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Modification lien données

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module3/exo1/Untitled.ipynb 0 → 100644
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{
"cells": [],
"metadata": {},
"nbformat": 4,
"nbformat_minor": 4
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module3/exo2/.ipynb 0 → 100644
View file @ 388fa44d
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Incidence du syndrome grippal"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"import pandas as pd\n",
"import isoweek"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Les données de l'incidence du syndrome grippal sont disponibles du site Web du [Réseau Sentinelles](http://www.sentiweb.fr/). Nous les récupérons sous forme d'un fichier en format CSV dont chaque ligne correspond à une semaine de la période demandée. Nous téléchargeons toujours le jeu de données complet, qui commence en 1984 et se termine avec une semaine récente."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"data_url = \"http://www.sentiweb.fr/datasets/incidence-PAY-3.csv\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Voici l'explication des colonnes données [sur le site d'origine](https://ns.sentiweb.fr/incidence/csv-schema-v1.json):\n",
"\n",
"| Nom de colonne | Libellé de colonne |\n",
"|----------------|-----------------------------------------------------------------------------------------------------------------------------------|\n",
"| week | Semaine calendaire (ISO 8601) |\n",
"| indicator | Code de l'indicateur de surveillance |\n",
"| inc | Estimation de l'incidence de consultations en nombre de cas |\n",
"| inc_low | Estimation de la borne inférieure de l'IC95% du nombre de cas de consultation |\n",
"| inc_up | Estimation de la borne supérieure de l'IC95% du nombre de cas de consultation |\n",
"| inc100 | Estimation du taux d'incidence du nombre de cas de consultation (en cas pour 100,000 habitants) |\n",
"| inc100_low | Estimation de la borne inférieure de l'IC95% du taux d'incidence du nombre de cas de consultation (en cas pour 100,000 habitants) |\n",
"| inc100_up | Estimation de la borne supérieure de l'IC95% du taux d'incidence du nombre de cas de consultation (en cas pour 100,000 habitants) |\n",
"| geo_insee | Code de la zone géographique concernée (Code INSEE) http://www.insee.fr/fr/methodes/nomenclatures/cog/ |\n",
"| geo_name | Libellé de la zone géographique (ce libellé peut être modifié sans préavis) |\n",
"\n",
"La première ligne du fichier CSV est un commentaire, que nous ignorons en précisant `skiprows=1`."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"On vérifie qu'une copie locale n'existe pas. Pour cela, on se donne un nom de fichier, data_file, ainsi qu'un répertoire, folder_path. S'il n'existe pas, on le crée à partir de data_url, en sauvegardant les données localement. On travaillera ensuite avec ces données locales."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"import os.path\n",
"data_file = \"inciden-PAY-3.csv\"\n",
"folder_path = \"myLocalisation/\"\n",
"if not (os.path.exists(folder_path + data_file)) : \n",
" df = pd.read_csv(data_url)\n",
" df.to_csv(folder_path + data_file, sep = '\\t')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"raw_data = pd.read_csv(data_file, skiprows=1)\n",
"raw_data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Y a-t-il des points manquants dans ce jeux de données ? Oui, la semaine 19 de l'année 1989 n'a pas de valeurs associées."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"raw_data[raw_data.isnull().any(axis=1)]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Nous éliminons ce point, ce qui n'a pas d'impact fort sur notre analyse qui est assez simple."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"data = raw_data.dropna().copy()\n",
"data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Nos données utilisent une convention inhabituelle: le numéro de\n",
"semaine est collé à l'année, donnant l'impression qu'il s'agit\n",
"de nombre entier. C'est comme ça que Pandas les interprète.\n",
" \n",
"Un deuxième problème est que Pandas ne comprend pas les numéros de\n",
"semaine. Il faut lui fournir les dates de début et de fin de\n",
"semaine. Nous utilisons pour cela la bibliothèque `isoweek`.\n",
"\n",
"Comme la conversion des semaines est devenu assez complexe, nous\n",
"écrivons une petite fonction Python pour cela. Ensuite, nous\n",
"l'appliquons à tous les points de nos donnés. Les résultats vont\n",
"dans une nouvelle colonne 'period'."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"def convert_week(year_and_week_int):\n",
" year_and_week_str = str(year_and_week_int)\n",
" year = int(year_and_week_str[:4])\n",
" week = int(year_and_week_str[4:])\n",
" w = isoweek.Week(year, week)\n",
" return pd.Period(w.day(0), 'W')\n",
"\n",
"data['period'] = [convert_week(yw) for yw in data['week']]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Il restent deux petites modifications à faire.\n",
"\n",
"Premièrement, nous définissons les périodes d'observation\n",
"comme nouvel index de notre jeux de données. Ceci en fait\n",
"une suite chronologique, ce qui sera pratique par la suite.\n",
"\n",
"Deuxièmement, nous trions les points par période, dans\n",
"le sens chronologique."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"sorted_data = data.set_index('period').sort_index()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Nous vérifions la cohérence des données. Entre la fin d'une période et\n",
"le début de la période qui suit, la différence temporelle doit être\n",
"zéro, ou au moins très faible. Nous laissons une \"marge d'erreur\"\n",
"d'une seconde.\n",
"\n",
"Ceci s'avère tout à fait juste sauf pour deux périodes consécutives\n",
"entre lesquelles il manque une semaine.\n",
"\n",
"Nous reconnaissons ces dates: c'est la semaine sans observations\n",
"que nous avions supprimées !"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"periods = sorted_data.index\n",
"for p1, p2 in zip(periods[:-1], periods[1:]):\n",
" delta = p2.to_timestamp() - p1.end_time\n",
" if delta > pd.Timedelta('1s'):\n",
" print(p1, p2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Un premier regard sur les données !"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"sorted_data['inc'].plot()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Un zoom sur les dernières années montre mieux la situation des pics en hiver. Le creux des incidences se trouve en été."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"sorted_data['inc'][-200:].plot()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Etude de l'incidence annuelle"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Etant donné que le pic de l'épidémie se situe en hiver, à cheval\n",
"entre deux années civiles, nous définissons la période de référence\n",
"entre deux minima de l'incidence, du 1er août de l'année $N$ au\n",
"1er août de l'année $N+1$.\n",
"\n",
"Notre tâche est un peu compliquée par le fait que l'année ne comporte\n",
"pas un nombre entier de semaines. Nous modifions donc un peu nos périodes\n",
"de référence: à la place du 1er août de chaque année, nous utilisons le\n",
"premier jour de la semaine qui contient le 1er août.\n",
"\n",
"Comme l'incidence de syndrome grippal est très faible en été, cette\n",
"modification ne risque pas de fausser nos conclusions.\n",
"\n",
"Encore un petit détail: les données commencent an octobre 1984, ce qui\n",
"rend la première année incomplète. Nous commençons donc l'analyse en 1985."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"first_august_week = [pd.Period(pd.Timestamp(y, 8, 1), 'W')\n",
" for y in range(1985,\n",
" sorted_data.index[-1].year)]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"En partant de cette liste des semaines qui contiennent un 1er août, nous obtenons nos intervalles d'environ un an comme les périodes entre deux semaines adjacentes dans cette liste. Nous calculons les sommes des incidences hebdomadaires pour toutes ces périodes.\n",
"\n",
"Nous vérifions également que ces périodes contiennent entre 51 et 52 semaines, pour nous protéger contre des éventuelles erreurs dans notre code."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"year = []\n",
"yearly_incidence = []\n",
"for week1, week2 in zip(first_august_week[:-1],\n",
" first_august_week[1:]):\n",
" one_year = sorted_data['inc'][week1:week2-1]\n",
" assert abs(len(one_year)-52) < 2\n",
" yearly_incidence.append(one_year.sum())\n",
" year.append(week2.year)\n",
"yearly_incidence = pd.Series(data=yearly_incidence, index=year)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Voici les incidences annuelles."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"yearly_incidence.plot(style='*')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Une liste triée permet de plus facilement répérer les valeurs les plus élevées (à la fin)."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"yearly_incidence.sort_values()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Enfin, un histogramme montre bien que les épidémies fortes, qui touchent environ 10% de la population\n",
" française, sont assez rares: il y en eu trois au cours des 35 dernières années."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"yearly_incidence.hist(xrot=20)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.4"
}
},
"nbformat": 4,
"nbformat_minor": 1
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module3/exo2/analyse-syndrome-var.ipynb 0 → 100644
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module4/src_Python3_challenger.ipynb 0 → 100644
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Risk Analysis of the Space Shuttle: Pre-Challenger Prediction of Failure"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this document we reperform some of the analysis provided in \n",
"*Risk Analysis of the Space Shuttle: Pre-Challenger Prediction of Failure* by *Siddhartha R. Dalal, Edward B. Fowlkes, Bruce Hoadley* published in *Journal of the American Statistical Association*, Vol. 84, No. 408 (Dec., 1989), pp. 945-957 and available at http://www.jstor.org/stable/2290069. \n",
"\n",
"On the fourth page of this article, they indicate that the maximum likelihood estimates of the logistic regression using only temperature are: $\\hat{\\alpha}=5.085$ and $\\hat{\\beta}=-0.1156$ and their asymptotic standard errors are $s_{\\hat{\\alpha}}=3.052$ and $s_{\\hat{\\beta}}=0.047$. The Goodness of fit indicated for this model was $G^2=18.086$ with 21 degrees of freedom. Our goal is to reproduce the computation behind these values and the Figure 4 of this article, possibly in a nicer looking way."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Technical information on the computer on which the analysis is run"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will be using the python3 language using the pandas, statsmodels, numpy, matplotlib and seaborn libraries."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"3.6.4 |Anaconda, Inc.| (default, Mar 13 2018, 01:15:57) \n",
"[GCC 7.2.0]\n",
"uname_result(system='Linux', node='a7ade41352bb', release='4.4.0-164-generic', version='#192-Ubuntu SMP Fri Sep 13 12:02:50 UTC 2019', machine='x86_64', processor='x86_64')\n",
"IPython 7.12.0\n",
"IPython.core.release 7.12.0\n",
"PIL 7.0.0\n",
"PIL.Image 7.0.0\n",
"PIL._version 7.0.0\n",
"_csv 1.0\n",
"_ctypes 1.1.0\n",
"_curses b'2.2'\n",
"decimal 1.70\n",
"argparse 1.1\n",
"backcall 0.1.0\n",
"cffi 1.13.2\n",
"csv 1.0\n",
"ctypes 1.1.0\n",
"cycler 0.10.0\n",
"dateutil 2.8.1\n",
"decimal 1.70\n",
"decorator 4.4.1\n",
"distutils 3.6.4\n",
"ipaddress 1.0\n",
"ipykernel 5.1.4\n",
"ipykernel._version 5.1.4\n",
"ipython_genutils 0.2.0\n",
"ipython_genutils._version 0.2.0\n",
"ipywidgets 7.2.1\n",
"ipywidgets._version 7.2.1\n",
"jedi 0.16.0\n",
"json 2.0.9\n",
"jupyter_client 6.0.0\n",
"jupyter_client._version 6.0.0\n",
"jupyter_core 4.6.3\n",
"jupyter_core.version 4.6.3\n",
"kiwisolver 1.1.0\n",
"logging 0.5.1.2\n",
"matplotlib 2.2.3\n",
"matplotlib.backends.backend_agg 2.2.3\n",
"numpy 1.15.2\n",
"numpy.core 1.15.2\n",
"numpy.core.multiarray 3.1\n",
"numpy.lib 1.15.2\n",
"numpy.linalg._umath_linalg b'0.1.5'\n",
"numpy.matlib 1.15.2\n",
"optparse 1.5.3\n",
"pandas 0.22.0\n",
"_libjson 1.33\n",
"parso 0.6.0\n",
"patsy 0.5.1\n",
"patsy.version 0.5.1\n",
"pexpect 4.8.0\n",
"pickleshare 0.7.5\n",
"platform 1.0.8\n",
"prompt_toolkit 3.0.3\n",
"ptyprocess 0.6.0\n",
"pygments 2.5.2\n",
"pyparsing 2.4.6\n",
"pytz 2019.3\n",
"re 2.2.1\n",
"scipy 1.1.0\n",
"scipy._lib.decorator 4.0.5\n",
"scipy._lib.six 1.2.0\n",
"scipy.fftpack._fftpack b'$Revision: $'\n",
"scipy.fftpack.convolve b'$Revision: $'\n",
"scipy.integrate._dop b'$Revision: $'\n",
"scipy.integrate._ode $Id$\n",
"scipy.integrate._odepack 1.9 \n",
"scipy.integrate._quadpack 1.13 \n",
"scipy.integrate.lsoda b'$Revision: $'\n",
"scipy.integrate.vode b'$Revision: $'\n",
"scipy.interpolate._fitpack 1.7 \n",
"scipy.interpolate.dfitpack b'$Revision: $'\n",
"scipy.linalg 0.4.9\n",
"scipy.linalg._fblas b'$Revision: $'\n",
"scipy.linalg._flapack b'$Revision: $'\n",
"scipy.linalg._flinalg b'$Revision: $'\n",
"scipy.ndimage 2.0\n",
"scipy.optimize._cobyla b'$Revision: $'\n",
"scipy.optimize._lbfgsb b'$Revision: $'\n",
"scipy.optimize._minpack 1.10 \n",
"scipy.optimize._nnls b'$Revision: $'\n",
"scipy.optimize._slsqp b'$Revision: $'\n",
"scipy.optimize.minpack2 b'$Revision: $'\n",
"scipy.signal.spline 0.2\n",
"scipy.sparse.linalg.eigen.arpack._arpack b'$Revision: $'\n",
"scipy.sparse.linalg.isolve._iterative b'$Revision: $'\n",
"scipy.special.specfun b'$Revision: $'\n",
"scipy.stats.mvn b'$Revision: $'\n",
"scipy.stats.statlib b'$Revision: $'\n",
"seaborn 0.8.1\n",
"seaborn.external.husl 2.1.0\n",
"seaborn.external.six 1.10.0\n",
"six 1.14.0\n",
"statsmodels 0.9.0\n",
"statsmodels.__init__ 0.9.0\n",
"traitlets 4.3.3\n",
"traitlets._version 4.3.3\n",
"urllib.request 3.6\n",
"zlib 1.0\n",
"zmq 17.1.2\n",
"zmq.sugar 17.1.2\n",
"zmq.sugar.version 17.1.2\n"
]
}
],
"source": [
"def print_imported_modules():\n",
" import sys\n",
" for name, val in sorted(sys.modules.items()):\n",
" if(hasattr(val, '__version__')): \n",
" print(val.__name__, val.__version__)\n",
"# else:\n",
"# print(val.__name__, \"(unknown version)\")\n",
"def print_sys_info():\n",
" import sys\n",
" import platform\n",
" print(sys.version)\n",
" print(platform.uname())\n",
"\n",
"import numpy as np\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"import statsmodels.api as sm\n",
"import seaborn as sns\n",
"\n",
"print_sys_info()\n",
"print_imported_modules()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Loading and inspecting data\n",
"Let's start by reading data."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
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" <th></th>\n",
" <th>Date</th>\n",
" <th>Count</th>\n",
" <th>Temperature</th>\n",
" <th>Pressure</th>\n",
" <th>Malfunction</th>\n",
" </tr>\n",
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" <tbody>\n",
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" <th>0</th>\n",
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" <td>11/28/83</td>\n",
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" <td>100</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>2/03/84</td>\n",
" <td>6</td>\n",
" <td>57</td>\n",
" <td>200</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>4/06/84</td>\n",
" <td>6</td>\n",
" <td>63</td>\n",
" <td>200</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td>8/30/84</td>\n",
" <td>6</td>\n",
" <td>70</td>\n",
" <td>200</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11</th>\n",
" <td>10/05/84</td>\n",
" <td>6</td>\n",
" <td>78</td>\n",
" <td>200</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>12</th>\n",
" <td>11/08/84</td>\n",
" <td>6</td>\n",
" <td>67</td>\n",
" <td>200</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>13</th>\n",
" <td>1/24/85</td>\n",
" <td>6</td>\n",
" <td>53</td>\n",
" <td>200</td>\n",
" <td>2</td>\n",
" </tr>\n",
" <tr>\n",
" <th>14</th>\n",
" <td>4/12/85</td>\n",
" <td>6</td>\n",
" <td>67</td>\n",
" <td>200</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>15</th>\n",
" <td>4/29/85</td>\n",
" <td>6</td>\n",
" <td>75</td>\n",
" <td>200</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>16</th>\n",
" <td>6/17/85</td>\n",
" <td>6</td>\n",
" <td>70</td>\n",
" <td>200</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>17</th>\n",
" <td>7/2903/85</td>\n",
" <td>6</td>\n",
" <td>81</td>\n",
" <td>200</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>18</th>\n",
" <td>8/27/85</td>\n",
" <td>6</td>\n",
" <td>76</td>\n",
" <td>200</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>19</th>\n",
" <td>10/03/85</td>\n",
" <td>6</td>\n",
" <td>79</td>\n",
" <td>200</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>20</th>\n",
" <td>10/30/85</td>\n",
" <td>6</td>\n",
" <td>75</td>\n",
" <td>200</td>\n",
" <td>2</td>\n",
" </tr>\n",
" <tr>\n",
" <th>21</th>\n",
" <td>11/26/85</td>\n",
" <td>6</td>\n",
" <td>76</td>\n",
" <td>200</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>22</th>\n",
" <td>1/12/86</td>\n",
" <td>6</td>\n",
" <td>58</td>\n",
" <td>200</td>\n",
" <td>1</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Date Count Temperature Pressure Malfunction\n",
"0 4/12/81 6 66 50 0\n",
"1 11/12/81 6 70 50 1\n",
"2 3/22/82 6 69 50 0\n",
"3 11/11/82 6 68 50 0\n",
"4 4/04/83 6 67 50 0\n",
"5 6/18/82 6 72 50 0\n",
"6 8/30/83 6 73 100 0\n",
"7 11/28/83 6 70 100 0\n",
"8 2/03/84 6 57 200 1\n",
"9 4/06/84 6 63 200 1\n",
"10 8/30/84 6 70 200 1\n",
"11 10/05/84 6 78 200 0\n",
"12 11/08/84 6 67 200 0\n",
"13 1/24/85 6 53 200 2\n",
"14 4/12/85 6 67 200 0\n",
"15 4/29/85 6 75 200 0\n",
"16 6/17/85 6 70 200 0\n",
"17 7/2903/85 6 81 200 0\n",
"18 8/27/85 6 76 200 0\n",
"19 10/03/85 6 79 200 0\n",
"20 10/30/85 6 75 200 2\n",
"21 11/26/85 6 76 200 0\n",
"22 1/12/86 6 58 200 1"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"data = pd.read_csv(\"https://app-learninglab.inria.fr/moocrr/gitlab/moocrr-session3/moocrr-reproducibility-study/raw/master/data/shuttle.csv\")\n",
"data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We know from our previous experience on this data set that filtering data is a really bad idea. We will therefore process it as such."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"pd.set_option('mode.chained_assignment',None) # this removes a useless warning from pandas\n",
"import matplotlib.pyplot as plt\n",
"\n",
"data[\"Frequency\"]=data.Malfunction/data.Count\n",
"data.plot(x=\"Temperature\",y=\"Frequency\",kind=\"scatter\",ylim=[0,1])\n",
"plt.grid(True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Logistic regression\n",
"\n",
"Let's assume O-rings independently fail with the same probability which solely depends on temperature. A logistic regression should allow us to estimate the influence of temperature."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<table class=\"simpletable\">\n",
"<caption>Generalized Linear Model Regression Results</caption>\n",
"<tr>\n",
" <th>Dep. Variable:</th> <td>Frequency</td> <th> No. Observations: </th> <td> 23</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Model:</th> <td>GLM</td> <th> Df Residuals: </th> <td> 21</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Model Family:</th> <td>Binomial</td> <th> Df Model: </th> <td> 1</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Link Function:</th> <td>logit</td> <th> Scale: </th> <td> 1.0000</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Method:</th> <td>IRLS</td> <th> Log-Likelihood: </th> <td> -3.9210</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Date:</th> <td>Tue, 26 May 2020</td> <th> Deviance: </th> <td> 3.0144</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Time:</th> <td>10:19:52</td> <th> Pearson chi2: </th> <td> 5.00</td> \n",
"</tr>\n",
"<tr>\n",
" <th>No. Iterations:</th> <td>6</td> <th> Covariance Type: </th> <td>nonrobust</td>\n",
"</tr>\n",
"</table>\n",
"<table class=\"simpletable\">\n",
"<tr>\n",
" <td></td> <th>coef</th> <th>std err</th> <th>z</th> <th>P>|z|</th> <th>[0.025</th> <th>0.975]</th> \n",
"</tr>\n",
"<tr>\n",
" <th>Intercept</th> <td> 5.0850</td> <td> 7.477</td> <td> 0.680</td> <td> 0.496</td> <td> -9.570</td> <td> 19.740</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Temperature</th> <td> -0.1156</td> <td> 0.115</td> <td> -1.004</td> <td> 0.316</td> <td> -0.341</td> <td> 0.110</td>\n",
"</tr>\n",
"</table>"
],
"text/plain": [
"<class 'statsmodels.iolib.summary.Summary'>\n",
"\"\"\"\n",
" Generalized Linear Model Regression Results \n",
"==============================================================================\n",
"Dep. Variable: Frequency No. Observations: 23\n",
"Model: GLM Df Residuals: 21\n",
"Model Family: Binomial Df Model: 1\n",
"Link Function: logit Scale: 1.0000\n",
"Method: IRLS Log-Likelihood: -3.9210\n",
"Date: Tue, 26 May 2020 Deviance: 3.0144\n",
"Time: 10:19:52 Pearson chi2: 5.00\n",
"No. Iterations: 6 Covariance Type: nonrobust\n",
"===============================================================================\n",
" coef std err z P>|z| [0.025 0.975]\n",
"-------------------------------------------------------------------------------\n",
"Intercept 5.0850 7.477 0.680 0.496 -9.570 19.740\n",
"Temperature -0.1156 0.115 -1.004 0.316 -0.341 0.110\n",
"===============================================================================\n",
"\"\"\""
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import statsmodels.api as sm\n",
"\n",
"data[\"Success\"]=data.Count-data.Malfunction\n",
"data[\"Intercept\"]=1\n",
"\n",
"logmodel=sm.GLM(data['Frequency'], data[['Intercept','Temperature']], \n",
" family=sm.families.Binomial(sm.families.links.logit)).fit()\n",
"\n",
"logmodel.summary()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The maximum likelyhood estimator of the intercept and of Temperature are thus $\\hat{\\alpha}=5.0849$ and $\\hat{\\beta}=-0.1156$. This **corresponds** to the values from the article of Dalal *et al.* The standard errors are $s_{\\hat{\\alpha}} = 7.477$ and $s_{\\hat{\\beta}} = 0.115$, which is **different** from the $3.052$ and $0.04702$ reported by Dallal *et al.* The deviance is $3.01444$ with 21 degrees of freedom. I cannot find any value similar to the Goodness of fit ($G^2=18.086$) reported by Dalal *et al.* There seems to be something wrong. Oh I know, I haven't indicated that my observations are actually the result of 6 observations for each rocket launch. Let's indicate these weights (since the weights are always the same throughout all experiments, it does not change the estimates of the fit but it does influence the variance estimates)."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<table class=\"simpletable\">\n",
"<caption>Generalized Linear Model Regression Results</caption>\n",
"<tr>\n",
" <th>Dep. Variable:</th> <td>Frequency</td> <th> No. Observations: </th> <td> 23</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Model:</th> <td>GLM</td> <th> Df Residuals: </th> <td> 21</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Model Family:</th> <td>Binomial</td> <th> Df Model: </th> <td> 1</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Link Function:</th> <td>logit</td> <th> Scale: </th> <td> 1.0000</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Method:</th> <td>IRLS</td> <th> Log-Likelihood: </th> <td> -23.526</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Date:</th> <td>Tue, 26 May 2020</td> <th> Deviance: </th> <td> 18.086</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Time:</th> <td>10:19:58</td> <th> Pearson chi2: </th> <td> 30.0</td> \n",
"</tr>\n",
"<tr>\n",
" <th>No. Iterations:</th> <td>6</td> <th> Covariance Type: </th> <td>nonrobust</td>\n",
"</tr>\n",
"</table>\n",
"<table class=\"simpletable\">\n",
"<tr>\n",
" <td></td> <th>coef</th> <th>std err</th> <th>z</th> <th>P>|z|</th> <th>[0.025</th> <th>0.975]</th> \n",
"</tr>\n",
"<tr>\n",
" <th>Intercept</th> <td> 5.0850</td> <td> 3.052</td> <td> 1.666</td> <td> 0.096</td> <td> -0.898</td> <td> 11.068</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Temperature</th> <td> -0.1156</td> <td> 0.047</td> <td> -2.458</td> <td> 0.014</td> <td> -0.208</td> <td> -0.023</td>\n",
"</tr>\n",
"</table>"
],
"text/plain": [
"<class 'statsmodels.iolib.summary.Summary'>\n",
"\"\"\"\n",
" Generalized Linear Model Regression Results \n",
"==============================================================================\n",
"Dep. Variable: Frequency No. Observations: 23\n",
"Model: GLM Df Residuals: 21\n",
"Model Family: Binomial Df Model: 1\n",
"Link Function: logit Scale: 1.0000\n",
"Method: IRLS Log-Likelihood: -23.526\n",
"Date: Tue, 26 May 2020 Deviance: 18.086\n",
"Time: 10:19:58 Pearson chi2: 30.0\n",
"No. Iterations: 6 Covariance Type: nonrobust\n",
"===============================================================================\n",
" coef std err z P>|z| [0.025 0.975]\n",
"-------------------------------------------------------------------------------\n",
"Intercept 5.0850 3.052 1.666 0.096 -0.898 11.068\n",
"Temperature -0.1156 0.047 -2.458 0.014 -0.208 -0.023\n",
"===============================================================================\n",
"\"\"\""
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"logmodel=sm.GLM(data['Frequency'], data[['Intercept','Temperature']], \n",
" family=sm.families.Binomial(sm.families.links.logit),\n",
" var_weights=data['Count']).fit()\n",
"\n",
"logmodel.summary()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Good, now I have recovered the asymptotic standard errors $s_{\\hat{\\alpha}}=3.052$ and $s_{\\hat{\\beta}}=0.047$.\n",
"The Goodness of fit (Deviance) indicated for this model is $G^2=18.086$ with 21 degrees of freedom (Df Residuals).\n",
"\n",
"**I have therefore managed to fully replicate the results of the Dalal *et al.* article**."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Predicting failure probability\n",
"The temperature when launching the shuttle was 31°F. Let's try to estimate the failure probability for such temperature using our model.:"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"data_pred = pd.DataFrame({'Temperature': np.linspace(start=30, stop=90, num=121), 'Intercept': 1})\n",
"data_pred['Frequency'] = logmodel.predict(data_pred)\n",
"data_pred.plot(x=\"Temperature\",y=\"Frequency\",kind=\"line\",ylim=[0,1])\n",
"plt.scatter(x=data[\"Temperature\"],y=data[\"Frequency\"])\n",
"plt.grid(True)"
]
},
{
"cell_type": "markdown",
"metadata": {
"hideCode": false,
"hidePrompt": false,
"scrolled": true
},
"source": [
"This figure is very similar to the Figure 4 of Dalal *et al.* **I have managed to replicate the Figure 4 of the Dalal *et al.* article.**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Computing and plotting uncertainty"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Following the documentation of [Seaborn](https://seaborn.pydata.org/generated/seaborn.regplot.html), I use regplot."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/conda/lib/python3.6/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
" return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
]
},
{
"data": {
"image/png": 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zsykqKmpzTWlpKaqqct111+Fyubj++uuZP3/+KX9/erqzK8WOeunA/7vmLP6/l77gaJ2b4tIa3tpSxg8uH4miKJEuXrdJS3fiTLKT5LBGuihhkZmZHOkihE081w3iv36dFVKAeOedd3jppZeorq5m8eLFFBYW4nQ6UVWVyy67rMMA0dF4xfFvcpqmUVxczHPPPYfH4+Haa69l/PjxDB48+KTlqamJ34Vl6elObrh8BE+tKqbJ7eejbw5jBi5v2aku1qWnO6mpcdFY7yajT0Kki9PtMjOTqaqKz9Xx8Vw36B3166yQAsTKlSu55ZZbmDJlStsnWyzcf//9HT4nJyeH8vLy4HFFRQVZWVntrklLSyMxMZHExEQmTpxISUnJKQNEvMtISeDGmSN5es02PD6NTd8cxumwMOWM/pEuWrfxazqqpmMxy0Q6IaJVSK/Op556ql1waDVt2rQOz48bN47S0lLKysrw+XwUFha2u/aSSy7h888/R1VV3G43RUVFDB06tJNViE/9Mpxcf/kILOZAq+utzQf4cmdVhEvVvZplZbUQUS2kALF48WLq679LT11XV8eSJUtO+hyLxcIDDzzA0qVLmTlzJldccQUFBQUsX76c5cuXAzB06FCmTJnC3LlzWbhwIVdffTXDhw8/jerEl0E5KSy6dDimlp651zbuYceBU88gixUeWRMhRFRTjBBeofPmzWPVqlWnPNcTKmuaqYjjfsLWPvpjfbGjklc37gXAajZx8+xRDMyOzcG04+vXx2nDYe/SXImoFM/92PFcN+gd9euskFoQuq7T3NwcPHa5XGhafC7kikYTRmRx+aTAILVf03l+3Q4qa+MjuZ8nThcEChEPQgoQs2fP5qabbmLVqlWsWrWKm2++mblz54a7bOIYU8b344Jx/YBAuoq/vRkfeZu8fg1Nj88FgULEupDa9rfeeitZWVls2LABwzC49tprQ1qvILqPoihcfu5Amtx+vt59lHqXj7+9VcKtc8fEfBeN26uR5JDZTEJEm5DfWa688kquvPLKcJZFnIJJUbhq6hBcHj+7DtZTWevmhbd3cNPMUVgtsfsG6/aqcbtoTohYFlKAqK6u5sUXX6SsrAxV/W5qYm/NnRRJFrOJxZcO55m12zh01MX+8kb+uWEXiy8djskUm6utNd3A69ewW82RLooQ4hghBYg777yToUOHMnnyZMxmeRFHmt1m5oYrRvKXVVupafCyrbSWNR+XMvf8QTGbksPtVSVACBFlQgoQDQ0N/PrXvw53WUQnJDms3DhzFH95Yysuj8qn2yro47Rx0VkDIl20LvH6NQzDiNkAJ0Q8CqnjuqCggIqKinCXRXRSRkoCN1wxElvL+MM7W8r4YkdlhEvVNYYRCBJCiOgRcgti7ty5nHXWWdjt9uB5GYOIvNzMJBZPH84L63agGwavb9pLksPKiIFpkS5ap3l8Ggm22J6RJUQ8CenVOHv2bGbPnh3usoguGp6XylVTh7Dy/T3oBix/dxdL54wmNzMp0kXrFOlmEiK6hBQgZHpr9Pve8EwaXD7e2VKGTw2str5t3hgyUmInpXZrN5O0IoSIDiGNQZSWlrJo0aJgNtbi4mL+8Ic/hLVgovOmntmfc0dnA+By+3nuzRKa3P4Il6pzJPWGENEjpADx4IMPcvvtt5OcHEj2NGrUKNatWxfWgonOUxSF2ecNYvSgwPhDdYOHF9aV4Iuhwd/WbiYhROSFFCAaGxu58MILg33DJpMJq1VWvkYjk0nhmmkF5Ldkez1Y5WL5+l1oMbIHtMxmEiJ6hBQgzGYzfr8/GCAqKiowmWI3tUO8s1pMXDdjOH1btvTccaCO1R/ui5lP5tLNJER0CHnDoDvuuIPa2lr+8Ic/sHjxYm666aZwl02chsQEKzfOHElyS46jLSWVbPjyUIRLFRqvT0OPkWAmRDwLabrI/Pnzyc3N5b333sPtdvP4448zceLEcJdNnKa05MBCumVrivH5ddZ/cZA+ThsTR2ad+skRZBBIveFMkG5MISIp5PmEEydOlKAQg/r3dbJk+nCefyuwkO6ND/aSnBj9C+ncHgkQQkRaSAFiwYIFHS5eWrlyZbcXSHS/gtxUFkwdwooYWkin6gZen4bdJgn8hIiUkALEPffcE3zs9XopLCwkKyu6uylEW2cNz6Q+xhbSNXtVCRBCRFBIAWLSpEltji+44AIZpI5BU8/sT73Lx6fbKoIL6W6dNyZqN+vx+jVUTcdilhlzQkRCl155TU1NlJWVdXdZRJgpisKcGFtI1+xVT32RECIsOj0Goes6Bw8e5MYbbwxrwUR4tC6k+2vhNg5UNAUX0v3gshGYo3BHutbtSE2SwE+IHtfpMQiz2Uxubi7Z2dlhK5QIL6vFxPUzRvDU6mKq6jzsOFDHqg/2cuWFQ6Iuk6phgMerkigzmoTocV0agxCxLzHByg+vGMVfVm2lsdnP5zuqSHHauHRiXqSL1k6zRwKEEJEQUoA499xzO/xk2Zq7/5NPPun2gonwS0u288MrRrJs9Ta8fo0NXx4iOdHGOaOjq3Wo6gZevyZ7VgvRw0IKEIsWLaKuro5rrrkGwzB49dVXyc7OZubMmeEunwizfhlOfnDZcJ57qwRNN1j90T6SE62MHpQe6aK10exRJUAI0cNCmsW0ZcsW/vM//5ORI0cyatQo7r//fjZu3MiAAQMYMGBAuMsowmzogD5cfdFQINDn/4/1u9hf3hjhUrXl82touh7pYgjRq4QUICorK6mpqQke19TUUFVVFbZCiZ43flhfZk3OB0DVDJ5fV0JFTXOES/WdQH6m6J2OK0Q8CqmL6YYbbmDevHlcfPHFAGzcuJFbb701rAUTPe/8cf1ocPn4oOgIHp/Gc28FFtKlJtkjXTQAmj1+nAmWqJtpJUS8CilALFmyhAkTJrBlyxYMw2DJkiWMGDEi3GUTETDjnIE0uf18teso9S4fz71Vwo/mjCExIfL7ROtGYK8Ihz3yZRGiNwj5lZabm4umaYwZMyac5RERZlIUrpo6hCa3n10H66msdfPC2yXcNGsUNkvkB4ndXlUChBA9JKQxiI0bNzJr1izuvPNOAL799ltuu+22sBZMRI7ZZGLx9OHkZjoBOFDRxPJ3d0XFILFP1fGrkS+HEL1BSAHiySefZOXKlaSkpAAwbtw4Dhw4ENaCiciyW83ccMXINtuWvr5pb1RsWyr5mYToGSEn68vMzGxzbLPZur0wIro4E6zcOHMUKc7A//WXO4/y1qcHIh4kPD5VtiQVogeEFCCcTidHjx4Nzh759NNPSU5OPuXzNm3axIwZM5g+fTrLli074XVFRUWMGjWKdevWhVhs0VNaV1s77IHxhw+LjrDpm8MRLVNrfiYhRHiFFCB+8YtfcMstt3Dw4EGuu+467r777jYJ/DqiaRoPP/wwzzzzDIWFhaxdu5bdu3d3eN1vf/tbLrjggq7VQIRdTnoi188YibVlX4a3PytjS0llRMvU7JEAIUS4hTQdZPz48bzwwgt8+eWXAJx11lnB8YgTKSoqIj8/n7y8QPK3WbNmsX79eoYNG9bmuhdffJEZM2bw7bffdqX8oofk5ySzeHoBL769M7i3tcNmZuyQjIiUR/IzCRF+pwwQmqbx/e9/n1dffZWpU6eGfOOKigpycnKCx9nZ2RQVFbW75t133+X555/vVIBIT3eGfG0sitb6TU53YrFZeHZ1MYYBr7y3m74ZTkYP7lyQ6K76JdjMZPRxdMu9ulNm5qm7X2NVPNcN4r9+nXXKAGE2m0lLS8Pr9WK3h76itqOBzONXwD7yyCPcfffdmM2d+xRYU+Pq1PWxJD3dGdX1G5qTzOzzB7Hmo1JUzeDPrxZx86xRDMwO7YXV3fXze3yYTdGzJWlmZjJVVdGVx6q7xHPdoHfUr7NC6mIaNGgQS5YsYcaMGSQmJgbPL1my5ITPycnJoby8PHhcUVFBVlZWm2u2bt3KXXfdBUBtbS0bN27EYrFw6aWXdqoSomdNHpOD26vy7ucH8as6z71Vwi1zRtMvo+dbPs0eleREmVEnRDiEFCBcLhcFBQXs3bs35BuPGzeO0tJSysrKyM7OprCwkP/5n/9pc82GDRuCj++9914uuugiCQ4x4uKzBuDxanz4bSBv09/eLOFHc0bTN7Vnu3xatySV/ExCdL+TBojf/OY33HvvvTz22GN89NFHnH/++aHf2GLhgQceYOnSpWiaxoIFCygoKGD58uVAYI8JEbsUReGKcwfi9ql8saOKJrefvxZu50dzx5CW3HPJ/XQjkOU1GnJFCRFvFOMkq56uvPJKXn/99XaPI6myppmKOO4njPYxiOPpusE/N+zi272BdPAZKQncMnc0KSfo9glH/Sxmhb5RMlgdz/3Y8Vw36B3166yTju4dGzsivXpWRCeTSWHhxcMYMTAVgOoGD88Wbsfl8fdYGVTNwOeXvSKE6G4nDRA+n489e/awe/fuNo9bv4QAsJhNLL50OEP6B9bGVNa6+Vvhdtw9uNrZJQvnhOh2J+1imjZt2omfqCisX78+LIU6Geliil5ev8bf3tzOgYomAPKykrhp5ijstu+mMYezfpmpCRGf8hrP3RTxXDfoHfXrrJOO7B07y0iIU7FbzfzwipH8de12Dh11UVbZxPPrSvjhFSOx9cCKZ5nyKkT3ip4VRiIuJNgs3DhzJDnpgfUypeWNvPD2Dnxq+McImr2S5VWI7iRzA0W3S0ywctOsUTy9ZhtVdW72Hm7gpbd3ct2M09umdtfBOj4vqaS20Utasp2JI7MoyE0N/twwAusinAnW062CiKCt+6r5sOgIVXVuMlMdXHBGP8Z2Mp2L6B7SghBhkeSwcvPsUcENh3Yfqueld3bg72JLYtfBOt7+rIzqBi+6AdUNXt7+rIxdB+vaXCdZXmPb1n3VvLpxLxW1bnQDKmrdvLpxL1v3VUe6aL2SBAgRNimJNpbOHk1GS5DYdbCev7z2bZe2DP38BOnFjz+v6UaPzp4S3evDoiOdOi/CSwKECKsUZyBIpKcEVlcX761uaUl0LkjUNnpDPi+tiNhVVec+wXlPD5dEgAQI0QP6HBckdh2s58VODlyfKH1HR+f9mi4L52JU5glyeWWmJvRwSQRIgBA9JDXJzi2zR5OVFngD2H2onhfW7Qj5jXziyKxOnZeFc7HpgjP6deq8CC8JEKLH9Emyc9fiCcGB672HG3jurRK8vlMHiYLcVGZMyiMjxY5JgYwUOzMm5bWZxXQsr1+TVkQMGjs4gwVTh5Cd5sCkKGSnOVgwdYjMYoqQk66kjkaykjq2pac7KT1Yy1/Xbgv2K+dlJfHDK0bisHfvrGuLSSGjT0KPpgKP59W48Vw36B316yxpQYgel5Jo45Y5Y4KL6coqm3hm7Taa3N2b4E/VDZplRpMQXSYBQkREksPK0tmjGZAZ2IXuSHUzT6/ZRr3L162/p8ntR9M7P61WCCEBQkRQYoKlZT/rJCAwxXHZ6mKqG7pvSqNhQIOr51KPCxFPJECIiArkbhrFsAF9gMC6hmWriimvae623+H1a3h80tUkRGdJgBARZ7eauf7yEYwelAZAo9vP02uKOVDRfQOGDS6fdDUJ0UkSIERUsJhNLLp0ON8b3hcI7DP917Xb2XGgtlvurxtQ39S94xtCxDsJECJqmE0KV00dyvnjcoDAiugX397BVzuruuX+PlXv9plSQsQzCRAiqpgUhZnn5jNjUh4Q+OS/4v09bPr6cLfsi+5y+2UBnRAhkgAhoo6iKEw9cwALpg7B1LLGbd1nB1jzUSm6fnpBwgDqXT7ZWEiIEEiAEFFrwogsfnDZCKyWwJ/p5m0VvPyvnae9O52mGzQ1S1eTEKciAUJEtZH5aSydPRpnQiANx/b9tfx17XYam09vwLnZq0pXkxCnIAFCRL28rCRumz82uPFQWWUTf1lVTMVprpWod/m6ZVxDiHglAULEhIyUBG6bN4b87EDCsdpGL39ZVdxuy9HO0HSDRulqEuKEJECImOFMCOxzfeawwFoJr1/j+bdK+KS4vMstgWavGlK6cSF6IwkQIqZYzCYWXjyUSybkAoFpsGs+KmXVh/tQta6tlK5zebu0T7YQ8U4ChIg5iqJwyYRcrr1kGBax8CRbAAAeZUlEQVRzYB7sZ9srefbN7V1aCGcYUNvkPe0ptELEGwkQImadMbQvt84dQ4rTBkDpkUb+7/VvOVTV1Ol76bpBbaNXBq2FOIYECBHTBmQm8ZMrx5KXFUgZXtfk46nVxXzZhfQcfk2nrklmNgnRSgKEiHnJiTZumTOas0dmAaBqBivf39OlcQmvX6O20SsrrYVAAoSIExaziSsvHMKVUwZjbsnP8em2CpatLqa20dupe/lUnZoGj4xJiF5PAoSIK2ePyuZHc0fTp2Vc4mCViz++VkRJJ9OGq5pBTYNH9pAQvVpYA8SmTZuYMWMG06dPZ9myZe1+vnr1aubMmcOcOXO49tprKSkpCWdxRC+Rl5XMHQvGUZAb2KXO7dV4Yd0O3tq8v1NdTqpuUNPg7fL0WSFiXdgChKZpPPzwwzzzzDMUFhaydu1adu/e3eaa3NxcXnrpJdasWcPtt9/Or371q3AVR/QyzgQrN1w+kksm5NKSEJYPio6wbHUxNZ3Y81prmd0kQUL0RmELEEVFReTn55OXl4fNZmPWrFmsX7++zTXf+9736NMn8CnvzDPPpLy8PFzFEb2QyRRYL3HjrFEkO6xAoMvpD69+y9e7j4Z8H003qGmUxXSi97GE68YVFRXk5OQEj7OzsykqKjrh9StXruTCCy8M6d7p6c7TLl80k/p1r0npTkYO6cvzhdso3luN16/xyobd7CtvZNFlI0hMsIZ0HwOwOawkJ9owtW5U0YHMzORuKnn0iee6QfzXr7PCFiA6mkuuKB2/qDZv3szKlSv5+9//HtK9a2pcp1W2aJae7pT6hcmiS4bxcVYSb392AE032LKtgp37a1l48VCG9O8T0j1qCLRMkh1WHPb2L5/MzGSqqhq7ueTRIZ7rBr2jfp0Vti6mnJycNl1GFRUVZGVltbuupKSE+++/n//7v/8jLS0tXMURApOicMEZ/fjxlWPJSnMAgZTff127nbUfl4a8EZGuG9S7fDI2IeJe2ALEuHHjKC0tpaysDJ/PR2FhIdOmTWtzzeHDh7nzzjv57//+bwYPHhyuogjRRr8MJz+5chznjQ10gRrAx1vL+cPKb9lfHvonSK9fo7reQ5PbL6uvRVwKWxeTxWLhgQceYOnSpWiaxoIFCygoKGD58uUALFq0iD/96U/U1dXx0EMPAWA2m3nttdfCVSQhgqwWE7PPG8TI/DRe27iHuiYf1Q0elq0uZvLYHKafnYfdaj7lfQygye2n2eMnMcFKhiyuE3FEMWLso09lTTMVcdxPKGMQPa94XzVvbT5AzTErrpMcFvr2SUDVDNKS7UwcmUVBbuop79U3IwlPsxdnguWEY24d2bqvmg+LjlBV5yYz1cEFZ/Rj7OCMLtWnu639pJT3vzqEy6PiTLBw0VkDmD15UKSL1e1kDKK9sLUghIgFuw7W8d5Xh0mwW0hXoL7Jh6YbNLlVmtxNOOxm/JrB25+VAZwySOiGQZPbj8erkuK0YQuhFbJ1XzWvbtwbPK6odQePIx0k1n5SytqPSoHAJJOmZn/wOB6DhGhLUm2IXu3zksrg4wSbhcw0RzCXEwRWYVfWNuNy+9myvSLk+6otayfqm049kP1h0ZFOne9J7391qFPnRXyRACF6teMT+ZkUBZMJzOZAAkAIbChU7/Kxo6yessrOdUG4fYGB7JMFiqo69wnOh77iO1xOtAGTqwsbM4nYIwFC9GppyfZ258wmE1azmczUBFKcNlqHEvyqzp/fKGbl+3tobPaF/DsMAoHiaL2H2kYv/uOm02amOjp8XmZqQsi/I1ySHB0vInSe4LyILxIgRK82cWT7tTmJCZbgIHOSw0pWqoME23djCV/urOKJf37Dxq8PdTr9htevUd3gpabBg8enAnDBGf06vPZE53vSRWcN6NR5EV/MDz744IORLkRnuNx+XJ349BZrHA4b7jhuvkdb/TJSEkhLtlPX6MXr00hPsTPte7mMGJgWPNe3TwIzJg1kwohMDle5cHlUNN1gz6EGvt5VhdNhJSvNgaIoIddP0w08Po1mr0pmqoOcdAe1jV7cXo2sNAeXnzMw4gPUAMPzUkGBw9UuVE3H6bBy2aSBcTlA7XTaaY7j9xans31r+VRkmmuUicZpoN0p1uun6Qafbavg3S8O4vaqwfMDMp3MOHsgk87o36X6KYDNasZhN2O3mjs1Rban9IZpoPFev86Saa5CdILZpDB5bA5nFvTl/a8O8fHWcjTd4FCVi2ff3M5HxeVMO2tAcI/sUBkEup+8fg2TAgl2Cw6bBatFeoFF5EiAEKILHHYLV5ybzzmjs/nX52V8s7sagB37a9mxv5aRA9O4ZMIABmR2LlAA6AY0e1SaPSoWk0KC3UKCzRycVSVET5EAIcRpSE9J4JppBVw4vj/vbCljx4E6AEoO1FJyoJZR+Wlc/L0B5HYhUEBgPUWT20+T24/VbMJhN2OzSrAQPUMChBDdoF+GkxsuH0lNs5/XNuxi7+EGALbvr2X7/loKcvsw9cwBDO6X3OXxBb+m42/WAT9mk4LNYsJmNWOzmjCbJGCI7icBQohuNCw3laWzR7PvSAPrvzgYDBS7Dtaz62A9A7OTmHJGf0blp51006FT0XQDt0/D7QusqbCYFKxWMwk2c0hJBoUIhQQIIcJgcL+UYKDY+PVhdpYFup4OVDTx8r92kpGSwPnjcvje8MyQ8jWdiqobqF4Vt1fFZFJIsJlx2MxYLRIsRNdJgBAijAb3S2FwvxQOH3Wx8etDbN1Xg2FAdYOH1R+V8s6WMiaOzOLc0dmkp3TPymldN4KD3CaTgt1qJsFqxmo1YYrC6bMiekmAEKIH9O/rZNGlw6lp8PDR1nK+KKnEp+p4fBofFh3ho6IjjBiYxqTRWQzPTT2t7qdj6bqBu6VlAWAxK9gsZqwWE1aLSQa7xUlJgBCiB6WnJDDnvEFcOiGXz0sq+aS4nLomHwbfzXxKTbIxcWQWE4Zn0iep86tfT0bVDFRNhZYchQqBpIRmsxL4blICX2ZFBr6FBAghIsFhtzBlfH/OH9ePkgO1bC6uYPehegDqmny8+/lB1n9+kGG5fZgwIotR+WlhWTRn0DI7SgNom0RQAcxmBavFjM1iwq/qGIYRlau8RXjEXICw2wJ/rIYBhmGgG0bgcaQLJkQXmEwKowelM3pQOtX1Hj7bXsEXO6to9qgYfDf7KcFmZuyQDM4q6Et+TnKPjCUYfNficHvBXNtMba0bkynQ2jC1tjZMChaz0nIsrY54EnO5mIAO86W0CRaGga4TPA58P+ZnxwWX1u89qd3Lu+VEerqT2uNz+Rz3ZqCc4HFHJ5RjThiGgUHghW/oRkSCaqznYjqV7qifquls31/LFzuq2HWwrt3fZh+njXFDMzhjaAYD+jp77BN9KHVToKWLyhTsqlJQMGj7GgsMsSgoSiBImpRAoOmusZeukFxM7cVcC+JEFEXBfJovFL2lKXL8H/N3v+O44/bvxh09DJYvFJl9k7D2ULRqEyT1tsFUb32sR0dA7U0sZhPjhmQwbkgG9S4fX++q4qtdR6msDWwsVO/y8WHRET4sOkJ6sp0xg9MZOySdAZlJEZ+lZNAy5VbXTnltRxSFlhaJKfAaaqmPorRs5qQEXkvhCiqt7wGtL+Cuvo7jRdy0IOJFLH2K0Q0jGFjateCOCTCabqBqOrohLYiuMgyDI9XNfL3rKN/urabe1T4tdYrTxqj8NEblpzGkf0q3z1CK1v+7Y1stikLwb5CW861dYUDww06wW7r1b1U36JOayNHqplP/vtYgRUvrp+VLCf5cadNjYbScCwa3lu/KCY/DE4S60oKQABFlYilAdJZuGKSlOTlS3oCq66iqjqoHgky86Ik3Ud0wKKtoomhPNVv3VdPY3H7/CZvFxLDcPozIS2V4Xmq3zIaK1gDRXaKpfscGoZMFk1BiSes7/OCB6Z0uR9x0MYnoZ1IUbFYziQlt/+z0YAsjMHZ0oi4+aN/NB8d3A7R/0XR0L90ItGw0TUfXA62fWIlTJkUhPyeZ/JxkZp2Xz8HKJor31VC8r4aalj22farOttJatpXWApCd5qAgN5VhuX0YlJPcLau3RfgEW+KBo4iVQwKEiDiTScFmivwbVkfdZMd2Fai6garq+DU9asZgTIrCwOxkBmYnc/k5A6msc1PSkiCwrLIpWM6KWjcVtW4+/PYIZpNCXnYSQ/qlMKR/CnlZybLvhOiQBAghWnRmooOq6TR7VTxeNWpaHoqikJ2WSHZaIlPPHECzR2X3oTp2ltWxq6yexpatUDXdoPRII6VHGtnw5SEsZoXczCTyc5IZlBMINg67vDUICRBCdInFbCIl0Uayw4rHp+H2qvhUPdLFaiMxwcIZQ/tyxtC+GIZBRa2bPYfq2X2wntLyRryB1XGomkFpeSOl5Y1sbHluZqqDgdlJDMxKIjcriay0xMhVRESMBAghToOiKDjsFhx2C6qm40iw0mBSoGVaJhCcwRXpcuakJ5KTnsj54/qh6QaHj7rYe7ie0iON7K9oxOP7bmpqVZ2bqjo3X+yoAsBqNjGwXzJZqQ4G9HXSv6+TzFRHcHaQiE8SIIToJhazidRkO36Po93P/KqOT9Xw+rSoaGmYTQp5WUnkZSUx9czAoH1FTTP7yxs5UNHEgcpGahq8wev9ms6eg/XsOVgfPGcxK2SlJdIvPZGcjESy0xPJTnOQ5LD2uvUC8UoChBA9oDV7qjPBiq4beHwaXr+Gz69FRZoYk6LQL8NJvwwn544JnGty+zlU1URZZROHqlwcrna1mVKraoFWyOGjbaeGJiZYyEpzkJXqIDP4lUCfJHvEF/KJzpEAIUQPM5kUEhMsJCZY0A0Dn1/D69fx+qJnwBsgyWFlxMA0RgxMAyAtLZHSsloOH3Vx6KiL8ppmjlQ3U9vobfO8Zo8aHAQ/lsWs0LePg4yUBDL62MlISSA9JYH0FDspTrt0V0UhCRBCRJBJUUiwWUiwAU4bPr+Gx6/h8WlRt4BQURT6JNnpk2Rn1KDvFl15fCoVNW7Ka5qpqG2moiYwftHkbruAT9UMymuaKa9pbndvk6KQmmwjNclOWrI9+L1PUuBcH6dN9q6IAAkQQkQRm9WMzWomJTEwbuH1a3h8KqoWXcHiWAk2S3Dh3rGaPWpwsPtovZuqOg9H6z3UNHjQjgt+umFQ0+BtM+5xPGeChT5OGylOG8mJge8piVaSE20ktX53WCSjbDeSACFElGodt0hyBMYtvH4tONitaZHJxtsZiQkdBw5dN2ho9nG03kNto5eahkDQqGvyUdvobdfyaOXyqLg8Koer27dAjuWwW0hyWElyWHE6LDgTAo8TEyw4EywkJlhJtFuC3XxWs0kG1U9AAoQQMcBkap1OGzg2DAO/qqNqOn4tkDIkGqbThsJkUkhNCnQjdcSnatQ1+ahv8lLf5KOuyUu9y0eDy0e9y0d9ky+4hqMjrVusVtW5QyqPxRz4t01KtGGzmHDYLDjs5kDXn91Mgq3lsc0c/LJbLditppb9acwRTVMeThIghIhBSkteq+NzKum6gabrqNp3WXRVTUfTYydFu81iJis1MAvqRHx+jcZmP/UuH01uH43Nfhqb/TS523653P523VnHUzUj+PyuslpM2K1mbNbW74GNzY7/brWY2uwJfuyXxdzyuOW7peVx65awkZgBFtYAsWnTJh555BF0XWfhwoX86Ec/avNzwzB45JFH2LhxIwkJCfzmN79hzJgx4SySEHFr675qPiw6QlWdm8xUBxec0Y+xgzP4a+E2tmyvxKfqWM0K3xuRyYQRmXyytYKj9W7SUxKYOCKTYQNS2Xmwjs9LKqlt9JKWbGfiyCwOVjXx2bYKmn0aiTYzk0Znc/FZuScsx64O7gG0O1eQmxry8wtyU3nvq4OBcnhVEu2Wk5aj9R41DZ7AoHp+GpmpDnYfqqdkfy2NzX5sVhPpyQlYLSbcPhW/atDY7MPtVfH6Ojf92K/q+FUdQmu0dEnrPhmW1v3DW75bWjdoMitYTKaW/cQDu/tZWh+bTYwbkd3p3xm2dN+apjFjxgz+9re/kZ2dzdVXX80TTzzBsGHDgtds3LiRF198kaeffppvvvmGRx55hBUrVpzy3vGaDhviO903SP3CZeu+al7duLfdeWeChe0tGV1bGQTGBzKP+4Q+YUQmn5dUfnedAfUuLy63H5OiBPc5ALhkYh7TzhqAzncJDSHwxvz2Z2Vt7uvxqSiA3db28+iMSXntgkRHzwfISXfw7Z7qducv+t6AdkHiRPcYMziN4n217c63luPYdN87y2pZ92lZmw20DN1g7JB0UpPswXUsXn9g8WPr+FDrsU/VA18t56PBmv+Z1+nnhK0FUVRURH5+Pnl5eQDMmjWL9evXtwkQ69evZ/78+SiKwplnnklDQwOVlZVkZWWFq1hCxKUPi450eL5kf/s3RAC3R2137v2vDpGcaAseKwq43CqGAYpJaTOQ+9n2Cr5/8bA2zzcMg9c37cFibtsV4vYGfldigrXN+W92H2XC8CwCCd4DAemb3UeP6c//7rNrR8EBYMv2Smaek9/m6q92VnWYFn7L9kqcDmu781/trGLMoPRA11BLVtuvdx0NfBI/Lpl8vcvH3PMHd1iWYx37sVs3AlmAff5A4GidaND6uN2XprWMLwW6CP0tGYS1Y45VLbCXSmDsqeV7S5eiprXtZjwdYQsQFRUV5OTkBI+zs7MpKio66TU5OTlUVFScMkB0ZWekWCL1i22RqF9tk6/DlN260cEeGi27qR1/vcujkp6ScNzzA28wrcGh9XuzR+2wnnUufwfjIoACdlvb800elfy8tDbnGt0qCbb2qd9V3cBmaX/e49MYNrhv23p4tQ6z0R6t99C3g3GNZp/GiKGZAMGfu7zbOryH+5hre4OwBYiOeq6On0oWyjVCiFN74mdTI10E4PTL0R31iJZ7xIOwrSjJycmhvLw8eNxRy+D4a8rLy6V7SQghokTYAsS4ceMoLS2lrKwMn89HYWEh06ZNa3PNtGnTeOONNzAMg6+//prk5GQJEEIIESXC1sVksVh44IEHWLp0KZqmsWDBAgoKCli+fDkAixYtYurUqWzcuJHp06fjcDh49NFHw1UcIYQQnRS2aa5CCCFim2S1EkII0SEJEEIIIToU1bmYvF4vS5YswefzBVdm//SnP6Wuro6f//znHDp0iAEDBvC///u/9OnTJ9LF7ZLW8Zns7GyeeuqpuKrbtGnTcDqdmEwmzGYzr732WlzVr6Ghgfvvv5+dO3eiKAqPPvoogwcPjov67d27l5///OfB47KyMn76058yf/78uKjfc889x4oVK1AUheHDh/PYY4/hdrvjom4Azz//PCtWrMAwDBYuXMgPf/jDLr32oroFYbPZeP7551m9ejVvvPEGH3zwAV9//TXLli1j8uTJvPPOO0yePJlly5ZFuqhd9sILLzB06NDgcTzVDQJ/qKtWreK1114D4qt+jzzyCFOmTGHdunWsWrWKoUOHxk39hgwZwqpVq4L/dw6Hg+nTp8dF/SoqKnjhhRd49dVXWbt2LZqmUVhYGBd1A9i5cycrVqxgxYoVrFq1ivfff5/S0tIu1S+qA4SiKDidTgBUVUVVVRRFCaboAJg/fz7vvvtuJIvZZeXl5bz//vtcffXVwXPxUrcTiZf6NTU1sWXLluD/nc1mIyUlJW7qd6xPPvmEvLw8BgwYEDf10zQNj8eDqqp4PB6ysrLipm579uxh/PjxOBwOLBYLZ599Nv/617+6VL+oDhAQ+I+cN28e5513Hueddx7jx4+nuro6uF4iKyuLmpqaCJeyax599FH+7d/+DdMxO2DFS91a3XzzzVx11VX885//BOKnfmVlZaSnp3Pfffcxf/58fvnLX9Lc3Bw39TtWYWEhs2fPBuLj/y87O5ubbrqJiy++mAsuuICkpCQuuOCCuKgbwPDhw/n888+pra3F7XazadMmysvLu1S/qA8QZrOZVatWsXHjRoqKiti5c2eki9Qt3nvvPdLT0xk7dmykixI2y5cv5/XXX+fpp5/m5ZdfZsuWLZEuUrdRVZVt27axaNEi3njjDRwOR8x2SZyMz+djw4YNXH755ZEuSrepr69n/fr1rF+/ng8++AC3282qVasiXaxuM3ToUJYuXcpNN93E0qVLGTFiBGZz+zxWoYj6ANEqJSWFc845hw8++ICMjAwqKwNpiSsrK0lPTz/Fs6PPl19+yYYNG5g2bRp33XUXmzdv5u67746LurXKzg7kn8/IyGD69OkUFRXFTf1ycnLIyclh/PjxAFx++eVs27YtburXatOmTYwZM4a+fQMJ8eKhfh9//DG5ubmkp6djtVq57LLL+Oqrr+Kibq0WLlzI66+/zssvv0xqair5+fldql9UB4iamhoaGhoA8Hg8fPzxxwwZMiSYogPgjTfe4JJLLolkMbvkF7/4BZs2bWLDhg088cQTnHvuufz2t7+Ni7oBNDc309TUFHz80UcfUVBQEDf1y8zMJCcnh717A3swfPLJJwwdOjRu6teqsLCQWbNmBY/joX79+/fnm2++we12YxhGXP7fVVcH0qMfPnyYd955h9mzZ3epflG9krqkpIR7770XTdMwDIPLL7+cO+64g9raWn72s59x5MgR+vXrx+9//3tSUzvenSoWfPrppzz77LM89dRTcVO3srIyfvKTnwCBcaTZs2dz++23x039ALZv384vf/lL/H4/eXl5PPbYY+i6Hjf1c7vdXHTRRbz77rskJwdSe8fL/9+TTz7Jm2++icViYdSoUTzyyCO4XK64qBvA4sWLqaurw2KxcN999zF58uQu/d9FdYAQQggROVHdxSSEECJyJEAIIYTokAQIIYQQHZIAIYQQokMSIIQQQnQoqrO5CnEyCxcuxOfz4ff7KS0tpaCgAIDRo0fz2GOPRbh0oSkuLqasrCyuViqL+CHTXEXMO3jwIAsWLODTTz+NdFHaUVUVi+XEn8NWrFjBxx9/zO9+97tuv7cQp0v+ukRcWrlyJf/4xz/QNI2UlBQeeughBg0axIoVK1i3bh1Op5OdO3fSr18//uM//oPHH3+csrIyxo8fz+OPP46iKNx99904HA4OHDhAeXk555xzDr/61a+wWq00Njby6KOPsmvXLrxeL+eddx733HMPJpOJRYsWMWnSJL766isSExN58skng4sEvV4v48eP56GHHqKhoYE//elPuFwu5s2bxznnnMOSJUtYvHgxH330EQD79+8PHu/fv59FixZxzTXXsHnzZq666irmzZvHE088weeff47P52PUqFE8+OCDOByOCP8PiLhgCBHjysrKjEmTJgWPN2/ebNx6662G1+s1DMMw1q9fbyxZssQwDMN45ZVXjEmTJhnl5eWGYRjGTTfdZMyfP99obGw0fD6fMXPmTGPz5s2GYRjGL37xC2PevHmGy+UyfD6fcf311xt///vfDcMwjHvuucdYs2aNYRiGoWma8dOf/tRYuXKlYRiGce211xo//vGPDVVVgz+vq6sLPr7rrruMV155JVien/3sZ8Gyl5aWGuedd16Hx6Wlpcbw4cONdevWBX/+5JNPGk899VTw+LHHHjN+//vfn94/qBAtpAUh4s6GDRvYtm0bCxcuBMAwDFwuV/DnEyZMCCYSHD16NB6Ph6SkJABGjBjBgQMHOOeccwCYOXMmiYmJQCCH/vvvv8+iRYt47733KC4u5umnnwYCucIGDhwY/B1z5swJZtDUdZ1ly5bx4Ycfous6dXV1Xd6pLDExkRkzZrSpq9vtprCwEAhkXx0zZkyX7i3E8SRAiLhjGAbf//73ueOOOzr8ud1uDz42mUztjlVVPeF9FUUBAm/6Tz31FP379+/w2tagArBq1SqKior4+9//jtPp5I9//CNHjhzp8Hlmsxld14PHXq/3hPdtLdOvf/1rzj777A7vJ8TpkGmuIu60Zq2sqKgAAskCt27d2qV7vfXWW7jdbvx+P2vWrAm2LKZNm8ayZcvQNA0IZB4uKyvr8B6NjY2kpaXhdDqpr68PftoHcDqdNDY2Bo+zsrLweDzBe61du/aUdX322WeDgaSpqYk9e/Z0qa5CHE8ChIg75557LnfccQe33norc+fOZc6cObz//vtduteECRO4/fbbmT17Nnl5ecEtRn/1q1+h6zrz5s1jzpw53HLLLVRVVXV4jyuvvJK6ujpmz57NXXfd1ebT/vnnn09jYyNz587l0UcfxWazce+993LDDTdw3XXXYbVaT1q+2267jaFDh3L11VczZ84clixZwr59+7pUVyGOJ9NchTiBu+++mwkTJrBo0aJIF0WIiJAWhBBCiA5JC0IIIUSHpAUhhBCiQxIghBBCdEgChBBCiA5JgBBCCNEhCRBCCCE69P8DNrSqc6nmqFEAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sns.set(color_codes=True)\n",
"plt.xlim(30,90)\n",
"plt.ylim(0,1)\n",
"sns.regplot(x='Temperature', y='Frequency', data=data, logistic=True)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**I think I have managed to correctly compute and plot the uncertainty of my prediction.** Although the shaded area seems very similar to [the one obtained by with R](https://app-learninglab.inria.fr/moocrr/gitlab/moocrr-session3/moocrr-reproducibility-study/tree/master/challenger.pdf), I can spot a few differences (e.g., the blue point for temperature 63 is outside)... Could this be a numerical error ? Or a difference in the statistical method ? It is not clear which one is \"right\"."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"celltoolbar": "Hide code",
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.4"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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