{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# IntroStat Week 8\n", "\n", "Welcome to the 8th lecture in IntroStat\n", "\n", "During the lectures we will present both slides and notebooks. \n", "\n", "This is the notebook used in the lecture in week 8.\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pandas as pd\n", "import scipy.stats as stats\n", "import statsmodels.api as sm\n", "import statsmodels.formula.api as smf\n", "import statsmodels.stats.power as smp\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Height and weight" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Linear regression with height and weight data" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# data\n", "x = np.array([168, 161, 167, 179, 184, 166, 198, 187, 191, 179]) # height data\n", "y = np.array([65.5, 58.3, 68.1, 85.7, 80.5, 63.4, 102.6, 91.4, 86.7, 78.9]) # weight data" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# make scatter plot:\n", "plt.scatter(x,y)\n", "plt.ylabel(\"weight\")\n", "plt.xlabel(\"height\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Linear relationship?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now lets put data into a **pandas dataframe**:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " x y\n", "0 168 65.5\n", "1 161 58.3\n", "2 167 68.1\n", "3 179 85.7\n", "4 184 80.5\n", "5 166 63.4\n", "6 198 102.6\n", "7 187 91.4\n", "8 191 86.7\n", "9 179 78.9\n" ] } ], "source": [ "student = pd.DataFrame({'x': x, 'y': y}) # \"import pandas as pd\"\n", "print(student)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we do a **linear regression model**:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# for now we just run the code, we will understand it later\n", "\n", "# fit the model\n", "fitStudents = smf.ols(formula = 'y ~ x', data=student).fit() # OBS: use the statsmodels.formula.api library (smf)\n", "\n", "# Get prediction and confidence intervals\n", "x_pred = pd.DataFrame({'x': np.arange(160,200, 1)})\n", "pred = fitStudents.get_prediction(x_pred).summary_frame(alpha=0.05)\n", "\n", "plt.scatter(x,y)\n", "plt.plot(x_pred, pred[\"mean\"], color=\"red\")\n", "plt.ylabel(\"weight\")\n", "plt.xlabel(\"height\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The red line is the **regression line**.\n", "\n", "The regression line is a straight line.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "It is defined by a **slope** and an **intercept** with the y-axis." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: y R-squared: 0.932\n", "Model: OLS Adj. R-squared: 0.924\n", "No. Observations: 10 F-statistic: 110.3\n", "Covariance Type: nonrobust Prob (F-statistic): 5.87e-06\n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept -119.9581 18.897 -6.348 0.000 -163.535 -76.381\n", "x 1.1127 0.106 10.504 0.000 0.868 1.357\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 2.75e+03. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "c:\\Users\\pydni\\AppData\\Local\\anaconda3\\envs\\pernille\\Lib\\site-packages\\scipy\\stats\\_stats_py.py:1806: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=10\n", " warnings.warn(\"kurtosistest only valid for n>=20 ... continuing \"\n" ] } ], "source": [ "# later today we will be able to estimate values for the parameters: intercept and slope\n", "print(fitStudents.summary(slim=True))\n" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "# we will also be able to estimate standard error and conficence intervals for the parameters (also in table above)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# later today we will be able to make a prediction interval for \"future\" obervations (with other x-values)\n", "plt.scatter(x,y)\n", "plt.plot(x_pred, pred[\"mean\"], color=\"red\")\n", "plt.plot(x_pred, pred[\"obs_ci_lower\"], color=\"lightgrey\")\n", "plt.plot(x_pred, pred[\"obs_ci_upper\"], color=\"lightgrey\")\n", "plt.ylabel(\"weight\")\n", "plt.xlabel(\"height\")\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# and later today we will also be able to make a prediction interval for the mean at every value on the x-axis\n", "plt.scatter(x,y)\n", "plt.plot(x_pred, pred[\"mean\"], color=\"red\")\n", "plt.plot(x_pred, pred[\"mean_ci_lower\"], color=\"grey\")\n", "plt.plot(x_pred, pred[\"mean_ci_upper\"], color=\"grey\")\n", "plt.plot(x_pred, pred[\"obs_ci_lower\"], color=\"lightgrey\")\n", "plt.plot(x_pred, pred[\"obs_ci_upper\"], color=\"lightgrey\")\n", "plt.ylabel(\"weight\")\n", "plt.xlabel(\"height\")\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Estimating parameters $\\beta_0$ and $\\beta_1$" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# First we compute some simulated data, so we know the \"real\" beta_0 and beta_1 (and sigma)\n", "np.random.seed(23498)\n", "\n", "beta_0 = 50\n", "beta_1 = 200\n", "sigma = 90\n", "\n", "# choose som random x-values:\n", "x = stats.uniform.rvs(size = 20, loc=-2, scale = 6)\n", "# simulate y-values from statistical model:\n", "y = beta_0 + beta_1*x + stats.norm.rvs(size = 20, loc=0, scale = sigma)\n", "\n", "plt.scatter(x,y)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is now our \"Toy Data\" :-)\n", "\n", "Lets see if we can estimate the parameters " ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "13.795479789979595 225.76353862601528\n", "50 200\n" ] } ], "source": [ "# calculate estimates beta_0_hat and beta_1_hat:\n", "Sxx = np.sum((x - x.mean())**2)\n", "\n", "beta_1_hat = np.sum((x - x.mean())*(y - y.mean())) / Sxx\n", "beta_0_hat = y.mean() - beta_1_hat*x.mean()\n", "\n", "print(beta_0_hat, beta_1_hat)\n", "print(beta_0, beta_1)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot estimated model with data:\n", "plt.scatter(x,y)\n", "plt.plot([-2,4], [beta_0_hat + beta_1_hat*(-2), beta_0_hat + beta_1_hat*(4)], color=\"red\")\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Great! " ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# also plot the \"true\" underlying model (this is *only* possible because we have simulated data - IRL one cannot plot the \"true\" model):\n", "plt.scatter(x,y)\n", "plt.plot([-2,4], [beta_0_hat + beta_1_hat*(-2), beta_0_hat + beta_1_hat*(4)], color=\"red\")\n", "plt.plot([-2,4], [beta_0 + beta_1*(-2), beta_0 + beta_1*(4)], color=\"red\", linestyle='--')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Variation of $\\beta_0$ and $\\beta_1$" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "73.84511187771452 194.84106802781554\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# repeat with new sample:\n", "y = beta_0 + beta_1*x + stats.norm.rvs(size = 20, loc=0, scale = sigma) # y-data with new values of residuals\n", "\n", "# re-calculate parameters\n", "Sxx = np.sum((x - x.mean())**2)\n", "beta_1_hat = np.sum((x - x.mean())*(y - y.mean())) / Sxx\n", "beta_0_hat = y.mean() - beta_1_hat*x.mean()\n", "print(beta_0_hat, beta_1_hat)\n", "\n", "#plot:\n", "plt.scatter(x,y)\n", "plt.plot([-2,4], [beta_0_hat + beta_1_hat*(-2), beta_0_hat + beta_1_hat*(4)], color=\"red\")\n", "plt.plot([-2,4], [beta_0 + beta_1*(-2), beta_0 + beta_1*(4)], color=\"red\", linestyle='--')\n", "plt.ylim([-400,1000])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Estimate parameters and their standard errors (height and weight data)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " x y\n", "0 168 65.5\n", "1 161 58.3\n", "2 167 68.1\n", "3 179 85.7\n", "4 184 80.5\n", "5 166 63.4\n", "6 198 102.6\n", "7 187 91.4\n", "8 191 86.7\n", "9 179 78.9\n" ] } ], "source": [ "# Recall the height and weigth data:\n", "print(student)" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-119.95810730253355 1.11274217585693\n" ] } ], "source": [ "### 1 ### Estimate parameters beta_0_hat and bata_1_hat *manually*\n", "\n", "Sxx = np.sum((student[\"x\"] - student[\"x\"].mean())**2)\n", "\n", "beta_1_hat = np.sum((student[\"x\"] - student[\"x\"].mean())*(student[\"y\"] - student[\"y\"].mean())) / Sxx\n", "\n", "beta_0_hat = student[\"y\"].mean() - beta_1_hat*student[\"x\"].mean()\n", "\n", "print(beta_0_hat, beta_1_hat)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " x y y_pred residuals\n", "0 168 65.5 66.982578 -1.482578\n", "1 161 58.3 59.193383 -0.893383\n", "2 167 68.1 65.869836 2.230164\n", "3 179 85.7 79.222742 6.477258\n", "4 184 80.5 84.786453 -4.286453\n", "5 166 63.4 64.757094 -1.357094\n", "6 198 102.6 100.364844 2.235156\n", "7 187 91.4 88.124680 3.275320\n", "8 191 86.7 92.575648 -5.875648\n", "9 179 78.9 79.222742 -0.322742\n" ] } ], "source": [ "### 2 ### Estimate standard error for the parameters *manually* \n", "\n", "student[\"y_pred\"] = beta_0_hat + beta_1_hat*student[\"x\"]\n", "student[\"residuals\"] = student[\"y\"] - student[\"y_pred\"]\n", "print(student)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Theorem 5.8 (second part)\n", "Since ${\\sigma}^2$ is unknown, we use the central estimate for ${\\sigma}^2$\n", "\n", "\n", "$\\hat{\\sigma}^2 = \\frac{RSS(\\hat{\\beta}_0, \\hat{\\beta}_1)}{n - 2} = \\frac{\\sum_{i=1}^n e_i^2}{n - 2}$\n", "\n", "where:\n", "- $ \\hat{\\sigma}^2 $ is the estimated variance of the errors,\n", "- $ RSS(\\hat{\\beta}_0, \\hat{\\beta}_1) $ is the residual sum of squares for the estimates $\\hat{\\beta}_0$ and $\\hat{\\beta}_1$,\n", "- $ n $ is the number of observations,\n", "- $ e_i $ represents the residuals (errors) for each observation $ i $.\n", "\n", "$\\hat{\\sigma}_{\\beta_0} = \\hat{\\sigma} \\sqrt{\\frac{1}{n} + \\frac{\\bar{x}^2}{S_{xx}}}$\n", "\n", "$\\hat{\\sigma}_{\\beta_1} = \\hat{\\sigma} \\sqrt{\\frac{1}{S_{xx}}}$" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "18.897051763916973 0.10593909266894098\n" ] } ], "source": [ "RSS = np.sum(student[\"residuals\"]**2)\n", "sigma_hat = np.sqrt(RSS/(10-2))\n", "\n", "se_beta_0_hat = sigma_hat*np.sqrt(1/10 + student[\"x\"].mean()**2 / Sxx)\n", "\n", "se_beta_1_hat = sigma_hat*np.sqrt(1/Sxx)\n", "\n", "print(se_beta_0_hat, se_beta_1_hat)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: y R-squared: 0.932\n", "Model: OLS Adj. R-squared: 0.924\n", "No. Observations: 10 F-statistic: 110.3\n", "Covariance Type: nonrobust Prob (F-statistic): 5.87e-06\n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept -119.9581 18.897 -6.348 0.000 -163.535 -76.381\n", "x 1.1127 0.106 10.504 0.000 0.868 1.357\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 2.75e+03. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "c:\\Users\\skhalid\\Miniconda3\\Lib\\site-packages\\scipy\\stats\\_axis_nan_policy.py:418: UserWarning: `kurtosistest` p-value may be inaccurate with fewer than 20 observations; only n=10 observations were given.\n", " return hypotest_fun_in(*args, **kwds)\n" ] } ], "source": [ "### automatic ### Do it all with inbuilt python function smf.ols\n", "fitStudents = smf.ols(formula = 'y ~ x', data=student).fit() # OBS: use the statsmodels.formula.api library (smf)\n", "print(fitStudents.summary(slim=True))" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Intercept -119.958107\n", "x 1.112742\n", "dtype: float64\n" ] } ], "source": [ "# Get parameters\n", "print(fitStudents.params)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Intercept 18.897052\n", "x 0.105939\n", "dtype: float64\n" ] } ], "source": [ "# Get parameter standard errors\n", "print(fitStudents.bse)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "15.061388599105827\n", "15.06138859910578\n" ] } ], "source": [ "# get estimate of sigma^2:\n", "print(fitStudents.scale)\n", "print(sigma_hat**2) #compare to the one we calculated *manualy*" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0 66.982578\n", "1 59.193383\n", "2 65.869836\n", "3 79.222742\n", "4 84.786453\n", "5 64.757094\n", "6 100.364844\n", "7 88.124680\n", "8 92.575648\n", "9 79.222742\n", "dtype: float64\n" ] } ], "source": [ "# get fitted values:\n", "print(fitStudents.fittedvalues)" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "image/png": 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kg/Lmm2/KMAydeOKJ+vLLLzV9+nT16dNHV155pWw2m6ZMmaLZs2fr+OOPV3Z2tmbOnKmsrCyNHj06FOUAAIKFoWsIk5AEFJfLpRkzZuibb75Renq6xowZo3vuuUft27eXJN16663au3evJk2apKqqKg0fPlzFxcV+d/4AACLERx9JjbvcF10kvf66NfUg5gV9Dko4MAcFAMKofXvpwAHz2u7dkjOEHyyImGTpHBQAQIzYudN7SqdhODn6aO+1JoQThBgBBQDg75xzpB49zGtr10qVldbUg7jDpxkDAA7Zu1fq1Ml/PfquBkCUo4MCAPCaMcM/nCxcSDiBJeigAEC8Y+gaIhAdFACIZy+84B9OZs1i6BosRwcFAOLVwIHS+vXmtR9+kFJSrKkHaIAOCgDEm2++8XZHGoaTCy/0dk0IJ4gQBBQAiCd33y11725eKy+Xli61ph6gCZziAYB44HZLdrt5bc4c6bbbrKkHaAYBBQBi3fPPS7/9rXlt1y4pK8uaeoAW4BQPAMSq/fulLl3M4eTqq73XmhBOEOHooABALFq2TMrLM69t3Cj9/OfW1AO0EgEFAGKJYUjDh0sffnho7X/+R1q+PObmmtR7DK0qrdSe6lplpCZrSHa6EhNia4/xjIACALHi00+lk04yr73zjnTWWdbUE0LFG8tUULRJZa5a35rTnqxZ+Tka2Y9PWo4FXIMCALHgqqvM4aRrV2nfvpgNJ5ML15nCiSSVu2o1uXCdijeWWVQZgomAAgDRbNcu76mbp58+tFZYKO3ZI7Vvb11dIVLvMVRQtEmBPr7w4FpB0SbVe/iAw2hHQAGAaHXPPVK3buY1t1saN86aesJgVWmlX+ekIUNSmatWq0orw1cUQoJrUAAg2gQaunbPPdLtt1tTTxjtqW46nLTlOEQuAgoARJPCQuk3vzGvxdHQtYzU5KAeh8jFKR4AiAb790vHHGMOJxMnxt3QtSHZ6XLak9XUzcQ2ee/mGZKdHs6yEAIEFABhV+8xVLLtO72+YZdKtn3HBY3NeecdqUMH6bvvDq19+qn0979bV5NFEhNsmpWfI0l+IeXg97Pyc5iHEgM4xQMgrJhf0QqG4R2y9sEHh9aGD5dWrIi5oWutMbKfU/PHD/T7/8jB/0cxxWYYRtT908Xtdstut8vlciktLc3qcgC00MH5FY3/0jn4q3b++IH8cjlo40apf3/zWowOXWsrJslGn9b8/qaDAiAsmptfYZN3fsW5OQ5+yUycKD311KHvjzlG2r07JueaHInEBJtye3exugyECNegAAgL5le0wMGhaw3DyfPPS99+SzhB3CGgAAgL5lc04957/YeuuVzS+PHW1ANYjFM8AMKC+RVNqK6WGp+Lnz1b+uMfrakHiBB0UACEBfMrAnjhBf9w8s03hBNABBQAYcL8igb275cyMsynb6680ntb8c9+Zl1dQAQhoAAIm4PzKxx282kchz05fm4xfvdd79C1b789tPbpp+YLYwFwDQqA8BrZz6lzcxzxN7/CMKSERv8mPP106b334nroGtAUAgqAsIu7+RUvvyxddpl57e23pXPOsaYeIAoQUAAglAJ1R/btY64J0AyuQQGAUFizxj+c5OV5T/UQToBm0UEBgGCz2yW327y2c6f/IDYATSKgAECw7N7tf5twhw5SXZ019QBRjFM8ABAM+fn+4eSjjwgnQBvRQQGAI/Hjj9JRR/mvG4E+txlAS9FBAYC2+tOf/MNJYSHhBAgCOigA0FqBhq5JUn194HUArcY7CQBaY+FC/xDyhz80HVoAtAkdFABoqUBD12pqpI4dw18LEOOI+wDQnHXr/MPJ2Wd7uyaEEyAk6KAAwOEcfbRUVWVe27FD6t7dknKAeEFAAYBAysqkrCzzWrt20v791tQDxBlO8QBAY6NG+YeTkhLCCRBGdFAA4CCGrgERgw4KAEjSXXf5h5PnnyecABahgwIgvjF0DYhIvPsAxK9XX/UPIbfeytA1IALQQQEQnwINXauuljp1Cn8tAPzwTwQA8WX9ev9w8otfeLsmhBMgYtBBARA/unaV/u//zGtffy316GFNPQCaREABEPvKyyWn07xms0kejzX1AGgWp3gAxLbRo/3DyYcfEk6ACEcHBUBsqq2VUlL815lrAkQFOigAYs/s2f7h5NlnCSdAFKGDAiB2MHQNiBm8YwHEhtde8w8ht9zC0DUgStFBARD9omDoWr3H0KrSSu2prlVGarKGZKcrMSFA3QAkEVAARLMNG6QBA8xrZ5whLV9uSTlNKd5YpoKiTSpz1frWnPZkzcrP0ch+zsP8JBC/6HsCiE6Zmf7hZPv2iAwnkwvXmcKJJJW7ajW5cJ2KN5ZZVBkQ2QgoAKJLRYX3lM6ePeZ1w5B69rSmpibUewwVFG1SoHuHDq4VFG1SvYe7i4DGCCgAoseYMZLDYV774IOIvX14VWmlX+ekIUNSmatWq0orw1cUECWCHlDq6+s1c+ZMZWdnKyUlRb1799bdd98to8FfIIZh6M4775TT6VRKSory8vK0devWYJcCIFbU1nq7Jq+9Zl43DGnYMGtqaoE91U2Hk7YcB8SToAeU+++/X/Pnz9ef//xnbd68Wffff7/mzp2rxx9/3HfM3LlzNW/ePC1YsEArV65Ux44dNWLECNXW8iYF0Mi99/oPXXv66YjtmjSUkZoc1OOAeBL0u3g+/PBDjRo1ShdeeKEkqVevXnrppZe0atUqSd7uyaOPPqo77rhDo0aNkiQ999xzyszM1OLFizV27NhglwQgGsXA0LUh2ely2pNV7qoNeB2KTZLD7r3lGIBZ0N/lw4YN07Jly/TFF19Ikj7++GO9//77Ov/88yVJpaWlKi8vV15enu9n7Ha7hg4dqpKSkoDPWVdXJ7fbbfoCEMMWL/YPIdOmRd3QtcQEm2bl50jyhpGGDn4/Kz+HeShAAEHvoNx2221yu93q06ePEhMTVV9fr3vuuUfjxo2TJJWXl0uSMjMzTT+XmZnpe6yxOXPmqKCgINilAohEgYauud1Samr4awmCkf2cmj9+oN8cFAdzUIDDCnpAefnll/XCCy/oxRdf1M9//nNt2LBBU6ZMUVZWliZMmNCm55wxY4amTZvm+97tdqt79+7BKhlAJPj4Y+mUU8xrp58uvf++JeUE08h+Tp2b42CSLNAKQQ8o06dP12233ea7lqR///76+uuvNWfOHE2YMEGOn24RrKiokNN56F8OFRUVOqXxX04/SUpKUlJSUrBLBRApnE6pcQe1tFTq1cuSckIhMcGm3N5drC4DiBpBP5n7ww8/KKHROeLExER5PB5JUnZ2thwOh5YtW+Z73O12a+XKlcrNzQ12OQAiUL3HUMm271S8bIP3lE7jcGIYMRVOALRe0ANKfn6+7rnnHr3xxhvavn27Fi1apIcfflgXX3yxJMlms2nKlCmaPXu2lixZok8//VS//e1vlZWVpdGjRwe7HAARpnhjmYbf/44qLxylkXmNRtW/915U3D4MIPSCforn8ccf18yZM3Xddddpz549ysrK0rXXXqs777zTd8ytt96qvXv3atKkSaqqqtLw4cNVXFys5GRmAQCxrHhjmW56dqW+ePBiv8ey/7BU8zv31kgL6gIQeWyGEX3/XHG73bLb7XK5XEpLS7O6HAAtUO8xdNflf1TBy3NM67dcMEWv9M/zzQR5/w9nc/EoEKNa8/s76B0UAPBjGEpMTFDjYQHHTn9dnoRE7yE69Lk0XEwKIHomHgGITu+/7zdcbea5v1OvPyz1hZOG+FwaABIdFAChdOyx3tuFG+gz7RXVtm/6ejM+lwaAREABEApffSX17m1a8lx3nU7vdonqXIE7JHwuDYCGOMUDILguvdQvnGj3biX85S98Lg2AFiOgAAiOqirv0LVXXjm0Nny4d67JT1OjD34ujcNuPo3jsCdr/viBfC4NAB9O8QA4cgUF0p/+ZF77+GPppJP8DuVzaQC0BAEFQNvt3y916GBea99e2rfvsD/G59IAaA6neAC0zUsv+YeTf/2r2XACAC1BBwVA6xiG31wTSVJ9feB1AGgD/jYB0HIffugfQh5/vOnQAgBtRAcFQMscd5y0bZt5be9e6aijrKkHQEzjnzwADu+rr7y3DzcMJ5Mne7smhBMAIUIHBUDTfvUraeFC89ru3b65JgAQKgQUAP6qqqSjjzavDRsmffCBJeUAiD+c4gFgdtdd/uFkwwbCCYCwooMCwCvQ0LXEROnAAWvqARDX6KAAkP7xD/9wsnQp4QSAZeigAPGMoWsAIhR/AwHxqqTEP4Q89hhD1wBEBDooQDw64QRp61bzWk2N1LGjNfUAQCP8MwmIJ6Wl3qFrDcPJtdd6uyaEEwARhA4KEC/GjpX++U/z2q5dUlaWNfUAwGEQUIBY53JJnTub14YOlT76yJJyAKAlOMUDxLLZs/3Dyfr1hBMAEY8OChCLAg1ds9kkj8eaegCgleigALHm5Zf9w0lREeEEQFShgwLEiqbmlxw44B1ZDwBRhA4KEAs++sg/nDz6qDe0EE4ARCE6KEC069NH2rLFvMbQNQBRjg4KEK22b/de+NownEyaxNA1ADGBDgoQjX79a+mll8xr33wj/exn1tQDAEFGQAGiSaCha4MHS6tWWVIOAIQKp3iAaHHvvf7hZN06wgmAmEQHBYh0Bw5I7dv7rxtG+GsBgDChgwJEsoUL/cPJkiWEEwAxjw4KEIkYugYgztFBASLNqlX+4eThhxm6BiCu0EEBIklOjrR5s3mtulrq1MmaegDAInRQgEjw9dfeoWsNw8k113i7JoQTAHGIDgpgtd/8RiosNK8xdA1AnCOgAFZxuyW73bw2aJC0erU19QBABOEUD2CF++7zDydr1xJOAOAndFCAcGLoGgC0CB0UIFxefdU/nCxeTDgBgADooAChxtA1AGg1OihAKK1e7R9OHnqIoWsA0Aw6KECo9O8vbdxoXmPoGgC0CB0UINh27PAOXWsYTiZOZOgaALQCHRQgmH77W+n5581rO3dK3bpZUw8ARCkCChAMgYauDRzonW0CAGg1TvEAR+r++/3DyZo1hBMAOAJ0UIC2YugaAIQMHRSgLV57zT+cLFpEOAGAIKGDArSWzea/xtA1AAgqOihAS61e7R9OHnyQoWsAEAJ0UICWOPlk6ZNPzGtut5Saak09ABDj6KAAh3Nw6FrDcHLlld6uCeEEAEKGDgrQlCuvlJ55xry2Y4fUvbsl5QBAPCGgAI1VV0tpaea1U06R1q+3pBwAiEec4gEaeuAB/3CyZg3hBADCjA4KIDF0DQAiDB0UYNEi/3Dy2muEEwCwEB0UxDeGrgFARKKDgvi0Zo1/OJk7l6FrABAhgh5QevXqJZvN5vd1/fXXS5Jqa2t1/fXXq0uXLurUqZPGjBmjioqKYJcBNG3AAGnwYPOa2y1Nn25NPQAAP0EPKKtXr1ZZWZnv66233pIkXXrppZKkqVOnqqioSAsXLtTy5cu1e/duXXLJJcEuA/C3c6e3a7Jhw6G1CRMYugYAEchmGKG9EnDKlClaunSptm7dKrfbra5du+rFF1/UL3/5S0nS559/rr59+6qkpESnnXZai57T7XbLbrfL5XIprfEtoUAgV10lPf20eY2hawAQVq35/R3Si2T37dunwsJCTZs2TTabTWvXrtX+/fuVl5fnO6ZPnz7q0aPHYQNKXV2d6urqfN+73e5Qlo1YEmjoWv/+/p+rAwCIKCG9SHbx4sWqqqrSFVdcIUkqLy9Xhw4d1LlzZ9NxmZmZKi8vb/J55syZI7vd7vvqzr960RIPPugfTlavJpwAQBQIaQflySef1Pnnn6+srKwjep4ZM2Zo2rRpvu/dbjchBU2rr5faBfhfm7kmABA1QtZB+frrr/X222/r6quv9q05HA7t27dPVVVVpmMrKirkcDiafK6kpCSlpaWZvoCAFi/2Dyevvko4AYAoE7IOytNPP62MjAxdeOGFvrVTTz1V7du317JlyzRmzBhJ0pYtW7Rjxw7l5uaGqhTEi0BD1/bvD9xNAQBEtJB0UDwej55++mlNmDBB7Rr8crDb7Zo4caKmTZumd999V2vXrtWVV16p3NzcFt/BA/hZt84/nNx3n7drQjgBgKgUkr+93377be3YsUNXXXWV32OPPPKIEhISNGbMGNXV1WnEiBH63//931CUgXgwaJC0dq15zeXyvzgWABBVQj4HJRSYgwJ9843/DJPf/EZ67jlr6gEANKs1v7/5LB5En6uv9g8nX39NOAGAGMIJekSPmhr/kfT9+kmffmpNPQCAkKGDglap9xgq2fadXt+wSyXbvlO9J0xnCB9+2D+crFxJOAGAGEUHBS1WvLFMBUWbVOaq9a057cmalZ+jkf2coflDGboGAHGJDgpapHhjmSYXrjOFE0kqd9VqcuE6FW8sC/4fumSJfzh55RXCCQDEATooaFa9x1BB0SYFigWGJJukgqJNOjfHocSEAMPS2oKhawAQ1+igoFmrSiv9OicNGZLKXLVaVVp55H/Y+vX+4WTOHIauAUCc4W98NGtPddPhpC3HNWnwYGnNGvMaQ9cAIC7RQUGzMlKTg3qcn127vF2ThuFk3Dhv14RwAgBxiYCCZg3JTpfTnqymri6xyXs3z5Ds9NY/+aRJUrdu5rXt26XCwtY/FwAgZhBQ0KzEBJtm5edIkl9IOfj9rPyc1l0gW1Pj7Zo88cShtZwcb9ekZ88jqhcAEP0IKGiRkf2cmj9+oBx282kchz1Z88cPbN0clEcfDTx07bPPjrxQAEBM4CJZtNjIfk6dm+PQqtJK7amuVUaq97ROizsnTQ1d83gC31YMAIhbdFDQKokJNuX27qJRp/xMub27tDycFBX5h5OXX/ae0iGcAAAaoYOC0GPoGgCgleigIHT++1//cHLvvQxdAwA0i98SCI1AXZP/+z+pS5fw1wIAiDp0UBBc27b5h5Pevb1dE8IJAKCFCCgInsGDpeOOM6999pn05ZfW1AMAiFqc4sGRc7mkzp39141An38MAEDz6KDgyNx4o384+de/CCcAgCNCBwVtw9A1AEAI0UFB6z3xhH84efDBgEPX6j2GSrZ9p9c37FLJtu9U76GzAgBoHh0UtE6g7khdndShg99y8cYyFRRtUpmr1rfmtCdrVn5O6z67BwAQd+igoGWWL/cPJ+PGebsmTYSTyYXrTOFEkspdtZpcuE7FG8tCWS0AIMrRQUHzAnVNvv1WOuaYgIfXewwVFG1SoJM5hiSbpIKiTTo3x9Hyz/IBAMQVOiho2ldf+YeTXr28XZMmwokkrSqt9OucNGRIKnPValVpZXDqBADEHAIKAjvtNO8E2IY2bpRKS5v90T3VTYeTthwHAIg/nOKBmdst2e3+662Ya5KRmhzU4wAA8YcOCg656Sb/cLJ0aauHrg3JTpfTnqymri6xyXs3z5Ds9DaVCQCIfXRQEPSha4kJNs3Kz9HkwnWySaaLZQ8+26z8HC6QBQA0iQ5KvFuxwj+cPPBAwKFrrTGyn1Pzxw+Uw24+jeOwJ2v++IHMQQEAHBYdlHg2dqz0z3+a15oYutYWI/s5dW6OQ6tKK7WnulYZqd7TOnROAADNIaDEo6+/9t4u3NBVV0lPPhn0Pyoxwabc3l2C/rwAgNjGKZ54c8cd/uGkpiYk4QQAgLaigxIvvv9eSm9018zDD0tTp1pTDwAAh0FAiQd//7t0zTXmtYoKKSPDmnoAAGgGp3hiWV2ddNRR5nBy443eO3QIJwCACEYHJVYVF0vnn29e+/xz6cQTTUv1HoO7bAAAEYeAEms8HmnQIGn9+kNr553nDSyN5poUbyxTQdEm0wf7Oe3JmpWfw5wSAIClOMUTS9avlxITzeHk/felN98MGE4mF67z+9ThcletJheuU/HGsnBUDABAQASUWHH55dLAgYe+79lT2r9fOv10v0PrPYYKijYp0CfsHFwrKNqkek/rPoMHAIBgIaBEux07vN2Rf/zj0NrLL0vbtwf+fB1Jq0or/TonDRmSyly1WlVaGdxaAQBoIQJKNJs509spaaimRrr00sP+2J7qpsNJW44DACDYuEg2GgUauvbQQ9K0aS368YzU5OYPasVxAAAEGx2UaPPUU/7hpLy8xeFEkoZkp8tpT1ZTNxPb5L2bZ0h2ehNHAAAQWgSUaFFXJ3XsKE2ceGjt+uu9Q9cyM1v1VIkJNs3Kz5Ekv5By8PtZ+TnMQwEAWIaAEg2Ki6XkZOmHHw6tff659Oc/t/kpR/Zzav74gXLYzadxHPZkzR8/kDkoAABLcQ1KJPN4pMGDpXXrDq01MXStLUb2c+rcHAeTZAEAEYeAEqnWrzfPNZGk996Thg8P6h+TmGBTbu8uQX1OAACOFKd4ItG4ceZw0qOHd+hakMMJAACRig5KJNmxw3+uycsvNzvXBACAWEMHJVLMmtWmoWsAAMQiOihWq6qSjj7avPbgg9LNN1tSDgAAkYCAYqWnnjLPNZGksjLJ4bCmHgAAIgSneKxQVyelpprDyXXXeYeuEU4AAKCDEnZvvimNHGle27xZ6tPHmnoAAIhAdFDCxTCkU081h5O8PO8wNsIJAAAmdFDCYcMGacAA89qKFdL//I8l5QAAEOnooITauHHmcNK9u3foGuEEAIAm0UEJlUBD1/7xD+myy6ypBwCAKEIHJRT+9Cf/cFJdTTgBAKCF6KAEU6Chaw88IN1yiyXlAAAQrQgowfL009JVV5nXGLoGAECbhOQUz65duzR+/Hh16dJFKSkp6t+/v9asWeN73DAM3XnnnXI6nUpJSVFeXp62bt0ailJCb98+KS3NHE5+9zuGrgEAcASCHlC+//57nX766Wrfvr3+/e9/a9OmTXrooYd0dINTH3PnztW8efO0YMECrVy5Uh07dtSIESNUW1sb7HJC6z//kZKSvNeXHLRpkzR/vnU1AQAQA2yGYRjBfMLbbrtNH3zwgd57772AjxuGoaysLN1888265adrM1wulzIzM/XMM89o7Nixzf4ZbrdbdrtdLpdLaWlpwSy/ZQxDGjJEatAV0tlnS2+/Ldls4a8HAIAo0Jrf30HvoCxZskSDBg3SpZdeqoyMDA0YMEBPPPGE7/HS0lKVl5crLy/Pt2a32zV06FCVlJQEu5zg+/hjKSHBHE6WL5eWLSOcAAAQJEEPKF999ZXmz5+v448/Xm+++aYmT56sm266Sc8++6wkqby8XJKUmZlp+rnMzEzfY43V1dXJ7Xabvizxm99Ip5xy6PusLO/QtTPOsKYeAABiVNDv4vF4PBo0aJDuvfdeSdKAAQO0ceNGLViwQBMmTGjTc86ZM0cFBQXBLLN1du6UevQwr730ktSC01EAAKD1gt5BcTqdysnJMa317dtXO3bskCQ5frqzpaKiwnRMRUWF77HGZsyYIZfL5fvauXNnsMtuWkGBfzipriacAAAQQkEPKKeffrq2bNliWvviiy/U86fJqtnZ2XI4HFq2bJnvcbfbrZUrVyo3NzfgcyYlJSktLc30FXJVVd5rSv70p0Nr99/vvUC2U6fQ//kAAMSxoJ/imTp1qoYNG6Z7771Xv/rVr7Rq1Sr97W9/09/+9jdJks1m05QpUzR79mwdf/zxys7O1syZM5WVlaXRo0cHu5y2CTR0bfduyem0ph4AAOJM0APK4MGDtWjRIs2YMUN33XWXsrOz9eijj2rcuHG+Y2699Vbt3btXkyZNUlVVlYYPH67i4mIlJycHu5zWMQypa1fpu+8OrV17rbRggXU1AQAQh4I+ByUcQjYH5T//kUaMOPT9Z59Jja6nAQAAbdOa3998Fk9DJ58s/frXUm2t9MorzDUBAMAiBJQG6rtmaNVd87SnulYZX1VqSHa6EhMIKQAAhBsB5SfFG8tUULRJZa5DnwfktCdrVn6ORvbj4lgAAMIpJJ9mHG2KN5ZpcuE6UziRpHJXrSYXrlPxxjKLKgMAID7FfUCp9xgqKNqkQFcKH1wrKNqkek/UXUsMAEDUivuAsqq00q9z0pAhqcxVq1WlleErCgCAOBf3AWVPddPhpC3HAQCAIxf3ASUjtWXD4Vp6HAAAOHJxH1CGZKfLaU9WUzcT2+S9m2dIdno4ywIAIK7FfUBJTLBpVr53WmzjkHLw+1n5OcxDAQAgjOI+oEjSyH5OzR8/UA67+TSOw56s+eMHMgcFAIAwY1DbT0b2c+rcHIdWlVZ6J8mmJjNJFgAAixBQGkhMsCm3dxerywAAIO5xigcAAEQcAgoAAIg4BBQAABBxCCgAACDiEFAAAEDEIaAAAICIQ0ABAAARh4ACAAAiDgEFAABEnKicJGsYhiTJ7XZbXAkAAGipg7+3D/4eP5yoDCjV1dWSpO7du1tcCQAAaK3q6mrZ7fbDHmMzWhJjIozH49Hu3buVmpoqm63pD/Nzu93q3r27du7cqbS0tDBWaB32zJ5jFXtmz7EqnvZsGIaqq6uVlZWlhITDX2USlR2UhIQEdevWrcXHp6WlxfyL3hh7jg/sOT6w5/gQL3turnNyEBfJAgCAiENAAQAAESemA0pSUpJmzZqlpKQkq0sJG/YcH9hzfGDP8SEe99wSUXmRLAAAiG0x3UEBAADRiYACAAAiDgEFAABEHAIKAACIOFEZUFasWKH8/HxlZWXJZrNp8eLFfsds3rxZF110kex2uzp27KjBgwdrx44dvsdra2t1/fXXq0uXLurUqZPGjBmjioqKMO6idYKx51/84hey2Wymr9/97ndh3EXrNLfnxns5+PXAAw/4jqmsrNS4ceOUlpamzp07a+LEiaqpqQnzTlouGHvu1auX3+P33XdfmHfScs3tuaamRjfccIO6deumlJQU5eTkaMGCBaZjoun9HIz9xtp7uaKiQldccYWysrJ01FFHaeTIkdq6davpmGh6jaXg7DnaXudgi8qAsnfvXp188sn6y1/+EvDxbdu2afjw4erTp4/++9//6pNPPtHMmTOVnJzsO2bq1KkqKirSwoULtXz5cu3evVuXXHJJuLbQasHYsyRdc801Kisr833NnTs3HOW3SXN7briPsrIyPfXUU7LZbBozZozvmHHjxumzzz7TW2+9paVLl2rFihWaNGlSuLbQasHYsyTdddddpuNuvPHGcJTfJs3tedq0aSouLlZhYaE2b96sKVOm6IYbbtCSJUt8x0TT+zkY+5Vi571sGIZGjx6tr776Sq+//rrWr1+vnj17Ki8vT3v37vUdF02vsRScPUvR9ToHnRHlJBmLFi0yrV122WXG+PHjm/yZqqoqo3379sbChQt9a5s3bzYkGSUlJaEqNWjasmfDMIwzzzzT+P3vfx+6wkIo0J4bGzVqlHH22Wf7vt+0aZMhyVi9erVv7d///rdhs9mMXbt2harUoGnLng3DMHr27Gk88sgjoSsshALt+ec//7lx1113mdYGDhxo/PGPfzQMI7rfz23Zr2HE1nt5y5YthiRj48aNvrX6+nqja9euxhNPPGEYRnS/xobRtj0bRnS/zsEQlR2Uw/F4PHrjjTd0wgknaMSIEcrIyNDQoUNN7bW1a9dq//79ysvL86316dNHPXr0UElJiQVVH5mW7PmgF154Qcccc4z69eunGTNm6Icffgh/wSFQUVGhN954QxMnTvStlZSUqHPnzho0aJBvLS8vTwkJCVq5cqUVZQZVoD0fdN9996lLly4aMGCAHnjgAR04cMCCCoNj2LBhWrJkiXbt2iXDMPTuu+/qiy++0HnnnScp9t7Pze33oFh5L9fV1UmSqdubkJCgpKQkvf/++5Ji7zVuyZ4PipXXuS2i8sMCD2fPnj2qqanRfffdp9mzZ+v+++9XcXGxLrnkEr377rs688wzVV5erg4dOqhz586mn83MzFR5ebk1hR+BluxZkn7961+rZ8+eysrK0ieffKI//OEP2rJli1577TWLd3Dknn32WaWmpppavuXl5crIyDAd165dO6Wnp0fl69xYoD1L0k033aSBAwcqPT1dH374oWbMmKGysjI9/PDDFlV6ZB5//HFNmjRJ3bp1U7t27ZSQkKAnnnhCZ5xxhiTF3Pu5uf1KsfVePhg0ZsyYob/+9a/q2LGjHnnkEX3zzTcqKyuTFHuvcUv2LMXW69wWMRdQPB6PJGnUqFGaOnWqJOmUU07Rhx9+qAULFvh+WceSlu654bUX/fv3l9Pp1DnnnKNt27apd+/e4S88iJ566imNGzfO75qbWNbUnqdNm+b775NOOkkdOnTQtddeqzlz5kTlKO3HH39cH330kZYsWaKePXtqxYoVuv7665WVlWX6F3WsaMl+Y+m93L59e7322muaOHGi0tPTlZiYqLy8PJ1//vkyYnTQeUv3HEuvc1vEXEA55phj1K5dO+Xk5JjW+/bt62udORwO7du3T1VVVaZEXlFRIYfDEc5yg6Ilew5k6NChkqQvv/wyqv9nf++997Rlyxb985//NK07HA7t2bPHtHbgwAFVVlZG5evcUFN7DmTo0KE6cOCAtm/frhNPPDEM1QXPjz/+qNtvv12LFi3ShRdeKMkbujZs2KAHH3xQeXl5MfV+bsl+A4n29/Kpp56qDRs2yOVyad++feratauGDh3qOz0bS6/xQc3tOZBof51bK+auQenQoYMGDx6sLVu2mNa/+OIL9ezZU5L3f4z27dtr2bJlvse3bNmiHTt2KDc3N6z1BkNL9hzIhg0bJElOpzOU5YXck08+qVNPPVUnn3yyaT03N1dVVVVau3atb+2dd96Rx+PxvdGjVVN7DmTDhg1KSEjwO90VDfbv36/9+/crIcH8V1ViYqKvcxhL7+eW7DeQWHkv2+12de3aVVu3btWaNWs0atQoSbH1GjfW1J4DiZXXuaWisoNSU1OjL7/80vd9aWmpNmzYoPT0dPXo0UPTp0/XZZddpjPOOENnnXWWiouLVVRUpP/+97+SvP9DTJw4UdOmTVN6errS0tJ04403Kjc3V6eddppFuzq8I93ztm3b9OKLL+qCCy5Qly5d9Mknn2jq1Kk644wzdNJJJ1m0q8Nrbs+S5Ha7tXDhQj300EN+P9+3b1+NHDlS11xzjRYsWKD9+/frhhtu0NixY5WVlRW2fbTGke65pKREK1eu1FlnnaXU1FSVlJRo6tSpGj9+vI4++uiw7aM1mtvzmWeeqenTpyslJUU9e/bU8uXL9dxzz/muqYm29/OR7jcW38sLFy5U165d1aNHD3366af6/e9/r9GjR/suDI6211g68j1H4+scdNbeRNQ27777riHJ72vChAm+Y5588knjuOOOM5KTk42TTz7ZWLx4sek5fvzxR+O6664zjj76aOOoo44yLr74YqOsrCzMO2m5I93zjh07jDPOOMNIT083kpKSjOOOO86YPn264XK5LNhNy7Rkz3/961+NlJQUo6qqKuBzfPfdd8bll19udOrUyUhLSzOuvPJKo7q6Okw7aL0j3fPatWuNoUOHGna73UhOTjb69u1r3HvvvUZtbW0Yd9E6ze25rKzMuOKKK4ysrCwjOTnZOPHEE42HHnrI8Hg8vueIpvfzke43Ft/Ljz32mNGtWzejffv2Ro8ePYw77rjDqKurMz1HNL3GhnHke47G1znYbIYRo1chAQCAqBVz16AAAIDoR0ABAAARh4ACAAAiDgEFAABEHAIKAACIOAQUAAAQcQgoAAAg4hBQAABAxCGgAACAiENAAQAAEYeAAgAAIg4BBQAARJz/D4LPX93iRTrbAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot:\n", "plt.scatter(student[\"x\"], student[\"y\"])\n", "plt.plot(student[\"x\"], fitStudents.fittedvalues, color=\"red\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Hypothesis test for parameters" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: y R-squared: 0.932\n", "Model: OLS Adj. R-squared: 0.924\n", "No. Observations: 10 F-statistic: 110.3\n", "Covariance Type: nonrobust Prob (F-statistic): 5.87e-06\n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept -119.9581 18.897 -6.348 0.000 -163.535 -76.381\n", "x 1.1127 0.106 10.504 0.000 0.868 1.357\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 2.75e+03. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "c:\\Users\\pydni\\AppData\\Local\\anaconda3\\envs\\pernille\\Lib\\site-packages\\scipy\\stats\\_stats_py.py:1806: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=10\n", " warnings.warn(\"kurtosistest only valid for n>=20 ... continuing \"\n" ] } ], "source": [ "fitStudents = smf.ols(formula = 'y ~ x', data=student).fit() # OBS: use the statsmodels.formula.api library (smf)\n", "print(fitStudents.summary(slim=True))" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Intercept 0.000221\n", "x 0.000006\n", "dtype: float64\n" ] } ], "source": [ "# Warning!! The p-values appear to be zero but they are in reality only smaller than 0.000\n", "\n", "# print the pvalues seperately to be sure:\n", "print(fitStudents.pvalues)" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-6.347997036566651\n" ] } ], "source": [ "# we can also do the test manually (here only for the intercept):\n", "\n", "# calculate \"t_obs\"\n", "t_obs_int = -119.9581/18.897\n", "print(t_obs_int)" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.00022108433338164315\n" ] } ], "source": [ "# find corresponding pvalue:\n", "print(2*stats.t.cdf(t_obs_int, df=10-2)) # obs! df = n - 2 (2 is the number of parameters)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Confidence interval for parameters" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: y R-squared: 0.932\n", "Model: OLS Adj. R-squared: 0.924\n", "No. Observations: 10 F-statistic: 110.3\n", "Covariance Type: nonrobust Prob (F-statistic): 5.87e-06\n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept -119.9581 18.897 -6.348 0.000 -163.535 -76.381\n", "x 1.1127 0.106 10.504 0.000 0.868 1.357\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 2.75e+03. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "c:\\Users\\pydni\\AppData\\Local\\anaconda3\\envs\\pernille\\Lib\\site-packages\\scipy\\stats\\_stats_py.py:1806: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=10\n", " warnings.warn(\"kurtosistest only valid for n>=20 ... continuing \"\n" ] } ], "source": [ "fitStudents = smf.ols(formula = 'y ~ x', data=student).fit() \n", "print(fitStudents.summary(slim=True))" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-163.53466013972562\n", "-76.38153986027439\n" ] } ], "source": [ "# we can also calculate CI *manually*\n", "\n", "# here only for the intercept:\n", "\n", "print(-119.9581 + stats.t.ppf(0.025, df=10-2)*18.897)\n", "print(-119.9581 - stats.t.ppf(0.025, df=10-2)*18.897)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Confidence interval for the line" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " x y\n", "0 0.507929 85.844021\n", "1 1.935535 519.486580\n", "2 1.619628 275.358640\n", "3 -1.996896 -477.868342\n", "4 -1.363155 -413.276293\n", "5 1.304766 131.195526\n", "6 3.004870 679.832200\n", "7 3.459938 764.296535\n", "8 2.056708 520.693047\n", "9 -0.629292 -84.292611\n", "10 0.506390 115.618570\n", "11 -0.562325 -101.450199\n", "12 1.056394 182.941453\n", "13 2.801986 729.915799\n", "14 -1.942645 -455.967857\n", "15 0.509977 188.065774\n", "16 3.968193 914.620017\n", "17 1.163689 385.099272\n", "18 -1.418796 -194.803230\n", "19 -0.938826 -92.997100\n" ] } ], "source": [ "# Simulated data from underlying linear model:\n", "np.random.seed(23498)\n", "\n", "beta_0 = 50\n", "beta_1 = 200\n", "sigma = 90\n", "\n", "# choose som random x-values:\n", "x = stats.uniform.rvs(size = 20, loc=-2, scale = 6)\n", "# simulate y-values from statistical model:\n", "y = beta_0 + beta_1*x + stats.norm.rvs(size = 20, loc=0, scale = sigma)\n", "\n", "data = pd.DataFrame({'x': x, 'y': y}) # OBS: use the pandas library (pd)\n", "print(data)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is new set of \"Toy data\"" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(data[\"x\"],data[\"y\"])\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: y R-squared: 0.963\n", "Model: OLS Adj. R-squared: 0.961\n", "No. Observations: 20 F-statistic: 468.9\n", "Covariance Type: nonrobust Prob (F-statistic): 2.43e-14\n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept 13.7955 19.969 0.691 0.498 -28.157 55.748\n", "x 225.7635 10.426 21.655 0.000 203.860 247.667\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n" ] } ], "source": [ "# fit a linear regression model\n", "linfit = smf.ols(formula = 'y ~ x', data=data).fit()\n", "print(linfit.summary(slim=True))" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " mean mean_se mean_ci_lower mean_ci_upper obs_ci_lower \\\n", "0 -437.731597 34.066943 -509.303589 -366.159606 -624.530446 \n", "1 -435.473962 33.979179 -506.861567 -364.086357 -622.202241 \n", "2 -433.216327 33.891507 -504.419741 -362.012912 -619.874265 \n", "3 -430.958691 33.803930 -501.978113 -359.939269 -617.546521 \n", "4 -428.701056 33.716448 -499.536685 -357.865427 -615.219007 \n", "\n", " obs_ci_upper \n", "0 -250.932749 \n", "1 -248.745683 \n", "2 -246.558388 \n", "3 -244.370862 \n", "4 -242.183105 \n" ] } ], "source": [ "# Make predictions and confidence intervals\n", "x_pred = pd.DataFrame({'x': np.arange(-2,4,.01)})\n", "\n", "pred = linfit.get_prediction(x_pred).summary_frame(alpha=0.05) \n", "\n", "print(pred.head())" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot all the predictions:\n", "plt.scatter(data[\"x\"],data[\"y\"])\n", "plt.plot(x_pred, pred[\"mean\"], color=\"red\")\n", "plt.plot(x_pred, pred[\"mean_ci_lower\"], color=\"grey\")\n", "plt.plot(x_pred, pred[\"mean_ci_upper\"], color=\"grey\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We could also calculate this interval *manually* " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Prediction interval for parameters" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " mean mean_se mean_ci_lower mean_ci_upper obs_ci_lower \\\n", "0 -437.731597 34.066943 -509.303589 -366.159606 -624.530446 \n", "1 -435.473962 33.979179 -506.861567 -364.086357 -622.202241 \n", "2 -433.216327 33.891507 -504.419741 -362.012912 -619.874265 \n", "3 -430.958691 33.803930 -501.978113 -359.939269 -617.546521 \n", "4 -428.701056 33.716448 -499.536685 -357.865427 -615.219007 \n", "\n", " obs_ci_upper \n", "0 -250.932749 \n", "1 -248.745683 \n", "2 -246.558388 \n", "3 -244.370862 \n", "4 -242.183105 \n" ] } ], "source": [ "# Same data as above\n", "\n", "# now we want the prediction interval for individual (new/future) observations\n", "\n", "print(pred.head())" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot all the predictions:\n", "plt.scatter(data[\"x\"],data[\"y\"])\n", "plt.plot(x_pred, pred[\"mean\"], color=\"red\")\n", "plt.plot(x_pred, pred[\"obs_ci_lower\"], color=\"lightgrey\")\n", "plt.plot(x_pred, pred[\"obs_ci_upper\"], color=\"lightgrey\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot all the predictions:\n", "plt.scatter(data[\"x\"],data[\"y\"])\n", "plt.plot(x_pred, pred[\"mean\"], color=\"red\")\n", "plt.plot(x_pred, pred[\"obs_ci_lower\"], color=\"lightgrey\")\n", "plt.plot(x_pred, pred[\"obs_ci_upper\"], color=\"lightgrey\")\n", "plt.plot(x_pred, pred[\"mean_ci_lower\"], color=\"grey\")\n", "plt.plot(x_pred, pred[\"mean_ci_upper\"], color=\"grey\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Correlation and $R^2$" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " x y y_pred residuals\n", "0 168 65.5 66.982578 -1.482578\n", "1 161 58.3 59.193383 -0.893383\n", "2 167 68.1 65.869836 2.230164\n", "3 179 85.7 79.222742 6.477258\n", "4 184 80.5 84.786453 -4.286453\n", "5 166 63.4 64.757094 -1.357094\n", "6 198 102.6 100.364844 2.235156\n", "7 187 91.4 88.124680 3.275320\n", "8 191 86.7 92.575648 -5.875648\n", "9 179 78.9 79.222742 -0.322742\n" ] } ], "source": [ "# Recall student height and weight data\n", "print(student)" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: y R-squared: 0.932\n", "Model: OLS Adj. R-squared: 0.924\n", "No. Observations: 10 F-statistic: 110.3\n", "Covariance Type: nonrobust Prob (F-statistic): 5.87e-06\n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept -119.9581 18.897 -6.348 0.000 -163.535 -76.381\n", "x 1.1127 0.106 10.504 0.000 0.868 1.357\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 2.75e+03. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "c:\\Users\\pydni\\AppData\\Local\\anaconda3\\envs\\pernille\\Lib\\site-packages\\scipy\\stats\\_stats_py.py:1806: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=10\n", " warnings.warn(\"kurtosistest only valid for n>=20 ... continuing \"\n" ] } ], "source": [ "fitStudents = smf.ols(formula = 'y ~ x', data=student).fit() # OBS: use the statsmodels.formula.api library (smf)\n", "print(fitStudents.summary(slim=True))" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[1. 0.96560343]\n", " [0.96560343 1. ]]\n", "[[1. 0.93238999]\n", " [0.93238999 1. ]]\n" ] } ], "source": [ "print(np.corrcoef(student[\"x\"], student[\"y\"]))\n", "print(np.corrcoef(student[\"x\"], student[\"y\"])**2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "compare with R-squared in the table" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Model validation in Python" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(student[\"x\"], student[\"y\"])\n", "plt.plot(student[\"x\"], fitStudents.fittedvalues, color=\"red\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Inspect the residuals (and assumption about normality):" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "image/png": 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JKldOmjnT+qQ9AADgdBSlcoDEJENbo67oQtxNhQT4q1bJgvL2spgdFgAHcJXfu5+fn2JjY5PNP3LkiIKDg50eDwDHMfO4k+H3Ngzpq6+k3r2ly5clb2/pzTelwYOlv/XmBJA2VznPAOB4zvq9U5TycMv3R2vY0oOKjrlpmxcW5K8hrSLVvFKYiZEByG6u9Ht/8skn9d577+mb//VGsFgsOn36tN566y0988wzTo0FgOOYedzJ8HufPSu98or044/W6SpVrL2jqlVzaHyAp3Gl8wwAjuXM3ztjSnmw5fuj1eOLnXZfJEk6H3NTPb7YqeX7o02KDEB2c7Xf+7hx4xQfH6+QkBDduHFDDRo0UJkyZRQQEKARI0Y4NRYAjmHmcSdD720Y1oHLIyOtBSkfH2n4cGnbNgpSQCa52nkGAMdx9u+dnlIeKjHJ0LClB2Wk8JohySJp2NKDeiwylC63gJtzxd97UFCQVq1apU2bNmnv3r2Kj49XtWrV1KRJE6e8PwDHMvO4k5H3/mzOGjXbNVuWNWusL9SqZe0dVbFitsYC5ASueJ4BwDHM+L1TlPJQW6OuJKts/p0hKTrmprZGXVGd0oWcFxiAbOfKv/dHHnlEjzzyiFPfE4DjmXncSeu9LUaSOu74UW9unCPL7QTreFEjRlifruftna1xADmFK59nAMheZvzeKUp5qAtxqX+RsrIcANflKr/3Tz75JMPL9u7d24GRAHA0M487qW2z1OU/NHrZJ6p59qAk6VL1h1R4wTypTJlsjwHISVzlPAOA45nxe3ebotSoUaO0aNEi/f7778qdO7fq1q2r0aNHq1y5cmaH5pJCAjL2JJmMLgfAdbnK7/2jjz7K0HIWi8VhRSlyBeAcZh53/rlN76REdd+6SH03fSm/xNuK982tUQ0764lPh6pwGZ72ieTIFZnjKucZABzPjN+72xSlNmzYoJ49e6pmzZq6c+eO3n77bTVt2lQHDx5U3rx5zQ7P5dQqWVBhQf46H3MzxftBLZJCg6yPdQTg3lzl9x4VFeXQ7WcEuQJwDjOPO39/73IXovThso/1wPljkqT1JavrneY9lRReXO+VLpzt7w3PQK7IHFc5zwDgeGb83t2mKLV8+XK76dmzZyskJEQ7duxQ/fr1TYrKdXl7WTSkVaR6fLFTFsnuC3V3OLIhrSIZjBDwAPze/x+5AnAOM4873l4WDW1eRr/3GqRXf/1GPkmJuuqfT8Mbd9OiSo0li0VTcsgxD1lDrsgczjOAnMOM37vbFKX+KSYmRpJUsGDqFbqEhAQlJCTYpmNjYx0elytpXilMUzpU07ClB+0GKwsN8teQVpFqXinMxOgAZCdX+L33799fw4cPV968edW/f/80lx0/frzD45HIFYAjmXbc2bpVzbp0UbMDByRJy++vo3cf66GL+axXdznHQWaRK9LnCucZAJzD2b93i2EYKfXKcmlJSUl68skndfXqVW3atCnV5YYOHaphw4Ylmx8TE6PAwEBHhuhSEpMMbY26ogtxNxUSYO1qx5UMwDPd6+89NjZWQUFBWTpONmrUSN9//73y58+vRo0apbnsunXrMrXtrCBXAM7htPOMGzekwYOl8eOlpCQpOFiJEz/V1uqNdSE+gXMcJ7qXXOFqyBWZQ7sCyDmc1a5wy6JUjx49tGzZMm3atEnFihVLdbmUrmiEh4fnuOQBABnlSQ0NcgXgQTZulLp2lY5Zx45S+/bShAlSYcaNMgO5glwBAOnJaK7wcmJM2aJXr1768ccftW7dujQThyT5+fkpMDDQ7g8A4HhdunRRXFxcsvnXrl1Tly5dHP7+5ArAQ8TFST17Sg0aWAtS990nLV0qffEFBSncM3IFAJjPbYpShmGoV69e+v7777V27VqVLFnS7JAAAKmYM2eObty4kWz+jRs3NHfuXIe9L7kC8CArV0qVKkmTJ1unu3WTDhyQnnjC3Ljg9sgVAOA63Gag8549e+rLL7/UkiVLFBAQoPPnz0uSgoKClDt3bpOjAwBI1m66hmHIMAzFxcXJ39/f9lpiYqL++9//KiQkxGHvT64APMBff0kDBkizZlmnS5aUpk+XHn3U3LjgMcgVAOA63GZMKYsl5QG1Zs2apU6dOmVoG550/zsAOMK9Hie9vLxSPV5L1mP5sGHD9M4779xLmGluPyXkCsBNLFkivfKKdP68ZLFIvXtLI0ZIefOaHRn+xt2Pk+QKAHC8jB4n3aanlJvUzgAgR1u3bp0Mw1Djxo313Xff2T1e29fXVxERESpatKjD3p9cAbipixel116Tvv7aOl2unPT559LDD5sbFzwSuQIAXIfbFKUAAK6vQYMGkqSoqCiFh4fLy8tthi4EYAbDkBYssBakLl+WvL2lN96QhgyR/nb7LwAA8EwUpQAA2S4iIkJXr17V1q1bdeHCBSUlJdm9/uKLL5oUGQCXcfas1KOH9Wl6kvTAA9LMmVL16ubGBQAAnIaiFAAg2y1dulTt27dXfHy8AgMD7cbvsFgsFKWAnMwwrMWnAQOkmBjJx0d6913prbckX1+zowMAAE5EUQoAkO0GDBigLl26aOTIkcqTJ4/Z4QBwFSdPSt26SatXW6dr1bKOHVWpkqlhAQAAc2RpsI8zZ87ojz/+sE1v3bpVffv21WeffZZtgQEA3NfZs2fVu3dvClIArJKSpIkTrcWn1aut40WNHSv98gsFqRyOdgUA5GxZKko9//zzWrdunSTp/Pnzeuyxx7R161a98847eu+997I1QACA+2nWrJm2b99udhgAXMGRI1KDBlLv3tK1a1L9+tLevdbb97y9zY4OJqNdAQA5W5Zu39u/f79q1aolSfrmm29UqVIlbd68WStXrtQrr7yiwYMHZ2uQAAD30rJlS73xxhs6ePCgKleuLB8fH7vXn3zySZMiA+A0d+5I48dLgwdLCQlSvnzS6NHSK69IPJkT/0O7AgBytiwVpW7fvi0/Pz9J0urVq22Ni/Llyys6Ojr7ogMAuKVu3bpJUopXuS0WixITE50dEgBn2rdP6txZ2rHDOt2smTRtmhQRYW5ccDm0KwAgZ8vSZaqKFStq6tSp+vnnn7Vq1So1b95cknTu3DkVKlQoWwMEALifpKSkVP8oSAEe7NYtaehQqXp1a0Eqf35p1ixp2TIKUkgR7QoAyNmyVJQaPXq0pk2bpoYNG6pdu3aqUqWKJOmHH36wdb8FAABADrJtm7UYNWyYdPu21KaNdPCg1KmTZLGYHR1cFO0KAMjZsnT7XsOGDXXp0iXFxsaqQIECtvndu3fnSUsAAEnStWvXtGHDBp0+fVq3bt2ye613794mRQUg2924Ye0dNXas9Sl7wcHSp59Kzz5LMQrpol0BADlblopSkuTt7W2XOCSpRIkS9xoPAMAD7Nq1Sy1atND169d17do1FSxYUJcuXVKePHkUEhJCUQrwFD//LHXtKh09ap1+/nnp44+lwoXNjQtuhXYFAORcGS5KVa1aVZYMXu3auXNnlgMCALi/fv36qVWrVpo6daqCgoL066+/ysfHRx06dFCfPn3MDg/AvYqLkwYNkiZNsk4XLSpNnSq1amVuXHALtCsAAHdluCjVpk0bB4YBAPAku3fv1rRp0+Tl5SVvb28lJCSoVKlS+vDDD9WxY0c9/fTTZocIIKtWrZK6dZNOnbJOv/SSNGaMdVBzIANoVwAA7spwUWrIkCGOjAMA4EF8fHzk5WV9lkZISIhOnz6tChUqKCgoSGfOnDE5OgBZ8tdf0oAB1qfpSVKJEtL06VKTJqaGBfdDuwIAcFeWx5QCACA1VatW1bZt21S2bFk1aNBAgwcP1qVLlzRv3jxVqlTJ7PAAZNaSJVKPHlJ0tHXw8l69pJEjpXz5zI4MAAC4Ma+srJSYmKixY8eqVq1aCg0NVcGCBe3+AAA528iRIxUWFiZJGjFihAoUKKAePXro4sWL+uyzz0yODkCGXbwotWsntWljLUiVK2cd3PyTTyhIIVvQrgCAnC1LRalhw4Zp/Pjxatu2rWJiYtS/f389/fTT8vLy0tChQ7M5RACAu6lRo4YaNWokyXr73vLlyxUbG6sdO3aoSpUqJkcHIF2GIS1YIEVGWv/r7S0NHCjt3i09/LDZ0cGD0K4AgJwtS0Wp+fPna/r06RowYIBy5cqldu3aacaMGRo8eLB+/fXX7I4RAAAAznLunLVnVLt20qVL0gMPSL/9Jo0aJfn7mx0dPAztCgDI2bI0ptT58+dVuXJlSVK+fPkUExMjSXriiSf07rvvZl90AAC3VLJkyTQf933ixAknRgMgQwzDOoh5//5STIzk4yO9+6701luSr6/Z0cFD0a4AgJwtS0WpYsWKKTo6WsWLF1fp0qW1cuVKVatWTdu2bZOfn192xwgAcDN9+/a1m759+7Z27dql5cuX64033jAnKACpO3lS6t5dWrXKOl2zpjRzpsSDCeBgtCsAIGfLUlHqqaee0po1a1S7dm299tpr6tChgz7//HOdPn1a/fr1y+4YAQBupk+fPinOnzRpkrZv3+7kaACkKilJmjzZOl7UtWvW2/OGD5f69pVy8ZBmOB7tCgDI2SyGYRj3upEtW7Zoy5YtKlu2rFq1apUdcTlEbGysgoKCFBMTo8DAQLPDAQCX4+jj5IkTJ/Tggw8qNjY227edXcgVyDGOHJG6dpU2bbJO16snff65VLasuXHB5TnyOEm7AgA8Q0aPk9lyCaxOnTqqU6dOdmwKAODBvv32Wx7xDZjtzh1p/Hhp8GApIUHKl08aPVp65RXJK0vPwAGyDe0KAMhZslSUmjt3bpqvv/jii1kKBgDgGapWrWo30LlhGDp//rwuXryoyZMnmxgZkMPt2yd16SLdvY22aVPps8+kiAhz40KORbsCAHK2LBWl/jlWyO3bt3X9+nX5+voqT548JA8AyOHatGljN+3l5aXg4GA1bNhQ5cuXNycoICe7dUsaOdL6d/u2lD+/9NFHUseOUhpPygQcjXYFAORsWSpK/fXXX8nmHT16VD169OCpSgAADRkyxOwQANy1bZu1d9T+/dbpNm2sg5uHhZkaFiDRrgCAnC7bHqtStmxZffDBB+rQoYN+//337NosAMANnT17Vt99952OHDkiX19flStXTs8995wKFChgdmhAznHjhjRkiDRunPUpe8HB0qefSs8+S+8ouDTaFQCQc2Trs35z5cqlc+fOZecmAQBuZvLkyerfv79u3bple9JGbGys+vfvrxkzZqhdu3YyDEO7d+9W1apVTY4W8FA//2x9st7Ro9bp55+XPv5YKlzY3LiADKJdAQA5Q5aKUj/88IPdtGEYio6O1qeffqqHH344WwIDALifn376Sb1791bfvn01YMAAhf3v9qDo6GiNGTNGHTt2VHh4uCZPnqzy5ctTlAKyW1ycNGiQNGmSdbpoUWnqVKlVK3PjAlJBuwIAcrYsFaX+OYCtxWJRcHCwGjdurHHjxmVHXAAANzRmzBgNHDhQ77//vt38sLAwjR8/Xnny5NFjjz2m0NBQjRo1yqQoAQ+1apXUrZt06pR1+qWXpDFjrIOaAy6KdgUA5GxZKkolJSVldxwAAA+wc+dOTZs2LdXXX3jhBY0cOVIbNmxQ8eLFnRgZ4MGuXpUGDJBmzrROlyghTZ8uNWliZlRAhtCuAICczcvsAAAAniMxMVE+Pj6pvu7j46PcuXNTkAKyy5IlUmSktSBlsUivvSbt20dBCgAAuIUM95Tq379/hjc6fvz4LAUDAHBvFStW1JIlS9SvX78UX1+8eLEqVqzo5KgAD3TxotS7t7RggXX6/vuthSnG4IEboF0BALgrw0WpXbt22U3v3LlTd+7cUbly5SRJR44ckbe3t6pXr569Ef7DpEmTNGbMGJ0/f15VqlTRxIkTVatWLYe+JwAgY3r27KkePXrIz89P3bt3V65c1jRz584dTZs2Tf/5z380efJkh8dBroDHMgzp66+tPaIuXZK8vaXXX5eGDJFy5zY7OiBDaFcAAO7KcFFq3bp1tv8fP368AgICNGfOHBUoUECS9Ndff6lz586qV69e9kf5P19//bX69++vqVOnqnbt2powYYKaNWumw4cPKyQkxGHvCwDImI4dO2rfvn3q1auXBg0apNKlS8swDJ04cULx8fHq3bu3OnXq5NAYyBXwWOfOST16SHefVvbAA9beUQ5uuAPZjXYFAOAui2EYRmZXuu+++7Ry5cpkt2Ds379fTZs21blz57ItwL+rXbu2atasqU8//VSSdWDE8PBwvfbaaxo4cGC668fGxiooKEgxMTEKDAx0SIwA4M6y6zj566+/6quvvtLRo0clSWXLllW7du300EMPZVeoqSJXwOMYhjRrltS/vxQTI/n4SP/5jzRwoOTra3Z0yIGy8zhJuwIAPFNGj5NZevpebGysLl68mGz+xYsXFRcXl5VNpuvWrVvasWOHBg0aZJvn5eWlJk2aaMuWLSmuk5CQoISEBNt0bGysQ2IDANh76KGHnFKA+idyBTzOyZNS9+7SqlXW6Zo1rb2jKlUyNSwgu9CuAICcLUtP33vqqafUuXNnLVq0SH/88Yf++OMPfffdd+ratauefvrp7I5RknTp0iUlJiaqSJEidvOLFCmi8+fPp7jOqFGjFBQUZPsLDw93SGwAANdAroDHSEqSJk2yFp9WrZL8/aUxY6RffqEgBY9CuwIAcrYsFaWmTp2qxx9/XM8//7wiIiIUERGh559/Xs2bN3fKALYZNWjQIMXExNj+zpw5Y3ZIAAAXQ66AyzlyRGrYUOrVS7p2TapXT9qzxzqgea4sdXIHXBbtCgDI2bJ0ZpMnTx5NnjxZY8aM0fHjxyVJpUuXVt68ebM1uL8rXLiwvL299eeff9rN//PPPxUaGpriOn5+fvLz83NYTEBmJCYZ2hp1RRfibiokwF+1ShaUt5fF7LAAj0KugFu7c0f66CNp8GDp5k0pb17pww+lV16RvDJ+HZF8A3dCuwLIPI7z8CT3dLktb968euCBB7IrljT5+vqqevXqWrNmjdq0aSPJOiDhmjVr1KtXL6fEAGTV8v3RGrb0oKJjbtrmhQX5a0irSDWvFGZiZIBnIVfAbe3bJ3XpIm3fbp1u2lT67DMpIiJTmyHfwF3RrgAyhuM8PE2Gi1JPP/20Zs+ercDAwHTv7160aNE9B5aS/v37q2PHjqpRo4Zq1aqlCRMm6Nq1a+rcubND3g/IDsv3R6vHFzv1z8dcno+5qR5f7NSUDtVIIPBId+7c0fr163X8+HE9//zzCggI0Llz5xQYGKh8+fI57H3JFXArt25Jo0ZJI0ZIt29L+fNL48dLnTpJlsxd9SbfwF3QrgCyhuM8PFGGi1JBQUGy/O/kKCgoyGEBpaVt27a6ePGiBg8erPPnz+vBBx/U8uXLkw1SCLiKxCRDw5YeTJY4JMmQZJE0bOlBPRYZSpdbeJRTp06pefPmOn36tBISEvTYY48pICBAo0ePVkJCgqZOneqw9yZXwG1s327tHbVvn3W6dWtp8mSpaNFMb4p8A3dCuwLIPI7z8FQWwzBS+l57pNjYWAUFBSkmJkaBgYFmh4McYMvxy2o3/dd0l/uq20OqU7qQEyIC0pZdx8k2bdooICBAn3/+uQoVKqQ9e/aoVKlSWr9+vbp166ajR49mY9TZi1wBh7txQxo6VBo71vqUvcKFpU8/lZ57LtO9o+4i38CZOE6yD+B8HOfhbjJ6nMzSmFI3btyQYRjKkyePJOsV8e+//16RkZFq2rRp1iIGPNCFuJvpL5SJ5QB38fPPP+uXX36Rr6+v3fwSJUro7NmzJkUFuIBNm6SuXa1P2JOkdu2kjz+WgoPvabPkG7gr2hVAxnCch6fK+KNc/qZ169aaO3euJOnq1auqVauWxo0bp9atW2vKlCnZGiDgzkIC/LN1OcBdJCUlKTExMdn8P/74QwEBASZEBJgsPl7q3VuqX99akAoLk5Yskb788p4LUhL5Bu6LdgWQMRzn4amyVJTauXOn6tWrJ0n69ttvFRoaqlOnTmnu3Ln65JNPsjVAwJ3VKllQYUH+Su1mDIusT8uoVbKgM8MCHK5p06aaMGGCbdpisSg+Pl5DhgxRixYtzAsMMMPq1VLlytLEiZJhWHtKHTwoPflktr0F+QbuinYFkDEc5+GpslSUun79uu1K98qVK/X000/Ly8tLDz30kE6dOpWtAQLuzNvLoiGtIiUpWQK5Oz2kVSSDEcLjjBs3Tps3b1ZkZKRu3ryp559/3nbr3ujRo80OD3COq1ell16SHntMOnlSioiQVq6UZsywPmUvG5Fv4K5oVwAZw3EenipLRakyZcpo8eLFOnPmjFasWGG73/vChQsM9Af8Q/NKYZrSoZpCg+y70oYG+fPYVnisYsWKac+ePXr77bfVr18/Va1aVR988IF27dqlkJAQs8MDHO+HH6SKFaXPP7dOv/aatH+/tUDlIOQbuCPaFUDGcZyHJ8rS0/e+/fZbPf/880pMTFTjxo21atUqSdKoUaO0ceNGLVu2LNsDzQ48JQNmSkwytDXqii7E3VRIgLVrLVcy4Go4TrIPcI8uXpT69JG++so6ff/91sLUI484LQTyDRwtO4+TtCuAzOM4D3eQ0eNklopSknT+/HlFR0erSpUq8vKydrjaunWrAgMDVb58+axF7WAkDwBI270cJ3/44YcML/tkNo6lk93IFcgSw5C++Ubq1Uu6dEny8pJef10aOlTKndvs6IBsld3HSdoVAOB5MnqczJXVNwgNDVV8fLxWrVql+vXrK3fu3KpZs6YsFiq0AJATtWnTJkPLWSyWFJ/MB7itc+ekV1+1Pk1Psg5qPnOmVKOGuXEBboJ2BQDkXFkqSl2+fFnPPfec1q1bJ4vFoqNHj6pUqVLq2rWrChQooHHjxmV3nKaieyQApC8pKcnsEADnMgxp9mypXz8pJkby8ZHeeUcaNEjy9bVblHMJIGW0KzgWAMjZslSU6tevn3x8fHT69GlVqFDBNr9t27bq37+/RyWP5fujNWzpQUXH3LTNCwvy15BWkQwkBwBATnXqlNS9u/VpepK1V9TMmdZeUv/AuQSQOtoVHAsA5GxZevreypUrNXr0aBUrVsxuftmyZT3q0a3L90erxxc77RKHJJ2PuakeX+zU8v3RJkUGAK5vzZo1euKJJ1S6dGmVLl1aTzzxhFavXm12WMC9SUqSJk2SKlWyFqT8/aUPP5S2bEm1IMW5BJA62hUcCwDkbFkqSl27dk158uRJNv/KlSvy8/O756BcQWKSoWFLDyqlUeDvzhu29KASk7I0TjwAeLTJkyerefPmCggIUJ8+fdSnTx8FBgaqRYsWmjRpktnhAVlz5IjUsKF1MPP4eOsT9fbskd54Q8qVvPM55xJA+mhXWHEsAJBTZakoVa9ePc2dO9c2bbFYlJSUpA8//FCNGjXKtuDMtDXqSrIrGX9nSIqOuamtUVecFxQAuImRI0fqo48+0ldffaXevXurd+/e+vLLL/XRRx9p5MiRZocHZM6dO9KYMVKVKtLPP0t580oTJ0obNkj335/qapxLAOmjXcGxAEDOlqUxpcaMGaPGjRtr+/btunXrlt58800dOHBAV65c0ebNm7M7RlNciEs9cWRlOQDISa5evarmzZsnm9+0aVO99dZbJkQEZNH+/VKXLtK2bdbpxx6TPvtMKlEi3VU5lwDSR7si88sBgCfJdE+p27dvq3fv3lq6dKkeeeQRtW7dWteuXdPTTz+tXbt2qXTp0o6I0+lCAvyzdTkAyEmefPJJff/998nmL1myRE888YQJEQGZdOuW9N57UrVq1oJUUJD0+efSihUZKkhJnEsA6aFdkbXlAMCTZLqnlI+Pj/bu3asCBQronXfecURMLqFWyYIKC/LX+ZibKd7/bZEUGmR9jCsAwF5kZKRGjBih9evXq06dOpKkX3/9VZs3b9aAAQP0ySef2Jbt3bu3WWECKdu+3do7at8+6/STT0pTpkhFi2ZqM5xLAGmjXWHFsQBATmYxDCPTI+r169dPfn5++uCDDxwRk8PExsYqKChIMTExCgwMTHf5u0/JkGSXQCz/+++UDtV4fCsAj5LZ42RqSpYsmaHlLBaLTpw4keX3cYTs2gdwQzduSMOGWcePSkqSChe2jh3Vtq1ksaS/fgo4l4Anys7jJO0KK44FADxNRo+TWRpT6s6dO5o5c6ZWr16t6tWrK2/evHavjx8/PiubdTnNK4VpSodqGrb0oN3ghKFB/hrSKpLEAQCpiIqKMjsEIHM2bZK6drU+YU+S/v1v6ZNPpODge9os5xJA2mhXcCwAkLNlqSi1f/9+VatWTZJ05O7J2/9Ysngl0VU1rxSmxyJDtTXqii7E3VRIgLVrrbeXZ31OAABypPh46e23pU8/lQxDCguTpk613rKXTTiXAFJHu4JjAYCcLUtFqXXr1mV3HC7N28uiOqULmR1GqhKTDJIbAJdiGIa+/fZbrVu3ThcuXFBSUpLd64sWLTIpMsAqMcnQ4S++V8Sgvsp77ox1Zpcu0rhxUv782f5+rn4uAZiFdoVroV0BwNmyVJSC61i+PzpZN+AwugEDMFnfvn01bdo0NWrUSEWKFPG4q91wb6t/+V3X+/TXk9uXSZL+CAzRmGf66/F+L6q5AwpSAOAOaFcAMANFKTd2d8DEf45Ufz7mpnp8sTNTAyZyVQRAdpo3b54WLVqkFi1amB0KXJyz88+OT+eo0qD+Co2/IkmaU62lPqzfUdf98uiHTOZOAPAUtCsAmIWilJtKTDI0bOnBFB8ra8j6JI9hSw/qscjQdJMAV0UAZLegoCCVKlXK7DDg4pyafy5dUtJrvVV9wVeSpBMFiuqtx3trW3gl2yKZyZ0A4CloVwAwk5fZASBrtkZdsTvY/5MhKTrmprZGXUlzO3evivxzW3eviizfH50d4QLIYYYOHaphw4bpxo0bZocCF+W0/GMY0tdfS5GR8lrwlRItXppa+xk93nmiXUFKynjuBABPQrsCgJnoKeWmLsSlnjgyulx2XhUBgL977rnn9NVXXykkJEQlSpSQj4+P3es7d+40KTK4Aqfln+hoqUcPackSSVJsmXLqUPdl7Q27P83VMppjAcAT0K4AYCaKUm4qJMD/npfLzFURV35KCADX07FjR+3YsUMdOnRgoHMk4/D8YxjSnDlSv37S1atSrlzSf/6jg89119456RdEM5pjAcAT0K4AYCaKUm6qVsmCCgvy1/mYmylekbBICg2yDiyYmuy4KgIAKfnpp5+0YsUKPfLII2aHAhfk0Pxz6pT08svSihXW6Ro1pJkzpcqVVTPJuOfcCQCehnYFADMxppSb8vayaEirSEnWRPF3d6eHtIpMs3tsdlwVAYCUhIeHKzAw0Oww4KIckn+SkqTJk6VKlawFKT8/afRoacsWqXJlSdmTOwHA09CuAGAmilJurHmlME3pUE2hQfYH99Ag/ww9tvXuVZHU0otF1qdlcMUYQGaNGzdOb775pk6ePGl2KHBB2Z5/jh6VGjWSevaU4uOlhx+W9uyR3nzTeuve39xr7gQAT0S7AoBZLIZhpNRL0yPFxsYqKChIMTExHnUFPzHJ0NaoK7oQd1MhAdaDfUav8t59SoYku+66d9fmBB3IWbLrOFmgQAFdv35dd+7cUZ48eZINdH7lius+3cxTc4WryZb8k5goffSR9O670s2bUt680gcfSK++Knmlfd3tXnInkNNxnPTcfUC7AkB2yehxkjGlPIC3lyXLAwbevSoybOlBu8EJQ4P8NaRVJIkDQJZMmDDB7BDg4u45/+zfL3XpIm3bZp1u0kSaPl0qUSJD738vuRMAPBXtCgDORk8pSOKKMQArjpPsA2fLdP65dcvaG+r996Xbt6WgIGncOGuBiqc8Ak7BcZJ9kBbaFQAkekohk7hiDMBRbt68qVu3btnN4wQed2Uq/+zYYS0+7d1rnW7VSpo6VSpa1HEBAgAyhXYFgMxgoHMAQLa7du2aevXqpZCQEOXNm1cFChSw+wMy5eZNaeBAqXZta0GqcGHpyy+lJUsoSAEAALgxtyhKnTx5Ul27dlXJkiWVO3dulS5dWkOGDEl25R0A4BrefPNNrV27VlOmTJGfn59mzJihYcOGqWjRopo7d65D3pNc4aE2b5YefFAaPdo6sPm//y0dPCi1a8ftegAyjVwBAK7FLW7f+/3335WUlKRp06apTJky2r9/v7p166Zr165p7NixZocHAPiHpUuXau7cuWrYsKE6d+6sevXqqUyZMoqIiND8+fPVvn37bH9PcoWHiY+X3nlHmjhRMgwpLEyaMkVq3drsyAC4MXIFALgWtx3ofMyYMZoyZYpOnDiR4XUYkBAA0pZdx8l8+fLp4MGDKl68uIoVK6ZFixapVq1aioqKUuXKlRUfH5+NUaeOXOGmVq+WunWTTp60TnfpIo0dK3HrJ+ASPO04Sa4AgOzn8QOdx8TEqGDBgmkuk5CQoISEBNt0bGyso8MCAEgqVaqUoqKiVLx4cZUvX17ffPONatWqpaVLlyp//vxOi4Nc4WZiYqTXX5dmzLBOR0RIn30mNW1qblwAPBq5AgDM4xZjSv3TsWPHNHHiRL388stpLjdq1CgFBQXZ/sLDw50UIQDkbJ07d9aePXskSQMHDtSkSZPk7++vfv366Y033nBKDOQKN/Pjj1Jk5P8XpHr2lPbtoyAFwKHIFQBgLlNv3xs4cKBGjx6d5jKHDh1S+fLlbdNnz55VgwYN1LBhQ824e+KaipSuaISHh9PNFgBS4ajbEU6ePKmdO3eqTJkyeuCBBzK1LrnCw126JPXpY32aniSVLWstTNWvb25cAFLlireukSsAwLVkNFeYWpS6ePGiLl++nOYypUqVkq+vryTp3LlzatiwoR566CHNnj1bXl6Z6+jligkUAFyJKx4nyRUeyjCkhQulXr2kixclLy9pwABp2DApd26zowOQBlc8TpIrAMC1uMWYUsHBwQoODs7QsmfPnlWjRo1UvXp1zZo1K9OJAwDgeFu2bNHly5f1xBNP2ObNnTtXQ4YM0bVr19SmTRtNnDhRfn5+Gd4mucIDRUdLr74qLV5sna5USfr8c6lWLVPDAuC+yBUA4J7c4gh89uxZNWzYUMWLF9fYsWN18eJFnT9/XufPnzc7NADA37z33ns6cOCAbXrfvn3q2rWrmjRpooEDB2rp0qUaNWqUQ96bXOEGDEOaPds6dtTixVKuXNKQIdKOHRSkADgFuQIAXItbPH1v1apVOnbsmI4dO6ZixYrZvWbi3YcAgH/YvXu3hg8fbptesGCBateurenTp0uSwsPDNWTIEA0dOjTb35tc4eJOn5a6d5dWrLBOV68uzZwpZXKMMQC4F+QKAHAtbtFTqlOnTjIMI8U/AIDr+Ouvv1SkSBHb9IYNG/T444/bpmvWrKkzZ8445L3JFS4qKUmaMkWqWNFakPLzk0aPln79lYIUAKcjVwCAa3GLohQAwD0UKVJEUVFRkqRbt25p586deuihh2yvx8XFycfHx6zw4GxHj0qNGlnHj4qPlx5+WNqzR3rzTeutewAAAMjRKEoBALJNixYtNHDgQP38888aNGiQ8uTJo3r16tle37t3r0qXLm1ihHCKxERp3DhrT6iNG6W8eaWJE63/X66c2dEBAADARXCZEgCQbYYPH66nn35aDRo0UL58+TRnzhzb47claebMmWratKmJEcLhDhyQunSRtm61TjdpIk2fLpUoYWpYAAAAcD0UpQAA2aZw4cLauHGjYmJilC9fPnl7e9u9vnDhQuXLl8+k6OBQt29LH3wgDR9u/f+gIGtvqS5dJIvF7OgAAADggihKAQCyXVBQUIrzCxYs6ORI4BQ7dliLT3v3WqdbtbIObn7ffebGBQAAAJfGmFIAACBrbt6UBg2Sate2FqQKFZK+/FJasoSCFAAAANJFTykAAJB5mzdLXbtKhw9bp9u2lT75RAoJMTcuAAAAuA16SgEAgIy7dk3q00eqV89akAoNlb7/XlqwgIIUAAAAMoWeUgAAIGPWrJG6dZOioqzTnTtbBzMvUMDcuAAAAOCW6CkFAADSFhNjLUY1aWItSBUvLi1fLs2cSUEKAAAAWUZRCgAApO7HH6WKFaUZM6zTPXtK+/dLzZqZGxcAAADcHrfvAQCA5C5dkvr2lebPt06XKSN9/rlUv76pYQEAAMBz0FMKAAD8P8OQFi6UIiOtBSkvL+mNN6S9eylIAQAAIFvRUwoAAFhFR1tvz/v+e+t0xYrWcaNq1TI3LgAAAHgkekoBAJDTGYY0Z461d9T330u5ckmDB0s7dlCQAgAAgMPQUwoAgJzs9Gnp5ZetT9OTpOrVrWNHValiblwAAADwePSUAgAgJ0pKkqZMsd6it3y55OcnffCB9OuvFKQAAADgFPSUAgAgpzl2THrpJWnDBuv0ww9be0eVK2duXAAAAMhR6CkFAEBOkZgojRsnPfCAtSCVJ4/0ySfSxo0UpAAAAOB09JQCACAnOHBA6tpV+u036/Sjj0rTp0slS5obFwAAAHIsekoBAODJbt+W3n9fqlrVWpAKDJRmzJBWraIgBQAAAFPRUwoAAE+1c6fUpYu0Z491ulUr6+Dm991nblwAAACA6CkFAIDnuXlTevttqVYta0GqUCHpyy+lJUsoSAEAAMBl0FMKAABP8ssv1rGjfv/dOt22rXUw85AQc+MCAAAA/oGeUgAAeIJr16S+faVHHrEWpEJDpe+/lxYsoCAFAAAAl0RPKQAA3N3atdJLL0lRUdbpTp2k8eOlAgVMDQsAAABICz2lAABwVzExUvfu0qOPWgtSxYtLy5dLs2ZRkAIAAIDLoygFAIA7+uknqWJFafp06/Srr0r790vNmpkbFwAAAJBB3L4HAIA7uXxZ6tNHmj/fOl2mjDRjhtSggblxAQAAAJlETykAANzFt99KkZHWgpSXl/T669KePRSkAAAA4JboKQUAgKs7f17q2VNatMg6XbGiNHOmVKuWuXEBAAAA94CeUgAAuCrDkObOtfaOWrRIypVLGjxY2rGDghQAAADcHj2lAABwRadPSy+/bH2aniRVq2btHVWlirlxAQAAANnE7XpKJSQk6MEHH5TFYtHu3bvNDgcA4ILcOlckJUlTp1pv0Vu+XPLzk0aNkn77jYIUAGQjt84VAOAh3K4o9eabb6po0aJmhwEAcGFumyuOHZMaN5Z69JDi46W6daXdu6WBA6237gEAso3b5goA8CBuVZRatmyZVq5cqbFjx5odCgDARbllrkhMlMaPlx54QNqwQcqTR/r4Y2njRql8ebOjAwCP45a5AgA8kNtcdv3zzz/VrVs3LV68WHny5DE7HACAC3LLXHHggNS1q/X2PEl69FHps8+kUqXMjQsAPJRb5goA8FBu0VPKMAx16tRJr7zyimrUqJHh9RISEhQbG2v3BwDwTG6XK27flt5/3zqA+W+/SYGB0vTp0qpVFKQAwEHcLlcAgIcztSg1cOBAWSyWNP9+//13TZw4UXFxcRo0aFCmtj9q1CgFBQXZ/sLDwx30SQAAjuKRuWLXLqlWLendd6Vbt6QnnrD2mHrpJclicfz7A4CH8chcAQA5gMUwDMOsN7948aIuX76c5jKlSpXSc889p6VLl8rytxP1xMREeXt7q3379pozZ06K6yYkJCghIcE2HRsbq/DwcMXExCgwMDB7PgTgIRKTDG2NuqILcTcVEuCvWiULytuLxnFOExsbq6CgIJc6TnpUrrh5U3rvPenDD63jSBUqJH3yidSundOKUfzWAdwrcgXtCiAtnGtAyniuMLUolVGnT5+26yJ77tw5NWvWTN9++61q166tYsWKZWg7rphAAVewfH+0hi09qOiYm7Z5YUH+GtIqUs0rhZkYGZzNnY+TLp8rtmyRunSRfv/dOv3cc9LEiVJISPa9Rzr4rQPIDuQK994HgCNxroG7MnqcdIuBzosXL243nS9fPklS6dKlM5w4AKRs+f5o9fhip/5ZnT4fc1M9vtipKR2qkUDgFlw2V1y7Jv3nP9an6RmGFBoqTZ4sPfWUU8Pgtw4ALpwrAA/AuQaywi0GOgfgGIlJhoYtPZgscUiyzRu29KASk1y+QyXgmtaulR54QJowwVqQ6tRJOnjQ6QUpfusAAMCRONdAVrlFT6l/KlGihNzgrkPA5W2NumLXtfafDEnRMTe1NeqK6pQu5LzAgGxgaq6IiZHefFP67DPrdHi49f+bNzclHH7rAJAy2hVA9uBcA1lFTykgB7sQl3riyMpyACT99JNUseL/F6R69JD27zetICXxWwcAAI7FuQayyi17SgHIHiEB/tm6HJCjXb4s9e0rffGFdbpMGWnGDKlBA1PDkvitAwAAx+JcA1lFTykgB6tVsqDCgvyV2gNaLbI+LaNWyYLODAtwP99+K0VGWgtSXl7SgAHSnj0uUZCS+K0DAADH4lwDWUVRCsjBvL0sGtIqUpKSJZC700NaRcrbK7X0AuRw589LzzwjPfusdOGCtTD1yy/S2LFSnjxmR2fDbx0AADgS5xrIKopSQA7XvFKYpnSoptAg+660oUH+PLYVSI1hSHPnWotQixZJuXJJ774r7dwp1a5tdnQp4rcOAAAciXMNZAVjSgFQ80pheiwyVFujruhC3E2FBFi71nIlA0jBmTPSyy9Ly5ZZp6tVk2bOlKpUMTeuDOC3DgAAHIlzDWQWRSkAkqxdbnk8K5CGpCRp+nTpjTekuDjJz08aOlR6/XVrTyk3wW8dAAA4EucayAz3OYsGAMAsFy5IbdtK69dbp+vWlT7/XCpf3tSwAAAAAHfGmFIAAKQnf37p0iXr4OUffyxt3EhBCgAAALhH9JQCACA9vr7Sl19KefNKpUqZHQ0AAADgEShKAQCQEZUrmx0BAAAA4FG4fQ8AAAAAAABOR1EKAAAAAAAATkdRCgAAAAAAAE5HUQoAAAAAAABOR1EKAAAAAAAATkdRCgAAAAAAAE5HUQoAAAAAAABOR1EKAAAAAAAATkdRCgAAAAAAAE5HUQoAAAAAAABOR1EKAAAAAAAATkdRCgAAAAAAAE5HUQoAAAAAAABOR1EKAAAAAAAATkdRCgAAAAAAAE5HUQoAAAAAAABOR1EKAAAAAAAATkdRCgAAAAAAAE5HUQoAAAAAAABOR1EKAAAAAAAATpfL7AAAwFkSkwxtjbqiC3E3FRLgr1olC8rby2J2WHADfHcAAABwF+eG2YeiFIAcYfn+aA1belDRMTdt88KC/DWkVaSaVwozMTK4Or47AAAAuItzw+zF7XsAPN7y/dHq8cVOu8QhSedjbqrHFzu1fH+0SZHB1fHdAQAAwF2cG2Y/typK/fTTT6pdu7Zy586tAgUKqE2bNmaHBMDFJSYZGrb0oIwUXrs7b9jSg0pMSmkJuKPsyhV8dwDAc9GuAJBZnBs6htvcvvfdd9+pW7duGjlypBo3bqw7d+5o//79ZocFwMVtjbqS7ErG3xmSomNuamvUFdUpXch5gcEhsjNX7Dj5F98dAPBAtCsAZAXtCsdwi6LUnTt31KdPH40ZM0Zdu3a1zY+MjDQxKgDu4EJc6okjK8vBdWV3rrgYz3cHADwN7QoAWUW7wjHc4va9nTt36uzZs/Ly8lLVqlUVFhamxx9/nCsaANIVEuCfrcvBdWV3rgjOx3cHADwN7QoAWUW7wjHcoih14sQJSdLQoUP1n//8Rz/++KMKFCighg0b6sqVK6mul5CQoNjYWLs/ADlLrZIFFRbkr9Qe0GqR9WkZtUoWdGZYcIDszhXVSxTguwMAHoZ2BYCsol3hGKYWpQYOHCiLxZLm3++//66kpCRJ0jvvvKNnnnlG1atX16xZs2SxWLRw4cJUtz9q1CgFBQXZ/sLDw5310QC4CG8vi4a0snbJ/2cCuTs9pFWkvL1SSy8wm1m5gu8OALgP2hUAHI1zQ8ewGIZh2tDwFy9e1OXLl9NcplSpUtq8ebMaN26sn3/+WY888ojttdq1a6tJkyYaMWJEiusmJCQoISHBNh0bG6vw8HDFxMQoMDAwez4EALewfH+0hi09aDc4YViQv4a0ilTzSmEmRuZaYmNjFRQU5FLHSbNzBd8dALBHrqBdAeRknBtmTEZzhakDnQcHBys4ODjd5apXry4/Pz8dPnzYljxu376tkydPKiIiItX1/Pz85Ofnl23xAnBfzSuF6bHIUG2NuqILcTcVEmDtWsuVDNdndq7guwMArs/sXAEg5+DcMHu5xdP3AgMD9corr2jIkCEKDw9XRESExowZI0l69tlnTY4OgLvw9rLweFYP5shcwXcHADwD7QoA2YFzw+zjFkUpSRozZoxy5cqlF154QTdu3FDt2rW1du1aFShQwOzQAAAuglwBAEgPuQIAXIepY0o5myve/w4AroTjJPsAANLDcZJ9AADpyehx0tSn7wEAAAAAACBnoigFAAAAAAAAp6MoBQAAAAAAAKejKAUAAAAAAACnc5un72WHu2O6x8bGmhwJALimu8fHHPQMjGTIFQCQNnIFuQIA0pPRXJGjilJxcXGSpPDwcJMjAQDXFhcXp6CgILPDMAW5AgAyhlxBrgCA9KSXKyxGDrrEkZSUpHPnzikgIEAWi8XutdjYWIWHh+vMmTM81jWL2If3jn1479iH98YwDMXFxalo0aLy8sqZd3inlStcWU767uekzyrlrM+bkz6r5L6fl1zhmFzhrt8HZ2IfpY39kz72Ufqyax9lNFfkqJ5SXl5eKlasWJrLBAYG8uW8R+zDe8c+vHfsw6zLqVe978pIrnBlOem7n5M+q5SzPm9O+qySe35ecoXjcoU7fh+cjX2UNvZP+thH6cuOfZSRXJEzL20AAAAAAADAVBSlAAAAAAAA4HQUpf7Hz89PQ4YMkZ+fn9mhuC324b1jH9479iFyqpz03c9Jn1XKWZ83J31WKed9XqSN70P62EdpY/+kj32UPmfvoxw10DkAAAAAAABcAz2lAAAAAAAA4HQUpQAAAAAAAOB0FKUAAAAAAADgdB5dlNq4caNatWqlokWLymKxaPHixcmWOXTokJ588kkFBQUpb968qlmzpk6fPm17/ebNm+rZs6cKFSqkfPny6ZlnntGff/7pxE9hrvT2ocViSfFvzJgxtmWuXLmi9u3bKzAwUPnz51fXrl0VHx/v5E9invT2YXx8vHr16qVixYopd+7cioyM1NSpU+2W4XuY9j78888/1alTJxUtWlR58uRR8+bNdfToUbtlcvo+hGcaMWKE6tatqzx58ih//vwZWscwDA0ePFhhYWHKnTu3mjRpkuz34oqykksaNmyYLD+98sorToo4cyZNmqQSJUrI399ftWvX1tatW9NcfuHChSpfvrz8/f1VuXJl/fe//3VSpPcuM5919uzZyf4N/f39nRht1mXkPPSf1q9fr2rVqsnPz09lypTR7NmzHR4nnO/s2bPq0KGDChUqpNy5c6ty5cravn277XV3PU5nlxIlSqTYvujZs6ckzukkKTExUe+++65Kliyp3Llzq3Tp0ho+fLj+Plx0Tv8excXFqW/fvoqIiFDu3LlVt25dbdu2zfZ6Ttw/6eWljOwTR7TtPboode3aNVWpUkWTJk1K8fXjx4/rkUceUfny5bV+/Xrt3btX7777rt3JTr9+/bR06VItXLhQGzZs0Llz5/T000876yOYLr19GB0dbfc3c+ZMWSwWPfPMM7Zl2rdvrwMHDmjVqlX68ccftXHjRnXv3t1ZH8F06e3D/v37a/ny5friiy906NAh9e3bV7169dIPP/xgW4bvYer70DAMtWnTRidOnNCSJUu0a9cuRUREqEmTJrp27ZptuZy+D+GZbt26pWeffVY9evTI8DoffvihPvnkE02dOlW//fab8ubNq2bNmunmzZsOjPTeZTWXdOvWzS5Pffjhh06INnO+/vpr9e/fX0OGDNHOnTtVpUoVNWvWTBcuXEhx+V9++UXt2rVT165dtWvXLrVp00Zt2rTR/v37nRx55mX2s0pSYGCg3b/hqVOnnBhx1qWX//8pKipKLVu2VKNGjbR792717dtXL730klasWOHgSOFMf/31lx5++GH5+Pho2bJlOnjwoMaNG6cCBQrYlnHX43R22bZtm91vftWqVZKkZ599VhLndJI0evRoTZkyRZ9++qkOHTqk0aNH68MPP9TEiRNty+T079FLL72kVatWad68edq3b5+aNm2qJk2a6OzZs5Jy5v5JLy9lZJ84pG1v5BCSjO+//95uXtu2bY0OHTqkus7Vq1cNHx8fY+HChbZ5hw4dMiQZW7ZscVSoLiulffhPrVu3Nho3bmybPnjwoCHJ2LZtm23esmXLDIvFYpw9e9ZRobqslPZhxYoVjffee89uXrVq1Yx33nnHMAy+h//0z314+PBhQ5Kxf/9+27zExEQjODjYmD59umEY7EN4vlmzZhlBQUHpLpeUlGSEhoYaY8aMsc27evWq4efnZ3z11VcOjPDeZDWXNGjQwOjTp48TIrw3tWrVMnr27GmbTkxMNIoWLWqMGjUqxeWfe+45o2XLlnbzateubbz88ssOjTM7ZPazZvS77eoycg715ptvGhUrVrSb17ZtW6NZs2YOjAzO9tZbbxmPPPJIqq+763Hakfr06WOULl3aSEpK4pzuf1q2bGl06dLFbt7TTz9ttG/f3jAMvkfXr183vL29jR9//NFu/t02Vk7fP4aRPC9lZJ84qm3v0T2l0pKUlKSffvpJ999/v5o1a6aQkBDVrl3brgvbjh07dPv2bTVp0sQ2r3z58ipevLi2bNliQtSu7c8//9RPP/2krl272uZt2bJF+fPnV40aNWzzmjRpIi8vL/32229mhOly6tatqx9++EFnz56VYRhat26djhw5oqZNm0rie5iehIQESbLr4ejl5SU/Pz9t2rRJEvsQuCsqKkrnz5+3+y0EBQWpdu3aLv1buJdcMn/+fBUuXFiVKlXSoEGDdP36dUeHmym3bt3Sjh077P5NvLy81KRJk1T/TbZs2WK3vCQ1a9bMpf8Npax9Vsl6m3tERITCw8PVunVrHThwwBnhOp27/rsic3744QfVqFFDzz77rEJCQlS1alVNnz7d9rq7Hqcd5datW/riiy/UpUsXWSwWzun+p27dulqzZo2OHDkiSdqzZ482bdqkxx9/XBLfozt37igxMTHZ7d65c+fWpk2bcvz+SUlG9omj2vY5tih14cIFxcfH64MPPlDz5s21cuVKPfXUU3r66ae1YcMGSdL58+fl6+ubbJyOIkWK6Pz58yZE7drmzJmjgIAAu+6z58+fV0hIiN1yuXLlUsGCBdmH/zNx4kRFRkaqWLFi8vX1VfPmzTVp0iTVr19fEt/D9Nw9ERk0aJD++usv3bp1S6NHj9Yff/yh6OhoSexD4K673/ciRYrYzXf130JWc8nzzz+vL774QuvWrdOgQYM0b948dejQwdHhZsqlS5eUmJiYqX+T8+fPu92/oZS1z1quXDnNnDlTS5Ys0RdffKGkpCTVrVtXf/zxhzNCdqrU/l1jY2N148YNk6JCdjtx4oSmTJmismXLasWKFerRo4d69+6tOXPmSHLf47SjLF68WFevXlWnTp0kcU5318CBA/Xvf/9b5cuXl4+Pj6pWraq+ffuqffv2kvgeBQQEqE6dOho+fLjOnTunxMREffHFF9qyZYuio6Nz/P5JSUb2iaPa9rmyvKabS0pKkiS1bt1a/fr1kyQ9+OCD+uWXXzR16lQ1aNDAzPDc0syZM9W+fXu3GYDUVUycOFG//vqrfvjhB0VERGjjxo3q2bOnihYtmuyKKZLz8fHRokWL1LVrVxUsWFDe3t5q0qSJHn/8cbvBHgF3MXDgQI0ePTrNZQ4dOqTy5cs7KSLHyehnzaq/j3FQuXJlhYWF6dFHH9Xx48dVunTpLG8XzlOnTh3VqVPHNl23bl1VqFBB06ZN0/Dhw02MDMiapKQk1ahRQyNHjpQkVa1aVfv379fUqVPVsWNHk6NzPZ9//rkef/xxFS1a1OxQXMo333yj+fPn68svv1TFihVt49AVLVqU79H/zJs3T126dNF9990nb29vVatWTe3atdOOHTvMDg3/kGOLUoULF1auXLkUGRlpN79ChQq2W35CQ0N169YtXb161a4a/+effyo0NNSZ4bq8n3/+WYcPH9bXX39tNz80NDTZ4KV37tzRlStX2IeSbty4obffflvff/+9WrZsKUl64IEHtHv3bo0dO1ZNmjThe5gB1atX1+7duxUTE6Nbt24pODhYtWvXtnUtZR/CnQwYMMB2RTg1pUqVytK2737f//zzT4WFhdnm//nnn3rwwQeztM17kdHPml25pHbt2pKkY8eOuUxRqnDhwvL29k725Ki0jk+hoaGZWt5VZOWz/tPdHgHHjh1zRIimSu3fNTAwULlz5zYpKmS3sLCwFNsf3333nSTXO06b6dSpU1q9erUWLVpkm8c5ndUbb7xh6y0lWS+8nDp1SqNGjVLHjh35HkkqXbq0NmzYoGvXrik2NlZhYWFq27at7bxCytn7558ysk8c1bbPsbfv+fr6qmbNmjp8+LDd/CNHjigiIkKStaHr4+OjNWvW2F4/fPiwTp8+bXfVDtarGNWrV1eVKlXs5tepU0dXr161q0ivXbtWSUlJtsZBTnb79m3dvn1bXl72P0Vvb29bbz6+hxkXFBSk4OBgHT16VNu3b1fr1q0lsQ/hXoKDg1W+fPk0/3x9fbO07ZIlSyo0NNTutxAbG6vffvvNlN9CRj9rduWS3bt3S5LdyZbZfH19Vb16dbt/k6SkJK1ZsybVf5M6derYLS9Jq1atcvnjWVY+6z8lJiZq3759LvVvmF3c9d8VmfPwww+n2f5wteO0mWbNmqWQkBDbhVuJc7q7rl+/nmb7ge/R/8ubN6/CwsL0119/acWKFWrdujX7JwUZ2ScOa9tneYh0NxAXF2fs2rXL2LVrlyHJGD9+vLFr1y7j1KlThmEYxqJFiwwfHx/js88+M44ePWpMnDjR8Pb2Nn7++WfbNl555RWjePHixtq1a43t27cbderUMerUqWPWR3K69PahYRhGTEyMkSdPHmPKlCkpbqN58+ZG1apVjd9++83YtGmTUbZsWaNdu3bO+gimS28fNmjQwKhYsaKxbt0648SJE8asWbMMf39/Y/LkybZt8D1Mex9+8803xrp164zjx48bixcvNiIiIoynn37abhs5fR/CM506dcrYtWuXMWzYMCNfvny230lcXJxtmXLlyhmLFi2yTX/wwQdG/vz5jSVLlhh79+41WrdubZQsWdK4ceOGGR8hw9LLJX/88YdRrlw547fffjMMwzCOHTtmvPfee8b27duNqKgoY8mSJUapUqWM+vXrm/URUrVgwQLDz8/PmD17tnHw4EGje/fuRv78+Y3z588bhmEYL7zwgjFw4EDb8ps3bzZy5cpljB071jh06JAxZMgQw8fHx9i3b59ZHyHDMvtZhw0bZqxYscI4fvy4sWPHDuPf//634e/vbxw4cMCsj5Bh6eWugQMHGi+88IJt+RMnThh58uQx3njjDePQoUPGpEmTDG9vb2P58uVmfQQ4wNatW41cuXIZI0aMMI4ePWrMnz/fyJMnj/HFF1/YlnHX43R2SkxMNIoXL2689dZbyV7jnM4wOnbsaNx3333Gjz/+aERFRRmLFi0yChcubLz55pu2ZXL692j58uXGsmXLjBMnThgrV640qlSpYtSuXdu4deuWYRg5c/+kl5cysk8c0bb36KLUunXrDEnJ/jp27Ghb5vPPPzfKlClj+Pv7G1WqVDEWL15st40bN24Yr776qlGgQAEjT548xlNPPWVER0c7+ZOYJyP7cNq0aUbu3LmNq1evpriNy5cvG+3atTPy5ctnBAYGGp07d7ZrMHm69PZhdHS00alTJ6No0aKGv7+/Ua5cOWPcuHFGUlKSbRt8D9Pehx9//LFRrFgxw8fHxyhevLjxn//8x0hISLDbRk7fh/BMHTt2TPG3sW7dOtsykoxZs2bZppOSkox3333XKFKkiOHn52c8+uijxuHDh50ffCall0uioqLsPvvp06eN+vXrGwULFjT8/PyMMmXKGG+88YYRExNj0idI28SJE43ixYsbvr6+Rq1atYxff/3V9lqDBg3s8q5hWIvx999/v+Hr62tUrFjR+Omnn5wccdZl5rP27dvXtmyRIkWMFi1aGDt37jQh6sxLL3d17NjRaNCgQbJ1HnzwQcPX19coVaqU3W8XnmPp0qVGpUqVDD8/P6N8+fLGZ599Zve6ux6ns9OKFSsMSSl+bs7pDCM2Ntbo06ePUbx4ccPf398oVaqU8c4779id/+b079HXX39tlCpVyvD19TVCQ0ONnj172rVXc+L+SS8vZWSfOKJtbzEMRgIGAAAAAACAc+XYMaUAAAAAAABgHopSAAAAAAAAcDqKUgAAAAAAAHA6ilIAAAAAAABwOopSAAAAAAAAcDqKUgAAAAAAAHA6ilIAAAAAAABwOopSAAAAAAAAcDqKUgAAwKWtX79eFotFV69eNTuUTLFYLFq8eHG2ba9EiRKaMGFCtm3PLCdPnpTFYtHu3bslue+/L4CcwzAMde/eXQULFrQdvxo2bKi+ffs6LYbZs2crf/78Dn0PjscwA0UpAABgGovFkubf0KFDzQ4xXUOHDtWDDz6YbH50dLQef/xxp8Zy5coV9e3bVxEREfL19VXRokXVpUsXnT592qlx3NWpUye1adPGbl54eLiio6NVqVIlU2ICgMxavny5Zs+erR9//NF2/Fq0aJGGDx9uWyalCwfOKCQB7i6X2QEAAICcKzo62vb/X3/9tQYPHqzDhw/b5uXLl0/bt283IzTdunVLvr6+WV4/NDQ0G6NJ35UrV/TQQw/J19dXU6dOVcWKFXXy5En95z//Uc2aNbVlyxaVKlXKqTGlxNvb2+n7BgDuxfHjxxUWFqa6deva5hUsWNDEiADPQU8pwMkuXryo0NBQjRw50jbvl19+ka+vr9asWWNiZADgfKGhoba/oKAgWSwWu3n58uWzLbtjxw7VqFFDefLkUd26de2KV5K0ZMkSVatWTf7+/ipVqpSGDRumO3fu2F4/ffq0WrdurXz58ikwMFDPPfec/vzzT9vrd3s8zZgxQyVLlpS/v78k6erVq3rppZcUHByswMBANW7cWHv27JFkvQo+bNgw7dmzx9a7a/bs2ZKS3773xx9/qF27dipYsKDy5s2rGjVq6LfffpNkbfC0bt1aRYoUUb58+VSzZk2tXr06U/vynXfe0blz57R69Wo9/vjjKl68uOrXr68VK1bIx8dHPXv2tC2b0hX9Bx980K5n2vjx41W5cmXlzZtX4eHhevXVVxUfH297/W4PgBUrVqhChQrKly+fmjdvbis0Dh06VHPmzNGSJUts+2b9+vXJbt9LyaZNm1SvXj3lzp1b4eHh6t27t65du2Z7ffLkySpbtqz8/f1VpEgR/etf/8rUvgKAjOrUqZNee+01nT59WhaLRSVKlJAku9v3GjZsqFOnTqlfv352x7vOnTsrJiYmWe/fhIQEvf7667rvvvuUN29e1a5dW+vXr7d739mzZ6t48eLKkyePnnrqKV2+fDnNOOvWrau33nrLbt7Fixfl4+OjjRs3SpLmzZunGjVqKCAgQKGhoXr++ed14cKFVLeZUk/gCRMm2PbBXTNmzFCFChXk7++v8uXLa/LkybbXbt26pV69eiksLEz+/v6KiIjQqFGj0vwsyFkoSgFOFhwcrJkzZ2ro0KHavn274uLi9MILL6hXr1569NFHzQ4PAFzWO++8o3Hjxmn79u3KlSuXunTpYnvt559/1osvvqg+ffro4MGDmjZtmmbPnq0RI0ZIkpKSktS6dWtduXJFGzZs0KpVq3TixAm1bdvW7j2OHTum7777TosWLbIVTZ599llduHBBy5Yt044dO1StWjU9+uijunLlitq2basBAwaoYsWKio6OVnR0dLJtSlJ8fLwaNGigs2fP6ocfftCePXv05ptvKikpyfZ6ixYttGbNGu3atUvNmzdXq1atMnzbXVJSkhYsWKD27dsn64WUO3duvfrqq1qxYoWuXLmS4f3t5eWlTz75RAcOHNCcOXO0du1avfnmm3bLXL9+XWPHjtW8efO0ceNGnT59Wq+//rok6fXXX9dzzz1nK1RFR0fb9TJIzfHjx9W8eXM988wz2rt3r77++mtt2rRJvXr1kiRt375dvXv31nvvvafDhw9r+fLlql+/foY/FwBkxscff6z33ntPxYoVU3R0tLZt25ZsmUWLFqlYsWJ677337I53EyZMUGBgoG3e3eNjr169tGXLFi1YsEB79+7Vs88+q+bNm+vo0aOSpN9++01du3ZVr169tHv3bjVq1Ejvv/9+mnG2b99eCxYskGEYtnlff/21ihYtqnr16kmSbt++reHDh2vPnj1avHixTp48qU6dOt3T/pk/f74GDx6sESNG6NChQxo5cqTeffddzZkzR5L0ySef6IcfftA333yjw4cPa/78+cmKWsjhDACmePXVV43777/feP75543KlSsbN2/eNDskADDVrFmzjKCgoGTz161bZ0gyVq9ebZv3008/GZKMGzduGIZhGI8++qgxcuRIu/XmzZtnhIWFGYZhGCtXrjS8vb2N06dP214/cOCAIcnYunWrYRiGMWTIEMPHx8e4cOGCbZmff/7ZCAwMTHaMLl26tDFt2jTbelWqVEkWtyTj+++/NwzDMKZNm2YEBAQYly9fzuDeMIyKFSsaEydOtE1HREQYH330UYrLnj9/3pCU6uuLFi0yJBm//fZbqtuqUqWKMWTIkFTjWbhwoVGoUCHb9KxZswxJxrFjx2zzJk2aZBQpUsQ23bFjR6N169Z224mKijIkGbt27TIM4///ff/66y/DMAyja9euRvfu3e3W+fnnnw0vLy/jxo0bxnfffWcEBgYasbGxqcYKANnpo48+MiIiIuzmNWjQwOjTp49tOqXjakp57dSpU4a3t7dx9uxZu/mPPvqoMWjQIMMwDKNdu3ZGixYt7F5v27ZtijnyrgsXLhi5cuUyNm7caJtXp04d46233kp1nW3bthmSjLi4OMMwkh+PU8pv/9wXpUuXNr788ku7ZYYPH27UqVPHMAzDeO2114zGjRsbSUlJqcaBnI0xpQCTjB07VpUqVdLChQu1Y8cO+fn5mR0SALi0Bx54wPb/YWFhkqQLFy6oePHi2rNnjzZv3mzrGSVJiYmJunnzpq5fv65Dhw4pPDxc4eHhttcjIyOVP39+HTp0SDVr1pQkRUREKDg42LbMnj17FB8fr0KFCtnFcuPGDR0/fjzDse/evVtVq1ZNdQyS+Ph4DR06VD/99JOio6N1584d3bhxI9MDlBt/u0KeksyMkbV69WqNGjVKv//+u2JjY3Xnzh3b/syTJ48kKU+ePCpdurRtnbCwsDRvBcmIPXv2aO/evZo/f75tnmEYSkpKUlRUlB577DFFRESoVKlSat68uZo3b66nnnrKFhMAuLJ9+/YpMTFR999/v938hIQEW645dOiQnnrqKbvX69Spo+XLl6e63eDgYDVt2lTz589XvXr1FBUVpS1btmjatGm2ZXbs2KGhQ4dqz549+uuvv2y9dU+fPq3IyMhMf5Zr167p+PHj6tq1q7p162abf+fOHQUFBUmy3v742GOPqVy5cmrevLmeeOIJNW3aNNPvBc9FUQowyfHjx3Xu3DklJSXp5MmTqly5stkhAYBL8/Hxsf2/xWKRJLvb34YNG6ann3462Xp3x4bKiLx589pNx8fHKywsLNlYH5Iy9USl3Llzp/n666+/rlWrVmns2LEqU6aMcufOrX/961+6detWhrYfHBxsK7Cl5NChQ8qVK5dKliwpyXpr3j8LWLdv37b9/8mTJ/XEE0+oR48eGjFihAoWLKhNmzapa9euunXrlq0A9Pd/E8n675JeYSw98fHxevnll9W7d+9krxUvXly+vr7auXOn1q9fr5UrV2rw4MEaOnSotm3bxlOuALi8+Ph4eXt7a8eOHfL29rZ77e/jKGZF+/bt1bt3b02cOFFffvmlKleubGtjXLt2Tc2aNVOzZs00f/58BQcH6/Tp02rWrFmquSa9XHF3nMHp06erdu3adsvd/WzVqlVTVFSUli1bptWrV+u5555TkyZN9O23397TZ4XnoCgFmODWrVvq0KGD2rZtq3Llyumll17Svn37FBISYnZoAOCWqlWrpsOHD6tMmTIpvl6hQgWdOXNGZ86csfWWOnjwoK5evZrm1eFq1arp/PnzypUrV6pjYPj6+ioxMTHN+B544AHNmDFDV65cSbG31ObNm9WpUyfblfH4+HidPHkyzW3+nZeXl5577jnNnz9f7733nt24Ujdu3NDkyZP11FNP2a5cBwcH2z35MDY2VlFRUbbpHTt2KCkpSePGjZOXl3UI0m+++SbD8dyVkX3zT9WqVdPBgwdT/beUpFy5cqlJkyZq0qSJhgwZovz582vt2rUpFiUBwBlSOt6lNK9q1apKTEzUhQsXbGM9/VOFChVsD8K469dff003htatW6t79+5avny5vvzyS7344ou2137//XddvnxZH3zwgS0Ppvd02+DgYJ0/f16GYdguBv39IRVFihRR0aJFdeLECbVv3z7V7QQGBqpt27Zq27at/vWvf6l58+ap5kPkPAx0DpjgnXfeUUxMjD755BO99dZbuv/+++0G7AUAZM7gwYM1d+5cDRs2TAcOHNChQ4e0YMEC/ec//5EkNWnSRJUrV1b79u21c+dObd26VS+++KIaNGigGjVqpLrdJk2aqE6dOmrTpo1WrlypkydP6pdfftE777xjO5kvUaKEoqKitHv3bl26dEkJCQnJttOuXTuFhoaqTZs22rx5s06cOKHvvvtOW7ZskSSVLVvWNrj6nj179Pzzz9t6gWXUiBEjFBoaqscee0zLli3TmTNntHHjRjVr1kxeXl76+OOPbcs2btxY8+bN088//6x9+/apY8eOdlfsy5Qpo9u3b2vixIk6ceKE5s2bp6lTp2Yqnrv7Zu/evTp8+LAuXbpkd4U9NW+99ZZ++eUX2wC/R48e1ZIlS2wDnf/444/65JNPtHv3bp06dUpz585VUlKSypUrl+n4ACC7lChRQhs3btTZs2d16dIl27z4+HitWbNGly5d0vXr13X//ferffv2evHFF7Vo0SJFRUVp69atGjVqlH766SdJUu/evbV8+XKNHTtWR48e1aeffprmrXt35c2bV23atNG7776rQ4cOqV27drbX7vY0vXtc/+GHHzR8+PA0t9ewYUNdvHhRH374oY4fP65JkyZp2bJldssMGzZMo0aN0ieffKIjR45o3759mjVrlsaPHy/J+iTXr776Sr///ruOHDmihQsXKjQ0lJ6tsKEoBTjZ+vXrNWHCBM2bN0+BgYHy8vKyNQymTJlidngA4JaaNWumH3/8UStXrlTNmjX10EMP6aOPPlJERIQk621lS5YsUYECBVS/fn01adJEpUqV0tdff53mdi0Wi/773/+qfv366ty5s+6//379+9//1qlTp1SkSBFJ0jPPPKPmzZurUaNGCg4O1ldffZVsO76+vlq5cqVCQkLUokULVa5cWR988IGtEDR+/HgVKFBAdevWVatWrdSsWTNVq1YtU/ugcOHC+vXXX9WoUSO9/PLLKlmypBo0aKDExETt3r3bNg6XJA0aNEgNGjTQE088oZYtW6pNmzZ2Y0NVqVJF48eP1+jRo1WpUiXNnz8/S4/w7tatm8qVK6caNWooODhYmzdvTnedBx54QBs2bNCRI0dUr149Va1aVYMHD1bRokUlWW+bXLRokRo3bqwKFSpo6tSp+uqrr1SxYsVMxwcA2eW9997TyZMnVbp0advYhHXr1tUrr7yitm3bKjg4WB9++KEkadasWXrxxRc1YMAAlStXTm3atNG2bdtUvHhxSdJDDz2k6dOn6+OPP1aVKlW0cuVK20WW9LRv315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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# residuals:\n", "residuals = fitStudents.resid\n", "fittedvalues = fitStudents.fittedvalues\n", "\n", "fig, (ax0, ax1, ax2) = plt.subplots(1,3,figsize=(12,4))\n", "\n", "# plot residuals versus x-values:\n", "ax0.scatter(student[\"x\"],student[\"residuals\"])\n", "ax0.set_xlabel(\"x\")\n", "ax0.set_ylabel(\"residuals\")\n", "\n", "# qq-plot of resiudals:\n", "sm.qqplot(residuals,ax=ax1, line='s')\n", "ax1.set_title(\"QQ plot of residuals\")\n", "\n", "# plot residuals versus fitted values:\n", "ax2.scatter(fittedvalues,residuals)\n", "ax2.set_xlabel(\"fitted values\")\n", "ax2.set_ylabel(\"residuals\")\n", "\n", "plt.tight_layout()\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Another example:\n", "\n", "beta_0 = 50\n", "beta_1 = 200\n", "sigma = 90\n", "\n", "# choose som random x-values:\n", "x = stats.uniform.rvs(size = 90, loc=0, scale = 20)\n", "# simulate y-values from statistical model:\n", "y = beta_0 + beta_1*x + x*stats.norm.rvs(size = 90, loc=0, scale = sigma)\n", "\n", "plt.scatter(x,y)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Is the normal assumption fulfilled here??" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [], "source": [ "\n", "data = pd.DataFrame({'x': x, 'y': y}) # OBS: use the pandas library (pd)\n", "linfit = smf.ols(formula = 'y ~ x', data=data).fit()\n", "\n", "data[\"residuals\"] = linfit.resid\n", "fittedvalues = linfit.fittedvalues\n" ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "fig, (ax0, ax1, ax2) = plt.subplots(1,3,figsize=(12,4))\n", "\n", "# plot residuals versus x-values:\n", "ax0.scatter(data[\"x\"],data[\"residuals\"])\n", "ax0.set_xlabel(\"x\")\n", "ax0.set_ylabel(\"residuals\")\n", "\n", "# qq-plot of resiudals:\n", "sm.qqplot(data[\"residuals\"],ax=ax1, line='s')\n", "ax1.set_title(\"QQ plot of residuals\")\n", "\n", "# plot residuals versus fitted values:\n", "ax2.scatter(fittedvalues,data[\"residuals\"])\n", "ax2.set_xlabel(\"fitted values\")\n", "ax2.set_ylabel(\"residuals\")\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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": "3.11.9" } }, "nbformat": 4, "nbformat_minor": 2 }