From f96aefc0e3d110d9f982cdfd0497c2755da599f3 Mon Sep 17 00:00:00 2001 From: Gerardo Marx Date: Wed, 27 May 2026 20:45:17 -0600 Subject: [PATCH] last session --- 8-correlation/gdp-satisfaction.csv | 30 ++ 8-correlation/session.ipynb | 446 +++++++++++++++++++++++++++++ 9-confident-hypothesis/main.ipynb | 336 +++++++++++++++++++++- 3 files changed, 805 insertions(+), 7 deletions(-) create mode 100644 8-correlation/gdp-satisfaction.csv create mode 100644 8-correlation/session.ipynb diff --git a/8-correlation/gdp-satisfaction.csv b/8-correlation/gdp-satisfaction.csv new file mode 100644 index 0000000..ea65e6f --- /dev/null +++ b/8-correlation/gdp-satisfaction.csv @@ -0,0 +1,30 @@ +Country,GDP per capita,Life satisfaction +Russia,9054.914,6.0 +Turkey,9437.372,5.6 +Hungary,12239.894,4.9 +Poland,12495.334,5.8 +Slovak Republic,15991.736,6.1 +Estonia,17288.083,5.6 +Greece,18064.288,4.8 +Portugal,19121.592,5.1 +Slovenia,20732.482,5.7 +Spain,25864.721,6.5 +Korea,27195.197,5.8 +Italy,29866.581,6.0 +Japan,32485.545,5.9 +Israel,35343.336,7.4 +New Zealand,37044.891,7.3 +France,37675.006,6.5 +Belgium,40106.632,6.9 +Germany,40996.511,7.0 +Finland,41973.988,7.4 +Canada,43331.961,7.3 +Netherlands,43603.115,7.3 +Austria,43724.031,6.9 +United Kingdom,43770.688,6.8 +Sweden,49866.266,7.2 +Iceland,50854.583,7.5 +Australia,50961.865,7.3 +Ireland,51350.744,7.0 +Denmark,52114.165,7.5 +United States,55805.204,7.2 diff --git a/8-correlation/session.ipynb b/8-correlation/session.ipynb new file mode 100644 index 0000000..17aaa3e --- /dev/null +++ b/8-correlation/session.ipynb @@ -0,0 +1,446 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 21, + "id": "1f46f36b", + "metadata": {}, + "outputs": [], + "source": [ + "# data ussing a linear model\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "m = 500\n", + "theta0 = 2.5\n", + "theta1 = 5\n", + "disp = 4\n", + "x = np.linspace(0, 5, m)\n", + "y = theta0+theta1*x+disp*np.random.randn(m)" + ] + }, + { + "cell_type": "markdown", + "id": "6d309848", + "metadata": {}, + "source": [ + "$(x_m,y_m)$" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "0419e9fb", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.scatter(x,y,color='black', alpha=0.3, marker='o')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "089205c7", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "np.float64(0.8681163370978059)" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Pearson coefficient\n", + "xMean = x.mean()\n", + "yMean = y.mean()\n", + "\n", + "#Sxx \n", + "xSum = 0 \n", + "for i in range(len(x)):\n", + " xSum = xSum+(x[i]-xMean)**2\n", + " pass\n", + "Sxx = xSum\n", + "\n", + "Syy = np.sum((y-yMean)**2)\n", + "\n", + "Sxy = np.sum((x-xMean)*(y-yMean))\n", + "r = Sxy/np.sqrt(Sxx*Syy)\n", + "r" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "f798a04a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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CountryGDP per capitaLife satisfaction
0Russia9054.9146.0
1Turkey9437.3725.6
2Hungary12239.8944.9
3Poland12495.3345.8
4Slovak Republic15991.7366.1
5Estonia17288.0835.6
6Greece18064.2884.8
7Portugal19121.5925.1
8Slovenia20732.4825.7
9Spain25864.7216.5
10Korea27195.1975.8
11Italy29866.5816.0
12Japan32485.5455.9
13Israel35343.3367.4
14New Zealand37044.8917.3
15France37675.0066.5
16Belgium40106.6326.9
17Germany40996.5117.0
18Finland41973.9887.4
19Canada43331.9617.3
20Netherlands43603.1157.3
21Austria43724.0316.9
22United Kingdom43770.6886.8
23Sweden49866.2667.2
24Iceland50854.5837.5
25Australia50961.8657.3
26Ireland51350.7447.0
27Denmark52114.1657.5
28United States55805.2047.2
\n", + "
" + ], + "text/plain": [ + " Country GDP per capita Life satisfaction\n", + "0 Russia 9054.914 6.0\n", + "1 Turkey 9437.372 5.6\n", + "2 Hungary 12239.894 4.9\n", + "3 Poland 12495.334 5.8\n", + "4 Slovak Republic 15991.736 6.1\n", + "5 Estonia 17288.083 5.6\n", + "6 Greece 18064.288 4.8\n", + "7 Portugal 19121.592 5.1\n", + "8 Slovenia 20732.482 5.7\n", + "9 Spain 25864.721 6.5\n", + "10 Korea 27195.197 5.8\n", + "11 Italy 29866.581 6.0\n", + "12 Japan 32485.545 5.9\n", + "13 Israel 35343.336 7.4\n", + "14 New Zealand 37044.891 7.3\n", + "15 France 37675.006 6.5\n", + "16 Belgium 40106.632 6.9\n", + "17 Germany 40996.511 7.0\n", + "18 Finland 41973.988 7.4\n", + "19 Canada 43331.961 7.3\n", + "20 Netherlands 43603.115 7.3\n", + "21 Austria 43724.031 6.9\n", + "22 United Kingdom 43770.688 6.8\n", + "23 Sweden 49866.266 7.2\n", + "24 Iceland 50854.583 7.5\n", + "25 Australia 50961.865 7.3\n", + "26 Ireland 51350.744 7.0\n", + "27 Denmark 52114.165 7.5\n", + "28 United States 55805.204 7.2" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "#GDP vs life satisfaction:\n", + "import pandas as pd\n", + "data = pd.read_csv('gdp-satisfaction.csv')\n", + "data" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "id": "08b9f450", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0 Russia\n", + "1 Turkey\n", + "2 Hungary\n", + "3 Poland\n", + "4 Slovak Republic\n", + "5 Estonia\n", + "6 Greece\n", + "7 Portugal\n", + "8 Slovenia\n", + "9 Spain\n", + "10 Korea\n", + "11 Italy\n", + "12 Japan\n", + "13 Israel\n", + "14 New Zealand\n", + "15 France\n", + "16 Belgium\n", + "17 Germany\n", + "18 Finland\n", + "19 Canada\n", + "20 Netherlands\n", + "21 Austria\n", + "22 United Kingdom\n", + "23 Sweden\n", + "24 Iceland\n", + "25 Australia\n", + "26 Ireland\n", + "27 Denmark\n", + "28 United States\n", + "Name: Country, dtype: str" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = data[\"GDP per capita\"]\n", + "y = data[\"Life satisfaction\"]\n", + "labels = data[\"Country\"]\n", + "labels" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "id": "deaf6ab9", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "plt.scatter(x,y, color=\"black\", alpha=0.4, marker=\"v\")\n", + "# for i, row in data.iterrows():\n", + "# plt.annotate(data[\"Country\"], (data[\"Life satisfaction\"], data[\"GDP per capita\"]))\n", + "# pass\n", + "# #plt.ylim([0,20])\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".venv (3.14.3)", + "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": "3.14.3" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/9-confident-hypothesis/main.ipynb b/9-confident-hypothesis/main.ipynb index 54fb3b8..89a424d 100644 --- a/9-confident-hypothesis/main.ipynb +++ b/9-confident-hypothesis/main.ipynb @@ -5,7 +5,7 @@ "id": "5b299da0", "metadata": {}, "source": [ - "Lab Example 1 — Sampling variability and CLT\n", + "# Lab Example 1 — Sampling variability and CLT\n", "\n", "Objective: show that individual measurements vary, but sample means are more stable.\n", "\n", @@ -19,7 +19,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "id": "07e7f5cc", "metadata": {}, "outputs": [ @@ -96,7 +96,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 4, "id": "615beff5", "metadata": {}, "outputs": [ @@ -146,7 +146,7 @@ "\n", "Suggested question:\n", "\n", - "Does the confidence interval include 10\\,\\Omega?" + "Does the confidence interval include $10\\,\\Omega$?" ] }, { @@ -160,16 +160,16 @@ "\n", "For the resistor example:\n", "\n", - "H_0: \\mu = 10\n", + "$H_0$: $\\mu = 10$\n", "\n", - "H_a: \\mu \\neq 10\n", + "$H_a$: $\\mu \\neq 10$\n", "\n", "Python:\n" ] }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 7, "id": "2fee9dc6", "metadata": {}, "outputs": [ @@ -192,6 +192,328 @@ "print(\"t statistic:\", t_statistic)\n", "print(\"p-value:\", p_value)" ] + }, + { + "cell_type": "markdown", + "id": "365d78c7", + "metadata": {}, + "source": [ + "If p-value < 0.05, reject H0.\n", + "If p-value >= 0.05, do not reject H0.\n", + "\n", + "A hypothesis test does not prove that the true resistance is exactly 10\\,\\Omega. It only evaluates whether the observed difference is large compared with random variation." + ] + }, + { + "cell_type": "markdown", + "id": "2cc4f360", + "metadata": {}, + "source": [ + "# Lab Example 4 — Comparing two measurement methods\n", + "\n", + "Objective: connect with engineering experiments.\n", + "\n", + "Two instruments measure the same nominal resistor. Determine whether their mean readings are different." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "3cf2b671", + "metadata": {}, + "outputs": [], + "source": [ + "method_A = np.array([10.01, 9.98, 10.03, 9.97, 10.02, 10.00, 10.04, 9.99])\n", + "method_B = np.array([10.08, 10.05, 10.07, 10.03, 10.06, 10.09, 10.04, 10.08])" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "0379e400", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "t statistic: -5.019011475427952\n", + "p-value: 0.0001995796758233766\n" + ] + } + ], + "source": [ + "t_statistic, p_value = stats.ttest_ind(method_A, method_B, equal_var=False)\n", + "\n", + "print(\"t statistic:\", t_statistic)\n", + "print(\"p-value:\", p_value)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "a5ddea29", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/var/folders/0c/2g7zyqyd3lj21c3yr8x3168m0000gn/T/ipykernel_3163/4104677222.py:1: MatplotlibDeprecationWarning: The 'labels' parameter of boxplot() has been renamed 'tick_labels' since Matplotlib 3.9; support for the old name will be dropped in 3.11.\n", + " plt.boxplot([method_A, method_B], labels=[\"Method A\", \"Method B\"])\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.boxplot([method_A, method_B], labels=[\"Method A\", \"Method B\"])\n", + "plt.ylabel(\"Resistance [ohms]\")\n", + "plt.title(\"Comparison of measurement methods\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "5bb81aef", + "metadata": {}, + "source": [ + "Assuming the test was:\n", + "\n", + "$H_0$: $\\mu_A = \\mu_B$\n", + "\n", + "$H_a$: $\\mu_A \\neq \\mu_B$\n", + "\n", + "and using:\n", + "\n", + "$\\alpha = 0.05$\n", + "\n", + "then:\n", + "\n", + "$p = 0.0001996 < 0.05$\n", + "\n", + "Therefore, you reject $H_0$." + ] + }, + { + "cell_type": "markdown", + "id": "6490f025", + "metadata": {}, + "source": [ + "At the 5% significance level, the two-sample t-test provides sufficient evidence to conclude that the mean measurements obtained with Method A and Method B are different. Since the test statistic is negative, Method A has a lower sample mean than Method B.\n", + "\n", + "This result may suggest that the two instruments or methods are not equivalent. The difference could be due to:\n", + "\n", + "* calibration offset,\n", + "* systematic bias,\n", + "* different sensor accuracy,\n", + "* different measurement procedure,\n", + "* environmental or operator effects." + ] + }, + { + "cell_type": "markdown", + "id": "3d06cc2f", + "metadata": {}, + "source": [ + "# Lab Example 5 — Bootstrap confidence interval\n", + "\n", + "Objective: show computational inference without relying only on formulas.\n", + "\n", + "Use the same measurement dataset:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "c4179929", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Bootstrap 95% CI: [ 9.976 10.02268333]\n" + ] + } + ], + "source": [ + "np.random.seed(10)\n", + "\n", + "B = 5000\n", + "bootstrap_means = []\n", + "\n", + "for i in range(B):\n", + " bootstrap_sample = np.random.choice(measurements, size=n, replace=True)\n", + " bootstrap_means.append(bootstrap_sample.mean())\n", + "\n", + "bootstrap_means = np.array(bootstrap_means)\n", + "\n", + "ci_bootstrap = np.percentile(bootstrap_means, [2.5, 97.5])\n", + "\n", + "print(\"Bootstrap 95% CI:\", ci_bootstrap)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "5ca91c65", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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SkpJcj9XusD169LBKlixpur7bWe9i3Yc1ncOHDzddoLV7/TXXXGPNmjXLdIfWbba0x3jjjTdM+nX/G264wdUd+1I2btxozkevZ/ny5a0hQ4ZYH3744SW7nr/33numO7R239XnrFq1qtW3b1/rxIkTbsfX4+lxtYtx2mPqunbL9ySzrudbtmwxQwjo61CsWDGre/fu1rlz59weq92QtauydknW/e666y7TnT79MS+WtvRdz5V2B9fn1tdar5W+7vqapGV3PZ8+fbrb9ot1iU9v3bp1Vnx8vFWoUCGrQIECVvPmza3ly5d7PF5Wup7bXapr1apl5cmTxy0d+np6Gj4g/ftM6Xv6tddeM/vr663Xv379+ib/pH/N08vsefQ5PA3d4Om9cejQIbNN3+OaV7V7fMuWLa33338/R/nG03Onf58gtEXon0AHXACyT0uu9Be6DsSmA9gBANzRZgcAADgawQ4AAHA0gh0AAOBotNkBAACORskOAABwNIIdAADgaAwq+P/zruzfv98MtpXbw6ADAIDs0dFzdFognfj5YgN7EuyImEAnO/PNAACAwNu7d69UqFAh0/sJdkRcw9rrxcrOvDMIb2eTkqXhsAVmfdVLLaVADNkKIM8hN5w8edIUVqSd8NkTPpXTzAisgQ7BDryVJylZIvMWcL2HCHYA/yLPIb1LNUGhgTIAAHA0gh0AAOBoVGMBORQVGSGdrq3gWgfgX+Q5eIsRlP+/gVNsbKycOHGCNjsAADjs+5tqLAAA4GhUYwE+GNTq3IUUs54/OoqBKQE/I8/BW5TsADmkgU6tAfPMYgc9APyHPAdvEewAAABHI9gBAACORrADAAAcjWAHAAA4GsEOAABwNIIdAADgaIyzA+RQZESEtKtTxrUOwL/Ic/AW00UwXQQAAI6eLoKSHQCOF9dvdpb33T0ywa9pAZD7aLMDAAAcjWAHyKGzScmm5EAXXQfgX+Q5eItgBwAAOBrBDgAAcDSCHQAA4GgEOwAAwNEIdgAAgKMR7AAAAEdjUEHAB0PXN69e0rUOwL/Ic/AWwQ6QQ/mio2TSww25jkAuIc/BW1RjAQAARyPYAQAAjkawA/hg6Pqar8w1C9NFAP5HnoO3aLMD+MC5CylcRyAXkefgDUp2AACAoxHsAAAARyPYAQAAjkawAwAAHI1gBwAAOBq9sQAfDF3fqEpx1zoA/yLPwVsEO4APhq7//IkmXEcgl5Dn4C2qsQAAgKMR7AAAAEcj2AF8MHT9tUPmm4XpIgD/I8/BW7TZAXzg6JkkriOQi8hz8AbBDgBkU1y/2Vned/fIBK4zECBUYwEAAEcj2AEAAI5GsAMAAByNYAcAADgaDZQBHwxdf3WFWNc6AP8iz8FbBDuAD4au/6Z7M64jkEvIc/AWwQ4AR3f5BgDa7AAAAEcj2AFy6FxSijQdudAsug7Av8hz8BbVWEAOWWLJn8fPudYB+Bd5Dt6iZAcAADgawQ4AAHA0gh0AAOBoBDsAAMDRCHYAAICjBU2wM3LkSImIiJCePXu6tp0/f166desmJUqUkEKFCkmnTp3k0KFDbo/bs2ePJCQkSIECBaRUqVLSt29fSU5ODsAZIFxFSIRUK1XILLoOgDyH4BIUXc9Xr14t7733nlx99dVu23v16iWzZ8+W6dOnS2xsrHTv3l06duwoy5YtM/enpKSYQKdMmTKyfPlyOXDggDz44IMSHR0tw4cPD9DZINzkj4mS+b1vCnQygLBBnkPIleycPn1a7r//fvnggw+kWLFiru0nTpyQDz/8UEaPHi0tWrSQ+vXry6RJk0xQ89NPP5l9vv/+e9myZYt88sknUq9ePWnbtq0MGTJExo4dK0lJSQE8KwAAECwCHuxoNZWWzrRq1cpt+9q1a+XChQtu22vUqCGVKlWSFStWmNv6v06dOlK6dGnXPvHx8XLy5EnZvHlzps+ZmJho9km7AAAAZwpoNda0adNk3bp1phorvYMHD0pMTIwULVrUbbsGNnqfvU/aQMe+374vMyNGjJBBgwb56CwQ7nTo+tvf/dGs6+znWsQOgDyH4BGwkp29e/fKs88+K59++qnky5cvV5+7f//+pprMXjQtQE6Grt9++LRZmC4C8D/yHEIm2NFqqsOHD8u1114refLkMcuSJUtkzJgxZl1LaLTdzfHjx90ep72xtEGy0v/pe2fZt+19PMmbN68UKVLEbQEAAM4UsGCnZcuWsmnTJlm/fr1radCggWmsbK9rr6oFCxa4HrNt2zbT1bxJkybmtv7XY2jQZJs/f74JXmrVqhWQ8wIAAMElYG12ChcuLLVr13bbVrBgQTOmjr29a9eu0rt3bylevLgJYHr06GECnMaNG5v727RpY4Kazp07y+uvv27a6bz88sum0bOW3gAAAATFODuZefPNNyUyMtIMJqg9qLSn1bhx41z3R0VFyaxZs+Spp54yQZAGS126dJHBgwcHNN0AACB4BFWws3jxYrfb2nBZx8zRJTOVK1eWOXPm5ELqAABAKAqqYAcIRTpFRPmi+V3rAMhzCC4EO0AO6bg6y/q14DoCuYQ8h5AbQRkAAMCfCHYAAICjEewAOXT+wj/TReii6wD8izwHb9FmB8ihVMuSjftOuNYB+Bd5Dt6iZAcAADgawQ4AAHA0gh0AAOBoBDsAAMDRCHYAAICj0RsL8IHiBWO4jkAuIs/BGwQ7QA4ViMkj615pzXUEcgl5Dt6iGgsAADgawQ4AAHA0gh3AB0PX3/3eCrMwXQTgf+Q5eIs2O4APhq5fueuoax2Af5Hn4C1KdgAAgKMR7AAAAEcj2AEAAI5GsAMAAByNYAcAADgavbEAH8gfHcV1BHIReQ7eINgBfDB0/a9DbuE6ArmEPAdvUY0FAAAcjWAHAAA4GsEO4IOh6x+etMosTBcB+B95Dt6izQ7gg6HrF2074loH4F/kOXiLkh0AAOBoBDsAAMDRCHYAAICj0WYHgN/E9Zud5X13j0zglQDgF5TsAAAAR6NkBwCCEKVigO8Q7AA+GLqeKhgg95Dn4C2qsQAAgKMR7AAAAEcj2AF8MHT905+uNQvTRQD+R56Dtwh2AB8MXT9n00GzMF0E4H/kOXiLYAcAADgawQ4AAHA0gh0AAOBoBDsAAMDRCHYAAICjEewAAABHY7oIIIfyR0fJlsHxrnUA/kWeg7cIdoAcioiIMHP1AMgd5Dl4i2osAADgaAQ7QA4lJqfIc19sMIuuA/Av8hy8RbAD5FBKqiX/XbfPLLoOwL/Ic/AWwQ4AAHA0gh0AAOBoBDsAAMDRCHYAAICjEewAAABHI9gBAACOxrCvgA+Grl/7civXOgD/Is/BWwQ7gA+Gri9RKC/X0SHi+s0OdBJwCeQ5eItqLAAA4GiU7AA+GLp+6KxfzfrLt9aUvHmoygL8iTwHb1GyA/hg6PqPf/rDLEwXAfgfeQ7eItgBAACORrADAAAcjWAHAAA4GsEOAABwtIAGO+PHj5err75aihQpYpYmTZrId99957r//Pnz0q1bNylRooQUKlRIOnXqJIcOHXI7xp49eyQhIUEKFCggpUqVkr59+0pycnIAzgYAAASjgAY7FSpUkJEjR8ratWtlzZo10qJFC2nfvr1s3rzZ3N+rVy/59ttvZfr06bJkyRLZv3+/dOzY0fX4lJQUE+gkJSXJ8uXL5aOPPpLJkyfLgAEDAnhWAAAgmERYlmVJEClevLiMGjVK7rzzTilZsqRMnTrVrKutW7dKzZo1ZcWKFdK4cWNTCnTrrbeaIKh06dJmnwkTJsgLL7wgR44ckZiYmCw958mTJyU2NlZOnDhhSpgAb6SmWvLn8XNmvXzR/BIZGcEFzMZoxLtHJjh6lGNvzs+f184JyHPw9vs7aNrsaCnNtGnT5MyZM6Y6S0t7Lly4IK1a/TPnkKpRo4ZUqlTJBDtK/9epU8cV6Kj4+Hhz8nbpEOBvGtxULF7ALAQ6gP+R5xByIyhv2rTJBDfaPkfb5Xz11VdSq1YtWb9+vSmZKVq0qNv+GtgcPHjQrOv/tIGOfb99X2YSExPNYtPgCAAAOFPAg53q1aubwEaLoL788kvp0qWLaZ/jTyNGjJBBgwb59TkQPpKSU+Xf328z633aVJeYPEFTYAo4EnkO3gr4p7KW3lxxxRVSv359E4TUrVtX3n77bSlTpoxpeHz8+HG3/bU3lt6n9H/63ln2bXsfT/r372+CK3vZu3evX84N4SE5NVXeX/q7WXQdAHkOwSXgwU56qamppopJg5/o6GhZsGCB675t27aZruZa7aX0v1aDHT582LXP/PnzTSMlrQrLTN68eV3d3e0FAAA4U0CrsbSEpW3btqbR8alTp0zPq8WLF8u8efNM6+quXbtK7969TQ8tDUh69OhhAhztiaXatGljgprOnTvL66+/btrpvPzyy2ZsHg1oAAAAAhrsaInMgw8+KAcOHDDBjQ4wqIFO69atzf1vvvmmREZGmsEEtbRHe1qNGzfO9fioqCiZNWuWPPXUUyYIKliwoGnzM3jw4ACeFQAACCYBDXY+/PDDi96fL18+GTt2rFkyU7lyZZkzZ44fUgcAAJwg6NrsAAAA+BLBDgAAcLSAj7MDhLp8eaLk+143utZDjbdTL4Tb1AQIPqGe55D7CHYAHwxdf2XpwlzHHArF+a4QGOQ5eItqLAAA4GjZCnZ+//1336cECOGh69+c/5tZdB0AeQ4OCHZ0eofmzZvLJ598YibwBMKZThHx9oLtZmG6CIA8B4cEO+vWrTMDAOroxjoH1RNPPCGrVq3yfeoAAAACEezUq1fPTNa5f/9+mThxohkBuVmzZlK7dm0ZPXq0HDlyJKfpAgAACHwD5Tx58kjHjh1l+vTp8tprr8mOHTukT58+UrFiRdc0EAAAACEb7KxZs0aefvppKVu2rCnR0UBn586dZuZxLfVp376971IKAACQW+PsaGAzadIk2bZtm7Rr106mTJli/uuknapKlSoyefJkiYuLy87hAQAAAhvsjB8/Xh555BF56KGHTKmOJ6VKlbrkRJ8AAABBGexs3779kvvExMRIly5dsnN4IKTkzRMlX3dr6loHQJ6DA4IdrcIqVKiQ/Otf/3Lbrg2Vz549S5CDsBIVGSF1KxYNdDKAsEGeQ640UB4xYoRcdtllHquuhg8fnp1DAgAABE/Jzp49e0wj5PQqV65s7gPCiU4RMWnZLrP+cNMqEpOHKecA8hxCPtjREpyNGzdm6G21YcMGKVGihK/SBoQEnSJixHdbzXrnJpUlhvl1AfIcgkq2foLee++98swzz8iiRYskJSXFLAsXLpRnn31W7rnnHt+nEgAAIDdLdoYMGSK7d++Wli1bmlGUVWpqqhk1mTY7AAAg5IMd7Vb++eefm6BHq67y588vderUMW12AAAAQj7YsV155ZVmAQAAcFSwo210dDqIBQsWyOHDh00VVlrafgcAACBkgx1tiKzBTkJCgtSuXVsiIiJ8nzIAAIBABTvTpk2TL774wkz+CYQ7nSLis8cau9YBkOfgkAbKV1xxhe9TA4To0PVNqjK+FECeg6OCneeee07efvtteffdd6nCAoAsiOs3m+sEhFKw8+OPP5oBBb/77ju56qqrJDo62u3+GTNm+Cp9QNC7kJIqn636Z5qUextWkugoposAyHMI+WCnaNGicscdd/g+NUCIBjsDvt5s1u+sX4FgByDPwQnBzqRJk3yfEgAAAD/Idnl7cnKy/PDDD/Lee+/JqVOnzLb9+/fL6dOnfZk+AACA3C/Z+eOPP+SWW26RPXv2SGJiorRu3VoKFy4sr732mrk9YcKEnKUKAAAgkCU7OqhggwYN5NixY2ZeLJu249FRlQEAAEK6ZOd///ufLF++3Iy3k1ZcXJz8+eefvkobAABAYEp2dC4snR8rvX379pnqLAAAgJAu2WnTpo289dZb8v7775vbOjeWNkweOHAgU0gg7MRERcrEhxq41gGQ5xBcshXsvPHGGxIfHy+1atWS8+fPy3333Sfbt2+Xyy67TD777DPfpxIIYnmiIqVFjdKBTgYQNshzyJVgp0KFCrJhwwYzIejGjRtNqU7Xrl3l/vvvd2uwDAAAEJLBjnlgnjzywAMP+DY1QIiOoDzz538a5ne4pjwjKAPkOTgh2JkyZcpF73/wwQezmx4gJIOdvl9uNOsJV5cl2AHIc3BCsKPj7KR14cIFOXv2rOmKXqBAAYIdAAAQNLLVdUQHE0y7aJudbdu2SbNmzWigDAAAgorP+slWq1ZNRo4cmaHUBwAAIJB8OiiINlrWyUABAABCus3ON99843bbsiw5cOCAvPvuu9K0aVNfpQ0AACAwwU6HDh3cbusIyiVLlpQWLVqYAQcBAABCOtjRubEAiGuKiLH3XetaB3JbXL/ZWd5398gECXXkOeTaoIIA/j8TRUWa8XUA5A7yHHIl2Ondu3eW9x09enR2ngIAEOBSIKeUBAHZCnZ+/vlns+hggtWrVzfbfvvtN4mKipJrr/2nON9uywM4XXJKqszbfMisx19V2vzqBECeQ4gHO7fddpsULlxYPvroIylWrJjZpoMLPvzww3LDDTfIc8895+t0AkErKSVVuk1dZ9a3DI53fLDjbckA4GvhlueQc9l6h2iPqxEjRrgCHaXrQ4cOpTcWAAAI/WDn5MmTcuTIkQzbddupU6d8kS4AAIDABTt33HGHqbKaMWOG7Nu3zyz//e9/pWvXrtKxY0ffpAwAACBQbXYmTJggffr0kfvuu880UjYHypPHBDujRo3yRboAAAACF+wUKFBAxo0bZwKbnTt3mm1Vq1aVggUL+iZVAAAAPpKjJuw6H5YuOuO5Bjo6RxYAAEDIl+z8/fffctddd8miRYvMWDrbt2+Xyy+/3FRjaa8s5sdCOImOipRRd17tWgdAnkNwydYnc69evSQ6Olr27NljqrRsd999t8ydO9eX6QOCngY4/2pQ0SwEOwB5Dg4p2fn+++9l3rx5UqFCBbftWp31xx9/+CptAAAAgQl2zpw541aiYzt69KjkzZs356kCQmy6iKXb/xl36sZqJRnNFSDPwQnVWDolxJQpU1y3td1OamqqvP7669K8eXNfpg8IiaHrH5m8xiy6DoA8BweU7GhQ07JlS1mzZo0kJSXJ888/L5s3bzYlO8uWLfN9KgEAAHKzZKd27dpmlvNmzZpJ+/btTbWWjpysM6HreDsAAAAhW7KjIybfcsstZhTll156yT+pAgAACFTJjnY537hxo6+eHwAAIPiqsR544AH58MMPc/zkI0aMkOuuu04KFy4spUqVkg4dOsi2bdvc9jl//rx069ZNSpQoIYUKFZJOnTrJoUOH3PbR8X4SEhJMDzE9Tt++fSU5OTnH6QMAAGHaQFkDiYkTJ8oPP/wg9evXzzAn1ujRo7N0nCVLlphARgMePeaLL74obdq0kS1btriOqQMYzp49W6ZPny6xsbHSvXt30z7IbgidkpJiAp0yZcrI8uXLzfQVDz74oCmBGj58eHZODwAAOEiE5cWEVr///rvExcWZnliZHjAiQhYuXJitxBw5csSUzGgQdOONN8qJEyekZMmSMnXqVLnzzjvNPlu3bpWaNWvKihUrpHHjxvLdd9/JrbfeKvv375fSpUubfbQ90QsvvGCOFxMTc8nnPXnypAmk9PmKFCmSrbQjfF1ISZXPVu0x6/c2rBRyoyjH9Zsd6CQgiO0emSDBJtTzHHwnq9/fXpXs6AjJWnKic2LZ00OMGTPGFWTklCZWFS9e3Pxfu3ataRDdqlUr1z41atSQSpUquYId/V+nTh23NMTHx8tTTz1lusNfc801GZ4nMTHRLGkvFpBd+kH7YJM4LiCQS8hz8JZX4XD6QiAtVdFu576ggxL27NlTmjZtarq2q4MHD5qSmaJFi7rtq4GN3mfvkz7Ysm/b+3hqK6SRoL1UrFjRJ+cAAACCT47K/ryoAbskbbvzyy+/yLRp08Tf+vfvb0qR7GXv3r1+f044V0qqJSt2/m0WXQdAnkNw8aoaS9vj6JJ+W05po+NZs2bJ0qVL3SYX1UbHOkLz8ePH3Up3tDeW3mfvs2rVKrfj2b217H3S0/m7mMMLvpKYnCL3fvCTWd8yOF4KxGSr3T8A8hz8JI+3JTkPPfSQK1DQbuFPPvlkht5YM2bMyPLxevToIV999ZUsXrxYqlSp4na/9vTSXlULFiwwXc6Vdk3XruZNmjQxt/X/sGHD5PDhw6Zxs5o/f75pqFSrVi1vTg8AAIR7sNOlS5cM4+3ktOpKe1p9/fXXZqwdu42NtqPJnz+/+d+1a1fp3bu3abSsAYwGRxrgaONkpV3VNajp3LmzmbNLj/Hyyy+bY1N6AwAAvAp2Jk2a5NMrNn78ePP/5ptvzvA8WoKk3nzzTYmMjDQlO9qDSntajRs3zrVvVFSUqQLT3lcaBGkpkwZlgwcP9mlaAQBAaApo44KsNHDOly+fjB071iyZqVy5ssyZM8fHqQMAeDMOUzCOyQMoRmICAACORrADAAAcjT6yQE4zUWSk9G9bw7UOwL/Ic/AWwQ6QQzF5IuWJm6pyHYFcQp6Dt/gZCgAAHI2SHSCHdIqIX/78ZxLb2uVjJSoy56OKAyDPwXco2QF8MF1E+7HLzKLrAPyLPAdvEewAAABHI9gBAACORrADAAAcjWAHAAA4GsEOAABwNIIdAADgaIyzA+Q0E0VGyrMtq7nWAfgXeQ7eItgBfDB0fa/WV3IdgVxCnoO3+BkKAAAcjZIdIIdSUy3ZceS0Wb+iZCGJZLoIwK/Ic/AWwQ6QQ+eTU6TNm0vN+pbB8VIghmwF+BN5Dt7iUxkIEXH9Zmd5390jE/yaFgAIJbTZAQAAjkawAwAAHI1gBwAAOBrBDgAAcDSCHQAA4Gj0xgJymokiI+XxGy93rQPwL/IcvEWwA/hg6PoX29XkOgK5hDwHb/EzFAAAOBolO4APhq7/8/g5s16+aH6miwD8jDwHb1GyA/hg6PobXl9kFl0H4F/kOXiLYAcAADgawQ4AAHA0gh0AAOBoBDsAAMDRCHYAAICj0fUccKC4frMDnQQACBoEO0AORUVGSOfGlV3rAPyLPAdvEewAOZQ3T5QM6VCb6wjkEvIcvEWbHQAA4GiU7AA5ZFmWHD2TZNaLF4yRiAiqsgB/Is/BWwQ7QA6du5Ai9Yf+YNa3DI6XAjFkK8CfyHPwFtVYAADA0Qh2AACAoxHsAAAARyPYAQAAjkawAwAAHI1gBwAAOBp9ZAEfDF3f6doKrnUA/kWeg7cIdgAfDF3/xl11uY5ALiHPwVtUYwEAAEejZAfwwdD1OqKryh8dxXQRgJ+R5+AtSnaAHNJAp9aAeWaxgx4A/kOeg7cIdgAAgKMR7AAAAEejzQ4QIHH9ZnPtASAXULIDAAAcjWAHAAA4GsEOAABwNNrsADkUGREh7eqUca0D8C/yHLxFsAPkUL7oKBl3f32uI5BLyHPwFtVYAADA0Qh2AACAoxHsADl0NinZjJmji64D8C/yHLxFsAMAAByNYAcAADgawQ4AAHC0gAY7S5culdtuu03KlSsnERERMnPmTLf7LcuSAQMGSNmyZSV//vzSqlUr2b59u9s+R48elfvvv1+KFCkiRYsWla5du8rp06dz+UwAAECwCmiwc+bMGalbt66MHTvW4/2vv/66jBkzRiZMmCArV66UggULSnx8vJw/f961jwY6mzdvlvnz58usWbNMAPX444/n4lkAAIBgFtBBBdu2bWsWT7RU56233pKXX35Z2rdvb7ZNmTJFSpcubUqA7rnnHvn1119l7ty5snr1amnQoIHZ55133pF27drJv//9b1NiBAAAwlvQttnZtWuXHDx40FRd2WJjY6VRo0ayYsUKc1v/a9WVHego3T8yMtKUBGUmMTFRTp486bYAORm6vnn1kmZhugjA/8hzcMx0ERroKC3JSUtv2/fp/1KlSrndnydPHilevLhrH09GjBghgwYN8ku6EZ5D1096uGGgkwGEDfIcHFOy40/9+/eXEydOuJa9e/cGOkkAACDcgp0yZf6ZRfrQoUNu2/W2fZ/+P3z4sNv9ycnJpoeWvY8nefPmNb230i4AAMCZgrYaq0qVKiZgWbBggdSrV89s07Y12hbnqaeeMrebNGkix48fl7Vr10r9+v/MOr1w4UJJTU01bXuA3Bq6vv6QH8z62ldaSYGYoM1WgF/plClZtXtkQrafhzwHbwX0U1nHw9mxY4dbo+T169ebNjeVKlWSnj17ytChQ6VatWom+HnllVdMD6sOHTqY/WvWrCm33HKLPPbYY6Z7+oULF6R79+6mpxY9sZCbzl1I4YID5DkEqYAGO2vWrJHmzZu7bvfu3dv879Kli0yePFmef/55MxaPjpujJTjNmjUzXc3z5cvnesynn35qApyWLVuaXlidOnUyY/MAAIJXbpUCAQEPdm6++WYznk5mdFTlwYMHmyUzWgo0depUP6UQAACEuqBtoAwAAOALBDsAAMDRCHYAAICj0UcW8MHQ9Y2qFHetA/Av8hy8RbAD+GDo+s+faMJ1BHIJeQ7eohoLAAA4GsEOAABwNIIdIId06Pprh8w3i64D8C/yHLxFmx3AB46eSeI6ArmIPAdvULIDAAAcjWAHAAA4GsEOAABwNIIdAADgaAQ7AADA0eiNBfhg6PqrK8S61gH4F3kO3iLYAXwwdP033ZtxHYFcQp6Dt6jGAgAAjkawAwAAHI1gB8ihc0kp0nTkQrPoOgD/Is/BW7TZAXLIEkv+PH7OtQ7Av8hz8BYlOwAAwNEIdgAAgKMR7AAAAEejzQ7gQ7UGzON6AkCQIdgBLiGu32yuEQCEMIIdAEBIiZAIqVaqkGsduBSCHQBASMkfEyXze98U6GQghNBAGQAAOBrBDgAAcDSCHQBAyE0X0Xr0ErMwRQuygjY7AICQmy5i++HTrnXgUijZAQAAjkawAwAAHI1gBwAAOBptdgAAYTvq+e6RCX5NC4IDJTsAAMDRKNkBAIQUnSKifNH8rnXgUgh2AAAhN13Esn4tAp0MhBCCHQCAY9rgAJ7QZgcAADgawQ4AAHA0gh0AAOBoBDsAAMDRCHYAAICjEewAAABHI9gBAACORrADAAAcjWAHAAA4GsEOAABwNIIdAADgaAQ7AADA0ZgIFGE5UeDukQl+SwsAZ3528LkRugh2AADIAgKj0EU1FgAAcDSCHQAA4GgEOwAAwNEIdgAAgKMR7AAAAEcj2AEAAI5G13OEJW/H5QEAhC6CHQAAfIyBToML1VgAAMDRCHYAAICjUY2FoEW7GgCALxDsIFcRwAAAcptjqrHGjh0rcXFxki9fPmnUqJGsWrUq0EkCAABBwBElO59//rn07t1bJkyYYAKdt956S+Lj42Xbtm1SqlSpQCfP8SitAQAEM0cEO6NHj5bHHntMHn74YXNbg57Zs2fLxIkTpV+/foFOXsgFJLtHJvg1LQAA5KaQD3aSkpJk7dq10r9/f9e2yMhIadWqlaxYsSKgaQtVlNQAgDM+d/nx6pBg56+//pKUlBQpXbq023a9vXXrVo+PSUxMNIvtxIkT5v/Jkyd9nr7aA+dled9fBsWLv6QmnvXbsQEAwalSr+le7e/N91AwfL/Z39uWZTk72MmOESNGyKBBgzJsr1ixogRS7FsBfXoAQJiLfSs0v99OnTolsbGxzg12LrvsMomKipJDhw65bdfbZcqU8fgYrfLSBs221NRUOXr0qJQoUUIiIiL8nuZQoNGyBn979+6VIkWKBDo5YYVrz7UPN7znufbZpSU6GuiUK1fuovuFfLATExMj9evXlwULFkiHDh1cwYve7t69u8fH5M2b1yxpFS1aNFfSG2o00CHY4dqHG973XPdwUySEP+svVqLjmGBHaSlNly5dpEGDBtKwYUPT9fzMmTOu3lkAACB8OSLYufvuu+XIkSMyYMAAOXjwoNSrV0/mzp2bodEyAAAIP44IdpRWWWVWbQXvaTXfwIEDM1T3wf+49oHDtee6h5u8YfJZH2Fdqr8WAABACHPM3FgAAACeEOwAAABHI9gBAACORrADAAAcjWAnTOgIkz179pTKlStL/vz55frrr5fVq1df9DFjx46VmjVrmv2rV68uU6ZMybDP8ePHpVu3blK2bFnTmv/KK6+UOXPm+PFMQou/rruOJaX36T460nWvXr3k/PnzEs6WLl0qt912mxlJVUdCnzlzptv92hdDh6fQ96peN50sePv27Zc8rr4ecXFxki9fPmnUqJGsWrXK7X697poHdAT2QoUKSadOnTKM6O5kgbjuOuJ9jx49XHmgUqVK8swzz7jmOQwXgXrPpz1+27ZtPT530NHeWHC+u+66y6pVq5a1ZMkSa/v27dbAgQOtIkWKWPv27fO4/7hx46zChQtb06ZNs3bu3Gl99tlnVqFChaxvvvnGtU9iYqLVoEEDq127dtaPP/5o7dq1y1q8eLG1fv36XDyz8Lvun376qZU3b17zX6/5vHnzrLJly1q9evWywtmcOXOsl156yZoxY4b2MLW++uort/tHjhxpxcbGWjNnzrQ2bNhg3X777VaVKlWsc+fOZXpMfR1iYmKsiRMnWps3b7Yee+wxq2jRotahQ4dc+zz55JNWxYoVrQULFlhr1qyxGjdubF1//fVWuAjEdd+0aZPVsWNHky927Nhhrn21atWsTp06WeEkUO952+jRo622bdt6fO5gQ7ATBs6ePWtFRUVZs2bNctt+7bXXmoziSZMmTaw+ffq4bevdu7fVtGlT1+3x48dbl19+uZWUlOSnlIc2f133bt26WS1atLjoPuEu/YdvamqqVaZMGWvUqFGubcePHzdBowaUmWnYsKG53raUlBSrXLly1ogRI1zHiI6OtqZPn+7a59dffzXPv2LFCivc5NZ19+SLL74wX9IXLlywwlFuX/uff/7ZKl++vHXgwIGQCHaoxgoDycnJkpKSYook09JizR9//NHjYxITEz3ur8WZFy5cMLe/+eYbadKkiSnC19Gqa9euLcOHDzfPBf9dd60KW7t2rato+ffffzdVh+3ateOyZ2LXrl1mdHUtxk87n44W0a9YscLjY5KSksx1TvuYyMhIc9t+jN6vr0vafWrUqGGqVTI7bjjx13X3RKuwdG6nPHkcM1Zu0F77s2fPyn333WequzKbcDvYEOyEgcKFC5ugZMiQIbJ//37zBfzJJ5+YN++BAwc8PiY+Pl7+85//mDe+/mhYs2aNua0f7H/99ZfrS/bLL780x9Mv21deeUXeeOMNGTp0aC6fYXhdd/2QGTx4sDRr1kyio6OlatWqcvPNN8uLL76Yy2cYOvRDX6WfQkZv2/elp9dbX7OLPUb/62TE6ScSvthxw4m/rrunx2g+e/zxx32W9lDnz2vfq1cv86Orffv2EioIdsLExx9/bL48y5cvbxoSjxkzRu69914TtXuigYs2PGvcuLH5QtU3tU62quzH6OzypUqVkvfff9/MPK9zlL300ksyYcKEXD23cLvuixcvNiVo48aNk3Xr1smMGTNk9uzZ5sMeCDcnT56UhIQEqVWrlrz66quBTo7jffPNN7Jw4ULTSSKUEOyECf31v2TJEjl9+rTs3bvXVS1y+eWXe9xfq04mTpxoiit3794te/bsMa3ztbSiZMmSZh9t4a+9r6KiolyP015E+gtAi0Phn+uuAVHnzp3l0UcflTp16sgdd9xhgp8RI0aYABQZ2UXt6XtJ6e3MiuEvu+wy896+2GP0v77XtVdiVo8bTvx13dP2drzllltM/vjqq6/MDwT499ovXLhQdu7caUoztcrQrjbUXohawhysCHbCTMGCBU2QcuzYMZk3b94liyH1w6NChQomA0ybNk1uvfVWVwlD06ZNZceOHW5fsL/99ps5vhbtwz/XXQOh9CVDdsDJVHeeValSxXxYL1iwwK1EYOXKlaaq0RN9D2uJZdrH6Htdb9uP0fv1tUq7z7Zt20yQmtlxw4m/rrt9nDZt2pj9tbQhfVu3cOeva9+vXz/ZuHGjrF+/3rWoN998UyZNmiRBK9AtpJE75s6da3333XfW77//bn3//fdW3bp1rUaNGrl6UvXr18/q3Lmza/9t27ZZH3/8sfXbb79ZK1eutO6++26rePHipquzbc+ePaabdPfu3c3+2uuoVKlS1tChQ3lZ/Xjdtfu6XnftUWEft2rVqqabezg7deqU6SGii360abdYXf/jjz9c3XC1C+3XX39tbdy40Wrfvn2Gbrjay+2dd95x64arvVcmT55sbdmyxXr88cfNMQ4ePOjW9bxSpUrWwoULTddz7VGnS7gIxHU/ceKEyUd16tQxXc+1R5C9JCcnW+EiUO/59EKhNxbBTpj4/PPPTTdx7Zqp3RG1a6F2Q7R16dLFuummm1y39U1er149K3/+/GZcGM0kW7duzXDc5cuXmw8dzRx6/GHDhoXVh00grrt2rX311VdNgJMvXz4zxsvTTz9tHTt2zApnixYtMh+66Re9xnZX3FdeecUqXbq0eb+2bNnSBJdpVa5c2QSTaekXgQYz+hpqt9yffvrJ7X794tDrX6xYMatAgQLWHXfcYb50w0Ugrntmz6lL2h8GTheo93woBjsR+ifQpUsAAAD+QpsdAADgaAQ7AADA0Qh2AACAoxHsAAAARyPYAQAAjkawAwAAHI1gBwAAOBrBDgAAcDSCHQDGQw89JBEREa6lRIkSZpJFnQfHl3SCUz2+PadOVuhs1vXq1eOVApAtBDsAXDS4OXDggFl08j+d0VgnIQ0VOqM8AKRHsAPAJW/evGamZF20JEVnON67d68cOXLEtc+mTZukRYsWkj9/flP68/jjj8vp06fdZkkePHiwmbVdj6fHmTt3rttszOqaa64xJTw333yzub148WJp2LChmSG+aNGi0rRpU/njjz9k8uTJMmjQINmwYYOr1Em3KV0fP3683H777eZxw4YNk5SUFOnatat5Hk1j9erV5e23385QitWhQwdz3JIlS0qRIkXkySeflKSkpEzfDfqcmq5Zs2aZYxYoUEDuvPNOMwv9Rx99JHFxcVKsWDF55plnTBpsiYmJ0qdPHylfvrxJY6NGjcy52v7++2+59957zf16zDp16shnn33m9tx6jfS4zz//vBQvXty8PlraBSCLAj05F4DgoJMH6sSjaWdUfuKJJ6wrrrjCSklJMdtOnz5tlS1b1urYsaO1adMma8GCBWYWZXviQaUzL+skpjoru05i+vzzz1vR0dFmJne1atUqM3HgDz/8YCbM/Pvvv83kprGxsVafPn3MLNY6IarOuqyzN589e9Z67rnnrKuuuso1s7VuU3qcUqVKWRMnTrR27txp9tcZ5QcMGGCtXr3azAr/ySefmAk6dVLWtOdaqFAhM6v8L7/8Ys2aNcsqWbKk9eKLL2Z6fSZNmmTOo3Xr1ta6deusJUuWWCVKlLDatGljZpzfvHmz9e2335rJE3XmaNujjz5qXX/99dbSpUvNuY0aNcpMymhfj3379pltOlu1nsOYMWOsqKgoM+u9TSeL1WuqE8Dq4z766CMrIiLCzHgP4NIIdgC4AgD9ki1YsKBZNJDQwGbt2rWuK/T++++b2b016LHNnj3bioyMtA4ePGhulytXzho2bJjbVb3uuuvMzOBKZ6XWY+uXu00DHt22ePFij6+Gzspct27djB9gIlbPnj0v+QrqbPOdOnVyO9fixYtbZ86ccW0bP368CYDswM5TsKPPpwGLTYNBDaQ0MLTFx8eb7UqDL72mf/75p9uxdPbp/v37Z5rehIQEE+ClDXaaNWuW4Zq+8MILlzx3AJaVJ6slQACcr3nz5qZaSB07dkzGjRsnbdu2lVWrVknlypXl119/lbp165rqGJtWN2nV1bZt20y10f79+822tPS2VkNlRqtmtGopPj5eWrduLa1atZK77rpLypYte8k0N2jQIMO2sWPHysSJE2XPnj1y7tw5Uz2VvoGznodWG9maNGliquO02k7P1RPdv2rVqq7bpUuXNtVXhQoVctt2+PBhV5WfVmldeeWVbsfRqi2tAlR6//Dhw+WLL76QP//806RV70+bNnX11Ve73dZrYz8PgIsj2AHgokHMFVdc4br9n//8R2JjY+WDDz6QoUOH+vVKTZo0ybRL0fY9n3/+ubz88ssyf/58ady48UUflzbwUtOmTTNtZN544w0TwBQuXFhGjRolK1euzHEao6Oj3W5rmyFP2zT4Uxo8RUVFydq1a83/tOwASdOmbYreeust015Hz6dnz54Z2g9d7HkAXBzBDoBM6RdqZGSkKR1RNWvWNA11z5w54woyli1bZvbRRrva0LdcuXJm20033eQ6jt7WxscqJibG/E/biNemjZZ16d+/vwlUpk6daoIdfYyn/T3R57r++uvl6aefdm3buXNnhv20pEnPS0uj1E8//WQCkIoVK/rsHaHnounWEpgbbrgh0/S2b99eHnjgAXNbA5jffvtNatWq5bN0AOGO3lgAXLT65ODBg2bRKqsePXqY0onbbrvN3H///fdLvnz5pEuXLvLLL7/IokWLzD6dO3c21Teqb9++8tprr5nSGa3a0h5dOqbOs88+a+4vVaqUCTC0BOfQoUNy4sQJ2bVrlwlwVqxYYXpgff/997J9+3YTXCmtKtJ99Dh//fWXSWdmqlWrJmvWrJF58+aZoOGVV16R1atXZ9hPS06019aWLVtkzpw5MnDgQOnevbsJ3HxFq6/0mj344IMyY8YMcw5aJThixAiZPXu2K71agrV8+XJzzZ944glzXQD4DsEOABcNQLQtiC7aRVqDhOnTp7u6h2s7Eg0ijh49Ktddd53pet2yZUt59913XcfQqqjevXvLc889Z6pl9JjffPON+VJXOnbPmDFj5L333jOlQFqqocfdunWrdOrUyQQI2p29W7du5otf6XYdA0jbFGlX8fRds9PSx3Ts2FHuvvtucw7atTttKY9N061puvHGG82+2n3dH925tXpOgx29Hlr6pV3e9bpWqlTJ3K/Vdddee61pr6TXWbuV6z4AfCdCW2n78HgAEPS0MfTx48dl5syZgU4KgFxAyQ4AAHA0gh0AAOBoVGMBAABHo2QHAAA4GsEOAABwNIIdAADgaAQ7AADA0Qh2AACAoxHsAAAARyPYAQAAjkawAwAAHI1gBwAAiJP9H1slAguioXl0AAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.hist(bootstrap_means, bins=40)\n", + "plt.axvline(ci_bootstrap[0], linestyle=\"--\")\n", + "plt.axvline(ci_bootstrap[1], linestyle=\"--\")\n", + "plt.xlabel(\"Bootstrap mean\")\n", + "plt.ylabel(\"Frequency\")\n", + "plt.title(\"Bootstrap distribution of the mean\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "52a1d044", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Original mean: 12.2\n", + "95% bootstrap CI: 11.77 12.620000000000001\n" + ] + } + ], + "source": [ + "#Lab Example 7 — Bootstrap confidence interval for the mean\n", + "\n", + "#Goal: connect directly with your previous lab.\n", + "\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "np.random.seed(42)\n", + "\n", + "data = np.array([12.1, 11.8, 10.9, 13.0, 12.5, 11.7, 12.9, 13.2, 11.5, 12.4])\n", + "\n", + "B = 5000\n", + "bootstrap_means = []\n", + "\n", + "for _ in range(B):\n", + " sample_boot = np.random.choice(data, size=len(data), replace=True)\n", + " bootstrap_means.append(np.mean(sample_boot))\n", + "\n", + "bootstrap_means = np.array(bootstrap_means)\n", + "\n", + "ci_low, ci_high = np.percentile(bootstrap_means, [2.5, 97.5])\n", + "\n", + "plt.hist(bootstrap_means, bins=30, edgecolor=\"black\")\n", + "plt.axvline(ci_low, linestyle=\"--\", label=\"2.5%\")\n", + "plt.axvline(ci_high, linestyle=\"--\", label=\"97.5%\")\n", + "plt.axvline(data.mean(), linestyle=\"-\", label=\"Original mean\")\n", + "plt.xlabel(\"Bootstrap means\")\n", + "plt.ylabel(\"Frequency\")\n", + "plt.title(\"Bootstrap distribution of the mean\")\n", + "plt.legend()\n", + "plt.show()\n", + "\n", + "print(\"Original mean:\", data.mean())\n", + "print(\"95% bootstrap CI:\", ci_low, ci_high)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "4d7d77da", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "True beta_0: 3\n", + "Estimated beta_0: 3.717585051473372\n", + "True beta_1: 2\n", + "Estimated beta_1: 1.6815735189709737\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "np.random.seed(42)\n", + "\n", + "n = 40\n", + "beta_0 = 3\n", + "beta_1 = 2\n", + "sigma = 4\n", + "\n", + "x = np.linspace(0, 10, n)\n", + "error = np.random.normal(0, sigma, n)\n", + "y = beta_0 + beta_1 * x + error\n", + "\n", + "X = np.column_stack((np.ones(n), x))\n", + "\n", + "beta_hat = np.linalg.inv(X.T @ X) @ X.T @ y\n", + "\n", + "b0_hat, b1_hat = beta_hat\n", + "\n", + "y_hat = b0_hat + b1_hat * x\n", + "\n", + "plt.scatter(x, y, label=\"Data\")\n", + "plt.plot(x, y_hat, label=\"OLS fitted line\")\n", + "plt.xlabel(\"x\")\n", + "plt.ylabel(\"y\")\n", + "plt.title(\"OLS estimation\")\n", + "plt.legend()\n", + "plt.show()\n", + "\n", + "print(\"True beta_0:\", beta_0)\n", + "print(\"Estimated beta_0:\", b0_hat)\n", + "print(\"True beta_1:\", beta_1)\n", + "print(\"Estimated beta_1:\", b1_hat)" + ] } ], "metadata": {