{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# HIDDEN\n",
    "\n",
    "from datascience import *\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "\n",
    "import matplotlib\n",
    "matplotlib.use('Agg', warn=False)\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plots\n",
    "plots.style.use('fivethirtyeight')\n",
    "import warnings\n",
    "warnings.simplefilter(action=\"ignore\", category=FutureWarning)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# HIDDEN \n",
    "\n",
    "baby = Table.read_table('baby.csv')\n",
    "hybrid = Table.read_table('http://www.stat.ufl.edu/~winner/data/hybrid_reg.csv')\n",
    "hybrid = hybrid.drop(['carid', 'mpgmpge'])\n",
    "hybrid = hybrid.relabel('accelrate', 'acceleration')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# HIDDEN\n",
    "\n",
    "def standard_units(x):\n",
    "    return (x - np.mean(x))/np.std(x)\n",
    "\n",
    "def correlation(table, x, y):\n",
    "    x_in_standard_units = standard_units(table.column(x))\n",
    "    y_in_standard_units = standard_units(table.column(y))\n",
    "    return np.mean(x_in_standard_units * y_in_standard_units)\n",
    "\n",
    "def slope(table, x, y):\n",
    "    r = correlation(table, x, y)\n",
    "    return r * np.std(table.column(y))/np.std(table.column(x))\n",
    "\n",
    "def intercept(table, x, y):\n",
    "    a = slope(table, x, y)\n",
    "    return np.mean(table.column(y)) -  a * np.mean(table.column(x))\n",
    "\n",
    "def fitted_value(table, x, y, given_x):\n",
    "    a = slope(table, x, y)\n",
    "    b = intercept(table, x, y)\n",
    "    return a * given_x  + b\n",
    "\n",
    "def fit(table, x, y):\n",
    "    a = slope(table, x, y)\n",
    "    b = intercept(table, x, y)\n",
    "    return a * table.column(x) + b\n",
    "\n",
    "def scatter_fit(table, x, y):\n",
    "    table.scatter(x, y, s=15)\n",
    "    plots.plot(table.column(x), fit(table, x, y), lw=2, color='darkblue')\n",
    "    plots.xlabel(x)\n",
    "    plots.ylabel(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The methods that we have developed for inference in regression are valid if the regression model holds for our data. If the data do not satisfy the assumptions of the model, then it can be hard to justify calculations that assume that the model is good.\n",
    "\n",
    "In this section we will develop some simple descriptive methods that can help us decide whether our data satisfy the regression model.\n",
    "\n",
    "We will start with a review of the details of the model, which specifies that the points in the scatter plot are generated at random as follows.\n",
    " \n",
    "- Tyche creates the scatter plot by starting with points that lie perfectly on a straight line and then pushing them off the line vertically, either above or below, as follows:\n",
    "    - For each $x$, Tyche finds the corresponding point on the true line, and then adds an error.\n",
    "    - The errors are drawn at random with replacement from a population of errors that has a normal distribution with mean 0 and an unknown standard deviation.\n",
    "    - Tyche creates a point whose horizontal coordinate is $x$ and whose vertical coordinate is \"the height of the true line at $x$, plus the error\". If the error is positive, the point is above the line. If the error is negative, the point is below the line.\n",
    "- We get to see the resulting points but not the true line on which the points started out nor the random errors that Tyche added."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### First Diagnostic: The Scatter Plot\n",
    "It is always helpful to start with a visualization. Continuing the example of estimating birth weight based on gestational days, let us look at a scatter plot of the two variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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bzbFjx4DQFFFpaSnFxcWkpqaSm5vLT37yExYtWkRBQQFXXnkln3zyCe+99154v0JSUhIL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\ngAgIgiAIQgkREARBEAQA/h96YOarTLOvQwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1028b3240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "baby.scatter('Gestational Days', 'Birth Weight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The points do appear to be roughly clustered around a straight line. There is no strikingly noticeable curve in the scatter. \n",
    "\n",
    "A plot of the regression line through the scatter plot shows that about half the points are above the line and half are below the line almost symmetrically, supporting the model's assumption that Tyche is adding random errors that are normally distributed with mean 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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vCbbuKMPnV5EliSxbGrpuoBsGa9dvjtskp7NouUQEnWsMerpYX3fTpgX3rKws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\nMS2NWoqMCK1yJJPp+G5uzri5ObMj9RA7Ug+JPgWhTpruX7lw0w4cuMb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j4+PD3r17q90v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\nREAQBEEQABEQBEEQhOtEQBAEQRAA+H+QjywTNpT4iwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a9a0fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scatter_fit(baby, 'Gestational Days', 'Birth Weight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Second Diagnostic: A Residual Plot\n",
    "We cannot see the true line that is the basis of the regression model, but the regression line that we calculate acts as a substitute for it. So also the vertical distances of the points from the regression line act as substitutes for the random errors that Tyche uses to push the points vertically off the true line.\n",
    "\n",
    "As we have seen earlier, the vertical distances of the points from the regression line are called *residuals*. There is one residual for each point in the scatter plot. The residual is the difference between the observed value of $y$ and the fitted value of $y$:\n",
    "\n",
    "For the point $(x, y)$,\n",
    "\n",
    "$$\n",
    "\\mbox{residual} ~~ = ~~ y ~-~\n",
    "\\mbox{fitted value of }y\n",
    "~~ = ~~ y ~-~\n",
    "\\mbox{height of regression line at }y\n",
    "$$\n",
    "\n",
    "The table ``baby_regression`` contains the data, the fitted values and the residuals:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>Gestational Days</th> <th>Birth Weight</th> <th>Fitted Value</th> <th>Residual</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>284             </td> <td>120         </td> <td>121.748     </td> <td>-1.74801</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>282             </td> <td>113         </td> <td>120.815     </td> <td>-7.8149 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>279             </td> <td>128         </td> <td>119.415     </td> <td>8.58477 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>282             </td> <td>108         </td> <td>120.815     </td> <td>-12.8149</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>286             </td> <td>136         </td> <td>122.681     </td> <td>13.3189 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>244             </td> <td>138         </td> <td>103.086     </td> <td>34.9143 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>245             </td> <td>132         </td> <td>103.552     </td> <td>28.4477 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>289             </td> <td>120         </td> <td>124.081     </td> <td>-4.0808 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>299             </td> <td>143         </td> <td>128.746     </td> <td>14.2536 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>351             </td> <td>140         </td> <td>153.007     </td> <td>-13.0073</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>\n",
       "<p>... (1164 rows omitted)</p"
      ],
      "text/plain": [
       "Gestational Days | Birth Weight | Fitted Value | Residual\n",
       "284              | 120          | 121.748      | -1.74801\n",
       "282              | 113          | 120.815      | -7.8149\n",
       "279              | 128          | 119.415      | 8.58477\n",
       "282              | 108          | 120.815      | -12.8149\n",
       "286              | 136          | 122.681      | 13.3189\n",
       "244              | 138          | 103.086      | 34.9143\n",
       "245              | 132          | 103.552      | 28.4477\n",
       "289              | 120          | 124.081      | -4.0808\n",
       "299              | 143          | 128.746      | 14.2536\n",
       "351              | 140          | 153.007      | -13.0073\n",
       "... (1164 rows omitted)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "baby2 = baby.select(['Gestational Days', 'Birth Weight'])\n",
    "fitted = fit(baby, 'Gestational Days', 'Birth Weight')\n",
    "residuals = baby.column('Birth Weight') - fitted\n",
    "baby_regression = baby2.with_columns([\n",
    "        'Fitted Value', fitted,\n",
    "        'Residual', residuals\n",
    "    ])\n",
    "baby_regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once again, it helps to visualize. The figure below shows four of the residuals; for each of the four points, the length of the red segment is the residual for that point. There is one such residual for each of the other 1170 points as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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w6J7H2bqjFK9PRZYkMmwp6LqBbhisXb85ZpOcc0XrJSI4t8ZgzWsbeDjkdU8T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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a9bf908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "points = Table().with_columns([\n",
    "        'Gestational Days', [148, 244, 338, 351],\n",
    "        'Birth Weight', [116, 138, 102, 140]\n",
    "    ])\n",
    "\n",
    "scatter_fit(baby, 'Gestational Days', 'Birth Weight')\n",
    "for i in range(4):\n",
    "    f = fitted_value(baby, 'Gestational Days', 'Birth Weight', points.column(0)[i])\n",
    "    plots.plot([points.column(0)[i]]*2, [f, points.column(1)[i]], color='red', lw=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "According to the regression model, Tyche generates errors by drawing at random with replacement from a population of errors that is normally distributed with mean 0. To see whether this looks plausible for our data, we will examine the residuals, which are our substitutes for Tyche's errors.\n",
    "\n",
    "A *residual plot* can be drawn by plotting the residuals against $x$. The function ``residual_plot`` does just that. The function ``regression_diagnostic_plots`` draws the origbinal scatter plot as well as the residual plot for ease of comparison."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def residual_plot(table, x, y):\n",
    "    fitted = fit(table, x, y)\n",
    "    residuals = table[y] - fitted\n",
    "    t = Table().with_columns([\n",
    "            x, table[x],\n",
    "            'residuals', residuals\n",
    "        ])\n",
    "    t.scatter(x, 'residuals', color='r')\n",
    "    xlims = [min(table[x]), max(table[x])]\n",
    "    plots.plot(xlims, [0,0], color='darkblue', lw=2)\n",
    "    plots.title('Residual Plot')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def regression_diagnostic_plots(table, x, y):\n",
    "    scatter_fit(table, x, y)\n",
    "    residual_plot(table, x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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vCbbuKMPnV5EliSxbGrpuoBsGa9dvjtskp7NouUQEnWsMerpYX3fTpgX3rKws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\nREAQBEEQABEQBEEQhOtEQBAEQRAA+H+QjywTNpT4iwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109fb0400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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rSPLFUYROgewcBCFcQrXJfvNNf4O6MxIdrd74IyIwLrgALS8PY+RIf9uMYNQL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\nvPh/KxsgbncflC0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ad9ba58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "regression_diagnostic_plots(baby, 'Gestational Days', 'Birth Weight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The height of each red point in the plot above is a residual. Notice how the residuals are distributed fairly symmetrically above and below the horizontal line at 0. Notice also that the vertical spread of the plot is fairly even across the most common values of $x$, in about the 200-300 range of gestational days. In other words, apart from a few outlying points, the plot isn't narrower in some places and wider in others.\n",
    "\n",
    "All of this is consistent with the model's assumptions that the errors are drawn at random with replacement from a normally distributed population with mean 0. Indeed, a histogram of the residuals is centered at 0 and looks roughly bell shaped."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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8Op0OU6ZMgVKpRHp6ukFbaxy3RqPBsmXL4OfnBxcXF3h5eeG9995DaWlpjX6t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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b347588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "baby_regression.select('Residual').hist()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These observations show us that the data are fairly consistent with the assumptions of the regression model. Therefore it makes sense to do inference based on the model, as we did in the previous section."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using the Residual Plot to Detect Nonlinearity\n",
    "Residual plots can be used to detect whether the regression model does not hold. The most serious departure from the model is non-linearity.\n",
    "\n",
    "If two variables have a non-linear relation, the non-linearity is sometimes visible in the scatter plot. Often, however, it is easier to spot non-linearity in a residual plot than in the original scatter plot. This is usually because of the scales of the two plots: the residual plot allows us to zoom in on the errors and hence makes it easier to spot patterns."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"https://upload.wikimedia.org/wikipedia/commons/7/75/Dugong_dugon.jpg\"/>\n",
    "\n",
    "As an example, we will study a [dataset](http://www.statsci.org/data/oz/dugongs.html) on the age and length of dugongs, which are marine mammals related to manatees and sea cows. The data are in a table called `dugong`. Age is measured in years and length in meters. The ages are estimated; most dugongs don't keep track of their birthdays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>Age</th> <th>Length</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>1   </td> <td>1.8   </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1.5 </td> <td>1.85  </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1.5 </td> <td>1.87  </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1.5 </td> <td>1.77  </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2.5 </td> <td>2.02  </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>4   </td> <td>2.27  </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>5   </td> <td>2.15  </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>5   </td> <td>2.26  </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>7   </td> <td>2.35  </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>8   </td> <td>2.47  </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>\n",
       "<p>... (17 rows omitted)</p"
      ],
      "text/plain": [
       "Age  | Length\n",
       "1    | 1.8\n",
       "1.5  | 1.85\n",
       "1.5  | 1.87\n",
       "1.5  | 1.77\n",
       "2.5  | 2.02\n",
       "4    | 2.27\n",
       "5    | 2.15\n",
       "5    | 2.26\n",
       "7    | 2.35\n",
       "8    | 2.47\n",
       "... (17 rows omitted)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dugong = Table.read_table('http://www.statsci.org/data/oz/dugongs.txt')\n",
    "dugong"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is a regression of length (the response) on age (the predictor). The correlation between the two variables is about 0.83, which is quite high."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.82964745549057139"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(dugong, 'Age', 'Length')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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O6vfv349WrVohOjoajo6OcHBwwOTJk5GRkSFgpUS6KTb2Pvr124sLFzLQqlU9HD7swaDX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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c0df710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scatter_fit(dugong, 'Age', 'Length')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "High correlation notwithstanding, the plot shows a curved pattern that is much more visible in the residual plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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XrhorlPTDw4eFmDjxGGJj78PAQIIFC3pgwABjtiUmekUv1fWyQYMG6N27t6Zq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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109cb2320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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RK+jtmJpqejtEpH9aewzr1q3D5MmT0axZM6xdu7bKu6AXL15c48XRc+IdvURU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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b789518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "regression_diagnostic_plots(dugong, 'Age', 'Length')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At the low end of ages, the residuals are almost all negative; then they are almost all positive; then negative again at the high end of ages. Such a discernible pattern would have been unlikely had Tyche been picking errors at random with replacement and using them to push points off a straight line. Therefore the regression model does not hold for these data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As another example, the dataset `us_women` contains the average weights of U.S. women of different heights in the 1970s. Weights are measured in pounds and heights in inches. The correlation is spectacularly high – more than 0.99."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.99549476778421608"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "us_women = Table.read_table('us_women.csv')\n",
    "correlation(us_women, 'height', 'ave weight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The points seem to hug the regression line pretty closely, but the residual plot flashes a warning sign: it is U-shaped, indicating that the relation between the two variables is not linear."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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5eQT2vyZDMQud0qr8n376aW7cuEHr1q3p3bs38+fPx8vLC3t7+8d6sRMnThAU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\nCH8AsBDhDwAWIvwBwEJX4YVlEH8qHEgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d9912e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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IseT1JScH0uho2CkUQE6OqdMQEQEArEwdQBRycmATEgJJVhbsCwpgc/48HkRFATKZqZMR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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10dac0320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "regression_diagnostic_plots(us_women, 'height', 'ave weight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These examples demonstrate that even when correlation is high, fitting a straight line might not be the right thing to do. Residual plots help us decide whether or not to use linear regression."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using the Residual Plot to Detect Heteroscedasticity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Heteroscedasticity* is a word that will surely be of interest to those who are preparing for Spelling Bees. For data scientists, its interest lies in its meaning, which is \"uneven spread\". \n",
    "\n",
    "Recall the table `hybrid` that contains data on hybrid cars in the U.S. Here is a regression of fuel efficiency on the rate of acceleration. The association is negative: cars that accelearate quickly tend to be less efficient."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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BgiqPUZcLYCnZ2dmqiAPMjyU25hTpu37Eu3lpK9rN1Y1+vbrQPeIOo/W3NGxEUHt/Q1nm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\n7+9PSEgI8fHxnDp1SvFYKpo+fToeHh6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DB2JiYozml61YWhk3bhz+/v78+9//ZtOmTRQV\nFeHn50dUVBSdO3eucr8y0dHRLFq0iBUrVpCWlkbHjh1ZuXIlixcvNtqnU6dOJCQksG7dOtatW4de\nr+fHH3+kdevWlY7Zr18/3n//fRYtWsT48eNp0KABvXv3Zv78+VV2nyyvquXCMckcqkII4YCk5i6E\nEA5IkrsQQjggSe5CCOGAJLkLIYQDkuQuhBAOSJK7EEI4IEnuQgjhgCS5CyGEA5LkLoQQDuj/A3BV\nlPQjUxRUAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10db4c400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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qRdUMFkV+LoCOicDd3R2FQoFKpdLYXrxNoVCQkpJikACFMIi0NByXLlVPjOe4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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ddf59e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "regression_diagnostic_plots(hybrid, 'acceleration', 'mpg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice how the residual plot flares out towards the low end of the accelerations. In other words, the variability in the size of the errors is greater for low values of acceleration than for high values. Such a pattern would be unlikely under the regression model, because the model assumes that Tyche picks the errors at random with replacement *from the same normally distributed population*.\n",
    "\n",
    "Uneven vertical variation in a residual plot can indicate that the regression model does not hold. Uneven variation is often more easily noticed in a residual plot than in the original scatter plot."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Accuracy of the Regression Estimate\n",
    "We will end our discussion of regression by pointing out some interesting mathematical facts that lead to a measure of the accuracy of regression. We will leave the proofs to another course, but we will demonstrate the facts by examples. Note that all of the facts hold for all scatter plots, whether or not the regression model is good.\n",
    "\n",
    "**Fact 1.**\n",
    "No matter what the shape of the scatter diagram, the residuals have an average of 0. \n",
    "\n",
    "In all the residual plots above, you have seen the horizontal line at 0 going through the center of the plot. That is a visualization of this fact.\n",
    "\n",
    "As a numerical example, here is the average of the residuals in the regression of birth weight on gestational days of babies:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-6.3912532279613784e-15"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(baby_regression.column('Residual'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That doesn't look like 0, but in fact it is a very small number that is 0 apart from rounding error.\n",
    "\n",
    "Here is the average of the residuals in the regression of the length of dugongs on their age:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.8783559897689243e-16"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dugong_residuals = dugong.column('Length') - fit(dugong, 'Age', 'Length')\n",
    "np.mean(dugong_residuals)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once again the mean of the residuals is 0 apart from rounding error. \n",
    "\n",
    "This is analogous to the fact that if you take any list of numbers and calculate the list of deviations from average, the average of the deviations is 0."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Fact 2.** No matter what the shape of the scatter diagram, the SD of the fitted values is $|r|$ times the SD of the observed values of $y$.\n",
    "\n",
    "To understand this result, it is worth noting that the fitted values are all on the regression line whereas the observed values of $y$ are the heights of all the points in the scatter plot and are more variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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vCbbuKMPnV5EliSxbGrpuoBsGa9dvjtskp7NouUQEnWsMerpYX3fTpgX3rKws\nkpKSOnssbNu2jTfeeCMqiNzS/RUIehqtCcHFO7498g3lh45TUnYwEBA2K+zZd4TJY0eQlZkWuKbJ\nhMkkIcsSwX8uyUkWTCYTGRmpzCgcTU2dkx2f7UNVdWQpUJB2pq4Bn6rGbJLT3jHGOz5eEL2rjUF7\nv6MLkTZ5CMuWLePVV1/lmmuuadZb7xy2b9/OqVOnKCgoCG3TNI2f//znvPTSS3zxxRfk5eWhaRq1\ntbURXkJVVRXTpk2Le+5EaqydSHOBxJhPnaMRl9uFophwuVyoqsbhw4epq4nOOvr929vY+XlgzlMn\njuC782ec8/xrfvduIHYgSYFlIsNgwwefIMsymRlWNF3H0eDGZAKzYkKWZFKtSdTUOfF4vfz+Tx9y\nvPIkmqah6Sq6HjivoRs4nW4UWSYrIyU05ugxtj6+c81p7rSRoRqNLFtalDEoLMzi+efHd+pvoT3f\nUW+ho2MhcQ3CL37xi1B2j2EYHDhwgMLCQmbNmkVmZmbU8StXrvzGg7nzzjv59re/HfrbMAxuvvlm\nbrnlFm6//XYAJkyYgNlsZsuWLRFB5eD44pEoQaREC4j1xvnEy5aZN/d4aDniW7MncNmUiVHvq6lz\nsqf8BDZbIFi6p/wEWdl5ra5nn6l1UHm6gSxbOnUNjfhVDXtmGj6/jmEElocMw0CSZFRNI9liwuP1\ngxTwFnRdp6a+kV37jjFi6AA+/+IwhJWwGYDD6WbsqOHYsnLRm8cVHOPOzyu4b+nNccd4ptYRcXzJ\nF0dZ9J2UmIVox483MmbMGxHb/v737zBhQk7UsZ3Bub6jC524BuGZZ56Juf3QoUMxt7fVILhcrtA5\ndF3n2LFjlJWVYbfbyc/PJycn8oehKAp5eXkMGzYMAJvNxm233caqVavIzc0NpZ2OGTOGq666qk1j\nEAjOl9ayZcKF4FrePMOrjk9V1TK0DTLTLZk0bjj19Y3sO3iMS0YMYv/BsyqjHq8PVVPRNAOP14/P\n78fvV9Gb148a3R7K9n2FySRhsSio/kCXtSCarvM/b33An/728TcSozty7HRcwbtbb93E++8fizi+\nqyuPW/uOBK3EEOrq6tr1X1spLS1l5syZzJw5E4/HQ1FRETNnzqSoqKjN5ygqKuKGG25gyZIlXH/9\n9aSnp/Pmm2/GrWkQCDqC1kTqgmTZ0lrNslEUE6qutUvoLWINXtMYNWIQyRYLGWkppKUmk5aaDJKE\nYlKQJFCFTS8/AAAgAElEQVQ1DZNJjhl707SA/kSsfV6vH8MwQmJ0DocLt9sbqkM4V4wg2HQnN9sW\nJXiXmflKtxuDILG+I0GALm+QM2PGjHYZkLKysqhtFouFp556iqeeeqojhyYQdCpHjp2mprYB3TC4\nae4w7r/jpjbfmO69fR6v/eF9Dh89hSRJZGZYSU+z0uB0Y0tLJSXJjK4bqKoaWCYyInWNIpACdQup\nKck0NXlDgWg9zGOAs4tKhmGcs44gvOmO1RqZgNLVwWPB+SPKegWCNtIeyYnwp+kcu43CSQVU1zgw\ngNxsG1/s+5qaOmfcLJeWT+M7S/fz1bHTyHKg8uBMrTPQ3MZkot7ZeLZYTVHQdR2jZZlyGBIBHSOz\nYsJkklEUBbPZRHKyBcMwsFqTUBQZa0oSimJi2z/3sWlrSSC11TDiZucUDMuPku8ePvQPUccdPPwv\ncccm6F7a5CFkZWVFBJiDSJKEJEmkp6czYcIE7r//fubMmdM5IxUIegDnkpyA2HGGYEtLRZGxWMwc\nOHScH/7sN6RZk6OeuGO9v77BhaZpgBT6N9jo8tDoOisj4/e7SEqyhETwWroISc19EjxePx6vH0mC\nrIw0brlxBmVffsXJ07Vohk6/vGwOfX0iJHWdlKRgsbhxOgNGJyszflZO8PM5csTJ1bPfjdg3eZaD\nzJxo2RtBz6FNBmH58uWsW7cOr9fL3LlzycvLo6qqis2bN5OUlMSNN97Itm3buPXWW/n973/P9ddf\n39njFgi6jdaWeeocjXGrcq+bNZktH+/mwKFKTp2pp6GxiRx7RsQxsap6XW4P24r3IklShJaRLEmh\noDEE7v8eb0DKIlbpjt+vQgsJPLfHy+4vv+JMnYMTVTVAIG3V5faQkmxBkuTAOwwp/hJUCy4e/seI\ncQLMufV04P9tiJkIuo82GYTk5GQGDx7Mn/70J5KTk0Pbm5qauPnmm8nJyeGjjz5iwYIF/OpXvxIG\nQSCIQXCd/Uc/+w3ORjeSLHGmtoG87Exq6pyh43x+Fa/Pj9msoKpas2dhwm5Lx+fzoxkGvub97ZG8\nNgjISKMFbtYmWSbJYsHvV6mrcwZu+IZBTZ2TJIuZS0YMwmJWaHA2Yk2xoiiBFWZZir/SHC9e0BZh\nO0H306YYwtq1a1m2bFmEMQBISUnh3nvv5b//+78xmUzcdtttfPHFF50yUIGgN5BlS2s1zpCdlU6q\nNZlse0agoY1hYLGYeOSJ17j7oef44c9eZN/Bo+z8fD87S/djsZiwmBUsFoVsewaKWSEvx4YtIxWl\nnUWihhGQ0A7niktHcd2syTR5fYFWmppOo7uJ3GwbyRYLsiRz5WWXcN2syc1y13Lcp/zWgsdBTSZB\nz6ZNHkJNTQ2qqsbc5/f7qakJuJp2u13ITAgueFqLM4RLROdlZzJ57HD27D+CYjbh86ns+GwfsiSR\nnpqMroPPpzGjcDTFpeXkZWdy/VVTuG/JPGrqnOz+8it++h+/xelyYegGVmsKhmHgcp97nd5iVhg2\nuD//esvVXDSwD6//eQsnTteCYaAoJvrm2vnPh+8gOyudw4cPM3To0FZjJyKTKDFok0GYMGECTz75\nJJdddhn9+p0tVjlx4gRPPvkkEycGqv2OHTtG3759O2ekAkEvorWn4Zbd0+5+KFK7K/C0rmNgcPzk\nmVB7zW3Fe9mz/wg//NmLVHx1guoaB16fn4xUK01eH253EyARI54cRbAt5/fuf5KMdCu2jFTMigm/\nqqFpOsdPniE7K531Gz5qVQzu0CEHkydHZhI9++wVLF066pyfkaDn0SaDUFRUxPz585k4cSJTpkwh\nNzeXqqoqPv30U6xWK7/5zW8AOHz4MLfe2rVqiQLBueiM9etves7w9wU9BlmSmDJuBNtL9gEGSWYF\nTdf4rOxgoAezIuPx+SjZU4EsB0TuvD6VeqcLWZJAkgmYAil2VDkGkizR0OjGYraAEQg5W8wKSAYH\nj5wMicHphs6mrSURstWd7RWIuEPX06YGORBYNlqzZg2ffvopp0+fpm/fvlx66aXce++9UVLUgs6j\nN2r/tEZnz+dcBVUdfc7znU94Xv+Sn/wKwzD4suIoDY1uUlOS8asqKclJGIaOu8mHNSUJk0mm0eXB\n6/UiSRJaK7UH8ZBlGUPXSU1NwZ6VxqB+eZyqrqO23smIiwZQW9+Aqqo0NHowDIN/u+1b/PSeWzvd\nGHTG9xYk0f4NdSRtrlTOzs7mZz/7WWeORSDoUM7VmKW7zhn+5BsUvMvOSg/9PaNwNB9+vJsGpwuL\nxYyimHC63FiUQG/l5GQztgxrc52AgT0znYbGJjQ9dpyvNXRdR1Fkcu0Z6JqB0+XmTK2DPrlZZNpS\nqTpTR02dE4vZHJLI7grPoKO/N0Hb6HLpCoHgQib8yTcpSaHiqxMBg5CZzoih/fF6m2/qUuBp369q\n4PGGeoU3NgeMx44cwov/eT/3rHie02fqUFUt+mKtECw0VRQJDImvK6vRdZ1TZxSksL7k+f1yyUhL\nwp6VhcWi8N66aFVS+6gdLL6vhnXPP9y+D0PQ44hrEG688UaeffZZLr74Ym688ca4wnEB2V2JDRs2\ndNogBYLz4VxN37/pOX1+lRmFY9p8zvAn3/CMIpNioqa+gerPHEwcE1D1LT94nIw0Kw0uNz6fzoA+\nOVQ2F45ZzAp7y48Gqpd1DZ9fbXd2n2EYZNnScDd58PrPehaqpmOWZE6eriUzI435c6dSVV3F9p1V\nfPpBdsQ5krJOkZF/BJDZWVpO+aHjMSWv20tnfG+CthHXIIT/wIKvRUqpoLfRFqmJ8zlnsHq4uHQ/\na363oUPXuI+eqKbR7cGsKJhNJsxmM9deNZn/9+cPUVUNv6rh87t5+sU/0uB0A60I2YWhmGTUsDoE\nh9MVVVGsaTqa5gsFmA0Mfv0LDYg0Bjs/u45v/evP6Cw5tM743gTnJq5B+Nvf/hbztUDQ2zjf9f3W\njikuLQ+perZ1jTv8yVeWJKZNueTsklFWBiMu6o+z0UNNbQMZqSk0uJoAg755dvYdPIY1yYLDH7iJ\nS5KEz69isZhRG1ytXleWA5IXaouitJbGIBxJDnguK390KmpfMF4wdVIBO0vLm1+P7BDvIBxhCLoe\nEUMQCJppLbOlo1IgWz75hgeVAZ588Y/s/vIwRqBPJgC19U48Xj+qqoMR1DMy2LP/SJuu2dqNvyUZ\n6daQHMb2t6Nv8HNuPR3yiNY9/zDlhwJNejraGAi6hzb7e5WVlaxYsYKZM2cybtw4vvzySwDWrFnD\nZ5991mkDFAi6gtaa36z53Qbufug57n7oOdb8bkO7ZLBjES7jkGO3UTAsn/UbPmLJT37F63/aSpPH\ni6upCVXT0Y1Ae8uTVbU0uNwRXc46AwmJjDQrTYevitp37eIzUZ9NwbB8YQwSiDZ5CPv27eP666/H\nZDIxZcoUysrK8PkCqorHjh3j888/59VXX+3UgQoE3UFkINgfKs4KPumHP93Hez/E9yyCHsKWj3dj\nGEazRIxEakoyja6mQNIG56487gjSrMk8uuwulv9oX8R2a4aHybNrgCR8vmZPRZCQtMkgPProoxQU\nFPDWW2+RkpJCbm5uaF9hYSGrVq3qtAEKBF1BvMyW4A39yLHTnKltwDAM1q7fzE/vuZX1Gz5qtXjq\nXMVVEX2Wq2vJ75eLxazg86uY5EDv4yaPr7OnHqLx4MwoYzD7ltOMv2QAOTlDeG39+9TUO0OSFh0Z\nSBf0DNpkEHbu3Mkrr7xCenp6lMhdUMZCIOjtxMpsCXY7+/x/DiFLUqg4q/zQ8ZjFU3WOxpARaa24\nKuh56EagMAwDVFWjf99sVFWnT04mNfUNnKlxUNciaGwxm9B0A5Mso2raOWMEqSlJuM4lk33i2qhN\nm7bMIMuWhqw3kZWdx6atJeT3z8ViUUSxWILSJoMgy3LcOoSampooWWyBoLcS6wZ3ttuZCYtFQfXH\nLgJbu34zWz4uJdWaSuGkgnNe62hlFbWOQFcyuy2NXz52Z2j5qabOySNPvEZNvTPqfT6/htQsV9SW\ngLFB7H+7IWIYg5wxn7D4vh1kZ6Zzw+wJ3Lf0ZixmJWTgBIlJm4LKEydO5PXXX4+57+2336awsLBD\nByUQ9CSC3c5kSQoFkQuG5UcElgsnjWwWoAsEpYtLyymcVIDq13C7vRROGhltbKRAbY9hBJL+w2MR\nBcPyGXPJYBripJQGjMG51/JlWaJPjg053r/0GMbAPmo7jgYXkiRR62hkyyd7+azsIGNHDgmbT4Hw\nDhKQNnkIP/3pT5k/fz7f/va3ueWWWwD4xz/+wYsvvsiGDRt45513OnWQAkF3E2s5qaWMdXHp/oj3\nhMtWt6WAbe36zRQ35/XPnj6exfNn8dr6D3C63BGegARYrSn4fX58cfqUBNF1g1PV9YDUXI/QbET8\naVB9ReTBssoV806xr+LspiaPl73lR/nu/U9iMSvk98uhb66d4tLyDi/IE3Q/bfIQpk+fzrp16/j6\n66+5//77Afj5z3/Ozp07WbduHZdeemmnDlIg6AnE6voV3BZKRVXPpqICoQK2lumaQKAaWJKQJAlV\na26VGZb2mp2VzrhRQ6KUrE2KzMhhAwLtMNtAk8eLRJhHceLaKGPQd/ynfGtxA8kWM9mZGdgyUtE0\nDU3T0I1AvMKvahw+eioQ94g1H0GvJ66H4HQ6SU8/68Jee+21XHvttRw6dIjq6mrsdjsXX3xxlwxS\nIOgN3Hv7PC4dnc/QoUMjMpTiMWhAHvn9A2JxsVI5167fzPGTZyIkYyQJzEpAFM/j87d5bCFp7BhL\nRPR/D0myc8WloyI8nidf/CNv/u9H+HwqmqYjtdEACXovcT2EIUOGcNVVV/HII4/wt7/9jbq6OgCG\nDRvG1KlThTEQCGKQZUuLylByu71RBWxBjyLYp/j6WVO4btZkVL9GvcNF/7523vt7CXX1jbTM5/B6\nfXGTPFoljjEA8Pp8/HVzMTV1TnLsNmrqnOyvOE7/vnZMioym6ygmExdfNIBkiyXCC4pl+M7UOiK2\nh/8d73VX053X7qnEbZDz2GOPsWPHDsrKylBVFUmSGDlyJFdccQXTpk1j2rRp9OnTp6vHe8GTaM09\nEnk+4XUGMwpH89N7orsJtixcu/kHq9nx6T68fn/MDCJZktANg+QkMx5v2z2EeMZAliVMJhOKSSbJ\nYmbsyItIT0vG2ehh74Gvyc22kZmejKrCfzx8B1MnjQyNOV4dRsv6CyBC8jso8R3+uqOb4LRGRUUF\nm3fs77QGPL2ZuB7C6tWr+fDDDzly5Ah//vOf+clPfkJmZib/8z//w9KlSxk5ciRTpkzhhz/8IW++\n+WZXjlkg6PGEVzhbrUkUl5ZHPY22NAblh45TUnYQv6ZFKQsH/QGz2USqNbntxsCf2qpnYFZMmEwy\nSBI59gx0w2Bnc7vO3Gwb1TUOVE3n5humM3XSyNB4a+qcbNpaEiX10VICZNPWktBxuqGzs7Qc3TAi\nXnd1PKLO0RhXpuRC55xZRqmpqcyaNYtZs2YB4PV6KSkpYceOHWzbto3XX3+d119/nYULF7bpgtu3\nb+e5556jrKyMkydPsmbNGhYvXgyAqqqsXr2aDz74gCNHjpCens6MGTNYtWoV+fln9VK8Xi+PPvoo\nf/7zn/F4PFx55ZU888wz9O/f/3w+A4Ggy4lXxez1+dE0LSKQbDLJKCZT8z4dr8/TtovEMATWodtQ\nNS+qFhTJkxg/6iKqqh3UOVzU1jtD1dFDBvYhLzuT+//1aubOnh4x9k1bS0IexJCBYqUgUWiXmLnf\n76e0tJQdO3awY8cOSktLMQyDoUOHtvkcbrebMWPGUFRUREpKSsRaqMvloqysjOXLl/PRRx+xbt06\njh8/zi233IKmnS0GWrFiBRs3bmTt2rW88847OJ1OFixY0Ka8bIGgK2hNAC+WkF5QNTQ1JTni34Qs\nScgYeH1+FJOM3taeJDGMgTTgPexZKSAFjIFJDpxv34FjaLqOBMiSTKo1GVXVUf0a18+awkVhN/zg\n2K3WpJAH4XZ7Q/NrOe/w2IgsyUydNDIwp7DX5yMQ+E3IsqV9I3HCRCZuDAECN+h//vOfbN++PWQA\nVFVlzJgxXH755UydOpVp06ZFaBu1h/z8fJ5++mkWLVoU95jy8nKmTp3Kjh07uOSSS3A4HIwYMYIX\nXnghVBNRWVnJ2LFjeeutt5g9e/Z5jaW3kMhr7olAy/nEErc7U+vg7oeeC1X9Hv76JH1z7QCcqqol\nLzeTr46e5sTpmvMbRJwlIoti4opLR1H8+QHcHi8mWUY2ySRbLFw0qA/paVYsZgVZkvjPh+8IvdVR\nV81lUybGHLvb7eWXj90ZpXjact4t+0jHet1VBL+j7rh2TyfuktGcOXPYs2cPiqIwadIkrrjiCh58\n8EEuvfTSiHTUzqahoQGAzMxMAHbt2oXf74+48Q8YMICCggKKi4sT3iAIehexbjYt23ACoWY7SIEU\n1Nq6hvO7YCvxAp+qsfWTPaHNmq4jyaDpGhVfnQAJ8vtks2TBXD74+POQmF1aahJ3f+8G7r19XpQI\n4PWzpsSUv45Vr3Gu112NMATRxDUIpaWlWK1W/uVf/oWZM2cybdo08vLyunJs+Hw+Hn30Ua6//nr6\n9esHQFVVFSaTCbvdHnFsbm4u1dXVXTo+geB8OFPrYMG8K0Py2Y888Vpo36D+edz13eu5a/n/bVed\nAaoVqmZEb282BrEYkp+HxWymqqYek8mEYRhkZ2UwZ/oEHlz9KrWOQMqro8EVkv3OsdtEe8sEJq5B\neP/999mxYwfbt2/nxz/+MfX19QwdOpTLL7+cyy+/nGnTpnHRRRd12sBUVeUHP/gBTqeT9evXf+Pz\nVVRUnPugXkIizQUurPn8/u1t7Pw8sH/qxBF8d/4Mxhb0D227fNLF2NNk7DYrjS532/ogxPIK+n4I\ncuuyFlU19TQ1+TAIaB5ZLAp+1cfXXx/B7Xbhdjfh13QwDL46doLDhw9TV5MWcY66mt6pdJwov7mO\nXm6NaxCmTJkSSivVdZ29e/eGgsmPP/441dXV9OnTJ2QgfvCDH3TYoFRV5fvf/z779+9n48aNoeUi\ngLy8PDRNo7a2NsJLqKqqYtq0aXHPmSjr1Im+5t7baW0+Z2od7Ck/gc2WAUDJF0dZ9J0Ufv7g0ohW\nmjl2G9+9eQ5rXtuIw9l6v+TWlohaw6yYSE6y0OTxg2EE+jQjMeOycUyaMJZrZ53ky4OVSICimEhJ\nTg5VYPd2Eu0315G0Wf567NixjB07lrvvvhuAkpISnnnmGd5++23efvvtDjMIfr+fpUuXUl5ezsaN\nG6MC1hMmTMBsNrNly5aIoPKBAweE6qqg13Dk2Gmqaxw8uPpVrps1GSAiDXXpgrls+Xg3B76qxOX2\n4I21fHSexkCWZUYOH8TBI5UExbEtFjO5dhslew5y90PPUTipgCnjLkY3DFS/l7TUtHOdVpAAtMkg\nQKDvQTDbaMeOHezduxdd15FlmfHjx7f5gi6Xi0OHDgEBsa1jx45RVlaG3W6nX79+3H777ezatYs3\n3ngDwzA4ffo0ADabjeTkZGw2G7fddhurVq0iNzeXzMxMVq5cyZgxY7jqqqvaN3uBoAsIf/ovnFTA\nlo93U13jIDfbhtWaxKatJQChlNJNW0u4evpECicXcPDrSvz+jjMGJlli6OC+zJ4+joNHTgRSXKVA\neqtJkVEUGd3Q2Va8l8ljh7Nn/xFcqi8qbRY6Ln7QWkaSoGuJm3Z6/Pjx0M1/x44doTU3i8XCxIkT\nmTZtGldccQWFhYWkpbX96WHbtm3cdNNNgYtLUqgic/HixTz00EOMHz8+YnuQF154IZSeGgw2v/XW\nW3g8HmbOnHnBFKYlmrub6PNZ87sNvPaH96mpcyLLElkZadizMqiqqePioYHsHLfby94DR3A2NqE1\nP2RlpKZQ52iMiCFIgGxY0U62L3gcer8UqDPIykzjkuGD2HvgSEgeIyPDikky0dDopsnjxTAMpoy7\nmBmFo7nq0uGhtNNztQVtL63JXHSWpESi/eY6krgewtixYwFISUlhypQpfOc732H69OlMmTKFlJSU\n877gjBkzQkJ5sWhtXxCLxcJTTz3FU089dd7j6E2IJ6beyZlaB5u2llBT58QwDBwNbjRNJ79/Dops\nwu32YjErTBo3nM/KKjAINMzRNI16Z3RA2ThxLVG92vpsAVPbspEMAzRDp97hwuF04XJ7sJjNAekK\nXUKTA5IZfr8a6I6myBSXlnPVpcND82mtLej5fD7h5wt6SsEUXNGms+uJaxAee+wxrrjiCiZOnIjF\nYunKMQnCaPkENXfayG4ekaA9HD9VjbPRDQTy/oMMGpDHfz58B9lZ6dTUOXn59XcDOwJqEtGc5xJR\nLFRNo2zfVwB4fYFMpEZXE2mpKWTZAt7+eampCno9caUrfvKTn1BYWCiMQTcSS+KgrrkHr6B3oMgm\nzGalObVTJj3ViqrqzJk+IWQMAFKSzYCB1Kw+ak0O+3fXRmNg+gb9CnTDIMuWhsPpxpZhxZ6ZhizJ\nzJk+gSxbGuWHjlNT54xqG9oaZ2odlB86Hlc4rjWZCyEp0T20OagsEAjaT7AJjs+vcuJ0DXnZWQB8\n/OkX/Pf6zdTUOwGDJo+PNGsKmRmpNDS6aXQ1C9i1wzPQYshlQyBttE9OJk6nmyavF3+MZjyyLDOg\nbw75/SR++didof7OOXYbN93xGF8cCGgtTZ1UwEtP3t/c7nM/xaX7Y671h8dOsjPTuWPBNTHjAbGK\n3ETRW/fRLnE7QdcSSyAt6NILeiZ1jsaImE94ExzFZCLTloqimNjx2T5q6huQJHA2NoER6H9cXeOg\n0dWEpiodtkwkSxIut4cRwwbENAaKSSYzI5UkizlKiqL80HF27zuCySRjMsnsLC3n4JGTFJeWR0hc\nB8X54GzspK6+EZNJptbRyKatJa16Ci3lLIQx6B6Eh9DDafkElSgVlolAy2D/mt9tYMPmHaRaU0NP\nzcHvL1yiwudX0XWjuem9gabraLpOkzcgOx3TEPTZCibfOcckSUT1YParGq4mD42NTVHH59gzGD64\nf6j2IcduC8lbA0weOxyj2ViF93B2uT0oionqWkdEPYVoNNO7EQahFyCelnoeLYP9C+ZdGYj3KGfj\nPcEMmXBZ6KBgnMWi4G7y4vO16IwWwxjI+Ztjdk+LRSx17EDmkEb54cqofaqqkZJiobi0nKUL5nKm\n1sFrf3ifuvpArGrfwaMAOJwuzGaFWZeP47/W/i+79x3G7w90Uhw6uB9Wa1LEnK+bNZlT1bWh+ovr\nZ00Rv+NegDAIAkE7iZV+efX0ifj8Kv5m9VKfXw31Jw56EgvmXcmmrSXk988FDD7/4hAjh+Vz+OtT\nOF1utONzoy/W/z1SU1Jwe7xoWsf3+9B1A59fQ5YC566pc1JT58RkklFVDYfTxeiLB5KRnoaq6vxw\n6XwW3/ckaakpqKpKQ2NTzBt9uGcUlOMQ9HzabBA0TaO0tJTjx4/j8UR3bGqtp4FAkOi8vfkTTlXV\nUlVTh9lcRZYtjUeeeC2ib3DhpIJAfr/ZhM/nR5ZlbBlp9MnLon7b9KhzSv3fwyCwPNPmxjjtpNHd\nROmeCvL75bB+w0csmHcl2ZnpVJ6uweP1oesGFYdPMHhgX/L75kS8V1EULGYzqho7K0jEAnofbTII\n+/fvZ/HixXz11VdxjxEGQXCh0LInQOGkkRSX7mfokH6kpyVx+GgV+f1yQn2Dx48aisWiUFxaTuGk\nAopLy0Mdw1yNKuXbRkdfpNkYJFkUFEXBrJjISLNyprYBr8+PbuhRy0NmRY4KGksQUzHVYlZItSbj\ndDWRZDGT3y8ntORz67wZrHltIz6/iskkoWo6p6vruPlbgb7KUycVsOOzfQDMmjaO//r3fwt9LoLe\nTZsMwgMPPICmabz22muMGjVK1CYILnjCg/0AxaX7gYCKqCzHT95bumAuSxcEloaGD/1D1P7kQdvx\nqmclK7w+Fa9PRZZlfD4/Xp8fSZIwm0z4/JF1y35VRzHJqM1LS8GgtaKY0FQNk0nGwMAwJKwpSciy\njER0EVpQWG/3vsOhc2WkW1m64BoArrh0NDV1jc2vRwlDkEC0ySCUlZXx/PPPM3/+/M4ej6AHIyQ0\nIgn/HIIegyRJTJ1UEFommjhmKD6fhixJEUsqmZmvRJ3vkaJMfvWqH0mXkIxAsZgcuGOj6zpen0pS\nkgWP1wfxwgnSWa/AMAysKUnNAWkDDLCYzQzJ74OqaVTXOEi1JpOZcbYILTi+2dPHs3vfVxiGgaIo\nJFnMQFhP5ZTAQ+H5ykuI31LPpE0GISsri6SkpM4ei6AH09GiZolG0GM4fPgwl02ZyJlaR3PxVjkQ\niB8su/1GILYx+I//25cF865kW/Fejp+s5mhldaBPQeDODgSkL4JBazVOgFkNWzIyDGjyeAFIspi5\n9YYZ3LfkJgqG5fPUi3/k9T9vocHpjhofBLyEbcV70Q0d1e+LkL8+WllFbXPFvP086mLEb6nn0qbC\ntGXLlvHqq6+iaVHSWoILgFgSGvGKjC4EztQ6Ys4/x26LKBwMFm9ZrUkUl5ZzptYR0xhcu/gMWz7e\nTU2dk8ljh1Nb3xihexSOX9WilIBbwzACS0KSJHHkeBXZWemh77PR5cFsVmhodLNpawk7m5e9gnO5\nbtZkki0WJEmKlKlo9kIkiK271Arit9Sziesh/OIXvwitLRqGEWpAM2vWrIgOZkFWrlzZeaMUCHoI\n5/t0q2uxYwbXLj4DBJ66H1z9KgDGORpntjfhSJYkVFXj+KlAz/G16zez/9CxgNqpxYzPp7J732EW\nLiti2pRLWPf8w8BZr+fpF94IyVQUTipgUP888vvlhs4tSBziGoRnnnkm5vZgc5uWCIOQuLTMqrlQ\nRcfaI/8c/pn9/S+5aGqkM/7FF4t4+8OtbPn4ND6/ClJA9tnnU/H5Wu+F3F4MDCxmM4rJRE2dk+LS\ncs+RzJgAACAASURBVLKzMgIBa68PTdexpiRjNivsLC2n/NDxCPmK3fu+DrX9LC4tZ+zIIZTsOYjF\nrLT7tyB+Sz2buAahLX0JBBcOsUTIBK1z7+3zWPmjU1Hb6+vvCu1vKWsBBJZkYkhQhO3GpMikJCXj\n8XrJzEjD51cDGkgxlprGXXJRKHAMcPREFY4GFylJZjIzUnG5PSQlmds0p6MnqgIGjOi4Q1sRv6We\nS5tiCMeOHcPni62j4vf7OXbsWIcOStAzudALjYJPt263F7fbe86n21jxgjm3no5YM8+x2ygYln9W\nxFDVsCZb4hoDkxxIGTUrCiaTRHqaFcNo1kWK8SZZBovZEsoiys5Kx+dVUTUNSZZJTrIwfvRFaJqO\npulMnTQywjvIsduYOnEEql/D4XChqjpWa1JEXOR8uNB/Sz2VNmUZjRs3jg8++IDJkydH7fviiy+Y\nM2cOtbW1HT44gaAn09pafyxjkDP6E46eiJ2VE+4tLFz2BPUNjcSKKyuKwtTJI/nPh5ZQ52jkP/7r\nTUr3VOD2eKOMiEmWSU9L4fEHvsfwIf3Isdu4+QerqayqAcMgyWLGMAzyjRxuu2U2i+fPijAGQb47\nfwZ/+WAXH368G4fTxZFjpxkysE/rH46gV/KN5a/9fr/oriS4IAjl4Dc/IcfKkNE0I6YxyB79Sauh\n4uB5srPSURSZlBhp3rIso+s6JWUHARg+pB+Txw5H1bSYHoXZojBtyiimThpJjt1G+aHjlJQF1v6R\nJFxNXmzpVqzWJL7Y93WoB0JL6hyNbCveizUlidxsG9U1jrgeUrwMLEHvIK6HUF9fT319fSjFrbKy\nkuzs7Ihj3G43b775Jn36iKcFQe+mIwqlFix4j/feOxqx7S8bZvLsb9ehG4En7+TmKv/w6wXlpv1+\nlamTRjKofx59crJwN3k5UnkKt8uDx6ei6wG5Co/Xx7q3t7KzpJyvj1eF2mAGMSsKIy7qT0aalSsu\nHRXa/sb//p1GtwcJCbNiwjAMBjTrE4WL8bXkrXd3svfA18iSRLY9g9EXD+aXj90Z5U2Ey2Z3hBS2\nKF7reuIahBdffDGiif3tt98e9yQPP/xwx45KIOhC2ppK2lqGTLxis+f/3x/YV3EUl8dLSpKFqZNG\nsn7DR2E6SAX8ceM2TpyqwedX2b3/K/L7ZnP8ZE2oqCwcwwj0RH759XcDmkYxZLH9qsqZWgcDB+SG\nMqEA9uw/gt2WRp2jEb+qMXRQX5IsZg4fOQkSPPLEa1HzP1ProGz/UXKzbZypbaC6xsHN37oiyhi0\nlM0+VV17XhXMQUTxWvcQ1yDccMMNDBo0CID77ruPBx98kCFDhkQck5SUxMiRIxkzZkynDlIg6Cza\nk0oKsTNkYhmDg4f/hbsfei4gQgekJFkYNWIQzsYmNm0tQVEC1/vw491UnXHgUzUkScLvVzlxujai\nGU0QCUhPs6IbBo2u6GY34dTWO3G5PCHJCQh4ASOG5qOqKhISrz+3nJo6Jw+ufhVFMaEbRtz5DxnY\nh/597KiqHtJiCn+CD5fNhrMy2udjENr7nQg6jrgGYdy4cYwbNw5N03A4HNx6663k5uZ25dgEgh5J\n+I0pljGor78rah1dliTMZiVUIOZ0Bm7o6ekp2NJTcTV5CKoQeTw+dCNGRFkKSFEEb7qtoWo6Xxw4\nwk//7dbQstS+g0epb3BhVkzMmjYuNI9T1bWhJ/uszMigdzDLaE/5CWRJ5vpZk0Lna9kgKDszPSRp\nkZ2VHjcmIei5tCmo/Nhjj7Fnz57/396dx0VV9Q8c/8wM+yI7iCCoOCGKO6W5o6ktpvWkaZq5lBn2\nPJWlidZj5hKlUqYhllZaWplLpS1mT+AvtcQ9zZI0l9xZh51htt8f49wYGBDZZgbP+/XSF3O5c+cc\nLtzvPfec8z0NXRZBaHSW1q2uSUepXm+583jn/2LMjiuXyfH18sDH2wO5TEbfHh1wkCswgPGib5Dx\n6EOxtAz2x9XFCUdHR7yauVvMWe0gl+Pk5Hg9U6mM6sZyyOWAwfhYy7TGMQbw8nTD1cWJ7NxC9h0+\nSXZugSnvHQaMuZCycwvMjjVuRF/efeM/vPvGf5g2YZjF9BMAE0cPpr0yjPbKMCY9PKTWd/Q1OSdC\nw7jhsFOFQkFISAhFRUWNUR5BaHTVTZSy9Cx7wYIDJCYeNdvvhf/6c/TkCea+9Tn3D7lotp5yRWmH\n09FjIDe3gLwC49/VD5++xulzV4ibs4KLl7MsjkjS6PRoikvR65yQy2UY9KAzGCyueeDk6GgxDbdc\nLqeouJRffzemqvDx9sBBrqBTVCv+vpxJrqrQ4vrINbkg1+eEMzF5zTpq1EKYNGkSycnJqNWVO7kE\noSmwNFHK0p2wt/fqSsHg9JmH2X/8V/QG49oD5Yejll9TGYzP1qOjwslVFSKTy/H19mB32gnAOIxU\npzWg0VpOImlKUldyfSUzmUwmBYOKOYXKyjTc1iYEPx9PsnML6NujA56erqjVxo5oudz4CKugoAS1\nRkNefjG5qkIC/byqHFJb/mdV1R18fU44u9GxxBDX+lejiWlFRUWcO3eOrl27MmjQIIKCgirNPahp\nLqO9e/eyYsUKjh07xpUrV0hKSmLs2LFm+yQkJPDRRx+hUqno3r07S5cupV27f7ItqtVqXn75ZbZu\n3UppaSn9+vUjMTGRFi1a1KgMglAbP26qPLxapZrC4uRN0rBMTw8X2oRV/j1MWredtZ//QHZuAV6e\n7nh5uiNXyMjNKyJHVcgHG3cyefQQ8gv/aYnLZODu5sq08ffx5uqtyOXGBW60Wl3lJKMVmgl6A+w/\nepLOg6fh7OxkLJunK8rWLcjMzr/eZwHFpWq0Oh0Bvl54eboTXsMJZ9a+gxejkBpGjVoIiYmJXLly\nhStXrrB+/XoSExNZunSp2b+aKi4uJjo6moSEBFxdXSsFlmXLlrFy5UoWL15MSkoKAQEBPPjggxQW\nFkr7zJ49m6+//poPPviAb7/9loKCAkaPHo2+ipTBglAb5e+Ev//Ev9L3T595mKycPNIOpxPg54UB\n4+ieHt0izS6Spmf4uapCFAo5+YXF6PQ6snPykQGBfl6kHU7n9LkrqNUa6X0GA3Tr2IY5z4yhdVgQ\nOp0evc6Aq4szvt7NQCbDgDFwWBp+qtdDUYnxgq8qKCQvr8g4ukkGzTxc0Wi0GIDmAT4083QHmYHi\nYnWNn9tbK/2ESKHdcGrUQqjPRHeDBw9m8GDjUnxPP/202fcMBgPJyclMnz6d++83Rvzk5GSUSiWb\nN29m4sSJ5OXlsX79elauXEn//v0BePfdd+nYsSO7du1i4MCB9VZWQZj22LBKCeqcnWX0GX6VqbNW\n0KNbJPDPsMz8/AJpWGZ1ggP9CA70w83VGScnB7QaHVu+24NGpzP2DxgMyGUyuka3JWnddjDIcHN1\nwcPdGQ83V9q0CkalKmT/r+k3TIddXFyKVqcnN7+IQ8eNs5zv7N6O5IT/sGj5Z2Rkqzj+x1n0BgPD\nh0Twn4nDxXP7W1SdU1fUp/Pnz5ORkWF2UXdxcaFXr16kpaUBcPToUTQajdk+ISEhREZGSvsIQn1Y\nseIYPj5rzLZ9+fUA7rjnonR3mnY4nR7dIo131lo9/XoY1xgu/3zbtNiMj7cHOp0eX28PRgzpyfAh\nPYxrFWh0tGnVnEO/nsbT3dV4t28Aby9P9h1KZ8s3e8lW5ePkpECt1qDWaLhyLQdVQVG1wUAuN66r\njAwcFPLrWQeMOYxOpP+Nj5cHfXt0IDM7D73BWK7f/jjfgD/R+iFGITWcGrUQGsu1a9cAKs138Pf3\n5+pV411aRkYGCoUCX19fs30CAgLIzMxsnIIKTV5VM48T12zgxJ/nCfDzspjgzWAwWHy+XT55nZ+P\np3QBG31/P6bGL2f9lhRKSstwcJDj4uyIi5MT3s3cSf/rAqXqsuspp40dBaqCIuMSmxbI5TIwwLC7\netA80IfPt/8kfU+VXzmATB49hE+/3IUqv4jcvCJkZNTuB9bIrN2H0VRV2ULw8fHh0KFD0te+vr74\n+PhY/Ffx4twQRAI9obFUNfPYlNjOlOBNlVdEdFQr41KZDnL0Bj0pP//GjtRD6A0GaeZv+ZZCZESo\n2QXs9LkrHPz1NFqdHoVcjk6rR6/X4+TsSGZ2nrQkp15vkHIZ6fWGKleuVMjl+Ps2IzevkD9OXZA+\nq7C4FHdXZ+QyGeoyDV2jI6T0Ew4OChRyea2WxLSksUb/iBTa9a/KFsKLL75IcHCw9HV16utibUqS\nl5mZSUhIiLQ9MzOTwMBAAAIDA9HpdOTk5JgFooyMDHr16lXlsU+dOlUvZbQFTakuYFv1uf32XZW2\nHTgwgDNnzlBUbOyUDfD1oKiomNLSYvakHeOv81dRqzVotDoUchkuLpnIri9G08zTlTNnzpCbbcwh\nBEgX+Q1f7WbnT79SUFQCGFDI5VKuoqycPPR6A4VFxZTvLzYlmyx/ox8W4o8McHSQ4+bqgquLE3kF\nBcaspCVqdHoDCpmM6MiWaLQ6dDods568j/0Hj6DKL8LP2x1fLzfA+LdsKm95NT1HG77azb4jxn17\ndlUybkRfgEp1tzZb+p2rC6VSWa/HqzIgzJ492+LXDSk8PJygoCBSUlLo0qULAKWlpezbt48FCxYA\n0KVLFxwdHUlJSWHkyJGAMROrac3nqtT3D85aTp061WTqArZTH4PBUKm/IDLSm7S0UdLr+4dcJGXP\nr5RptLi6utA8KICyMi3qsototMYFZ2QyUJfpcHNVIJPJcXZyok2bNmYJ7UypHr5JOUpOXiEKuQyt\nVo9BZpxbYAAUCjl6vQ4Lg4cquXw155/1zzFmO3V1cSS/sEQaeSeXy8nIKaBNy2AG9enCgRMXpfL4\n+nihVhszpg7q04U7YrqaHb+m5ygrJ4/j6Zel5TaPp1/Gxy+wUt2tPUTUVn7nbFGj9yEUFRVJ6zLr\n9XouXLjAsWPH8PX1JTQ0lLi4OBITE1EqlURERLB06VI8PDyki7+Xlxfjx4/nlVdeISAgAG9vb156\n6SWio6MZMGBAY1dHaAJSUi7yr399Z7bt+PFHaNnS/G624pKXZWVaNBotzk6OODs5olAo0Gi0yOUy\nopThODkqkMvknD53hR2ph3BzM65xkLLnVwJ8vbmWpcLZ2ZFmnm6oy7TMnPoQG7f9xJ9nL9ao3HKZ\ncb6BwfDPYj0ywEGhkIahyq7/7+nuSqCfD6/FT8TPx5Ops1ZIyePUaq20vb4fwWTnFohEdXak2oCQ\nn5/PgQMH0Gg09OnTBw8PD/78809ef/11fv/9d/z8/HjyyScZMWJEjT/w8OHDDB8+HDA2TxMSEkhI\nSGDs2LEkJSXx7LPPUlJSwsyZM1GpVMTExLB161bc3d2lYyQkJKBQKJg0aRKlpaX079+f9957T/Qz\nCDetc+fPOH/ePHfPorebVwoGJqbn1s7OxgXpAYIDfdHqdGTnFuDTzI0O7VpL8wmcnR1ZtPwzs47o\nX/84w8FjpygsLqGwuBSF3NgqePuDLylRa4z9Dxo9MkAmN84nkGYky2XIkGHAgFwmx6DXVVpHWS6X\nSdlSdXrjyCKZXIaHm0uVCefqIxhYSg8uEtzZF5lKpbLYKD19+jQjRozg8uXLgPHZ/caNGxk5ciQG\ng4Hw8HDOnj1LXl4eW7ZsITY2tlELfqtqas1da9bHUufx0LFZaDU63n3jP5UmlwHSkFJTamsAuUzO\na/ETAcjLzeSOmK5k5eRJLQkHRwXnLlwjMzuPVqFB/PHXBTzcXCgqLqW4RI2Huys6nQ6NVoebqzMG\ngwGDAToow3Bzc+HPsxfx82qGq6szPbtH4u7qwqdf7SI7p8BiKuzmgT44OTiSmZuHQa8HA7i5ufDU\n+Pt4Mc7Y0i4/EmpQny5MmzCsyp/TzZ6jigvb3MxnNYam9jdUn6psISxatAgXFxe+/PJLPDw8mD9/\nPmPHjqVjx458+umnuLi4UFxczOjRo1m2bJkICIJdqSoYWGIp1TOA0/W1BrQanXSHfeqU8eJsaT2B\nQD9vnp54P9PmvAOAq4sTZWUalK1bcPL0BbRaHfkFxQA4OMhxc3Pm8rVsSkrKcG3uzKA+nXkx7p8+\njZQ9v3L+ckalgFBUVEr4bUFk5uah1ZlaDwYmjx4s7dOQwzYrHk8MEbUfVQ47TUtLY+bMmfTv35/u\n3buzePFirly5wpQpU3BxcQHAzc2NKVOm8PvvvzdagQWhrioGg+nTO7Po7eYWJzpVleq5JhOjKk6g\nuic2hrsHdKdnt0h0OuMQUmXrEDzcXCunnjBAfkEx1zJz8fX2wNvLnd1pJ0j/66KULsPV1RlNmbbS\nYjrGeQsa1OoyaVtxSVmltNaNOWxTDBG1D1W2EK5du0abNm2k16bV0iomkGvevDlZWZbvrATBlhw7\nlk2/flvNtp0+/Sj+/q4AN3UXW9O7Xkv7ffJOPOl/GTuOIyNCSf/rInGz3+HXP85cnwtgfN7fXhnG\nX+evkJtXxOFjp9Hp9cxYsIa+PTqYfYazoyMl1y/+5fvR5HI5jg4KNFodWp2OT75K5dXnx9+wbsKt\nq8oWgl6vR6FQSK/Lf12e6MgV7MHQodsqBQOVaooUDMDyXWx9pHq2tF9kRKg0MSwyIpS7Y7vj5eEG\nMhmODgraKUM5dzGDoAAfdFoduXkF+Hp74ubmLKXLMGUwRWYcampaNMfTwxVfL09atvBHozEOJ/Xx\nMqalEEnghOpUO8ro0qVL+Pn5AaDVGn+xLl++jLe3t7SPqdNZEGxVVctc1lRDPwNPWredtMPpdIhs\nRZlWw5WruZw8dRG1RouHq4vF2cOTRw9h8ugh5dZEllOm0aLV6lk+/ym+2vkLZRot2TkF+Hp7ENm2\nJVqN5XUWBMGk2oAwYcKEStvGjRvXYIURhPpW12BgYmnxnPJ5iWp7512+j0JvMHD85FnAODHNoDaQ\noyrA3d0Fr2Ye5KgKCC725Z7YGLNWSt8eHdiddgIXJycGDTQO9Uw7nI6bmzPBQb7GGcvFarP3NbaK\nI48E21RlQHjnnXdqfBDx2EiwRRWDQVxcNAkJd9b5uOUXu/Hz9kTZpoU007djZAvmzaj9kMZStQat\nTotejzTLuLCoBFdnJwIDvFn63yekR02msqRdnw/Ro1uktOaxiWl0U8X3NSaxmI39qDIgiJaAYK8y\nMoq57bYNZtvOnXsMb2/nOh+74mI32ap8Mg/m0TU6AicnR/YdOUVWTl6VcxgqKj+ZS6vV4eFunJ9Q\nUvrPCCG93oBaowGDzGyiV8URUGmH06XPLj9B7J7YGKsFg/JlBDFT2dbZVPprQairTz/9k7i4/zPb\nNmjUNTZ8tdMqd6Y1uTuumBJDXabh2B9nKSgqBuPSCDgoFIQGV161rSpi7L9QGza1QI4g1MXtt39e\nKRgMHZuF3qBnR+qhehlhU3GxGz+fZnTv1BatVo9Wo+PObrdVmsOgN+iNqbHLpcK2lCLaz8eTHt0i\nkclk+Pl64qBQILuehkIml9O3R7TZxb38CKjiYjU9urWr9P3qgkH6Xxel4a8NRSxmY19EC0FoEir2\nF/TqFYhryHHOXcgiKycfg8HABxt3ms30ra3yd/Rf7fzF7Bn+g3d1Mdv370sZ5FxP/ex7PfVzxVYD\nGB+l/H0pA7VWQ4CPFyMG38lXP/xCrup62mhvD7OZxuXLUlRcyu60E6QdPknSuu2VWiEVH1ll5eQx\nNX45R347A0DPbpF88k58nX8uVRGtFfshAoJg9yoGg88+G8Ldd4ezOLmMIx//hVwmI+D6QvYVn+/X\nlukYaYfTzZ7hD7i9rfmOsnKjRmWVs3/uSDUuQuXgIOfcxQy0Oi2Xr+Zw9sJVvDzdpfk/DlXMAzLN\nWi6fSbX8M3pLwWfbzjQOHT+Fs5Mjbq7O7DucTvpfFxu0n0EEAvsgAoJgt7KzS4mI+Nhs299/T6BZ\nMyfAOFZ/d9oJHBwU0kL2N6M+hkqGtQgkNNi4JKy8mtF4RcWlaLRaZDIZMpmM/IJiWoU2l5bplMvM\nn+7W5PFXxQ7d8sEHoEyjxcXZ6eYrJTRZog9BsEubNp2uFAxUqilSMIB/nvebFrK/mefXSeu2M3XW\nCqbOWkHSuu0W97H0fLz8imCm78tlMuQyGYP6dCEyIrRyfqPY7shk8uszjY1rIjs6OtC3ZwfkMjly\nmdys7OXLtnH7Tzf9jN7D3RWfZh4YDAZ0Oh09u7Wz2igkwbZUmf5asE1NLXVvberTu/cWTpzIMdtW\n3WSzm73TN6W3Nt1ZW0qHXdXxTfWpmC674udbusOfGr+cQ8dOA9Arpj2fvDOr0nFOn7vCouWf4ebm\nTFmZBq1Wz4dvTpeOUbGMFVNPGzBIr6OjWjF2xIAbBgPxO3frEI+MBLtSsb/gzjuD+O674dW+p6Gf\nX1d3Ea5qqKm/r1el/ba891+zpHflj22aDJeZnYe6TIuHmwt6g+GGneWWOnRFB69QFfHISLAbFYPB\n+vWDbxgMqmJp2KfJzQyVzMrJk1JSg3Ex+Yrpsst/v/z7Ku6XlZNnlvSu/L6myXCOjg6Agdy8AnQ6\nHb7enuxOO2F2/Ip1qzj8VKSiFqoiWgiCzcvNLaV1a/P+gvPnJ+DlVbsO0ZuZLAZV30lXTGExcfRg\nbu9gfjH/+3IGMxaswcnRoV7TNhgMUFqm4cq1bHJUBVIrQaSJEOpCtBAEm/bFF39VCgYq1ZRaB4Oq\n7swtqXgnXf7OOysnj+0708jOLUChkJOTVyiN4ik/WQzAzc250mfdTCuk/GQ4Uzprby8PtFodao0G\nX28P0q4PHS1ftx2phxp84pnQtIgWgmCz+vf/gl9/NV98qTaZSutDxTvvouJSTv51gaLiUpycHM2G\nb1ZMRVGVm5mwZdrX1Kl8JSOHvPxCDBhTW1RkWsN5xoI13B3bXbQUhBoRLQTBJnl7rzYLBt27B9RL\nMKjuzryqfoWKrYodqYfYnXaCoAAfHB0dUJdpaObhxj2xMdKwU39fL2mIaXGxmuJiNYP6dJGOV748\n1QWDimXy8fKge8e25KgKcHJyxNnJkeycfKKjws0+LzM7j0A/L9zcnKttBQlCeaKFINicip3H69bd\nxYgRrevt+JbuzGvz7L1VyyBaBPlSXFLG8vlPERkRyqlTp6rcf8+B3/hxz9Eaf0b5Mjk7O3Dq7GWy\ncwvw8nTDq5kbnUNbc+FyFlk5eRw+9peUtuKuPl2ZsWCNNHtZEGpKtBAEm6FSqSsFg7Nnx9drMDAp\nf2d+o36Fiq0K02QyrUaHXCZnxJCeFsfym47r5uaMg4OCfYfT0Rv0ODgq2LYzjX2HT1osm2nkUvmF\nc/bs/53MrDwUCjn5hSVgkFFSUkaOqoCgAB8cHORSAj/TkpwioZxws0QLQbAJBw9mcNddX5lts1Z/\ngSW1Gc+fnVtAmUYrTXAzOXzsNLn5hYyZlkCvmCizxHKmVkGZRsvVjBzatArm70sZFJeUggycdU64\nODsRGuzPS8+MYdHyz8jIVnHsj3NmcxJEQjmhNkQLQbC6hQsPWDUY1HTEz82M509at505r6/lakYO\nZ85fQS6T0bNbJMUlZeTmF+Ls5Iijo4OUWA7MWypubs4gA1VeEbl5hfh6e+Ls6Gjsr/B05Z7YGHp2\na0ffHh3IzM5DBgSWS+B3o/IJgiWihSBY1YABuykq+ifp3DPPdGL+/B6NXo76vKMuf2Fv0yqY4mI1\nr8VPJDIilH2HTzJmWsL1CWbVC2sRyJRx9/DW6i/w9nKnrExLfn4Ri+In0rNbO6DuCfwEoTybayFo\ntVrmz59P586dad68OZ07d2bhwoXodOa/6AkJCURFRREcHMywYcM4edLy81jBdnl7rzYLBjt23G+V\nYGDSUHfUTo4O0tKXPbu1o1dMFDqdHp1Ob5ZYrmJLxdnZkdUbviNHlc+Zc1e4eDmT/KJiliRvlhLu\n1SWBnyBUZHMthMTERD788ENWrVpF+/bt+e2335g2bRrOzs7MnDkTgGXLlrFy5UpWrlxJ27ZtWbx4\nMQ8++CAHDhzAw8PjBp8gWFtxsZYWLT4023bhwgQ8PZtGKubyaxqXabT07dEBQFqL4ZN34ivlLDKp\nOIfBwVFBm/BgVHlFyAAvL3fAfN2D6lo39ZHCW7h12FxAOHz4MPfccw9Dhw4FoGXLlgwdOpSDBw8C\nYDAYSE5OZvr06dx/v3HYXnJyMkqlks2bNzNx4kRrFV2ogSNHMomN/dJsmy11HteX8iuZbfp6N5u2\n7yYsJFAablpdhlFLF2+nGzxisvQekcZCuFk298ho8ODB/PTTT9J47pMnT7Jnzx4pQJw/f56MjAwG\nDhwovcfFxYVevXqRlpZmlTILNfP664cqBYMDBwZYpzANzLSSmYODglxVITl5hZXWVTbtZ+l1dUNd\na/Jo6GZSdAiCic21EJ544gkuX77MHXfcgYODA1qtlhkzZjB58mQArl27BkBAQIDZ+/z9/bl69Wqj\nl1eomdatPyI3Vy29fuqpaF5//c5qJ3I1dVWtrWx6LVJXC43N5gLCqlWr2LBhAx988AHt2rXj2LFj\nxMfHExYWxvjx46t9r6yaJQoF66k42eybb4bRu3ewlUrTOMr3I/h4G/u1yq98VtXylqbZxTtSD3FX\nn66VHi3VNBCU/3xAdDYLNWJzK6YplUpmzJjB1KlTpW1Lly7lk08+4fDhw5w7d46uXbuSmppKly5d\npH0efvhh/P39WblypcXj3sp3otZSWqqjb9/dZttSU/vg4WFz9yENJjev0Oy1KddRbl4hc9/6HAcH\nY0AoKS0DgwFXV2cuXc0hR1VA21bB9L29HeNG9K3z55df2lNoOup75Teb+8s0GAzI5eZdG3K5HIPB\nGLfCw8MJCgoiJSVFCgilpaXs27ePBQsWVHncprJknr0s//frr1n07/+F2TZLnce2Wp/ajs6pqj4V\nn98rlUruH3JRuoO/d2BPDBjYkXqIvIISggP98Pfz4Xj6ZXz8Aq16d2+r56i2mlp96pPNBYT79kRR\noQAAHMtJREFU7ruPZcuWER4eTmRkJMeOHWPlypU88sgjgPGxUFxcHImJiSiVSiIiIli6dCkeHh6M\nHDnSyqUXAJYsOcyiRYfMttnTSKL6Hp1jOt7flzJAZpxwVlUfgUhMJ1iTzQWE1157DU9PT2bMmEFm\nZiZBQUFMnDiRF198Udrn2WefpaSkhJkzZ6JSqYiJiWHr1q24u7tbseQCQGTkeq5dK5FeT5nSniVL\neluxRDen/LP9wqIStu1Mk8b71+V4eoOenLxCZEBocIDZPILyTInpxLN/wRpsLiC4u7uzcOFCFi5c\nWO1+8fHxxMfHV7uP0Lgqdh5v23Yf/fq1sFJp6saUgA5gavxytrz330b7bJGYTrAWm5uHINif0lJt\npWBw7txjdhkM/H29iI4KJze/EJlMhrOTI0d+O1PrpShNo33kMjm+Xh74eHsgl8lueOcvEtMJ1mBz\nLQTBvhw/nk3fvlvNttlTfwFU7kAeOyKWdZ//D4XCOAKoYh6t6t5rSfk7fhNL+2fl5JGdW4Cfj6cI\nBoJViIAg1Npbbx3l1VcPmG2zt2BgqQM5MiKUXjFRpP5yHI1Gi3czd/6350ilOQE30/l8owt80rrt\nrP38B2NA8PZk4ujBItWE0OjEIyOhVqKjPzULBpMmtbO7YFBdeofl8+Po1K41PbpG0r2T0mLKifpK\nDZGVk8eO1EPkqgpRKOTk5BVKq58JQmMSLQThplXsL/jyy3sZMCDESqVpOB5uLpVWOxOEpky0EIQa\nU6t1Ftc8ttdgUN1KaTdaRa2mq6zVtBx3x3bHx9sDnU6Pr7cH98TG1Oh4FZPjCUJd2FzqCqF61ppl\nmZFRzG23bTDbVh+PiGxh1mh1HcM36jSu+P261OdmO5UbK721LZyj+tTU6lOfRAtBuKG0tGsNEgxs\nRXVDPG80/LM+h4f6+3pJK6uVZ6kVINJbCw1B9CEI1Vq16jfi43+RXm/YMJj77mtlvQI1YZbu+MUi\nN0JjEi0EoUqjR+8wCwZHjoxu0sGgIZ7H1/SYlu740/+6WGUrwNSHUVysprhYbZZWW7QUhNoSLQSh\nEp1Oj5/f+2bbLl+ehJtb0/11aYg78ca8uzdgEK0Joc5EC0Ewk5VVYhYMlEovcnOfaNLBoCGex9/s\nMS2NWoqMCK1yJJPp+G5uzri5ObMj9RA7Ug+JPgWhTpruX7lw0w4cuMbgwduk108/3ZFFi3pasUS3\nFktJ7USiO6ExiRaCAMDq1SfMgsH69YNvqWDQo1tkvcwpMKntPAVLo5aq2lb++PfExnB3bPd6rYNw\n6xEtBIGxY3fy7bfnpdeHDj1MRMStcTEp/9y9R7dIJo8eUm8X0oa+u7d0fNGaEOpCBIRbWFPvPK7J\npLLyC92nHU5n8ugh9VqGhr4wW2o5CEJtNY2/fOGmZWeXEhHxsfS6VStPjhwZjUwms2Kp6o8YcSMI\nN0/0IdyCDh3KMAsGTz0VzdGjY5pMMKjpCJ/6zEckCE2BaCHcYt5//3deeGGv9Pqjj+5i+PDWViyR\ndYlRPILwDxEQbiGPPfY/tm07K70+eHAUbdt6W7FEDcN051/ThepFIBAEIxEQbgF6vQFf3zVm2y5d\nmoi7u6OVStTwbubO31Lnc02WxhSEpkYEhCYuJ6eUNm3+6S9o2dKDY8eaTn9BdWqbQlp0SAu3KtGp\n3IQdOZJpFgyefLIDx48/cksEg5q42YRygtDUiRZCE7V27R8899yecq8H8cADbaxYIkEQbJ1oITRB\nkyb9aBYM9u8fJYKBBVUllOvRLZLiYrUYiircckQLoQnR6w0EBr6PVvvPqqgXL07Ew6Ppdh7XVcXO\n56R120k7nA4YU1lMmzDMmsUThEYlWghNRG5uKb6+a6RgEBLiTm7uEyIYVGBpARlT8rjyfQpubs6k\nHU4X/QfCLcUmA8LVq1d56qmnaNu2Lc2bN6dnz57s3bvXbJ+EhASioqIIDg5m2LBhnDx50kqltb6j\nR7No3fqfzuPHH4/ixImxovO4gqR125k6awVTZ60gad12axdHEGyOzQUElUrF0KFDkclkbNq0if37\n97N48WICAgKkfZYtW8bKlStZvHgxKSkpBAQE8OCDD1JYWGjFklvHRx+dZMCAL6TX778/kMTEPlYs\nkW2qSToLkcpCuNXZXB/C8uXLadGiBcnJydK2sLAw6WuDwUBycjLTp0/n/vuN48OTk5NRKpVs3ryZ\niRMnNnaRreaJJ1LYvPkv6fW+fSNp187HiiWyfyKVhXArs7kWwjfffEO3bt2YNGkSSqWSvn37snr1\naun758+fJyMjg4EDB0rbXFxc6NWrF2lpadYocqPT6w00b/6BWTC4cGGCCAbVuJm7f0sL0gjCrcDm\nWgjnzp3j/fff5+mnn+b555/n2LFjzJo1C4ApU6Zw7do1ALNHSAD+/v5cvXq10cvb2PLzNWZpKAID\nXUlPHyf6C2pA3P0LQvVsLiDo9Xq6d+/Of//7XwA6duzImTNnWLNmDVOmTKn2vdVdFE+dOlWv5bSG\n9PQCHn30kPT6wQeDmTMnktOnT1uxVHVnjXOTm53RYMduCr9rFTW1OjWV+iiVyno9ns0FhObNmxMZ\nGWm2TalUcvHiRQCCgoIAyMzMJCQkRNonMzOTwMDAKo9b3z+4xrZ+fTr//vc/wWD16lhGjWprxRLV\nj1OnTtnluakq+Z291qc6Ta1OTa0+9cnmAkLPnj35888/zbadPn1a6lgODw8nKCiIlJQUunTpAkBp\naSn79u1jwYIFjV7exvDMMz/x0Ufp0utffnmIqChfK5bo1iaS3wlNlc11Kk+bNo2DBw+SmJjImTNn\n+PLLL3nvvfd44oknAONjobi4OJYtW8b27dv5/fffmTZtGh4eHowcOdLKpa9/Op3eLBikpvYRwcCK\naroamyDYI5trIXTt2pUNGzYwf/58lixZQsuWLXn55Zd5/PHHpX2effZZSkpKmDlzJiqVipiYGLZu\n3Yq7u7sVS94wFAo5S5f25u+/C3j11Tvsvr9AEATbZXMBAWDIkCEMGTKk2n3i4+OJj49vpBJZ1xNP\ntLd2EYTrbnY1NkGwJzYZEATBlonhq0JTJQKCYDPsadlKeyijINwsERAEmyBG7giC9dncKCPh1iNG\n7giCbRABQRAEQQBEQBBsgEg7LQi2QfQhCDZBjNwRBOsTAUGwGSIQCIJ1iUdGgiAIAiACgiAIgnCd\nCAiCIAgCIAKCIAiCcJ0ICIIgCAIgAoIgCIJwnQgIgiAIAiACgiAIgnCdCAiCIAgCIAKCIAiCcJ0I\nCIIgCAIgAoIgCIJwnQgIgiAIAiACgiAIgnCdCAiCIAgCIAKCIAiCcJ0ICIIgCAIgAoIgCIJwnc0H\nhDfffBMfHx9mzpxptj0hIYGoqCiCg4MZNmwYJ0+etFIJBUEQmgabDggHDhxg3bp1dOjQAZlMJm1f\ntmwZK1euZPHixaSkpBAQEMCDDz5IYWGhFUsrCIJg32w2IOTl5fHkk0+SlJSEt7e3tN1gMJCcnMz0\n6dO5//77iYqKIjk5mcLCQjZv3mzFEguCINg3mw0Izz33HA888AB9+vTBYDBI28+fP09GRgYDBw6U\ntrm4uNCrVy/S0tKsUVRBEIQmwcHaBbBk3bp1nDt3jjVr1gCYPS66du0aAAEBAWbv8ff35+rVq41X\nSEEQhCbG5gLCqVOnWLBgATt27EChUADGx0TlWwlVKR84miqlUmntItQrUR/b19Tq1NTqU59s7pHR\n/v37yc7OpmfPnvj7++Pv78/PP//M+++/T0BAAH5+fgBkZmaavS8zM5PAwEBrFFkQBKFJsLkWwrBh\nw+jevbv02mAw8PTTT9O2bVuef/55IiIiCAoKIiUlhS5dugBQWlrKvn37WLBggbWKLQiCYPdsLiB4\neXnh5eVlts3V1RUvLy/atWsHQFxcHImJiSiVSiIiIli6dCkeHh6MHDnSGkUWBEFoEmwuIFgik8nM\n+geeffZZSkpKmDlzJiqVipiYGLZu3Yq7u7sVSykIgmDfZCqV6sa9tYIgCEKTZ3Odyjeyd+9exowZ\nQ/v27fHx8eGTTz6ptM+N0lqo1WpmzpxJREQEISEhPPLII1y+fLmxqmDmRvWJi4vDx8fH7N+QIUPM\n9rGl+rz55pvExsYSFhZG27ZtGTNmDH/88Uel/ezlHNWkPvZ0jlavXk3v3r0JCwsjLCyMIUOGsHPn\nTrN97OXcmNyoTvZ0fiypbfqe2tTJ7gJCcXEx0dHRJCQk4OrqWmmoaU3SWsyePZuvv/6aDz74gG+/\n/ZaCggJGjx6NXq9v7OrcsD4ymYzY2Fj+/PNP6d/nn39uto8t1Wfv3r1MmTKFnTt3sm3bNhwcHHjg\ngQdQqVTSPvZ0jmpSH3s6RyEhIcyfP5+ffvqJXbt20a9fP8aNG8fx48cB+zo3Na2TPZ2fiuqSvqc2\ndbLrR0ahoaEsWbKERx55BDCOSGrXrh1Tp07l+eefB4wjkJRKJQsWLGDixInk5eWhVCpZuXKl1Al9\n6dIlOnbsyObNm81mQFu7PmC8u8nJyWHjxo0W32PL9QEoKioiLCyMTz75hKFDh9r9OapYH7D/c9S6\ndWvmzZvHY489ZtfnpjxTnSZMmGC35ycvL48BAwawYsUKXn/9ddq3b8/ixYsb9G/I7loI1alJWouj\nR4+i0WjM9gkJCSEyMtImU1/IZDL27duHUqkkJiaGZ599lqysLOn7tl6fgoIC9Hq9lI/K3s9RxfqA\n/Z4jnU7Hli1bUKvV9OrVy+7PDVSuE9jv+alL+p7a1skuRhnVVE3SWmRkZKBQKPD19TXbJyAgoNJk\nN1tw1113MXz4cMLDwzl//jwLFy5k+PDh7Nq1CycnJ5uvT3x8PJ06deKOO+4A7P8cVawP2N85OnHi\nBEOGDEGtVuPq6sqHH36IUqmULhT2eG6qqhPY3/mBuqfvqW2dmlRAqI69prX417/+JX0dFRVFly5d\n6NixI99//z3333+/FUt2Y3PmzGH//v189913Nfr52/o5qqo+9naObrvtNvbu3UteXh5fffUVjz/+\nONu3b6/2PbZ+bqqqU9euXe3u/FgzfU+TemQUFBQEVJ/WIjAwEJ1OR05Ojtk+GRkZdpH6onnz5rRo\n0YKzZ88Ctluf2bNn88UXX7Bt2zbCw8Ol7fZ6jqqqjyW2fo4cHR1p1aoVnTt3Zu7cucTExLB69Wq7\nPTdQdZ0ssfXzUx/pe2pbpyYVEMLDw6W0FiamtBY9evQAoEuXLjg6Oprtc+nSJf78809pH1uWlZXF\nlStXpD9eW6zPrFmzpItn27Ztzb5nj+eouvpYYg/nqDydToder6dVq1Z2d26qYqqTJbZ+foYNG8Yv\nv/zCnj172LNnD7t376Zr166MHDmS3bt3m6XvMamv86SIj4+f12A1awBFRUWcPHmSa9eu8fHHH9O+\nfXs8PT3RaDR4eXmh0+l46623aNu2LTqdjpdeeomMjAyWLVuGk5MTLi4uXL16lTVr1hAdHU1eXh7T\np0/Hy8uLV199tdGbxtXVR6FQMH/+fDw9PdFqtRw/fpxnnnkGg8HAkiVLbLI+M2bMYOPGjXz44YeE\nhIRQVFREUVERMpkMJycnZDKZXZ2jG9WnqKjIrs7RvHnzcHZ2Rq/Xc+nSJZKTk9m0aRPz58+ndevW\ndnVualKnwMBAuzo/YOwgNrUM/P39CQgI4PPPP6dly5aMHTu2Qf+G7K4P4fDhwwwfPhwwPi9LSEgg\nISGBsWPHkpSUVKO0FgkJCSgUCiZNmkRpaSn9+/fnvffes8ovc3X1SUxM5I8//mDjxo3k5eURFBRE\nv379WLdunc3W5/3330cmkzFixAiz7fHx8cyaNQuoWeoRW6nTjeqjUCjs6hxlZGTw5JNPkpGRQbNm\nzYiOjmbLli3ExsYC9nVualKn0tJSuzo/ValN+p7a1Mmu5yEIgiAI9adJ9SEIgiAItScCgiAIggCI\ngCAIgiBcJwKCIAiCAIiAIAiCIFwnAoIgCIIAiIAgCIIgXCcCglBv9u/fz+TJk+nQoQOBgYGEhYUx\ncOBAEhISpAyN9SkvL4+EhAR+/fXXWh8jISGBn376qdL2uLg4OnXqVJfi1Yvdu3fj4+PD3r17q90v\nISHBbEWwli1b0r17d6ZMmWKWvkAQqmN3M5UF27RixQpeeeUV+vXrx8svv0yrVq0oKipi3759fPjh\nhxw+fJhNmzbV62eqVCoWL15MaGgonTt3rtUxFi9ezIwZM+jXr5/Z9lmzZlFQUFAfxWxU33//PQqF\nguLiYs6dO8e2bdt46KGHePjhh1m1apXNzLwVbJMICEKd/fTTT8ydO5dp06axaNEis+/dddddPP/8\n83z11VcN9vk1SQt8s+9v1apVnY5pLTExMcjlxoZ/3759GT9+PCtXruSll16iY8eO/Pvf/7ZyCQVb\nJh4ZCXX29ttvExAQwKuvvmrx+25ubmbLgoJxLelXXnmFTp06ERgYSOfOnUlMTDS7OBcWFjJz5kyi\no6MJCgpCqVTywAMPcOrUKc6fP0+XLl0AY14X06OSTz/9FICUlBRGjRpFu3btaNGiBb169eKdd94x\ny4Dp4+MDQGJiovT+N954A7D8yOjq1atMnTpVyjbZu3fvSmvzbtiwAR8fHw4ePMiUKVMICwsjKiqK\nWbNmoVarzfZ97bXX6NevH2FhYURERDB8+HAOHjxY4597TU2bNo1OnTqxatUqaZtarWb27Nn06tWL\n0NBQIiMjGTNmDKdOnZL2OXr0KD4+Pnz77beVjhkXF0eHDh2k87Vp0yb69u1LaGgoYWFh9OrVi7Vr\n19Z7XYSGJVoIQp1otVr27t3L8OHDcXCo2a+TVqvloYceIj09nRdffJH27dtz4MABlixZQm5uLgsX\nLgSMC9Ls2LGDuXPnEhERQXZ2Nvv37yc/P5+OHTvy8ccfM378eF544QXuuece4J87+/Pnz9OvXz+m\nTJmCm5sbR44c4Y033iA7O5tXXnkFgB9++IHBgwczbtw4Jk2aBECLFi2kcpZ/vFJUVMR9991Hfn4+\nr7zyCiEhIWzcuJGpU6dSUlLChAkTzOo4depURo4cyccff8z+/ft5/fXX8fb2Zvbs2dI+V65cIS4u\njpYtW1JcXMzGjRu599572bVrF+3bt7/JM1G9u+66izfffJNLly4REhKCWq2msLCQ559/nuDgYFQq\nFWvWrGHw4MHs37+fwMBAunTpQrdu3Vi7di333nuvdCyVSsWXX37Jc889h0wm45dffmHq1Kk89dRT\nLFy4EIPBQHp6Ovn5+fVaB6HhiYAg1ElOTg5qtZqWLVtW+p5WqzV7bQoYmzdvZt++fXz77bfceeed\nANIz/DfeeIPp06fj5+fHwYMHefjhh3n00UelYwwbNkz6umPHjoBxjYXu3bubfZbpAg/GR0I9e/ZE\nrVbzzjvvSAEhJiYGgODg4ErvN73PZMOGDZw5c4avv/6a3r17AzBo0CAyMjJYuHAhjz32mFkAGTVq\nFPHx8QD079+fgwcPsmXLFrOAsGLFCulrnU7HwIEDOXbsGB999BGvv/56pfLURWhoKGBcfjEkJIRm\nzZqZfb5eryc2NpbIyEg2b97MtGnTAHj88cf5z3/+w4ULF6Rz/Nlnn6HRaHjssccAOHjwIF5eXrz2\n2mvS8QYMGFCv5Rcah3hkJDSIa9euERAQYPbP9Ljmxx9/pGXLltxxxx1otVrpX2xsLBqNhgMHDgDQ\ntWtXNmzYwJtvvsmRI0fQ6XQ1/vyrV6/y3HPPER0dTWBgIAEBASxatIj8/PxarZP7888/ExISIgUD\nk1GjRpGVlcXJkyfNtg8dOtTsdfv27bl48aLZtl27djFs2DDatGkj5b0/ffo0f/31102X70ZMwa18\n0Priiy8YNGgQ4eHh+Pn5ERISQmFhodnnP/TQQ3h5ebFu3Tpp29q1axk6dCjBwcEAdOvWDZVKxZNP\nPsmOHTtQqVT1Xn6hcYiAINSJr68vLi4uXLhwwWy7v78/qamppKamMmHCBLMLUWZmJhcuXJAugqZ/\ngwYNQiaTScv+LV68mEmTJrF+/XoGDhyIUqlkzpw5lJSUVFsmvV7PI488wg8//MCLL77I9u3bSU1N\n5YUXXsBgMFBaWnrT9czNzZVW2CrPtC03N9dsu6l/wsTJycmsD+Ho0aOMGjUKT09P3nnnHX788UdS\nU1OJjo6uVflu5NKlS2bl/e6775g8eTLt2rXj/fffJyUlhdTUVPz9/c0+39nZmXHjxrFhwwZ0Oh0/\n//wz6enpTJ48Wdqnd+/erF27lkuXLjF+/Hipr+fEiRP1Xg+hYYlHRkKdODg40KtXL1JTU9FoNDg6\nOgKgUCikTt+goCCzxy9+fn6Eh4dX2ekYFhYGgLu7O3PnzmXu3LlcvHiRL7/8kldffRUnJyfmzZtX\nZZnOnj3L0aNHee+99xg1apS03VLnaE35+PhYvHM3za+oGABuZPv27Tg5ObF+/XppIXUwBhZvb+9a\nl7MqO3fupGXLllIfydatW4mIiCApKUnaR6PRVFqDF2Dy5MkkJSXxzTff8PXXXxMeHs6gQYPM9hkx\nYgQjRoyguLiY3bt3M2/ePEaOHMnvv/8uhrraEdFCEOrsmWeeMeusvZFBgwZx6dIl3N3d6dKlS6V/\nvr6+ld4TGhrKv//9b6Kiovjjjz8A490rUOmOuri4GMCsk1uj0bBp06ZKFycnJ6cq78jL79unTx8u\nXbpEWlqa2T6bN28mMDCQdu3a1aju5ctoGh5q8n//93/SnXx9SkpK4rfffuPpp582+/zygQiMfQOW\n1iFu3bo1sbGxLF++nG3btlXqQC/Pzc2NoUOHMmHCBK5evVqp5STYNtFCEOqsf//+zJs3j3nz5nHi\nxAnGjBlDWFgYarWa06dPs3XrVjw8PKQL7MMPP8yGDRsYMWIETz/9NNHR0ZSVlXH27Fl27NjBJ598\ngouLC4MHD+bee+8lKioKd3d39u7dy4kTJxg3bhwAgYGB+Pr6smXLFtq3b4+bmxutWrWiXbt2tGzZ\nkgULFiCXy3FwcGDlypXIZLJKcw4iIyP5/vvvGTRoEF5eXgQHB9O8eXPAvFN57NixrFq1ivHjx/Py\nyy/TokULPv/8c3bt2sXbb79903fBgwcPZtWqVcTFxTFu3DhOnz7N0qVLadGiRZ3mVRw4cAC5XE5p\naak0Me1///sfY8eOZerUqWaf/+233zJnzhyGDh3KkSNHWL16NV5eXhY///HHH2fcuHE4OTkxfvx4\ns+8tWrSIrKws+vbtS1BQEJcvX+bdd9+lU6dOFoO7YLtEQBDqxTPPPEOPHj1YtWoVCxYsICsrCxcX\nF5RKJQ899BCTJ0+WLpoODg5s3bqVt956i3Xr1nH+/Hnc3Nxo06YNQ4YMkR479e7dmy+++IK33noL\nnU5Hq1atSEhI4MknnwRALpezfPlyFixYwAMPPIBOpyMpKYlHHnmEDRs28OKLLxIXF4evry/jxo0j\nJCSE5557zqzcS5YsYdasWYwZMwa1Wi2tlVxxDVs3Nze++eYb5s6dy6uvvkphYSFKpbLSYynAYnCo\neLyBAwfyxhtvkJSUxPbt22nfvj2rVq1iyZIlld5fk2Bj2ufuu++WyhsUFCSttWtaM9lkwoQJXLx4\nkQ0bNrB27Vq6devGp59+yqOPPmrx84YMGYKrqytDhw7F39/f7Hu333477777LnPmzCE3N5eAgAAG\nDhzISy+9dMNyC7ZFrKksCMINpaam8q9//YuvvvqqUpoPoekQAUEQhCqdPXuWc+fOMWfOHFxcXEhN\nTbV2kYQGJDqVBUGo0uLFixk1ahQuLi5mqS+Epkm0EARBEARAtBAEQRCE60RAEARBEAAREARBEITr\nREAQBEEQABEQBEEQhOtEQBAEQRAA+H+QjywTNpT4iwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a97c1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scatter_fit(baby, 'Gestational Days', 'Birth Weight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The fitted values of birth weight are, therefore, less variable than the observed values of birth weight. But how much less variable?\n",
    "\n",
    "The scatter plot shows a correlation of about 0.4:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.40754279338885108"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(baby, 'Gestational Days', 'Birth Weight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is ratio of the SD of the fitted values and the SD of the observed values of birth weight:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.40754279338885108"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fitted_birth_weight = baby_regression.column('Fitted Value')\n",
    "observed_birth_weight = baby_regression.column('Birth Weight')\n",
    "np.std(fitted_birth_weight)/np.std(observed_birth_weight)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The ratio is $r$. Thus the SD of the fitted values is $r$ times the SD of the observed values of $y$.\n",
    "\n",
    "The example of fuel efficiency and acceleration is one where the correlation is negative:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.5060703843771186"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(hybrid, 'acceleration', 'mpg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5060703843771186"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fitted_mpg = fit(hybrid, 'acceleration', 'mpg')\n",
    "observed_mpg = hybrid.column('mpg')\n",
    "np.std(fitted_mpg)/np.std(observed_mpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The ratio of the two SDs is $|r|$. Thus the SD of the fitted values is $|r|$ times the SD of the observed values of fuel efficiency."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The relation says that the closer the scatter diagram is to a straight line, the closer the fitted values will be to the observed values of $y$, and therefore the closer the variance of the fitted values will be to the variance of the observed values. \n",
    "\n",
    "Therefore, the closer the scatter diagram is to a straight line, the closer $r^2$ will be to 1, and the closer $r$ will be to 1 or -1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Fact 3.** No matter what the shape of the scatter diagram, the SD of the residuals is $\\sqrt{1-r^2}$ times the SD of the observed values of $y$. In other words, the root mean squared error of regression is $\\sqrt{1-r^2}$ times the SD of $y$.\n",
    "\n",
    "This fact gives a measure of the accuracy of the regression estimate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, we will demonstrate this by example. In the case of gestational days and birth weights, $r$ is about 0.4 and $\\sqrt{1-r^2}$ is about 0.91:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.91318611003278638"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r = correlation(baby, 'Gestational Days', 'Birth Weight')\n",
    "np.sqrt(1 - r**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9131861100327866"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "residuals = baby_regression.column('Residual')\n",
    "observed_birth_weight = baby_regression.column('Birth Weight')\n",
    "np.std(residuals)/np.std(observed_birth_weight)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus the SD of the residuals is $\\sqrt{1-r^2}$ times the SD of the observed birth weights.\n",
    "\n",
    "It will come as no surprise that the same relation is true for the regression of fuel efficiency on acceleration:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.862492183185677"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r = correlation(hybrid, 'acceleration', 'mpg')\n",
    "np.sqrt(1 - r**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.862492183185677"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "residuals = hybrid.column('mpg') - fitted_mpg\n",
    "observed_mpg = hybrid.column('mpg')\n",
    "np.std(residuals)/np.std(observed_mpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us examine the extreme cases of the general fact that the SD of the residuals is $\\sqrt{1-r^2}$ times the SD of the observed values of $y$. Remember the residuals always average out to 0.\n",
    "- If $r=1$ or $r=-1$, then $\\sqrt{1-r^2} = 0$. Therefore the residuals have an average of 0 and an SD of 0 as well; therefore, the residuals are all equal to 0. This is consistent with the observation that if $r = \\pm 1$, the scatter plot is a perfect straight line and there is no error in the regression estimate. \n",
    "- If $r=0$, the $\\sqrt{1-r^2} =1$ and the SD of the regression estimate is equal to the SD of $y$. This is consistent with the observation that if $r=0$ then the regression line is a flat line at average of $y$, and the root mean square error of regression is the root mean squared deviation from the average of $y$, which is the SD of $y$.\n",
    "\n",
    "For every other value of $r$, the rough size of the error of the regression estimate is somewhere between 0 and the SD of $y$."
   ]
  }
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