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Notes/Documents/Arbeit/IFN/Programmieren WiSe 25 26/Jupyter/5.SciPy.ipynb

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"# 5. Programmierübung: SciPy\n",
"\n",
"<div style=\"display:flex;\">\n",
" <div style=\"text-align: left\">\n",
" Willkommen zur fünften Programmierübung Einführung in Python 3.\n",
" </div>\n",
" <img style=\"float: right; margin: 0px 15px 15px 0px\" src=\"https://www.python.org/static/img/python-logo-large.c36dccadd999.png?1576869008\" width=\"100\" />\n",
"</div>\n",
"\n",
"Wenn Sie Fragen oder Verbesserungsvorschläge zum Inhalt oder Struktur der Notebooks haben, dann können sie eine E-Mail an Phil Keier ([p.keier@hbk-bs.de](mailto:p.keier@hbk-bs.de?subject=[SigSys]%20Feedback%20Programmierübung&amp)) oder Martin Le ([martin.le@tu-bs.de](mailto:martin.le@tu-bs.de?subject=[SigSys]%20Feedback%20Programmierübung&amp)) schreiben.\n",
"\n",
"Link zu einem Python Spickzettel: [hier](https://s3.amazonaws.com/assets.datacamp.com/blog_assets/PythonForDataScience.pdf)\n",
"\n",
"Der Großteil des Python-Tutorials stammt aus der Veranstaltung _Deep Learning Lab_ und von [www.python-kurs.eu](https://www.python-kurs.eu/python3_kurs.php) und wurde für _Signale und Systeme_, sowie _Einführung in die Programmierung für Nicht Informatiker_ angepasst.\n",
"\n",
"---"
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"source": [
"# Was ist SciPy\n",
"\n",
"SciPy steht für Scientific Python und ist eine Open-Source-Bibliothek, die auf der bewährten Architektur von NumPy aufbaut. Sie bietet eine Vielzahl von Funktionen, die speziell für ingenieurtechnische und wissenschaftliche Anwendungen entwickelt wurden. In diesem Zusammenhang möchten wir uns insbesondere mit Teilen des Statistikmoduls von SciPy vertraut machen.\n",
"\n",
"__Für dieses Notebook schauen Sie bitte in die [SciPy Docs](https://docs.scipy.org/doc/scipy/tutorial/index.html)!!!__ Dort sind alle Funktionen beschrieben die wir hier bearbeiten und noch mehr!\n",
"\n",
"---"
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"SciPys wird meist als `sp` importiert da für diese Aufgabe nur das Statistik modul nötig ist wird einfach dieses importiert. Aufgrund des kurzen schlüssigen namens findet keine umbenennung statt:"
]
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"source": [
"from scipy import stats"
]
},
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"---"
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"source": [
"# Lineare Regression\n",
"\n",
"## Mathematische Definition\n",
"\n",
"Ausgehend von dem stochastischen Zusammenhang: $$Y = f(X) + \\epsilon$$\n",
"Hierfür gilt: \n",
"- $Y$ ist die abhängige Variable, auch `Outcome`\n",
"- $X$ die unabhängige Variable, auch `Covariant`\n",
"- $\\epsilon$ der Fehler, auch `random Noise`\n",
"\n",
"Für $\\epsilon$ wird angenommen, dass der erwartete Durschnitt gleich 0 ist $E(\\epsilon)=0$. Das bedeutet, dass die Verteilung des Fehlers zum erwarteten Wert bei genügend Datenpunkten sich gegenseitig aufheben: $$\\lim_{\\epsilon\\rightarrow\\infty} f(x_\\epsilon) = 0;\\quad x \\in X$$\n",
"Auch wird angenommen, dass die Varianz der Fehler $\\epsilon$ konstant ist. $$Var(\\epsilon) = \\sigma^2$$\n",
"## Motivation\n",
"\n",
"Die **lineare Regression** ist eine grundlegende Methode zur Modellierung von Beziehungen zwischen Variablen. Sie hilft, Zusammenhänge zu verstehen und ermöglicht Vorhersagen auf Basis vorhandener Daten. Durch die Bestimmung einer linearen Beziehung zwischen einer abhängigen und einer oder mehreren unabhängigen Variablen können wir Trends identifizieren und zukünftige Werte schätzen. Ihre Einfachheit, Effizienz und die Möglichkeit, auch bei großen Datensätzen präzise Ergebnisse zu erzielen, machen sie zu einem wertvollen Werkzeug in der Datenanalyse und ein Fundament für komplexere Modelle.\n",
"\n",
"Dafür geht man davon aus, dass es zwei unabhängige Variablen $x_1$ & $x_2$ gibt, für die eine Zukünftige Aussage getätigt werden soll. Hierfür wird eine fehlerminimierte Gerade $g(x)$ zwischen die Datenpunkte gelegt. Daraus resultierenden lässt sich mit $g(x)$ eine zukünftige Vorhersage in einem bestimmten Fehlerbereich tätigen.\n",
"\n",
"Aus der Schule sollte die Geraden Gleichung $g(x) = m\\cdot x+b$ bekannt sein. Dabei beschreibt $m$ die Steigung (Slope) & $b$ den Schnittpunkt mit der y-Achse (interception). Die **lineare regression** bietet daher die Möglichkeit diese beiden Parameter herauszufinden.\n",
"\n",
"Für das folgende Beispiel werden zwei (pseudo-)zufällig erzeugte Datensets generiert, auf welche dann die lineare regression angewandt wird. "
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u1bJly3TPPfdoypQpCg0N1axZszRhwgTddNNNuuOOO7R371699NJLVVojU5FbbrlFV155pebNm6eJEycqKSlJiYmJmjJlioqLi+VyufTaa68FrJWpimHDhqlv376aOnWqvvjiC3Xt2lUFBQUVBsenn35at9xyi2644Qb95Cc/0bfffqv58+erWbNmmj59+iX8pFUzZswY/fnPf9a7776r0aNH+50Jqsr36nzNmjXTiBEjNH/+fDkcDiUmJuqtt96q8GaPzz//vPr166fu3bvr7rvv1mWXXabDhw9rw4YNOnDggLZt2yZJ6tq1q1JTU9WzZ0+1bNlSH374ofLz8zVp0qSaOyDA+er+QinAHt555x3jxz/+sZGUlGQ0bdrUaNy4sXH55Zcb9913n3H48OGA/n/84x+Na665xggLCzNatGhhDBgwwCgsLPRt/+c//2n84Ac/MMLDw40OHTr4LufWeZfAnj592hg1apTRvHlzQ5LfJbPLly83unbtajRq1CjgEtmPPvrIyMjIMFq1amWEhYUZHTt2NEaOHGmsWrXK16f8UuGjR49W+DO/9tprRr9+/YzIyEgjMjLSSEpKMiZOnGjs2rXLr9/vfvc7IyEhwQgLCzN69eplrF+/3hgwYEDQl19Xdonu4sWL/X6uHTt2GIMGDTKaNm1qtG7d2rj77ruNbdu2BfzsWVlZRmRkZMD+yn/ecx0/ftwYO3as4XK5jGbNmhljx441Pvroowovbf/HP/5h9O3b1wgPDzdcLpcxbNgwY8eOHRV+xvnHtLKaBgwYYHTr1q2ywxPgu+++M6Kjow1Jxttvvx2wPdjv1fmXXxuGYRw9etT40Y9+ZERERBgtWrQwJkyYYHz88ccVHovPP//cuOuuu4z27dsboaGhRkxMjHHrrbca+fn5vj6zZs0yrrvuOqN58+ZGeHi4kZSUZMyePTvglgVATXIYRpCrzgAAACyGNTIAAMC2CDIAAMC2CDIAAMC2CDIAAMC2CDIAAMC2CDIAAMC26v0N8bxer7766itFRUVVeot3AABgLYZh6NSpU+rQoYNCQio/71Lvg8xXX32luLg4s8sAAADVsH//fsXGxla6vd4HmaioKEnfHwiXy2VyNfVXWVmZVq5cqZtvvlmhoaFml9OgMRbWwDhYB2NhHVUZC7fbrbi4ON/v8cqYGmTWr1+vp59+Wps3b9bBgwe1bNkyDR8+3LfdMAw99thjevHFF3XixAn17dtXCxYsUOfOnYP+jPLpJJfLRZCpRWVlZYqIiJDL5eIvCpMxFtbAOFgHY2Ed1RmLiy0LMXWx75kzZ3T11Vfr+eefr3D73Llz9eyzz2rhwoX64IMPFBkZqbS0NP33v/+t40oBAIAVmXpG5pZbbtEtt9xS4TbDMJSbm6tHHnnE99j6P//5z2rXrp1ef/113XnnnXVZKgAAsCDLrpHZu3evDh06pEGDBvnamjVrpuuvv14bNmyoNMiUlpaqtLTU99rtdkv6/nRWWVlZ7RbdgJUfW46x+RgLa2AcrIOxsI6qjEWw42XZIHPo0CFJUrt27fza27Vr59tWkTlz5mjGjBkB7StXrlRERETNFokAhYWFZpeA/8VYWAPjYB2MhXUEMxYlJSVB7cuyQaa6HnroIU2ePNn3unzV880338xi31pUVlamwsJCDR48mMV0JmMsrIFxsA7GwjqqMhblMyoXY9kg0759e0nS4cOHFR0d7Ws/fPiwevToUen7wsLCFBYWFtAeGhrKF7gOcJytg7GwBsbBOhgL6whmLIIdK8s+oiAhIUHt27fXqlWrfG1ut1sffPCBbrjhBhMrAwAAVmHqGZnTp0/rs88+873eu3evtm7dqpYtWyo+Pl45OTmaNWuWOnfurISEBE2bNk0dOnTwu9cMAABouEwNMh9++KFuvPFG3+vytS1ZWVlavHixfvWrX+nMmTO65557dOLECfXr108rVqxQkyZNzCoZAABYiKlBJjU1VYZhVLrd4XBo5syZmjlzZh1WBQAALsbj9ahoX5EOnjqo6KhopcSnyBnirPM6LLvYFwAAVF9tBo2CnQXKXpGtA+4DvrZYV6zyhuQpIzmjRj4jWAQZAADqmdoMGgU7C5S5NFOG/GdUit3FylyaqfyR+XUaZix71RIAAKi68qBxboiR/i9oFOwsqPa+PV6PsldkB4QYSb62nBU58ng91f6MqiLIAABQT9R20CjaVxQQkM7/jP3u/SraV1St/VcHQQYAgHqitoPGwVMHa7RfTSDIAABQT9R20IiOir54pyr0qwkEGQAA6onaDhop8SmKdcXKIUeF2x1yKM4Vp5T4lGrtvzoIMgAA1BO1HTScIU7lDcnz7ev8fUtS7pDcOr2fDEEGAIB6oi6CRkZyhvJH5ivGFePXHuuKrfNLryXuIwMAQL1SHjQquo9M7pDcGgkaGckZSu+Szp19AQBAzauLoOEMcSq1U2qN7a+6CDIAANRDVgkatY01MgAAwLYIMgAAwLYIMgAAwLYIMgAAwLYIMgAAwLYIMgAAwLYIMgAAwLYIMgAAwLYIMgAAwLYIMgAAwLYIMgAAwLYIMgAAwLYIMgAAwLYIMgAAwLYIMgAAwLYamV0AAAD1jcfrUdG+Ih08dVDRUdFKiU+RM8Rpdln1EkEGAIAaVLCzQNkrsnXAfcDXFuuKVd6QPGUkZ5hYWf3E1BIAADWkYGeBMpdm+oUYSSp2FytzaaYKdhaYVFn9RZABAKAGeLweZa/IliEjYFt5W86KHHm8nrourV4jyAAAUAOK9hUFnIk5lyFD+937VbSvqA6rqv8IMgAA1ICDpw7WaD8EhyADAEANiI6KrtF+CA5BBgCAGpASn6JYV6wcclS43SGH4lxxSolPqePK6jeCDAAANcAZ4lTekDxJCggz5a9zh+RyP5kaRpABAKCGZCRnKH9kvmJcMX7tsa5Y5Y/M5z4ytYAb4gEAUIMykjOU3iWdO/vWEYIMAAA1zBniVGqnVLPLaBCYWgIAALZFkAEAALZFkAEAALZFkAEAALZFkAEAALZFkAEAALZFkAEAALZFkAEAALZFkAEAALZFkAEAALZFkAEAALZFkAEAALZFkAEAALZFkAEAALZFkAEAALZFkAEAALZFkAEAALZFkAEAALZFkAEAALZFkAEAALZFkAEAALZFkAEAALZFkAEAALZl6SDj8Xg0bdo0JSQkKDw8XImJiXr88cdlGIbZpQEAAAtoZHYBF/LUU09pwYIF+tOf/qRu3brpww8/1Pjx49WsWTPdf//9ZpcHAABMZukg8/777ys9PV1Dhw6VJHXq1EmvvPKKNm7caHJlAADACiwdZPr06aNFixZp9+7duuKKK7Rt2za99957mjdvXqXvKS0tVWlpqe+12+2WJJWVlamsrKzWa26oyo8tx9h8jIU1MA7WwVhYR1XGItjxchgWXnDi9Xr161//WnPnzpXT6ZTH49Hs2bP10EMPVfqe6dOna8aMGQHtS5YsUURERG2WCwAAakhJSYlGjRqlkydPyuVyVdrP0kHmr3/9q375y1/q6aefVrdu3bR161bl5ORo3rx5ysrKqvA9FZ2RiYuL07Fjxy54IHBpysrKVFhYqMGDBys0NNTscho0xsIaGAfrYCysoypj4Xa71bp164sGGUtPLf3yl7/U1KlTdeedd0qSunfvri+//FJz5sypNMiEhYUpLCwsoD00NJQvcB3gOFsHY2ENjIN1MBbWEcxYBDtWlg4yJSUlCgnxv0Lc6XTK6/WaVBEAoCHweD0q2lekg6cOKjoqWinxKXKGOM0uCxWwdJAZNmyYZs+erfj4eHXr1k0fffSR5s2bpx//+MdmlwYAqKcKdhYoe0W2DrgP+NpiXbHKG5KnjOQMEytDRSwdZObPn69p06bp5z//uY4cOaIOHTpowoQJevTRR80uDQBQDxXsLFDm0kwZ8l8+WuwuVubSTOWPzCfMWIylg0xUVJRyc3OVm5trdikAgHrO4/Uoe0V2QIiRJEOGHHIoZ0WO0rukM81kIZZ+RAEAAHWlaF+R33TS+QwZ2u/er6J9RXVYFS6GIAMAgKSDpw7WaD/UDYIMAACSoqOia7Qf6gZBBgAASSnxKYqNiq10u0MOxbnilBKfUodV4WIIMgAASFq+a7m+/e7bCrc55JAk5Q7JZaGvxVj6qiUAAOpCZZddl2sZ3lKLhi3i0msL4owMAKBBu9Bl1+XCG4UrvUt6HVaFYBFkAAAN2sUuu5akA6cOcNm1RTG1BACwtUt9LhKXXdsbQQYAYFs18VwkLru2N6aWAAC2VL5A9/xpofLnIhXsLAhqPynxKYp1xfquTDofl11bG0EGAGA7F3sukiTlrMiRx+u56L6cIU7lDcmTpIAww2XX1keQAQDYTk0/FykjOUP5I/MV44rxa491xfLEa4tjjQwAwHZqY4FuRnKG0rukX9LCYdQ9ggwAwHZqa4GuM8Sp1E6p1agIZmFqCQBgOyzQRTmCDADAdligi3IEGQCALbFAFxJrZAAANsYCXRBkAAC2xgLdho2pJQAAYFsEGQAAYFsEGQAAYFsEGQAAYFsEGQAAYFsEGQAAYFsEGQAAYFsEGQAAYFsEGQAAYFsEGQAAYFs8ogAAYAser4dnKiEAQQYAYHkFOwuUvSJbB9wHfG2xrljlDcnjKdcNHFNLAABLK9hZoMylmX4hRpKK3cXKXJqpgp0FJlUGKyDIAAAsy+P1KHtFtgwZAdvK23JW5Mjj9dR1abAIggwAwLKK9hUFnIk5lyFD+937VbSvqA6rgpWwRgYAYCnnLurdcXRHUO85eOpgLVcFqyLIAAAso6JFvcGIjoqupYpgdQQZAIAllC/qrWg9TGUccijWFauU+JRarAxWxhoZAIDpLrSotzIOOSRJuUNyuZ9MA0aQAQCY7mKLeisS64pV/sh87iPTwDG1BAAwXbCLdR9JeURd23Tlzr7wIcgAAEwX7GLdgZcNVGqn1NotBrbC1BIAwHQp8SmKdcX61r2czyGH4lxxLOpFAIIMAMB0zhCn8obkSVJAmGFRLy6EIAMAsISM5Azlj8xXjCvGr51FvbgQ1sgAACwjIzlD6V3SfXf2ZVEvLoYgAwCwFGeIkwW9CBpTSwAAwLYIMgAAwLYIMgAAwLYIMgAAwLYIMgAAwLYIMgAAwLYIMgAAwLYIMgAAwLYIMgAAwLYIMgAAwLYIMgAAwLYIMgAAwLYIMgAAwLYIMgAAwLYsH2SKi4s1ZswYtWrVSuHh4erevbs+/PBDs8sCAAAW0MjsAi7km2++Ud++fXXjjTfqnXfeUZs2bbRnzx61aNHC7NIAAIAFWDrIPPXUU4qLi9NLL73ka0tISDCxIgAAYCWWDjJvvPGG0tLSNGLECK1bt04xMTH6+c9/rrvvvrvS95SWlqq0tNT32u12S5LKyspUVlZW6zU3VOXHlmNsPsbCGhgH62AsrKMqYxHseDkMwzAuqapa1KRJE0nS5MmTNWLECG3atEnZ2dlauHChsrKyKnzP9OnTNWPGjID2JUuWKCIiolbrBQAANaOkpESjRo3SyZMn5XK5Ku1n6SDTuHFj9erVS++//76v7f7779emTZu0YcOGCt9T0RmZuLg4HTt27IIHApemrKxMhYWFGjx4sEJDQ80up0FjLKyBcbAOxsI6qjIWbrdbrVu3vmiQsfTUUnR0tLp27erXlpycrNdee63S94SFhSksLCygPTQ0lC9wHeA4WwdjYQ2Mg3UwFtYRzFgEO1aWvvy6b9++2rVrl1/b7t271bFjR5MqAgAAVmLpIPPAAw/oX//6l5544gl99tlnWrJkiRYtWqSJEyeaXRoAALAASweZ3r17a9myZXrllVd05ZVX6vHHH1dubq5Gjx5tdmkAAMACLL1GRpJuvfVW3XrrrWaXAQAALMjSZ2QAAAAuhCADAABsiyADAABsiyADAABsiyADAABsiyADAABsiyADAABsiyADAABsiyADAABsiyADAABsiyADAABsiyADAABsiyADAABsiyADAABsiyADAABsiyADAABsiyADAABsiyADAABsiyADAABsiyADAABsiyADAABsiyADAABsK+gg89VXX9VmHQAAAFUWdJDp1q2blixZUpu1AAAAVEnQQWb27NmaMGGCRowYoa+//ro2awIAAAhK0EHm5z//uf7973/r+PHj6tq1q958883arAsAAOCiGlWlc0JCglavXq3nnntOGRkZSk5OVqNG/rvYsmVLjRYIAABQmSoFGUn68ssvVVBQoBYtWig9PT0gyAAAANSVKqWQF198Ub/4xS80aNAgffLJJ2rTpk1t1QUAAHBRQQeZIUOGaOPGjXruued011131WZNAAAAQQk6yHg8Hv373/9WbGxsbdYDAAAQtKCDTGFhYW3WAQAAUGU8ogAAANgWlxwBAPx4vB4V7SvSwVMHFR0VrZT4FDlDnGaXBVSIIAMA8CnYWaDsFdk64D7ga4t1xSpvSJ4ykjNMrAyoGFNLAABJ34eYzKWZfiFGkordxcpcmqmCnQUmVQZUjiADADbh8Xq09ou1emX7K1r7xVp5vJ4a3Xf2imwZMgK2lbflrMip0c8EagJTSwBgMRWtUVm+a3mtTvkU7SsKOBNzLkOG9rv3q2hfkVI7pV7y5wE1hSADABZS0RqVVuGtdPzb4wF9y6d88kfmX3KYOXjqYI32A+oKU0sAYBGVrVGpKMRINTvlEx0VXaP9gLpCkAEAC7jQGpULOXfK51KkxKco1hUrhxwVbnfIoThXnFLiUy7pc4CaRpABAAu42BqVi7nUKR9niFN5Q/IkKSDMlL/OHZLL/WRgOQQZALCASw0iNTHlk5GcofyR+Ypxxfi1x7pia2QdDlAbWOwLABZQ3SDikEOxrtgam/LJSM5Qepd07uwL2yDIAIAFlK9RKXYXB71OpramfJwhTi6xhm0wtQQAFhDMGpVW4a382pnyATgjAwCWUb5GpaIb3+UOyWXKB6gAQQYALORia1SY8gH8EWQAwGJYowIEjzUyAADAtggyAADAtggyAADAtggyAADAtggyAADAtggyAADAtggyAADAtggyAADAtggyAADAtggyAADAtggyAADAtggyAADAtggyAADAtmwVZJ588kk5HA7l5OSYXQoAALAA2wSZTZs26YUXXtBVV11ldikAAMAibBFkTp8+rdGjR+vFF19UixYtzC4HAABYRCOzCwjGxIkTNXToUA0aNEizZs26YN/S0lKVlpb6XrvdbklSWVmZysrKarXOhqz82HKMzcdYWAPjYB2MhXVUZSyCHS/LB5m//vWv2rJlizZt2hRU/zlz5mjGjBkB7StXrlRERERNl4fzFBYWml0C/hdjYQ2Mg3UwFtYRzFiUlJQEtS+HYRjGpRZUW/bv369evXqpsLDQtzYmNTVVPXr0UG5uboXvqeiMTFxcnI4dOyaXy1UXZTdIZWVlKiws1ODBgxUaGmp2OQ0aY2ENjIN1MBbWUZWxcLvdat26tU6ePHnB39+WPiOzefNmHTlyRNdee62vzePxaP369XruuedUWloqp9Pp956wsDCFhYUF7Cs0NJQvcB3gOFsHY2ENjIN1MBbWEcxYBDtWlg4yAwcO1Pbt2/3axo8fr6SkJD344IMBIQYAADQslg4yUVFRuvLKK/3aIiMj1apVq4B2AADQ8Nji8msAAICKWPqMTEXWrl1rdgkA6gmP16OifUU6eOqgoqOilRKfImcIU9aAndguyABATSjYWaDsFdk64D7ga4t1xSpvSJ4ykjNMrAxAVTC1BKDBKdhZoMylmX4hRpKK3cXKXJqpgp0FJlUGoKoIMgAaFI/Xo+wV2TIUeAut8racFTnyeD11XRqAaiDIAGhQivYVBZyJOZchQ/vd+1W0r6gOqwJQXayRARC0+rA49uCpgzXaD4C5CDIAglJfFsdGR0XXaD8A5mJqCcBF1afFsSnxKYp1xcohR4XbHXIozhWnlPiUOq4MQHUQZABcUH1bHOsMcSpvSJ4kBYSZ8te5Q3JtN2UGNFQEGQAXVB8Xx2YkZyh/ZL5iXDF+7bGuWOWPzLfVVBnQ0LFGBsAF1dfFsRnJGUrvkm77xctAQ0eQAXBB9XlxrDPEqdROqWaXAeASMLUE4IJYHAvAyggyAC6IxbEArIwgA+CiWBwLwKpYIwMgKCyOBWBFBBkAF1QfHksAoP4iyACoVH15LAGA+os1MgAqVJ8eSwCg/iLIAAhQ3x5LAKD+IsgACFAfH0sAoH4iyAAIUF8fSwCg/iHIAAhQnx9LAKB+IcgACMBjCQDYBUEGQAAeSwDALggyACrEYwkA2AE3xANQKR5LAMDqCDIALsgZ4lRqp1SzywCACjG1BAAAbIsgAwAAbIsgAwAAbIsgAwAAbIsgAwAAbIsgAwAAbIsgAwAAbIsgAwAAbIsgAwAAbIsgAwAAbIsgAwAAbIsgAwAAbIsgAwAAbIsgAwAAbIsgAwAAbIsgAwAAbIsgAwAAbIsgAwAAbIsgAwAAbIsgAwAAbIsgAwAAbIsgAwAAbIsgAwAAbIsgAwAAbKuR2QUAsCaP16OifUU6eOqgoqOilRKfImeI0+yyAMAPQQZAgIKdBcpeka0D7gO+tlhXrPKG5CkjOcPEygDAH1NLAPwU7CxQ5tJMvxAjScXuYmUuzVTBzgKTKgOAQAQZAD4er0fZK7JlyAjYVt6WsyJHHq+nrksDgAoRZAD4FO0rCjgTcy5Dhva796toX1EdVgUAlSPIAPA5eOpgjfYDgNpGkAHgEx0VXaP9AKC2EWQA+KTEpyjWFSuHHBVud8ihOFecUuJT6rgyAKgYQQaAjzPEqbwheZIUEGbKX+cOyeV+MgAsgyADwE9GcobyR+YrxhXj1x7rilX+yHzuIwPAUix9Q7w5c+aooKBAn376qcLDw9WnTx899dRT6tKli9mlAfVaRnKG0rukc2dfAJZn6SCzbt06TZw4Ub1799Z3332nX//617r55pu1Y8cORUZGml0eUCus8mgAZ4hTqZ1S6/xzAaAqLB1kVqxY4fd68eLFatu2rTZv3qz+/fubVBVQe3g0AABUjaWDzPlOnjwpSWrZsmWlfUpLS1VaWup77Xa7JUllZWUqKyur3QIbsPJjG+wx9ng92nBggw6dPqT2TdvrhtgbGvy0xZu73tTYZWNlyFB4SLiv/evTX2ts/ljpdmlYl2EX3U9VxwK1g3GwDsbCOqoyFsGOl8MwjMB7kVuQ1+vVbbfdphMnTui9996rtN/06dM1Y8aMgPYlS5YoIiKiNksEAAA1pKSkRKNGjdLJkyflcrkq7WebIHPvvffqnXfe0XvvvafY2NhK+1V0RiYuLk7Hjh274IHApSkrK1NhYaEGDx6s0NDQSvude9bhXOWX9r58+8tBnXWob97b956GLhl60X5/H/V39Yvvd8E+wY4FahfjYB2MhXVUZSzcbrdat2590SBji6mlSZMm6a233tL69esvGGIkKSwsTGFhYQHtoaGhfIHrwIWOs8frUXZhtkq8JRVud8ihnMIcpXdNb3DTTIdKDulb77dB9Qv2e8x33hoYB+tgLKwjmLEIdqwsfR8ZwzA0adIkLVu2TKtXr1ZCQoLZJeES8EDCyvFoAACoHksHmYkTJ+ovf/mLlixZoqioKB06dEiHDh3St99e/F+usB4eSFg5Hg0AANVj6SCzYMECnTx5UqmpqYqOjvb9efXVV80uDdXAWYfK8WgAAKgeSwcZwzAq/DNu3DizS0M1cNbhwng0AABUnS0W+6J+KD/rkLk0Uw45/K5c4qzD93g0AABUDUEGdar8rENFd6/NHZLLWQfxaAAAqAqCDOocZx0AADWFIANTcNYBAFATLL3YFwAA4EI4I2NDHq+HaRkAAESQsZ2CnQUVLpTNG5LHQlkAQIPD1JKNFOwsUObSzIDb/Be7i5W5NFMFOwtMqgwAAHMQZGzC4/Uoe0V2wFOjJfnaclbkyOP11HVpAACYhiBjEzxwEQCAQAQZm+CBiwAABCLI2AQPXAQAIBBBxiZ44CIAAIEIMjZR/sBFSQFhhgcuAgAaKoJMHfN4PVr7xVq9sv0Vrf1ibZWuMip/4GKMK8avPdYVq/yR+dxHBgDQ4HBDvDpUEzez44GLAAD8H4JMHSm/md3594Epv5ldVc6o8MBFAAC+x9RSHeBmdgAA1A6CTB3gZnYAANQOgkwd4GZ2AADUDoJMHeBmdgAA1A6CTB3gZnYAANQOgkwd4GZ2AADUDoJMHeFmdgAA1DzuI1OHuJkdAAA1iyBTx7iZHQAANYepJQAAYFsEGQAAYFsEGQAAYFsEGQAAYFsEGQAAYFsEGQAAYFsEGQAAYFsEGQAAYFsEGQAAYFsEGQAAYFsEGQAAYFsEGQAAYFsEGQAAYFsEGQAAYFsEGQAAYFsEGQAAYFsEGQAAYFsEGQAAYFsEGQAAYFuNzC7Ajjxej4r2FengqYOKjopWSnyKnCFOs8sCAKDBIchUUcHOAmWvyNYB9wFfW6wrVnlD8pSRnGFiZQAANDxMLVVBwc4CZS7N9AsxklTsLlbm0kwV7CwwqTIAABomgkyQPF6Psldky5ARsK28LWdFjjxeT12XBgBAg0WQCVLRvqKAMzHnMmRov3u/ivYV1WFVAAA0bASZIB08dbBG+wEAgEtHkAlSdFR0jfYDAACXjiATpJT4FMW6YuWQo8LtDjkU54pTSnxKHVcGAEDDRZAJkjPEqbwheZIUEGbKX+cOyeV+MgAA1CGCTBVkJGcof2S+Ylwxfu2xrljlj8znPjIAANQxbohXRRnJGUrvks6dfQEAsACCTDU4Q5xK7ZRqdhkAADR4TC0BAADbIsgAAADbIsgAAADbIsgAAADbIsgAAADbskWQef7559WpUyc1adJE119/vTZu3Gh2SQAAwAIsH2ReffVVTZ48WY899pi2bNmiq6++WmlpaTpy5IjZpQEAAJNZPsjMmzdPd999t8aPH6+uXbtq4cKFioiI0B//+EezSwMAACaz9A3xzp49q82bN+uhhx7ytYWEhGjQoEHasGFDhe8pLS1VaWmp77Xb7ZYklZWVqaysrHYLbsDKjy3H2HyMhTUwDtbBWFhHVcYi2PGydJA5duyYPB6P2rVr59ferl07ffrppxW+Z86cOZoxY0ZA++uvv66IiIhaqRP/Z/ny5WaXgP/FWFgD42AdjIV1BDMWJSUlkiTDMC7Yz9JBpjoeeughTZ482fe6uLhYXbt21U9/+lMTqwIAANVx6tQpNWvWrNLtlg4yrVu3ltPp1OHDh/3aDx8+rPbt21f4nrCwMIWFhfleN23aVPv371dUVJQcDket1tuQud1uxcXFaf/+/XK5XGaX06AxFtbAOFgHY2EdVRkLwzB06tQpdejQ4YL9LB1kGjdurJ49e2rVqlUaPny4JMnr9WrVqlWaNGlSUPsICQlRbGxsLVaJc7lcLv6isAjGwhoYB+tgLKwj2LG40JmYcpYOMpI0efJkZWVlqVevXrruuuuUm5urM2fOaPz48WaXBgAATGb5IHPHHXfo6NGjevTRR3Xo0CH16NFDK1asCFgADAAAGh7LBxlJmjRpUtBTSTBHWFiYHnvsMb/1STAHY2ENjIN1MBbWURtj4TAudl0TAACARVn+zr4AAACVIcgAAADbIsgAAADbIsgAAADbIsig2ubMmaPevXsrKipKbdu21fDhw7Vr1y6zy4KkJ598Ug6HQzk5OWaX0iAVFxdrzJgxatWqlcLDw9W9e3d9+OGHZpfV4Hg8Hk2bNk0JCQkKDw9XYmKiHn/88Ys+uweXbv369Ro2bJg6dOggh8Oh119/3W+7YRh69NFHFR0drfDwcA0aNEh79uyp1mcRZFBt69at08SJE/Wvf/1LhYWFKisr080336wzZ86YXVqDtmnTJr3wwgu66qqrzC6lQfrmm2/Ut29fhYaG6p133tGOHTv0zDPPqEWLFmaX1uA89dRTWrBggZ577jnt3LlTTz31lObOnav58+ebXVq9d+bMGV199dV6/vnnK9w+d+5cPfvss1q4cKE++OADRUZGKi0tTf/973+r/Flcfo0ac/ToUbVt21br1q1T//79zS6nQTp9+rSuvfZa/e53v9OsWbPUo0cP5ebmml1WgzJ16lT985//VFFRkdmlNHi33nqr2rVrpz/84Q++th/96EcKDw/XX/7yFxMra1gcDoeWLVvme9SQYRjq0KGDfvGLX2jKlCmSpJMnT6pdu3ZavHix7rzzzirtnzMyqDEnT56UJLVs2dLkShquiRMnaujQoRo0aJDZpTRYb7zxhnr16qURI0aobdu2uuaaa/Tiiy+aXVaD1KdPH61atUq7d++WJG3btk3vvfeebrnlFpMra9j27t2rQ4cO+f091axZM11//fXasGFDlfdnizv7wvq8Xq9ycnLUt29fXXnllWaX0yD99a9/1ZYtW7Rp0yazS2nQ/vOf/2jBggWaPHmyfv3rX2vTpk26//771bhxY2VlZZldXoMydepUud1uJSUlyel0yuPxaPbs2Ro9erTZpTVohw4dkqSARw21a9fOt60qCDKoERMnTtTHH3+s9957z+xSGqT9+/crOztbhYWFatKkidnlNGher1e9evXSE088IUm65ppr9PHHH2vhwoUEmTq2dOlS/c///I+WLFmibt26aevWrcrJyVGHDh0Yi3qEqSVcskmTJumtt97SmjVrFBsba3Y5DdLmzZt15MgRXXvttWrUqJEaNWqkdevW6dlnn1WjRo3k8XjMLrHBiI6OVteuXf3akpOTtW/fPpMqarh++ctfaurUqbrzzjvVvXt3jR07Vg888IDmzJljdmkNWvv27SVJhw8f9ms/fPiwb1tVEGRQbYZhaNKkSVq2bJlWr16thIQEs0tqsAYOHKjt27dr69atvj+9evXS6NGjtXXrVjmdTrNLbDD69u0bcBuC3bt3q2PHjiZV1HCVlJQoJMT/15zT6ZTX6zWpIkhSQkKC2rdvr1WrVvna3G63PvjgA91www1V3h9TS6i2iRMnasmSJVq+fLmioqJ8c5vNmjVTeHi4ydU1LFFRUQFrkyIjI9WqVSvWLNWxBx54QH369NETTzyhkSNHauPGjVq0aJEWLVpkdmkNzrBhwzR79mzFx8erW7du+uijjzRv3jz9+Mc/Nru0eu/06dP67LPPfK/37t2rrVu3qmXLloqPj1dOTo5mzZqlzp07KyEhQdOmTVOHDh18VzZViQFUk6QK/7z00ktmlwbDMAYMGGBkZ2ebXUaD9OabbxpXXnmlERYWZiQlJRmLFi0yu6QGye12G9nZ2UZ8fLzRpEkT47LLLjMefvhho7S01OzS6r01a9ZU+PshKyvLMAzD8Hq9xrRp04x27doZYWFhxsCBA41du3ZV67O4jwwAALAt1sgAAADbIsgAAADbIsgAAADbIsgAAADbIsgAAADbIsgAAADbIsgAAADbIsgAAADbIsgAsBWPx6M+ffooIyPDr/3kyZOKi4vTww8/bFJlAMzAnX0B2M7u3bvVo0cPvfjiixo9erQk6a677tK2bdu0adMmNW7c2OQKAdQVggwAW3r22Wc1ffp0ffLJJ9q4caNGjBihTZs26eqrrza7NAB1iCADwJYMw9BNN90kp9Op7du367777tMjjzxidlkA6hhBBoBtffrpp0pOTlb37t21ZcsWNWrUyOySANQxFvsCsK0//vGPioiI0N69e3XgwAGzywFgAs7IALCl999/XwMGDNDKlSs1a9YsSdI//vEPORwOkysDUJc4IwPAdkpKSjRu3Djde++9uvHGG/WHP/xBGzdu1MKFC80uDUAd44wMANvJzs7W22+/rW3btikiIkKS9MILL2jKlCnavn27OnXqZG6BAOoMQQaAraxbt04DBw7U2rVr1a9fP79taWlp+u6775hiAhoQggwAALAt1sgAAADbIsgAAADbIsgAAADbIsgAAADbIsgAAADbIsgAAADbIsgAAADbIsgAAADbIsgAAADbIsgAAADbIsgAAADbIsgAAADb+v+Q9kerfsbGowAAAABJRU5ErkJggg==",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"rand = np.random.default_rng(42) # RNG with fixed seed\n",
"\n",
"# Generate, Scale, round and sort random numbers for an increasing slope\n",
"scalar: int = 10\n",
"x: np.array = np.round(np.sort(rand.random(20) * scalar), decimals=2)\n",
"y: np.array = np.round(np.sort(rand.random(20) * scalar), decimals=2)\n",
"\n",
"# Plot these values\n",
"plt.title(\"Scattered Random Values\")\n",
"plt.grid()\n",
"plt.xlabel(\"X\")\n",
"plt.ylabel(\"Y\")\n",
"plt.scatter(x,y, color='g')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "083ba4ea-8e6f-4286-8049-1c8e3f22c004",
"metadata": {
"nbgrader": {
"grade": false,
"grade_id": "cell-caa85fe6a76214bf",
"locked": true,
"schema_version": 3,
"solution": false,
"task": false
}
},
"source": [
"Aus den erzeugten Daten ist klar ersichtlich, dass diese einem Trend folgen. Mittels SciPy wollen wir diesen Trend darstellen.\n",
"\n",
"Dazu wird die Funktion `linregress` verwendet. Diese verlangt, wie aus der [Dokumentation](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.linregress.html#scipy.stats.linregress) zu entnehmen, zwei arrays mit Daten. \n",
"\n",
"Die Ausgabe ist aufgespalten in 5 Parameter:\n",
"- slope: die Steigung `m` der Geraden\n",
"- intercept: der Punkt an dem die Gerade die y-Achse trifft oder das `b`\n",
"- rvalue: der Pearson Korrelations Koefficient, welcher voerst ignoriert wird\n",
"- pvalue: der p-Wert das die Nullhypothese stimmt, wird auch ignoriert\n",
"- stderr: der Standard Error der Steigung, unter der Annahme einer Normalverteilung der Daten *(PCGs sind Normalverteilt)*"
]
},
{
"cell_type": "code",
"execution_count": 50,
"id": "9c1959d8-5bac-45fa-9aa2-47fa79943d72",
"metadata": {
"nbgrader": {
"grade": false,
"grade_id": "cell-553a583b633273d5",
"locked": true,
"schema_version": 3,
"solution": false,
"task": false
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Slope: 0.00011705479307062861\n",
"Intercept: 0.12499266634828204\n",
"Std Err: 0.002148109946128207\n"
]
}
],
"source": [
"slope, intercept, _, _, stderr = stats.linregress(x,y)\n",
"print(f\"Slope: {slope}\\nIntercept: {intercept}\\nStd Err: {stderr}\")"
]
},
{
"cell_type": "markdown",
"id": "2c2bd060-bb4c-440f-9a04-72382c9a33eb",
"metadata": {
"nbgrader": {
"grade": false,
"grade_id": "cell-111845c39238eeee",
"locked": true,
"schema_version": 3,
"solution": false,
"task": false
}
},
"source": [
"Aus `slope` & `intercept` lässt sich folglich eine Gerade definieren:"
]
},
{
"cell_type": "code",
"execution_count": 45,
"id": "1e30868c-f11f-43bd-a60b-200ec00e903f",
"metadata": {
"nbgrader": {
"grade": false,
"grade_id": "cell-49d79f2b8dcf7315",
"locked": true,
"schema_version": 3,
"solution": false,
"task": false
}
},
"outputs": [],
"source": [
"def line(x: float) -> float:\n",
" '''\n",
" Evaluates the rounded line from the previous\n",
" evaluated linear regression model\n",
"\n",
" Note: Output rounded to 2 decimal places\n",
" '''\n",
" res: float = slope * x + intercept\n",
" rounded: np.float64 = np.round(res, decimals=2)\n",
" return float(rounded)"
]
},
{
"cell_type": "markdown",
"id": "8fdd9724-5c61-471d-a121-787f2d56f132",
"metadata": {
"nbgrader": {
"grade": false,
"grade_id": "cell-a63e440ba0b57186",
"locked": true,
"schema_version": 3,
"solution": false,
"task": false
}
},
"source": [
"Diese kann über den gesamten bereich dargestellt werden. Dazu werden die bereits bekannten x-Werte verwendet:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "0a59d146-4ae3-429a-a67e-7c158d5ebac7",
"metadata": {
"nbgrader": {
"grade": false,
"grade_id": "cell-5239bfcad5788ae3",
"locked": true,
"schema_version": 3,
"solution": false,
"task": false
}
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Calculate the Line using vectorization\n",
"regline: np.array = np.vectorize(line)(x)\n",
"\n",
"# Plot tvalues\n",
"plt.title(\"Scattered Random Values\")\n",
"plt.grid()\n",
"\n",
"plt.xlabel(\"X\")\n",
"plt.ylabel(\"Y\")\n",
"\n",
"plt.scatter(x,y, color='g', label=\"Original Data\")\n",
"plt.plot(x, regline, color='m', label=\"Fitted line\")\n",
"\n",
"plt.legend()\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "802bf60a-e402-4912-96bf-baa6cd398c6e",
"metadata": {
"nbgrader": {
"grade": false,
"grade_id": "cell-e0da661ffad2086e",
"locked": true,
"schema_version": 3,
"solution": false,
"task": false
}
},
"source": [
"Mit diesem Model lässt sich dementsprechend die \"Zukunft\" vorhersagen. Hierfür können wir im folgenden einfach die Werte für `-1` & `11` berechnen und diese dem Plot hinzufügen:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "e62f6248-5813-4df0-9715-a72d3a5467f8",
"metadata": {
"nbgrader": {
"grade": false,
"grade_id": "cell-92a5bbb041e28a56",
"locked": true,
"schema_version": 3,
"solution": false,
"task": false
}
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Future Values\n",
"fut: np.array = np.array([line(-1), line(11)])\n",
"\n",
"# Calculate extended Line using vectorization\n",
"ext_range: np.array = np.arange(-1,12)\n",
"regline: np.array = np.vectorize(line)(ext_range)\n",
"\n",
"# Plot values\n",
"plt.title(\"Scattered Random Values\")\n",
"plt.grid()\n",
"\n",
"plt.xlabel(\"X\")\n",
"plt.ylabel(\"Y\")\n",
"\n",
"plt.scatter(x,y, color='g', label=\"Original Data\")\n",
"plt.plot(ext_range, regline, color='m', label=\"Fitted Line\")\n",
"plt.scatter((-1, 11), fut, color='r', label=\"Predicted Data\")\n",
"\n",
"plt.legend()\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "04f002a5-4339-4225-9515-848513347697",
"metadata": {
"nbgrader": {
"grade": false,
"grade_id": "cell-6c8576c776d11325",
"locked": true,
"schema_version": 3,
"solution": false,
"task": false
}
},
"source": [
"Wie zu erwarten liegen beide Werte auf der Geraden.\n",
"\n",
"Um deren Werte zu ermitteln lassen sich diese mittels print einfach ausgeben, dies sollte immer mit Angabe des Standard Errors erfolgen. Sonst ist unklar wie genau die Daten sind:"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "563d452b-350c-4628-a97d-5d9ce268f4c4",
"metadata": {
"nbgrader": {
"grade": false,
"grade_id": "cell-7677ec5dda3e8e13",
"locked": true,
"schema_version": 3,
"solution": false,
"task": false
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Prediction of f(11) = 10.16, with standard deviation 0.07\n"
]
}
],
"source": [
"print(\"Prediction of f(11) = {}, with standard deviation {}\".format(line(11), np.round(stderr, decimals=2)))"
]
},
{
"cell_type": "markdown",
"id": "5e81b1a9-4155-4bfd-8613-2530dbe61f03",
"metadata": {
"nbgrader": {
"grade": false,
"grade_id": "cell-facd8e8ef9f4aed1",
"locked": true,
"schema_version": 3,
"solution": false,
"task": false
}
},
"source": [
"### Aufgabe\n",
"\n",
"*7 Punkte*\n",
"\n",
"Bestimme mittels Linearer Regression die *best fit* Funktion für die beiden gegebenen Datensets `x_data` & `y_data`, unter beachtung folgender Punkte:\n",
"\n",
"- Plotte das Ergebnis angemessen\n",
"- Nutze SciPys `linregress` Funktion, speichere den Output vor dem entpacken in der Variablen `l`\n",
"- Definiere die Funktion `reg_line` mit einem Eingabeparameter\n",
"- Bestimme die Werte für `-0.3` & `3.4` speichere diese als liste in variablen `future`\n",
"\n",
"Markdown Zeile (0 Punkte bei nicht beantworten):\n",
"- Erkläre die berechneten Werte `slope`, `intercept` & `stderr` in eigenen Worten und setze diese in den Kontext stochastischer Analytik.\n",
"- Interpretiere den resultierenden Plot nutze hierfür gerne Reale Beispiele."
]
},
{
"cell_type": "code",
"execution_count": 39,
"id": "f5b801bc-450e-417b-aeea-9b69d638fb64",
"metadata": {
"nbgrader": {
"grade": false,
"grade_id": "cell-cb5b277089c75c40",
"locked": true,
"schema_version": 3,
"solution": false,
"task": false
}
},
"outputs": [],
"source": [
"import numpy as np\n",
"random = np.random.default_rng(420)\n",
"\n",
"# two scuffed up One-Liners :)\n",
"x_data: np.array = np.sort(np.round(random.random(40)*np.pi, decimals=2))\n",
"y_data: np.array = np.flip(np.sort(np.round(random.random(40)*np.sqrt(2), decimals=2)))"
]
},
{
"cell_type": "code",
"execution_count": 59,
"id": "2645541f-c30f-487e-be65-3ec5ac22d427",
"metadata": {
"nbgrader": {
"grade": true,
"grade_id": "cell-12b5b631856ffe41",
"locked": false,
"points": 1,
"schema_version": 3,
"solution": true,
"task": false
}
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# BEGIN SOLUTION\n",
"slope, intercept, _, _, stderr = stats.linregress(x_data,y_data)\n",
"\n",
"def reg_line(x: float) -> float:\n",
" return float(np.round(slope*x+intercept,decimals=2))\n",
"\n",
"ext: tuple = (-0.3, 3.4)\n",
"rl: np.array = np.vectorize(reg_line)(ext)\n",
"\n",
"future: list = [reg_line(x) for x in ext]\n",
"# Plot values\n",
"plt.title(\"Scattered Random Values\")\n",
"plt.grid()\n",
"\n",
"plt.xlabel(\"X\")\n",
"plt.ylabel(\"Y\")\n",
"\n",
"plt.scatter(x_data,y_data, color='g', label=\"Original Data\")\n",
"plt.plot(ext, rl, color='m', label=\"Fitted Line\")\n",
"plt.scatter(ext, future, color='r', label=\"Predicted Data\")\n",
"\n",
"plt.legend()\n",
"\n",
"plt.show()\n",
"# END SOLUTION"
]
},
{
"cell_type": "markdown",
"id": "de8c0d91-1da1-49ed-9987-7fd2f23db0c8",
"metadata": {},
"source": [
"# BEGIN SOLUTION\n",
"# END SOLUTION"
]
},
{
"cell_type": "code",
"execution_count": 60,
"id": "aa34ed84-f200-4863-be0b-40ff5492c654",
"metadata": {
"nbgrader": {
"grade": true,
"grade_id": "cell-8f20c3645d0a9b46",
"locked": true,
"points": 6,
"schema_version": 3,
"solution": false,
"task": false
}
},
"outputs": [],
"source": [
"# Hier werden ihre Lösungen getestet\n",
"\n",
"# Check if reg_line is defined\n",
"assert 'reg_line' in dir()\n",
"\n",
"# Check if reg_line gives right output\n",
"assert reg_line(10) == -3.04\n",
"\n",
"# Check if future values are calculated right\n",
"assert future == [1.51, -0.12]\n",
"\n",
"### BEGIN HIDDEN TESTS\n",
"sl, ip, _, _, se = stats.linregress(x_data,y_data)\n",
"slope, intercept, _, _, stderr = l\n",
"\n",
"assert slope == sl\n",
"assert intercept == ip\n",
"assert stderr == se\n",
"\n",
"### END HIDDEN TESTS"
]
},
{
"cell_type": "markdown",
"id": "cbc252e7-a49b-4a30-ae51-ce3a95a3f932",
"metadata": {},
"source": [
"### Aufgabe\n",
"\n",
"*15 Punkte*\n",
"\n",
"Gegeben ist die Geburtenzahl insgesamt der Stadt Braunschweig `geburten_bs`. (Quelle: [Landesamt für Statistik Niedersachsen (LSN)](https://www.braunschweig.de/politik_verwaltung/statistik/jahrbuch/jahrbuch/02_38_export.pdf))\n",
"\n",
"Bestimme mittels Linearer Regression die Geburtenzahl für das Jahr 2030. Nutze dir die dafür gegebenen Mittel. Achte darauf auch eine angemessene Visualisierung zu finden.\n",
"\n",
"Bestimme auch die Geburtenrate für das Jahr 2028 mittels:\n",
"$$\\text{Birth Rate} = \\frac{B}{P} * 1000$$\n",
"\n",
"mit:\n",
"- $B$ = Zahl der Lebengeborenen\n",
"- $P$ = Bevölkerung zur Jahresmitte\n",
"\n",
"Nutze für $P$ den aktuellen Wert aus dem Jahr 2025 $254.867$. (Quelle: [G 2.01 Entwicklung der Einwohnerzahl seit 1988](https://www.braunschweig.de/politik_verwaltung/statistik/jahrbuch/jahrbuch/02_01_export_Grafik.pdf))\n",
"\n",
"Erkläre & Interpretiere in der Markdownzeile (Keine Antwort 0 Punkte) deine Berechnung, übe auch Kritik an der verwendeten Methodik aus. \n"
]
},
{
"cell_type": "code",
"execution_count": 58,
"id": "78db2b92-00ea-43a2-a4cc-ffc6125cfd64",
"metadata": {},
"outputs": [],
"source": [
"geburten_bs = {\n",
" 2000: 2091,\n",
" 2001: 1989,\n",
" 2002: 2016,\n",
" 2003: 1946,\n",
" 2004: 1987,\n",
" 2005: 1994,\n",
" 2006: 1986,\n",
" 2007: 2126,\n",
" 2008: 2048,\n",
" 2009: 2042,\n",
" 2010: 2193,\n",
" 2011: 2154,\n",
" 2012: 2208,\n",
" 2013: 2199,\n",
" 2014: 2300,\n",
" 2015: 2410,\n",
" 2016: 2567,\n",
" 2017: 2371,\n",
" 2018: 2474,\n",
" 2019: 2434,\n",
" 2020: 2282,\n",
" 2021: 2471,\n",
" 2022: 2328,\n",
" 2023: 2066,\n",
" 2024: 2041,\n",
"}"
]
},
{
"cell_type": "code",
"execution_count": 74,
"id": "702ab8d8-1bff-485e-9b3a-2bc56480d199",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2481.41\n",
"9.608580161417525\n"
]
},
{
"data": {
"image/png": 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/fr1a2W+++UZ4eXkJMzMz0ahRI/H7778Xedm9tsvp8cwtD+7duyfGjBkj/P39hZWVlbC1tRXNmzcXW7du1Vhv586dokWLFsLCwkKoVCoREBAgvv32W2l5cduyWbNmAoA4ceKENO+ff/4RAISHh4fWdtLlfVj4svsCBZf3K5VKERAQII4cOSKaNGkiOnfurHVfRGVBIcRLjFYkIiJ6SXl5eXB0dETfvn3x5ZdfGro6JFMcQ0RERGUmIyNDY7zTxo0bkZyczEd3kEHxDBEREZWZiIgIjB8/Hq+//jrs7e3x119/4auvvkLt2rVx5swZmJmZGbqKJFMcVE1ERGWmRo0a8PDwwGeffYbk5GRUrVoVgwcPxv/+9z+GITIoniEiIiIi2eMYIiIiIpI9BiIiIiKSPY4h0kFeXh5u3boFGxsb3jiMiIioghBC4OHDh3Bzc9N4dmFhDEQ6uHXrFjw8PAxdDSIiIiqBv//+W+2u/9owEOnAxsYGQH6DqlQqA9eGiIiIdJGWlgYPDw/p7/jzMBDpoKCbTKVSMRARERFVMLoMd+GgaiIiIpI9BiIiIiKSPQYiIiIikj2OIdKj3NxcZGdnG7oaRFQKTE1NYWxsbOhqEFEpYSDSAyEEEhMTkZKSYuiqEFEpsrOzg4uLC+9HRlQJMRDpQUEYcnJygqWlJT8siSoZIQQeP36MpKQkAICrq6uBa0RE+sZA9JJyc3OlMGRvb2/o6hBRKbGwsAAAJCUlwcnJid1nRJUMB1W/pIIxQ5aWlgauCRGVtoLfc44VJKp8GIj0hN1kRJUff8+JKi8GIiIiIpI9BiIyuHbt2mHcuHHPLRMZGQmFQoH4+HjMmjULjRo1KpO6laYNGzbAzs7O0NWQBYVCgR07dhi6GkRUjjEQyVxiYiLef/99+Pj4wNzcHM7OzmjZsiVWr16Nx48fG7p6knr16uH27dvw8PDAxIkTER4erra8LMNFWloapk+fjrp168LCwgL29vZo1qwZFixYgAcPHpRJHXRRWUNAZQnERFS+8CozGbt+/TpatmwJOzs7zJ07F/Xr14dSqcSFCxfwxRdfwN3dHT179jR0NQEAJiYmcHFxAQBYW1vD2traIPVITk5Gq1atkJaWho8//hhNmjSBra0toqKisH79emzZsgVjxowxSN0KZGVlwczMzKB10EV2djZMTU0NXQ2thBDIzc2FiQk/IonkgmeIZGz06NEwMTHB6dOn0b9/f9SuXRteXl7o1asXdu/ejR49ekhlU1JSMGzYMDg6OkKlUqFDhw44d+6ctPzcuXNo3749bGxsoFKp0KRJE5w+fVpafuTIEbRr1w6WlpaoUqUKgoOD1c6m5OXlYfLkyahatSpcXFwwa9YstbrOnz8f9erVg6WlJTw8PDBmzBikp6cDACIiIvDOO+8gNTUVCoUCCoUCs2bNQkREhDT97GvIkCHSdn/++We88sorMDc3h5eXF2bPno2cnJwi2+zDDz9EQkICTp48iXfeeQcNGjSAp6cnOnXqhG+//RajR4+WymZmZmLixIlwd3eHlZUVmjdvjoiICI1t7tixA7Vq1YK5uTmCg4Px999/S8uGDBmC3r17q5UfN24c2rVrJ023a9cOoaGhGDduHBwcHBAcHIwaNWoAAPr06QOFQiFN63LMCoUCa9euRZ8+fWBpaYlatWph586dRbYJANSoUQMff/wxBg4cCCsrK7i7u2PlypVqZRQKBVavXo2ePXvCysoKn3zyCQBg9erV8Pb2hpmZGfz8/LBp06bn7quwU6dO4bXXXoODgwNsbW3Rtm1b/PXXXxrl7t27V+QxFbxXfvvtNzRp0gRKpRKHDx8uVj2IqIIT9EKpqakCgEhNTdVY9uTJE3H58mXx5MmTpzPz8oRITzfMKy9Pp2O6d++eUCgUYt68eTqVDwoKEj169BCnTp0S165dExMmTBD29vbi/v37Qggh6tatK9566y1x5coVce3aNbF161YRGRkphBDi7NmzQqlUilGjRonIyEhx8eJFsXz5cnH37l0hhBBt27YVKpVKzJo1S1y7dk18/fXXQqFQiD/++EPa/6effioOHDgg4uLixL59+4Sfn58YNWqUEEKIzMxMsXTpUqFSqcTt27fF7du3xcOHD0VmZqY0ffv2bbF//35hbm4uvvrqKyGEEAcPHhQqlUps2LBBxMbGij/++EPUqFFDzJo1S2sb5ObmCjs7O/Hf//5XpzYbNmyYaNGihTh48KCIiYkRCxcuFEqlUly7dk0IIcT69euFqampaNq0qTh69Kg4ffq0CAgIEC1atJC2ERISInr16qW23ffff1+0bdtWmm7btq2wtrYWkyZNElevXhVXr14VSUlJAoBYv369uH37tkhKStL5mAGIatWqiS1btojo6Gjx3nvvCWtra+lnrY2np6ewsbER8+bNE1FRUeKzzz4TxsbGaj9DAMLJyUmsW7dOxMbGihs3boht27YJU1NTsXLlShEVFSUWLVokjI2Nxf79+4vc18yZM0XDhg2l6fDwcLFp0yZx5coVcfnyZTF06FDh7Ows0tLSdD6mAwcOCACiQYMG4o8//hAxMTFaj1fr7zsRlVvP+/tdGAORDoodiNLThQAM80pP1+mYjh8/LgCIbdu2qc23t7cXVlZWwsrKSkyePFkIIcShQ4eESqUSGRkZamW9vb3FmjVrhBBC2NjYiA0bNmjd18CBA0XLli2LrEvbtm1Fq1at1OY1a9ZMTJkypch1fvjhB2Fvby9Nr1+/Xtja2hZZ/t69e8LLy0uMHj1amtexY0cxd+5ctXKbNm0Srq6uWreRmJgoAIjFixerzX/llVekNhswYIAQQogbN24IY2NjcfPmTbWyHTt2FFOnTpXqDEAcP35cWn7lyhUBQJw4cUIIoXsgaty4sUZ9AYjt27dr7P9FxwxATJs2TZpOT08XAMRvv/2mrVmEEPmBqHPnzmrz3njjDdGlSxe17Y4bN06tTIsWLcTw4cPV5r3++uuia9euRe6rcCAqLDc3V9jY2IhffvlF52MqCEQ7duwocrtCPP1991zoKTALOr+IyDCKE4jYZUZqTp48icjISNStWxeZmZkA8rvD0tPTYW9vL43fsba2RlxcHGJjYwEAYWFhGDZsGIKCgvC///1Pmg/kXyHWsWPH5+63QYMGatOurq7SYxIAYN++fejYsSPc3d1hY2ODt99+G/fv39dp4Hd2djb69esHT09PLFu2TJp/7tw5zJkzR+2Yhg8fjtu3bxdrQPn27dsRGRmJ4OBgPHnyBABw4cIF5ObmwtfXV237f/75p1rbmJiYoFmzZtK0v78/7OzscOXKFZ33DwBNmjTRqZyux/zsz8PKygoqlUrt56FNYGCgxnTh42jatKna9JUrV9CyZUu1eS1btizW8d+5cwfDhw9HrVq1YGtrC5VKhfT0dCQkJKiV0+WYCtePiOSDIwZLg6Ul8O/4FoPsWwc+Pj5QKBSIiopSm+/l5QXg6WMKACA9PR2urq5ax78UXNk1a9YsvPnmm9i9ezd+++03zJw5E9999x369Omjtq2iFB5cq1AokJeXBwCIj49H9+7dMWrUKHzyySeoWrUqDh8+jKFDhyIrK+uFdwkfNWoU/v77b5w8eVJtkGx6ejpmz56Nvn37aqxjbm6uMc/R0RF2dnYabVa9enUAgI2NjfSA3/T0dBgbG+PMmTMaj3gozoBwIyMjCCHU5mm7S7KVlZVO29P1mJ/383gZutazOEJCQnD//n0sW7YMnp6eUCqVCAwMRFZWllo5XY6pNOpHRBUDA1FpUCiAcv7Bam9vj9deew0rVqzA2LFjn/uH4JVXXkFiYiJMTEzUBucW5uvrC19fX4wfPx4DBw7E+vXr0adPHzRo0ADh4eGYPXt2iep65swZ5OXlYdGiRTAyyj+puXXrVrUyZmZmyM3N1Vh38eLF2Lp1K44eParxrLlXXnkFUVFR8PHx0akeRkZG6N+/P7755hvMmDEDbm5uRZZt3LgxcnNzkZSUhNatWxdZLicnB6dPn0ZAQAAAICoqCikpKahduzaA/BB28eJFtXUiIyN1ujrL1NRUo02Ke8zFcfz4cY3pguMoSu3atXHkyBGEhIRI844cOYI6derovN8jR45g1apV6Nq1KwDg77//xr1794pRcyIiXmUma6tWrUJOTg6aNm2K77//HleuXEFUVBS++eYbXL16VTqzERQUhMDAQPTu3Rt//PEH4uPjcfToUXz00Uc4ffo0njx5gtDQUERERODGjRs4cuQITp06Jf0xnDp1Kk6dOoXRo0fj/PnzuHr1KlavXq3zHy0fHx9kZ2dj+fLluH79OjZt2oTPP/9crUyNGjWQnp6O8PBw3Lt3D48fP8a+ffswefJkLFy4EA4ODkhMTERiYiJSU1MBADNmzMDGjRsxe/ZsXLp0CVeuXMF3332HadOmFVmXuXPnwt3dHQEBAVi3bh3Onz+P2NhYbN++HceOHZPazNfXF4MGDcLgwYOxbds2xMXF4eTJk5g3bx52794tbc/U1BRjx47FiRMncObMGQwZMgSvvvqqFJA6dOiA06dPY+PGjYiOjsbMmTM1AlJRatSogfDwcCQmJkpX9JXkmHV15MgRLFiwANeuXcPKlSvxww8/4P3333/uOpMmTcKGDRuwevVqREdHY/Hixdi2bRsmTpyo835r1aqFTZs24cqVKzhx4gQGDRqk01lJIiI1pT+kqWhz584VTZs2FdbW1sLR0VH06tVLXL16Va1M27ZtBQC1V+GrfG7cuCG6du0qLCwshKOjo5g4caLIzs5WK3PgwAHRuHFjYWZmJry9vcX69et1rmexB1VXILdu3RKhoaGiZs2awtTUVFhbW4uAgACxcOFC8ejRI6lcWlqaGDt2rHBzcxOmpqbCw8NDDBo0SCQkJIjMzEwxYMAA4eHhIczMzISbm5sIDQ1Va5OIiAjRokULoVQqhZ2dnQgODhYPHjwQQuT/jN9//321evXq1UuEhIRI04sXLxaurq7CwsJCBAcHi40bNwoA0jaEEGLkyJHC3t5eABAzZ84UM2fO1HjvAFDb7p49e0SLFi2EhYWFUKlUIiAgQHzxxRfPbbOUlBQxdepU4e/vL5RKpbCwsBANGjQQ06dPV7syKSsrS8yYMUPUqFFDmJqaCldXV9GnTx9x/vx5IcTTgeA//fST8PLyEkqlUgQFBYkbN26o7W/GjBnC2dlZ2NraivHjx4vQ0FCNQdWF208IIXbu3Cl8fHyEiYmJ8PT01PmYoWUwtq2t7XN/Zzw9PcXs2bPF66+/LiwtLYWLi4tYtmyZWhlt2xVCiFWrVgkvLy9hamoqfH19xcaNG4vcjxBCTJ8+XTRp0kSa/uuvv0TTpk2Fubm5qFWrlvjhhx+Ep6enWLJkic7HVDCo+tn3kzYcVE1UsRRnULVCiEIDFMpQ586dMWDAADRr1gw5OTn48MMPcfHiRVy+fFnqwmnXrh18fX0xZ84caT1LS0uoVCoAQG5uLho1agQXFxcsXLgQt2/fxuDBgzF8+HDMnTsXABAXF4d69eph5MiRGDZsGMLDwzFu3Djs3r0bwcHBL6xnWloabG1tkZqaKu23QEZGBuLi4lCzZk2t406I5KBGjRoYN27cCx/Bog8jR47EP//8g127dpX6vgor+H3vsrsLbjy6ofN6YqbBPmaJZO15f78LM+gYoj179qhNb9iwAU5OTjhz5gzatGkjzbe0tJTuUlzYH3/8gcuXL2Pfvn1wdnZGo0aN8PHHH2PKlCmYNWsWzMzM8Pnnn6NmzZpYtGgRgPxxC4cPH8aSJUt0CkREZHgPHz7E2bNnsW3bNnz44YeGrg4RVTLlagxRwdiOqlWrqs3fvHkzHBwcUK9ePUydOlXt8uBjx46hfv36cHZ2luYFBwcjLS0Nly5dksoEBQWpbTM4OBjHjh3TWo/MzEykpaWpvYjIsGbMmIH//Oc/6NOnD0aOHGno6hBRJVNurjLLy8vDuHHj0LJlS9SrV0+a/+abb8LT0xNubm44f/48pkyZgqioKGzbtg1A/sNJnw1DAKTpxMTE55ZJS0vDkydPNAZgzps3r8RXRBHJUXx8fKnvY8mSJViyZEmp74eI5KncBKIxY8bg4sWLGs8PGjFihPR9/fr14erqio4dOyI2Nhbe3t6lUpepU6ciLCxMmk5LS4OHh0ep7IuIiEh2hADu3AGuXQOiovK/GhkB8+cbrErlIhCFhoZi165dOHjwIKpVq/bcss2bNwcAxMTEwNvbGy4uLjh58qRamTt37gCANO7IxcVFmvdsGZVKpfXyXKVSCaVSWeLjISIiIuTfpDg6+mnoeTYAFR6O4uAg30AkhMDYsWOxfft2REREoGbNmi9cJzIyEkD+ox2A/McDfPLJJ0hKSoKTkxMAYO/evVCpVNLN3QIDA/Hrr7+qbWfv3r0ajxogIirPFLMVxSrPq9uoTOTkAPHx6mGn4OvNm0Wvp1AANWoAfn6Ar2/+Ky8v/0yRARg0EI0ZMwZbtmzBzz//DBsbG2nMj62tLSwsLBAbG4stW7aga9eusLe3x/nz5zF+/Hi0adNGei5Rp06dUKdOHbz99ttYsGABEhMTMW3aNIwZM0Y6yzNy5EisWLECkydPxrvvvov9+/dj69atajfIIyIi/WKAq0SEAJKStIee2FhAyyOFJA4OT0PPs+HH2xsoR7erMWggWr16NYD8ew09a/369RgyZAjMzMywb98+LF26FI8ePYKHhwf69eundlddY2Nj7Nq1C6NGjUJgYCCsrKwQEhKidt+imjVrYvfu3Rg/fjyWLVuGatWqYe3atbzknoiI6FmPHuV3cWkLPv9eCa6VuTlQq1Z+4Hk2/NSqBRS6cry8MniX2fN4eHjgzz//fOF2PD09NbrECmvXrh3Onj1brPoRERFVOrm5RXdx/fNP0espFICnp+bZHj8/oFo1g3V16Uu5GFRNFd+sWbOwY8cOaYwXlY74+HjUrFkTZ8+eRaNGjQxdHSIqr4QA7t5VDzsF38fGAllZRa9rb68ZeHx9AR+fctXFpW8MRKWouP3nL6sk/e+JiYnSA0f/+ecf2NrawsfHB2+99RZCQkJgaWlZCjUtnsocAoYMGYKUlBTs2LHD0FUhooro8eOiu7hSUopeT6l82sVVeGyPvX2ZVb88YSCSsevXr6Nly5aws7PD3LlzUb9+fSiVSly4cAFffPEF3N3d0bNnT4PWMet5/8WUI9nZ2TA1NTV0NbTKzc2FQqGAUQU/nU0vhwOcK7DcXODGDe1ne/7+u+j1FAqgenXtoad69QrfxaVvbA0ZGz16NExMTHD69Gn0798ftWvXhpeXF3r16oXdu3ejR48eUtmUlBQMGzYMjo6OUKlU6NChA86dO6exzTVr1sDDwwOWlpbo37+/9DgWIH8cV+GHf/bu3RtDhgyRpmvUqIGPP/4YgwcPhkqlwogRI6TbMTRu3BgKhUJtEP7atWtRu3ZtmJubw9/fH6tWrZKWxcfHQ6FQYNu2bWjfvj0sLS3RsGHDIh/ZUkChUGD16tXo0qULLCws4OXlhR9//FFju99//z3atm0Lc3NzbN68GXl5eZgzZw6qVasGpVKJRo0aaTyv70X27NmDVq1awc7ODvb29ujevTtiY2M1yl2/fr3IY9qwYQPs7Oywc+dO1KlTB0qlEgkJCcjMzMTEiRPh7u4OKysrNG/eHBEREcWqHxGVEiGAe/eAI0eA9euBDz4A+vYF6tYFLC3zr8jq0gUYNw5YtQrYt+9pGKpSBXj1VSAkBPjkE+DHH4Hz5/MHSMfHA7//DixfDoSGAp065V/qzjCkgWeIZOr+/fv4448/MHfuXFhZWWkto1A8/Y/y9ddfh4WFBX777TfY2tpizZo16NixI65duyY9ey4mJgZbt27FL7/8grS0NAwdOhSjR4/G5s2bi1W3Tz/9FDNmzMDMmTMB5N+eISAgAPv27UPdunVhZmYGIP8ZdzNmzMCKFSvQuHFjnD17FsOHD5euNCzw0Ucf4dNPP0WtWrXw0UcfYeDAgYiJiYGJSdFv/+nTp+N///sfli1bhk2bNmHAgAG4cOECateuLZX54IMPsGjRIjRu3Bjm5uZYtmwZFi1ahDVr1qBx48ZYt24devbsiUuXLqFWrVo6HfujR48QFhaGBg0aID09HTNmzECfPn0QGRmpdobnRcf0+PFjzJ8/H2vXroW9vT2cnJwQGhqKy5cv47vvvoObmxu2b9+Ozp0748KFCzrXj4he0pMnml1cBd8/eFD0ekpl/hgebQOaZdrFpW8MRDIVExMDIQT8/PzU5js4OCAjIwNAfhCZP38+Dh8+jJMnTyIpKUm6t9Onn36KHTt24Mcff5Qer5KRkYGNGzfC3d0dALB8+XJ069YNixYtku4arosOHTpgwoQJ0rSxsTEAwN7eXm07M2fOxKJFi9C3b18A+bdXuHz5MtasWaMWiCZOnIhu3boBAGbPno26desiJiYG/v7+Rdbh9ddfx7BhwwAAH3/8Mfbu3Yvly5ernYEaN26ctO+CNpkyZQoGDBgAAJg/fz4OHDiApUuXYuXKlTode79+/dSm161bB0dHR1y+fFntGX8vOqbs7GysWrUKDRs2BAAkJCRg/fr1SEhIgJubm7SNPXv2YP369Zg7d65O9atMTt86XazyTd2allJNqNLJzc0/e1N4TE9UFJCQ8Px1q1fXPqC5enXg389CKh0MRKTm5MmTyMvLw6BBg5CZmQkAOHfuHNLT02Ff6L+QJ0+eqHXnVK9eXQpDQP4dwvPy8hAVFVWsQNS06Yv/8Dx69AixsbEYOnQohg8fLs3PycmBra2tWtmCm3gCT+9wnpSU9NxAVPgu5oGBgRpX0D1bz7S0NNy6dQstW7ZUK9OyZUutXYtFiY6OxowZM3DixAncu3cPeXl5APIDzbOB6EXHZGZmplbmwoULyM3Nha+vr9r+MjMzNX6uRKSj+/e1h56YGODfz0+t7Ow079dTcBVXObiQRa4YiGTKx8cHCoUCUVFRavO9vLwAQO0Zb+np6XB1ddU63sTOzk7nfRoZGWnceypby91Ni+rCe1Z6ejoA4Msvv5Seb1fAuNB/Uc8Odi7oBiwIGi9Dl3oWV48ePeDp6Ykvv/wSbm5uyMvLQ7169TQGl7/omCwsLNS6PNPT02FsbIwzZ85otI+1tbXej4Oo0sjIyA842oJPcnLR65mZ5QccbWd7HBzyBzxTucJAJFP29vZ47bXXsGLFCowdO/a5f9xfeeUVJCYmwsTEBDVq1CiyXEJCAm7duiV1yRw/fhxGRkZSt5yjoyNu374tlc/NzcXFixfRvn3759a1YMxQbm6uNM/Z2Rlubm64fv06Bg0a9MLjLa7jx49j8ODBatONGzcusrxKpYKbmxuOHDmCtm3bSvOPHDmCgIAAnfZ5//59REVF4csvv0Tr1q0BAIcPHy7hEahr3LgxcnNzkZSUJG2biP6Vl/f8Lq7n3UTYw0N76PH0ZBdXBcNAJGOrVq1Cy5Yt0bRpU8yaNQsNGjSAkZERTp06hatXr6JJkyYAgKCgIAQGBqJ3795YsGABfH19cevWLezevRt9+vSRuo7Mzc0REhKCTz/9FGlpaXjvvffQv39/qbusQ4cOCAsLw+7du+Ht7Y3Fixcj5Xn3yfiXk5MTLCwssGfPHlSrVg3m5uawtbXF7Nmz8d5778HW1hadO3dGZmYmTp8+jQcPHiAsLOyl2uaHH35A06ZN0apVK2zevBknT57EV1999dx1Jk2ahJkzZ8Lb2xuNGjXC+vXrERkZqfOg8ipVqsDe3h5ffPEFXF1dkZCQgA8++OCljqOAr68vBg0ahMGDB0sDwe/evYvw8HA0aNBAGo9EVKklJ2u/X090dP6ZoKLY2mofzOzjA5TCmWIyDAYiGfP29sbZs2cxd+5cTJ06Ff/88w+USiXq1KmDiRMnYvTo0QDyu2R+/fVXfPTRR3jnnXdw9+5duLi4oE2bNnB2dpa25+Pjg759+6Jr165ITk5G9+7d1QYhv/vuuzh37hwGDx4MExMTjB8//oVnhwDAxMQEn332GebMmYMZM2agdevWiIiIwLBhw2BpaYmFCxdi0qRJsLKyQv369TUu7S+J2bNn47vvvsPo0aPh6uqKb7/9FnXq1HnuOu+99x5SU1MxYcIEJCUloU6dOti5c+dzr+DKy8uTrgwzMjLCd999h/feew/16tWDn58fPvvsM41n/ZXU+vXr8X//93+YMGECbt68CQcHB7z66qvo3r27XrZPVC5kZuZ3cWkLPvfuFb2eqWnRXVyOjuzikgGFeNEDxQhpaWmwtbVFamoqVCqV2rKMjAzExcWhZs2aMK/EtzSXE4VCge3bt6N3796lvq/OnTvDx8cHK1asKPV9kbqSXGVW8PveZXcX3Hh0Q+d1n73J4cvcINFQ65ZUqe0zLy//mVvaQs+NG/nLi1KtWtFdXM+5FQdVTM/7+10Yf/pEBvDgwQMcOXIEERERGDlypKGrQ1Q+PXigfp+egq/R0fn38ymKSqX9Kq5atdjFRUViICIygHfffRenTp3ChAkT0KtXL0NXh8hgzHIA72TA9z6A+fPVw8/du0WvaGqaf/dmbY+lcHJiFxcVGwMRUSFl0Yu8ffv2Ut8HUXmhyAPcH+aHHr97/369n/+1RgpgXPAr972Wiwjc3TUDj59f/uMn2MVFesR3ExER6UdKitoZnu+35YeeWsmAleYtxyRpZkCUA9Cs3ZvqZ3xq1QJ4nywqIwxEesKx6USVX8HvuYCMf98zM4Hr17Xfs6dQF1f/Z77PNgKuVwGi7IFr9vkB6Jp9/vQdawAKQMx8eosKQwwCJ3ljIHpJBXcMfvz4sdrdnYmo8nn8+DEA4F7Gcy7frgwEir6KKy7u+VdxublJXVth8V9I4SfeDsjhfQqpHGMgeknGxsaws7NDUlISAMDS0lLtkQlEVE7lFKOsyL+TeFJSEuzs7PA493GpVass2WQ8HctTeGwPZnsUvaK19dNurcJdXDY2UrEls78o/YMg0hMGIj0ouBNzQSgiovLvXoruZ3kEBKzsrGBnZ1esBxWXC1lZwPXr6HFVPfD43QNcHj1nPWNjwMtL+x2aXVx4FRdVOgxEeqBQKODq6gonJyetDyslotLjv8Jf57JXQ69K33dZ0UXn9QQEro+/rvFg3HJDAG7/XsX17NkefFMrv4srNxc7i1j1trXmuJ5r9kDU4if5l7YTyQQDkR4ZGxuX3w9MokqqOHeMfvZu8sVZD0C5+N22yXgm9BQKP9Za/xeLyf9iZYUzqkdPw4790+DzsKgb7DMMkcwwEBERlSMmuYDXg6dhByNGSIOa0xKLXi9HkX8V17VnzvasCduf38Xl6oqmc4zK7BiIKiIGIiKisiYAl3TNgcx+9/LDkInaFeRfqq2aaKV+yXpBALpeBcgu9Im+RoeHJ+uiOJfA8/J3qqgYiIiISol15r9jeb79Vrps/VRE/jxVVtHrPTJ9GngG9J0uDWi23RaAND5DmqhUMBAREb0Ek9z8x09oO9vjlv5voS/elMo3/fdrrgKIs9O8SeE1e+CmCsC/J2UGzJwjrZv2axkcEJFMMRAREb2IAJCYKJ3lWfj708HN3g8A0+fcp/COFeD8SmvpZoW9zk7BNXsgVksXFxEZDn8diYj+ZZVZ9FVcmO0qlZtYaL3HJuqDmZ8d25NqAYiZB6WyO2dPKZuDIaJiYSAiInnJyQHi4tD12tOwUxCA3B8+Zz0jo/wnrPv5YWnyb2rdXLdsAMGLuIgqNAYiIqp8BOD0SMvjKL71B2JjgZwc7C5i1buW+SGn8Liey4sfA0olAGB8MR88SkTlHwMREVVcjx6h0W3NOzT73QdsM7WtEJX/xcIC51RPtN6hOaWoZzT/G4aIqHJiICKi8i0nB7hxQ/Op61FRwM2bOFvEannIf8L6s4Fn5fi9+YObq1VDo48Nf+dpIio/GIiIyPCEAO7e1Qw8164BMTHAc54ReNcSWh9JEVMVyCz09ImVQUGlfCBEVFExEBGRXuhyN2OLLKBWcn7X1taGHz8NPdeuASkpRa9obg7UqqX51HVfXzgtt9ffQRCRbDEQEZFeGeUBninaL12vnvZMwR+nq62XB+CG3dMzPAVnfKIcgL9VGRBGFwBcAACIED4egoj0i4GIqJIpznOngBI+e0oI4N49ta6tbT/nhx6fZECZW/Sq9y3yg06LjiHSWZ564f9BbFUggw9YJyIDYSAioqI9fpw/hkfb2J4HD9SK9nnm+wxjINoeiK6qfqPCKAcg2TK/jJi5QSp/6WLpHwoR0fMwEBHJXW4ukJCgPp6n4PuEhKLXUyiA6tWlR1KMvb5S6ub62xbI440KiagCYSAikgMB2D/WHNPjex/APCsgU+tNe/JVqfJ0EPOzA5p9fACLpzftWTF7ZekfBxFRKWEgIqpMnjxBvTvan7xeNaOolTIBM7Mir+KCg0NZHgERkUEwEBFVNHl5+V1Z2sb1JCTgwnPGSN+wVb9fT5QD8Puc6/ldX8bGTwdkJ/z72vv8qpRoQDYRUTnEQERUXt2/rx52Cr6Pjn5uF9cDc2g8kiLq3xsVPjHTskLNmqV3DEREFQQDEZEhZWTkX8WlbUDz/ftFr2dmlj+GR0sXV9WVTgCfPUpEVCwMRESlLS8P+Ptv7V1cN27k39OnKNWqqQeeWrXyv3p6AiZF/PoyDBERFRsDEdEL6HqjQ7sn+YOXj7f5Wj34REfnnwkqiq2t5kBmX9/88GNlpaejICKi52EgIioGsxzAO1nz8nW/+4Dj438LfRWiuaKp6dMursLdXI6O+ff0ISIig2EgIiosLw+4eVM6y7P0t6fhxzMVMH5OD9c/NkC1Zh00Q8/zuriIiMjg+AlN8pWSojmmp+D15IlU7P1Cq6WZaT6O4tq/j6l4pATEzPAyPQwiInp5DERUuWVmArGx2i9fv3u36PVMTABvb8DPDwvv7VS7d88da3DgMhFRJcNAVA6UydPJK7OCLi5toSc+Pn95UdzctA9orllT6uKaXMyfDxERVTwMRFRxpKRo3qun4Cqux4+LXs/GRnvo8fUFrK3LrPpERFR+MRBR+ZKVpdnFVfA1Kano9Qq6uLQ9i8vZmVdxERHRczEQUdkTArh1SzPwREUBcXEv7uIqfOl6QReXqWnZHQMRlVschkAlwUBEpSc1tegurkePil7P2lrzLE/BXZptbMqu/kREJBsMRPRysrLyz+poO9tz507R6xkbA15e6md5/PzyXy4u7OIiIqIyxUBELyYEcPu29geQXr8O5OYWva6Li/YBzV5esujiKs6pe562JyIyHAYieiotLb87S9vNCtPTi17PykrzLE/BtEpVdvWvRDgGgsgw+LsnXwYNRPPmzcO2bdtw9epVWFhYoEWLFpg/fz78/PykMhkZGZgwYQK+++47ZGZmIjg4GKtWrYKzs7NUJiEhAaNGjcKBAwdgbW2NkJAQzJs3DybPPCohIiICYWFhuHTpEjw8PDBt2jQMGTKkLA+3fMjO1t7Fde1a/lmgohgb5w9c1nYVl5sbu7iIiKhCM2gg+vPPPzFmzBg0a9YMOTk5+PDDD9GpUydcvnwZVv8+5Xv8+PHYvXs3fvjhB9ja2iI0NBR9+/bFkSNHAAC5ubno1q0bXFxccPToUdy+fRuDBw+Gqakp5s6dCwCIi4tDt27dMHLkSGzevBnh4eEYNmwYXF1dERwcbLDjLzVCAImJ2i9dv34dyMkpel0nJ/WzPAVfvbwAM7OyOwYiIqIyZNBAtGfPHrXpDRs2wMnJCWfOnEGbNm2QmpqKr776Clu2bEGHDh0AAOvXr0ft2rVx/PhxvPrqq/jjjz9w+fJl7Nu3D87OzmjUqBE+/vhjTJkyBbNmzYKZmRk+//xz1KxZE4sWLQIA1K5dG4cPH8aSJUsqdiB6+LDoLq6HD4tez9IS8PXFd9mRuPbM87iiqwKpFkkAkgAcAh4DOJv/4mlhIiKqzMrVGKLU1FQAQNWqVQEAZ86cQXZ2NoKCgqQy/v7+qF69Oo4dO4ZXX30Vx44dQ/369dW60IKDgzFq1ChcunQJjRs3xrFjx9S2UVBm3LhxWuuRmZmJzMxMaTotLU1fh1hsJrlAjZT8J6373s9/IaJ9fui5davoFY2M8ru4Cl/F5esLuLsDCgUG8pEUREREAMpRIMrLy8O4cePQsmVL1KtXDwCQmJgIMzMz2NnZqZV1dnZGYmKiVObZMFSwvGDZ88qkpaXhyZMnsLCwUFs2b948zJ49W2/HVlz+d4H5e/PDj/cDwFTjPoURT791ctI+rsfbm11cREREOio3gWjMmDG4ePEiDh8+bOiqYOrUqQgLC5Om09LS4OHhUWb7zzECel57Ov3Y5Gm31jV7YPrwTU/P+hQKi5UZr/4gIqLSUi4CUWhoKHbt2oWDBw+iWrVq0nwXFxdkZWUhJSVF7SzRnTt34OLiIpU5efKk2vbu/HtDwGfL3Cl0k8A7d+5ApVJpnB0CAKVSCaVSqZdjK4k4O2B016cB6KYNIIyeLp/+1lvS9xUtJBiqvhWtnYiIqGwZvbhI6RFCIDQ0FNu3b8f+/ftRs2ZNteVNmjSBqakpwsPDpXlRUVFISEhAYGAgACAwMBAXLlxA0jMP/ty7dy9UKhXq1KkjlXl2GwVlCrZR3uQaA6sDgP1ewD+26mGIiIiI9M+gZ4jGjBmDLVu24Oeff4aNjY005sfW1hYWFhawtbXF0KFDERYWhqpVq0KlUmHs2LEIDAzEq6++CgDo1KkT6tSpg7fffhsLFixAYmIipk2bhjFjxkhneUaOHIkVK1Zg8uTJePfdd7F//35s3boVu3fvNtixExERUflh0HMPq1evRmpqKtq1awdXV1fp9f3330tllixZgu7du6Nfv35o06YNXFxcsG3bNmm5sbExdu3aBWNjYwQGBuKtt97C4MGDMWfOHKlMzZo1sXv3buzduxcNGzbEokWLsHbt2op9yT0RERHpjUHPEAnx4nEa5ubmWLlyJVauXFlkGU9PT/z666/P3U67du1w9uzZYteRiIiIKj+OTiEiIiLZKxdXmVHFwiu2iIiosuEZIiIiIpI9BiIiIiKSPQYiIiIikj0GIiIiIpI9BiIiIiKSPQYiIiIikj0GIiIiIpI9BiIiIiKSPQYiIiIikj0GIiIiIpI9BiIiIiKSPQYiIiIikj0GIiIiIpI9BiIiIiKSPQYiIiIikj0GIiIiIpI9BiIiIiKSPQYiIiIikj0GIiIiIpI9BiIiIiKSPQYiIiIikj0GIiIiIpI9BiIiIiKSPQYiIiIikj0GIiIiIpI9BiIiIiKSPQYiIiIikj0GIiIiIpI9BiIiIiKSPQYiIiIikj0GIiIiIpI9BiIiIiKSPQYiIiIikj0GIiIiIpI9BiIiIiKSPQYiIiIikj0GIiIiIpI9E10L9u3bV+eNbtu2rUSVISIiIjIEnQORra1tadaDiIiIyGB0DkTr168vzXoQERERGQzHEBEREZHslSgQ3blzB2+//Tbc3NxgYmICY2NjtRcRERFRRaJzl9mzhgwZgoSEBEyfPh2urq5QKBT6rhcRERFRmSlRIDp8+DAOHTqERo0a6bk6RERERGWvRF1mHh4eEELouy5EREREBlGiQLR06VJ88MEHiI+P13N1iIiIiMqezl1mVapUURsr9OjRI3h7e8PS0hKmpqZqZZOTk/VXQyIiIqJSpnMgWrp0aSlWg4iIiMhwdA5EISEhpVkPIiIiIoMp0VVmz8rIyEBWVpbaPJVK9bKbJSIiIiozJRpU/ejRI4SGhsLJyQlWVlaoUqWK2ouIiIioIilRIJo8eTL279+P1atXQ6lUYu3atZg9ezbc3NywceNGfdeRiIiIqFSVqMvsl19+wcaNG9GuXTu88847aN26NXx8fODp6YnNmzdj0KBB+q4nERERUakp0Rmi5ORkeHl5AcgfL1RwmX2rVq1w8OBB/dWOiIiIqAyUKBB5eXkhLi4OAODv74+tW7cCyD9zZGdnp7fKEREREZWFEgWid955B+fOnQMAfPDBB1i5ciXMzc0xfvx4TJo0Sa8VJCIiIiptJQpE48ePx3vvvQcACAoKwtWrV7FlyxacPXsW77//vs7bOXjwIHr06AE3NzcoFArs2LFDbfmQIUOgUCjUXp07d1Yrk5ycjEGDBkGlUsHOzg5Dhw5Fenq6Wpnz58+jdevWMDc3h4eHBxYsWFCSwyYiIqJKqkSBKCEhAZmZmdK0p6cn+vbti3r16iEhIUHn7Tx69AgNGzbEypUriyzTuXNn3L59W3p9++23assHDRqES5cuYe/evdi1axcOHjyIESNGSMvT0tLQqVMneHp64syZM1i4cCFmzZqFL774ohhHTERERJVZia4yq1GjBmrXro2dO3fC29tbmn/37l3UrFkTubm5Om2nS5cu6NKly3PLKJVKuLi4aF125coV7NmzB6dOnULTpk0BAMuXL0fXrl3x6aefws3NDZs3b0ZWVhbWrVsHMzMz1K1bF5GRkVi8eLFacCIiIiL5KtEZIgCoXbs2AgICEB4erjZfCPHSlXpWREQEnJyc4Ofnh1GjRuH+/fvSsmPHjsHOzk4KQ0B+F56RkRFOnDghlWnTpg3MzMykMsHBwYiKisKDBw+07jMzMxNpaWlqLyIiIqq8ShSIFAoFVq1ahWnTpqFbt2747LPP1JbpS+fOnbFx40aEh4dj/vz5+PPPP9GlSxfpDFRiYiKcnJzU1jExMUHVqlWRmJgolXF2dlYrUzBdUKawefPmwdbWVnp5eHjo7ZiIiIio/ClRl1nBWaDx48fD398fAwcOxIULFzBjxgy9Vm7AgAHS9/Xr10eDBg3g7e2NiIgIdOzYUa/7etbUqVMRFhYmTaelpTEUERERVWIl7jIr0KVLFxw9ehQHDhxA9+7d9VGnInl5ecHBwQExMTEAABcXFyQlJamVycnJQXJysjTuyMXFBXfu3FErUzBd1NgkpVIJlUql9iIiIqLKq0SBqG3btmpjcurUqYPjx4/Dzs5O72OInvXPP//g/v37cHV1BQAEBgYiJSUFZ86ckcrs378feXl5aN68uVTm4MGDyM7Olsrs3bsXfn5+fBAtERERAShhIDpw4IDGHakdHBzw559/Ii8vT+ftpKenIzIyEpGRkQCAuLg4REZGIiEhAenp6Zg0aRKOHz+O+Ph4hIeHo1evXvDx8UFwcDCA/IHdnTt3xvDhw3Hy5EkcOXIEoaGhGDBgANzc3AAAb775JszMzDB06FBcunQJ33//PZYtW6bWJUZERETyVqIxRACQl5eHmJgYJCUlqYUghUKB1q1b67SN06dPo3379tJ0QUgJCQnB6tWrcf78eXz99ddISUmBm5sbOnXqhI8//hhKpVJaZ/PmzQgNDUXHjh1hZGSEfv36qQ3ytrW1xR9//IExY8agSZMmcHBwwIwZM3jJPREREUlKFIiOHz+ON998Ezdu3NDoIlMoFDrfh6hdu3bP7WL7/fffX7iNqlWrYsuWLc8t06BBAxw6dEinOhEREZH8lCgQjRw5Ek2bNsXu3bvh6uqq10vtiYiIiMpaiQJRdHQ0fvzxR/j4+Oi7PkRERERlrkSDqps3by5d+k5ERERU0ZXoDNHYsWMxYcIEJCYmon79+jA1NVVb3qBBA71UjoiIiKgslCgQ9evXDwDw7rvvSvMUCgWEEMUaVE1ERERUHpQoEMXFxem7HkREREQGU6JA5Onpqe96EBERERlMiZ9ltmnTJrRs2RJubm64ceMGAGDp0qX4+eef9VY5IiIiorJQokC0evVqhIWFoWvXrkhJSZHGDNnZ2WHp0qX6rB8RERFRqStRIFq+fDm+/PJLfPTRRzA2NpbmN23aFBcuXNBb5YiIiIjKQokCUVxcHBo3bqwxX6lU4tGjRy9dKSIiIqKyVKJAVLNmTekJ9c/as2cPateu/bJ1IiIiIipTJbrKLCwsDGPGjEFGRgaEEDh58iS+/fZbzJs3D2vXrtV3HYmIiIhKVYkC0bBhw2BhYYFp06bh8ePHePPNN+Hm5oZly5ZhwIAB+q4jERERUakqUSACgEGDBmHQoEF4/Pgx0tPT4eTkpM96EREREZWZEo0h6tChA1JSUgAAlpaWUhhKS0tDhw4d9FY5IiIiorJQokAUERGBrKwsjfkZGRk4dOjQS1eKiIiIqCwVq8vs/Pnz0veXL19GYmKiNJ2bm4s9e/bA3d1df7UjIiIiKgPFCkSNGjWCQqGAQqHQ2jVmYWGB5cuX661yRERERGWhWIEoLi4OQgh4eXnh5MmTcHR0lJaZmZnByclJ7c7VRERERBVBsQKRp6cnsrOzERISAnt7ez71noiIiCqFYg+qNjU1xfbt20ujLkREREQGUaKrzHr16oUdO3bouSpEREREhlGiGzPWqlULc+bMwZEjR9CkSRNYWVmpLX/vvff0UjkiIiKislCiQPTVV1/Bzs4OZ86cwZkzZ9SWKRQKBiIiIiKqUEoUiOLi4vRdDyIiIiKDKdEYIiIiIqLKpERniN59993nLl+3bl2JKkNERERkCCUKRA8ePFCbzs7OxsWLF5GSksKHuxIREVGFU6JApO0+RHl5eRg1ahS8vb1fulJEREREZUlvY4iMjIwQFhaGJUuW6GuTRERERGVCr4OqY2NjkZOTo89NEhEREZW6EnWZhYWFqU0LIXD79m3s3r0bISEheqkYERERUVkpUSA6e/as2rSRkREcHR2xaNGiF16BRkRERFTelCgQHThwQN/1ICIiIjKYEgWiAklJSYiKigIA+Pn5wcnJSS+VIiIiIipLJRpUnZaWhrfffhtubm5o27Yt2rZtC3d3d7z11ltITU3Vdx2JiIiISlWJAtHw4cNx4sQJ7N69GykpKUhJScGuXbtw+vRp/Pe//9V3HYmIiIhKVYm6zHbt2oXff/8drVq1kuYFBwfjyy+/ROfOnfVWOSIiIqKyUKIzRPb29rC1tdWYb2triypVqrx0pYiIiIjKUokC0bRp0xAWFobExERpXmJiIiZNmoTp06frrXJEREREZUHnLrPGjRtDoVBI09HR0ahevTqqV68OAEhISIBSqcTdu3c5joiIiIgqFJ0DUe/evUuxGkRERESGo3MgmjlzZmnWg4iIiMhgSvxw15SUFKxduxZTp05FcnIyAOCvv/7CzZs39VY5IiIiorJQosvuz58/j6CgINja2iI+Ph7Dhw9H1apVsW3bNiQkJGDjxo36ricRERFRqSnRGaKwsDAMGTIE0dHRMDc3l+Z37doVBw8e1FvliIiIiMpCiQLRqVOntF5J5u7urnYpPhEREVFFUKJApFQqkZaWpjH/2rVrcHR0fOlKEREREZWlEgWinj17Ys6cOcjOzgYAKBQKJCQkYMqUKejXr59eK0hERERU2koUiBYtWoT09HQ4OTnhyZMnaNu2LXx8fGBtbY1PPvlE33UkIiIiKlUlusrM1tYWe/fuxZEjR3Du3Dmkp6fjlVdeQVBQkL7rR0RERFTqinWG6MmTJ9i1a5c0vWvXLsTExCAxMRG//vorJk+ejIyMDL1XkoiIiKg0FesM0ddff43du3eje/fuAIAVK1agbt26sLCwAABcvXoVrq6uGD9+vP5rSkRERFRKinWGaPPmzRgxYoTavC1btuDAgQM4cOAAFi5ciK1bt+q1gkRERESlrViBKCYmBvXr15emzc3NYWT0dBMBAQG4fPmy/mpHREREVAaK1WWWkpKCzMxMafru3btqy/Py8tSWExEREVUExTpDVK1aNVy8eLHI5efPn0e1atV03t7BgwfRo0cPuLm5QaFQYMeOHWrLhRCYMWMGXF1dYWFhgaCgIERHR6uVSU5OxqBBg6BSqWBnZ4ehQ4ciPT1do16tW7eGubk5PDw8sGDBAp3rSERERJVfsQJR165dMWPGDK1Xkj158gSzZ89Gt27ddN7eo0eP0LBhQ6xcuVLr8gULFuCzzz7D559/jhMnTsDKygrBwcFq+x80aBAuXbqEvXv3YteuXTh48KDaOKe0tDR06tQJnp6eOHPmDBYuXIhZs2bhiy++KMaRExERUWVWrC6zDz/8EFu3boWfnx9CQ0Ph6+sLAIiKisKKFSuQk5ODDz/8UOftdenSBV26dNG6TAiBpUuXYtq0aejVqxcAYOPGjXB2dsaOHTswYMAAXLlyBXv27MGpU6fQtGlTAMDy5cvRtWtXfPrpp3Bzc8PmzZuRlZWFdevWwczMDHXr1kVkZCQWL16sMUCciIiI5KlYZ4icnZ1x9OhR1K5dGx988AH69OmDPn36YOrUqahTpw4OHz4MZ2dnvVQsLi4OiYmJajd7tLW1RfPmzXHs2DEAwLFjx2BnZyeFIQAICgqCkZERTpw4IZVp06YNzMzMpDLBwcGIiorCgwcP9FJXIiIiqtiKfafqmjVrYs+ePUhOTkZMTAwAwMfHB1WrVtVrxRITEwFAI2A5OztLyxITE+Hk5KS23MTEBFWrVlUrU7NmTY1tFCyrUqWKxr4zMzPVBodre5AtERERVR4lenQHAFStWhUBAQH6rEu5MW/ePMyePdvQ1SAiIqIyUqKHu5YFFxcXAMCdO3fU5t+5c0da5uLigqSkJLXlOTk5SE5OViujbRvP7qOwqVOnIjU1VXr9/fffL39AREREVG6V20BUs2ZNuLi4IDw8XJqXlpaGEydOIDAwEAAQGBiIlJQUnDlzRiqzf/9+5OXloXnz5lKZgwcPIjs7Wyqzd+9e+Pn5ae0uAwClUgmVSqX2IiIiosrLoIEoPT0dkZGRiIyMBJA/kDoyMhIJCQlQKBQYN24c/u///g87d+7EhQsXMHjwYLi5uaF3794AgNq1a6Nz584YPnw4Tp48iSNHjiA0NBQDBgyAm5sbAODNN9+EmZkZhg4dikuXLuH777/HsmXLEBYWZqCjJiIiovKmxGOI9OH06dNo3769NF0QUkJCQrBhwwZMnjwZjx49wogRI5CSkoJWrVphz549MDc3l9bZvHkzQkND0bFjRxgZGaFfv3747LPPpOW2trb4448/MGbMGDRp0gQODg6YMWMGL7knIiIiiUEDUbt27SCEKHK5QqHAnDlzMGfOnCLLVK1aFVu2bHnufho0aIBDhw6VuJ5ERERUuZXbMUREREREZYWBiIiIiGSPgYiIiIhkj4GIiIiIZI+BiIiIiGSPgYiIiIhkj4GIiIiIZI+BiIiIiGSPgYiIiIhkj4GIiIiIZI+BiIiIiGSPgYiIiIhkj4GIiIiIZI+BiIiIiGSPgYiIiIhkj4GIiIiIZI+BiIiIiGSPgYiIiIhkj4GIiIiIZI+BiIiIiGSPgYiIiIhkj4GIiIiIZI+BiIiIiGSPgYiIiIhkj4GIiIiIZI+BiIiIiGSPgYiIiIhkj4GIiIiIZI+BiIiIiGSPgYiIiIhkj4GIiIiIZI+BiIiIiGSPgYiIiIhkj4GIiIiIZI+BiIiIiGSPgYiIiIhkj4GIiIiIZI+BiIiIiGSPgYiIiIhkj4GIiIiIZI+BiIiIiGSPgYiIiIhkj4GIiIiIZI+BiIiIiGSPgYiIiIhkj4GIiIiIZI+BiIiIiGSPgYiIiIhkj4GIiIiIZI+BiIiIiGSPgYiIiIhkj4GIiIiIZI+BiIiIiGSPgYiIiIhkj4GIiIiIZI+BiIiIiGSPgYiIiIhkj4GIiIiIZK9cB6JZs2ZBoVCovfz9/aXlGRkZGDNmDOzt7WFtbY1+/frhzp07attISEhAt27dYGlpCScnJ0yaNAk5OTllfShERERUjpkYugIvUrduXezbt0+aNjF5WuXx48dj9+7d+OGHH2Bra4vQ0FD07dsXR44cAQDk5uaiW7ducHFxwdGjR3H79m0MHjwYpqammDt3bpkfCxEREZVP5T4QmZiYwMXFRWN+amoqvvrqK2zZsgUdOnQAAKxfvx61a9fG8ePH8eqrr+KPP/7A5cuXsW/fPjg7O6NRo0b4+OOPMWXKFMyaNQtmZmZlfThERERUDpXrLjMAiI6OhpubG7y8vDBo0CAkJCQAAM6cOYPs7GwEBQVJZf39/VG9enUcO3YMAHDs2DHUr18fzs7OUpng4GCkpaXh0qVLRe4zMzMTaWlpai8iIiKqvMp1IGrevDk2bNiAPXv2YPXq1YiLi0Pr1q3x8OFDJCYmwszMDHZ2dmrrODs7IzExEQCQmJioFoYKlhcsK8q8efNga2srvTw8PPR7YERERFSulOsusy5dukjfN2jQAM2bN4enpye2bt0KCwuLUtvv1KlTERYWJk2npaUxFBEREVVi5foMUWF2dnbw9fVFTEwMXFxckJWVhZSUFLUyd+7ckcYcubi4aFx1VjCtbVxSAaVSCZVKpfYiIiKiyqtCBaL09HTExsbC1dUVTZo0gampKcLDw6XlUVFRSEhIQGBgIAAgMDAQFy5cQFJSklRm7969UKlUqFOnTpnXn4iIiMqnct1lNnHiRPTo0QOenp64desWZs6cCWNjYwwcOBC2trYYOnQowsLCULVqVahUKowdOxaBgYF49dVXAQCdOnVCnTp18Pbbb2PBggVITEzEtGnTMGbMGCiVSgMfHREREZUX5ToQ/fPPPxg4cCDu378PR0dHtGrVCsePH4ejoyMAYMmSJTAyMkK/fv2QmZmJ4OBgrFq1Slrf2NgYu3btwqhRoxAYGAgrKyuEhIRgzpw5hjokIiIiKofKdSD67rvvnrvc3NwcK1euxMqVK4ss4+npiV9//VXfVSMiIqJKpEKNISIiIiIqDQxEREREJHsMRERERCR7DEREREQkewxEREREJHsMRERERCR7DEREREQkewxEREREJHsMRERERCR7DEREREQkewxEREREJHsMRERERCR7DEREREQkewxEREREJHsMRERERCR7DEREREQkewxEREREJHsMRERERCR7DEREREQkewxEREREJHsMRERERCR7DEREREQkewxEREREJHsMRERERCR7DEREREQkewxEREREJHsMRERERCR7DEREREQkewxEREREJHsMRERERCR7DEREREQkewxEREREJHsMRERERCR7DEREREQkewxEREREJHsMRERERCR7DEREREQkewxEREREJHsMRERERCR7DEREREQkewxEREREJHsMRERERCR7DEREREQkewxEREREJHsMRERERCR7DEREREQkewxEREREJHsMRERERCR7DEREREQkewxEREREJHsMRERERCR7DEREREQkewxEREREJHsMRERERCR7DEREREQkewxEREREJHsMRERERCR7sgpEK1euRI0aNWBubo7mzZvj5MmThq4SERERlQOyCUTff/89wsLCMHPmTPz1119o2LAhgoODkZSUZOiqERERkYHJJhAtXrwYw4cPxzvvvIM6derg888/h6WlJdatW2foqhEREZGBySIQZWVl4cyZMwgKCpLmGRkZISgoCMeOHTNgzYiIiKg8MDF0BcrCvXv3kJubC2dnZ7X5zs7OuHr1qkb5zMxMZGZmStOpqakAgLS0tNKpYEbxiqvVo4zWNcQ+5bZuRatvRVy3otW3Iq5b0eqr13Wp3Cn4+QghXlxYyMDNmzcFAHH06FG1+ZMmTRIBAQEa5WfOnCkA8MUXX3zxxRdfleD1999/vzAryOIMkYODA4yNjXHnzh21+Xfu3IGLi4tG+alTpyIsLEyazsvLQ3JyMuzt7aFQKEq9vkB+qvXw8MDff/8NlUpVJvusiNhOumE76YbtpDu2lW7YTroprXYSQuDhw4dwc3N7YVlZBCIzMzM0adIE4eHh6N27N4D8kBMeHo7Q0FCN8kqlEkqlUm2enZ1dGdRUk0ql4i+RDthOumE76YbtpDu2lW7YTropjXaytbXVqZwsAhEAhIWFISQkBE2bNkVAQACWLl2KR48e4Z133jF01YiIiMjAZBOI3njjDdy9exczZsxAYmIiGjVqhD179mgMtCYiIiL5kU0gAoDQ0FCtXWTlkVKpxMyZMzW67kgd20k3bCfdsJ10x7bSDdtJN+WhnRRC6HItGhEREVHlJYsbMxIRERE9DwMRERERyR4DEREREckeAxERERHJHgNRKZk3bx6aNWsGGxsbODk5oXfv3oiKilIrk5GRgTFjxsDe3h7W1tbo16+fxt20ExIS0K1bN1haWsLJyQmTJk1CTk6OWpmIiAi88sorUCqV8PHxwYYNG0r78PSqrNoqIiICCoVC45WYmFgmx/my9NVO7733Hpo0aQKlUolGjRpp3df58+fRunVrmJubw8PDAwsWLCitw9K7smqn+Ph4re+n48ePl+bh6Y0+2uncuXMYOHAgPDw8YGFhgdq1a2PZsmUa+6rIn1Fl1U78fALu37+Pzp07w83NDUqlEh4eHggNDdV4XlypvZ/087QwKiw4OFisX79eXLx4UURGRoquXbuK6tWri/T0dKnMyJEjhYeHhwgPDxenT58Wr776qmjRooW0PCcnR9SrV08EBQWJs2fPil9//VU4ODiIqVOnSmWuX78uLC0tRVhYmLh8+bJYvny5MDY2Fnv27CnT430ZZdVWBw4cEABEVFSUuH37tvTKzc0t0+MtKX20kxBCjB07VqxYsUK8/fbbomHDhhr7SU1NFc7OzmLQoEHi4sWL4ttvvxUWFhZizZo1pX2IelFW7RQXFycAiH379qm9n7Kyskr7EPVCH+301Vdfiffee09ERESI2NhYsWnTJmFhYSGWL18ulanon1Fl1U78fBIiOTlZrFq1Spw6dUrEx8eLffv2CT8/PzFw4ECpTGm+nxiIykhSUpIAIP78808hhBApKSnC1NRU/PDDD1KZK1euCADi2LFjQgghfv31V2FkZCQSExOlMqtXrxYqlUpkZmYKIYSYPHmyqFu3rtq+3njjDREcHFzah1RqSqutCj5wHjx4UHYHU4pK0k7PmjlzptY/9KtWrRJVqlSR2k0IIaZMmSL8/Pz0fxBloLTaqSAQnT17trSqXqZetp0KjB49WrRv316armyfUaXVTvx80m7ZsmWiWrVq0nRpvp/YZVZGUlNTAQBVq1YFAJw5cwbZ2dkICgqSyvj7+6N69eo4duwYAODYsWOoX7++2t20g4ODkZaWhkuXLkllnt1GQZmCbVREpdVWBRo1agRXV1e89tprOHLkSGkfTqkpSTvp4tixY2jTpg3MzMykecHBwYiKisKDBw/0VPuyU1rtVKBnz55wcnJCq1atsHPnTv1U2gD01U6pqanSNoDK9xlVWu1UgJ9PT926dQvbtm1D27ZtpXml+X5iICoDeXl5GDduHFq2bIl69eoBABITE2FmZqbx0FhnZ2epzzgxMVHj0SIF0y8qk5aWhidPnpTG4ZSq0mwrV1dXfP755/jpp5/w008/wcPDA+3atcNff/1VykelfyVtJ13o0pYVRWm2k7W1NRYtWoQffvgBu3fvRqtWrdC7d+8KGYr01U5Hjx7F999/jxEjRkjzKtNnVGm2Ez+fnho4cCAsLS3h7u4OlUqFtWvXSstK8/0kq0d3GMqYMWNw8eJFHD582NBVKfdKs638/Pzg5+cnTbdo0QKxsbFYsmQJNm3apPf9lSa+p3RTmu3k4OCAsLAwabpZs2a4desWFi5ciJ49e+p9f6VJH+108eJF9OrVCzNnzkSnTp30WLvyozTbiZ9PTy1ZsgQzZ87EtWvXMHXqVISFhWHVqlV6rqUmniEqZaGhodi1axcOHDiAatWqSfNdXFyQlZWFlJQUtfJ37tyBi4uLVKbwlS8F0y8qo1KpYGFhoe/DKVWl3VbaBAQEICYmRk9HUDZepp10UdK2LG9Ku520ad68uSzfT5cvX0bHjh0xYsQITJs2TW1ZZfmMKu120kaun08uLi7w9/dHz549sWbNGqxevRq3b9+WlpXW+4mBqJQIIRAaGort27dj//79qFmzptryJk2awNTUFOHh4dK8qKgoJCQkIDAwEAAQGBiICxcuICkpSSqzd+9eqFQq1KlTRyrz7DYKyhRsoyIoq7bSJjIyEq6urno+otKhj3bSRWBgIA4ePIjs7Gxp3t69e+Hn54cqVaq8/IGUsrJqJ23k+H66dOkS2rdvj5CQEHzyySca+6non1Fl1U7ayPH9VFheXh4AIDMzE0Apv59eelg2aTVq1Chha2srIiIi1C6hfPz4sVRm5MiRonr16mL//v3i9OnTIjAwUAQGBkrLCy4l79Spk4iMjBR79uwRjo6OWi+7nzRpkrhy5YpYuXJlhbqkVYiya6slS5aIHTt2iOjoaHHhwgXx/vvvCyMjI7Fv374yPd6S0kc7CSFEdHS0OHv2rPjvf/8rfH19xdmzZ8XZs2elq8pSUlKEs7OzePvtt8XFixfFd999JywtLSvMZfdl1U4bNmwQW7ZsEVeuXBFXrlwRn3zyiTAyMhLr1q0r0+MtKX2004ULF4Sjo6N466231LaRlJQklanon1Fl1U78fBJi9+7dYt26deLChQsiLi5O7Nq1S9SuXVu0bNlSKlOa7ycGolICQOtr/fr1UpknT56I0aNHiypVqghLS0vRp08fcfv2bbXtxMfHiy5duggLCwvh4OAgJkyYILKzs9XKHDhwQDRq1EiYmZkJLy8vtX1UBGXVVvPnzxfe3t7C3NxcVK1aVbRr107s37+/rA7zpemrndq2bat1O3FxcVKZc+fOiVatWgmlUinc3d3F//73vzI6ypdXVu20YcMGUbt2bWFpaSlUKpUICAhQu6S4vNNHO82cOVPrNjw9PdX2VZE/o8qqnfj5JMT+/ftFYGCgsLW1Febm5qJWrVpiypQpGrciKK33k+LfAyEiIiKSLY4hIiIiItljICIiIiLZYyAiIiIi2WMgIiIiItljICIiIiLZYyAiIiIi2WMgIiIiItljICIiWYuPj4dCoUBkZKShq0JEBsRARESVzpAhQ9C7d29DV4OIKhAGIiKiYsrNzZUeOklElQMDERFVanv27EGrVq1gZ2cHe3t7dO/eHbGxsRrlrl+/jvbt28PS0hINGzbEsWPHpGUbNmyAnZ0ddu7ciTp16kCpVCIhIaEsD4OIShkDERFVao8ePUJYWBhOnz6N8PBwGBkZoU+fPhpneD766CNMnDgRkZGR8PX1xcCBA5GTkyMtf/z4MebPn4+1a9fi0qVLcHJyKutDIaJSZGLoChARlaZ+/fqpTa9btw6Ojo64fPky6tWrJ82fOHEiunXrBgCYPXs26tati5iYGPj7+wMAsrOzsWrVKjRs2LDsKk9EZYZniIioUouOjsbAgQPh5eUFlUqFGjVqAIBGl1eDBg2k711dXQEASUlJ0jwzMzO1MkRUufAMERFVaj169ICnpye+/PJLuLm5IS8vD/Xq1UNWVpZaOVNTU+l7hUIBAGrdahYWFtJ8Iqp8GIiIqNK6f/8+oqKi8OWXX6J169YAgMOHDxu4VkRUHjEQEVGlVaVKFdjb2+OLL76Aq6srEhIS8MEHHxi6WkRUDnEMERFVOnl5eTAxMYGRkRG+++47nDlzBvXq1cP48eOxcOFCQ1ePiMohhRBCGLoSRET61LlzZ/j4+GDFihWGrgoRVRA8Q0RElcaDBw+wa9cuREREICgoyNDVIaIKhGOIiKjSePfdd3Hq1ClMmDABvXr1MnR1iKgCYZcZERERyR67zIiIiEj2GIiIiIhI9hiIiIiISPYYiIiIiEj2GIiIiIhI9hiIiIiISPYYiIiIiEj2GIiIiIhI9hiIiIiISPb+H04T2JHKtT0LAAAAAElFTkSuQmCC",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# BEGIN SOLUTION\n",
"years = list(geburten_bs.keys())\n",
"births = list(geburten_bs.values())\n",
"slope, intercept, _, _, stderr = stats.linregress(years, births)\n",
"\n",
"def reg_line(x: float) -> float:\n",
" return float(np.round(slope*x+intercept, decimals=2))\n",
"\n",
"births_2028 = reg_line(2028)\n",
"births_2030 = reg_line(2030)\n",
"\n",
"p_2025 = 254867\n",
"\n",
"birth_rate_2028 = births_2028 / p_2025 * 1000\n",
"\n",
"print(births_2030)\n",
"print(birth_rate_2028)\n",
"\n",
"# Plot\n",
"xs = np.linspace(min(years), 2030, 31)\n",
"ys = np.array(\n",
" [reg_line(x) for x in range(2000,2031)]\n",
")\n",
"\n",
"plt.bar(\n",
" years, births,\n",
" label=\"Geburten pro Jahre\",\n",
" color=\"g\"\n",
")\n",
"\n",
"plt.plot(\n",
" xs, ys,\n",
" label=\"Geschätze Geburten pro Jahr\",\n",
" color=\"r\"\n",
")\n",
"\n",
"plt.title(\"Geburten Braunschweig\")\n",
"plt.xlabel(\"Jahr\")\n",
"plt.ylabel(\"Geburtenzahl\")\n",
"plt.legend()\n",
"\n",
"plt.show()\n",
"\n",
"# END SOLUTION"
]
},
{
"cell_type": "markdown",
"id": "5ce09493-4265-4b43-a615-d377863144b0",
"metadata": {},
"source": [
"# BEGIN SOLUTION\n",
"# END SOLUTION"
]
},
{
"cell_type": "markdown",
"id": "8369e788-5862-488b-a003-d3cd31ebaa99",
"metadata": {
"nbgrader": {
"grade": false,
"grade_id": "cell-59872a1e95590378",
"locked": true,
"schema_version": 3,
"solution": false,
"task": false
}
},
"source": [
"---"
]
},
{
"cell_type": "markdown",
"id": "02656b99-d250-4a21-bc2d-46007806d81d",
"metadata": {
"nbgrader": {
"grade": false,
"grade_id": "cell-455ed6a04d0d701f",
"locked": true,
"schema_version": 3,
"solution": false,
"task": false
}
},
"source": [
"# Verteilungen\n",
"\n",
"## Probability Density Function - Normal Verteilung\n",
"\n",
"### Motivation\n",
"\n",
"Es wurden Daten über die Körperlänge eines Bienenvolkes erhoben, dementsprechend liegen diskrete Werte über die deren Körperlängen vor. Logischerweise repräsentiert dies nur das erhobene Bienenvolk, dieses arbeitet aber kontinuierlich weiter und erzeugt nachkommen. Die Population verändert sich. \n",
"\n",
"Daher ist anzunehmen, dass auch Werte zwischen den bereits Erhobenen auftreten können. Um dies zu Modellieren wird eine Normalverteilung benötigt.\n",
"\n",
"Schauen wir uns dazu erst die Gaussche Normalverteilung an, diese hat ihren Mittelpunkt bei $x=0$, bezeichnet als Erwartungswert $\\mu$, und eine Standardabweichung $\\sigma = 1$. Mathematisch ist sie definiert als $$p(x|\\mu,\\sigma)=\\frac{1}{\\sqrt(2\\pi\\sigma^2)}e^{-\\frac{(x-\\mu)^2}{2\\sigma^2}}$$\n",
"\n",
"SciPy bietet hierfür das `norm` objekt aus dem `stats` Modul an, dieses verlangt die beiden Parameter $\\mu$ & $\\sigma$, das auf dem `norm` Objekt kann dann die Funktion `pdf` mit einem Paramter als Stepsize oder einem Array aufgerufen werden. Nach Plotten ergibt sich folglich die Normalverteilung (von -4 bis 4):"
]
},
{
"cell_type": "code",
"execution_count": 42,
"id": "2803dcac-bb3b-4aff-a3c9-c0085148c376",
"metadata": {
"nbgrader": {
"grade": false,
"grade_id": "cell-54174b5f7d8309db",
"locked": true,
"schema_version": 3,
"solution": false,
"task": false
}
},
"outputs": [
{
"data": {
"image/png": 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Hp0+fxnvvvYdp06aZ+uK8/vrr2LZtGyZMmGAaMnv58mV89dVX2L17d5O7Gjfi5uaG1atX45FHHsHtt9+OOXPmwNvbG1lZWfjxxx8xZswYvPfeexZ/vRcvXoz//Oc/OHr0KJydnU3bvb29ER8fj5dffhlTp07Ffffdh7Nnz+L999/H8OHDTf1IOtLo0aPh4eGB+fPn45lnnoFEIsGGDRssCnuzZ8/GypUrkZCQgCFDhmDgwIFmzz/yyCP48ssv8eSTT2LHjh0YM2YM9Ho9zpw5gy+//BK//PJLs52mr+Xk5ITQ0FBs2rQJ/fv3h6enJwYPHozBgwdj1apVGDt2LIYMGYIFCxYgKCgI+fn5SE1NRU5ODo4ePdrqa1Gr1XjggQewcuVKSCQSBAcHY+vWrbfUD2bGjBkYMWIE/va3vyE9PR0hISH4/vvvTaG9rXediABwWDN1Denp6UJsbKzQt29fQalUCk5OTkJISIjw5JNPCmlpaWb75uTkCDNnzhTc3d0FtVotPPDAA0JeXl6zQ023bdsmDB48WJDL5cKAAQOETz/9tMmw5uTkZGH69OmCv7+/IJfLBX9/f2Hu3LnCuXPnTPt88MEHwvjx44Vu3boJCoVCCA4OFp577jmhrKzM7PNdunRJmDdvnuDt7S0oFAohKChIWLhwoVBbWysIwtVhzdcPfW5pCOuOHTuE6OhoQa1WC0qlUggODhYeffRR4eDBgzf8el47rPl6jdd/7bDmRu+9954QEhIiODo6Cj4+PkJsbKxw5coVs30mTJjQ7BDvxuG2b731Vqtqae5r8ccffwgjR44UnJycBH9/f+H55583DVm+0RDgRgaDQQgICBAACK+99lpzXxpBp9MJy5YtEwYNGiQoFArBw8NDGDp0qPDyyy+bfT8BCAsXLmz2HHv27BGGDh0qyOXyJj93Fy5cEObNmyf4+voKjo6OQo8ePYR77rlH+Prrr5t8TW52TYWFhcL9998vqFQqwcPDQ/jrX/8qnDhxotlhzc19P6//WW8855///GfB1dVVUKvVwqOPPir88ccfAgDhiy++aPZ6iVpDIggW3ksmIiKywObNmzFz5kzs3r0bY8aMEbscslEMLERE1G6qq6vNRj/p9XpMmTIFBw8ehEajsWhkFNG12IeFiIjazdNPP43q6mqMGjUKtbW1+Pbbb7Fnzx68/vrrDCt0S3iHhYiI2s3GjRvx9ttvIz09HTU1Nejbty9iY2OxaNEisUsjG8fAQkRERFaP87AQERGR1WNgISIiIqtnF51uDQYD8vLy4OrqyomJiIiIbIQgCCgvL4e/v7/ZSu7NsYvAkpeX12RRMSIiIrIN2dnZphnHW2IXgaVx6vLs7Gy4ubmJXA0RERG1hlarRUBAgOl1/EbsIrA0NgO5ubkxsBAREdmY1nTnYKdbIiIisnoMLERERGT1GFiIiIjI6jGwEBERkdVjYCEiIiKrx8BCREREVo+BhYiIiKweAwsRERFZPQYWIiIisnptCiyrVq1CYGAglEolIiMjsX///lYd98UXX0AikWDGjBlm2wVBwNKlS+Hn5wcnJydERUXh/PnzbSmNiIiI7JDFgWXTpk2Ii4tDQkICDh8+jPDwcERHR6OgoOCGx2VmZuLZZ5/FuHHjmjz35ptv4t1338WaNWuwb98+ODs7Izo6GjU1NZaWR0RERHbI4sDyzjvvYMGCBYiJiUFoaCjWrFkDlUqFdevWtXiMXq/HQw89hJdffhlBQUFmzwmCgBUrVuBf//oXpk+fjrCwMHzyySfIy8vD5s2bLb4gIiIisj8WLX6o0+lw6NAhxMfHm7ZJpVJERUUhNTW1xeNeeeUVdO/eHY8//jh+//13s+cyMjKg0WgQFRVl2qZWqxEZGYnU1FTMmTOnyflqa2tRW1tr+lir1VpyGURkA8pr6rDvYgnSCytQUqmD0lEGHzcFhvX2RH8fl1YtlkZE9sOiwFJUVAS9Xg8fHx+z7T4+Pjhz5kyzx+zevRv/+9//kJaW1uzzGo3GdI7rz9n43PUSExPx8ssvW1I6EdmIQ5dKsHZXBrafzofeIDS7Tw93J8wb1RtzI3vBTenYyRUSkRgsCiyWKi8vxyOPPIK1a9fCy8ur3c4bHx+PuLg408darRYBAQHtdn4i6nz52hq88sMp/Hj8smlbYDcVwgPc4eWiQE2dHpeKq3DwUglyS6uR+PMZrP39Iv41LRTTI/x5x4XIzlkUWLy8vCCTyZCfn2+2PT8/H76+vk32v3DhAjIzM3HvvfeathkMBuMndnDA2bNnTcfl5+fDz8/P7JwRERHN1qFQKKBQKCwpnYis2M5zhXjm8yMoq66DTCrB/bf3wONjgzDA17XJvjV1enx/NA9rdl7AxcJKLNmUhm2nNHhrVjicFR36HoyIRGRRp1u5XI6hQ4ciOTnZtM1gMCA5ORmjRo1qsn9ISAiOHz+OtLQ00+O+++7DHXfcgbS0NAQEBKBPnz7w9fU1O6dWq8W+ffuaPScR2Zf/7c7Aox/tR1l1HYb0UOP7RWPw5qzwZsMKACgdZXhwWACSFo/Hs1P6w1EmwU/HNZj5/h+4XFbdydUTUWex+O1IXFwc5s+fj2HDhmHEiBFYsWIFKisrERMTAwCYN28eevTogcTERCiVSgwePNjseHd3dwAw275kyRK89tpr6NevH/r06YMXX3wR/v7+TeZrISL7sjL5PN7efg4AMHdEAF66bxAUDrJWHSt3kGLRpH4YFdwNT356GOfyK/DgB6nY+JeRCPBUdWTZRCQCiwPL7NmzUVhYiKVLl0Kj0SAiIgJJSUmmTrNZWVmQSi0bLf3888+jsrISTzzxBEpLSzF27FgkJSVBqVRaWh4R2Yg1Oy+Ywsrf7uyPpyf3a9N5hvb2xOaFY/DntXtxqbgKc9fuxbdPjUZ3V/79ILInEkEQmu+Gb0O0Wi3UajXKysrg5uYmdjlEdBPfH83DM58fAQC8MDUEsRODb/mcmrIazPkwFZnFVRjcww2bnhjFPi1EVs6S12+uJUREnep4Thme/fIoAOCxMX3aJawAgK9aiY9jRsDTWY4TuVr87cujsIP3Y0TUgIGFiDqNtqYOCzcehk5vQNRAH/xr2sB2PX+glzP+O38Y5DIpkk5q8L/dGe16fiISDwMLEXUKQRDwwtfHkFVShZ4eTnj7gXBIpe0/d8rtvTzw4j3GIPTGz2dwJOtKu38OIup8DCxE1Ck2HcjGzyc0cJRJ8N6fb4da1XEz1D48sjfuCfNDvUHAs18dRU2dvsM+FxF1DgYWIupw+doa/Pun0wCA56IHICLAvUM/n0QiwWszBsPbVYELhZX4T8NoJCKyXQwsRNShBEHAi5tPoLymHuE91Xh8bNDND2oH7io5EmcOAQCs/f0iDrNpiMimMbAQUYdKOqHBtlP5cJBK8Mb9YZB1QL+VlkSF+uBPt/WAQQD++d2JFhdTJCLrx8BCRB2mWqfHq1tPAQCenBCMgX6dP0/Sv+4JhZvSAacva/H5/qxO//xE1D4YWIiow/z394vIK6uBv1qJRZP6ilKDp7Mcf5syAACwfNtZlFbpRKmDiG4NAwsRdYh8bQ1W77wAAHjhrhAoHVu3RlBHeCiyFwb4uKK0qg7vsAMukU1iYCGiDrH8l7Oo0ulxWy933BfuL2otDjIpEu4LBQBs3JeFzKJKUeshIssxsBBRu0svKMfXh3MAAEvvCYVE0nkdbVsyOtgLEwd4o94gYMWvvMtCZGsYWIio3a349TwEAYge5IPbenmIXY7Jsw19WbYczcMZjVbkaojIEgwsRNSuzmi02HrsMgBgSVR/kasxN7iHGncP8YUgAG9v410WIlvCwEJE7WrF9vMAgGlhfqIMY76ZuDv7QyoBtp/Kx4ncMrHLIaJWYmAhonZzRqNF0kkNJBJgyeR+YpfTrL7dXXFvQyfg91PSRa6GiFqLgYWI2s2HOy8CAO4e4od+Pq4iV9Oy2InBAICfT2hwobBC5GqIqDUYWIioXeSWVuP7o3kAgL+O75z1gtoqxNcNUQN9IAjAmpQLYpdDRK3AwEJE7WLd7gzUGwSMDu6GsJ7uYpdzU0/dYbzL8t2RXOSWVotcDRHdDAMLEd2ysqo60zo9T1j53ZVGt/fywMggT9QbBHyyJ1PscojoJhhYiOiWfbrvEqp0eoT4umJCf2+xy2m1v4w1hqvP92ehSlcvcjVEdCMMLER0S2rr9fjoj0wAwF8nBFnFrLatNSmkO3p3U0FbU49vD+eKXQ4R3QADCxHdkqQTGhRV1MLHTYF7wsRdM8hSUqkE80cFAgA+3pMJQRDELYiIWsTAQkS3ZEPqJQDA3BG94CizvT8ps4b1hLNchvSCCuxOLxK7HCJqge39dSEiq3EqT4uDl67AQSrBn0f0ErucNnFTOuKBYQEAYGraIiLrw8BCRG22YW8mACB6sC+6uynFLeYWzB8dCIkE+O1MATKLKsUuh4iawcBCRG1SVl2HzUeME8U9MrK3yNXcmj5ezhjfzzi66YsD2SJXQ0TNYWAhojb55lAOquv06O/jgsg+nmKXc8vmNjRpfX0oB3V6g8jVENH1GFiIyGKCIOCzfcbOto+MCrSpocwtmTywO7xcFCiqqEXy6XyxyyGi6zCwEJHFDmddwYXCSjg5yjAjwraGMrfEUSbFA8N6AgA27mezEJG1YWAhIot9eSAHgHFVZlelo8jVtJ85w42jhX4/X4jskiqRqyGia7UpsKxatQqBgYFQKpWIjIzE/v37W9z322+/xbBhw+Du7g5nZ2dERERgw4YNZvs8+uijkEgkZo+pU6e2pTQi6mCVtfXYeszY2fbBhjsS9qJ3N2eM6dsNggB8dZB3WYisicWBZdOmTYiLi0NCQgIOHz6M8PBwREdHo6CgoNn9PT098c9//hOpqak4duwYYmJiEBMTg19++cVsv6lTp+Ly5cumx+eff962KyKiDvXT8cuo1OkR2E2FEXbQ2fZ6jZ1vNx3Mht7AmW+JrIXFgeWdd97BggULEBMTg9DQUKxZswYqlQrr1q1rdv+JEydi5syZGDhwIIKDg7F48WKEhYVh9+7dZvspFAr4+vqaHh4eHm27IiLqUF8dNDYHPTAswC46217vzlAfeKgcka+txR+c+ZbIalgUWHQ6HQ4dOoSoqKirJ5BKERUVhdTU1JseLwgCkpOTcfbsWYwfP97suZSUFHTv3h0DBgxAbGwsiouLWzxPbW0ttFqt2YOIOt7FwgrszyyBVALcf7t9NQc1UjjIcG+4sSPxt4dzRK6GiBpZFFiKioqg1+vh4+Njtt3HxwcajabF48rKyuDi4gK5XI5p06Zh5cqVuPPOO03PT506FZ988gmSk5OxbNky7Ny5E3fddRf0en2z50tMTIRarTY9AgICLLkMImqjrw8ZX8An9PeGr9p2Z7a9mT81hLGkkxpU1NaLXA0RAYBDZ3wSV1dXpKWloaKiAsnJyYiLi0NQUBAmTpwIAJgzZ45p3yFDhiAsLAzBwcFISUnB5MmTm5wvPj4ecXFxpo+1Wi1DC1EHMxgEbD6SCwCYNdS+f9/Ce6oR5O2Mi4WV+Pn4ZdNaQ0QkHovusHh5eUEmkyE/33xSpfz8fPj6+rb8SaRS9O3bFxEREfjb3/6GWbNmITExscX9g4KC4OXlhfT09GafVygUcHNzM3sQUcc6kFmCvLIauCgcMHlgd7HL6VASicTU5PXt4VyRqyEiwMLAIpfLMXToUCQnJ5u2GQwGJCcnY9SoUa0+j8FgQG1tbYvP5+TkoLi4GH5+fpaUR0QdaHOacSjz1MG+UDrKRK6m4824rQcAIPViMXKucE4WIrFZPEooLi4Oa9euxfr163H69GnExsaisrISMTExAIB58+YhPj7etH9iYiK2b9+Oixcv4vTp03j77bexYcMGPPzwwwCAiooKPPfcc9i7dy8yMzORnJyM6dOno2/fvoiOjm6nyySiW6GrN+Cn45cBADMieohcTefo4e6EUUHdAABbGsIaEYnH4j4ss2fPRmFhIZYuXQqNRoOIiAgkJSWZOuJmZWVBKr2agyorK/HUU08hJycHTk5OCAkJwaefforZs2cDAGQyGY4dO4b169ejtLQU/v7+mDJlCl599VUoFIp2ukwiuhUpZwtQVl2H7q4KjAruJnY5neZPt/dA6sVifHs4B09NDLbLYdxEtkIiCILNz4yk1WqhVqtRVlbG/ixEHWDhZ4fx4/HLeHxsH7x4T6jY5XSa8po6DH3tV+jqDfh58TgM9OPfF6L2ZMnrN9cSIqIbKq+pw68Nqxd3leagRq5KR0waYOxg/MNRNgsRiYmBhYhuKOmEBrX1BgR5O2Nwj653h+GecGPn/x+O5cEObkgT2SwGFiK6ocYOpzMienTJPhyTQrpDJZchu6Qax3LKxC6HqMtiYCGiFhVV1GLPBeN6OtMj/EWuRhwquQOiBhoHFbBZiEg8DCxE1KKkExoYBCCspxq9uzmLXY5o7gkzNgttPXYZBq7gTCQKBhYiatHPJ4xzr9w9pGtP4jhhgDdclQ7QaGtw8NIVscsh6pIYWIioWcUVtUi9YFw1/e7BXTuwKBxkiB5kXH5k6zE2CxGJgYGFiJq17VQ+DAIwuIcbenVTiV2O6BqbhX46fhn1eoPI1RB1PQwsRNSsxqn47+rid1cajenrBQ+VI4oqdNiXUSJ2OURdDgMLETVxpVKHPY3NQV28/0ojR5kUU0KNzUK/nNSIXA1R18PAQkRNbDulgd4gYKCfG/p4dd3RQdebOsQYWJJOaDhaiKiTMbAQURM/HTfeQZjW8AJNRqODu8FV4YCC8locyS4VuxyiLoWBhYjMlFbp8Ee6cbK4u9gcZEbhIMOkgca1hdgsRNS5GFiIyMz2U/moNwgI8XVFsLeL2OVYnamDrjYLcW0hos7DwEJEZjg66MYmDPCGwkGKrJIqnL5cLnY5RF0GAwsRmZTX1GF3Q3PQ3ey/0iyV3AET+nsDAJLYLETUaRhYiMgk5Wwh6vQCgryd0c/HVexyrNbUwQ3Dm08wsBB1FgYWIjLZfiofAHBnqI/IlVi3ySE+cJBKcDa/HBcLK8Quh6hLYGAhIgCArt6AHWcLAABTGFhuSK1yxKjgbgCAX07mi1wNUdfAwEJEAIB9GcUor6mHl4sCEQEeYpdj9RqbhZIaVrQmoo7FwEJEAK42B0UN7A6ZVCJyNdZvSqgvJBLgaE4Z8kqrxS6HyO4xsBARBEEwBZYpg9gc1BrergoM7WW8E5V8ms1CRB2NgYWIcCJXi8tlNVDJZRgd7CV2OTZj8kBjuPv1dIHIlRDZPwYWIsL2U8bhueP7eUPpKBO5GttxZ6hxmv7UC8WorK0XuRoi+8bAQkTYxuagNgn2dkHvbiro9Ab8fr5Q7HKI7BoDC1EXl11ShTOacsikEkwK6S52OTZFIpFgcgibhYg6AwMLURfXeHdlRKAn3FVykauxPVENzUK/nSmA3sDFEIk6CgMLURfX2H+Fs9u2zfBAT7gqHVBSqUNa9hWxyyGyWwwsRF1YWVUdDmQaX2QZWNrGUSbFHQOMd1nYLETUcRhYiLqwnecLoTcI6O/jggBPldjl2KzJAxsCyynOx0LUURhYiLqwHWeMdwTuYGfbWzKxv3F24PMFFbhUXCl2OUR2qU2BZdWqVQgMDIRSqURkZCT279/f4r7ffvsthg0bBnd3dzg7OyMiIgIbNmww20cQBCxduhR+fn5wcnJCVFQUzp8/35bSiKiV9AYBKQ2LHU4awMByK9QqR4wI9ATAZiGijmJxYNm0aRPi4uKQkJCAw4cPIzw8HNHR0SgoaP6X1NPTE//85z+RmpqKY8eOISYmBjExMfjll19M+7z55pt49913sWbNGuzbtw/Ozs6Ijo5GTU1N26+MiG4oLfsKrlTVwU3pgKG9udjhrWpsFuI0/UQdw+LA8s4772DBggWIiYlBaGgo1qxZA5VKhXXr1jW7/8SJEzFz5kwMHDgQwcHBWLx4McLCwrB7924AxrsrK1aswL/+9S9Mnz4dYWFh+OSTT5CXl4fNmzff0sURUct+a2gOmjCgOxxkbB2+VVEN0/TvzyhBWXWdyNUQ2R+L/krpdDocOnQIUVFRV08glSIqKgqpqak3PV4QBCQnJ+Ps2bMYP348ACAjIwMajcbsnGq1GpGRkS2es7a2Flqt1uxBRJb57YxxZtZJId4iV2IfAr2c0be7C+oNAnae46y3RO3NosBSVFQEvV4PHx/z4Y8+Pj7QaDQtHldWVgYXFxfI5XJMmzYNK1euxJ133gkApuMsOWdiYiLUarXpERAQYMllEHV5eaXVOH1ZC6kEmNCf/VfaC5uFiDpOp9wHdnV1RVpaGg4cOIB///vfiIuLQ0pKSpvPFx8fj7KyMtMjOzu7/Yol6gJ2NHS2va2XBzydObtte2mcpn/nuULOekvUzhws2dnLywsymQz5+ebvHvLz8+Hr69vicVKpFH379gUARERE4PTp00hMTMTEiRNNx+Xn58PPz8/snBEREc2eT6FQQKFQWFI6EV2jcTgz1w5qX7f3coer0gGlVXVIyy5lZ2aidmTRHRa5XI6hQ4ciOTnZtM1gMCA5ORmjRo1q9XkMBgNqa2sBAH369IGvr6/ZObVaLfbt22fROYmodWrq9NidXgSAgaW9OcikGN/f2Ceoccg4EbUPi5uE4uLisHbtWqxfvx6nT59GbGwsKisrERMTAwCYN28e4uPjTfsnJiZi+/btuHjxIk6fPo23334bGzZswMMPPwzAuNrpkiVL8Nprr+H777/H8ePHMW/ePPj7+2PGjBntc5VEZJJ6sRg1dQb4qZUI8XUVuxy70zhN/w4GFqJ2ZVGTEADMnj0bhYWFWLp0KTQaDSIiIpCUlGTqNJuVlQWp9GoOqqysxFNPPYWcnBw4OTkhJCQEn376KWbPnm3a5/nnn0dlZSWeeOIJlJaWYuzYsUhKSoJSqWyHSySia107u61EIhG5GvszoeEOy4lcLQrKa9DdlX/HiNqDRBAEm+8ZptVqoVarUVZWBjc3N7HLIbJagiBg7LIdyC2txv/mD8PkgVzwsCPc995uHMspw1uzwvDAMI5iJGqJJa/fnC2KqAs5X1CB3NJqKBykGB3sJXY5dmtiQ7NQylnOx0LUXhhYiLqQxtltRwV3g5NcJnI19uuOAcZmoV3nC1GnN4hcDZF9YGAh6kJ+a1iYbzJHB3WosJ7u8HSWo7ymHocvXRG7HCK7wMBC1EWUVdfhUJbxxXMiV2fuUDKpxNT5dgebhYjaBQMLURfxR3oR9AYBfbu7IMBTJXY5dm/iAM7HQtSeGFiIuoidDe/0G9/5U8ca388bEglwRlOOvNJqscshsnkMLERdgCBcXUGYgaVzeDjLcVuAOwCOFiJqDwwsRF3AufwKaLQ1UDpKMaKPp9jldBl3mIY3s1mI6FYxsBB1ATvPGV8wRwZ1g9KRw5k7yx0No7H+SC9Cbb1e5GqIbBsDC1EXwOYgcYT6ucHbVYFKnR4HMzm8mehWMLAQ2bnK2nocyOBwZjFIpRJMbBzefIbNQkS3goGFyM7tvVgMnd6AXp4qBHbjcObONpGrNxO1CwYWIjt3bXMQV2fufGP7ekEqAS4UViKXw5uJ2oyBhcjOsf+KuNQqR9zWywMAsOschzcTtRUDC5EdyyiqxKXiKjjKJBgV3E3scrqs8f2MYXEn52MhajMGFiI7trOh38TwQE84KxxErqbrmtAwTf8f6UVcvZmojRhYiOwYm4Osw5AearirHFFeW4+07FKxyyGySQwsRHaqpk6P1IvFAK6+wydxyKQSjGtoFmI/FqK2YWAhslMHMktQU2eAj5sCA3xcxS6nyxvfzwsAAwtRWzGwENmpa1dn5nBm8TU2yx3LLUNJpU7kaohsDwMLkZ262n+Fs9tag+5uSoT4ukIQgN/P8y4LkaUYWIjsUG5pNc4XVEAqMU5cRtahsS/RTjYLEVmMgYXIDjX2k7itlwfUKkeRq6FGE0wdb4tgMAgiV0NkWxhYiOxQY/+ViRzObFWGBnrAyVGGoopanNZoxS6HyKYwsBDZmTq9AX+kFwHgcGZro3CQYXTDjMO7zhWJXA2RbWFgIbIzR7JKUV5bD09nOQb7q8Uuh64zvn9jPxau3kxkCQYWIjvT+EI4vp8XpFIOZ7Y2jcObD126goraepGrIbIdDCxEdsY0nJnNQVYp0MsZvTxVqNMLSL1QLHY5RDaDgYXIjhSU1+BErrEzZ+NU8GR9Gu+ycNZbotZjYCGyI783dOQc0kMNLxeFyNVQS672Y2FgIWotBhYiO8LVmW3DqOBucJRJkFVShcyiSrHLIbIJbQosq1atQmBgIJRKJSIjI7F///4W9127di3GjRsHDw8PeHh4ICoqqsn+jz76KCQSidlj6tSpbSmNqMvSGwTTlO/jGVismovCAUN7ewAAdnGafqJWsTiwbNq0CXFxcUhISMDhw4cRHh6O6OhoFBQ0P0QvJSUFc+fOxY4dO5CamoqAgABMmTIFubm5ZvtNnToVly9fNj0+//zztl0RURd1IrcMV6rq4KpwwG293MUuh26icY2nxkn+iOjGLA4s77zzDhYsWICYmBiEhoZizZo1UKlUWLduXbP7f/bZZ3jqqacQERGBkJAQ/Pe//4XBYEBycrLZfgqFAr6+vqaHh4dH266IqItq7MA5um83OMrY2mvtxvc3rvGUerEYtfV6kashsn4W/VXT6XQ4dOgQoqKirp5AKkVUVBRSU1NbdY6qqirU1dXB09PTbHtKSgq6d++OAQMGIDY2FsXFLQ/3q62thVarNXsQdXWNTQtcndk2DPR1g5eLAlU6PQ5lXhG7HCKrZ1FgKSoqgl6vh4+Pj9l2Hx8faDSaVp3jhRdegL+/v1nomTp1Kj755BMkJydj2bJl2LlzJ+666y7o9c2/60hMTIRarTY9AgICLLkMIrujranD4axSAFffuZN1k0olpu/VTvZjIbqpTr1v/MYbb+CLL77Ad999B6VSado+Z84c3HfffRgyZAhmzJiBrVu34sCBA0hJSWn2PPHx8SgrKzM9srOzO+kKiKzTnvQi6A0Cgryd0dNDJXY51EqNo7nYj4Xo5iwKLF5eXpDJZMjPzzfbnp+fD19f3xseu3z5crzxxhvYtm0bwsLCbrhvUFAQvLy8kJ6e3uzzCoUCbm5uZg+irmxnw/wr4zlZnE0Z29cLEglwRlOOfG2N2OUQWTWLAotcLsfQoUPNOsw2dqAdNWpUi8e9+eabePXVV5GUlIRhw4bd9PPk5OSguLgYfn5+lpRH1CUJgmDqcMv5V2xLNxcFhvQwLlDJWW+JbsziJqG4uDisXbsW69evx+nTpxEbG4vKykrExMQAAObNm4f4+HjT/suWLcOLL76IdevWITAwEBqNBhqNBhUVFQCAiooKPPfcc9i7dy8yMzORnJyM6dOno2/fvoiOjm6nyySyXxeLKpFbWg25TIrIIM+bH0BWZQJnvSVqFQdLD5g9ezYKCwuxdOlSaDQaREREICkpydQRNysrC1Lp1Ry0evVq6HQ6zJo1y+w8CQkJeOmllyCTyXDs2DGsX78epaWl8Pf3x5QpU/Dqq69CoeDU4kQ30/jOfEQfT6jkFv9Kk8jG9/fGyt/SsbuhH5KMK2wTNatNf90WLVqERYsWNfvc9R1lMzMzb3guJycn/PLLL20pg4hw9Z05RwfZptsC3OGqdEBpVR2O55YhIsBd7JKIrBJnlyKyYTV1euy9aJyziNPx2yYHmRRjghuGN3O0EFGLGFiIbNjBzCuoqTPAx02BAT6uYpdDbTRhgDFscl0hopYxsBDZsMYXuHH9vCGRsO+DrWq8O3Yk6wrKqupErobIOjGwENmwXee4OrM96OHuhL7dXWAQgD8uFIldDpFVYmAhslGashqc0ZRDIgHG9WWHW1vHWW+JboyBhchGNTYHhfV0h4ezXORq6FaNv2Y+FkEQRK6GyPowsBDZKNPstv14d8UeRPbxhMJBCo22BucLKsQuh8jqMLAQ2SC9QcDu9Ib1g9h/xS4oHWWIDOoGgM1CRM1hYCGyQcdzy1BaVQdXpQMnGrMjjf1YOLyZqCkGFiIb1NgcNLavFxxk/DW2FxMaZivel1GCap1e5GqIrAv/0hHZoJ0czmyXgr1d0MPdCbp6A/ZmFItdDpFVYWAhsjFl1XVIyy4FwMBibyQSiWlNKPZjITLHwEJkY/Y0rOob7O2MHu5OYpdD7Yz9WIiax8BCZGMaX8h4d8U+je7rBZlUgouFlcguqRK7HCKrwcBCZEMEQcCucxzObM/clI64vZc7AN5lIboWAwuRDblQWInc0mrIHaQY2aeb2OVQB+E0/URNMbAQ2ZDG0UGRfTzhJJeJXA11lMa7Z3suFKNObxC5GiLrwMBCZENMqzP3Y3OQPRvsr4ansxwVtfU4fOmK2OUQWQUGFiIbUVOnx76GuTnYf8W+SaUSjGtYI6rxrhpRV8fAQmQjDmSWoKbOAF83Jfr7uIhdDnUwDm8mMsfAQmQjGpuDxvXzgkQiEbka6mjjGpr9TuRqUVheK3I1ROJjYCGyEY1NAxMGsDmoK/B2VWCQvxsAYHc677IQMbAQ2YDLZdU4l18BqcS44CF1DRzeTHQVAwuRDfi9YbK4sJ7ucFfJRa6GOktj5+rfzxfBYBBEroZIXAwsRDZgJ6fj75Ju7+UBF4UDiit1OJmnFbscIlExsBBZOb1BwO7zxjssE/qzOagrkTtIMSrYOKPxznMFIldDJC4GFiIrl5ZdirLqOrgpHRDe013scqiTmYY3NzQLEnVVDCxEVm7nWeM763H9veEg469sV9MYWA5lXYG2pk7kaojEw79+RFYupWE480T2X+mSAjxVCPJyht4gYE96sdjlEImGgYXIihWW1+JYThkAzr/SlTV2tuY0/dSVMbAQWbHG2W0H93BDd1elyNWQWK72YymEIHB4M3VNbQosq1atQmBgIJRKJSIjI7F///4W9127di3GjRsHDw8PeHh4ICoqqsn+giBg6dKl8PPzg5OTE6KionD+/Pm2lEZkV642B3UXuRISU2SQJ+QOUuSWVuNCYaXY5RCJwuLAsmnTJsTFxSEhIQGHDx9GeHg4oqOjUVDQ/JC7lJQUzJ07Fzt27EBqaioCAgIwZcoU5ObmmvZ588038e6772LNmjXYt28fnJ2dER0djZqamrZfGZGN0xsE/N4w/8pENgd1aSq5A0YEegK4eteNqKuxOLC88847WLBgAWJiYhAaGoo1a9ZApVJh3bp1ze7/2Wef4amnnkJERARCQkLw3//+FwaDAcnJyQCMd1dWrFiBf/3rX5g+fTrCwsLwySefIC8vD5s3b76liyOyZWnZpSitMg5njghwF7scEtkE9mOhLs6iwKLT6XDo0CFERUVdPYFUiqioKKSmprbqHFVVVairq4Onp/HdQkZGBjQajdk51Wo1IiMjWzxnbW0ttFqt2YPI3qQ0DGcez+HMhKsdb/dlFKOmTi9yNUSdz6K/gkVFRdDr9fDx8THb7uPjA41G06pzvPDCC/D39zcFlMbjLDlnYmIi1Gq16REQEGDJZRDZhJSzjc1B7L9CQH8fF/i6KVFTZ8C+jBKxyyHqdJ36tu2NN97AF198ge+++w5KZdtHPMTHx6OsrMz0yM7ObscqicRXWF6L47kNw5k5/woBkEgkpp+FxrtvRF2JRYHFy8sLMpkM+fn5Ztvz8/Ph6+t7w2OXL1+ON954A9u2bUNYWJhpe+NxlpxToVDAzc3N7EFkT64dzuztqhC5GrIWd4Q0Bhb2Y6Gux6LAIpfLMXToUFOHWQCmDrSjRo1q8bg333wTr776KpKSkjBs2DCz5/r06QNfX1+zc2q1Wuzbt++G5ySyZzsa3kFzODNda0xfLzjKJMgoqkRGEYc3U9dicZNQXFwc1q5di/Xr1+P06dOIjY1FZWUlYmJiAADz5s1DfHy8af9ly5bhxRdfxLp16xAYGAiNRgONRoOKigoAxtucS5YswWuvvYbvv/8ex48fx7x58+Dv748ZM2a0z1US2ZB6vQG/N6zO3PiOmggAXJWOGN4wvHnHGTYLUdfiYOkBs2fPRmFhIZYuXQqNRoOIiAgkJSWZOs1mZWVBKr2ag1avXg2dTodZs2aZnSchIQEvvfQSAOD5559HZWUlnnjiCZSWlmLs2LFISkq6pX4uRLbqaI5xdWa1kyMiAjzELoeszKSQ7thzoRg7zhbgsbF9xC6HqNNIBDuY51mr1UKtVqOsrIz9Wcjmvb3tLFb+lo57wvzw3p9vF7scsjLpBRWIemcn5DIpjiy9E84Ki993ElkNS16/ObkDkZUx9V/hcGZqRrC3M3p5qqDTG/BHepHY5RB1GgYWIitSUF6DE7nGiRA5nJmaI5FIcEfDUg07OFqIuhAGFiIrsuuc8R3zkB5qDmemFt0RYrz7lnK2gKs3U5fBwEJkRVJMzUG8u0ItGxnUDUpHKS6X1eCMplzscog6BQMLkZWo1xtME8YxsNCNKB1lGBPsBQD4jcObqYtgYCGyEmnZpdDW1HM4M7XKtc1CRF0BAwuRlUhueKc8ob83ZFKJyNWQtWsMLIcuXUFplU7kaog6HgMLkZVIPm1cT2vyQA5nppvr4e6EAT6uMAjArvMc3kz2j4GFyApkl1ThXH4FZFIJhzNTq01sWLqB0/RTV8DAQmQFGjtODu3tAXeVXORqyFZMaphccOe5QugNHN5M9o2BhcgK/NrQHBTF5iCywO29PeCqdEBJpQ5Hc0rFLoeoQzGwEImsorYe+y6WAAAmhfiIXA3ZEkeZFOP7s1mIugYGFiKR7T5fCJ3egMBuKgR7O4tdDtmYOxqahXZweDPZOQYWIpElnza+0EwK8YFEwuHMZJmJA7whkQAncrXQlNWIXQ5Rh2FgIRKRwSCY3hmz/wq1hZeLAhEB7gCA5DP54hZD1IEYWIhEdDSnFEUVOrgqHDAs0FPscshGRQ009n369RQDC9kvBhYiETU2B40f4A25A38dqW3uDDUGlj8uFKOytl7kaog6Bv9CEomocTr+ySFsDqK269fdBb08VdDVG/A7Z70lO8XAQiSS3NJqnL6shVQCTBzAwEJtJ5FIrjYLnWazENknBhYikTTObnt7Lw94OnN2W7o1jc1Cv50p4Ky3ZJcYWIhE8lvDO+FJHB1E7WBYoAfUTo4oqdThSNYVscshancMLEQiqNLV448LxQCujvAguhWOMinuGGCc9XY7m4XIDjGwEIlg9/ki6OoN6OnhhH7dXcQuh+xEVCiHN5P9YmAhEsH2U42LHXJ2W2o/4/t7w1EmwYXCSlwsrBC7HKJ2xcBC1Mnq9QbTSI7oQb4iV0P2xE3piJFB3QBcneOHyF4wsBB1soOXruBKVR3cVY4YHughdjlkZxr7RLEfC9kbBhaiTrbtpPGFZHKIDxxk/BWk9jW5YdTZwcwSXKnUiVwNUfvhX0uiTiQIArad0gAApgzi6CBqfz09VBjo5waDANPCmkT2gIGFqBOdvlyOnCvVUDpKMb6ft9jlkJ26s+Euy3aOFiI7wsBC1Il+OWm8uzKunzec5DKRqyF71Ti8eee5QtTU6UWuhqh9MLAQdaJtDe94p4SyOYg6zmB/NXzdlKjS6bHnAhdDJPvQpsCyatUqBAYGQqlUIjIyEvv3729x35MnT+L+++9HYGAgJBIJVqxY0WSfl156CRKJxOwREhLSltKIrFZ2SZVpsUPObksdSSqVILqhj1TSCY3I1RC1D4sDy6ZNmxAXF4eEhAQcPnwY4eHhiI6ORkFB8527qqqqEBQUhDfeeAO+vi3POTFo0CBcvnzZ9Ni9e7elpRFZtca7KyP6eMKDix1SB4sebPx7u/1UPur1BpGrIbp1FgeWd955BwsWLEBMTAxCQ0OxZs0aqFQqrFu3rtn9hw8fjrfeegtz5syBQqFo8bwODg7w9fU1Pby8vCwtjciqbWvovzIllJPFUccbEegJT2c5rlTVYX9GidjlEN0yiwKLTqfDoUOHEBUVdfUEUimioqKQmpp6S4WcP38e/v7+CAoKwkMPPYSsrKwW962trYVWqzV7EFmz4opaHMg0vmjcyf4r1AkcZFLc2dD0+DObhcgOWBRYioqKoNfr4eNj/gfXx8cHGk3bfyEiIyPx8ccfIykpCatXr0ZGRgbGjRuH8vLyZvdPTEyEWq02PQICAtr8uYk6Q/KZAhgEINTPDQGeKrHLoS5iakOz0C8nNTAYBJGrIbo1VjFK6K677sIDDzyAsLAwREdH46effkJpaSm+/PLLZvePj49HWVmZ6ZGdnd3JFRNZpnF2W04WR51pdN9ucFU4oKC8Fkeyr4hdDtEtsSiweHl5QSaTIT/ffDKi/Pz8G3aotZS7uzv69++P9PT0Zp9XKBRwc3MzexBZq4raeuw6XwiAix1S51I4yDCpYRI5jhYiW2dRYJHL5Rg6dCiSk5NN2wwGA5KTkzFq1Kh2K6qiogIXLlyAn59fu52TSCy/nSmArt6APl7OCPF1Fbsc6mKmNoTkpJMaCAKbhch2WdwkFBcXh7Vr12L9+vU4ffo0YmNjUVlZiZiYGADAvHnzEB8fb9pfp9MhLS0NaWlp0Ol0yM3NRVpamtndk2effRY7d+5EZmYm9uzZg5kzZ0Imk2Hu3LntcIlE4vrp2GUAwF2DfSGRSESuhrqaCQO8oXSUIrukGifzOECBbJeDpQfMnj0bhYWFWLp0KTQaDSIiIpCUlGTqiJuVlQWp9GoOysvLw2233Wb6ePny5Vi+fDkmTJiAlJQUAEBOTg7mzp2L4uJieHt7Y+zYsdi7dy+8vbnWCtm2ytp60wJ0dw/hHUPqfCq5Ayb098YvJ/Pxy0kNBvdQi10SUZtIBDu4R6jVaqFWq1FWVsb+LGRVth7Lw6KNR9DLU4Wdz03kHRYSxeYjuViyKQ19u7vg17gJYpdDZGLJ67dVjBIislc/Hzd2dLx7iB/DConmjpDucJRJkF5QgfSC5qeLILJ2DCxEHaRap8dvZ4zNQdPYHEQiUjs5YnSwcfZwjhYiW8XAQtRBUs4WoLpOj54eThjcg02VJK67hxhHC21t6AROZGsYWIg6yI/HjS8M09gcRFYgepAvHKQSnNGUI72gQuxyiCzGwELUAWrqrjYH3cXmILIC7io5xvYzNgttPZYncjVElmNgIeoAKWcLUaXTo4e7E8J7chgpWYd7wvwBGJuF7GCAKHUxDCxEHeDnE5wsjqzPlEE+kMukSC+owNl8jhYi28LAQtTOqnV6bD9lXG/r7jA2B5H1cFM6YsIA44ScW4+y8y3ZFgYWonb26+l8VOn0CPB0wm0B7mKXQ2TmnoYQvfVYHpuFyKYwsBC1s++PGjs03hfuz+YgsjpRA32gdJQis7gKJ3K5thDZDgYWonZUVlWHnWcLAQD3hfcQuRqippwVDpgU0h0ARwuRbWFgIWpHSScvQ6c3YICPKwb4uopdDlGz7uVoIbJBDCxE7cjUHBThL3IlRC27I6Q7nOUy5JZW40h2qdjlELUKAwtROynQ1mDPhWIAxv4rRNZK6ShDVKgPAOD7NDYLkW1gYCFqJ8bb68DtvdwR4KkSuxyiG5oe0dgslId6vUHkaohujoGFqJ1suWZ0EJG1G9fPG92c5Siq0OH39CKxyyG6KQYWonZwqbgSR7NLIZUA08IYWMj6OcqkuLchXH93OFfkaohujoGFqB009gMY09cL3q4Kkashap2ZtxmH3m87pUFFbb3I1RDdGAML0S0SBAGb04zvUO9lcxDZkLCeagR5OaOmzoCkExqxyyG6IQYWolt0NKcMFworoXSU4q7BvmKXQ9RqEonEdJfluyM5IldDdGMMLES36OtD2QCAqYN84ap0FLkaIsvMaAgsey4U43JZtcjVELWMgYXoFtTW6/FDw6q39w/tKXI1RJYL8FRheKAHBIFzspB1Y2AhugXJpwtQVl0HXzclRgd7iV0OUZvMvM0Ytr87wtFCZL0YWIhuwTeHjO3+M2/vAZmUKzOTbZo2xA9ymRRnNOU4lccVnMk6MbAQtVFheS1SzhlXZr7/djYHke1SqxxNKzh/e5idb8k6MbAQtdGWtFzoDQIiAtzRt7uL2OUQ3ZJZDX2wvj2SC109p+on68PAQtRGXzc0B7GzLdmDiQO80d1VgZJKHZJP54tdDlETDCxEbXAyrwxnNOWQy6S4N8xP7HKIbpmDTGoK35sOZotcDVFTDCxEbfDNIeNoiqjQ7nBXyUWuhqh9PDgsAACw61wh52Qhq8PAQmShmjq9aVbQWWwOIjvSx8sZI/p4wiAAXx9k51uyLgwsRBb65aQGV6rq4KdWYkL/7mKXQ9SuZjfcZfnyUDYMBkHkaoiualNgWbVqFQIDA6FUKhEZGYn9+/e3uO/Jkydx//33IzAwEBKJBCtWrLjlcxKJ6fP9WQCMt8859wrZm7uH+MFV4YDskmrsvVgsdjlEJhYHlk2bNiEuLg4JCQk4fPgwwsPDER0djYKCgmb3r6qqQlBQEN544w34+ja/MJyl5yQSy8XCCuy9WAKpBHhweIDY5RC1Oye5DPdGGFcdZ+dbsiYWB5Z33nkHCxYsQExMDEJDQ7FmzRqoVCqsW7eu2f2HDx+Ot956C3PmzIFCoWiXcxKJZdMB4x/wiQO6o4e7k8jVEHWMxmahn09oUFZVJ3I1REYWBRadTodDhw4hKirq6gmkUkRFRSE1NbVNBbTlnLW1tdBqtWYPoo6mqzeY5l6Zw7srZMfCeqoR4usKXb0Bm9O4vhBZB4sCS1FREfR6PXx8fMy2+/j4QKPRtKmAtpwzMTERarXa9AgI4IsHdbztp/JRXKlDd1eFaRpzInskkUgwd0QvAMCney9BENj5lsRnk6OE4uPjUVZWZnpkZ7OdlTretZ1tHWQ2+atD1Gozb+8BlVyG8wUV2JdRInY5RJYFFi8vL8hkMuTnm0/bnJ+f32KH2o44p0KhgJubm9mDqCNlFFVid3oRJBJgNpuDqAtwUzpixm09AAAb9l4SuRoiCwOLXC7H0KFDkZycbNpmMBiQnJyMUaNGtamAjjgnUXvbkGr8gz2hvzcCPFUiV0PUOR6O7A0A+OWEBgXaGpGroa7O4vvacXFxWLt2LdavX4/Tp08jNjYWlZWViImJAQDMmzcP8fHxpv11Oh3S0tKQlpYGnU6H3NxcpKWlIT09vdXnJBJTZW09vjpkbHacPzpQ3GKIOlGovxuG9fZAvUHAFwfY9E7icrD0gNmzZ6OwsBBLly6FRqNBREQEkpKSTJ1ms7KyIJVezUF5eXm47bbbTB8vX74cy5cvx4QJE5CSktKqcxKJ6bsjuSivqUcfL2dM6OctdjlEneqRUb1x8NIVbNyXhacmBrP/FolGIthB92+tVgu1Wo2ysjL2Z6F2JQgColfswrn8Ciy9JxSPje0jdklEnaq2Xo/Rib+huFKHNQ8PxdTBbeuvSNQcS16/GZWJbiD1YjHO5VdAJZdh1jAudEhdj8JBZupo/klqprjFUJfGwEJ0A5/sMXa2/dPtPeCmdBS5GiJx/DmyF6QSYM+FYpzRcKJOEgcDC1ELckurse2UcfLCeaMCxS2GSEQ9PVS4a7AfAOB/v2eIXA11VQwsRC3YkHoJBgEYHdwN/X1cxS6HSFSPjzP239qSlofC8lqRq6GuiIGFqBkVtfX4bJ+xOShmDDvaEt3eywO39XKHTm/gRHIkCgYWomZ8sT8L5TX1CPZ2xmSuG0QEAPjL2CAAwGd7L6GmTi9yNdTVMLAQXadOb8BHf2QCABaMC4JUKhG3ICIrET3IBz3cnVBcqcPmI1zFmToXAwvRdX46fhm5pdXwcpGb1lIhIsBBJkXMmEAAwP92Z3AVZ+pUDCxE1xAEAR/uuggAmD8qEEpHmcgVEVmXB4cHwEXhgPMFFdhxtkDscqgLYWAhukbqhWKczNPCyVGGh0f2FrscIqvjpnTEnyN7AQBW7bjAuyzUaRhYiK7xQcPdlQeH9YSHs1zkaois01/G9oFcJsWhS1ewP6NE7HKoi2BgIWpwLKcUO88VQiaV4PGG0RBE1FR3NyUeaFiqYlXKBZGroa6CgYWowcrf0gEA08P90aubSuRqiKzbkxOCIZNKsOtcIY7llIpdDnUBDCxEAE7labH9VD4kEuCpO/qKXQ6R1QvwVGF6uD8A4P0dvMtCHY+BhQjAezvOAwCmDfFD3+4uIldDZBtiJwYDAJJOanA+v1zkasjeMbBQl3c+vxw/nzAucvj0pH4iV0NkO/r5uCJ6kA8AYNWOdJGrIXvHwEJd3ns70iEIwNRBvhjgy0UOiSzRGPK3HM3jXRbqUAws1KVdKKzAD0fzAACLJrHvCpGlBvdQY+ogXwgC8M72c2KXQ3aMgYW6tHe2nYNBAKIG+mBwD7XY5RDZpP+7sz8kEuDnExqcyC0TuxyyUwws1GUdzynDj8cvQyIBno3uL3Y5RDZrgK8r7msYMcS7LNRRGFioy3rzlzMAgJkRPRDi6yZyNUS2bUlUf8ikEvx2pgCHLl0RuxyyQwws1CXtSS/C7+eL4CiT4P/u5N0VolvVx8sZs243zn779razIldD9oiBhbocQRCw7BfjH9Q/j+iFAE/OakvUHp6e3BeOMgn2XChGCldypnbGwEJdzi8n83E0uxQquQyLOO8KUbvp6aHC/FGBAIDXfzqNer1B3ILIrjCwUJeiqzdgWZKx78pjY/rA21UhckVE9uXpSf3grnLEufwKbDqYLXY5ZEcYWKhLWb8nExlFlfByUeDJhmnFiaj9qFWOWDzZeOfyP9vPobymTuSKyF4wsFCXUVRRi3eTjWsGPT91AFwUDiJXRGSfHorsjT5eziiq0GHNTi6MSO2DgYW6jLe3nUV5bT2G9FCbRjMQUfuTO0gRf1cIAGDt7xnIuVIlckVkDxhYqEs4kVuGLw4Y29MT7g2FVCoRuSIi+3ZnqA9GBnlCV2/Aa1tPi10O2QEGFrJ7giDgla2nIAjAfeH+GBboKXZJRHZPIpEg4d5BkEklSDqpwY4zHOZMt4aBheze14dysD+jBEpHKf7ecJuaiDreQD83PDYmEACQ8P1J1NTpxS2IbBoDC9m14opa/Psn4+3oJVH94e/uJHJFRF3L4qj+8HVTIqukCu/vSBe7HLJhbQosq1atQmBgIJRKJSIjI7F///4b7v/VV18hJCQESqUSQ4YMwU8//WT2/KOPPgqJRGL2mDp1altKIzLz7x9Po7SqDiG+rnh8bB+xyyHqclwUDki4NxQAsGbnRVwsrBC5IrJVFgeWTZs2IS4uDgkJCTh8+DDCw8MRHR2NgoLm2yf37NmDuXPn4vHHH8eRI0cwY8YMzJgxAydOnDDbb+rUqbh8+bLp8fnnn7ftioga7D5fhG+P5EIiAd64PwyOMt5QJBLD1MG+mNDfGzq9Af/87gQMBkHsksgGSQRBsOgnJzIyEsOHD8d7770HADAYDAgICMDTTz+Nv//97032nz17NiorK7F161bTtpEjRyIiIgJr1qwBYLzDUlpais2bN7eqhtraWtTW1po+1mq1CAgIQFlZGdzcuOouATV1ekSv2IVLxVWYP6o3Xp4+WOySiLq0S8WViF6xCzV1Brw6YzAeGdlb7JLICmi1WqjV6la9flv0llOn0+HQoUOIioq6egKpFFFRUUhNTW32mNTUVLP9ASA6OrrJ/ikpKejevTsGDBiA2NhYFBcXt1hHYmIi1Gq16REQEGDJZVAX8Pa2s7hUXAVfNyWejR4gdjlEXV7vbs54Yaqx03viT6eRXcK5WcgyFgWWoqIi6PV6+Pj4mG338fGBRqNp9hiNRnPT/adOnYpPPvkEycnJWLZsGXbu3Im77roLen3zPcrj4+NRVlZmemRnc70KumrfxWL8d3cGAOC1GYPhqnQUuSIiAoD5owIxoo8nqnR6PPf1UTYNkUWsYm7yOXPmmP4/ZMgQhIWFITg4GCkpKZg8eXKT/RUKBRQKLlpHTVXU1uPZr49CEIAHh/VEVKjPzQ8iok4hlUrw1qwwTF3xO/ZeLMGn+y5hXsPqzkQ3Y9EdFi8vL8hkMuTn55ttz8/Ph6+vb7PH+Pr6WrQ/AAQFBcHLywvp6RwCR5b594+nkF1SjR7uTnjxnlCxyyGi6/Tu5myaDynxpzMcNUStZlFgkcvlGDp0KJKTk03bDAYDkpOTMWrUqGaPGTVqlNn+ALB9+/YW9weAnJwcFBcXw8/Pz5LyqIvbdlKDz/cbmweXPxDOpiAiK/XIyN4YHdwN1XV6LNp4BLX1nFCObs7icZ5xcXFYu3Yt1q9fj9OnTyM2NhaVlZWIiYkBAMybNw/x8fGm/RcvXoykpCS8/fbbOHPmDF566SUcPHgQixYtAgBUVFTgueeew969e5GZmYnk5GRMnz4dffv2RXR0dDtdJtm7nCtVeParowCABeP6YFRwN5ErIqKWSKUS/Gd2BDyd5Th1WYvEn86IXRLZAIsDy+zZs7F8+XIsXboUERERSEtLQ1JSkqljbVZWFi5fvmzaf/To0di4cSM+/PBDhIeH4+uvv8bmzZsxeLBxmKlMJsOxY8dw3333oX///nj88ccxdOhQ/P777+ynQq1Spzfg6c+PQFtTj/AAdzwXzen3iaydj5sSbz8YDgD4eE8mfjnZ/MANokYWz8NijSwZx032J/Gn0/hg10W4Kh3w0zPjEOCpErskImql1386jQ93XYTayRE/LR6HHlw+o0vpsHlYiKzNz8cv44NdFwEAb80KZ1ghsjHPThmA8AB3lFXX4ckNh7hAIrWIgYVs1hmNFn9r6Lfy+Ng+mDq45ZFnRGSd5A5SvDf3NnioHHE8twx//+YY7ODGP3UABhaySVcqdVjwyUFU6fQY29cL8Xex3wqRrQrwVOH9h4ZCJpVgc1oePmy4a0p0LQYWsjm6egMWbjyM7JJqBHg6YeXc2+DAhQ2JbNqo4G6mVZ3fSDqDHWebX1CXui7+lSebIggC/v7NMey5UAyVXIa184bBw1kudllE1A4eGdkbc4YHQBCApzcewYncMrFLIivCwEI25e1t5/DtkVzIpBK8/9DtCPHlqDAieyGRSPDK9MGI7OOJitp6PPrRAWQVc5FEMmJgIZuxYe8lvLfDuFzD6zMHY+KA7iJXRETtTe4gxdr5wzDQzw1FFbWYt24fiipqxS6LrAADC9mEbw7lYOmWEwCAZyb3w+zhvUSuiIg6ipvSEetjhqOnhxMyi6sQ89EBlNfUiV0WiYyBhazeD0fz8FzDCszzR/XG/0X1E7skIupg3d2U+OSxEfB0luN4bhnmrdsPLUNLl8bAQlYt6cRl/N+mNBgEYM7wACTcOwgSiUTssoioEwR5u+CTx0ZA7eSII1mlmPc/hpaujIGFrNY3h3Lw1GeHUW8QMCPCH/+eOQRSKcMKUVcyuIcan/0lEu4qR6Rll+KR/+1HWTVDS1fEwEJWaUNqJv721VEYBOCBoT3x9oMRkDGsEHVJg3uosfEvI+GhcsTR7FLM+XAv8rU1YpdFnYyBhayKwSDg7W1n8eKWkwCAR0cHYtn9YQwrRF1cqL8bNi4YCS8XBU5f1uJP7+/B+fxyscuiTsTAQlajpk6PZ744gpW/GYcuPzOpLxLuDWUzEBEBAAb6ueG7p0YjyMsZuaXVuH/1HuzPKBG7LOokDCxkFYoqajF37V5sPXYZjjIJ3pwVhrgpA9jBlojMBHiq8E3saAzt7QFtTT0e/u8+bNyXxQUTuwAGFhLdgcwS3PPubhzJKoXayRGfPBaJB4cFiF0WEVkpD2c5PvtLJO4e4gud3oB/fHccL3xzDDV1erFLow7EwEKiMRgErNl5AXM+3AuNtgbB3s749qnRGBXcTezSiMjKKR1lWPXn2/HC1BBIJcCXB3PwwJpUTuVvxxhYSBQF5TX4yycH8cbPZ6A3CJge4Y/vF41FsLeL2KURkY2QSCSInRiMTx6LhIfKEcdzy3DX/9uFLw9ks4nIDkkEO/iuarVaqNVqlJWVwc2Ni+FZM0EQsCUtDwnfn0RZdR3kDlK8dO8gzB0RwP4qRNRmOVeq8H+b0nAg8woA4M5QHyT+aQi8XBQiV0Y3YsnrNwMLdRpNWQ2WbjmBbafyAQCD/N3w9oPhXHGZiNqF3iDgw10X8c72s6jTC/BQOSL+roGYNbQnRxtaKQYWsiq19Xr8b3cG3vstHVU6PRxlEjw9qR9iJwbDUcZWSSJqXyfzyvC3L4/ijMY4T8uw3h54beZgvjmyQgwsZBUEQcCvpwvw+k+nkVFUCQC4vZc7XpsxBKH+/D4RUcep0xvw8R+Z+M+v51Cl00MmlWD28AAsmdwP3d2UYpdHDRhYSFSCIOCP9GIs33YWadmlAABvVwXi7wrBjIgevDVLRJ0mr7Qar/xwCkknNQAApaMUj4/tgyfGB0Pt5ChydcTAQqIwGATsPFeI1TsvmGafdHKU4dExgXhqYjBclfzjQETi2J9Rgjd+Po3DWaUAABeFAx4a2QuPj+nDOy4iYmChTlVTp8e3h3Pxv90XcaHQ2PQjl0nx0MheiJ0YjO6u/GNAROITBAHbTuXj7W1ncS6/AgAgd5DiT7f1wMMje2NwD7XIFXY9DCzU4QRBwMk8Lb46mI0tR/NQWmVc7t1V4YC5kb0QMyYQfmonkaskImrKYBDw25kCvJ+SbrrjAgDhAe54KLIX7g3zh5NcJl6BXQgDC3WY7JIqJJ3Q4JvDOaYe+ADQ08MJj43pgweHB8BF4SBihURErSMIAg5kXsGGvZeQdOIy6vTGl0NnuQx3hvrg3nB/jOvnDbkDRzN2FAYWajeCIOBcfgW2n9Ig6aQGJ3K1pufkDlJMCfXBA8MCMLavF2TsTEtENqqoohZfHczBxv2XkF1SbdqudnLE5IHdMXFAd4zv5wV3lVzEKu0PAwvdkrzSavyRXmR8XChGYXmt6TmpBBge6Il7wvxwX3gPqFXsSEtE9kMQBBzOKsXWY3n48dhlFFz39y8iwB0TB3RHZB9PhAe4Q+nIpqNbwcBCrVZZW48TuWVIyy7F0ZxSpGWVIq+sxmwfpaMUo4K6YepgX0QN9EE3TnVNRF2A3iDgQGYJfjtTgJSzBaaOuo0cZRIM7qHGsN4eiAjwQKi/G3p7qjh1gwUYWKiJap0emcWVOJdfjvP5FThfYPw3s7gShut+AqQSIKynO8b29cKYvl64vbc7FA58F0FEXVtuaTV2ni3E7vRCHMy8Ynb3pZFKLkOIrytC/d0wwMcVgV7OCOzmDH93JzabN6PDA8uqVavw1ltvQaPRIDw8HCtXrsSIESNa3P+rr77Ciy++iMzMTPTr1w/Lli3D3XffbXpeEAQkJCRg7dq1KC0txZgxY7B69Wr069evVfV09cBSW69HcYUORRW1KKqoxeWyGmSXVCPnShWyr1Qj90oViip0LR7vp1YivKc7Inq5I7ynO4b0VLPjLBHRDQiCgJwr1TiQWYKDl67gZG4ZzmjKUVtvaHZ/uUyKAE8n9PEyhhcfNyV83ZTwVTc83JRw7oJ/dzs0sGzatAnz5s3DmjVrEBkZiRUrVuCrr77C2bNn0b179yb779mzB+PHj0diYiLuuecebNy4EcuWLcPhw4cxePBgAMCyZcuQmJiI9evXo0+fPnjxxRdx/PhxnDp1CkrlzefwsNXAIggCausNxkedHrX1BtTU6VGl06O8ph4VtXXQ1tSjvKYe5TV1Zv82BpTCilqU19S36vO5KR3Qz8cV/X1c0K+7K/o3/J+TJhER3bp6vQGZxZU4mafFqctaXCioRGZxJbKKq6DTNx9krqV0lMJDJYe7Sg5PZ0e4q+TwUDnCQyWH2skRzgoHqOQyOMsdoFIY/3VWOMBZIYNK7gAnRxkcZRKbWvm+QwNLZGQkhg8fjvfeew8AYDAYEBAQgKeffhp///vfm+w/e/ZsVFZWYuvWraZtI0eOREREBNasWQNBEODv74+//e1vePbZZwEAZWVl8PHxwccff4w5c+a06wVbok5vQOJPZ2AQBNQbDNAbBNTrBegFwfh/gwBDw7/mHxuaPK9rCCY11wSTlpJ4WzjKJOjmrICXqxw+rkoEeKrQ08MJPT2M/wZ4qNhBlohIBHqDgMtl1cgsqkJmcSU0ZTW4XFaDfG0NNNoa5JfVoLy2dW88b0YiARxlUihkUsgdpHBs+FfuIIVcJoWjw9XnpFIJHKQSSCUSyKSATCqBTCqFTAJIpRLIJBI4yBqfl0Auk+Jf94S2S52NLHn9tuj+k06nw6FDhxAfH2/aJpVKERUVhdTU1GaPSU1NRVxcnNm26OhobN68GQCQkZEBjUaDqKgo0/NqtRqRkZFITU1tNrDU1taitvZq26FWq22yT3swCALW/ZHRIee+nlQCKB1lxoeDFK5KR7gqHRoejnBp+L9bw3ZPZzm8XBTwcjH+q3ZytKlUTUTUVcikkoY3jyqM7efV7D4VtfUoqdDhSpXxUVpVh5JKHUqrdLhSVYey6jpU6fSo0tWjsrYelTo9qhr+raytR31DZ0RBAHT1BujqDUDTLja3RO7Q/oHFEhYFlqKiIuj1evj4+Jht9/HxwZkzZ5o9RqPRNLu/RqMxPd+4raV9rpeYmIiXX37ZktLbxFEqRezEYDhIjelSJpFAJpM0fGxMoTKZ1Ox5B9k1+0qvplO5gxQKBxmUjlf/VTrKoHAw/usgta3beERE1H5cFA5wUTigVzdVm47X1RtQrdOjVq9HnV4whRZdvQE6/dV/6675WG+42mKgNwgwXPN/03MNrQoGgyD6a5RN9vCJj483u2uj1WoREBDQ7p9HKpXghakh7X5eIiKi9tTY7APYb9O/RfMNe3l5QSaTIT8/32x7fn4+fH19mz3G19f3hvs3/mvJORUKBdzc3MweREREZL8sCixyuRxDhw5FcnKyaZvBYEBycjJGjRrV7DGjRo0y2x8Atm/fbtq/T58+8PX1NdtHq9Vi3759LZ6TiIiIuhaLm4Ti4uIwf/58DBs2DCNGjMCKFStQWVmJmJgYAMC8efPQo0cPJCYmAgAWL16MCRMm4O2338a0adPwxRdf4ODBg/jwww8BABKJBEuWLMFrr72Gfv36mYY1+/v7Y8aMGe13pURERGSzLA4ss2fPRmFhIZYuXQqNRoOIiAgkJSWZOs1mZWVBKr1642b06NHYuHEj/vWvf+Ef//gH+vXrh82bN5vmYAGA559/HpWVlXjiiSdQWlqKsWPHIikpqVVzsBAREZH949T8REREJApLXr8t6sNCREREJAYGFiIiIrJ6DCxERERk9RhYiIiIyOoxsBAREZHVY2AhIiIiq8fAQkRERFaPgYWIiIisnk2u1ny9xrnvtFqtyJUQERFRazW+brdmDlu7CCzl5eUAgICAAJErISIiIkuVl5dDrVbfcB+7mJrfYDAgLy8Prq6ukEgk7XpurVaLgIAAZGdn2+W0//Z+fYD9X6O9Xx9g/9do79cH2P818vraRhAElJeXw9/f32wdwubYxR0WqVSKnj17dujncHNzs8sfwkb2fn2A/V+jvV8fYP/XaO/XB9j/NfL6LHezOyuN2OmWiIiIrB4DCxEREVk9BpabUCgUSEhIgEKhELuUDmHv1wfY/zXa+/UB9n+N9n59gP1fI6+v49lFp1siIiKyb7zDQkRERFaPgYWIiIisHgMLERERWT0GFiIiIrJ6DCxERERk9RhY2qC2thYRERGQSCRIS0sTu5x2dd9996FXr15QKpXw8/PDI488gry8PLHLaheZmZl4/PHH0adPHzg5OSE4OBgJCQnQ6XRil9au/v3vf2P06NFQqVRwd3cXu5xbtmrVKgQGBkKpVCIyMhL79+8Xu6R2s2vXLtx7773w9/eHRCLB5s2bxS6pXSUmJmL48OFwdXVF9+7dMWPGDJw9e1bsstrV6tWrERYWZpoBdtSoUfj555/FLqvDvPHGG5BIJFiyZEmnf24GljZ4/vnn4e/vL3YZHeKOO+7Al19+ibNnz+Kbb77BhQsXMGvWLLHLahdnzpyBwWDABx98gJMnT+I///kP1qxZg3/84x9il9audDodHnjgAcTGxopdyi3btGkT4uLikJCQgMOHDyM8PBzR0dEoKCgQu7R2UVlZifDwcKxatUrsUjrEzp07sXDhQuzduxfbt29HXV0dpkyZgsrKSrFLazc9e/bEG2+8gUOHDuHgwYOYNGkSpk+fjpMnT4pdWrs7cOAAPvjgA4SFhYlTgEAW+emnn4SQkBDh5MmTAgDhyJEjYpfUobZs2SJIJBJBp9OJXUqHePPNN4U+ffqIXUaH+OijjwS1Wi12GbdkxIgRwsKFC00f6/V6wd/fX0hMTBSxqo4BQPjuu+/ELqNDFRQUCACEnTt3il1Kh/Lw8BD++9//il1GuyovLxf69esnbN++XZgwYYKwePHiTq+Bd1gskJ+fjwULFmDDhg1QqVRil9PhSkpK8Nlnn2H06NFwdHQUu5wOUVZWBk9PT7HLoGbodDocOnQIUVFRpm1SqRRRUVFITU0VsTJqq7KyMgCw2985vV6PL774ApWVlRg1apTY5bSrhQsXYtq0aWa/j52NgaWVBEHAo48+iieffBLDhg0Tu5wO9cILL8DZ2RndunVDVlYWtmzZInZJHSI9PR0rV67EX//6V7FLoWYUFRVBr9fDx8fHbLuPjw80Go1IVVFbGQwGLFmyBGPGjMHgwYPFLqddHT9+HC4uLlAoFHjyySfx3XffITQ0VOyy2s0XX3yBw4cPIzExUdQ6unxg+fvf/w6JRHLDx5kzZ7By5UqUl5cjPj5e7JIt1tprbPTcc8/hyJEj2LZtG2QyGebNmwfBildwsPT6ACA3NxdTp07FAw88gAULFohUeeu15RqJrMnChQtx4sQJfPHFF2KX0u4GDBiAtLQ07Nu3D7GxsZg/fz5OnToldlntIjs7G4sXL8Znn30GpVIpai1dfi2hwsJCFBcX33CfoKAgPPjgg/jhhx8gkUhM2/V6PWQyGR566CGsX7++o0tts9Zeo1wub7I9JycHAQEB2LNnj9Xe4rT0+vLy8jBx4kSMHDkSH3/8MaRS68/tbfkefvzxx1iyZAlKS0s7uLqOodPpoFKp8PXXX2PGjBmm7fPnz0dpaand3fmTSCT47rvvzK7VXixatAhbtmzBrl270KdPH7HL6XBRUVEIDg7GBx98IHYpt2zz5s2YOXMmZDKZaZter4dEIoFUKkVtba3Zcx3JoVM+ixXz9vaGt7f3Tfd799138dprr5k+zsvLQ3R0NDZt2oTIyMiOLPGWtfYam2MwGAAYh3JbK0uuLzc3F3fccQeGDh2Kjz76yCbCCnBr30NbJZfLMXToUCQnJ5texA0GA5KTk7Fo0SJxi6NWEQQBTz/9NL777jukpKR0ibACGH9OrflvpiUmT56M48ePm22LiYlBSEgIXnjhhU4LKwADS6v16tXL7GMXFxcAQHBwMHr27ClGSe1u3759OHDgAMaOHQsPDw9cuHABL774IoKDg6327oolcnNzMXHiRPTu3RvLly9HYWGh6TlfX18RK2tfWVlZKCkpQVZWFvR6vWmuoL59+5p+bm1FXFwc5s+fj2HDhmHEiBFYsWIFKisrERMTI3Zp7aKiogLp6emmjzMyMpCWlgZPT88mf3Ns0cKFC7Fx40Zs2bIFrq6upr5HarUaTk5OIlfXPuLj43HXXXehV69eKC8vx8aNG5GSkoJffvlF7NLahaura5M+R419HDu9L1Knj0uyExkZGXY3rPnYsWPCHXfcIXh6egoKhUIIDAwUnnzySSEnJ0fs0trFRx99JABo9mFP5s+f3+w17tixQ+zS2mTlypVCr169BLlcLowYMULYu3ev2CW1mx07djT7vZo/f77YpbWLln7fPvroI7FLazePPfaY0Lt3b0Eulwve3t7C5MmThW3btoldVocSa1hzl+/DQkRERNbPNhrwiYiIqEtjYCEiIiKrx8BCREREVo+BhYiIiKweAwsRERFZPQYWIiIisnoMLERERGT1GFiIiIjI6jGwEBERkdVjYCEiIiKrx8BCREREVu//A7CAb7hglZYWAAAAAElFTkSuQmCC",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.arange(-4, 4, 0.01) # Plot between -4 and 4 with stepsize 0.01\n",
"y = stats.norm(0,1).pdf(x) # Calculate pdf with mu=0, sigma=1\n",
"\n",
"# Plot\n",
"plt.title(\"Gaussche Normalverteilung\")\n",
"plt.plot(x, y)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "ca2f768f-16ff-47ff-b898-fe0b8cf3511f",
"metadata": {
"nbgrader": {
"grade": false,
"grade_id": "cell-259b8d6cb9d76981",
"locked": true,
"schema_version": 3,
"solution": false,
"task": false
}
},
"source": [
"Um herauszufinden wie viel Prozent einer Population innerhalb dieser Normalverteilung fallen wird die Funktion `ppf` (Percent Point Function) verwendet.\n",
"\n",
"Am Beispiel 90% der Population:"
]
},
{
"cell_type": "code",
"execution_count": 43,
"id": "0e5e7709-90a2-4a30-b49f-cbb243aa4e4b",
"metadata": {
"nbgrader": {
"grade": false,
"grade_id": "cell-5a9ed9588ce2ea27",
"locked": true,
"schema_version": 3,
"solution": false,
"task": false
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"90% of the Population fall into the range 1.282.\n"
]
}
],
"source": [
"percentile = stats.norm(0,1).ppf(0.9)\n",
"print(f\"90% of the Population fall into the range {percentile:0.3f}.\")"
]
},
{
"cell_type": "markdown",
"id": "96afa424-d697-4c60-aa9b-4655491f4f13",
"metadata": {
"nbgrader": {
"grade": false,
"grade_id": "cell-5102a53fda328278",
"locked": true,
"schema_version": 3,
"solution": false,
"task": false
}
},
"source": [
"Um dies zu veranschaulichen:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "4f5d7f54-856f-4e12-8251-d0cdc5c0f002",
"metadata": {
"nbgrader": {
"grade": false,
"grade_id": "cell-5d84b05b2808a672",
"locked": true,
"schema_version": 3,
"solution": false,
"task": false
}
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 900x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(9,6))\n",
"ax.plot(x,y, color='r')\n",
"\n",
"# filling under the curve\n",
"x_fill = np.arange(-4, percentile, 0.01)\n",
"y_fill = stats.norm(0,1).pdf(x_fill)\n",
"ax.fill_between(x_fill, y_fill, 0, color='g')\n",
"plt.title(\"Filled Percentile under Normal Curve\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "1f7a26f6-36d8-4561-ad68-db6c19c7720e",
"metadata": {
"nbgrader": {
"grade": false,
"grade_id": "cell-c469fe12a69725b1",
"locked": true,
"schema_version": 3,
"solution": false,
"task": false
}
},
"source": [
"Machen wir dies alles am Beispiel der Fuchsrote Lockensandbiene fest. Diese ist laut [Bundesministerium für Ernährung und Landwirtschaft](https://www.bmel.de/DE/themen/landwirtschaft/artenvielfalt/bienen-fuettern/wildbienen-honigbienen-und-co.html) 12-14 mm groß. Daher lässt sich annehmen das die meisten Bienen $\\mu=13mm$, mit einer Standardabweichung von $\\sigma=1mm$ haben. Wir wollen nun wissen wie groß 95% der Bienen sind, rechnen wir dies mittels `ppf` aus:"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "6d57bdf0-8e75-4760-8159-d42effd9ea62",
"metadata": {
"nbgrader": {
"grade": false,
"grade_id": "cell-360e11812d2e9932",
"locked": true,
"schema_version": 3,
"solution": false,
"task": false
}
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 900x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mu = 13 # Mean\n",
"sigma = 1 # std deviation in mm\n",
"\n",
"x_norm = np.linspace(10, 16, 100) # Normaldistribution range from 10-16mm \n",
"y_norm = stats.norm(mu, sigma).pdf(x_norm) # Calculate normal\n",
"\n",
"# Height of 95th percentile of bees\n",
"percentile = stats.norm(mu,sigma).ppf(0.95)\n",
"\n",
"x_percentile = np.arange(x_norm[0], percentile, 0.01)\n",
"y_percentile = stats.norm(mu,sigma).pdf(x_percentile)\n",
"\n",
"# Plot\n",
"fig, ax = plt.subplots(figsize=(9,6))\n",
"ax.plot(x_norm, y_norm, color='r')\n",
"\n",
"# filling under the curve\n",
"ax.fill_between(x_percentile, y_percentile, 0, alpha=0.2, color='#FE0000')\n",
"\n",
"\n",
"# Set text\n",
"ax.text(0.5,0.25,\n",
" f\"95th percentile of bees fall under {percentile:.2f}mm\",\n",
" ha='center', va='center', transform=ax.transAxes,\n",
" bbox={'facecolor':'#fafafa','alpha':1,'edgecolor':'none','pad':1},\n",
" color='#de2e0b'\n",
" )\n",
"\n",
"# Show\n",
"plt.title(\"Filled Percentile under Normal Curve\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "e9c59eb8-bfb1-46f2-bf1f-af1ffe59e190",
"metadata": {
"nbgrader": {
"grade": false,
"grade_id": "cell-7718d285f36c2fad",
"locked": true,
"schema_version": 3,
"solution": false,
"task": false
}
},
"source": [
"### Aufgabe \n",
"\n",
"*20 Punkte*\n",
"\n",
"Gegeben sind die nach Altersgruppe aufgeschlüsselten Durschnittskörpergrößen (in cm) von Frauen in Deutschland. (Zu finden beim [Statistischen Bundesamt](https://www.destatis.de/DE/Themen/Gesellschaft-Umwelt/Gesundheit/Gesundheitszustand-Relevantes-Verhalten/Tabellen/koerpermasse-frauen.html))\n",
"\n",
"Gehe wie folgt vor *(8 Punkte)*:\n",
"\n",
"- Berechne das arithmetische Mittel nutze dafür NumPy. und speichere das Ergebnis mit einer Genauigkeit von 1 Dezimalstelle nach dem Komma in der Variablen `avg_height`.\n",
"- Gegeben ist auch die Standardabweichung von 15cm, stelle die Normalverteilung mittels `norm.pdf` auf. Speichere den Wert in `norm_height` und finde einen geeigneten linespace zum plotten.\n",
"- Berechne folgend die Körpergröße unter die 80% aller Frauen (nach Datenset) fallen. Speichere den Wert in der Variablen `avg_percentile`.\n",
"- Plotte das Ergebnis. Orientiere dich gerne an dem Bienenbeispiel. Finde eine geeignete Darstellung. *Tipp: Da die Y-Achse in diesem Beispiel keinen Sinn ergibt kannst du sie einfach austellen mit `plt.yticks([])`*\n",
"\n",
"Markdown Zeile (0 Punkte bei nicht beantworten) *(12 Punkte)*:\n",
"- Beschreibe die gegebenen Daten, nutze dazu die verlinkte und weitere Quellen. (Quellenangaben nicht vergessen)\n",
"- Beschreibe den resultierenden Plot und setze diesen in Kontext zum Datenset.\n",
"- Stelle die Annahmen der Aufgabe in Frage und setze diese in Kontext.\n",
"- Beurteile die Aussage aus resultierender Berechnung: \"Frauen sind im durchschnitt ungeeignet Basketball zu spielen!\""
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "3983d224-e885-43bd-aadd-4e276a56a370",
"metadata": {
"nbgrader": {
"grade": false,
"grade_id": "cell-048d8330d555432a",
"locked": true,
"schema_version": 3,
"solution": false,
"task": false
}
},
"outputs": [],
"source": [
"# Given\n",
"avg_height_per_woman = {\n",
" \"18 - 20\": 167.6,\n",
" \"20 - 25\": 167.7,\n",
" \"25 - 30\": 167.3,\n",
" \"30 - 35\": 167.2,\n",
" \"35 - 40\": 167.3,\n",
" \"40 - 45\": 167.5,\n",
" \"45 - 50\": 167.1,\n",
" \"50 - 55\": 167.1,\n",
" \"55 - 60\": 166.9,\n",
" \"60 - 65\": 165.4,\n",
" \"65 - 70\": 164.5,\n",
" \"70 - 75\": 163.9,\n",
" \"75+\": 162.8\n",
"}\n",
"\n",
"avg_height = None\n",
"norm_height = None\n",
"avg_percentile = None"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "2c2e2cf6-c743-4cb0-a329-2240205fc7da",
"metadata": {
"nbgrader": {
"grade": true,
"grade_id": "cell-a59f2b3230aad3d6",
"locked": false,
"points": 3,
"schema_version": 3,
"solution": true,
"task": false
}
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 900x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# BEGIN SOLUTION\n",
"avg_height = np.round(np.mean(list(avg_height_per_woman.values())), decimals=1)\n",
"\n",
"\n",
"std_sigma = 15\n",
"norm_height = stats.norm(avg_height, std_sigma).pdf(norm_x)\n",
"norm_x = np.linspace(120, 220, 1000)\n",
"# Height of 80th percentile of woman heights\n",
"avg_percentile = stats.norm(avg_height, std_sigma).ppf(0.8)\n",
"\n",
"x_percentile = np.arange(norm_x[0], avg_percentile, 0.01)\n",
"y_percentile = stats.norm(avg_height, std_sigma).pdf(x_percentile)\n",
"\n",
"# Plot\n",
"fig, ax = plt.subplots(figsize=(9,6))\n",
"ax.plot(norm_x, norm_height, color='r')\n",
"\n",
"# filling under the curve\n",
"ax.fill_between(x_percentile, y_percentile, 0, alpha=.5, color='#fa0000')\n",
"\n",
"\n",
"# Set text\n",
"ax.text(0.4,0.18,\n",
" f\"80th percentile of Womens heigth\\n fall under {avg_percentile:.1f}cm\",\n",
" ha='center', va='center', transform=ax.transAxes,\n",
" bbox={'facecolor':'#fafafa','alpha':1,'edgecolor':'none','pad':1},\n",
" color='#de2e0b'\n",
" )\n",
"\n",
"# Show\n",
"plt.title(\"Woman Height Normal Distribution\")\n",
"plt.xlabel(\"Height\")\n",
"plt.yticks([]) # hide y\n",
"plt.show()\n",
"# END SOLUTION"
]
},
{
"cell_type": "markdown",
"id": "9ed860df-a2c4-4d99-a020-2312212419dc",
"metadata": {},
"source": [
"# BEGIN SOLUTION\n",
"# END SOLUTION"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "d9f8aeae-6b51-4645-b578-19693a07ece3",
"metadata": {
"nbgrader": {
"grade": true,
"grade_id": "cell-26f141bc8b12d7fe",
"locked": true,
"points": 3,
"schema_version": 3,
"solution": false,
"task": false
}
},
"outputs": [],
"source": [
"# Hier werden ihre Lösungen getestet...\n",
"import math \n",
"\n",
"# Check if average height is close to real value\n",
"assert math.isclose(avg_height, 166.3, rel_tol=.2) # 1 Punkt\n",
"\n",
"# Check if norm height is close to real value\n",
"assert math.isclose(np.round(np.sum(norm_height), decimals=1), 10, rel_tol=.2) # 1 Punkt\n",
"\n",
"# Check if percentile is close to real value\n",
"assert math.isclose(avg_percentile, 179, rel_tol=.2) # 1 Punkt"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"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": "3.11.6"
}
},
"nbformat": 4,
"nbformat_minor": 5
}