{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Robust Linear Models" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt\n", "from statsmodels.sandbox.regression.predstd import wls_prediction_std" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimation\n", "\n", "Load data:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "data = sm.datasets.stackloss.load(as_pandas=False)\n", "data.exog = sm.add_constant(data.exog)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Huber's T norm with the (default) median absolute deviation scaling" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-41.02649835 0.82938433 0.92606597 -0.12784672]\n", "[9.79189854 0.11100521 0.30293016 0.12864961]\n", " Robust linear Model Regression Results \n", "==============================================================================\n", "Dep. Variable: y No. Observations: 21\n", "Model: RLM Df Residuals: 17\n", "Method: IRLS Df Model: 3\n", "Norm: HuberT \n", "Scale Est.: mad \n", "Cov Type: H1 \n", "Date: Tue, 17 Dec 2019 \n", "Time: 23:42:49 \n", "No. Iterations: 19 \n", "==============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "var_0 -41.0265 9.792 -4.190 0.000 -60.218 -21.835\n", "var_1 0.8294 0.111 7.472 0.000 0.612 1.047\n", "var_2 0.9261 0.303 3.057 0.002 0.332 1.520\n", "var_3 -0.1278 0.129 -0.994 0.320 -0.380 0.124\n", "==============================================================================\n", "\n", "If the model instance has been used for another fit with different fit parameters, then the fit options might not be the correct ones anymore .\n" ] } ], "source": [ "huber_t = sm.RLM(data.endog, data.exog, M=sm.robust.norms.HuberT())\n", "hub_results = huber_t.fit()\n", "print(hub_results.params)\n", "print(hub_results.bse)\n", "print(hub_results.summary(yname='y',\n", " xname=['var_%d' % i for i in range(len(hub_results.params))]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Huber's T norm with 'H2' covariance matrix" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-41.02649835 0.82938433 0.92606597 -0.12784672]\n", "[9.08950419 0.11945975 0.32235497 0.11796313]\n" ] } ], "source": [ "hub_results2 = huber_t.fit(cov=\"H2\")\n", "print(hub_results2.params)\n", "print(hub_results2.bse)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Andrew's Wave norm with Huber's Proposal 2 scaling and 'H3' covariance matrix" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Parameters: [-40.8817957 0.79276138 1.04857556 -0.13360865]\n" ] } ], "source": [ "andrew_mod = sm.RLM(data.endog, data.exog, M=sm.robust.norms.AndrewWave())\n", "andrew_results = andrew_mod.fit(scale_est=sm.robust.scale.HuberScale(), cov=\"H3\")\n", "print('Parameters: ', andrew_results.params)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "See ``help(sm.RLM.fit)`` for more options and ``module sm.robust.scale`` for scale options\n", "\n", "## Comparing OLS and RLM\n", "\n", "Artificial data with outliers:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "nsample = 50\n", "x1 = np.linspace(0, 20, nsample)\n", "X = np.column_stack((x1, (x1-5)**2))\n", "X = sm.add_constant(X)\n", "sig = 0.3 # smaller error variance makes OLS<->RLM contrast bigger\n", "beta = [5, 0.5, -0.0]\n", "y_true2 = np.dot(X, beta)\n", "y2 = y_true2 + sig*1. * np.random.normal(size=nsample)\n", "y2[[39,41,43,45,48]] -= 5 # add some outliers (10% of nsample)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example 1: quadratic function with linear truth\n", "\n", "Note that the quadratic term in OLS regression will capture outlier effects. " ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 4.82458099 0.55057398 -0.01504094]\n", "[0.44879492 0.06928788 0.00613091]\n", "[ 4.4485574 4.7321673 5.01076564 5.28435242 5.55292764 5.8164913\n", " 6.07504341 6.32858395 6.57711293 6.82063036 7.05913622 7.29263052\n", " 7.52111326 7.74458445 7.96304407 8.17649214 8.38492864 8.58835358\n", " 8.78676697 8.98016879 9.16855906 9.35193776 9.53030491 9.70366049\n", " 9.87200452 10.03533698 10.19365789 10.34696723 10.49526502 10.63855125\n", " 10.77682591 10.91008902 11.03834057 11.16158055 11.27980898 11.39302585\n", " 11.50123115 11.6044249 11.70260709 11.79577772 11.88393678 11.96708429\n", " 12.04522024 12.11834463 12.18645746 12.24955873 12.30764843 12.36072658\n", " 12.40879317 12.4518482 ]\n" ] } ], "source": [ "res = sm.OLS(y2, X).fit()\n", "print(res.params)\n", "print(res.bse)\n", "print(res.predict())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Estimate RLM:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 4.75652165 0.53825171 -0.00527687]\n", "[0.14075398 0.02173051 0.00192282]\n" ] } ], "source": [ "resrlm = sm.RLM(y2, X).fit()\n", "print(resrlm.params)\n", "print(resrlm.bse)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Draw a plot to compare OLS estimates to the robust estimates:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(12,8))\n", "ax = fig.add_subplot(111)\n", "ax.plot(x1, y2, 'o',label=\"data\")\n", "ax.plot(x1, y_true2, 'b-', label=\"True\")\n", "prstd, iv_l, iv_u = wls_prediction_std(res)\n", "ax.plot(x1, res.fittedvalues, 'r-', label=\"OLS\")\n", "ax.plot(x1, iv_u, 'r--')\n", "ax.plot(x1, iv_l, 'r--')\n", "ax.plot(x1, resrlm.fittedvalues, 'g.-', label=\"RLM\")\n", "ax.legend(loc=\"best\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example 2: linear function with linear truth\n", "\n", "Fit a new OLS model using only the linear term and the constant:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[5.43082312 0.40016454]\n", "[0.39373415 0.03392573]\n" ] } ], "source": [ "X2 = X[:,[0,1]]\n", "res2 = sm.OLS(y2, X2).fit()\n", "print(res2.params)\n", "print(res2.bse)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Estimate RLM:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[4.96600288 0.4900169 ]\n", "[0.10874737 0.00937011]\n" ] } ], "source": [ "resrlm2 = sm.RLM(y2, X2).fit()\n", "print(resrlm2.params)\n", "print(resrlm2.bse)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Draw a plot to compare OLS estimates to the robust estimates:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAFlCAYAAAAzqTv+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAgAElEQVR4nOzdd3iU1RLA4d+XTaVIqAqhhRYpoYsgKiUUUQREFFREbAhWEFFRKUpV9KqYUKUqgogUUQHpvRM60ksKHUIS0ja73/1jTEIUSCHJbpJ57+ND8u1m9wT27uw5Z86MYZomSimllMpZLo4egFJKKZUfaQBWSimlHEADsFJKKeUAGoCVUkopB9AArJRSSjmABmCllFLKAVxz8slKlChhVqxYMSefUimllHKYnTt3XjJNs+TNbsvRAFyxYkV27NiRk0+plFJKOYxhGKdvdZsuQSullFIOoAFYKaWUcgANwEoppZQD5Oge8M1YrVZCQ0OJi4tz9FCylaenJ2XLlsXNzc3RQ1FKKeUEHB6AQ0NDKVy4MBUrVsQwDEcPJ1uYpsnly5cJDQ3F19fX0cNRSinlBBy+BB0XF0fx4sXzbPAFMAyD4sWL5/lZvlJKqfRzeAAG8nTwTZIffkellFLp5xQB2JkMHTqUL7/88pa3L1y4kIMHD+bgiJRSSuVFuS4ALwwOo+noVfh++AdNR69iYXBYzj6/BmCllFJZIFcF4IXBYQycv4+wiFhMICwiloHz991xEB4xYgR+fn60atWKw4cPAzB58mTuu+8+6tSpw5NPPklMTAybNm3it99+Y8CAAdStW5fjx4/f9H5KKaVUWnJVAB6z7DCxVluqa7FWG2OWHc70Y+7cuZM5c+YQHBzM/Pnz2b59OwCdO3dm+/bt7Nmzh+rVqzNlyhQeeOABOnTowJgxY9i9ezeVK1e+6f2UUkqptDj8GFJGhEfEZuh6eqxfv54nnniCAgUKANChQwcA9u/fzyeffEJERATR0dG0bdv2pj+f3vsppZRycleuQLFiOfZ0uWoGXMbbK0PX0+tmGco9e/YkMDCQffv2MWTIkFseIUrv/ZRSSjkh04T16+HJJ8HHB86ezbGnzlUBeEBbP7zcLKmueblZGNDWL9OP+fDDD7NgwQJiY2OJiopi8eLFAERFRVG6dGmsViuzZs1Kvn/hwoWJiopK/v5W91NKKeXETDPl6/79Yc0a6NsXcrBaYa5agu5UzweQveDwiFjKeHsxoK1f8vXMqF+/Pl27dqVu3bpUqFCBhx56CIBhw4Zx//33U6FCBfz9/ZODbrdu3Xj11VcZO3Ys8+bNu+X9lFJKOaELF2DCBJgxA7ZvlyXnn36CMmXgn63InGKYN34KyGYNGzY0/90P+NChQ1SvXj3HxuBI+el3VUopp7JnD3z7LcyaBQkJ0K4dfPcdVK6crU9rGMZO0zQb3uy2XDUDVkoppTLs1CmoW1dmuC+/DG+/Dffe6+hRpb0HbBjGVMMwLhiGsf9f198yDOOwYRgHDMP4IvuGqJRSSmVAZCR8843s7QJUrAhz5kBoKIwb5xTBF9I3A54OBAIzky4YhtEC6AjUNk0z3jCMUtkzPKWUUiqdjh2TZeVp0yAqCh5+GBITwdUVunZ19Oj+I80ZsGma64Ar/7rcBxhtmmb8P/e5kA1jU0oppdLnhx+gWjUYPx46dpQEq7VrJfg6qcweQ6oGPGQYxlbDMNYahnFfVg5KKaWUuq24OJg6VYIsQMuW8PHHcPq0BOOGN817ciqZDcCuQFGgMTAAmGvcot+eYRi9DMPYYRjGjosXL2by6ZRSSikgPBwGDYJy5SShKqn+go8PDBsGpUs7dnwZkNm5eSgw35QzTNsMw7ADJYD/RFjTNCcBk0COIWV2oNnl8uXLBAQEAHDu3DksFgslS5YEYNu2bbi7uztyeEoppZJ88AH8739gs8Hjj0vhjObNHT2qTMtsAF4ItATWGIZRDXAHLmXZqHJQ8eLF2b17NyC9gAsVKsR7772X6j6maWKaJi4uuapwmFJK5W6JibBwoQRbDw/w9YU335T/svn8bk5IzzGk2cBmwM8wjFDDMF4GpgKV/jmaNAd4wczJih454NixY9SqVYvevXtTv359QkJC8Pb2Tr59zpw5vPLKKwCcP3+ezp0707BhQxo1asSWLVscNWyllMr9rlyBzz+XgPvUU7BggVzv3Ru+/jpPBF9IxwzYNM1nbnFT9yweC337wj+T0SxTt64cB8uMgwcPMm3aNCZMmEBiYuIt7/f222/z/vvv07hxY06dOkX79u3Zv3//Le+vlFLqJmJjoV8/mDlTvg4IkHO7jz7q6JFlC+fNz3YClStX5r770k7wXrFiBYcPp/Qkvnr1KrGxsXh53VmXJqWUyvPsdjh8GKpXB09PKRn53HNSrcrf39Gjy1ZOFYAzO1PNLgULFkz+2sXFhRtX2W9sO2iapiZsKaVURkRFwfTpUjjj7FmpUlWkCGzcCPkk3yZ//JZZwMXFhaJFi3L06FHsdjsLkvYkgFatWhEUFJT8/e6sXkdXSqm8IiwM3n0XypaVWW6xYjBpUkononwSfEEDcIZ8/vnnPPLIIwQEBFC2bNnk60FBQWzcuJHatWtTo0YNJk+e7MBRKqWUkzFNiI6Wry9fllnvY4/Bli3y3zPP5GgfXmeh7QhzUH76XZVSithY6bU7dqzs5/74o1y/dAlKlHDs2HLI7doR6gxYKaVU1goLk7KQ5crBK6/IDLhNm5Tb80nwTYtTJWEppZTKxUwTDEMyar/6Cjp0gHfekWpVN69WnK/pDFgppVTmJSTIMvP998Nff8m1/v2lNeDChdCihQbfW9AZsFJKqYy7eBEmTpRCGWfPSivApIJF99zj2LHlEhqAlVJKZYxpQpMmcPw4tG0LU6bIn/noCFFW0ACslFLq9mw2WLRIlppnz5YjQ0FBUL68VLBSmaIfV4DQ0FA6duxI1apVqVy5Mu+88w4JCQmsWbOG9u3b/+f+v//+O/Xq1aNOnTrUqFGDiRMnOmDUSimVza5ehS+/lOYHTz4JO3bAiRNyW9u2GnzvUL4PwKZp0rlzZzp16sTRo0c5cuQI0dHRfPzxxze9v9VqpVevXixevJg9e/YQHBxM81zcj1IppW7q77+lWtWAAVCxIvz6qyRW+fk5emR5Rr5fgl61ahWenp68+OKLAFgsFr7++mt8fX1p0aLFf+4fFRVFYmIixYsXB8DDwwM/fUEqpXI7ux2WLIFz5+DllyXQvvMOdO0Kdeo4enR5knMFYAf0Izxw4AANGjRIde2uu+6ifPnyHDt27D/3L1asGB06dKBChQoEBATQvn17nnnmGVw0+UAplRtFRsKMGVIe8uhRqFkTXnxREqpGjnT06HJc0lHmnJDvo4Zpmhg3+du+1XWA77//npUrV9KoUSO+/PJLXnrppeweplJKZb2ffkppilC8uCRYBQfny2zm8HB4/XXo0SPnntO5ZsAO6EdYs2ZNfv3111TXIiMjCQkJoXLlyrf8OX9/f/z9/Xn++efx9fVl+vTp2TxSpZS6Q6YJK1ZI9rKfn5zdTapWlY7e585qYXAYY5YdJjwiljLeXgxo60enej7p+tkrV+Dzz2UBwGqF116T1fic+AyS/z7m/EtAQAAxMTHMnDkTAJvNRv/+/enZsycFktpj3SA6Opo1a9Ykf797924qVKiQU8NVSqmMu34dJkyQ5eU2bSTaADRsKA0ScnnwHTh/H2ERsZhAWEQsA+fvY2Fw2G1/Ljoahg8HX18YM0aSvA8fhsDAnFsAyPcB2DAMFixYwC+//ELVqlWpVq0anp6ejPxn72PlypWULVs2+b/g4GC++OIL/Pz8qFu3LkOGDNHZr1LKeX36qSwz9+kjPXdnzpQ6zXnEmGWHibXaUl2LtdoYs+zwTe8fHw/ffguVKsGgQVIpc+9eePLdMJ6fuwrfD/+g6ehVaQbwrOBcS9AOUq5cORYvXvyf682bNyc2NvY/1x966KGcGJZSSmWcacLmzVKpyjAkyapNG1lmTrqWh4RH/Pc9+mbXExPhhx9g6FA4cwZatpQcs/vvT5lFR9j2E+u6j7hIfwbOTwBI91J2ZmgAVkqpvCAmJqX37r59sGqVTO++/DLPBd0blfH2IuwmQbiMtxcg+7m//iqz3cOHZbV9yhRo1SrlvmOWHeaSbT2X3EcDdiJxh4QRjFnmnq0BON8vQSulVK4WGQkDB0rv3VdflWA7ZQo0biy35+HgCzCgrR9ebpZU17zcLLzXxo+lSyXgPv00WCwwfz5s3Zo6+J6NOsu+618nB18MMEkkzmXfLWfXWUVnwEoplduYJpw/L12HPDxkX7d5czlO9PDDeT7o3ihphnpjFnT7u/35pl9J1q2TIl4zZsBzz0kQTnLx+kW+2PgFgdsDiXe14pV4H3GWYEwzEQNXPO3+ybPo7KIBWCmlcou4OJgzR5aZL1+WbkQeHnDkCBQs6OjROUynej50qufD7t3wySfw0R/y2SQoCF55Bdzd5X6bQzaz5NgSQq6FMO/QPGKsMXSv3Z3GJXoxdlkUEQn7iXPZh6fdH29LLQa0zd4qhxqAlVLK2Z09K9Fk4kS4dEmOE338sWxwQr4OviAFvAYPls8m3t4wahS89Vbqv5YVJ1bw6KxHsdqtALT0bUlgu0Cql5SGEqULhjFmmTvhEdUzfJY4szQAK6WUMzJNSd11c4NduyRlt0MHWWZu0SJfLTPfSmgofPYZTJ0qCwEffSS9I7y9U+4TY41h3PZxDFk9JDn4WgwLrXxbJQdfSJlF5yRNwkIaMNStW5datWrx+OOPExERAcCpU6eoVavWf+6fVKQjKioq+do777yDYRhcunQpx8atlMqD4uPlvEyjRjBkiFxr106WmxculPMz+Tz4XroE/ftDlSowfbqUkDxxAkaMSAm+8YnxBG4LpPLYygxYPgD/u/3xsHhgMSy4W9xpXrG5I38FQAMwAF5eXuzevZv9+/dTrFgxgoKC0vyZKlWqsGjRIgDsdjurV6/GxydnPz0ppfKQs2cl4JYvLwWJo6NT+u26uEjJpnwuMlLqilSqJJWLu3WT7e+xY+FEwmZGrR/F+tPr+X7X91T9ripvLXmLasWrsa7nOra8soXVL6xmWIthrOyxkiblmjj618mdS9CbQzaz5tQamldsnuV/iU2aNGHv3r1p3u+ZZ57h559/pnv37qxZs4amTZuyZMmSLB2LUiofefdd+PlnaN9eNjBbtcr3M90ksbEwfryswl++DJ07w7BhUKOG3L45ZDMBMwOIT4zH/Od/9/vcz9SOUwnwDUhurNOkXBOnCLxJnCoA913al93nbt+O8Fr8Nfae34vdtONiuFD77toU8Shyy/vXvacu3zySviYPNpuNlStX8vLLL6d536pVq7Jo0SKuXr3K7Nmz6d69uwZgpVT6xMfDL79ITeapUyWp6rPPpDjxbZrA5DdWqywxf/ophIXJZ5KRI1OXrrabdr7b9h2xiSlndnvU7sH0TtNv2dHOWeS6Jehrcdewm5L5ZzftXIu7dsePGRsbS926dSlevDhXrlyhdevW6fq5zp07M2fOHLZu3arlKZVSaTt7VmohVqgAzz8P167BxYtyW9WqGnz/YbdLRnPNmtCrl9QYWbUKli9PCb6mabL48GLqT6zP7P2zMTBwwQUvVy96N+zt9MEXnGwGnJ6ZatJSQ4ItAXeLO7M6z7rjJYWkPeBr167Rvn17goKCePvtt9P8uW7dulG/fn1eeOEFXPJh/0ylVAbExcma6bVr8Oijks3cqlW+7L17K6YJf/4pJ6z27IFatWDRInj88ZTVeNM0WX5iOYNWD2Jb2DaqFKvCj0/8SAXvCqw/vT5btiazi1MF4PRoUq4JK3uszJY94CJFijB27Fg6duxInz590rx/+fLlGTFiBK1urGumlFIACQmyzLxqFXz/PXh6yjne+vUlfVelsm6dHCPauFGSrH78UZKskqpXbQ7ZzLTd09gWto095/dQvkh5pnSYQo86PXB1kVD2YPkHHfgbZFyuC8CQvRvp9erVo06dOsyZM4eHHnqIw4cPU7Zs2eTbv/7661T3f+2117JlHEqpXOrsWQm0EyZIuchq1eTcTMmSUpRYpbJrlwTeZcugdGlJtnr5ZTn+nOT7nd/z2h+vJW8/9m/SnxEtR+Dh6uGgUWeNNAOwYRhTgfbABdM0a/3rtveAMUBJ0zRz7QHY6OjoVN/f2JrQarX+5/5PPfXUTR/n1KlTWToupVQus3o1tG0r2UNJy8ytW+f7ZeaFwWGpajUPaOvHvV4+DBoE8+ZBsWLwxRfwxhvSsjjJ7nO7Gbx6MIuPpLwnWwwLxb2K5/rgC+mbAU8HAoGZN140DKMc0Bo4k/XDUkqpXCApm9nDA556SjoQ9e0rXYmqVnX06JxCUq/dWKsNgNNnTHq+aBK1z8TLy2DQICmqUeSGwywHLx5kyJohzDs4D29Pb3o36M2MPTOSc3+coYhGVkgzAJumuc4wjIo3uelr4H1gURaPSSmlnFt4uCwzT5woy8yPPioB2MtLpnIq2Zhlh4m12rBdd+fa5ipE7S4PQOkmIeyeX55SpeR+m0M28+uhX9l/YT9/Hf+Lgu4FGfzwYPo16Ye3pzc96vTItvoPjpKpPWDDMDoAYaZp7kkr1dswjF5AL5CkJaWUytVGjZLK/zabBN633pJlZnVToeetXNtajcgdvpiJLhTyD6VI06O43RVHqVISExYcWsBTvzyFzZRZ8nP+z/HNI99QokAJIGkJO5bwiNr87h3LgLZhOV63OTtkOAAbhlEA+Bhok577m6Y5CZgE0LBhQ/MW98kVZ7buhGne9FdXSjm7+HipUNWmjfS4q11bgu7rr2s2823ExEBgIIRPbElirBsF7g3H+8EjuBW/DkAZby/ORp1l5PqRjN8xPjn4WgwLNUvWTBV8b1zCDouIZeD8fQC5PghnJjOgMuAL7DEM4xRQFthlGMY9mRmAp6cnly9fztMByjRNLl++jKenp6OHopRKr7AwGDRIajO/8IJUhgB47DH43/80+N5CQoJkMlepAh98AHUa2Kj4ykZKdgxODr5ublGULDuXSmMrMWHnBB6r+hierp43bZSQtIR9o1irjTHLDufkr5UtMjwDNk1zH1Aq6ft/gnDDzGZBly1bltDQUC4mVYPJozw9PVMdZ1JKOSm7XapUzZ0ry8zt20s2c0CAo0fm1Gw2mD1b+kmcOAEPPigLBw895MnC4IoMXjKfMzGbcPe4QpSxgRMn4uheuzuDHx5M5WKVb1njPzwi9qbPd6vruUl6jiHNBpoDJQzDCAWGmKY5JasG4Obmhq92+VBKOVJcHKxdK0eIXFzA3R3eeUeWmStVcvTonJppwuLF8MknsG8f1K0r1aweeSSlelWhIoc4ZHuXRLdEsEOAbwCBjwZyb4l7kx/nVvUdynh7EXaTYFvG2yvbfqeckp4s6GfSuL1ilo1GKaVyUkiIrJdOmiRtdo4fl4A7bZqjR5YrrF4tRTS2bJF6Iz//DF26pBx7jrHGELQtiKFrhpJoTwRkjzfANyBV8L2dAW39Uu0BA3i5WRjQ1i/Lf5+clr9Phyul8qdTp+TYkK8vfP45PPQQrFypPXfTaft2Sfxu2RJCQ6XS5oEDUujLxQXiE+P5but3VPq2Eu+veB//u/3xsHjcdI83LZ3q+TCqsz8+3l4YgI+3F6M6++f6BCzIpaUolVIqw2JipExk5cpQsCBs2iQVIF5/XboTqTQdPChLzQsWQIkS8PXX0Lu3lLkGsNqsTNs9jeHrhhMSGUKzCs2Y9/Q8Hiz/4B31ce9UzydPBNx/0wCslMrbTp2CceNkmnbvvRJ4S5aEM2dSKv2r2zp5Uroo/vADFCok/Xn79YPCheX2DWc2MHbrWDaGbCQ8Kpz7fe5nWsdptPRtmXzENDtr+OdWGoCVUnnTli2yvPzbb5IN9MQTcn43iQbfNJ07B8OHyxa5xSILBh98ILNfkJ7sI9ePZPDqwZiYGBiMaT2G/k365/naDllBA7BSKu+IjpZI4eUFwcGwYQN8+KGsk5Yr5+jR5RpXr0pFzW+/hfgEk5INwnFreIhNxV3YEOJHx+JlWHxkMYNWD2Lv+b3JP+diuGC1WTX4ppMmYSmlcr9jx2RNtGxZmD5drr34omQ5jxihwTedoqNh5MiU3LT7msdQ8bX1eLbYjaVwPKERMby1YDrVxtaj45yOxFhjGPLwELxcvTKVYOV0tm2D+fNz7Ol0BqyUyp1ME5Yuhe++gyVLwNVVMpvvv19u18pz6RYfL8vMw4fDhQvw+OPydZ8/t2CLiCXe5RDRlhXEG4exWk7hHlGKKR2m0KNOD1xdXGlbpW3ubZQQFyfnpwIDYccOKeH1xBMph5izkQZgpVTukpAghTIMA4YNk7JLQ4bAa69JR3eVbjYb/Pij/PWdPg3NmkmG8wMPyO3hP8US5bKUK+5BYJhgQmHrExRL7MFL9TolP06uTLA6dQomTJDkvMuXoXp1CAqSKmg5tISuAVgplTscPCizlLlz4dAhyWSePVuCrru7o0eXq5imBNpPPpG/ygYNZAbcunVK7Ak+G8y1gsO5at8CyaX6XbBQGB/vuxw19Dtjt8t578BA+P13udapE7zxBrRokWOBN4nuASulnJfNBosWQatWULMmTJ0qtZnj4+X2ChU0+GaAacLy5dCoETz5pHw/b54U1mjTRuLPgQsH6DK3C/Un1SfBcogitnYYuIPpgoErRYy6ua8K1bVrMHYs1Kghv+jmzZKcd/Ik/PqrVBRxQOKYzoCVUs7HNOUN8eRJmaGUKyfZQa+8IjNflWFbtsDAgbBmjTR4mjYNuneXrfPNIZuZd3Ae+y/sZ/mJ5RR0L8jghwfTr0k/1hy6zuAl8wmJ2UG5Ag35rF3n3FMU48ABWVaeOROuX5f8gJkzpWSXh4ejR4eRk20AGzZsaO7YsSPHnk8plcvs3i3Lg7GxMGuWXFu/Hpo0kUihMmzfPllq/u03KFVKvu7VKyX+zD80n6d/eTq5H+9z/s/xzSPfJPfjzXUSE2XVJDBQPm14eMAzz8gyc8OGOT4cwzB2mqZ50yfWV7RSyrGsVtmQ/O47ObdboAD07JkyC37oIUePMFc6flySq376Ce66S05jvfOOVOEECI8KZ8S6EUzYOQG7aQekUULNkjVzZ/A9fx4mT4aJE6VAdYUKcpbqpZdSKoc4GQ3ASinH+uorWRutVEm+fvFFKFrU0aPKtcLDJTn8++/BzU0qV73/fspf6YXrF/h8w+eM2zGORHsij1d7nGXHl2G1WXPfOV7TlLX1oCBJzrNaZY83KAgee8zpq51pAFZK5RzThK1bZXnw6aehQweZ7fr7Q7t2KX3sVIZdviwTvu++k1XYXr1kubl0adnj/XP3n5yJOMOvh34lNjGW7rW7M6TZECoVrXRHjRIcIjYW5syR19GuXTLF79NHGmv45Z4EMQ3ASqns9+9iB3fdBU2bym333COzFZUp0dHSlejLLyEqShKrhg6VBQWAFSdW0G5Wu+R+vK0qteK7dt+l6seba87xnjwp/ZunTIErVyQzfvx4+aULFXL06DJMA7BSKvu1bClHP2rUkM5E3buntNJRmRIXJ3UkRo6EixclWXz4cIlJANcTrhO0PYhBq4YkB19w4R6PhqmCr9Oz22HFipSzuy4uUqnqjTekckgurjutAVgplbVMU7JPp06V6g5eXvDRR5Jc5YBiB7nZwuAwxiw7THhELGW8vRjQ1o/2/j7MmCEtAUNCICBAEqySKnDGJcYxaeckRq4fyfnr5/G0+4FxArBh4Mr6faVYWDXM+Y8SRUTAjBmyn3v0qKRwf/SRNNYoW9bRo8sSegxJKZU1oqOlYWxgoFStKl5cajU74OhHXrAwOIyB8/cRa5XjQaYJicd8YGdNwk+70aiRzH4DAuT+CbYEpgVPY/j64YRGhtKsQjMuhz9BVGQV4l0OEeeyD0+7Px726vh4e7Hxw5YO/O1uY98+Cbo//AAxMXIE7c03pXKIE5zdzSg9hqSUyl5nzkgiVWQk1K8vVR66dpXZr8qUMcsOE2u1YZoQd6IkEev9SDhfBK+7o1m40I0OHWQxYcOZDXy75Vs2hmzkbPRZGpdtzPSO02np25JKA/8EwMNeHQ979eTHDo+IddSvdXNWKyxcKIF37VpppJF0drdBA0ePLttoAFZKZZzNJh2ITp+WN8ly5eTPDh1kLVSXme9YeEQscaFFiVjrR3xocVyLxFC8/W4KVQ+jY8fHsJt2hq8dwZA1QzAxMTD4svWXvNvk3eR+vGW8vQi7SbAt4+0kH4zOnZOzuxMmyPmpihWlEfFLL8kKSh6nAVgplX5Xrsje7rhxkpFatarsyVkssh6qMuRme7yd6vmwezdELLyfiMMlsBSMo1jr/RSqcwbDYlKmiCe/Hf6NQasHsff83uTHcjFcSLAlJAdfgAFt/VItYwN4uVkcW8vZNCUhLzBQClFbrdC2rRTQaNfO6c/uZiU9dKeUSp9Zs8DHBwYMkCSYn3+WWrv56A0zKyXt8YZFxGICYRGx9J98nIfaxlCvHiSeLUbJlocp89pqCtc/DRY7NvfdXCzQn45zOhJjjWFos6F4uXphMSw3LaLRqZ4Pozr74+PthQH4eHsxqrO/YxKwYmLk+FCDBnIE7c8/ZdXk8GHJFWjfPt+9lnQGrJS6uYQEKRHp5wd168p/zz8vb5p16jh6dE7vVrPbJEl7vACJkZ5c21iV6H1lOeVm55NPoH9/F9acLMTgJcc4GfsHdtejxHCCCmYFpnaYyvN1nsfVxZU2ldvctohGp3o+js14PnEi5ezu1atQq5YsOT/3XK48u5uVNAArpVI7e1aOD02cKF+/+aaUV6pZU66rNP07gzksIpaB8/cBJAfD8IhYbDHuXNtcmajgCgAUrn8a7ybHGDasNQAX7X9yILEvdlep1fxek/cYETACd0tKC0anLKJht8Nff8ky859/ppzdfestqe2tOQKABmCl1I3efFMCb2Ki7Md9/z088oijR5Xr3Di7TRJrtTFm2WE61fMhMhISt9cgbEM5TKuFgrVC8W56FNcisfh4exF8NpjBawbz+5Hfk205tN8AACAASURBVH/eYlgo5lUsVfB1OhERkgE/bhwcOwZ33w2DBkldTB8nP3fsABqAlcrPYmJg/nx49lmZpfj4yCzl9dehShVHjy7XutUxn9CL8Xz5JYweDZcv+1K4+jkKN/0bt+LXAXBxC8Us9hv1J/1JUc+i9G7Qmxl7ZpBgS3DuRgl798oRoh9/lNdU06bw2WdydtfdiT8wOJgGYKXyo+PHZV9u6lTZlytTRspFDhzo6JHlGrfb4/338R/TZhC9rxzRm6sxIFKSfkeMgBAXG4OX7ON0zCoM91AizZ1culyIwQ8P5t0m71LEswg96vRwzkYJVqt8eAsKkp7NXl7yQe6NN6BePUePLlfQAKxUfnLhgrT7W7JEMk47d5Zl5wcfdPTIcpW09niTjv/EJNiIOVSGiA3VSLxaEL/a8UwcKyWMAU4f2srBxH7Y3GxgQnf/7nzzyDcUL5ByBtbp9njDwyUXYNIkyRGoVEk6Qbz4IhQr5ujR5SoagJXK665ehUOH4IEH5A3y8mXZl3vtNZn5qgxLa4+3Y10ftq/z5JvR7sScK0yBe6J4/5vLDH+7OIYB4VHhjFw/kvE7xmM3JcHKYlioUbJGquDrNEwTNmyQ2e6vv/43R0DbSGaKBmCl8qo9eyQLddYsaf8XEiId2rdscfTIcr1b7fGGR8Sydq30DNi0qTiVK8Nns6Bbt8K4uMCF6xf4fMPnjNsxjkR7Io9Xe5xlx5dhtVmdc4/3+nV5/QQFyT6vtze8/bb03tUcgTumAVipvGbDBtnL3bBB9uWee0725dzcHD2yPONmJR7jz91F3KYaNP9cFhYmToTqrTezIXQNy0/UZ93pdXy79VtiE2PpUacHgx4eRKWildgcstn59niPHZNM5qlT4do1Ofc9aZK8lgoUcPTo8gwNwErlBeHhcraydGlJjgkPh6++kn25okUdPbpc6XZJVjeWeLReKkTE+mrEHClNYW8bX34pSeS7L20mYGYAcYlxmEjXuW61ujG02VD8SqSUgnSaPV6bTSpSBQbKn66u0KWL5Ag88ICe3c0GGoCVyq1MU7JPg4IkG/WNN+Cbb6B5c+mfqvtymZZWklWnej5cCLfwyRCTi7vuwcXNRtdekUwacxd33QUx1hg+W/sZsYkps+S3G73Nt+2+dcjvc1tXrqSc3T1xQj7EDR0qZ3dLl3b06PK0NP8fahjGVMMwLhiGsf+Ga2MMw/jbMIy9hmEsMAzDO3uHqZRKZfp0WRZs1kwqDr3zjpzfBZmpaPC9I7dLsjp/XrZB33ziHiL3l6ZfX4Nzoa7MmXgX7gXiGLt1LJW+rcTS40txMVywGBa8XL3oVqubg36bWwgOhldekbPf770n6+Y//ywdroYM0eCbA9IzA54OBAIzb7i2HBhommaiYRifAwOBD7J+eEqpZKdPQwUpWci6dXKM6PvvpW+q7stlqZslWdnjXDnwW3kqDYP4eOmYN2iQdGK02qxM2jmNYeuGERoZSvOKzfn16V9xMVyca383IUGymAMDYdMmed306CGrJ7VrO3p0+U6aAdg0zXWGYVT817W/bvh2C9Ala4ellAJkX+6PP2SZ+a+/YPt2aNhQvvf01H25bHJjkpXd6kLUTl8it1TGHu9Gt27w6adQrRpsOLOBd3/5lk0hmwiPCqdJ2SbM6DSDlr4tkx/LKQJvWFhKfe/z5yWD+euvoWdPyWxWDpEVe8AvAT/f6kbDMHoBvQDKly+fBU+nVD4QHS1Bdvx4mfn6+Ehpv6QZsJeTNFTPowa09ePDX/ZzcYcP1zZVwXbdk4JVLjBsGPTrVgq7aWfY2hEMWTMEExMDgy9bf8m7Td5N1Y/XoZJyBAIDJUfAbodHH5WkqjZtdJvCCdxRADYM42MgEZh1q/uYpjkJmATQsGFD806eT6k878qVlGpCo0ZJSb+vvoIOHfQYUQ6x2SBqvw8RM+/mSpgrHmUvU737AYa9dg8d65Zh0d+LGLxmMHvP703+GRfDhQRbgnME3+hoObsbGAj790sWfN++kppdqZKjR6dukOkAbBjGC0B7IMA0TQ2sSmVWXJwkvwQFyZvngQPSJ/XYMShRwtGjy5XS6sV7M6YJixbBJ5/IP0G9eq5M/x7ati0OFGPZ8WU0+r4TO8J3ULVYVYY2G8rnGz93nkYJR45IJvP06XJ2t25dzRFwcpkKwIZhPIIkXTUzTTMma4ekVD5x5owE3SlTpDzkvfdKMkxiosx2NfhmSnp68f7bypVSvWrbNvDzg7lzpZHP1rDN9Pp9KltDt7Lvwj4qeldkWsdpdK/dHVcXV9pUbuPYJCubTep6BwbCsmXyukk6u9ukieYIOLk0A7BhGLOB5kAJwzBCgSFI1rMHsPyfJZctpmn2zsZxKpU32O1SKMPDQ7JQv/oKOnaUwNuihb5hZoG06jTfaNs2CbwrV0o285QpkhTs6gqTdk6izx99kms1D3hgAMNbDk/Vj9dhRTQuX5YqVePGwalTcoTos8/g1VfhnntyfjwqU9KTBf3MTS5PyYaxKJV3Xb0qS4Pjxsn5lYEDpRPRqVNQtqyjR5en3K5Oc5L9++UI0cKFULKk1C957TVJLN91dheDVw/mj6N/JN/fYlgo6lk0VfB1iF27ZLY7e7ZsXTRrBl98AZ06aY5ALqRpcEplp+BgmZX4+MC770KpUlCrltzm7q7BNxuU8b55hngZby9OnJAZbu3asGqVTBqPH5c6JscjD9BlbhcaTGrAppBN9G7YGy9XLyyGxbF7vAkJ8NNPUg6yQQPJF+jZU5ojrFkDTz2lwTeX0lKUSmU1m02KZIBk9KxZA927SxZq3boOHVp+cGOd5iRucQW4a9d93DtY/mneew8++ACOxGxm6KZ57LuwjxUnVlDIvRBDmg2hX+N+FPEsQo/aPRy3xxsaKud2J02SPs5Vq8pU/YUX9OxuHmHkZAJzw4YNzR07duTY8ymVo0JC5A1z6lTZ361YUWrrFiumb5g5LCkLOuRsIvY9flzcWg57oguvvCJLz2XKwPxD83n6l6exmRKon/d/nq8f+dqx/XhNE9aulWXmhQslZ6B9e8kRaN1az+7mQoZh7DRNs+HNbtMZsFJ3wjQlgycoCH77Tb5v317250DPXTpIq6o+HPjThzEzIDISnn1WqldVrgxhkWG88cdIJuyckJxgZTEsVC9Z3XHBNzoafvhBXkcHDsiHtv79oXdv8PV1zJhUttMArFRmmKZkLF+4INWFihSB99+XTJ6KFR09unwrPl4WIUaMkH+aDh1g+HDw94cL1y/Qf9nnjNsxjkR7Ih2qdWDp8aVYbVbH7fEePpxydjcyUvZ4p02Drl212lk+oAFYqYzYu1dmKWFh8PvvcPfdsGIFNGokKbTKIRITZQI5dKgcr27RAobP2MylgmsI96rP7JVrGbt1LLGJsfSo04NBDw+iUtFKbA7ZnPN7vDabvHaCgmD5cknGe/ppObvbqJEeRctHNAArlZakDjJBQbBxowTa556T87xubvDww44eYb5lt0uZ40GD4O+/4b775CxvgWqbafVDAHGJcZhInssztZ5hSLMh+JXwS/75HD3He+mSVKaaMEHqe5ctK1P1V16R7HiV72gAViot338vSTCVK0vhjJ49U+o1q//ITBnIjDJNaQ710UdyNLZGDQnEnTpBjPU6T879lNjElHO/bzd6m2/bfZvj4wSkg1VQEMyZI2vkLVvC//4n6+Ou+hacn+m/vlI3ujGpqmNHCbbPPSfJVNpBJk2ZKQOZUZs2SR2TdeukOdT06XLKy2rGMXbrREZuGMmF6xdwMVwwMHC3uNOtVrecHWdcHPzyi2Qzb9smtb1fflk+yNWoceePr/IEDcBKAUREwIwZ0v7v8GGpw9ymjdxWpAg88ohjx5dLZKQMZEbt2SPHqpO23r/7TmqcGK4JfB88jWHrhhEWFUZL35YMazEMA+OW+7vZNs4zZ2SJefJkWXL284OxY+Xs7l13Zf5xVZ6kAVgpkNnuunXQuLFk83TpoklVmZCeMpAZdewYDB4sK7hFisDIkfD227Dr8nq6LxrLxpCNnI0+ywPlHmDmEzNp6dsy+Wdvtb+bpeM0TSmrFRQk7ZRAlpffeAMCAjSpSt2SBmCV/8THw7x5UjBj3jzplzpihLRsq1/f0aPL1cp4exF2kyB2Y3nI9O69hoVJqcgpU6R3xYcfwoABUMTbznM/v8+cw/8DTMCgZ41BTO3yabr78aZnnGmKjEw5u3voEBQvLkfReveWtXGl0qAbWir/OH1asnbKlZNNwzNn4ORJue3BBzX4ZoEBbf3wcrOkuublZmFAW8k8Ttp7DYuIxSRl73VhcFjy/S9dgk49oihf0cak7+2UbBRC4MKzjBhhsvb8Qip9XZM5h7+SmSeAafDHvhAW7Q7PsnHe1qFDcmTIx0f+LFhQti9CQ2HUKA2+Kt10Bqzyh7AwyWI2TXj8canL3KqVJlVlsaSZ7K1muLfbew2o4sPXX8PoL+zEXi9EwVphFGl6BFfvGAav383Ig/M4FrEHT8OHItZniXSdh2kmYuCKJbFmhvZv0xrnfyQmwuLFMttduVLO7nbrJsvMjRpl8m9L5XdaC1rlTVeuSHrs2bMwZoxcmzxZEqt0huIwvh/+wb/fccxEF6KCK2DZW4NLl6BYzQt43H8I8+7tRFuWE28cwWo5hQf3MKHjKIbOKQZYiHc5RJzLPjzt/njYq2MAJ0c/lrUDvnhRjqGNHy+1vsuVgz595OxuyZJZ+1wqT9Ja0Cr/2LFDSvsl9Utt3jylO9Grrzp6dPnejXuvpt0gel9Zrm2sii3Ki1atJMHq6V+3E2lZwhW3cWCYYEJha2eKJT5Pz7qdmLx0FWERsXjYq+Nhr57qsbPMtm1yhOjnn6UQS0CAZDO3b69nd1WW0fU3lXcEBkoppLlz5djH7t2wenVKa0DlcAPa+uHpauH6odKEf/8wV5bWxu2ueD6dcJHly8FSdhcRBYdxxT0IkufKLlgohI/3XcmPken929uJi5O93EaN4P77YcEC+dB28KCUG+3USYOvylL6alK51/HjUnm/VStZWu7YUfZ4e/SQ8yrKqZgmuJ/1IWFeSS4ddsetRCT3Pr+XkX2LU7XsVZ6c25v5h+ZTyK0I3tbHuOayPHmPt4hRNznAZnj/Ni2nT6ec3b18GapXlw9zzz+vZ3dVttIArHIXmw2WLJFl5qVLJYmqaFEJwOXKwVtvOXqE6ibWr5cE9A0boFIld4ZM3oxbtTVUKVaJeUd+Y/bi2RRyL8TQZkPp27gvqw9FM3jJfEJidlCuQEM+a9c5VYDtVM/nzgpmJFU8CwyU5CqQD3BvvimdHPTsrsoBmoSlcpcWLWDNGihdGnr1kiVCn2yo36uyRHCwBN6lS+WfbPBgqNFmM21ntyQ+MR4TEw+LB/0a9+O9B97L/n68kZGyzBwUlFLxrFcvaSNZvnz2PrfKlzQJS+VOpgmbN8sb5tixUo2hd285+tGxo3QiUk7p8GHpUPTLL9K34osv5J/tamIYT87tR1xiHAAGBv2b9GdEwIjsHdCBAxJ0f/gBoqNlj/eHH+Cpp+R1pZQDaABWzic6Gn76SZaZ9+yRfbhevaRZedeujh5dvne7SlZnzkj1qunTpZLnoEHQvz/EWc7z8brRjN8xnkR7Iq6GKyYm7hZ32ldrnz0DTUyE336TZebVqyXQPvOMfBJoeNMJiVI5SgOwci4nT0LdurJUWKcOTJokb5qFCjl6ZIpbdxGKuOLCnt9LM26c3O+tt6RjkWvhK4zeOIax28YSlxjHC3VeYNDDgzgXfe6WjRLu2PnzKX13Q0NlaXn0aOlGVKJE1j6XUndAA7ByLKsVFi6ECxdkZlKxoiwzd+okjRE0Gcap/LuSlT3elbPrK/HyFyUhEV58UfZ5jySu4Nmlo9kcuplYayzdanVjSLMh+JWQTGbfor5ZG3hNE7ZskWXmuXPlddW6tcx+27fXo2jKKWkAVo4RGiqz28mT4dw5qF1bKgy5uMDnnzt6dOoWkroF2a0uRO2qSOSWytjj3CngF86uRWUo63ud95a/x4QdEwCwGBZmdppJ9zrds2dAsbHSJikwEHbtku2KPn2k1KjfHZ4LViqbaQBWOW/cOOknZ7fDo4/KG+Yjj2hd5lzgnsIFOLK+hFSvivbE0/cC3g8fpqLfdZZcncuoxaO4cP1Cqp8JiQzJ+oGcPCnlIadMkbKjNWvK992763aFypzERNi0CR5+OMeeUgOwyn5Xr0pWTvPmUK8eNG0K770nRz98fR09OvUvN0uy6lDHh9mz4eSEh7gS6oqHzxVKdAjGo9x54t1XctRlHv2WnaOlb0u61uxK36V9SbAl4G5xp3nF5lkzMLsdli+X2e4ff8gHtk6d5Oxus2a6XaEyxzQlc3DSJAgPh7//zrHVEw3AKvts3y6zkqS6zJ9+KgG4Th35TzmdfydZhV6N5c3R5+i7qxSnj7lRp44rr75/iQXXZnEyfi5XXP/GyhUeKPkAw1rMoqVvSwD8S/lnXZJVRIR8gBs3Do4ehVKl4JNPJDO+bNk7/I1VvmSzwc6dUnbUMKSGfJ068hqrXDnHhqEBWGWPtm3hr7+kV+oLL8gyswZdp3djklXc6eJcXedHQnhRPIvHMHu2G12esjNifRAH136K6WpiYPBV66/o16Qfxg0z0Cblmtx54N23L+XsbkwMNGkCQ4fCk0/q2V2VOWfPyrbF5MnS3erkSemOtmCBQ+p8awBWWePIEekc8/HHsjTYrh106KD1dHPY7c7opkd4RCzxZ4sQsc6PuFMlsRSKpVjbvRTyD8GjTgL1Jg1m/4X9yfd3MVyIt8WnCr53JCkrPjAQ1q2Tw8TPPisZ8vXrZ81zqPzn+HH44ANYtEj2egMC4MsvpTwbOKzJhgZglXlJhQ7Gj5duMW5usifn7w99+zp6dPnOrc7oAukKwgcPQuTv93HlQClcvBIo2uIgheqfIt59O5c9f6Lz3CNUK16NT5t/yugNo7N2j/fcOdmDmzhR9uF8faV81ksvQfFsLk+p8qaLF+HSJWmuUbCgJFj17StbF1WrOnp0gAZglVl//y1diMLCpAnC8OFS6OCeexw9snzr32d0AWKtNsYsO3zbAHzqlKzs/vADeHiVoMTDR3G573divJZyzjiM1XKaUl7lCGw9je61u+Pq4krrSq3vfI/XNOVNMSgI5s2T2W/bthKE27XTs7sq40xTOn9MmAC//irbFmvWyPtSSIjTvaY0AKv0MU1YtUoymrt0kUSFhx+Gbt3gscec7oWdHyWd0b3d9RuXqEtYilDqeF2Wzy+Eiwv06wcffujCoPXzmbB3IEn9eDtW7s3cZ77F3eKe/Dh3tMcbEyOJeYGB0rO5SBFZYu7TB6pVy9xjKjVnjmQzHzokr6nevWW2m8QJ36PSDMCGYUwF2gMXTNOs9c+1YsDPQEXgFPC0aZpXs2+YymGuXpVmCBMmSIX9OnUkCcbNTeo1qxx1uz3eMt5ehN0kCJfx9kr+2YHz9xEdZRC51Y/TOytiJrrQ5onrTPm2IOdddtJj2SCWHFuS/LMWw8L9FcqnCr6ZduKEZJlOnSqvq1q1ZLb73HOyRKhURpgmbNsmr6OCBaWaXuHC8vrq2hUKFHD0CNOUnsoH04FH/nXtQ2ClaZpVgZX/fK/ymqAgafXXr5/03J05U8r96XlLh0gKoGERsZik7PEuDA4DYEBbP7zcUn/K93KzJDeyH734KOfWVSR8Qksit1TBq8p5yry6lvMNZvP2xs40nNyQLaFb6NOwD16uXlgMy53v8drt0r+5fXuoUgW++Ua2Ltauhb17ZYaiwVdlRFSUTAjq15dytXPmyPU334StW6Ueai4IvpCOGbBpmusMw6j4r8sdgeb/fD0DWAN8kIXjUo6QtDTYsqUkwdx7r2Qx9+kjDRKUQ6W1x5s0E/73DPnRmj4EBsL2Lxpjv+6J+/1/4NF4ER4FihJh2Up4wjpOnizM0GZD6du4L0U8i/B87efvbI83IgKmTZMZ77FjcPfd0hqpVy/t36wyJz4e3nkHZs2Sjml16kggfvppuT2NSnp3ekIgO2R2D/hu0zTPApimedYwjFJZOCaV0/7+W17IM2bIG+eoUfDhh5KqHxDg6NGpf6Rnj/fGQGyzyXuVX2dJtLrLNxZLy5lElH2TBKxEAeCGj2s39rz9HcULpGQbZ3qPd88eWTmZNUs+0DVtCsOGQefO4J4Fy9gqf4mJkRrfDz4oZ78PHpQclN69U4popMOdnhDILtmehGUYRi+gF0D58uWz++lURpimJFAtWSJ7uk8+KbPdhx5y9MjUTaS1x5vENOUo7SefyPtV/fry+Sqk0HHe+ut/mFjBAEwoZu9M4GNjUgXfDLNaYf58Cbzr14OXV8rZ3Xr1Mv+4Kv86dEjyA2bMkJlveDh4e0tGcyZqxmf2hEB2y2z1+/OGYZQG+OfPC7e6o2mak0zTbGiaZsOSJUtm8ulUlgkJkXdjkE+P/v4wcqRcnz1bMpt1j9cppbXHC3Ic+/77ZcJps8Evv8Dvq8+z1OzHm6sfxOpyDAwXMF1wMTwY0OzZzL8BhYfL+aUKFSQbPixMihuEhko/Xg2+KqN27oQWLaBGDdm+eOQRmSAUKSK3Z7JhS3pWjxwhszPg34AXgNH//Lkoy0aksp7dLmUhx4+H33+XKVLbtrLPq63/co1b7fF2qufDli1ShGzVKjmWPWUKtH/qCl9vHcMLgWOJT4znhTovMKjZIM5Gnc38/q5pwsaNcoTo11+lGEu7dhJwtaOVyoyTJ2UVpVo1SZ46cwZGj5ZkqlJZs7uZ3tWjnGaYpnn7OxjGbCThqgRwHhgCLATmAuWBM8BTpmleSevJGjZsaO7YseMOh6wyZPdu2TM5flxezC+/LIkwFSs6emQqC+zfL0vNixZByZLydZU2K/jfttFsDt1MrDWWZ/yfYUizIVQrfgdnbK9fl2NngYGSveztLW+Qr78u2c1KZURionS0mjABli2Dp56SUrYgH/KyeBXu33vAIKtHozr7Z/sStGEYO03TbHiz29KTBf3MLW7S7BxnlDRDiY+XBKpKleQNcvhwTYTJQ06cgCFDJNepcGH5533l9esM3fQe7/wsWwwWw8LMJ2bSvXb3zD/RsWOyFDhtmiTo1akjJSOffVaPD6nM+e47KTMaGgplysDgwfDKKym3Z8MW2O1WjxxJK2HlFZGR8OOP8oly3z7JGgwIkEYIS5c6enQqi4SHS7CdPFny5t5/H95+N465JyZQe8ooLlxPnY4Rci0k409it8trJjBQ9t9cXSVB7803JatZcwRURtjtsHq19AO3WKRgRo0aMHYsPP54jjVCuPGEgLPQDZu84H//k7OVb7whL+ZJk+SNU+UZly9LM5cqVST4vvoqHDycQMUuE2j0YxX6LeuHfyl/JrafmPkiGleuwFdfSaH6xx6D4GBJsjpzRoodPPigBl+VfpcuwZgxsrfbqlXKe9Jnn8my8xNPOKwLkbPI3799bhUXJ+mt7dpBiRISfLt0kSNE992nb5J5SHS0FI8aM0YKAHXvDo/1Wc8vId/SZO5GzkWfo2m5pvzwxA+08G0BgH8p/4wlWQUHp5zdjYuTY2gjR8obpG5ZqIy6ehXeekveoxIS5PU0bBi0bi236/tTsjSTsLKSJmHdoaNH5WzctGkyWxk/Xg6kqzzhxko99xQsSI3Iuiye4c3Fi9Ll8dPP7Cy4PIxP136KiYmBwVdtvqJv474Z78ebkCBZzIGB0pGoQAGJ7q+/Lvu8SmXEtWty6LxJEzn/1qCBBN7evaFmTUePzqHuKAlLOYGEBNkr+esvWbLp1Elmuy1aOHpkKoskZWnGxNu5vr8sIRuqsSXKC//74vjtNw/OFlnIc2sGs//C/uSfcTFciEuMy1jwDQuTD3GTJsH587Km/fXX0LOnZDYrlRG7dslE4KefJCkvNFRWTYKDMzTTdcYykTlBA7CzCg2VqkLPPCMv6DJlZBnn5ZehdGlHj05lsS+WHObSvpJErPcj8Uoh3Etfpdiju0n0X8Obe39l59md+BX347PmnzFqwygSbAnp3+M1TVi3Tma7CxZIUsyjj0pSVZs2enZXZdzatZIBuG2bVD575hmZ7SZtWWQw+DpjmcicoAHYmdjtsHy5fKJcvFgyBtu0geLFZdlZ5TmmKfkoO8c2IOF8ESw1V1DwqQW4F7MT6bqWi4mH8I31ZXrH6TxX+zlcXVxpValV+vZ4o6NlXzcwUA4MFy0qna369JHjaUplxN9/y1ZF+fISYKOiJJP5+efvaPXEWctE5gQNwM5i40bo0UMOeJYqJSmvr74qwVflSRs3wkcfyeTUo6g7dz09g8jqr3IdK9cNcLEXoZJrXw69+XmqfrxpNko4ciTl7G5kpHSymjJFykXmkjZtykkkJEhh8QkT5CjRm2/KOd6HHoIDB7IkocpZy0TmBA3AjmKasGGDLNncf79UpqpQAUaM0IIZedyePVI28o8/4J57JAE5quoaBm34GAyr3Mk0KGZ24KtH30sVfG/JZoM//5TZ7l9/ySHhp56So2lNmmjmqcq4kSNlhnv+vLw/jRwJL70kt2Xh68lZy0TmBN38yWnXrsmbpL+/ND4YNUqu+/hIId9u3TT45lFHj8pWWd26MvsdNQoWbt7HiuKd+XDTo7i6XcPA8k+jBHf6N+uS9hLc5ctSVahKFejQQZaaP/tMzu7OmgUPPKDBV6WPzSaz3KSTMWfOSMu/P/+UUrYDB0pf5yyWniYjeZXOgHPSp5/Km2VMjJzXnTIFunZ19KhUNgsNlZg4dSq4+m6m2SdreL59JVaGLuKjGXMo7FGYT5t/St/GfTlw4UD69nd37ZIPcrNny9ndZs3ksHDHjjL7VSq9LlyQ96JJk6Rx9NatEnjHjcuRBD1nLROZE/QccHa6fh3mzpVZrZeXrDXu3i3Zgg0aOHp0KptdWB55KgAAIABJREFUvChNXYKCJL+u45ubWVysJQm2eExMPCwevNvkXd574D2KeRVL+wHj42HePHnAzZtlP7dHD1lmrlUr+38hlbecPQvvvivnwa1WOdbYp48cc9QPcVlGzwHntAMH5KzlzJmy5HzXXVJL9403HD0ylQMiI6U66FdfyWJHjx7Q671Q+m7qS3x4HAAGBv0f6M+IliPSfsDQUEmCmTxZZitVq+rZXZU5165J+7+6daXH7rZt8r7Uuzf45f0lX2ejATgrRUTIEuC6dbKP26ULvPaaZAyqPC82VlbtRo2Srdknn4S3PzrPggujabFgPIm2RMAFTDAMNwqb99/6wUwT1qyR2e7ChTKFbt9eslBbtdKzuypjbiyYUbZsypGio0f1teRAGoDv1PHjktbaubN8oixWTPZ5e/aUBq0qz7Na5cTPZ59JoanWreH9oZdZETOGdku/Iz4xnublunDyRDtibBeJc9mHp92fGWvcubdYWOq9rqgo6WoVGCil/YoVg/79ZYbi6+u4X1LlTsuWwaBBsH27bIM9+6wsMycl5mnwdSgNwJmRmCiFMiZMkCMf3t7SPcbDQyoNqXzBbpce4oMHS9vcxo2h79jlLIkeTcfVW4hNjOVZ/2cZ0mwIPSeHYLPG4kEJPOzVAYi131Bs4PBhme1Ony5BuH59iepdu8obp1LpdeSIfHArUUL2Q6Ki4NtvZS9EtyycigbgjPrjD+jVSxqzli0r7dpeeUWCr8oXTFNeBh9/DHv3yomyuQuus8r1PQbsnACAxbDwwxM/8Fzt5wAIjzjyn8dxsduouX01tBktFdDc3ODpp2VPrnFjPT6k0s9qhd9+k2XmlStlOWbQINkH6dJFX0tOSgNwWux2meX6+Mg7bfny0i1m/Hipp5vP+1nmN2vXSvWqTZugcmWY9kMcVytP4M2No7hw/UKq+565dib56xuLDRSNuUbXvcvpHvwnZSMvyAe54cPlg1w2nLNUeZhpymtn/HjJai5fXr5/+WW5XZeYnZpGj1s5f16WACdNkqzBXr0ks9nfXw6mq3xl1y4JvMuWSV+MwPEJmHWn8MmmEYQdDyPAN4Cnaz5N36V9b9ooYUBbP34M/JVu237j8UPr8LBZ2VKhDmGDhnN/3xf1g5xKP7tdug01aCAz2127JKt54kSZFFgsaT+Gcgr6//qbeeMNOfJhtULz5nKYs1MnR49KOcDff8tK3rx5sq3We+R6zlX8luHhGzm37BxNyzXlx84/Jgdb/1L+qQtpxMfD3Ll0Cgqi09atxLh7Mrd2a5Y1e5IuPdrmi2IDKotcviw5AhMmSPLnsWPSVOOXX/QDXC6lhThAmtvPnSuzXBcXqcd8+bJ8f++9jh6dcoAzZ6Rw2fTpclqj37t2EpsMY/TWTzExMTD4qs1X9G3c9+b9eENCUs7uXrwoZyzfeEMSYYoUyfHfR+ViISHyKfDnn6XqWdOmksncpYvmnuQCWojjZkwTtmyRN8mff5aZir+/vLg//tjRo1MOcuGC1JwfP15W995+x6RO14V8tWsw+7fuT76fi+FCXGJc6uBrmlJLNzAQFi2Sa48/Lmd3AwI0EUal3/XrcO6cJBp4eMDvv8OLL8pxtNq1HT26VBYGh+XLMpJZIX/u0J8+LYlUDzwgx4ZeflnO8jZt6uiRKQeZtS6cci1Pck/ZRL79zs5Dj0UzcdWfrLu3IS8u7YzVZuWz5p/h5eqFxbCk3uONioKgICIr+0FAAFeWruSHh7qy7LdNUkSjVSsNvip9Dh2Cd96RpM8XXpBrpUrJqYtx45wy+A6cv4+wiFhMICwiloHz97EwOMzRQ8sV8s8MeMcOqZLQsaO8uMuVg7fekvY0hQo5enTKQWJioM/Aa/w4qQT2Ejtxaz8Jr/LX2eS9gpXLD+Hr7cuMTjN41v9ZXF1caVWpVcoeb7S3zG5nzoSoKE6Xrsr0R/vxe/WHiHd1x2vLVUaVCdPZgErb8uVSQm316pRWkn36pNzupB3Sxiw7TKzVluparPWG8+3qtvJ2AI6OhjlzZJl5586Ulm2urnKQU+VbCQnSAGbYMDh7tgjujf4g4ZEnsBpWrAa42ItQya0ff7/5OW6WlML0TUrfR5Md52DoJ9I+0t0dunbllcKNWVG4Qqrn0DcidVuhoVC0KBQsKMUzTp6UIPzSSzLrzQXCb9LH93bXVWp5dwl66lSZ6b76quzvBgbKLFiXAvM1m00qPVavDq+/LltsxV+civ2RXuBiBQMwDQrb2mOPCkgJvkmbw5UqSdnRo0fl+9BQmDmTlf8Kvkn0jUilklRX4IknoEIFeTGCvE8dOwYffphrgi/I+faMXFep5Z0AHBsrS4HHjsn3vr4y2924UcoVvfGGZp/mY6YpeVF168Lzz0uDqqB5+yjxxhNcrvAyNiMCTAuYLhi44WWvK28i27ZJ5nK5cpKcV62a5A2cOCENyv+p961vROq27HZpj+XnB23bwoYN8P778Mgjcru7e6bO7y4MDqPp6FX4fvgHTUevyvG91wFt/fBySz1uLzcLA9pqZ6X0yP3HkP7+Ww6gz5gBV6+mlGBT6h+rVkkRja1hmynRcA3PPerLuaKLmHvgZwp7FOaxir3YcaAxUbaTxLnso3BCdZ79+yIfHF9J0YN7JEegZ09WNH+SIUftN832TEpGuXE/zMvNwqjO/roEnZ+dOgUVK8rXTZpIkH39dSkReYdHiJzlNadZ0Ld3u2NIuTcAm6ZUfVm6VJIWOneWFP1mzXSZWQEyef34Y1ixAkrW30xEh5ZYkX68nhZP3m3yLv0f6E+x/7d33+FRVVsDh397JoXQW1BIQKqIiBTz0YWACNKR6xUElKIiKoiiIFhQQcGGF6Q3EUGliaCChatyVTpIF5EiLQSCtARIm5n9/bEnEEIaSciZst7n4SGZORP24WTOmt3WCinJsq1RfLLgF+7931Ie2vkDxS/FmnHqgQPh4YdZtj82y5ud3IgEYFb2LVhgVi3v2mUWf5YqZdak5OGCzyZv/3Q5vWlqYcVDWDO8ZZ79OyJ3fHMfsFKmYkzz5mZ/nOTQFW67d5tBkC+/NAVhXht3jJWFn2VTtAm+CsWQxkN4q+Vb5oPcqlUmU9XXX5sf0LmzCbwtWlz+MPfe95uyXO3ZpW6YBFx/FhUF779vsrecOwc1a5ph5wIFzPN5vNtCFkB5P+8NwGAyVgmB6X2O/vwwe1dW4OIfYRQspBn2xini6ozl7R3TcFxwEKAC0GiC7EF0KNcCJk40JQD37jVzucOHwxNPmIT2acjNTqTL4TBTX6GhJnnGlClmNO7JJ+Huu2/oaFzqAh9pHxfewbsDsPALWQ3tfvRDNM+/7ODc7w1RNk3hxlsIbPY+E2xf4diWRJ86fXi12ascjzvO6o0LifzlCI3+734zJNigAcybZ/ZdZjInJzc7cZXoaJg1y6w/adAAvvjCLNA7ccJsLcoHQ9tUT3daRBZAeQ8JwMKjpV1okpJpB6B5xTDefRfeHVcGl1NRoOVnuOqP40LgH0AypXVL1j49lWrFKrFx/EcETZ3KiIPbSAwI5HDb+7ll5FCISHdq5hpysxOAqUM5fryZ33A4oHVr6NPnyvP5FHyByx9CZd2B95IALDxaepl2Ll6EwcMTOL8BYmMhpNYBaPMClwp+7d7Ha6NU0hAqxtWh2rRFXJo4mfonozlWtAxvN+/DwjvvJaFYScbay5LdGldys/Nj58+bZBkBAaYe5X//a9JFPvEEVKtmadNk3YF3y9UqaKXUc8BjgAZ2An211gkZHe+x1ZCEx6o0fAUpv6HaYSNuewXOr6uC62IB2nWK5/be0xi/cxQOzpnfQncijZ47KzJn+VECnQ42Vr2LGXe246cqEbhsV/YsympRkant201VjvnzzZ8uXcwnvsBACJGpB5E9N2QVtFIqDHgGuF1rHa+UWgR0Bz7O6c8UIq1yxUM4diaei7vDOPfbrThjCxJ0SzSl+k9gW/g8Vu48zp2lm3L6eC1O2meilYMgp6bPtuMcefARqrw2jG5z9pPex0xZQCWu4XSa6mhTppgkPgUKmHzxt95qni9a1Nr2CZ+S2yHoACBEKZUMFASO575JQhhaQ9OA2oyfE0xSgZ3YmoyhYOUokkqvJFrF0KR4Ez5t9D6RX24lacZMthRxsLhmMZJKtSH+k9FUaWJumuWKR8kCKpG5lD26SsHIkebvcePM/G7Jkla3TvioHAdgrXWUUup94AgQD/ygtf4h7XFKqf5Af4AK6WzvECItrc0020svwebNpShdfzX/tG2Ni2QuKQgrVIXZFQbTev461GM9wWYjqEsXGg0cSKN0ErHIAiqRrpS8zFOmwIYNpkxpgQKmIlFYGNh8J1Ov8Ew5/g1TSpUAOgOVgHJAIaVUr7THaa1naK0jtNYRoe68uUJkZN06aNnSLC49GaN5evJSbP/uBsoUSrCheGrNWdp0exm1wZ3q6tAhWLIEIiPT3XfZpW4YY7vWIqx4CAoz9yspIv3Y2bMmYUa1atC2rQm+jz9uSmSByfstwVfkg9wMQbcC/tZanwJQSi0FGgPz86Jhwr/s3Gli6ddfQ2gZzRPvr2RDoVeZfHIrFUJuJkjbcLpcBLk0LRLKwacTryufrqwWFSQmmt+XPXtg6FBo2hTefNP8Hnlovd38IClUrZObAHwEaKiUKogZgr4HkCXO4rocOGCm3D77dR3B1X+mw6ginLzpM6ZHr6dSYhnm/lGdHkv2sqliEKs71iKyw9M0erOv1c0W3iI+3iyqmjzZ7PmeOtUURfjjD5Pr289lts9egvCNl5s54A1KqSXA74AD2ArMyKuGCe+Rk0/QUVEwejTMng22W9Zh79eCRJXINy4IjS7I9F+K0Xd1DIEVCsLb79KoXz8alSqVT2ckvN6BAzBtmqkLfuaMCbYpSVeUkuDrlt4++7Q5zsWNk6tV0Frr14DX8qgtwgtd7yfo06fh7bdh0iSTSKjLU5v5vWJvDsYmAmBzwaDVl+gf0gaWDzRzdDmokyr8kNNp5m6VMnO8s2aZvbtPPy1V0jIgOc6tJSsNRK5k9gk6tbg4U6q5UiWzu+PeXjtoMaUjS0r+H6dOHyDQCXYXBKsAWo1daMpMduggwVdk7dQp86muShWzig/glVfMqubFizNcnCcy3oonW/Tyh6SiFLmS1SfohAQzEjhmjLlPtur+J0GNX+DrMyso+jeMWgOD425jd78OrL69IJHVWtOofKP8PAXhjbQ2q5cnT4ZFi8wK5hYtrqxeDpPh0+yQLXrWkgAsciWjKkFlixRk9mx44w04ehRqPbiY0DtG8KPzAAVPwEsbFc+X7kTJ0UNYVrgy7/3wF8d/iOebjfEMbRMl808ifVqb3mxSkhkhSUoyW4ieegpuv93q1nkdyXFurVzlgr5ekgva96SdA9YaHPvDYEtNjh8OpGmTnTgaPMj6In8CEOCCSWc788TwyRAWds3rwXwCl3264ir79pkVzL/9BuvXm57u+vWm6H2RIla3TogMZZYLWuaARa6kJLkoVyyE+AOhnJ7fjONL61Cn8C/06X8HG1vcycbCJviiwGGz8WqJEiyLMQ9ldw5Z+CGnE776Ctq0MbmYJ06EypVNdSKAhg0l+AqvJkPQIlPZ2WJU+mIYAd+GcebXZHqHzyXkwdeZXS2KJDu0OBbO6eA2bCszD60dKAKwO2pe3uYgqzBFhlauhM6dzXzuqFHw2GNQtqzVrRIiz0gAFhnKaovRtm0me9XvK6PpUHMYtn6L+PzmJOIDoUdgPV7rMZ3W00+igZuSbiPBtpMCrloEu2pcDrAZzSHLKkw/k3pRVY0aJhF427am8H379qYEoBA+RgKwyFBGw8Oj5h9hwdvlOLZoDU8W/A9hHb5k5l0aFNixMa/zXHrWMWnByxX/iahz8QS7ahDsupL8ICXAyipMP3fpEixYYALv77+bIeWqVc1zAQFmH68QPkoCsMhQ2mFgR2wBkn8N465d/6N/UH9+bbSL5+5WnCqYaiGfUhyJO3r526wCrKzC9HP9+8Onn5rFVFOmQK9eMq8r/IYEYJGhlOFh56UgSv1s55HdX9HLNocl/xdL55YBRIdAq1siebDWQwz+bjBJziSC7EFEVoy8/DOyE2ClUIKfcDrh229NoJ0wwVQjGjrUBOG775ZkGcLvSAAWGXqq4a18M/BbImJnk1BxAzEtFLXqBRNTGJqWb8hnLUdfDrZ3lLmD1YdWE1kx8ppEGhJg/dzp0ybp99SppnRk2bJw8KAJwLVrW906ISwjAVhcIz7qDBsGzKHxyincEnaQlr0h2Q4oTVjhcL7rPInWVVqjUvVYGpVvJBmsxLXi482c7rlzJh/zu++aeV1ZVCWEBGBxRfLGrewfMpmKaz6lOQmMj6jBWx2KkkwsADZl46n6fWlTtY3FLRUeKyHBlP9buxamT4eQEDPcXK8e3HGH1a0TwqNIAPZ3SUm4Fn/BP6MmU+avNZQnhDH/F8mSLof5M3kPFYpWIO5iAk6XkyB7EC0qtrC6xcITHTpkkn7PmmWGnG+7Dc6ehRIl4JFHrG6dEB5JArC/iopCT59B4sTpbC18ki8qlmR/hfv5695j7In/jkqFKjE3ci49avVgU9SmDOd3hWDlSpOX2WYziTOeftoURpBFVUJkSgKwP9Eafv0VJk1Cf7EU7XIxKbwRL/Y5gyvgDPAloSqU6R2m07dOXwLtZp5O5nfFVc6ehY8/hnLloFs3aNYMRo40marCw61unRBeQ3JB+4MLF8x8XO3a0Lw5cV/+l/ddz1HnjqW82e8kroBk94GKe8o/Qv+7+l8OvkJctn272TIUHg5DhpiazQCFC8Prr0vwFeI6SQD2ZX/9xYEejxEXejMMGMCOfZpHmUXVSt8y98197HzgfuJUNGg7aBtKB7Jut6lQJMRVnnkG6tSB+fOhRw/YuhXmzLG6VUJ4NRmC9jVOp5mTmzwZvv+e8rYAlhVpz4SEF1hbvBhB948g6abHSLQXo7zuCxfakmw7fDlPM65bLxdKEH4sKgpmzICBAyE01FQkqlgR+vY1C6uEELkmAdhXpEl24Ly5HOPKP88HUc9xMnwNtr4DoNgfJBNMuL0nOwZPpN4ba9FwTZ5mqUTkp7SGX36BSZNMEQSXyxS579bNFERo397qFgrhUyQAe7stW0xv9/PPISEBR5PmLK73Hk9+15nzgcexP9YXyq7CBYCd0knDCUiIoERICalEJK6Ij4cGDWDnTtPDfe45ePJJU39XCHFDyBywN0pMNAnsGzWCiAhYuJDkXn2YNXgnobtX0+OHptz02AuoZ6vhLPujeY0C0CTbDl5ViSgk0H7Vj5ZKRH5k716YOdN8HRICrVqZUZRjx+C99yT4CnGDSQ/Ymxw9alYzz5wJMTFw6604xk3gY92bV98vxonzp6n88IsklJ/IAVcS95R/kD0Hq3Dc/i5aO1AEUEzVkUpE/szphG++MaMmq1aZwPvAA6bX+8EHVrdOCL8iAdhCy7ZGZR38tIbVq80Nc9kyMy/XsSPOJwfywoa6TJ61i+SbxhHQ8iDB1Zfzt75Iz5o9ea35a1QtWZVlW6MY+W0Zjl7aTPmCEYxq21UqEfmrNWugZ084fBjCwuDNN83eXVlUJYQlJABbZNnWqKvq5Eadi2fE0p2Au2caF8e2sZMoNns6lWIOcz6kCCcffoJqI4eyfHtFnhmYzFHXL9DrPrA5cCgIct7JhHvGM6jZlXSRJsAOsuQchQfYvNl8aKtf3wwpV6tmerqdOpmC90IIy8g70CLvfb/3qiL1APHJThbOW0WXOb+T/NEc6ly8wI6bqzK07WC+qtGM+JPhFOhUjn1/xhMQOQEavQF2h3mxthHkrMOCtZpBzSw4IeE5EhNh0SIzarJhA9x3n6nDW7asGXYWQngECcAWSb3Vx+Zycs+BTTyy5RvuPrwNgoL48fZmTKvVlm1lbyUxugTnvqhOwrEi2BtPpdjIdzjviibIeStJ+m/AiSKAAq5asoXI302aBKNGwalTUL06fPihFEMQwkNJALZIueIhXDp+gu47fqDn1m8Jj43heJHSTG/djyfmjeXJDzaReKowp3+NIylgNdz2FbaH5uMscJw7w+/mTPRQLsTfSqJtz+UkGsGuGrKFyN9oDT//DA0bQsGC5vvGjU1BhFatpCCCEB5MArAVNm/m87XTuGnlMoKdyaytcCejWz7Gmtsb8+YDdTh4oQwXf6jHqX/2Q+9/gT0JFNhc5bkt8B3+12coy7cdN3PGyVeSaMgWIj8SFwfz5pke75498NFHJkvVoEHmjxDC40kAzi8JCbB4sblhbtxIhUKFONi1ByPDmrEm+CbKFQ9hSL0arJpVln/PdEGNNaheA9ABSeb1WlFct+Sttj1RSskWIn+VmAhDh8LcuRAbC3fdZSoTdetmdcuEENdJAvCNduTIlULlaeblKhcrxnzgzBl49114uosm6ZYVlBz2Kv8EbqV0SBin4wPQ2oVNBfJ8c9lC5JecTti9G+68E4KCTPazjh1NT7d+fRlmFsJLSQC+EbSGn34yq1CXLzePdexoEtvfc8/lG+aFC/DC+HV8/L+fSYwtTOnBn/NPgfUULVGZD5p/Qo9aPdgYtZHVh1YTWTFSavL6m5T83lOmmA9vx46ZPbu//AJ2e9avF0J4NAnAeSkuDj75xATePXugVCkzXPjkk3DLLZcPS0w0Ca1en7WOs51bQJNEM8dbsAwzWs6gT50+l+vxNirfSAKvvzl40CTJcOf3JjISxo2DIkXM8xJ8hfAJuQrASqniwCzgDkAD/bTW6/KiYV5lzx4TdD/5xAThiAgzR/fgg1CgwOXDHA6zbub11+GIYxMhvXpDQCIANmwMrD+Qx+963KKTEJZKSoJz56BMGRN0Fy2CPn3MauY77rC6dUKIGyC3PeAJwHda6weUUkFAwTxok3dwOODrr03g/fFHMzfXrZsZZq5f/6pDtYYvvoBXX4U/z+6g+P0j4eblBAYVxeEIxKVdBNmDaFW5lUUnIyxz/LgZDpk+3fR0FywwJQBPnoRChaxunRDiBspxAFZKFQWaAX0AtNZJQFLeNMuDnTplFlRNnWqKI5QvD2PGmJy6oaFXHao1/PADvPwybDn8J0U7vQ4VFqKDizG68WgGNxjMrphdMsfrj9avh/HjzSczpxPatYNHH73yvARfIXxebnrAlYFTwBylVG1gCzBYa30xT1rmaTZuNFuIFi6EpCRi6jflg+aPsaRsHW5ShRl6LIkuqeLv2rXw0kvwv5glBLYaAx234QoqxCsNXmFIoyGUCDEJ8GWO149cugTBwWYOd/ly+P57GDzYrBGoUsXq1gkh8pnSWufshUpFAOuBJlrrDUqpCUCs1vrVNMf1B/oDVKhQ4a7Dhw/nssn5KGUubtIk2LQJCheGPn34b+S/GLQt4apcziGBdsZ2rUUlWxgvvwwrfj1KUJdBJFU2q6ADbAEs776cdtXaWXU2wioHD5oRk9mzzSKA9u3NfG9goPR0hfBxSqktWuuI9J6z5eLnHgOOaa03uL9fAtRLe5DWeobWOkJrHRGaZojWYx0+DCNGmOHl3r3NwqpJkyAqCiZO5LV9rmsKKcSeDObxvnbqND3BqoDB2IdUxVHlaxRmy5HWmu0ntltxNsIKLpeZf+jYEapWhf/8x6SGDHPv2y5eXIKvEH4ux0PQWusTSqmjSqnqWuu9wD3AH3nXtHymtVlMNWmSWVwF0LmzWYXasuVVyQ5SFzxwxBbg/NqqXNgXAne/S0CXKThtSfSr24+2VdvSc2lPkpxJBNmDiKwYmc8nJfKd02mGmLWGxx83oygvvwwDBlwJvkIIQe5XQQ8CPnWvgD4I9M19k/JZbKzZMjR5MuzdC6VLw/Dh8MQTUKFCui8pVzyEI8cdnPkzlkvO9VBxPnRcDPZLPFS7FyObj6RqyaoA/PjIj7LIyh/s2WM+vH3/vclaFRxsSgBWqWK+FkKINHIVgLXW24B0x7Y93u7dJujOm2dSUjVoYPbx/vvfV+3dTSsuDiocimDtT+uhew+wJYOCgq7avN3yPwxq1uKq42WRlQ9zOmHFCpg4Ef77X7MVrXt386EuNNRsJxJCiAz4VyYsh8OsPp082ZRwCw42N8yBA03yjFSWbY26qtDBM82rE7UujDHvxnO68kxs3Ubisie7j7bRtWbba4Kv8HFr15ppivBweOstM+TsLeschBCW848AHBMDM2eaogjHjpm0kO+8A/36mSHnNJZtjWLE0p3EJzvRTsWfq0vT853COKtNJujRtyAomoiw+mw/sR2Hy0GQPYinGnWy4MREvtq+3fR2S5eGt9+Gpk1ND7h1awjwj7eSECLv+O5dQ2vYsMHMyy1ebFL9tW5ter/t22eaT/e97/dyKcnJ+SOniD1zEO1wwKPzoMgxGlS4mzdbLqDZLc1Yd3RdpvO7aXvRUi7QCyUnw5dfmsD722+m6P2TT5rnlDIJNIQQIgd8LwDHx5t0fpMnm7JtRYuaFahPPWVKAWZBa9i/pQin/0rG2ekJsCeBggBneUoljuZ/fV5GuVdEZza/m7oXDRB1Lp4RS3cCSBD2JkOHwoQJULmyKYjQt6+pSCSEELmUm33AnuXvv2HYMDMf16+f2f4xdarZuzthQraC76+/QtO7XcT8cRhnm14QYIIvWlHI1YIqRRtfDr5Zee/7vdfsFY5PdvLe93tzcnYiv2zcCA8/DJs3m+8HDDDb0v76C4YMkeArhMgz3t0Ddrlg1SozzLxiBdhscP/9Zu9u8+bZLlS+dSuMeEnz/cEVBLR+FUpvI8B1Ew4dALhQBFBc1WFom6yDeIrUe4Wz87iwUGKiyXg2caLJeFakCLRpYxbm3Xab+SOEEHnMewPwggWmvND+/aaE2yuvQP/+pgec3R+xZh1vffozu7YUwl7vc2i4gQrFq/BGi3mEOJrxxnfLOXppM+ULRjCqbdfrGjouVzy8t28qAAAQxklEQVSEqHSCbbniIdn+GSIfuFxQu7bZA169ugnCjzxipi6EEOIG8t4AHBdnAu8bb8C//nVdyQ6OHIGn317HN6VaQJlEaAclC5ZhzD0z6V27N4H2QAD+VW9Qjps3tE31q+aAweSLvp5etLgBtIY1a0wVog8+MKMmL75oPri1apXtURMhhMitHBdjyImIiAi9OWVuLbe0vu6bZUwMjB0Lk77ciKNzTyi5HwAbNl6PfJ1Xm7+axU+4PrIK2oPEx8Pnn5se7rZtJhfzpk0mT7MQQtwgmRVj8N4e8HUE3/PnzQLW9+dvJ77hSOj7FUUCi5LgDMSlXQTZg2hVuVWeN7FL3TAJuJ5gxw6Tz/v0abjjDpg+HXr2lGIIQghLeWUAzm7P8tIlsxvprel7OF/vNei9mCKBxXix6Zs80+AZdsXskjzNvkhrWL0azp6Frl2hRg3o1MnM7V7H4jwhhLiRvG4IOu3+WrhSizclCCcnm9KrL81bzNlaY+Dm7RQMKMSQxs8ypNEQSoTIVhKfdPEizJ9vVsXv2mUWV23dKgFXCGGZG1UP2BKZ7a91OuHTT6FqvaM8uboLZ+99EMpuI8BuZ3G3hYxuOVqCr6+aM8cspBowwBS6/+gjWLdOgq8QwmN53RB0evtotYb9m4pQs2E0e0PHou6fjs3uRKPQaLTWbD+xnXbVJG2gz0ip33zbbSbwhoebVKODBkGTJhJ4hRAez+t6wGn30SYcLkX04urExC3ir/uqYGswhUcjerPkwcUUCCiAXdkJsgcRWTHSmgaLvHXhAkyZAjVrwr33mgIbYL5euNAUSJDgK4TwAl7XA07ZXxtz8hDnT+3HqU/DQ0sg8CI9avXi9RYjqVrSbC358ZEfZZGVL3nxRRNwY2Phrrtg7lx48EGrWyWEEDnidQG4S90w/jyzhRG/PAPlkkFBzRJNWPTQDG4PvboAembFEoQXcLlMbuaGDc33MTGmktWgQeYx6ekKIbyY1wVgAB20G5vNiQuwKzs967a/JvgKLxYXZ3q3kyaZFJHbt8Odd5qFVRJ0hRA+wuvmgAEiK0YSHBAs87u+5p9/4NlnISzM9HKLFTPbilIqWUnwFUL4EK/sATcq30jmd32FywUnTkC5cmb70Lx5JmnGoEHQoIHVrRNCiBvGKwMwyPyu14uNNcPMEydCwYImYUaxYnD0qPleCCF8nFcOQQsvduAADB5s9u0+8wyUKgXDhpl9vSDBVwjhN7y2Byy8iMsFDgcEBcFvv8HUqdCtmxlmrl/f6tYJIYQl/DYAS6nAfJAyzDxpEvTvD88/D927Q5s2cPPNVrdOCCEs5ZcBOG1Bh6hz8YxYuhNAgnBe2LfPBN05c8yWogYNrqxkDg6W4CuEEPjpHHBmBR1EDqWuqvXUU2aYuXNn2LAB1q+HDh2sa5sQQnggv+wBp1fQIbPHRSZSkmZMmwbffWcWV334IZQoIT1dIYTIhM8G4MzmeMsVDyEqnWCbttCDyMT+/WaY+aOPTBCuX98k0ggPhxo1rG6dEEJ4PJ8cgk6Z4406F4/myhzvsq1RgCnoEBJov+o1IYF2hrapbkFrvdDp03D77aYqUadOZoh5wwaoU8fqlgkhhNfwyR5wZnO8XeqGXe4JyyrobLpwAT75BHbuNHO7pUqZjFXNmkHZsla3TgghvJJPBuDszPGmDsQiAwcOwOTJMHu22VJUvz7Ex0NIiNnHK4QQIsd8cgg6o7lcmeO9DkuWQLVqJlVk+/awdq0Zag6R/0MhhMgLPhmAZY43By5ehOnTYcUK833LlvDKK3D4MHz2GTRqJNWIhBAiD/lkAO5SN4yxXWsRVjwEBYQVD2Fs11oy5JyeQ4dMLubwcBgwwPR8AUqWhFGjTJUiIYQQeS7Xc8BKKTuwGYjSWntMtgWZ482GYcNg3DjTs+3a1RRJaNzY6lYJIYRfyIse8GBgTx78HHGjxcdfWVAFULcuvPii6QUvWgRNmsgwsxBC5JNcBWClVDjQHpiVN80RN8TRozBihBlmfuwx+PJL8/hDD8GYMeZxIYQQ+Sq3Q9DjgWFAkTxoi8hriYnw8MOwdKnJ1dyli6nB26yZ1S0TQgi/l+MesFKqAxCjtd6SxXH9lVKblVKbT506ldN/TmRXYqKpuQum8lBSEgwZYvb0fvEFNG8uw8xCCOEBlE5dxeZ6XqjUWOBhwAEUAIoCS7XWvTJ6TUREhN68eXOO/j2RhehoUxBh2jQ4d84MO5cpY3WrhBDCrymltmitI9J7Lsc9YK31CK11uNa6ItAd+Cmz4CtukIMHoVcvuOUWGD3a1N5dsQJCQ61umRBCiEz4ZCpKn5ecbAoipJT7W7HC1OAdOBCqVrW2bUIIIbIlTwKw1no1sDovfpbIxKlTMGOGqUJUrx58/TVUrgwnTpj5XiGEEF5DesDeYOdO+M9/TErIxERo3dr0eFNI8BVCCK8jAdhTOd3lFO12WLYMFi6Efv1g0CApeC+EED7AJ3NBe7WzZ+H996FKFbN/F8ze3WPHzNCzBF8hhPAJ0gP2FHv2mNJ/c+fCpUtmv27KNqJixaxtmxBCiDwnAdgTaG2KIfz9N/ToYXq8depY3SohhBA3kARgK8TFmZ7u/Pnw449QqBDMmwcVKkjyDCGE8BMyB5yfDh40aSHDw81iKq1NBiuAiAgJvkII4UekB5xf9u2D6tXNquYHHjC1dxs2tLpVQgghLCIB+EaJj4fPP4eTJ00pwGrVzCKrLl0gLMzq1gkhhLCYDEHntePH4ZVXzHzuo4+aPbwul3nu6acl+AohhAAkAOetjz82RRHGjIEmTeCnn2D9erDJf7MQQoiryRB0biQnw5IlZm63Xj1o3Ngsrho40ORoFkIIITIgXbOc+Ocf08utWNHs25092zx+663wwQcSfIUQQmRJesDXa/hwmDABEhKgVSuYPh3atbO6VUIIIbyM9ICz4nLBd99dKY5QtCg88gjs2gWrVkGHDjLHK4QQ4rpJDzgjcXEwZ47ZOrR/P3z1FXTsCC+9ZHXLhBBC+ADpuqV14QI895zJVjV4MISGwoIFcN99VrdMCCGED5EeMJiUkEePmr27ISHw7bdmaHnwYKhf3+rWCSGE8EH+HYATEuCzz8yiquhoOHIEChSAHTsgKMjq1gkhhPBh/jkEffIkjBx5JVuV1jB27JXFVBJ8hRBC3GD+1QNOTobAQPjrL3jzTbOoavBgaNEClLK6dUIIIfyI7wdgh8PkYx4/HmrXhsmToWlTUxqwYkWrWyeEEMJP+e4Q9Nmz8N57UKUK/PvfZo73zjvNc0pJ8BVCCGEp3+0Bv/QSTJsGkZHw4YdmVbPdbnWrhBBCCMBXesBam6xU7dub6kMAw4bB1q3w88/QubMEXyGEEB7Fu3vA8fEwf77ZRrR7N5QpA1FR5rlKlaxtmxBCCJEJ7w3ALpdZVLVvH9StC3PnQrduEBxsdcuEEEKILHlvALbZ4LXXoHx5uPtu2UYkhBDCq3hvAAbo2dPqFgghhBA54huLsIQQQggvIwFYCCGEsIAEYCGEEMICEoCFEEIIC0gAFkIIISyQ4wCslCqvlPpZKbVHKbVbKTU4LxsmhBBC+LLcbENyAM9rrX9XShUBtiilVmmt/8ijtgkhhBA+K8c9YK11tNb6d/fXccAeICyvGiaEEEL4sjyZA1ZKVQTqAhvSea6/UmqzUmrzqVOn8uKfE0IIIbxergOwUqow8AXwrNY6Nu3zWusZWusIrXVEaGhobv85IYQQwifkKgArpQIxwfdTrfXSvGmSEEII4ftyswpaAbOBPVrrD/KuSUIIIYTvy00PuAnwMNBSKbXN/addHrVLCCGE8GlKa51//5hSp4DDefgjSwP/5OHPs5Kci+fxlfMAORdP5Svn4ivnAXl/LrdordNdAJWvATivKaU2a60jrG5HXpBz8Ty+ch4g5+KpfOVcfOU8IH/PRVJRCiGEEBaQACyEEEJYwNsD8AyrG5CH5Fw8j6+cB8i5eCpfORdfOQ/Ix3Px6jlgIYQQwlt5ew9YCCGE8EpeEYCVUvcppfYqpfYrpYan83ywUmqh+/kN7tzUHic7JRyVUpFKqfOp9laPtKKt2aGUOqSU2ulu5+Z0nldKqQ/d12WHUqqeFe3MjFKqeqr/621KqVil1LNpjvHYa6KU+kgpFaOU2pXqsZJKqVVKqX3uv0tk8Nre7mP2KaV651+r05fBubynlPrT/fvzpVKqeAavzfR3Mb9lcC6vK6WissqbkNX9Lj9lcB4LU53DIaXUtgxe62nXJN37r6XvF621R/8B7MABoDIQBGwHbk9zzFPANPfX3YGFVrc7g3MpC9Rzf10E+Cudc4kEvrG6rdk8n0NA6Uyebwd8CyigIbDB6jZncT524ARm355XXBOgGVAP2JXqsXeB4e6vhwPvpPO6ksBB998l3F+X8MBzaQ0EuL9+J71zcT+X6e+ih5zL68ALWbwuy/ud1eeR5vlxwEgvuSbp3n+tfL94Qw+4PrBfa31Qa50ELAA6pzmmMzDX/fUS4B53qkyPov2vhGNn4BNtrAeKK6XKWt2oTNwDHNBa52WymBtKa/0LcCbNw6nfD3OBLum8tA2wSmt9Rmt9FlgF3HfDGpoN6Z2L1voHrbXD/e16IDzfG5YDGVyX7MjO/S7fZHYe7nvsg8Dn+dqoHMrk/mvZ+8UbAnAYcDTV98e4NmhdPsb9Zj0PlMqX1uWQyqSEI9BIKbVdKfWtUqpmvjbs+mjgB6XUFqVU/3Sez8618yTdyfhm4i3XBOAmrXU0mJsOUCadY7zt2gD0w4yopCer30VPMdA9nP5RBkOd3nRd7gZOaq33ZfC8x16TNPdfy94v3hCA0+vJpl26nZ1jPIbKvITj75gh0NrARGBZfrfvOjTRWtcD2gJPK6WapXnea66LUioI6AQsTudpb7om2eU11wZAKfUy4AA+zeCQrH4XPcFUoApQB4jGDN+m5U3X5SEy7/165DXJ4v6b4cvSeSzX18UbAvAxoHyq78OB4xkdo5QKAIqRs+GfG05lUcJRax2rtb7g/nolEKiUKp3PzcwWrfVx998xwJeY4bPUsnPtPEVb4Het9cm0T3jTNXE7mTLU7/47Jp1jvObauBe8dAB6aveEXFrZ+F20nNb6pNbaqbV2ATNJv41ecV3c99muwMKMjvHEa5LB/dey94s3BOBNQDWlVCV3L6U78FWaY74CUlalPQD8lNEb1UruOZNMSzgqpW5Omb9WStXHXKPT+dfK7FFKFVJKFUn5GrNYZleaw74CHlFGQ+B8ylCPB8rw07y3XJNUUr8fegPL0znme6C1UqqEeyi0tfsxj6KUug94Eeiktb6UwTHZ+V20XJr1D/eTfhuzc7/zBK2AP7XWx9J70hOvSSb3X+veL1avTMvOH8xq2r8wqwNfdj82CvOmBCiAGTrcD2wEKlvd5gzOoylm2GIHsM39px0wABjgPmYgsBuz+nE90NjqdmdwLpXdbdzubm/KdUl9LgqY7L5uO4EIq9udwbkUxATUYqke84prgvnQEA0kYz6lP4pZ//AjsM/9d0n3sRHArFSv7ed+z+wH+nrouezHzL2lvF9SdjuUA1Zm9rvogecyz/0+2IG56ZdNey7u76+533nSebgf/zjl/ZHqWE+/Jhndfy17v0gmLCGEEMIC3jAELYQQQvgcCcBCCCGEBSQACyGEEBaQACyEEEJYQAKwEEIIYQEJwEIIIYQFJAALIYQQFpAALIQQQljg/wFAXt3Jff+4bQAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "prstd, iv_l, iv_u = wls_prediction_std(res2)\n", "\n", "fig, ax = plt.subplots(figsize=(8,6))\n", "ax.plot(x1, y2, 'o', label=\"data\")\n", "ax.plot(x1, y_true2, 'b-', label=\"True\")\n", "ax.plot(x1, res2.fittedvalues, 'r-', label=\"OLS\")\n", "ax.plot(x1, iv_u, 'r--')\n", "ax.plot(x1, iv_l, 'r--')\n", "ax.plot(x1, resrlm2.fittedvalues, 'g.-', label=\"RLM\")\n", "legend = ax.legend(loc=\"best\")" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.5" } }, "nbformat": 4, "nbformat_minor": 1 }