PFrI9u/fz7333svDDz/Mpk2b2Lt3L21tbWM/X8jt8Kc//Ym2tjZuu+023G43AwMDCCFOq397e/uCrT9AQkICa9asIS7Ou9/sddddx1tvvYWu62PvWcjnwI4dO1izZg3x8fGAt4vj+eefD6hzALzXv4n+7s98fTptMS+eANauXcvu3bvp7OxkcHCQd955h6uvvnq2i+VXLpeLe+65h6effppNmzYBsHLlSmpqajhx4gSWZfHGG28s2Hb4r//6L9544w3+8Ic/cO+993LttdfyL//yLwQHB7N//37AO0NkodYf4JprrmHHjh309PRgWRYff/wxN954Y8CcAwUFBezatYuBgQGklHzwwQdcdtllAXUOwOR/92lpaRfcFvPiCSApKYn77ruPu+66C4/Hwx133MGKFStmu1h+9fzzzzM8PMyTTz459tqWLVt48skn+c53vsPw8DDr16/nxhtvnMVSzrynn36aRx55hL6+PpYtW8Zdd90120Xym5UrV/KNb3yDO++8E4/Hw5VXXsnWrVvJysoKiHNg3bp1HDt2jM2bN+NwOCgqKuJb3/oW119/fcCcAwDBwcGT/t1f6N+D2hFMURQlQM2LLiBFURTF91QAUBRFCVAqACiKogQoFQAURVEClAoAiqIoAUoFAGVBO3r0KPfeey8PPfQQzz//PAD5+fl0dnby/vvvj2XY3L59Oz/72c9ms6iKMuNUAFAWtKKiIn7+859P+LPPfe5zPPLII4A3ULjd7pksmqLMunmxEExRpuuTTz7h0UcfZfny5Wf97JVXXuHtt9/m7/7u73jppZewLIvIyEjuu+8+Xn75ZV588UVs2yYmJoYf/OAHZGdn89BDD9Hd3U19fT0bNmzgjjvu4Mc//jH9/f20tbVRUFDAT3/6U4KDgzl8+DCPPfYYg4ODOBwOHnjgAdra2vjNb37DSy+9BEBTUxNf+tKX+OCDDwgKCprp5lECnAoASsBbuXIlW7Zsoauri/vuu4+9e/fy2muv8cILLxAaGsqOHTv49re/zbZt2wAYGhrizTffBLyb1dx+++3cdttteDweNm/ezPbt27n22mu55557eOyxx9iwYQPFxcV873vf4/e//z1PPvkklZWV5Obm8vLLL/OFL3xBXfyVWaECgKKcYfv27Zw4cYItW7aMvdbT00N3dzcAF1988djr999/Pzt37uSXv/wltbW1tLa2MjAwQEVFBZqmsWHDBgCWL1/O66+/DsAXv/hFXn75ZR588EFeffVVfv3rX89c5RRlHBUAFOUMtm1z2223cf/994/9u7W1lejoaADCwsLG3vuP//iPWJbFTTfdxIYNG3C5XEgp0XX9rNS8FRUVZGVlsWXLFu644w4uu+wycnNzycjImLnKKco4ahBYUQBd18f2U123bh1vvvkmra2tALz44ot89atfnfBzO3bs4J577uHmm28G4PDhw1iWRVZWFkIIdu7cCUBJSQlf/epXsW2blJQUVq1axRNPPMHWrVtnoHaKMjH1BKAowBVXXMF3v/tdHn30UX7wgx/wzW9+k69//esIIYiIiOC5556bcLON++67j3vuuYewsDAiIiK49NJLqaurIygoiGeffZYnnniCn/zkJzgcDp599tmxvv7Nmzfz6KOPsn79+pmuqqKMUdlAFWWG2bbNj3/8Y1JTU/nWt74128VRApjqAlKUGdTX18fll1+Oy+Va8HnslblPPQEoiqIEKPUEoCiKEqBUAFAURQlQKgAoiqIEKBUAFEVRApQKAIqiKAFKBQBFUZQA9f8D7yavoHgNmacAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Generate an array of x-values consisting of 0 and 100 for the plot of the regression lines.\n",
    "x = np.array([0,100])\n",
    "#write a loop in which you plot a regression line with a slope and intercept given by the pairs bootstrap replicates\n",
    "for i in range(100):\n",
    "    #When plotting the regression lines in each iteration of the for loop, recall the regression equation y = a*x + b\n",
    "    #Here, a is bs_slope_reps[i] and b is bs_intercept_reps[i]\n",
    "    _ = plt.plot(x, bs_slop_reps[i]*x+bs_intercept_reps[i], linewidth=0.5, alpha=0.2, color='red')\n",
    "    \n",
    "_ = plt.plot(illiteracy, fertility, marker='.', linestyle='none')\n",
    "_ = plt.xlabel('illiteracy')\n",
    "_ = plt.ylabel('fertility')\n",
    "plt.margins(0.02)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generating a permutation sample\n",
    "In the video, you learned that permutation sampling is a great way to simulate the hypothesis that two variables have identical probability distributions. This is often a hypothesis you want to test, so in this exercise, you will write a function to generate a permutation sample from two data sets.\n",
    "\n",
    "Remember, a permutation sample of two arrays having respectively n1 and n2 entries is constructed by concatenating the arrays together, scrambling the contents of the concatenated array, and then taking the first n1 entries as the permutation sample of the first array and the last n2 entries as the permutation sample of the second array.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [],
   "source": [
    "def permutation_sample(data1, data2):\n",
    "    \"\"\"Generate a permutation sample from two data sets.\"\"\"\n",
    "    # Concatenate the data sets: data\n",
    "    data = np.concatenate((data1, data2))\n",
    "    # Permute the concatenated array: permuted_data\n",
    "    permuted_data = np.random.permutation(data)\n",
    "\n",
    "    # Split the permuted array into two: perm_sample_1, perm_sample_2\n",
    "    perm_sample_1 = permuted_data[:len(data1)]\n",
    "    perm_sample_2 = permuted_data[len(data1):]\n",
    "\n",
    "    return perm_sample_1, perm_sample_2\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [],
   "source": [
    "rain_june =np.array([  66.2,   39.7,   76.4,   26.5,   11.2,   61.8,    6.1,   48.4,\n",
    "         89.2,  104. ,   34. ,   60.6,   57.1,   79.1,   90.9,   32.3,\n",
    "         63.8,   78.2,   27.5,   43.4,   30.1,   17.3,   77.5,   44.9,\n",
    "         92.2,   39.6,   79.4,   66.1,   53.5,   98.5,   20.8,   55.5,\n",
    "         39.6,   56. ,   65.1,   14.8,   13.2,   88.1,    8.4,   32.1,\n",
    "         19.6,   40.4,    2.2,   77.5,  105.4,   77.2,   38. ,   27.1,\n",
    "        111.8,   17.2,   26.7,   23.3,   77.2,   87.2,   27.7,   50.6,\n",
    "         60.3,   15.1,    6. ,   29.4,   39.3,   56.3,   80.4,   85.3,\n",
    "         68.4,   72.5,   13.3,   28.4,   14.7,   37.4,   49.5,   57.2,\n",
    "         85.9,   82.1,   31.8,  126.6,   30.7,   41.4,   33.9,   13.5,\n",
    "         99.1,   70.2,   91.8,   61.3,   13.7,   54.9,   62.5,   24.2,\n",
    "         69.4,   83.1,   44. ,   48.5,   11.9,   16.6,   66.4,   90. ,\n",
    "         34.9,  132.8,   33.4,  225. ,    7.6,   40.9,   76.5,   48. ,\n",
    "        140. ,   55.9,   54.1,   46.4,   68.6,   52.2,  108.3,   14.6,\n",
    "         11.3,   29.8,  130.9,  152.4,   61. ,   46.6,   43.9,   30.9,\n",
    "        111.1,   68.5,   42.2,    9.8,  285.6,   56.7,  168.2,   41.2,\n",
    "         47.8,  166.6,   37.8,   45.4,   43.2])\n",
    "\n",
    "rain_november = np.array([  83.6,   30.9,   62.2,   37. ,   41. ,  160.2,   18.2,  122.4,\n",
    "         71.3,   44.2,   49.1,   37.6,  114.5,   28.8,   82.5,   71.9,\n",
    "         50.7,   67.7,  112. ,   63.6,   42.8,   57.2,   99.1,   86.4,\n",
    "         84.4,   38.1,   17.7,  102.2,  101.3,   58. ,   82. ,  101.4,\n",
    "         81.4,  100.1,   54.6,   39.6,   57.5,   29.2,   48.8,   37.3,\n",
    "        115.4,   55.6,   62. ,   95. ,   84.2,  118.1,  153.2,   83.4,\n",
    "        104.7,   59. ,   46.4,   50. ,  147.6,   76.8,   59.9,  101.8,\n",
    "        136.6,  173. ,   92.5,   37. ,   59.8,  142.1,    9.9,  158.2,\n",
    "         72.6,   28. ,  112.9,  119.3,  199.2,   50.7,   44. ,  170.7,\n",
    "         67.2,   21.4,   61.3,   15.6,  106. ,  116.2,   42.3,   38.5,\n",
    "        132.5,   40.8,  147.5,   93.9,   71.4,   87.3,  163.7,  141.4,\n",
    "         62.6,   84.9,   28.8,  121.1,   28.6,   32.4,  112. ,   50. ,\n",
    "         96.9,   81.8,   70.4,  117.5,   41.2,  124.9,   78.2,   93. ,\n",
    "         53.5,   50.5,   42.6,   47.9,   73.1,  129.1,   56.9,  103.3,\n",
    "         60.5,  134.3,   93.1,   49.5,   48.2,  167.9,   27. ,  111.1,\n",
    "         55.4,   36.2,   57.4,   66.8,   58.3,   60. ,  161.6,  112.7,\n",
    "         37.4,  110.6,   56.6,   95.8,  126.8])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing  permutation sampling\n",
    "To help see how permutation sampling works, in this exercise you will generate permutation samples and look at them graphically.\n",
    "\n",
    "We will use the Sheffield Weather Station data again, this time considering the monthly rainfall in July (a dry month) and November (a wet month). We expect these might be differently distributed, so we will take permutation samples to see how their ECDFs would look if they were identically distributed.\n",
    "\n",
    "The data are stored in the Numpy arrays rain_june and rain_november.\n",
    "\n",
    "As a reminder, permutation_sample() has a function signature of permutation_sample(data_1, data_2) with a return value of `permuted_data[:len(data_1)]`,` permuted_data[len(data_1):]`, where \n",
    "`permuted_data = np.random.permutation(np.concatenate((data_1, data_2)))`.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Write a for loop to 50 generate permutation samples\n",
    "for _ in  range(50):\n",
    "    #Generate a permutation sample\n",
    "    perm_samp_1, perm_samp_2 = permutation_sample(rain_june, rain_november)\n",
    "    #Generate the x and y values for an ECDF for each of the two permutation samples \n",
    "    x_1 , y_1 = ecdf(perm_samp_1)\n",
    "    x_2 , y_2 = ecdf(perm_samp_2)\n",
    "    #Plot the ECDF of the first permutation sample\n",
    "    _ = plt.plot(x_1, y_1, marker='.', linestyle='none', color='red', alpha=0.02)\n",
    "    _ = plt.plot(x_2, y_2, marker='.', linestyle='none', color='blue', alpha=0.02)\n",
    "#Generate x and y values for ECDFs for the rain_june and rain_november data    \n",
    "x_1 , y_1 = ecdf(rain_june)\n",
    "x_2 , y_2 = ecdf(rain_november)\n",
    "\n",
    "_ = plt.plot(x_1, y_1, marker='.', linestyle='none', color='red')\n",
    "_ = plt.plot(x_2, y_2, marker='.', linestyle='none', color='blue')\n",
    "\n",
    "plt.margins(0.02)\n",
    "\n",
    "_ = plt.xlabel('monthly rainfall (mm)')\n",
    "_ = plt.ylabel('ECDF')\n",
    "\n",
    "plt.show()\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generating permutation replicates\n",
    "A permutation replicate is a single value of a statistic computed from a permutation sample. As the `draw_bs_reps()` function you wrote in chapter 2 is useful for you to generate bootstrap replicates, it is useful to have a similar function, `draw_perm_reps()`, to generate permutation replicates. You will write this useful function in this exercise.\n",
    "\n",
    "The function has call signature draw_perm_reps(data_1, data_2, func, size=1). Importantly, func must be a function that takes two arrays as arguments. In most circumstances, func will be a function you write yourself.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw_perm_reps(data_1, data_2, func, size=1):\n",
    "    \"\"\"Generate multiple permutation replicates.\"\"\"\n",
    "\n",
    "    # Initialize array of replicates: perm_replicates\n",
    "    perm_replicates = np.empty(size)\n",
    "\n",
    "    for i in range(size):\n",
    "        # Generate permutation sample\n",
    "        perm_sample_1, perm_sample_2 = permutation_sample(data_1, data_2)\n",
    "\n",
    "        # Compute the test statistic\n",
    "        perm_replicates[i] = func(perm_sample_1, perm_sample_2)\n",
    "    #Return the array of replicates\n",
    "    return perm_replicates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [],
   "source": [
    "def diff_of_means(data_1, data_2):\n",
    "    \"\"\"Difference in means of two arrays.\"\"\"\n",
    "\n",
    "    # The difference of means of data_1, data_2: diff\n",
    "    diff = np.mean(data_1) - np.mean(data_2)\n",
    "\n",
    "    return diff"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Formulating and simulating a hypothesis\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A one-sample bootstrap hypothesis test\n",
    "Another juvenile frog was studied, Frog C, and you want to see if Frog B and Frog C have similar impact forces. Unfortunately, you do not have Frog C's impact forces available, but you know they have a mean of 0.55 N. Because you don't have the original data, you cannot do a permutation test, and you cannot assess the hypothesis that the forces from Frog B and Frog C come from the same distribution. You will therefore test another, less restrictive hypothesis: The mean strike force of Frog B is equal to that of Frog C.\n",
    "\n",
    "To set up the bootstrap hypothesis test, you will take the mean as our test statistic. Remember, your goal is to calculate the probability of getting a mean impact force less than or equal to what was observed for Frog B if the hypothesis that the true mean of Frog B's impact forces is equal to that of Frog C is true. You first translate all of the data of Frog B such that the mean is 0.55 N. This involves adding the mean force of Frog C and subtracting the mean force of Frog B from each measurement of Frog B. This leaves other properties of Frog B's distribution, such as the variance, unchanged.\n",
    "\n",
    "   #### Instructions\n",
    "\n",
    "    1-Translate the impact forces of Frog B such that its mean is 0.55 N.\n",
    "    2-Use your draw_bs_reps() function to take 10,000 bootstrap replicates of the mean of your translated forces.\n",
    "    3-Compute the p-value by finding the fraction of your bootstrap replicates that are less than the observed mean impact force of Frog B. Note that the variable of interest here is force_b.\n",
    "    4-Print your p-value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "force_b =np.array([ 0.172,  0.142,  0.037,  0.453,  0.355,  0.022,  0.502,  0.273,\n",
    "        0.72 ,  0.582,  0.198,  0.198,  0.597,  0.516,  0.815,  0.402,\n",
    "        0.605,  0.711,  0.614,  0.468])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value =  0.0057\n"
     ]
    }
   ],
   "source": [
    "translated_force_b = force_b - np.mean(force_b) +0.55\n",
    "\n",
    "bs_rep_translated_force_b = draw_bs_reps(translated_force_b, np.mean, 10000)\n",
    "\n",
    "p = np.sum(bs_rep_translated_force_b <= np.mean(force_b))/10000\n",
    "\n",
    "print('p-value = ', p)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A two-sample bootstrap hypothesis test for difference of means\n",
    "We now want to test the hypothesis that Frog A and Frog B have the same mean impact force, but not necessarily the same distribution, which is also impossible with a permutation test.\n",
    "\n",
    "To do the two-sample bootstrap test, we shift both arrays to have the same mean, since we are simulating the hypothesis that their means are, in fact, equal. We then draw bootstrap samples out of the shifted arrays and compute the difference in means. This constitutes a bootstrap replicate, and we generate many of them. The p-value is the fraction of replicates with a difference in means greater than or equal to what was observed.\n",
    "\n",
    "The objects forces_concat and empirical_diff_means are already in your namespace.\n",
    "\n",
    "#### Instructions\n",
    "\n",
    "    1-Compute the mean of all forces (from forces_concat) using np.mean().\n",
    "    2-Generate shifted data sets for both force_a and force_b such that the mean of each is the mean of the concatenated array of impact forces.\n",
    "    3-Generate 10,000 bootstrap replicates of the mean each for the two shifted arrays.\n",
    "    4-Compute the bootstrap replicates of the difference of means by subtracting the replicates of the shifted impact force of Frog B from those of Frog A.\n",
    "    5-Compute and print the p-value from your bootstrap replicates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "force_a =np.array([ 1.612,  0.605,  0.327,  0.946,  0.541,  1.539,  0.529,  0.628,\n",
    "        1.453,  0.297,  0.703,  0.269,  0.751,  0.245,  1.182,  0.515,\n",
    "        0.435,  0.383,  0.457,  0.73 ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value:  0.0048\n"
     ]
    }
   ],
   "source": [
    "forces_concat = np.concatenate((force_a, force_b))\n",
    "mean_force = np.mean(forces_concat)\n",
    "\n",
    "shifted_force_a = force_a - np.mean(force_a) + mean_force\n",
    "shifted_force_b = force_b - np.mean(force_b) + mean_force\n",
    "\n",
    "rep_shifted_force_a = draw_bs_reps(shifted_force_a, np.mean, 10000)\n",
    "rep_shifted_force_b = draw_bs_reps(shifted_force_b, np.mean, 10000)\n",
    "\n",
    "diff_rep = rep_shifted_force_a - rep_shifted_force_b\n",
    "emp_diff_mean = np.mean(force_a) - np.mean(force_b)\n",
    "\n",
    "p = np.sum(diff_rep >= emp_diff_mean) /len(diff_rep)\n",
    "print('p-value: ', p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The vote for the Civil Rights Act in 1964\n",
    "The Civil Rights Act of 1964 was one of the most important pieces of legislation ever passed in the USA. Excluding \"present\" and \"abstain\" votes, 153 House Democrats and 136 Republicans voted yea. However, 91 Democrats and 35 Republicans voted nay. `Did party affiliation make a difference in the vote?`\n",
    "\n",
    "To answer this question, you will evaluate the hypothesis that the party of a House member has no bearing on his or her vote. You will use the fraction of Democrats voting in favor as your test statistic and evaluate the probability of observing a fraction of Democrats voting in favor at least as small as the observed fraction of 153/244. (That's right, at least as small as. In 1964, it was the Democrats who were less progressive on civil rights issues.) To do this, permute the party labels of the House voters and then arbitrarily divide them into \"Democrats\" and \"Republicans\" and compute the fraction of Democrats voting yea.\n",
    "\n",
    "   #### Instructions\n",
    "\n",
    "    1-Construct Boolean arrays, dems and reps that contain the votes of the respective parties; e.g., dems has 153 True entries and 91 False entries.\n",
    "    2-Write a function, frac_yea_dems(dems, reps) that returns the fraction of Democrats that voted yea. The first input is an array of Booleans, Two inputs are required to use your draw_perm_reps() function, but the second is not used.\n",
    "    3-Use your draw_perm_reps() function to draw 10,000 permutation replicates of the fraction of Democrat yea votes.\n",
    "    4-Compute and print the p-value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value:  0.9998\n"
     ]
    }
   ],
   "source": [
    "dems = np.array([True] * 153 + [False] * 91)\n",
    "reps = np.array([True] * 136 + [False] * 36)\n",
    "\n",
    "def frac_yea_dems(dems, reps):\n",
    "    frac = np.sum(dems) / len(dems)\n",
    "    return frac\n",
    "perm_replicates = draw_perm_reps(dems, reps, frac_yea_dems, 10000)\n",
    "\n",
    "p = np.sum(perm_replicates >= (153/244)) / len(perm_replicates)\n",
    "print('p-value: ', p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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