prednasky/09/09_linearna-a-logisticka-regresia.ipynb

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   "source": [
    "# Lineárna a logistická regresia\n",
    "\n",
    "### Róbert Móro, Jakub Ševcech\n",
    "\n",
    "IAU, 21.11.2019"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Spätnú väzbu nám môžete nechať tu: https://tinyurl.com/iau2019-w09"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Pýtať sa môžete na http://slido.com#iau2019-w09"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Opakovanie z minulej prednášky: Vyhodnocovanie a výber modelov"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Go to Slido"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Klasifikácia vs. regresia"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "### Klasifikácia\n",
    "* Predikovaná premenná je kvalitatívna = kategorická (má množinu hodnôt)\n",
    "* Napr. klasifikácia mailov spam/nie spam"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "### Regresia\n",
    "* Predikovaná premenná je kvantitatívna = číselná (reálne číslo z intervalu)\n",
    "* Napr. predikcia ceny bytov"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Overovanie modelov strojového učenia"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Trénujem na trénovacej množine -> validujem na validačnej množine"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Vyberám model (jeho nastavenie) na základe úspešnosti na validačnej vzorke"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Úspešnosť na testovacej vzorke = odhad toho, ako sa bude model správať na nových dátach"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Metriky vyhodnocovania (klasifikácie)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Správnosť (accuracy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Presnosť (precision), úplnosť (recall), F1 skóre"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "ROC (Receiver Operator Curve)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Bias a variancia"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "*Bias* je chyba spôsobená aproximáciou zložitého problému jednoduchším modelom.\n",
    "\n",
    "*Variancia* nám hovorí, ako by sa zmenilo $f'$, ak by sme použili inú trénovaciu sadu."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "fragment"
    }
   },
   "source": [
    "Varianciu a bias vieme kontrolovať množstvom dát:\n",
    "\n",
    "* pridáme trénovacie dáta\n",
    "* pridáme ďalšie atribúty (zvýši sa tak zložitosť modelu)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Lineárna a logistická regresia"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Dnes sa pozrieme na 2 algoritmy (prístupy strojového učenia)\n",
    "\n",
    "### Lineárna regresia - regresia\n",
    "\n",
    "### Logistická regresia - klasifikácia"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<img src=\"img/excited.jpg\" alt=\"Neviem sa dočkať\" style=\"margin-left: auto; margin-right: auto; width:800px\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Lineárna regresia\n",
    "\n",
    "Používame vtedy, keď chceme:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Porozumieť vzťahu medzi závislou a nezávislými premennými"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Predikovať hodnoty závislej premennej na základe hodnôt nezávislých premenných"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Jednoduchá lineárna regresia\n",
    "\n",
    "Predpokladá lineárnu závislosť medzi závislou (predikovanou) a nezávislou premennou.\n",
    "\n",
    "$$ Y = \\beta_0 + \\beta_1X $$\n",
    "\n",
    "$Y$ - závislá premenná\n",
    "\n",
    "$X$ - nezávislá premenná\n",
    "\n",
    "$\\beta_0$ - konštanta (intercept)\n",
    "\n",
    "$\\beta_1$ - sklon krivky"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Parametre určujeme pomocou metódy najmenších štvorcov\n",
    "\n",
    "Angl. *(ordinary) least squares*\n",
    "\n",
    "<img src=\"img/least-squares.png\" alt=\"Metóda najmenších štvorcov\" style=\"margin-left: auto; margin-right: auto; width:400px\"/>\n",
    "\n",
    "Zdroj: https://en.wikipedia.org/wiki/File:Least_Squares.png"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Metóda najmenších štvorcov\n",
    "\n",
    "Zostatok (residual): $e_i = y_i - \\hat{y_i} = y_i - \\hat{\\beta_0} - \\hat{\\beta_1}x_i$\n",
    "\n",
    "Residual sum of squares: $RSS = \\sum_i^n{e_i^2}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Minimalizujeme chybu (RSS):\n",
    "\n",
    "$$ \\frac{\\partial RSS}{\\partial \\hat{\\beta_0}} = 0 \\,\\,\\,\\,\\,\\,\\,\\, \\frac{\\partial RSS}{\\partial \\hat{\\beta_1}} = 0 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Riešenie pre jednoduchý lineárny model:\n",
    "\n",
    "$$ \\hat{\\beta_1} = \\frac{\\sum_{i=1}^n{(x_i-\\overline{x})(y_i-\\overline{y})}}{\\sum_{i=1}^n{(x_i-\\overline{x})}} $$\n",
    "\n",
    "$$ \\hat{\\beta_0} = \\overline{y}-\\hat{\\beta_1}\\overline{x} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Na overenie parametrov modelu využívame štatistické testovanie hypotéz"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Nulová hypotéza ($H_0$):\n",
    "* Konštanta $\\beta_0 = 0$\n",
    "* Sklon krivky $\\beta_1 = 0$, t. j. medzi X a Y nie je žiadny vzťah"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Metrikou presnosti predikcie je štandardná chyba odhadu (residual standard error, RSE)\n",
    "\n",
    "$$ RSE = \\sqrt{\\frac{1}{n-2}RSS} = \\sqrt{\\frac{1}{n-2}\\sum_{i=1}^n{(y_i-\\hat{y_i})^2}} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Meraná je v jednotkách premennej Y."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Častejšie sa však stretnete s **MSE (Mean Squared Error)**, resp. s **RMSE (Root Mean Squared Error)**. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Platí, že $RMSE = RSE$, $RMSE = \\sqrt{MSE}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Zaujíma nás tiež, aké percento variability v dátach je vysvetlené použitými nezávislými premennými\n",
    "\n",
    "$$ R^2 = \\frac{TSS - RSS}{TSS} = 1 - \\frac{RSS}{TSS} $$\n",
    "\n",
    "kde $TSS$ (total sum of squares) = $\\sum{(y_i-\\overline{y})}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$R^2$ je nezávislé od jednotiek Y. Nadobúda hodnoty z intervalu $<0,1>$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Lineárna regresia v Pythone\n",
    "\n",
    "`statsmodels`: http://www.statsmodels.org/stable/regression.html\n",
    "\n",
    "`scikit-learn`: https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ".. _boston_dataset:\n",
      "\n",
      "Boston house prices dataset\n",
      "---------------------------\n",
      "\n",
      "**Data Set Characteristics:**  \n",
      "\n",
      "    :Number of Instances: 506 \n",
      "\n",
      "    :Number of Attributes: 13 numeric/categorical predictive. Median Value (attribute 14) is usually the target.\n",
      "\n",
      "    :Attribute Information (in order):\n",
      "        - CRIM     per capita crime rate by town\n",
      "        - ZN       proportion of residential land zoned for lots over 25,000 sq.ft.\n",
      "        - INDUS    proportion of non-retail business acres per town\n",
      "        - CHAS     Charles River dummy variable (= 1 if tract bounds river; 0 otherwise)\n",
      "        - NOX      nitric oxides concentration (parts per 10 million)\n",
      "        - RM       average number of rooms per dwelling\n",
      "        - AGE      proportion of owner-occupied units built prior to 1940\n",
      "        - DIS      weighted distances to five Boston employment centres\n",
      "        - RAD      index of accessibility to radial highways\n",
      "        - TAX      full-value property-tax rate per $10,000\n",
      "        - PTRATIO  pupil-teacher ratio by town\n",
      "        - B        1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town\n",
      "        - LSTAT    % lower status of the population\n",
      "        - MEDV     Median value of owner-occupied homes in $1000's\n",
      "\n",
      "    :Missing Attribute Values: None\n",
      "\n",
      "    :Creator: Harrison, D. and Rubinfeld, D.L.\n",
      "\n",
      "This is a copy of UCI ML housing dataset.\n",
      "https://archive.ics.uci.edu/ml/machine-learning-databases/housing/\n",
      "\n",
      "\n",
      "This dataset was taken from the StatLib library which is maintained at Carnegie Mellon University.\n",
      "\n",
      "The Boston house-price data of Harrison, D. and Rubinfeld, D.L. 'Hedonic\n",
      "prices and the demand for clean air', J. Environ. Economics & Management,\n",
      "vol.5, 81-102, 1978.   Used in Belsley, Kuh & Welsch, 'Regression diagnostics\n",
      "...', Wiley, 1980.   N.B. Various transformations are used in the table on\n",
      "pages 244-261 of the latter.\n",
      "\n",
      "The Boston house-price data has been used in many machine learning papers that address regression\n",
      "problems.   \n",
      "     \n",
      ".. topic:: References\n",
      "\n",
      "   - Belsley, Kuh & Welsch, 'Regression diagnostics: Identifying Influential Data and Sources of Collinearity', Wiley, 1980. 244-261.\n",
      "   - Quinlan,R. (1993). Combining Instance-Based and Model-Based Learning. In Proceedings on the Tenth International Conference of Machine Learning, 236-243, University of Massachusetts, Amherst. Morgan Kaufmann.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Priklad prevzaty z https://towardsdatascience.com/simple-and-multiple-linear-regression-in-python-c928425168f9\n",
    "\n",
    "from sklearn import datasets\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "\n",
    "data = datasets.load_boston()\n",
    "print(data.DESCR)"
   ]
  },
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib\n",
    "import seaborn as sns\n",
    "\n",
    "df = pd.DataFrame(data.data, columns=data.feature_names)\n",
    "df['MEDV'] = data.target\n",
    "\n",
    "# MEDV (target): Median value of owner-occupied homes in $1000's\n",
    "# RM: average number of rooms per dwelling\n",
    "sns.scatterplot('RM', 'MEDV', data=df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>MEDV</td>       <th>  R-squared:         </th> <td>   0.484</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.483</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   471.8</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 20 Nov 2019</td> <th>  Prob (F-statistic):</th> <td>2.49e-74</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>16:18:10</td>     <th>  Log-Likelihood:    </th> <td> -1673.1</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   506</td>      <th>  AIC:               </th> <td>   3350.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   504</td>      <th>  BIC:               </th> <td>   3359.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>  -34.6706</td> <td>    2.650</td> <td>  -13.084</td> <td> 0.000</td> <td>  -39.877</td> <td>  -29.465</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>RM</th>    <td>    9.1021</td> <td>    0.419</td> <td>   21.722</td> <td> 0.000</td> <td>    8.279</td> <td>    9.925</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>102.585</td> <th>  Durbin-Watson:     </th> <td>   0.684</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td> 612.449</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.726</td>  <th>  Prob(JB):          </th> <td>1.02e-133</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 8.190</td>  <th>  Cond. No.          </th> <td>    58.4</td> \n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                   MEDV   R-squared:                       0.484\n",
       "Model:                            OLS   Adj. R-squared:                  0.483\n",
       "Method:                 Least Squares   F-statistic:                     471.8\n",
       "Date:                Wed, 20 Nov 2019   Prob (F-statistic):           2.49e-74\n",
       "Time:                        16:18:10   Log-Likelihood:                -1673.1\n",
       "No. Observations:                 506   AIC:                             3350.\n",
       "Df Residuals:                     504   BIC:                             3359.\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const        -34.6706      2.650    -13.084      0.000     -39.877     -29.465\n",
       "RM             9.1021      0.419     21.722      0.000       8.279       9.925\n",
       "==============================================================================\n",
       "Omnibus:                      102.585   Durbin-Watson:                   0.684\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              612.449\n",
       "Skew:                           0.726   Prob(JB):                    1.02e-133\n",
       "Kurtosis:                       8.190   Cond. No.                         58.4\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = df.MEDV\n",
    "X = df.RM\n",
    "X = sm.add_constant(X)\n",
    "\n",
    "model = sm.OLS(y, X).fit()\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Iný zápis pomocou formuly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>MEDV</td>       <th>  R-squared:         </th> <td>   0.484</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.483</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   471.8</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 20 Nov 2019</td> <th>  Prob (F-statistic):</th> <td>2.49e-74</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>16:18:10</td>     <th>  Log-Likelihood:    </th> <td> -1673.1</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   506</td>      <th>  AIC:               </th> <td>   3350.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   504</td>      <th>  BIC:               </th> <td>   3359.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>  -34.6706</td> <td>    2.650</td> <td>  -13.084</td> <td> 0.000</td> <td>  -39.877</td> <td>  -29.465</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>RM</th>        <td>    9.1021</td> <td>    0.419</td> <td>   21.722</td> <td> 0.000</td> <td>    8.279</td> <td>    9.925</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>102.585</td> <th>  Durbin-Watson:     </th> <td>   0.684</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td> 612.449</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.726</td>  <th>  Prob(JB):          </th> <td>1.02e-133</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 8.190</td>  <th>  Cond. No.          </th> <td>    58.4</td> \n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                   MEDV   R-squared:                       0.484\n",
       "Model:                            OLS   Adj. R-squared:                  0.483\n",
       "Method:                 Least Squares   F-statistic:                     471.8\n",
       "Date:                Wed, 20 Nov 2019   Prob (F-statistic):           2.49e-74\n",
       "Time:                        16:18:10   Log-Likelihood:                -1673.1\n",
       "No. Observations:                 506   AIC:                             3350.\n",
       "Df Residuals:                     504   BIC:                             3359.\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept    -34.6706      2.650    -13.084      0.000     -39.877     -29.465\n",
       "RM             9.1021      0.419     21.722      0.000       8.279       9.925\n",
       "==============================================================================\n",
       "Omnibus:                      102.585   Durbin-Watson:                   0.684\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              612.449\n",
       "Skew:                           0.726   Prob(JB):                    1.02e-133\n",
       "Kurtosis:                       8.190   Cond. No.                         58.4\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from statsmodels.formula.api import ols\n",
    "\n",
    "model = ols(\"MEDV ~ RM\", df).fit()\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Lineárna regresia v `scikit-learn`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R^2: 0.483525\n",
      "-34.67062077643857 [9.10210898]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "y = df.MEDV\n",
    "X = df[['RM']]\n",
    "\n",
    "lm = LinearRegression().fit(X, y)\n",
    "print(\"R^2: %f\" % lm.score(X, y))\n",
    "print(lm.intercept_, lm.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1ad786c2a20>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = df.plot(x=\"RM\", y=\"MEDV\", style=\"o\")\n",
    "ax.set_ylabel(\"MEDV\")\n",
    "\n",
    "rm = df[[\"RM\"]].values\n",
    "xs = range(int(np.min(rm[:,0])), int(np.max(rm[:,0])+2))\n",
    "ys = [lm.predict([[x]]) for x in xs]\n",
    "ax.plot(xs, ys, 'r', linewidth=2.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Viacnásobná lineárna regresia\n",
    "\n",
    "Zovšeobecnenie jednoduchej lineárnej regresie pre viacero premenných.\n",
    "\n",
    "$$ Y = \\beta_0 + \\beta_1X_1 + \\beta_2X_2 + \\dots + \\beta_pX_p + \\epsilon $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Pri viacnásobnej regresii nás väčšinou zaujímajú odpovede na tieto otázky"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Je aspoň jeden prediktor užitočný pri predikcii Y?\n",
    "* Štatistické testovanie"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Pomáhajú všetky prediktory vysvetliť Y alebo len ich podmnožina?\n",
    "* Výber atribútov"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Pri viacnásobnej regresii nás väčšinou zaujímajú odpovede na tieto otázky"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Ako dobre model fituje dáta?\n",
    "* RSE, $R^2$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Ak máme hodnoty premenných, akú odpoveď (predikciu) máme očakávať, a aká je jej presnosť?\n",
    "* Intervaly istoty, predikčné intervaly"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Pri viacnásobnej regresii testujeme, či je aspoň jeden koeficient nenulový\n",
    "\n",
    "$H_0: \\beta_1 = \\beta_2 = \\dots = \\beta_p = 0$\n",
    "\n",
    "$$ F = \\frac{(TSS-RSS)/p}{RSS/(n-p-1)} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>MEDV</td>       <th>  R-squared:         </th> <td>   0.639</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.637</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   444.3</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 20 Nov 2019</td> <th>  Prob (F-statistic):</th> <td>7.01e-112</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>16:18:10</td>     <th>  Log-Likelihood:    </th> <td> -1582.8</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   506</td>      <th>  AIC:               </th> <td>   3172.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   503</td>      <th>  BIC:               </th> <td>   3184.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     2</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>   -1.3583</td> <td>    3.173</td> <td>   -0.428</td> <td> 0.669</td> <td>   -7.592</td> <td>    4.875</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>RM</th>        <td>    5.0948</td> <td>    0.444</td> <td>   11.463</td> <td> 0.000</td> <td>    4.222</td> <td>    5.968</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>LSTAT</th>     <td>   -0.6424</td> <td>    0.044</td> <td>  -14.689</td> <td> 0.000</td> <td>   -0.728</td> <td>   -0.556</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>145.712</td> <th>  Durbin-Watson:     </th> <td>   0.834</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td> 457.690</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 1.343</td>  <th>  Prob(JB):          </th> <td>4.11e-100</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 6.807</td>  <th>  Cond. No.          </th> <td>    202.</td> \n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                   MEDV   R-squared:                       0.639\n",
       "Model:                            OLS   Adj. R-squared:                  0.637\n",
       "Method:                 Least Squares   F-statistic:                     444.3\n",
       "Date:                Wed, 20 Nov 2019   Prob (F-statistic):          7.01e-112\n",
       "Time:                        16:18:10   Log-Likelihood:                -1582.8\n",
       "No. Observations:                 506   AIC:                             3172.\n",
       "Df Residuals:                     503   BIC:                             3184.\n",
       "Df Model:                           2                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept     -1.3583      3.173     -0.428      0.669      -7.592       4.875\n",
       "RM             5.0948      0.444     11.463      0.000       4.222       5.968\n",
       "LSTAT         -0.6424      0.044    -14.689      0.000      -0.728      -0.556\n",
       "==============================================================================\n",
       "Omnibus:                      145.712   Durbin-Watson:                   0.834\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              457.690\n",
       "Skew:                           1.343   Prob(JB):                    4.11e-100\n",
       "Kurtosis:                       6.807   Cond. No.                         202.\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = ols(\"MEDV ~ RM + LSTAT\", df).fit()\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>MEDV</td>       <th>  R-squared:         </th> <td>   0.741</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.734</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   108.1</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 20 Nov 2019</td> <th>  Prob (F-statistic):</th> <td>6.72e-135</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>16:18:10</td>     <th>  Log-Likelihood:    </th> <td> -1498.8</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   506</td>      <th>  AIC:               </th> <td>   3026.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   492</td>      <th>  BIC:               </th> <td>   3085.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>    13</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "     <td></td>        <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>   <td>   36.4595</td> <td>    5.103</td> <td>    7.144</td> <td> 0.000</td> <td>   26.432</td> <td>   46.487</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AGE</th>     <td>    0.0007</td> <td>    0.013</td> <td>    0.052</td> <td> 0.958</td> <td>   -0.025</td> <td>    0.027</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>B</th>       <td>    0.0093</td> <td>    0.003</td> <td>    3.467</td> <td> 0.001</td> <td>    0.004</td> <td>    0.015</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>CHAS</th>    <td>    2.6867</td> <td>    0.862</td> <td>    3.118</td> <td> 0.002</td> <td>    0.994</td> <td>    4.380</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>CRIM</th>    <td>   -0.1080</td> <td>    0.033</td> <td>   -3.287</td> <td> 0.001</td> <td>   -0.173</td> <td>   -0.043</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>DIS</th>     <td>   -1.4756</td> <td>    0.199</td> <td>   -7.398</td> <td> 0.000</td> <td>   -1.867</td> <td>   -1.084</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>INDUS</th>   <td>    0.0206</td> <td>    0.061</td> <td>    0.334</td> <td> 0.738</td> <td>   -0.100</td> <td>    0.141</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>LSTAT</th>   <td>   -0.5248</td> <td>    0.051</td> <td>  -10.347</td> <td> 0.000</td> <td>   -0.624</td> <td>   -0.425</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>NOX</th>     <td>  -17.7666</td> <td>    3.820</td> <td>   -4.651</td> <td> 0.000</td> <td>  -25.272</td> <td>  -10.262</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>PTRATIO</th> <td>   -0.9527</td> <td>    0.131</td> <td>   -7.283</td> <td> 0.000</td> <td>   -1.210</td> <td>   -0.696</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>RAD</th>     <td>    0.3060</td> <td>    0.066</td> <td>    4.613</td> <td> 0.000</td> <td>    0.176</td> <td>    0.436</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>RM</th>      <td>    3.8099</td> <td>    0.418</td> <td>    9.116</td> <td> 0.000</td> <td>    2.989</td> <td>    4.631</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>TAX</th>     <td>   -0.0123</td> <td>    0.004</td> <td>   -3.280</td> <td> 0.001</td> <td>   -0.020</td> <td>   -0.005</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ZN</th>      <td>    0.0464</td> <td>    0.014</td> <td>    3.382</td> <td> 0.001</td> <td>    0.019</td> <td>    0.073</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>178.041</td> <th>  Durbin-Watson:     </th> <td>   1.078</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td> 783.126</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 1.521</td>  <th>  Prob(JB):          </th> <td>8.84e-171</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 8.281</td>  <th>  Cond. No.          </th> <td>1.51e+04</td> \n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 1.51e+04. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                   MEDV   R-squared:                       0.741\n",
       "Model:                            OLS   Adj. R-squared:                  0.734\n",
       "Method:                 Least Squares   F-statistic:                     108.1\n",
       "Date:                Wed, 20 Nov 2019   Prob (F-statistic):          6.72e-135\n",
       "Time:                        16:18:10   Log-Likelihood:                -1498.8\n",
       "No. Observations:                 506   AIC:                             3026.\n",
       "Df Residuals:                     492   BIC:                             3085.\n",
       "Df Model:                          13                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const         36.4595      5.103      7.144      0.000      26.432      46.487\n",
       "AGE            0.0007      0.013      0.052      0.958      -0.025       0.027\n",
       "B              0.0093      0.003      3.467      0.001       0.004       0.015\n",
       "CHAS           2.6867      0.862      3.118      0.002       0.994       4.380\n",
       "CRIM          -0.1080      0.033     -3.287      0.001      -0.173      -0.043\n",
       "DIS           -1.4756      0.199     -7.398      0.000      -1.867      -1.084\n",
       "INDUS          0.0206      0.061      0.334      0.738      -0.100       0.141\n",
       "LSTAT         -0.5248      0.051    -10.347      0.000      -0.624      -0.425\n",
       "NOX          -17.7666      3.820     -4.651      0.000     -25.272     -10.262\n",
       "PTRATIO       -0.9527      0.131     -7.283      0.000      -1.210      -0.696\n",
       "RAD            0.3060      0.066      4.613      0.000       0.176       0.436\n",
       "RM             3.8099      0.418      9.116      0.000       2.989       4.631\n",
       "TAX           -0.0123      0.004     -3.280      0.001      -0.020      -0.005\n",
       "ZN             0.0464      0.014      3.382      0.001       0.019       0.073\n",
       "==============================================================================\n",
       "Omnibus:                      178.041   Durbin-Watson:                   1.078\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              783.126\n",
       "Skew:                           1.521   Prob(JB):                    8.84e-171\n",
       "Kurtosis:                       8.281   Cond. No.                     1.51e+04\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 1.51e+04. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = df.MEDV\n",
    "X = df[df.columns.difference(['MEDV'])]\n",
    "X = sm.add_constant(X)\n",
    "\n",
    "model = sm.OLS(y, X).fit()\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Pozor: $R^2$ monotónne stúpa so zvyšujúcim sa počtom prediktorov (RSS zas klesá)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.48352545599133423 0.5484256373971057 0.5612257226355395\n"
     ]
    }
   ],
   "source": [
    "from sklearn import preprocessing\n",
    "\n",
    "y = df.MEDV\n",
    "X = df[['RM']]\n",
    "\n",
    "X1 = sm.add_constant(X)\n",
    "model1 = sm.OLS(y, X1).fit()\n",
    "\n",
    "X2 = sm.add_constant(preprocessing.PolynomialFeatures(2).fit_transform(X))\n",
    "model2 = sm.OLS(y, X2).fit()\n",
    "\n",
    "X3 = sm.add_constant(preprocessing.PolynomialFeatures(3).fit_transform(X))\n",
    "model3 = sm.OLS(y, X3).fit()\n",
    "\n",
    "print(model1.rsquared, model2.rsquared, model3.rsquared)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Môžeme použiť upravenú hodnotu Adjusted-$R^2$:\n",
    "\n",
    "$$ Adjusted R^2 = 1 - \\frac{RSS / (n-p-1)}{TSS / (n-1)} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Lepšie je však porovnávať rôzne lineárne modely pomocou MSE (resp. RMSE) vypočítanej nad **testovacími (alebo validačnými) dátami**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Kvalitatívne prediktory (nominálne premenné)\n",
    "\n",
    "One-hot encoding = vytvorenie $k-1$ zástupných premenných. \n",
    "\n",
    "Dostaneme pre každú hodnotu nominálnej premennej iný lineárny model (posunutý o konštantu):\n",
    "\n",
    "Keď $x_i = 0$: $ y_i = \\beta_0 + \\beta_1x_i + \\epsilon_i = \\beta_0 + \\epsilon_i$ \n",
    "\n",
    "Keď $x_i = 1$: $ y_i = \\beta_0 + \\beta_1x_i + \\epsilon_i = \\beta_0 + \\beta_1 + \\epsilon_i$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>MEDV</td>       <th>  R-squared:         </th> <td>   0.508</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.506</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   259.6</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 20 Nov 2019</td> <th>  Prob (F-statistic):</th> <td>3.51e-78</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>16:18:10</td>     <th>  Log-Likelihood:    </th> <td> -1660.8</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   506</td>      <th>  AIC:               </th> <td>   3328.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   503</td>      <th>  BIC:               </th> <td>   3340.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     2</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "          <td></td>            <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>        <td>  -31.1831</td> <td>    2.682</td> <td>  -11.629</td> <td> 0.000</td> <td>  -36.452</td> <td>  -25.915</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>CRIM_CAT[T.True]</th> <td>   -2.9062</td> <td>    0.582</td> <td>   -4.994</td> <td> 0.000</td> <td>   -4.049</td> <td>   -1.763</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>RM</th>               <td>    8.7784</td> <td>    0.415</td> <td>   21.178</td> <td> 0.000</td> <td>    7.964</td> <td>    9.593</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>160.331</td> <th>  Durbin-Watson:     </th> <td>   0.712</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td> 997.456</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 1.230</td>  <th>  Prob(JB):          </th> <td>2.54e-217</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 9.423</td>  <th>  Cond. No.          </th> <td>    60.7</td> \n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                   MEDV   R-squared:                       0.508\n",
       "Model:                            OLS   Adj. R-squared:                  0.506\n",
       "Method:                 Least Squares   F-statistic:                     259.6\n",
       "Date:                Wed, 20 Nov 2019   Prob (F-statistic):           3.51e-78\n",
       "Time:                        16:18:10   Log-Likelihood:                -1660.8\n",
       "No. Observations:                 506   AIC:                             3328.\n",
       "Df Residuals:                     503   BIC:                             3340.\n",
       "Df Model:                           2                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "====================================================================================\n",
       "                       coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------------\n",
       "Intercept          -31.1831      2.682    -11.629      0.000     -36.452     -25.915\n",
       "CRIM_CAT[T.True]    -2.9062      0.582     -4.994      0.000      -4.049      -1.763\n",
       "RM                   8.7784      0.415     21.178      0.000       7.964       9.593\n",
       "==============================================================================\n",
       "Omnibus:                      160.331   Durbin-Watson:                   0.712\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              997.456\n",
       "Skew:                           1.230   Prob(JB):                    2.54e-217\n",
       "Kurtosis:                       9.423   Cond. No.                         60.7\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['CRIM_CAT'] = df['CRIM'] > df['CRIM'].median()\n",
    "\n",
    "model = ols(\"MEDV ~ RM + CRIM_CAT\", df).fit()\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1ad787aecc0>,\n",
       " <matplotlib.lines.Line2D at 0x1ad79de7748>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = df.plot(x=\"RM\", y=\"MEDV\", style=\"o\")\n",
    "ax.set_ylabel(\"MEDV\")\n",
    "\n",
    "rm = df[[\"RM\", \"CRIM_CAT\"]].values\n",
    "xs = range(int(np.min(rm[:,0])), int(np.max(rm[:,0])+2))\n",
    "\n",
    "no_crim = pd.DataFrame(columns=['RM','CRIM_CAT'])\n",
    "no_crim.RM = xs\n",
    "no_crim.CRIM_CAT = False\n",
    "ys1 = model.predict(no_crim)\n",
    "\n",
    "crim = pd.DataFrame(columns=['RM','CRIM_CAT'])\n",
    "crim.RM = xs\n",
    "crim.CRIM_CAT = True\n",
    "ys2 = model.predict(crim)\n",
    "\n",
    "ax.plot(xs, ys1, 'r', xs, ys2, 'g', linewidth=2.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Interakcie medzi prediktormi\n",
    "\n",
    "$$ Y = \\beta_0 + \\beta_1X_1 + \\beta_2X_2 + \\beta_3X_1X_2 + \\epsilon $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>MEDV</td>       <th>  R-squared:         </th> <td>   0.527</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.524</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   186.4</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 20 Nov 2019</td> <th>  Prob (F-statistic):</th> <td>3.36e-81</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>16:18:10</td>     <th>  Log-Likelihood:    </th> <td> -1650.9</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   506</td>      <th>  AIC:               </th> <td>   3310.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   502</td>      <th>  BIC:               </th> <td>   3327.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     3</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "           <td></td>              <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>           <td>  -48.2038</td> <td>    4.617</td> <td>  -10.442</td> <td> 0.000</td> <td>  -57.274</td> <td>  -39.134</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>CRIM_CAT[T.True]</th>    <td>   21.8475</td> <td>    5.545</td> <td>    3.940</td> <td> 0.000</td> <td>   10.952</td> <td>   32.743</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>RM</th>                  <td>   11.4402</td> <td>    0.719</td> <td>   15.905</td> <td> 0.000</td> <td>   10.027</td> <td>   12.853</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>RM:CRIM_CAT[T.True]</th> <td>   -3.9141</td> <td>    0.872</td> <td>   -4.488</td> <td> 0.000</td> <td>   -5.628</td> <td>   -2.201</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>162.045</td> <th>  Durbin-Watson:     </th> <td>   0.669</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td> 938.652</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 1.270</td>  <th>  Prob(JB):          </th> <td>1.49e-204</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 9.170</td>  <th>  Cond. No.          </th> <td>    181.</td> \n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                   MEDV   R-squared:                       0.527\n",
       "Model:                            OLS   Adj. R-squared:                  0.524\n",
       "Method:                 Least Squares   F-statistic:                     186.4\n",
       "Date:                Wed, 20 Nov 2019   Prob (F-statistic):           3.36e-81\n",
       "Time:                        16:18:10   Log-Likelihood:                -1650.9\n",
       "No. Observations:                 506   AIC:                             3310.\n",
       "Df Residuals:                     502   BIC:                             3327.\n",
       "Df Model:                           3                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "=======================================================================================\n",
       "                          coef    std err          t      P>|t|      [0.025      0.975]\n",
       "---------------------------------------------------------------------------------------\n",
       "Intercept             -48.2038      4.617    -10.442      0.000     -57.274     -39.134\n",
       "CRIM_CAT[T.True]       21.8475      5.545      3.940      0.000      10.952      32.743\n",
       "RM                     11.4402      0.719     15.905      0.000      10.027      12.853\n",
       "RM:CRIM_CAT[T.True]    -3.9141      0.872     -4.488      0.000      -5.628      -2.201\n",
       "==============================================================================\n",
       "Omnibus:                      162.045   Durbin-Watson:                   0.669\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              938.652\n",
       "Skew:                           1.270   Prob(JB):                    1.49e-204\n",
       "Kurtosis:                       9.170   Cond. No.                         181.\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = ols(\"MEDV ~ RM * CRIM_CAT\", df).fit()\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1ad79e26eb8>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot('RM', 'MEDV', data=df, hue='CRIM_CAT')\n",
    "\n",
    "rm = df[[\"RM\", \"CRIM_CAT\"]].values\n",
    "xs = range(int(np.min(rm[:,0])), int(np.max(rm[:,0])+2))\n",
    "\n",
    "no_crim = pd.DataFrame(columns=['RM','CRIM_CAT'])\n",
    "no_crim.RM = xs\n",
    "no_crim.CRIM_CAT = False\n",
    "ys_false = model.predict(no_crim)\n",
    "\n",
    "crim = pd.DataFrame(columns=['RM','CRIM_CAT'])\n",
    "crim.RM = xs\n",
    "crim.CRIM_CAT = True\n",
    "ys_true = model.predict(crim)\n",
    "\n",
    "sns.lineplot(xs, ys_false)\n",
    "sns.lineplot(xs, ys_true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Čo ak závislosť medzi prediktorom a predikovanou premennou nie je lineárna?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1ad79eaf5c0>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot('LSTAT', 'MEDV', data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Lineárny model môžeme rozšíriť o polynomiálnu transformáciu, resp. o iné typy transformácií (logaritmus, odmocnina, ...)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>MEDV</td>       <th>  R-squared:         </th> <td>   0.544</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.543</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   601.6</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 20 Nov 2019</td> <th>  Prob (F-statistic):</th> <td>5.08e-88</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>16:18:11</td>     <th>  Log-Likelihood:    </th> <td> -1641.5</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   506</td>      <th>  AIC:               </th> <td>   3287.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   504</td>      <th>  BIC:               </th> <td>   3295.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>   34.5538</td> <td>    0.563</td> <td>   61.415</td> <td> 0.000</td> <td>   33.448</td> <td>   35.659</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>LSTAT</th>     <td>   -0.9500</td> <td>    0.039</td> <td>  -24.528</td> <td> 0.000</td> <td>   -1.026</td> <td>   -0.874</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>137.043</td> <th>  Durbin-Watson:     </th> <td>   0.892</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td> 291.373</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 1.453</td>  <th>  Prob(JB):          </th> <td>5.36e-64</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 5.319</td>  <th>  Cond. No.          </th> <td>    29.7</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                   MEDV   R-squared:                       0.544\n",
       "Model:                            OLS   Adj. R-squared:                  0.543\n",
       "Method:                 Least Squares   F-statistic:                     601.6\n",
       "Date:                Wed, 20 Nov 2019   Prob (F-statistic):           5.08e-88\n",
       "Time:                        16:18:11   Log-Likelihood:                -1641.5\n",
       "No. Observations:                 506   AIC:                             3287.\n",
       "Df Residuals:                     504   BIC:                             3295.\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept     34.5538      0.563     61.415      0.000      33.448      35.659\n",
       "LSTAT         -0.9500      0.039    -24.528      0.000      -1.026      -0.874\n",
       "==============================================================================\n",
       "Omnibus:                      137.043   Durbin-Watson:                   0.892\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              291.373\n",
       "Skew:                           1.453   Prob(JB):                     5.36e-64\n",
       "Kurtosis:                       5.319   Cond. No.                         29.7\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm1 = ols(\"MEDV ~ LSTAT\", df).fit()\n",
    "lm1.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>MEDV</td>       <th>  R-squared:         </th> <td>   0.665</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.664</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   1000.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 20 Nov 2019</td> <th>  Prob (F-statistic):</th> <td>9.28e-122</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>16:18:11</td>     <th>  Log-Likelihood:    </th> <td> -1563.6</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   506</td>      <th>  AIC:               </th> <td>   3131.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   504</td>      <th>  BIC:               </th> <td>   3140.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "        <td></td>           <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>     <td>   52.1248</td> <td>    0.965</td> <td>   54.004</td> <td> 0.000</td> <td>   50.228</td> <td>   54.021</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>np.log(LSTAT)</th> <td>  -12.4810</td> <td>    0.395</td> <td>  -31.627</td> <td> 0.000</td> <td>  -13.256</td> <td>  -11.706</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>126.181</td> <th>  Durbin-Watson:     </th> <td>   0.918</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td> 323.855</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 1.237</td>  <th>  Prob(JB):          </th> <td>4.74e-71</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 6.039</td>  <th>  Cond. No.          </th> <td>    11.5</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                   MEDV   R-squared:                       0.665\n",
       "Model:                            OLS   Adj. R-squared:                  0.664\n",
       "Method:                 Least Squares   F-statistic:                     1000.\n",
       "Date:                Wed, 20 Nov 2019   Prob (F-statistic):          9.28e-122\n",
       "Time:                        16:18:11   Log-Likelihood:                -1563.6\n",
       "No. Observations:                 506   AIC:                             3131.\n",
       "Df Residuals:                     504   BIC:                             3140.\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "=================================================================================\n",
       "                    coef    std err          t      P>|t|      [0.025      0.975]\n",
       "---------------------------------------------------------------------------------\n",
       "Intercept        52.1248      0.965     54.004      0.000      50.228      54.021\n",
       "np.log(LSTAT)   -12.4810      0.395    -31.627      0.000     -13.256     -11.706\n",
       "==============================================================================\n",
       "Omnibus:                      126.181   Durbin-Watson:                   0.918\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              323.855\n",
       "Skew:                           1.237   Prob(JB):                     4.74e-71\n",
       "Kurtosis:                       6.039   Cond. No.                         11.5\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm2 = ols(\"MEDV ~ np.log(LSTAT)\", df).fit()\n",
    "lm2.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1ad79f496a0>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot('LSTAT', 'MEDV', data=df)\n",
    "\n",
    "lstat = df[[\"LSTAT\"]].values\n",
    "xs = range(int(np.min(lstat[:,0])), int(np.max(lstat[:,0])+2))\n",
    "\n",
    "data = pd.DataFrame(columns=['LSTAT'])\n",
    "data.LSTAT = xs\n",
    "\n",
    "ys1 = lm1.predict(data)\n",
    "ys2 = lm2.predict(data)\n",
    "\n",
    "sns.lineplot(xs, ys1)\n",
    "sns.lineplot(xs, ys2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Diagnostika lineárneho modelu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Figure(864x288)\n"
     ]
    },
    {
     "data": {
      "image/png": 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ptLccJFiBZbEYfgwscPzp7ya9O2L3Ylw3NmMsQH/opDndD9zluFvcoqr1GD/61c62U1T1z5hg6mWOG8jHOMVGHfeFizEpqisxKblXJxlzlXPcbifWzOVk4F0xdUBWAder6maIFMa8PLYjxxXlCUwMwT+dOTVgYhMW2aBgi8VyoKBplFsgcXmEWJJdW67HWMBcd7yVUft+hbEw7cEIh/9tY/oJf9/jnGcjsAKTBXBp1PYa4CyM2+AOjEv9f2KyKSbiCqDUeX+uwZR8QFU3YgTc34EvMAkxkrZLwDdoXSYhjMkO/HeMQPsYU+piVhv9uFwJLFHVrdqyTMIjwOVi6ztaHCR+XKXFYrFYLBaLxWKxWNLFWrAsFovFYrFYLBaLpZOwAstisVgsFovFYrFYOgkrsCwWi8VisVgsFoulk7ACy2KxWCwWi8VisVg6iQMm28mQIUO0oKCgp6dhsVgslnawZs2aPao6NPmRfRt7rbJYLJa+S6rXqh4XWCJSCtRg6go0qepJTs2GZzBpNEuBS1R1X1v9FBQU8P7776c9/ooVsGABbNwIquDxwFFHwd13w/TprY+95hqoqGjdj88HhYWwfj34/ZCdDXPnwgMPNLe96SbY5tQxHzsWfvEL8/eCBVBaCgUF8cdt7zml22eidu3tz2KxWFJFRLb09By6g/ZeqyzJWbl2O4te/JwdVQ2MzM/h1rOPZtrkUT09LYvFcgCR6rWqx9O0OwLrJKdmj7vtAUzR14UiMg8YpKq3tdXPSSedpOletFasgKuvNoKors4ILBHo3x+ysuCxx5qFxIoVcPnl5tjk59Tc1y23wCmnwKxZUFtr9rv7srKMMMvMNM/BoNnujtseYeOek2r8PtNtN3s2LFmSfn8Wi8WSDiKyRlVP6ul5dDXtuVZZWhJPSAHcvmI9DcHmmrM5Pi/3T59kRZbFYuk0Ur1W9VaB9TlwuqruFJERwOuqenSiPqB9F63CQigrg/37IRRqFkZeLwwcCKNHw7p1zcd++GHb/SXisMPMOOGwGQPMOO5Yw4Y1HxsImHHvvrt9Qsk9p8zM1n2655JOu7o66Ncv/f4sFoslHazAsqTCyrXb4wqprAwPVQ3BVsePys9h9bxvdecULRbLAUyq16rekORCgZdEZI2I/NDZNlxVdwI4z8PiNRSRH4rI+yLyfkU8v70klJYa8RJq/p1GxLz2+cz+6GPby5YtLcdwx4HW291xFyww4ioz0xybmWleL1jQ9ljuOcXrsz3t/P729WexWCwWS2ez6MXPW4grgIZgKK64AthR1dAd07JYLJYW9HgMFjBFVXeIyDDgZRH5LNWGqvo48DiYu4LpDlxQYKw2Xm+z0HGtSsGg2R99bHstWPFwDYdeb8vt7rilpZCT03JfKsLGPadoi1PsuaTTLjvbPKfbn8ViiU8wGKSsrAx/Kv7GByDZ2dmMHj0aX+ydG8tBR3tiptIVTCPzc5IfZLFYLJ1MjwssVd3hPJeLyJ+BrwK7RWRElItgeVeM7brhZWcbVzjXhS8nxzzffXfLY1ONwWoL1zVQxIzr8xmXu2g3wLvvNpaq9ggl95zi9dmednPnmhisdPuzWCzxKSsrIy8vj4KCAsQ1ZR8kqCqVlZWUlZUxbty4np6OpQeJdfXbXtXA7SvWA7Qpskbm57A9jsgalOvDHwy3ch1047MsFoulO+lRF0ER6Sciee7fwFnAx8Aq4ErnsCuBv3TF+NOnm5imI44wYic724irww9vHes0fboRG4mItUTFY/BgI048HhOX9fTT8OSTJp6pocE8u+Pefbc5NhAwgiwQSE3YuOcUr8/2tHvggfb1Z7FY4uP3+xk8ePBBJ64ARITBgwcftNY7SzOJXP0Wvfh5m+1uPftocnwtL7g5Pi/3nD+R+6dPYlR+DoKJvbIJLiwWS0/R0xas4cCfnYVGBrBUVf9XRP4B/FFEvg9sBS7uqglMn566WHjpJSOSwmGorm52K/T5ID8fKivNvrb4059ajxdvfHdbe9Kjp3NOqbRrb38WiyU+B6O4cjmYz93STCJXv2QugK5gSuRaaAWVxWLpDfSowFLVTcAJcbZXAmd2/4zaprTUWJH272+OoQLjNpcsx0ZGRnOSilTFSnuEja1ZZbFYLJ2LiIwB/gc4FAgDj6vqQ+2p2dhX6ewaU4lc/VKJmZo2eZQVUhaLpVfTG7II9gqWLl0aeXb/XrHCpC/v1y9AYSEMGgQ1NS3FVSq4tbW6OvueW8uqrMy4OpaVmdcrVnTdmBaLpe8hIlxxxRWR101NTQwdOpTzzjsPgCeffJKhQ4dSWFgYeXzyySeUlpaSk5PD5MmTOeaYY/jqV7/K73//ewBKS0sZPXo04RgzfmFhIe+99173nVzX0ATcrKrHAKcAc0TkWGAe8IqqHgW84rzu06xcu53Ce1+iYN7zFMx7nskLXuKuleu5fcV6tlc1oDTHS61cuz3SZsrCVxk373mmLHw1sr0tErn62Zgpi8VyINDTLoK9huLiYmbOnElxcTEA2dkzI3WomppqKCsbTCDgugXGU1jibG/p/uLxwIABRvDU1hprV35+11iXolO7g3kOBNKzmlkslt5FV1il+/Xrx8cff0xDQwM5OTm8/PLLjBrV0iJw6aWX8sgjj7TYVlpayhFHHMHatWsB2LRpE9OnTyccDjN79mzGjBnDm2++yWmnnQbAZ599Rk1NDV/96lc7NuEexikX4pYOqRGRT4FRwL8CpzuH/R54HbitB6aYFnetXE/xu9sIqeIVYcbXxnDftEmsXLudW//0IcFw8zVuX32Qp97Z2qqP6Hip9iSrSObqZ7FYLH0ZK7ASEK8OVWpEi68wPl89dXUBQqHB1NSEychoJD8/J2Jdgs4TP+1N7W6xWHonrlVataVVGjr+u3HOOefw/PPPc9FFF1FcXMyMGTN488030+rj8MMP58EHH+Tmm29m9uzZzJgxg2XLlkUE1rJly5gxY0bHJtrLEJECYDLwLjE1G51yI/Ha/BD4IcDYsWO7ZZ7RIioaD8bH0SWkGhFQr31W0UJcJWNHVUObySqSiSXr6mexWA5UrItgAhIV3jUkugCFIw+RECIPEgptIRj0EgwC1BIKVbF790727dvNvn37uPHGfUyaNImpU6cyadIkxowZ0+45FxTgjGPw+01sWE2NcXW0roIWS9+ivQXHU+Gyyy5j2bJl+P1+PvroI772ta+12P/MM8+0cBFsaIiffODEE0/ks89M+cJLLrmElStX0tTUFOnjsssu6/hkewki0h94FrhBVatTbaeqj6vqSap60tChQ7tugg6X/+5tnnpnaytxBS3FVTTF725rV42p9iarsFgslgMZa8FKQFuFd/3+WiCH1m9fGPACYcaN+zNbtrwHnAMYVz0Ioc4FTzUENLBjxwC2bdvAxo0bCQaDqCqTJk2iqKiIkpISioqK2LhxIwC7du2iqKgIgEcffbTVnKNrWYVCJhkHGBfFrrCYWSyWrqUrrdLHH388paWlFBcXc+6557baH89FMB4atYg/9NBDmThxIq+88grDhw/H5/Nx3HHHdXyyvQAR8WHE1dOq6t6u6paajdEkSzaxcu12Vn+5N+1+Q6rk5/ioagjG3e86wbu48VKLXvy83ckqLBZLenR2shlL12EFVgKixUp0Haq5c2HRImi+3ISBJny+bILBDMAPPMygQU1s2rQYEQ9Qj0g+MIDmS1R/IINwOIjqNOD5yNgbNmygvLyciooKysvLqaqqAiAYDFJeXs6+fSZJ1bJlyxg5ciRVVVVMmDABgMsv/3cWLx5MKDQRjwfy8poXaDYey2LpWyS60ZOs4HiqXHDBBdxyyy28/vrrVFZWtquPtWvXcswxx0Reu26Cw4cPP2DcA8Xkln8C+FRVH4za5dZsXEgX1mwEs7Cav2pDCwEUL94pWR2ptqhpbGrlQgjg8wqXnjyG1z6riLuwi47BApuswmLpCtpbnNvSM1iBlYDoOlQbNmQxejScdRb88Y9gxJGLAJlkZ0MwuBORLFSvYsOGECCIBFE1QqeqSoCBLcYJhzOAZwkEwpiSXzeR7BodDAZZvnw5e/fuZd++fagq5eXmxml29iKCwefIzW2kvr6S+vpM6ushHA4RCilVVfnk5GymqWk0Eyf2t2ncLZZeTPSNHp/PiKtUCo6nylVXXcXAgQOZNGkSr7/+etrtS0tLueWWW5gbVYX9wgsv5I477iA3N5dXX321cyba80wBrgDWi8g6Z9sdGGHV5TUbYxdW0cTGO3XENS8UVgbl+lAlIuQG5fq45/yJCRdwNlmFxdI9dCTe0dL9WIHVBm4dqvPPn8Hs2X/l6qvBGI+iHSXM3254ghFUGfj9Q4HduGFuOTlQVbUfyKfZ8iU0h8F5MKVUnkV1C37/vZiyK6kwjWBwPqqHUVKyF8ggI6MMGEAg0AhkO+NmEAoJodBIoJrPPlOuvjqPG264nvPPNzETrjvi7NmzWb16NWee+aitq2Wx9BAdKTieCqNHj+b666+Pu++ZZ57hrbfeirxevHgxI0eO5Msvv2Ty5Mn4/X7y8vKYO3cus2fPjhyXn5/PKaecwu7duxk3blznTLSHUdW3iE0R20yX12yMt7CKJlpUJaovlSpV9UE2L/yXtNrYZBUWS9fTV+MdD1a3RiuwolixAkpKHqK+fhiFhS0XMm6webhVhLCJuQq1uPYFMNfiYYTDHiCE3w+Q5ewXp108BCiguvphoBpYHeeYaezd+1NgNKam5SGoBoF6GhoGA48zZMjrVFefjrG29YvqW53XTQSDdajmsW3bbJYvPxsg4o6YnZ3N3/6Wze9+V4XH46WpqYEPP/Rw0UUwadIj3HbbeJYsWcLLL7/c1ltqsVg6SHsKjiejtra21bbTTz+d008/HYBZs2Yxa9asuG0TJbuI5i9/6TJPuYOSZAuo6HinW88+OqG1CyDH5yHb52VfffxYq/xcX9ztnc3BuuiyWNpLR4pz9xS9xa2xJ35vrMAC2LyZc9fU8x+rN9PQMBiPp5Gysv6RpBDQHGzu9YKTIKsFLbf3xwgZT+TZWL7S+SfoD/wCU9OyGb//HGARTU1ZTn+uy2EdEMDjaQKEPXu+gskKvBQjrEK0DFPOAyqdzIgFcWcQDt9JONzktDEWMNUwH310JcXF11FSUsLUqVP57LPPyM/PbxEL5lrA4iXjsFgsFkvqtGWVio13SsVl766V6+PWtgJzI7Gr6S2LLoulLxHv5klvj3fsDW6NPfV7YwXW5s2wcCH9Kg7hds8d1IQ8VJPHUs9tfBkex3/duZmZ4Y2ERmzmvYpxZGZCU1N0dnvj6peTY9Khq/qAXCAI+Gh/JnwFTMr2UOgCQqEHgLFUVyfqrx/GcqZAgPr6YcBKoBHY5xwzjGbLmQfVLCete2mCPguc8xvo9OsWUj6MnTtPAV6ipKSEQCDA9u3bY2LBsnnvvfeYMmUKAKtXr464HwKMHz+ekpIS1q9fn/pbYrFYLAchiaxSieKjYkWWm/hi2uRRrFy7nWfXbE84VlVDkJVrt3fpwqM3LLoslr5GX4x37A1ujT31e3NwCyxHXJGTQ1XTUL7ueYUh4Z3sYxBjqvfzP7k/4l+/fJphw+t55JiF/Ou2eeTXb2MJVzCW7TSQRRX5ZODn5Zrzmc5ytutwfsjjvMUZJHbZTwUjpPbseY9weCjN7oVtkYdxK8wkN7ec6moQ2YLqOIzoa+mWqDrASR+fqKhOKXAcret+hfniixlttGumuLgYgPfeey/ifgjw0UcfUVFRAcDSpUu57bbbmDBhAuPHj28RB3b//fdTVFRkLWEWi+WgJd2FVVt3bJPFcwFdfne3Nyy6LJa+SF+Ld+wNbo099Xtz8AqsKHGFKmfKK+SH9+Inm37UcWLgXQqD7/HRgCL25ORw1rE5PPD69ZzEmwymCgEyqCePegC+x+8BOJpNvM632cjhDKIaP5n4CPEY13ARf2QUOwji4zp+zZ+4NOk0w+HRNLsaJhNsXicrYYCjjipmzRqAl4Cb47Q1FqlDDoHa2pVAvOKX92LKvrjHu1RTXz8MTyeVqS4uLqasrIzy8nI++uijFnFgbsr6kpISDj30UHbt2tXiefz48UD8umAWi8VyoJDOwqqtO7apLCr4Ie63AAAgAElEQVS6+u5ub1h0WSyWrqc3uDX21O9NJy2R+yB/+IPJeawKr77KoZ4ygpJFI9kIyhDdzcBwFWfk/YP+wSDs3883gy9GxBUYyRLv4cEIrWHsYSw7OJTd3MO9TORTDmE/w9nDMmbgJ4OPOJYacqimH34yaSSDfzKOUymhOY7LHS0ZQk5OJfBDRox4x9l2FhAb0K5AEyJ7KC8H1Q+oqNjI3r2vEApdEHXcSmALzRkPw8B+IExubur1NHfuPIW9e18hENhNMPhezBipsWHDBkpKSlo9L1++nOXLlwPGEjZ16lTGjBnDnDlzmDNnDpMmTWLp0qWccMJ8CgshPx8KC01CE4vFYjkQSSSitlc14JHUPCu68u7urWcfTY6vdaKnusYmVq5N7L5osVj6FtMmj+LCr4zC6/zueEU4cexAFr34OePmPc+Uha92+f98vN+b7hB5B6/AuuIKU1jmvfegogLxNjFwcAY+AmTTSMCbQ+5AHwMDezi2shKWLSOXQMpOf7GCy31E788kzHF8Rj8a6U8DmTThI8zhbOFVTqeebLYxnD3ks588aslmN4NoIIt/Z37ccQOB3KhX01A9juakG256eMUkrMh1XARHAw2EQiMIhRa3EEBe708QqQL2AhWR9kcdVZzS+7Bz5ymsX38todAIoB7VUYRC/8WePe+hupfCQpx4rrZRnUYwaNqY52mtjikuLqakpISysrKI8NqwYQMPPriZjz6aw4YN+6mtLefLL/1ccsleTjhhPgBz5swBjECzWCyWvk5bd2ZDKWax6Mq7u9Mmj+L+6ZMYFJOxsKohyO0r1luR1QdZuXY7Uxa+2m2LZkvfwI35dH93Qqqs/nIv26saUJrdl7vy++L+3ozKz0GAUfk53D99Upe7Wh68AmvcOJg3zxSWGTgQUaWf10925j4q8jwcMthLjjcIQ4YwMBAAv79DEVXpkgFkE2QkFRxCNXnUkUuAIewniyDzWUATHvx4acTLfnIpZzDv+s+ggee5/bmd/IIRFLCJZve+aLknQD9ycwECiJgaXiCEw3dF5uH1riIv7xagBpMkI5/WFrHEfPHFDFTdvnHGziMcHgXUU1YG69dfC7QWTC4mc+JjqJo25vmxlC1hJl5MaGqqIxQy6elDoTDr138XIGIBKy4uZurUqUydOpWlS5dGHq5FzN1usXQ7mzebWhGbN3dKdw8//DDHHHMMgwYNYuHChQCsXLmSTz75JHLMk08+yY4dO9Lqt7S0lOOOO65T5mhpP7eefXTqNwMFfJ6WR3fH3d1pk0eRm9k6SsF1T7T0HdyYv+5cNFv6BqnEfHbH//y0yaNYPe9bbF74L6ye961uiWM7eGOwwIisn/0M7rgD/7Zt0NhIVVYWQY/H+JI1NcHJJ/Ph/v18u7wcDaRuweosYseLdU/MdMSTDz95+BnCPhQ4hTWcwhrm8hgNZJFJECFENQPpTz2KspXDuCn8BC9wJADhcBbQD9XBlJQ8BEwhGDyHQOBITJKNeoy4ynOsUuvwele1OX8Tq9UYtSU6hT1kZkIo5AOeJhAIsHdvGar3tui3vv4W52wDzpYAkOkIwbOSvocmo2J1zNYAqoe1OrakpAQw8V8urkWsqqqKysrKFsevXr2aVatWMWHCBHbt2sXtt9/OzJkzk87JYkkZN140GDTP8+aZ364OsHjxYl544YUWhYBXrlzJeeedx7HHHgsYgXXccccxcuTIDo1l6X6mTR7FDc+sS+lYVVh0yQktEmicMWEoi178nBufWdelmco6M/jc1tXqHuK9zzYrpCURqf4vH4gJbg5ugQURkfXOu+/y3eOOI/OVV8gMheDEE+FHP4KnnyYMcPbZeN58k3BVVbeLrHSJnl8GYfJo/uIOoTmT33j+SXHduXhpojJ8CE1kks8+wmSwq3ooR7KZ+7Wan3Kf02ue82giEPAAywiHPwbmA/ELi+bmljvFj10LVgZGYJkfY78fQiFXzFQRCo1AdbHz2g9AKDQGU+crmvgCKdEcqqsH0CzQADIR2YKxyKXO9u3bI5kRwWRHLC8vp7y8nGAwGNm3ZMkSxo8fz6OPPsqcOXNYtWoV+fn5FBUVMWXKlFYibMUKY6AoLTVGVbfIdaLtloOE6GQ8I0ZAVVWHRdY111zDpk2buOCCC7jqqqv48ssvmTlzJqtWreKNN97gvvvuY8aMGbz//vtcfvnl5OTk8Pbbb/PJJ59w0003UVtby5AhQ3jyyScZMWIEa9as4aqrriI3N5dTTz21k98AS3sZlOtLWEw4Gq9IiwQa3VkzprOCzw+Uulq9XSQmep8TWSgOxEVzV9CRz723f2faquEXe9yBRoddBEXkpM6YSI8ybhz/PXEiPPQQa4YP5/3hw41lq6gI5s2jPDcXHnoI/vIXPIMHRxzuNObR1xBgAHX0o5Ex7ORwtjCIaoawl4l8ThYB5nM/VeThx0sIDwE8VDGIN/k65Qxlh57JxZwTNyYK4KijihFx64OBieECEeNmWFPjHtnkbI/nprgNyIzp2RVIhhUroKTkIQKB3cBax62weQ7mEzJ9mEyLisdzX5rvWGq4sWCu6+Hy5cspKytjw4YNLF++nOLiYubMmcPSpUuZNGkS55zzOFdfDV9+6cd1m7z6avjJT8xzWZlZX7vbbYKOg4RocZXv3AjIzzevFy5st7vgb3/7W0aOHMlrr73GoEGDAPjGN77BBRdcwKJFi1i3bh233XYbJ510Ek8//TTr1q0jIyODuXPnsnz58oiguvPOOwFTTuHhhx/m7bff7pTTtqRPvPiXVAsGx8ZktWWN6GwSBZ+fMWFoWvE83TnnrqIvuNklep+9CRKnHIiL5s6mI597X/jOJEpoE01vL5bcXjojBut3IvKFiCwQkWPTaSgiY0TkNRH5VEQ2iMj1zvb5IrJdRNY5j3M7YZ7JGTeOJyZONGLLvTs8bhzPjB9vXhcVwYoVbAWCeKghhzJGsJPhLOFK/I7DXuwjTHNqid6KxHl2HwOoJxN1UtMbUfYN/sFg9jGcSpZxNY38mQCwJxCgLBDgvtWreamykp/t/i1nj1+A17sTU4trG8YaZYRWU5M7g+i4rpbWqdzcnxMtkMxzs0Dy+8/h6qtxLGX1wGhqan4eEVkmo+IPEdkO5DqZFq9O6t7YlbhCa8OGDfz9799AFYLBOvz+BkKhevx+P7/6VROqEArVU11dRUNDFapw4437kg9g6fu4mU7zY6ys+flm+x/+0G1T+fzzz/n444+ZOnUqhYWF3HfffZSVlbF//36qqqo47bTTALjiiiu6bU4WQ6JFVlVDcusVmIDvaLqzZky84PMLvzKKZ9dsT2vReCDU1eoLIjHR+xlS7ZEsbQcCHfncU2nb08lH4v2P/79TxnZ7womeoMMugqo6WUSOBi4DlotIACgGlqnqlrZb0wTcrKofiEgesEZEXnb2/VJVf97R+XU6RUV8bdgwysu/ATyOiAdVweM5hH8LL+HHPMR93MXOrH4MbiynkWy8DGBJxo+Y1fQbRlLe610MU0Fi/nbtU/2dx+B9+2hCGFe2lwllSwnxWwZSj+AlTC4Nms0A6vkltzCAPYRp5BG+z1YKiLVOZWe/QHV1NSL3oHqYUzz5fwmH76KiogDVTPr3B4/HVWsBIIv6+ltQraak5OfAIZiU81dRVBTk+eefj5p1zxIKjcEXNZWGhgZHcB2Czwe1tQ0Eg2axNGAA7NhhDp46dSqzZ89m5syZLF26NPIMJjbM1gbr41xxhbFUVVW1FFlVVSYDajeKGVVl4sSJraxUVVVVSIppvy1dQ1tWhWQZA+Mtgru7Zozrnui6Oj31ztZWxySL5zkQ6mr1BZGY6H0eFRWL1Vtd1XorHfnck7XtLa6zfa04cmfRKVkEVfVzVb1XVY8FrsQEtrwqIquTtNupqh84f9cAnwJ95FNYidf7Y8cyk4VZY9TwG7mMQyhlsm5klPciTh42gMO8RSyfOJ8xbGIuDzkJ2YUGfHzMBOrIopYcAnhauRvGXh57sxUsGmPtUnKpZzS7OIx6BgEDCXEINYykgv7UcRcLuIol3MB/8RmnsjV8Ans4nN16Mg++/jr7VVlTXs4/+DNneE9C5BDHcnUNqhNRzQOyqatzk2UYVD00NR0DLKe6eiwQjmQfTCUtfFfj959DSclDqO5FNZPamMSMqhl4PAGCMTehg0EiNchKSkoiMV/Rz8XFxSxfvjxSC8x1RwSbij4RK1bQ++qkuZlOGxqMqALz3NDQKYkuYsnLy6Om2We3xeujjz6aioqKiMAKBoNs2LCB/Px8Bg4cyFtvvQXA008/3alzsiQnHauCzyMMyvW1unMcfZe7rrEJn7e1aK4PdLxGVaK76dFWuES0teCM54YkwBkThnZovt1JIjHYm0RiW/WEeiJL24FAup979P9Qopp2btu+YBU9kOnUJBci4sHk8h4O9MMUTkq1bQEwGXgXmAJcKyLfA97HWLla+UWJyA+BHwKMHTu2g7NPH693Ffn5JVRUvER+/glUVtY6Fq0Aqr5IljuvdxXr1kFOzhMs9s9lMXMT9nkqJfySGxhKOYPZSxV55NCIjxBegjTiI5+6PmEFEyDW87a1K6KSR72TETHECMoj+wfXBp1k8jASeLGpiSaEQOh5fAzFTyZ7GcI+BvGAzuPopk95iu9QynhgIM3FkT3AIFyHzU8++T7w7wnnHQpdQEnJf1JfP8wRMxnA/6V0zjt3nsIXX8wgEDiEvXvL+MlPYO/eV4DRqJbi9/+KnTuPoqbmajIyfBh3SQ91dTmIZJOR4Uc1AxEoKFhFdfXFhMMZqAYBHyJuTNmdSefixoABbN26lZkzZ1JcXBxJsOFavaJxBVi0NexAz4q4YoWJbVNtGesGvSChiCuyFi6E6mpjueoCcQVw2WWX8YMf/ICHH36Y5cuXM2vWLK655ppIkovly5dz3XXXsX//fpqamrjhhhuYOHEiS5YsiSS5OPvsszt9Xp2FiKynjXtUqnp8N06n0+ioVSH2LndVQxCfR8j1eagPhiPH7asPcsMz65i/agPzL5iY9gK6rbvpqaRybktoTJs8ive37OXpd7a2iJF+ds12TjrskG5d7Lc36cCtZx/dKmFEb3Ozc8+jsy1VXZ3koasSQXRGv+l87rH/Q/Es1NFt+4JVtDPorYk+OkVgicg3gRmYYkYfA8uAG1V1f4rt+wPPAjeoarWI/Ab4KeY38qfAL4CrYtup6uPA4wAnnXRSjxl3VA9r4eIFINLUIo5oxQrw+3+MOaXE8ugtijiZD9oc71RKeIqZjGIHIQQB/GTRSA47Gc4xfI7XiZnqC8S6G8b+7T57AS9KlpMVMYsg+dTRxDb+i++zkSO4k5/hJUQ5Q2jCxyHspYwRHM4WaunPj1jMnxrcr+rzkbGak2QMB7Koqwvg9TY4cV2P4/ffivF8jcc0gsH5qB7JBx9kO2npq2hqOpxFiwCOxXjDHk5Nzc/55JMmQCIujR5PPf36DaCuLoNwOIvc3HKOOqqYESPeYfbsi5k9u5KamsF4vdt47LHBLFnyTkrvq99/DvX1txAKjaGkpLKVVSZabEVvAyJizGXJkiUt3BFdDgTxtWCBEVeZTohfZiYEAmZ7jwssaBZZf/iDcQvsBHFVWloKwKxZs5g1axYAU6ZMaVEH64gjjuDCCy+MvC4sLIyUMYjmK1/5Ch9++GHk9fz58zs8vy7iPOd5jvPsBrFdjgne7JO0tUBLxTUnnrgJhpVwgitqVUOQG59Zx/tb9nLftElt9h298PHEcVl076YnW/ClIjRe+6yilXpON1V4RxdqHXHJ6irx0tl0trtXR96zVNq2t/9k34VUx072eabzuSe6EeEVIazaqu2B4DqbjN7iBhmPDgssEdkGbMWIqntVdXea7X0YcfW0qq4AiO5DRH4HPNfReXYlIlsIBlsGohsrRGnk9YIFYCwp0UV/28dbFFFAWZvH/ILrmcsjNJJJiAyyaGxVB2s/AxnCXrxuZj+a5V/bMrB34M4vgzC51HEiH0W2jXBi3RSYwCYADmE/y7icRdzKYPbQEAjA/Pn8cY/whyuf4d66NwiTwa+5jtLQ4Xg8ITyeACDU19+Cx9NaYJlEGotQNZFoquKknR8AuD9iri2vH6rQ0DAIkQqiY8D69YOGhiDf+c6MFv1Pnw5LllzPe++957zezZIlyd8bv/8camp+7oxthOLVV8Nhh6XvHulmRczOzm4lvGbOnMnUqVMBePllEz7Z1yxfpaXGchWNz2e29xrGjTM5+i3txo0JFpEpqjolatc8x519Qc/MrGN0dGHelothIhR46p2tPPfhzoTWrFTutrvjt5XKeVSK59PRu/XxFmo3PrOOG55Zl/IcOloPqjfGqnS1daAj71kqbdvTfyqL9mT9prPwT/VzT/RdDquyeeG/tNreF6yiHaU312DrDAvWqSkks4iLmOjoJ4BPVfXBqO0jVHWn8/K7GKtYr8XjuQ+RPwGZqDZhkjTQIg24WayFaBZZXStfbuYhbuahpMf9mEe4n9vZx0Ca8EXqYNWRxVjMRxBvpr1NgCVzRYzePpYdgMlpGLr3Xo5mMD+v/QF+sshnPz/iMVbzdUqDhzOBjzmZtexrGogXZc+ePfy+spINgwcDsUWQo/+d+sWM7H7u7kq+pckzOraqI7guitXVhznj1eDxmAQgqvDFFzOSddGqr/r6YYRCX7JzZ/z7HLFWjWgrGCR2RYzeH318d1NQYNwCM6MqAQSDZrvlgKSfiJyqqm8BiMg3aP0P26dItECLXRyfMWEor31W0WKxnEjcpJIko6ohmHDRmIrbHxCZR+xC0L1BliodvVsfb77u+KneFT/QXLK6wzrQlUke2tt/Kov2ZP0m6mP+qg3tFqzpfsd70iraXW57vfl/rsNJLlR1i4hcKSIfiEid83jfiZ9KxhTgCuBbMSnZHxCR9SLyEXAGcGNH59mVeL2reOwxgDLMArqMSZMeaZEG3CzWev4Dj2UxcxlIDQWUcSSbGUIVw9jDOLZzGcXsZDjbGU4AQTGObtX04/84mTqyEl4A3fT0vblGmGD+AYZRSS51DGMPWQTJJsC3eIMr+D3f4B9k0sQwKhlCkPHhMHe9/Q/ufucdrn61gn82nU0jw6nhcGrox185jwJK2xgxA4+nAdWBNDYOAoYSDudGxVa1nxUrYP36ax23Rtdqlk84PIRQyIfPB/X1w9Luy+NpRHUU69df28LNcOfOUygshEBgN8HgewkTQ0RbvOJtcxNzxOIm5+jqxBx33w0ixi1Q1TyLdK3BSFMtUnQA0gvO/fvAoyJSKsbNYDFxXND7OvHStz/1ztZW6c/PmDA0bjKMbF9qy4NEQfOpLHCiXRndVM7QUlylWtunrQQMqZBsvqkkB0glYUFPp81OZw5dmSTBnUOiX4NUhHEq73d7koeksmjPz42fhdjdnqiPqoZgu+tWtec73hPJR7qzPldvTg7TGYWGvwfcANyMyUUwCvgJcH0ykaWqb6mqqOrxqlroPP6mqleo6iRn+wVR1qwuY8aM1O/sx2P6dBA5kaFDxyNyolN7qRmziAvQXAPK/VkJ01v5E5cymp2MYSfZhPASJpMw+dTwTd4ljwbmczcBvAQQmhBqyGEP+bzKaWzgGLYymoYoIRavSHNPY5z7wq3ivzKjtrnPHiCXJk7cs4fv1L/LWHbgI0w/GumHn3N4gXc5mXIG8yET+TG/5gsKCJBBPZl8QQErwxfzFt/kVN7EWL1ymT2bVt+ZdHFjicwso8/GS1NTf2prU7eSuX15PE1OhswAqq6rqxFX69dfS1kZQD2qozq9CLJbK8wVX3PmzGmxv7PE1/Tp8NhjMHq0SdA3erR53VXxV9nZ2VRWVnZYaOzbBxs2wNq15nlfHyiPpqpUVlaSnZ3dk3NYo6onAMcDJzjXnbYDX/sYK9du5+Y/fpjUgtQQDPHaZxUt6tTk5/gIA3WB5NYnl3h31QfmtF0GI7b+zbTJo7j17KPxiiSMpWqLePV20qmvk8qCbHtVQ5vCJNkCuDcUhk00h7tWrm91bl1lHUiWNTJVYZyK4GiPKEll0Z7o59vdnuoCP1XB6lqEogs7t/Ud70kh3xuKlfcGN8jOcBH8MfBdVS2N2vaqiFyIicv6n04Yo8tx3ZPiCa2Oii8wi7W8vFuoqbnRSX5RCrzIgAEXU11tEisYYhfH6ZGZuZ9AYDY5Ob+hoWF4h+edjJ8yn58yP+H+AjZzJ/dxKm8ylAo8hAjjpYEsBlDHG5zKubzkJKhvGaHW29wQXdwCzPHwAEPZC8Bg9vErrsOLa7sKczhbKWArfrL4G+fgJcwWRvLfy+7n+xkbyAkGaWgYSll1IQ+Fb6KwEDIyTgHeSzqv0lKTXCUQyI+7v6EBCgtTy0Do9tXivKWJ0lIYM8a4GkYnhogWYGPGJO53xQpzzIYNxRQWxrcSucdUVGykpKQyYtlbvnx5i9pe8VwRo1+7/Xz6aT3HHJPL3XcnFk3Tp3dfQovRo0dTVlZGRUXKSVZbUV8PlZXmbxFzUd++HQYPhtzcTppoF5Gdnc3o0aO7fVwR+X+q+pSI3BSzHYBoN/W+jLt4Tebe57KjqqGFi+HkBS8RSpThIgFekcgCcHtVQ1L3vlH5Oaye96205p3Kor4jMUzx3BRjEZrFZDx3uWQuWb0hXiTRHKIzMLrnlp/rY19964LVHbUOtOU+KsCFX0ntc0zFBa49bnKpxC7tT1DIu6ohyLh5z5Of68PnEYIp/C8l+27Hi2eMtv4mO767Ez90d7Fy6J3JYTpDYA2IEVcAqGqpiAzohP67lXhxILHbLrroIlatWsWECRMYP348GzduBGDixIkUFRWxJEEWguzsF/D7iwkEAoC5sBcVvcXzzz+Px3MhodADwGE0W7jcuJ09GAFWyoABv6K6egJwE81xPK5DXj2TJj3KmjUrOfPMJp577qfACR16PzpKKYfxA55o4wjhxzzMQubRRAb7ySOPWsJkUMoYjuVTMgmSgbYSXO7rEIKnF2ZNNKKq9TYPkENjRKgdzWbu3fY9ar2Z5IYbCek+qthNEW/z0D/nc2r9p3xVGwni4daxz/CVshO4dewzvBAYwEvuKhvjhvrxxznEN0wrWVmpW8kKCuCTTzJaiCzVjEhcUn39MCdbYjNuYohEAis6HbrH00hZWf9I4g13XtHHuMk5Yl0TExEtuKL7CQarKSvLjZt6PbpA88yZM5kzZw6PPvpoRJyVlpr3oi1xli4+n49xHcwEWFjYOm4sEDDWt3XrOjjBAxc3ziqvR2fRxaQa++SSn+tjysJXI4uTeAvqZIRUWyzo2lpS+rwS9+5ysnkPzGk5z85eREUv1OKJxHiiMZ44akvktbXw7OqYlWgBHI9455aV4SHH5+30JAltLbQVkxEyVVIR1ekK71QW7W0lZlFMWQOfV8jP8bG/IRg3i2Z0X22RrjDvaSHfU8XKexudIbDakqS9L+ioE3j00Udb3El3Wb9+feTvKVOm4Pf7Wwiwiy66iI0bN/L2229TV1fXoq3Xu4pw+FlU/xW4B5FxqG5mwIBf4febhWMwGCQ7eyjV1b9n2LBfUl7+DeAeoACRLXg89zFihD+q13uBnq6Y6sHrrSEU6k8iu89iktcGW8yPGc1WsmkkSAY+mlrUwSqhiDk8EnH1SycbYndbylrXAoMcAmSFAgTx4SHIMCoYxH4eqpuNhxCZBAkh3L3t+2zgaI7d9jBKmBPfXQu//jWXbtzImP9XwpoPn2Uk25nIpzSSyY38ircoAjwMSy38CjCCYsYMCIddkZUZiUtassS4GppYr2aSJYaITocu0pwO/YsvZkQE1oIF0NhorG2qw2hqCuPxBCKuidDSCpabW86KFa3FT6KxYlOvu6nq3efly5dz5pmPMmuWn8zMbAKBKsrK8ntPXSyHPpH5sJehqo85z/f29Fy6knTuEvu8Qq2/KSKq2ir0m4yURV0C9dXWvH0eoS7QRFVD8zwT3ZHviFCJXqjF9pPovUnn/U7Uz8AcX5ekEo8+Lpl1Lh77G4L88tLCThd+bb2f0DsSFCRbtKdi8QyGlH5ZGay75yzGzXs+4XHJBGu6FqH2WpA6S+QfDNkLU6EzBNYxTjKKWAQ4vBP673O44ivW8hUtysaMGUN+fj4zZsygtLSUQw89lF27dlFV9T75+VdQVFTEb37zG7Kzh+L3k4CViPwFVcXnc29ln9ViP5Rjaj/HI1qGhBCpRbUBGAxkJmiTHh5PAI9HCYXCtM71lxpvUcTxSRNJCu/wdX7D1eRRS0VMHawj2YSXZrsgNMeAVTGAgVRHnDO7Q3DF698DZBKkCY9j/aqLvGMhhAwUL3WcxAeEyMBDmHDYQ+C6mzg+ZzjH//4qjqSWoezBQwjFw8t8mzJG8jpnsnz3LM5trIfNmwG4dONG83cca8r06TBp0iORLIIiXzJp0nNMn34nS5aYhBzr11+LY4wlVoDFI5Eo2L+/+fv5xRdGXBkUVQ+hUDZffAH9+7e2grnp51MdK5EAcRN2VFRs5PLLIRAI0b8/7NvnJz+/tTg74YT5iMxPyf2wKygogE2bzHsVCoHXa8738IPyFzc9ROQB4D7MDcD/xZj5b1DVp3p0Yp1EW1kBZ3xtTIssgnWNzaKluwiGtdWd9JVrtye8w+8VoX92RivLWmxK7HiWp+1VDdzwzDru/esG7jk/veLIsQvsKQtfbddd+ehFazy3sRyfF5HWArUzUom7pGvVdMnP9XWJVS2ZOOkKS0dnWwhjrVyJrLauqEn0f5nj87Doxc+58Zl1CeeVrkUokWtnosQc0Lluhb3Zba876RSB1Ql9HHRs27Yt8nei9NQlJSUUFRVFLGC7du2iqKiIVatWccEFF7B48eKk43i91xIKPYHxjomWFrWIBMjOHkJDwy48HrPPXN8q8XiGEA57nDYhIAhkk570CFNQsIqysrOcftyEHh3OrdvPexYAACAASURBVBKXP3Epf+LShPt/zK+5j7vYxigOp5QGcvg113Eab/AGp3ELi+hHPeLMtAkvPkKtLGJhml39Ohs3VitWCHpRwjRH6HloogkPGYRQYGLDDho3Z0blewQv4Ujc10ie5iz/K7xfPhHuuANEGFZfDwsXmiK248bB5s1ctWGD+YRLSrhr7xPge5YyKeQXej1ffDEj4qrnWpwqK++ksnI4oPRLkug6UTr06MQb4bArnloGEYedr06sZcoU9IabboJ9+x6ivn4YhYUwaBDU1KSWet3NmJiXB9CA3z8QyIkSei3F2YoV8NFHcxg8uG33w1jipatvL2edBT//uXkvRKCpyZzvjh2Qn9/5bo2J6EpXyi7kLFX9iYh8F5P69WLgNaDPCKy2FouJ7h7HC4YvaOOueleyvaqBu1au575pk5LGXuXFEVfR/Uxe8BK1/qaIaInXy776xOnkU6U9d+VjF62xbmMDc3yI0Ob5xeszkatfIlHWXotQrHWzs+J4pk0exftb9vLUO1tb7UvkQtoRuiomKVqEJxPg8b4/Po/QFNY24/oStW3ru5co/LKqPsjKtdu7xa2wt7rtdSedIbByVPUzABHJUtVIYIaInAK0q0aWpaXLYTSuJWzVqlXk5+dTVVXFhAkTAJOQY926dcyYMYPXXnuNYHAV8H1CoTuBo2gWOpvIy/sV48Y9yYcfZmISsLtk0r9/GdXVNyMyHyhAdTPG5XAlIuvIyCggGKzDiK6BtJYbSnb2oxx77MsMGrSRNWtuwsSRhYB6p11G5NhmCZOOgNuHxxNA1cfxxw8mI+NnzjjxM5TFd0UUfuqM/Qan8ghzGcoe/sHJ7OZQJrCBk/mAfQzERxNCmHr6M4D95NKAN8F9K1cMxSOZhSzsxJTFEm3/ixViAvjCjS32R/+dQ4DhWkZhSOCDLPD58GdkGLPHwoW8Mfpy6n7xG47Zn4GPRsq+dQUnhkLksQk/25jFMl6rPp0HL57Hd2UE/UN+ar1b2MSvmcsvuJ37WVE2g1mzYPz4U+LGet19t7E+xaZDj05Pb0RT6wuE3w+NjRvZswfy8loKp4YGN+FDARBm06aWbZOlXo8VbV6vESy1tc3HRIsz464oSd0PY3HdEDuDl14yxan9fmPB8niMCN27F4YONUK2q90ao62JOTndM2Yn4d7GPRcoVtW9bqKLvkCyxaK7qLn3rxsii+OsjPi/RqnUuuoqnnpnK0+9szXpHKoagm0mzUg1ZqyjMSjtuSsfb9Hquo3Nv2BiUhczb8z3MhVXv3hiqr21zmITNHRmHE+iOKt+mRnt6r+tmw7dEZOUTATF+/7UB5ratMy6xLZ1hfmNz6xj0Yuft/oeJkrAoZBQWPbmelJ9lc4QWEuBE52/3476G0x9kRNbtbB0CtFWsGjcRdzMmTOZOnUqUMXnny9h164fIjIOj2cbQ4cu4fzz+3HmmXDhhYqqD2OlygSUo44qZs2alfh8fyM/P5+KiopIWmnVw6KSH/idRzYwAGMZ28KJJz7Htm0PA19lxIh3GDDgR1RXL8ItyisSQHUAHo8vYp1omUMwlth96ozrAYKUlsI3v/kOXu/3CIWKSTcbo8cD7/omc3zjK865DIp7XAGbuZaHGUg1/anh6/wfI9hFAB8elFr6kU81GYQII4TRSBbB6LOIFyNmUpsIihCKahfvWNeSFr1sSna2PsKMZQvsHgj/n717D4+qvBY//l0zmSQTEgh3YgBBC6JIhYrWHmyO1lZpPSoHbRGrvfxOT6nH1lvLEbVVtFpjtVptrYfetLXeq1LUWuVUkdZTVBCUouIFUAiYcAsQyGUu6/fH3jtMJjOTmWSSmYH1eZ48yVz23mt2knln7fd91ztmDEfu2AGqbHinjVG//joRLaKJEoawnfLIHhShjWKGswuAL/AXPhl9hWaC9GcXrZESBnIPEXw8wJe5M7KMn+25lPNW1OPjUE6sXo8InLL5GL5w5Hq+ceNYFizw5k+VMHKkN6RwfzI2fjy8/76TOITD+1+13w/RaDMiA9i9G7zPHdFoMa0dam342LvXST4GDXJ6c3bsCLYfK/6Dv1NuHqLRCrZuBdUSKiqckucRt52MT86cnqy2Dvvp6/lP777bRv/+xW6vG27sTpKVSdLXE7GJKfTNMbPkSRF5G2eI4H+JyFCcN5OCkO6HxZbQ/iVAvAWBl3+wo8MQwVwlV7HSiSH2PbAnMvmwmOgDeyYWrqxLOs+orrE5rWF7EdUOPQ7pbONzKzrG/i2cPGFohyqB4BaI6sbvP/YcJjtH6SShqdaJStbLkszClXVc/vCq9jEysUNDG/eFkv7d1DU2M3be0+0JS+O+ULeGs8WXUI+oUp2komHs7WTzshKdG2/bdHrjUs1xS5ZY9nVhioNBNhKs+IvlyR4zObB48eL2K839+zsfBEOhCTQ338EppzgfhEaNuoF9++ayZ88giou3cNhh93H55eO54oqRTJgwge3bt3coKS3yAapjgNhPtlHgnxQXfxKAqqpTic3/SkufYe/evUSj30f1UPz+TYTDv6ZfvyvYsyc+6n1AhEBACYXKoH321C6g3L0du35YoL13we9fRCRyK/A9Os/5iiS4z42+w3JkyYuMbWAs3+P2pI+PYT038d+cxIs0MJQFXMhl3MqhbCKMjzoOYQNjOI4VlLO3vU5kC8XsZBD92U0xbbRShgKlNFNEhDA+/O5rFveVCEIYKEKJkF5K6QOnxndjIz5VePllQquaGBLdQauU0J8IQfbhI4qPKKW0tTdOPpQhbCdMEfsoYSjbUPZ3B1zKnUznGXcGWZSxmz9gLxW04mfM+lpu/MY8rv71WFY9sZ4/TJ/O+U/8xXk933OHJa5fzzXXjGXOHCgpgR07GlAdAggVFbB7t/M33NjoDIfz+yEU6vzmr+q8RJ/PSXqGDx/PqlX1nZ7nDQ30krVIBFSdwqd+fwuBQBmtrZ2TszFjcHt99+uqwEe2FRVtIhQ6jOJi2LWrkUikElUoKoLm5n0Eg2W9nvQVaqENVZ0nIjcDu1U1IiL7gLNyHVe60rnSnG4p7mwLBvycfWw1j62o69acn1QUp7x7T+JO9GExWZIQ/yF27h9fB93fq9NVoQ3vsWTSfR2xiXE620RUufThVcxftIb5Z04E4MFXNnZKMrqbrHrnMNEH/UzOUaokINPhe1c+/kbCFUXT6d1U6DAPMdPhg5mWUI+VTlIT//e5ry2c8H/70pjerK7muCV6D7HCFNmXjWkkmuTnRLdNDiSqqBa7aOyHH97Btm0jaW0tY8+ew3n99fmcd955bNy4kcWLF/O9732PiRMnUlJSwqBBg5g06QlKS0soKupHIFCCSCnOrzp1cS6/fxGBwPEUFw9n0KBTELmSe++FYLABb5igz7cRv/9r+P3/QTC4HaenIIqzQLPXWyZ4BSqdnjeNG/p1JaWlv8BJQ9T9vgfYCW5vTCJtbQOAEfTkusMGxjKbR6migWNYwy/4DuPYQDFhymhjHBv4HEuYzBv8mc/TRJC1HM7X+D0Pcy4P8SUWMoN1jOFvfJrNVLOPUnwoYXzsJcg2BiH4iOBHEJroxx7600Q/d8ZYZ17h/yjCzlAZazZX0rjncF5/Awa01hMVZ39BN6ETtH34Y+zATQEChOmPUwXTH/fYBN6lgkaa6ceJvMQnWM5uKgn5g3xnXy1Pzl0KtbXO/K+rroJLLmFqfT3H1tfD1Vczc8p6FiyAMwYs5W96Jg8xm1u5nMm7l3JV9A7GFa1nwACvt6YEEHy+/T1a4PwciTi9V17hismTOy+C7P1fVHTIp4Xdu8HvD3H//TB06HhWrdqfXD3+OOzaBTCIhgYnhlTDD3vLuHEPIuL0GDU3t7Sfg4oKaHYnj/V20jdmjHOMWH2daHaHiJQBFwF3u3cdAkztwf6mi8haEXlPROZlI8ZU0lkENd1S3NnkLXo69dBBlAb2f7QoC2TjYwbtPQLxw+Yysbc13GHB1e8vXM1lD6/qsOjuZQ+v4uonOn84DUU04ZC5Sx9exdh5TzPG/Ro772mueOyNrCWYXmKcaWLp9Vp+79HXM17XLBXvHCYb/pjoHH33kdc7LXibaIHY2G26WpQ2diHd5lCi9Kr7MlkUt6tFdVMt+NudhalTJY2xyeFNMycl/V9J9B7S04W6TWfZ6MEaKSJ34ny+8n7GvW2/mTzQ0yvN5513Xqe5I87k9tL2ye07dlyC6nImTKgBnLlgo0ePZtq0aQDU1dXR2NjYad8zZ8Ipp/wnTz31FMXFxe1zygBqalp4+umnqaj4Crt3X4ozx2YdIotR/RwwBr9/E2VltzJz5r0dqteFw59BZBeqrZSUlNDa2ooz/DHI/jlfIOJ3hz4Kql5/Uu93vG5gDGeyf3iAzyc8Gv1S++0xrOd87uNm5vFV7uV4ltFGMT/mSk7gHxzHq0xhJY0MYB9lvMMRjOcdytjLcBoocq/nufUh3QStiE2MIkSASCjMS/JpBkdaKGMrUS2izR+kKNKGnwhBUl/5i58tF5tkVdFAkFZaKWUgjZzMC7zMKZTQxhXr50DbCTQXFbF76WtEP9rKtujhhH0++v/9DQZcfTUzzzqLz+29CuUjprKKbQxhZvQJmujHx3d+wE3lNzJiPPxn6yls3nQSdwd+wL598GV+zx84nw3RwxFx5iM586ia2bRpQKf5Qd5iysEgNDU1Af0Jh52ka9KknzNz5tVceOH+19hxja5GYBAwgPJyuO22vh0WV1W1jKuucpJEbwjkjh37i4NkM+lLVpwjdk6d0zPe94lmN90DrAD+xb29CXgUeCrTHYmIH7gL+Jy7n1dFZJGqvpmlWDtJ50pzruZWLf9gR6feq31Z+PAbDPg5ecLQpMUw/D5JK4nwkg5P/LA5cN4z97ZllhzFX2VuDWf3A393f5PZ7kWE/ecwk317v7NEvUOXPpx44b5kPbULV9Yxf9GaXq9+6R0/1dyuVMNAvbXN0pkvmcncsa54yd3c046gf7BzgZhUvVJWmCK7RHv4JiwiX031uKr+rkcHSNPUqVN1+fLlfXGogpMPi5I+8MADHRZgHj9+PEuXLmX16tU88MADXHHFFTQ0NHRIsE499VSefvpphg4dytatWwkEAoRCoQ7fKysrAaivr+eMM87gueeeo62tDZFGoBnVaEyCBVBFUVET4XAp4KeoyEc47Ay0cyrSeUVAvGQr8aK9/fuvdRd8TmYbpaUPEghczJ49Xt1Bj9MjV1ystLX9DyL/QXn5EPbsSdQZ7Iv5OUpRkZ9otJXDZDMXRu5AURZyNifxAks4mX/nCQ5hI8exnGrq8KH4iNJMCdsYxiscR5gAgtBCCUXBYh7gy3y1+W4myT8JqZ9RbKSCRordIhrJJJsp5/ZFsolRlLhTW+qKxlCkIcr9LXxsSgXvrlpHZZsQVWe+2UZG4fcXccSgBir2NbB7nw+fhvGhFNNKBD9N9GMrw1gfmMDoUUrR+jWoFvEOE9gn/fBpiLFsYK7cxptDaohG4URdysU7ruLOQT/i71LT4W9+8mR4881dDBkygB07tjNo0GA++mg7H//4YEaNOoMnn3yS4cOHU19f3/58rzR6OBx1/3Z2c8wx/dP6PzrjDGefPbF/DbAmJk4s55pr4MILnRgTPZaNpC9V3N4x3323jXHjint0TBFZoard7knK4DjLVXWqiKxU1Snufa+rasarsovIp4D5qnqae/tKAFW9Kdk2FRUVeuyxx3Yzese2plY27mimNRyhpMjPqEFBhpSXtD++bN32FFsXhiK/j3Ak2v76vNcbTxBKi300Z5AUlRT5iUSVcDS7idDBRBC0m6lfkc+H3ycJf5+ekiI/U0ZXdrhvW1Mr67buJdoHFw+8v7v44/lEOGyoUzI3VSwlRU7PVKLXmOi1JdKT/2OfSKfYinw+xgwp6/BeYTL34osvptVW9bgHq68SKNN9+XClOVEvWPxjn/vc5zoszOytEVZTU8PSpUvZs2cPH37YuaxrIn7/RiKRKjrOEysGmhGJAs6csqFDD2HLFh9FReD372pPxIqKKgiHy/D5Wtxy9c6/is+3iSlT/kBV1TKeeupPJOvt8vv/i3D4Wvr1A5+vgWg0yv5CIEJR0YdMmvQnXnvtB1RUvMXYsfeyenWIaNSZ0SQSRTXsbrP/TTIcBghQXzGW7+65BqgEfPydE93vn8brhTuRpdzOpRTTyiucwH18jRpe4A98BZ/Aefp7niv/Ch/6x3JdZBTXtl3FZF5jFwPYQznlNDGYHQDucMQoPpQQRYTwUUZbp4nnTlPiYw8VlNCCjygNDEEVSqLNDD60DIDyViWCjzYpJaAtDGMbuyKVFG+tIyphStRHG8UUEUJQiggTpIVhNHCobqZ1XRHrGYUAJ/I3dupA9lJKQEIsOmQO5zYuoLgYbt49B6GVm3fN4Yr+C1iyoaY91to563n527/i1abpHBf6Mx/unsJ5ehcLPrqBJ9Y8yOTJ0NLy+fbnx6/R5RTB6Me77yb7K3TELow8eXL3S5nHrwG2aVO5+3/txDhzpvN1xhmze5zIpWv/Mc/us2NmQZuIeF3ZiMjhdHyjyEQ1EFttaBPwyfgnicg3gW8ClJT0/MPNkPKSlB+SSor8KT+8FgK/CFMP27+Y+XsNTQmfp2hGyRUk/tBrMkuaFE34IT4d4WiUVJ18IsKoQZ2HsW3c0dwnyZXPPX6i40VV2bijuf3nVNsn+5tN9+8v2f9xVwmqkPj34veJJVd9qMcJlogsSvW4qp7Z02OYnvE+zOX7ejWLFy/udF9sUvbAAw9w0003tS/KPGLECMaPH9/++OzZs3nuuecAKCu7lT17bgWK3SFdTnVE+Bki33Jvt7kL5UYpLfV1mE8iEqV//w+oqbmEp556imHDhtHY2EhlZSVVVccDUFraQEvLMDqmGEJpaQPR6CJCoV8T6LCuXwsibfj95QwadErMfp5h1SrnQ+qWLSe0L+7rJVvORVZvSKPzAdsZ+uZUOiwpgdbW2PLmTtrzd47jOFbg9ciJ+Fiqn8Z5+4Ub5WpGFBURaoMPfGO5pfJHfHX3zQjC85WzOXnnQ0xmBZ9Sp2c4ip8GBhGimP7sYRclDMCpUKJIeyGOdYxhLxWM5kO2MoQX5CRGVzTzmX7L6F8zCfr3Z+vLuxnBdgLagiLUM5wjeQsfYSIqhAkQIIzfXTBZUIppI0AIwj4gzAjqUYQoRRzCZmd+Wn+l/9Cx/Kr+fCL7hF2+QWxnIINp5uZdc6gdswCo4S93r6fp+7UcFd3Gl/Y8wRaG8Il9/8MO+lPb8HU+zwn8/b0z+cne93nxh0v51x/UxK3RJe659tHc7CQ/if6fkiVFkPn/X6K5lG1tsG/f9zLbUZqylRjmE3Hqsf8PzgLDo0TkfmAa8LXu7jLBfZ0+2ajqL4FfgjPaYsmSJd08XHoSlfMO+IVIRBMWA8hXS2pPb/95yvXPpV2S3WROgLJif9rDI/0i/ORLx3RYDiBbKoMBVl17aqf7x857OmvzCPsV+6ksK+5Q9jy+imCy48VXBY7301mTmTGlOunaWNWVQZbM+0yXMSb6P45d0y7Z48mGFQod/6dM96S7rEc25mB9CucK3oPAy1jlwLzkXWkuZKl6wbzH77nnHt5++23OPLMf69Y9zpIlNfh8h6H6Lkce+SjR6GOUlIRZseJ0YAwjR8Levb+gtPRiWluLcC5kF3danymRiRN/w4oV3wHK8NYX8/tbmDjxN6xe7fSihUID4rYKdFhYN15V1bL2NaT+8pcHCYc7Xm3yEijnu/P2HgoJfn8rIkG3hwugmaKi9RQVPU9b21lEo6PdtZKa3XjB72+mra2ife2pLaVjuaL5RgAGlQzmmcBEotESbphUw+yVK3m78ih+VXw3n2p4nAoa2cNA+rOTr/N7WigmRDGrmcRQtlFGE68WT2NPtIIJI57k1C98Ab68AO6/H0T4e+B4Tg79g2Fs5UNGA7CNIQwlStRdQFnaqyY6gw7VrZMYcktrlNFMG8WU0kYUH8W0UdnqZEEj9CNa1U8DIwDYLQOoULijdQ4vXz6fj37xPAFtYwLvUSwhPqWv0Kz96Mc+ijXC2TzBOXv/xFaG0HrNHF5kASI1iMDZ0Ye5iSv4HV/jX3mR+Xodc+Y4PWPx/2PJkqLulDJPNpcyEhmV2Y7SkM3EMJ+oqorIJcCpwAk47dUlqrqtm7vcBMT+AkYCm3sWZc8lWjdnV0victXeB+Vkc2FyySvXvXBlHU0t4a43MN2W6dyziCozplRzy7Nrs55gees4xc9/GhAMJJ17lWkZ/71tEQL+MLe7yVAiyar8DQgG6FdSlDR56mrR73Qr83U1RyvZ48kWoraS630rGwnWCJwJvrOB84CncRZvXJOFfRuTkUS9YI6J7td8tyfsAkaMGMHixYu56KK1nHIKXHZZlM2b+yPyAZMmLUy4WG4sZ32vd2MKcGxg8uSnqapaxurVTi+ayL1upUOvyIazxliSJcw6KCtrYO/e8vb1mGIVFdE+d0zVqaY4YgRs27abYHA7paWfinn2jYwadTHh8NWsWROlutr5sL9pk7SXIL/+emeenqelxauqKPzo/T9ytf8KPn9iC08+WcPUqX9j5cqbiUaLAeE5TuMmruRKbuZVjucSuQWRKL8ru4IRI+C86HSYNw/GjoVRo6C2lur+b7By+ycoYy9HsJYgzbzMCSwOnsVVzVcxhB0IkfZy8W0EaKKcIiKU0sJe+rGJKg5jA34iRPHRQimNJRFGrFuH3y/4y8qpaqnn3chISkqg6tAB9N+7kzE/u4z3fKdxdPQNAjRTpZuJ4KOYVkqI4HOHJILSnz3UU8aI+XM4fcgCikNb+Fl4DsW0cQ3XU89QFjCH/25dwPXX13RKPrykaFR4PXPCC/hzeA4fBsZ2q5T5mDGd51KGQk4i7yz2nT3ZTAzz0DLgMFVNvAhNZl4FxonIWKAOOBenHcy5+HVzko2sisZ8UO6N0u09cd2TzseI7z7yel6s2ZWviv1CKNLdGVHd4xfJao9SLJ8I31+4ukPBlLrGZgJ+IeCTTpUKB5YFOP3jVRkvDxBb9CRRkjX3tCOY++jrnY63ty3Mvx3T+Xjixjmt9vlOxSrSXZw6XleFJ5I9biXXcy8bc7AiOMMt/iIiJTiJ1hIRuV5Vf9bT/RuTbfE9YXfddRcAM2c6Q+4eeOB1YKz7BatWreLMM8/knXfeYfz48UybNo0HH3R6t0pLn2H37t9RXFxMKBSiqmp/93tp6TPcfTfMmrWFcHgksIGKip9SVbU9rQRr3LgHeeedq911wmKvzykVFcLOnU04c7BA1ddeOS5RAldVtYwnn+w4Pyd+rs6cORCNFqHqw6kz4sPvb6K5eTCRyC/YsuWX7ft6/fUQRUVN9Os3mEd3nsOjzMIrCHJF4IeoFjGgaADfvxHuuWc85491ziVjx8K8eexZMp0FpT9iyxa4MHoHgvL7/peyKTCWpooqbt76dYboR0SJ0EoJIQLUM5QSHwSizbQQpIVSNlHNYWygjVLqy4IEaIIRI6ChgRJ/lOojh7PhtZeZOnWaU1+9vonX9XjG6AZ8RKmiHkGJ4qeUVhSlyB2WqPgop4k2StilldyxdTbluosIfooJoQjD2E4bpfxk3xwue88ZfhhrzBjwfbCei1prieoeLmqq5acl84iOGdv1H0Cc2LmUsZUCy8puBe7NeH+pFOoaV2k6GZgjIh/grP8gOJ1bH890R6oaFpFvA8/irFrw23y7uNhVJTLvqnZXa+fkws59obzsWcsnAb8zoqGv08/eTHgjqvxhWef51qGIMrAsQFlxUcKEZeqhg9ovFKTbo5Vs4V1wkpdEQyBDEeWFt7dy08xJCY+XrFpgX8lGYmd6Lhs9WLiJ1ek4ydUY4E7g8VTbGJOv4ochphqWOHr0aBYtWsSECRP46KOPmD17NgAtLS288cYbzJwJgwadQkNDAyJCaelQ4Pi04vBKcZ9/fgPNzUMBpagIVFsoLS0DWigqakK1P5GIMnIkFBX9nKqqZWklcLG8Xomvf307u3cfit8PIk34/V7DIrz77uz255eVNdDcPJjSUvAKhlRUHEIoBOFwCWVlDSxYMICZM+lQPh+AsWN5ePx4Lvu6s6jwlbuuQyRMRWAwIjD77ho2rrmHj675DhsZzx76UeXfTlVkA+8Ejub3ZRdy7q67maIvo+pnZb9Pc3T5evo31dOmfpg2DbZtg7fewp1k5yRXLS1w113s/q/n2drUxtH6BlsYzhg2UUILAvjcYYlRN1ncSSU+ogzRBgayA0Xc5AuiBBDCjKSOukg1Pw/NgaULoKZjIY2PLqtlH0G2MoCh0TYubq5lxJx5eAl8pr+jX1+9nuN3/IZXhv4H37hxLBde+ExG+0lHst6yfF/jKk2f7/op6VPVPwN/zuY+sylZuWvoeFU79kNZvvVkmY68D/PVlUH2toZ7vWR5PmncF+LaMya2Jw/eelNeIhObRHhDDLv6e071P9KYZPjj5sbm9uMlmmuVKnHrC1ZyPfeyUeTid8DRwDPAdar6zx5HZUye85Ku8847r70HLP7xiy66CIBzzjmHRYsWUVlZSU1NDdOmTWP06NFpVUT01gl75ZVXALj77npmzw615w0iSmUlHHpoLcuXX80ZZ6Qe1tjVse655xL+8pcHGTKknJ07YxuWNvbtG9Z+a9y4B1m9+tvtcUAxJSVw771wzz2z3f2lrioXm9Tt2zesfbjizJnAzBqG//wjWlqeoLl5MFMqdzB96938pf+FvB8dS9v4UZS0noIQYcZffwUbN7LlzDNpCAYZV1wMd94JGzfCnDmMiEad5GqBk/yU7ziepstq+afv40zgNbbIIVTrh0iREApHCeBDiLKdoUQQikTor84C1VH8+IgSxSnBq/gRwgynnvCgUTB/Pjz/vPPC1q9n+qpa3vtskP9dXok2tEFlGSdOhY+tqoX17rDJTH5HwusVEAAAIABJREFUU9Yzs6aW55r+zPyarRD6DEN27oSlS53Ebv16Zr3zDqxfn/G+YyXrLSuANa66pKof5DqGvpRsHolfpNNCorHDCg+2nqOygC8ra3b1tuq43ogx87Ix0jV7vPgue3hVr/SqVZYFUq4tFcu73VUhjlRzk5L9/8RukyxBS5W4mQNfNpZYvwAYD1wC/J+I7Ha/9ojI7izs35iC5CVed911Fxs3bmT16tXcdddd7UnZ7NmzmThxIueccw7gVEGM/Upk5kxnEdyRIwHKCAa3s2ABXc4Xy0RZWUOHioqO4g7FOaqqlnWIQ6SOBQsyn58zcybU1FzC9OmzWbWq8/bjxj2ICLwfHcsP5XLej45FBL5x41h+O3Eiv5k40Ukkamr48bHHsqF///3zvWpqYMEC6vz+9uQKYPqFYxlx+zxKyotZx2FIIMAb/Q6hKFhCGCVaUsZe+uF354DtpJJtMoxmymgmiFsEFwBnFS8hMmQ4FZVFToLlue8+CIX42NRKvvUt+NjH/uh8n1rpdAfdd19mJ2v9eqithWCQbcEgbN8Oc+ZwaDjsZEMPPwy1tQzbt8953vr1me0/7veyYIGzVl40WsLIkXTr92tyb+5pRxAM+DvcFwz4+cmXjkl6hXvGlGoqg4GEjx2o3vxhVjs2E+pX7Of8E0Z3+n1kwitiMHbe00yrfb7PqoqlcxwBXpr3GWZMqe6VggrBgB/Vzgsoe71F8bz5h6mSq67mJiX7/4ndJtlrtaISB7ceJ1iq6lPVCverf8xXhar2z0aQxhyIzjvvvPaky7sd++UlWbNnz+acc85pT8Quv3wsq1bBZz/7RWpqLsn6h14vqXHmYznfveIcsaqqlrFqFRQXDycQOL5XPnx3TOSCKT/o15eV8fD48R17bmpq+OLAgR2G7YGTZJ2zfB6t49/ksMULeKe6BH71K94qKqL41JP5Z8UISnwhWiihJKC8d92DvHnZb1CEvZQhKH5C+FBah1RTPqSsQxIHwAUXOBOX3IWz2zU2OvdfcEH6JyImuaKykmHNzbBkCQQCFIOTsM2ZA9u3O8lXMJiVJGvVE+u557BjWfXEekuuCtSMKdXcNHMS1ZVBBKcgQEmRj8seXsW02udZuLIu4Xbzz5xIwH9wFAUOBnwsXFnXq8nKhtrTWXP9dG6YMYmbZk7Cn2ap53hXPr6ausZmFNq/97bqymBayULscxIlJj2N4aaZk9orDMZL1FuUbP6hX5ylSrx9dlVEIvb/J9E26SRh5uCTlTlYvUFEpgN34Ewc/rWq1uY4JGP6VOwwxNh5YN7Pixcv5oEHHgDokIyBMzfM88c//jGj43pzv7yhe2VlDUSjV1BV1dL9F9MDXoGO4cPHs2pVffZ27M4FO7+mxvk+axZnXHwx9XfcwYbp0znx+gWsuuACahb/L4e5idPLwJF3zKEtWkyQFhoopipRcuXun3nznETH09jorFY8L8PhgW5vGFVV8MEHHFdfD4MGQWkpgW3boL4eSkthyRKGlZZCpVP8hNrazI/lcZO69h6x7u7H5Fx8RcF0hlcBhKMHR+W+1nCU+YvW9GqyEltZzjvX3RmG2RtFSFKt6xSbKKQqghKfUHivcf6iNZ3miHlzyPwiRFSprgxy8oShPP3Glk69TbHrPkHyOYKJEsBkQ/SiqqzPYD2odCr5ebFZUQnjycsES0T8wF045d83Aa+KyCJVfTO3kRmTX2KTsETfPdOmTQPoMPQw2TBE2D8fy+Ms4Nx54ccDkpd4zZrFFy++mPqYxOmTt82CT8K6c8/lsGuv5d0f/YiqRMlVzL68JGtIc3P3kitwertqa50EbckSRNVJqMJhSsD5uV8/2L2bo7dvd7aprITdu53kLNPJU/HDEb0esUSxZ2nel+l9ia7ox0/GX7iyrlcWj81nUaXXC0UkqiyXKPnoa14CA/uTl9jEJz5R8JKIyrIAqs6aVV5CAU4iGZtk9Csp6vQavQIdL8UttnvDjEmd1r6KP34ma0ulM38qW6yohImXlwkWTpm191R1HYCIPAScBViCZUyGYotwJOoJi5UsAXMSLAPArFkc+ZWv0Dp/Pl+8++4OCVhCbpLVsGRJ93uBYnvDjj0WrauDvXshEGCDz8ekQMC57fPxz8GDneWVuzMUEToNRwSS94hZL1dB6WoyfnwPl8mu+GR2/pkTEyYLN82c1CdFRmITKG+oqAAjBpQm7IFJlUR8f+Fq7l/2YadS5cn+lpL9LWbSW+Qlg7FzsLqbjBmTbdkoctEbqoHYQtOb3Ps6EJFvishyEVm+devWPgvOmANV7HDE2PlgNTU1HYYhxhbiqKmpoaqqKmcxFwS3V6xHyYeXZA0ezDuVbqGMykp2+3xOAhQKwUkn0VBW1v2hiLB/OKKXVHkq44pzJOvl6sG8L9O7upqM39WaWdnmzWvJBwPLAlmdM5RMbGKRan5PdZLfVTbPV2xyFT+368rHVyednxdv4cq6DsmVJ53117pjxpTq9nlP3npciWJOZ/6UMb0lX3uwEr2HdBoerKq/BH4JMHXq1INjsLgxObB48eL2n+N7vmLngkHnoYephiKaDLlJ1tolSzju+uth/nynDL2qMw/s+ed7NhQROg5HjE2yYnvEMunlMnmjqyv6fV1W2hsiNvm653I+VO7aMyYC3ZsXlYn4xCJZj83JE4YmXGz3Xw4fxIbtze3D9JpawoSSzJUL+IV+xZ2H6Hm83rR0ho6mcsuzazOav5aNXqR0Y7aheyZX8rUHaxMwKub2SGBzjmIxxnQhfuhhpkMRLQnLgNcbNmtWxzL0s2Y5QxHLynqW4Hg9Zc3N+ysgxveIpdvLZfJKV1f0+7KsdGwPTaYF9QI+4aezJjOwLL1S8l190BlYFmj/IJ6s5ygbMkksXng78aicN7fsaf+5rLiIWcePao859jQOLAtwyznHMP/MiUmP4SXUPV3HKZPEPNH6a91ha0+ZfJevPVivAuNEZCxQB5wLdP6UZowpSF0lYOAs0OwV5/BumzhuGfr2eWBegY6e9h51VZwjnV4uk5dSXdFP1MPVHamqwkHnRKMxjYIaIk5HLUB5qfPR5dozOs9h8nptvOILqeLwYvF6ryDxOQj4JGkvkV+EqCo+tzBEssdTVZZLVNghWaKwc1+o/bXUNTbz2Iq6LhOWZMU0vIS6p8Ugkm2fSFQ1Kz1KfVnAwpjuyMseLFUNA98GngXeAh5R1TW5jcoY05e8RZm9BCy2WAd07vmyXrAs84pzJOoRS6eXyxScRD1c558wOmEPSTIbak/npXmf4YYZk1h5zalsqD2dn86anHIeTDofimNzl537Qu0V+eLjveWcY1h17amsrz2duacdwWMr6jokVwG/UBkMJI0l0Tm45YvHcP4Jozu9fm/B5vW1p/OTLx2TdEHn9e45SZZcJZr/VJlm71yyRXZjzT9zYsp1mnq6jlMma15lKwGytadMvsvXHixU9c/An3MdhzEmP8X3fKXqCTPdlKpHLFsl6E1eSdXD5fW0JOutSDa8rqt5MN3pOfMSi2SJCySepxOKKP1Kilh1bfJlJxLFO2NKNVMPHZS0hHh310JKNpeopMhHMOBP65x0NSyuq9h6uo5Tou1PnjCUx1bU9VoFP1t7yuS7vE2wjDEmU4mSrPier1jxCzRbMpahbJSgNwUj2YLF0LMPz/Glt72FaLvSVWKR7Xk66ZQQz/QDfrJYdjWHuH3W5A4JxN7WcMqhfqn0RuxdbZ8qIc0GK2Bh8pklWMaYg1b8wsxeMmYJVwayNe/LFIze6D2I/bAcPyepu4lFIczTSRVjfAKR7cS2t1kCZA5mlmAZY0ycZPO+PDVuUQlLwMzBqjc/PGcrsSiEhWYzidGGxRlTOCzBMsaYDHnrgqUafhjPinAY0z3dTSwKISHJNEbrFTKmMFiCZYwxfSBZEQ5jTNe6m1gUQkJSCDEaYzKTl2XajTHGJGe9YcYYY0z+sgTLGGMKTGxvWPw8MEu+jDHGmNyyIYLGGFPA4ueB2VBEU6jiqwfm23wpY4xJlyVYxhhjjMmp+EqBdY3NXPn4agBLsowxBceGCBpjjEnKhhyavnDLs2s7lCoHaA5FuOXZtTmKyBhjus8SLGOMMUmlM+TQkjDTU5sTLLab6n5jjMlnlmAZY4zpEZv3ZXrqkMpgRvcbY0w+swTLGGOMMTk197QjCAb8He4LBvzMPe2IHEVkjDHdJ6qa6xiyQkT2AIU6WHsIsC3XQXRDocYNhRu7xd33CjX2Qov7UFUdmusgepu1Vcn5gv0H+csHVYu/qFgj4bZI0466aPPuHVnYdaH9L3gKNW4o3Ngt7r5XaLGn1VYdSFUE16rq1FwH0R0isrwQYy/UuKFwY7e4+16hxl6ocR8ErK3qYxZ33yvU2C3uvlfIsadiQwSNMcYYY4wxJksswTLGGGOMMcaYLDmQEqxf5jqAHijU2As1bijc2C3uvleosRdq3Ae6Qv69FGrsFnffK9TYLe6+V8ixJ3XAFLkwxhhjjDHGmFw7kHqwjDHGGGOMMSanLMEyxhhjjDHGmCw5IBIsEZkuImtF5D0RmZfreNIlIhtEZLWIrBKR5bmOJxUR+a2INIjIP2PuGyQii0XkXff7wFzGmEiSuOeLSJ173leJyBdyGWMiIjJKRF4QkbdEZI2IXOLeXwjnPFnseX3eRaRURF4RkdfduK9z7x8rIi+75/xhESnOdayxUsR9r4isjznfk3Md68HO2qreZ21V3yrUtqpQ2ymwtqpQFPwcLBHxA+8AnwM2Aa8Cs1X1zZwGlgYR2QBMVdW8X2BNRGqAJuD3qnq0e9+PgR2qWut+WBioqlfkMs54SeKeDzSp6q25jC0VEakCqlT1NRGpAFYAM4Cvkf/nPFnsXyKPz7uICNBPVZtEJAD8HbgEuBx4XFUfEpH/AV5X1btzGWusFHF/C3hKVf+Y0wANYG1VX7G2qm8ValtVqO0UWFtVKA6EHqzjgfdUdZ2qtgEPAWflOKYDjqouBXbE3X0W8Dv359/hvDnllSRx5z1V3aKqr7k/7wHeAqopjHOeLPa8po4m92bA/VLgM4D3xp935zxF3Ca/WFvVB6yt6luF2lYVajsF1lYVigMhwaoGNsbc3kSB/JPg/GE9JyIrROSbuQ6mG4ar6hZw3qyAYTmOJxPfFpE33GEZeTV0IZ6IjAGmAC9TYOc8LnbI8/MuIn4RWQU0AIuB94FGVQ27T8nL95f4uFXVO983uuf7dhEpyWGIxtqqXCqo9804ef2eGatQ26pCa6fA2qpCcCAkWJLgvkLJiKep6ieAzwMXuUMETO+7GzgcmAxsAX6S23CSE5Fy4DHgUlXdnet4MpEg9rw/76oaUdXJwEicHocjEz2tb6PqWnzcInI0cCUwATgOGATkzfCcg5S1VSZTef+e6SnUtqoQ2ymwtqoQHAgJ1iZgVMztkcDmHMWSEVXd7H5vAJ7A+ScpJPXuOGZvPHNDjuNJi6rWu//kUeBX5Ol5d8coPwbcr6qPu3cXxDlPFHuhnHcAVW0ElgAnAJUiUuQ+lNfvLzFxT3eHwKiqtgL3kMfn+yBhbVXuFMT7ZrxCec8s1Laq0NspsLYqnx0ICdarwDi3ekoxcC6wKMcxdUlE+rkTKxGRfsCpwD9Tb5V3FgFfdX/+KvCnHMaSNu9N3/Xv5OF5dyeD/gZ4S1Vvi3ko7895stjz/byLyFARqXR/DgKfxRmX/wJwjvu0vDvnSeJ+O+bDjeCMxc+r830QsrYqd/L+fTORfH/PhMJtqwq1nQJrqwpFwVcRBBCnjOZPAT/wW1W9McchdUlEDsO5EghQBDyQz3GLyIPAScAQoB64FlgIPAKMBj4EvqiqeTVJN0ncJ+F0/yuwAZjjjRXPFyJyIvA3YDUQde++CmeMeL6f82SxzyaPz7uIfBxnYrAf5+LTI6p6vfu/+hDO0IWVwPnulba8kCLu54GhOEPTVgHfiplgbHLA2qreZ21V3yrUtqpQ2ymwtqpQHBAJljHGGGOMMcbkgwNhiKAxxhhjjDHG5AVLsIwxxhhjjDEmSyzBMsYYY4wxxpgssQTLGGOMMcYYY7LEEixjjDHGGGOMyRJLsIzpQyLSqfSoiBwhIktEZJWIvCUivxSR09zbq0SkSUTWuj//Pma7O0SkTkR87u2vx2zTJiKr3Z9r+/I1GmOMKWzWVhnTM1am3Zg+JCJNqloed9+zwC9U9U/u7Umqujrm8SXA91R1ecx9Ppw1OjYD81R1Sdw+NwBTVXVb77wSY4wxByprq4zpGevBMib3qoBN3o3YBiuFk3FWO78bZ2FEY4wxpjdZW2VMmizBMib3bgeeF5FnROQyEalMY5vZwIPAE8C/iUigVyM0xhhzsLO2ypg0WYJlTI6p6j3AkcCjwEnAMhEpSfZ8ESkGvgAsVNXdwMvAqX0QqjHGmIOUtVXGpM8SLGPygKpuVtXfqupZQBg4OsXTpwMDgNXu+PUTsaEXxhhjepm1VcakxxIsY3JMRKZ7wyZEZAQwGKhLscls4BuqOkZVxwBjgVNFpKzXgzXGGHNQsrbKmPQV5ToAYw4yZSKyKeb2bcBI4A4RaXHvm6uqHyXa2G2YTgPmePep6l4R+TtwBvBw74RtjDHmIGJtlTE9YGXajTHGGGOMMSZLbIigMcYYY4wxxmSJJVjGGGOMMcYYkyWWYBljjDHGGGNMlliCZYwxxhhjjDFZYgmWMcYYY4wxxmSJJVjGGGOMMcYYkyWWYBljjDlgicjqXMdgjDHm4GILDRtjjCloIjIz2UPAiL6MxRhjjLEEyxhjTKF7GLgf0ASPlfZxLMYYYw5yopqoPTLGGGMKg4isAL6qqv9M8NhGVR2Vg7CMMcYcpGwOljHGmEJ3KbA7yWP/3peBGGOMMZZgmYOeiFwlIr9O87n3isgNvR1TXxGRT4vI2hwcd76I/KGvj2sOTKr6N1X9MMljy72fReTKvovKGJMJEVkiIt/IdRzGZIMlWCbvicgGEWkWkSYRqReRe0SkvJv7OklENsXep6o/UtWD8k3d/WB6RK7jSMX9/X8213GYA8IXcx2AMX1NRM4TkeVuG7pFRJ4RkRNjHh8vIo+KyDYR2SUib4jI5SLiF5ExIqLutk3u+/G8mG1VRPa6j9WJyG0i4k8RS4/b85iYrI6AyVuWYJlCcYaqlgOfAI4Dvp/pDvr6zTjbx7PGxJgek1wHYExfEpHLgZ8CPwKGA6OBXwBnuY8fDrwMbAQmqeoAnAsRU4GKmF1Vum3wbOAaEZke89gx7mP/CswC/l8XYfW4PTcm31mCZQqKqtYBzwBHA4jI10XkLRHZIyLrRGSO91yvt0pErhCRj4AH3W0Pibkad0j8cDX3St5H7pW8pSIyMZ3YRORrIvKSiNwuIjuA+e79/8+NcaeIPCsih8Zsc6qIrHWP9QsRedEbIpHp/sRxu4g0xFyF9M7TF0TkTfc81YnI92LPUUw8R7rDNBpFZI2InBnz2L0icpeIPO3u52W3cU50LrwrjN8Ukc3uVdPvpjh3Z7rHa3SPf6R7/304HwiedH9f/53O78KYJKyqkzloiMgA4HrgIlV9XFX3qmpIVZ9U1bnu064D/k9VL1fVLQCqulZVz1PVxvh9quo/gDW4bXDcY+8BLwGT04kvvj2Pi90nIt8XkQ/cNu337usBWOp+b3TbhU+lczxj+pIlWKagiMgo4AvASveuBuDfgP7A14HbReQTMZuMAAYBhwJfAT4PbFbVcvdrc4LDPAOMA4YBr+GUf07XJ4F17rY3isgM4CpgJjAU+BtOooeIDAH+CFwJDAbWAv/S3f0BpwI1wHigEudK4nb3sd8Ac1S1Aqcxez4+cBEJAE8Cz7nH+w5wv4jEDiGcjdMgDwTeA27s4nycjHMuTwXmSYKhfiIy3n0Nl7qv6c84CVWxql4AfIh7xVNVf9zF8YxJxXqwzMHkUzjLFDyR4jmfxWmHuuRexJsGTGR/Gxz7+ATg0zhtQzr7i2/PY33N/ToZOAwoB37uPlbjfq9024V/pHM8Y/qSJVimUCwUkUbg78CLOMMdUNWnVfV9dbyIkxx8Oma7KHCtqraqanM6B1LV36rqHlVtxek1OibmyllXNqvqz1Q17B5vDnCTqr6lqmE37slur9MXgDXulcUwcCfwUQ/2F8IZ0jEBZwmGt7wrku5jR4lIf1XdqaqvJYj9BJxGrFZV21T1eeApnKTK87iqvuIe+366vlJ5nXvVdDVwT9y+PLOAp1V1saqGgFuBIJ2TTWN66tFcB2BMHxoMbHPfr1M9Z0uKxz3bgB3Ar4F5qvrXmMdeE5G9wFvAEpwhiKkkbM/jfBm4TVXXqWoTzoXIc22ovCkUlmCZQjFDVStV9VBV/S8vWRKRz4vIMhHZ4b5hfwEYErPdVlVtSfcg4kzqrRWR90VkN7DBfWhIis1ibYy7fShwhzv0rRGngRKgGjgk9vnqLEq3KW77tPfnJkQ/B+4C6kXklyLS393ubJxz84E7DDHRkIpDgI2qGo257wM3Vk9sArgPJyFLJTb+D9xjJDruB94N9/gb445rTJdEpFRELnKH2/7W+/IeV9VEH+SMOVBtB4Z0kZRsB6rS2NcQVR2oqkeq6p1xj30Cpy2YhTPqol8X+0rYnsfp0C64PxfhzCMzJu9ZgmUKloiUAI/h9HgMV9VKnOFlscOA4udcdDUH4zycyb+fBQYAY7zDpRlW/P434gzNq4z5Cqrq/+FcNRwZ83ok9nY39oeq3qmqx+IM4RgPzHXvf1VVz8IZ+rcQeCRB7JuBUSIS+74wGqhL87UnErvA62j3GImOGzsvTdztvOPavBmTrvtwhgWfhnNlfCSwJ6cRGZM7/wBagBkpnvO/OBfgesQdRfKIe8xrero/4toFnPYjDNRjbYIpAJZgmUJWDJQAW4GwiHweZ65PKvXA4BRD/iqAVpyremUkHrqQif8BrhS3UIaIDBARr1T008AkEZnhXmG8COfDYbf2JyLHicgn3blUe3Ea1oiIFIvIl0VkgDsEbzcQSbDvl93t/ltEAiJyEnAG8FD3Xz4/EJEyN96vAw8neM4jwOkicoob+3dxfgf/5z5ejzMG35iufExVfwDsVdXfAacDk3IckzE5oaq7cJKdu9x2psx9b/+8iHjzWa8F/kVEbhGREQAi8jER+YOIVHbjsLXAN7199cCDwGUiMlacMu4/Ah52hztuxRn+b+2CyVuWYJmCpap7gItxPqDvxOl9WtTFNm/jvHGvc4fZxQ9Z+z3OUIQ64E1gWQ9jfAK4GXjIHXL4T5xCG6jqNpxyuD/GSeiOApbjJBcZ7w+n0MevcM7FB+4+b3UfuwDY4G7zLeD8BPtuA85097cNZxz9V9xz1l0v4kx4/itwq6o+l+C4a914fuYe9wycohZt7lNuAr7v/r6+14NYzIEv5H5vFKeCZmwvtDEHHVW9DbgcpxT6VpxREN/GGcmAqr6PUwxjDLBGRHbhjAxZTjd6f935ti/ijp7ogd/i9EgvBdbjXDD8jnuMfTgFll5y24UTengsY7JOnGkfxphcc4fmbQK+rKov5DqenhCRMTiNYqCLCdbGZI04Sxw8htNrdS/OvJAfqOqCXMZljDHm4GLVWIzJIRE5DWdoXjPOFT+hh71mxhzE/qqqO3Gueh8GICJjcxuSMcaYg40NETQmtz4FvM/+oXEz0i0nb4zp5LEE96W1xo8xxhiTLTZE0BhjTEFzFzidiDOfMXbuR39grqpOzElgxhhjDko2RNAYY0yhOwL4N6ASpyfYswf4z5xEZIwx5qB1wPRgDRkyRMeMGZPrMIwxxnTDihUrtqnq0J7sQ0Q+par/yFZMvcHaKmOMKVzptlUHTA/WmDFjWL58ecbbLVxZxy3PrqWusRm/CBFVqiuDzD3tCGZMqe703Ksef4N9oWin/YjAx4b2Y93WfURU8Ysw+5OjuGHGpPZt5y9aQ2OzU0V4YFmAa89wRq3c8uxaNjc2c0iS43b3NWW6z2TbdXd/xhiTLhH5IAu72S4if8VZePxoEfk4cKaq3pCFfWdFrtuqYMDHJ0ZXsmzdTmurjDEmQ+m2VQdMD9bUqVM100Zr4co6rnx8Nc2hzmuuBgN+bpo5qf3NeeHKOi5/ZBXRDE/X+SeMZuqhg5j76OuE4jb2Cfh9Qiiy//7442Yq0WtKZ5/Jtjv72GoeW1GX8f6MMSYTIrJCVaf2cB/e+jsLVHWKe98/VfXobMSYDdZW0R6ntVXGmEKTblt1UFcRvOXZtQkbLIDmUIRbnl3b4bmZNlgAD768kVueXdupwQKIKh0arPjjLlxZx7Ta5xk772mm1T7PwpV1XR4v0WuKfy2ZbPfgyxu7tT9jjMmBMlV9Je6+gl+HzdqqrreztsoYk08OmCGC3bG5MXU17NjHu3puMhFV6jLcdnNjc6erdHWNzVz5+GqAlFfjksWZyWuNFUnSw9nd82GMMb1om4gcDiiAiJwDbMltSD1nbVXXj1tbZYzJJwd1D9YhlcG0H+/qudl0SGWw21f3ksWZyWuN5Rfp1v6MMSYHLgIWABNEpA64FPhWbkPqOWurun7c2ipjTD45qBOsuacdQTDgT/hYMOBn7mlHdHiuL/H7d7f5BAL+jjv1jtvdq3uJXlP8a8lku9mfHNWt/RljTF9T1XWq+llgKDBBVU9U1WwUz8gpa6u63s7aKmNMPjmoE6wZU6q5aeYkqt0rXN4VsOrKYKeJsTOmVHPblyZTFkh8ypJcPOugMhho/3lgWYDbvjSZW845hurKIBJ33O5e3Yt9TfH77M52N8yY1K39GWNMXxORwSJyJ/A3YImI3CEig3MdV09ls60KJrk/lrVVxhjTMwd1FcHuSFUGdlrt80nHsPtFeP+mL2R0nO5UWDLGmEKUpSqCi4GlwB/cu74MnOT2auUFa6uMMaZwWRXBXuA1JHWNzSj7J/N6FZNOnpB83bGIalqVlTzdvbpnjDEHsUF20EiXAAAgAElEQVSq+kNVXe9+3QBU5jqovmZtlTHG5NZBXUUwU11N5n1sRepGKZ3KSrFmTKm2RsoYY9L3goicCzzi3j4HeDqH8eSEtVXGGJNb1oOVgWSTdusam7nuyTVJ1ynx2JocxhiTfSKyR0R2A3OAB4BW9+sh4LJcxpYLqdqq7z7yurVVxhjTyzLqwRKRfkCLqqZ+dz5AHVIZTDpufee+UFr76O01OVKNuzfGmAORqlbkOoZ8kqqtSrZeVDxrq4wxpvtS9mCJiE9EzhORp0WkAXgb2CIia0TkFhEZ15ODi8goEXlBRN5y93mJe/8gEVksIu+63wf25DjZMve0I+hp9dveXJOjq3H3xhhzoIppP76T61hyzdoqY4zJra6GCL4AHA5cCYxQ1VGqOgz4NLAMqBWR83tw/DDwXVU9EjgBuEhEjgLmAX9V1XHAX93bfW7hyjqm1T7P2HlPM632eQB6UnOxt9fk6O6Cj8YYcwBoEpG5wN5cB9LXrK0yxpj80lWC9Vm3ItMbqhr17lTVHar6mKqeDTzc3YOr6hZVfc39eQ/wFlANnAX8zn3a74AZ3T1GdyW7wtavOPFij4kEA74OlZXOPraaW55d294IZvtqXXcXfDTGmEImItcCRwA/BI4QkWtyHFKfyUZbdf4Jo62tMsaYLOpqDtZk4NVED4jIBap6n6qmN/moCyIyBpgCvAwMV9Ut4CRhIjIsyTbfBL4JMHr06GyE0S7ZFbZMhl3cNPPj7WPK49cK8RpBSL9SU1eSjbvvzaEexhiTa6p6nYjcAHwOOE1Vr891TH0lG23VDTMmtf9sbZUxxvRcVz1YvxGRu0WkfR0RETlaRJYCZ2crCBEpBx4DLlXV3elup6q/VNWpqjp16NDk63p0R7IraekOuxhYFujQGPXFkIi5px1BMNDxqmVvD/UwxphcE5FDgaWq+jdgSY7D6VM9bauq45Iaa6uMMabnukqwPgF8CKwUkf8nIrfjJEI/VtWsDNsTkYC7z/tV9XH37noRqXIfrwIasnGsTCS7kuaXrq8LBgN+rj1jYof7+mJIRPyCjwPLApQU+bjs4VW9MszDGGPyxBOq+hyAqv5vroPpSz1tq+KTmr5uq8CJ1UvirJ0yxhwIUiZYqhpW1ZuAXwC/Br4InKyqT2Xj4CIiwG+At1T1tpiHFgFfdX/+KvCnbBwvE8musM3+5KhO9wd8wsCyQKdV7GMnHvuSNHbZHhIxY0o1L837DLfPmkxLKEpjc8iqNBljDnQ9LZpXsAq5rfJi90rHWztljDlQpJyDJSKH4yRXEeBI4PPAUhG5UVXvycLxpwEXAKtFZJV731VALfCIiPwHTg/aF7NwrIx4w/sSrdMx9dBBXa7fET+OPdHaI705JCLVMA9ba8QYc4CpFpE7kz2oqhf3ZTB9qZDbKmunjDEHqq6KXDwLzFPVP7q314rII8BtIvINVZ3Wk4Or6t9JfuXxlJ7sOxtmTKnu9pt8ooYDnKEQEdUOQyK8Y2WTVWkyxhxEmoEVuQ4iVwq1rbJ2yhhzoBJNsaq7iJSralOSxz6bT2Pdp06dqsuXL+/148Rf7QNn2EV5aRGN+0LtVwkve3hV0knGwYA/YYM2sCzAtWdMzEoDNq32+YRVmqorg7w07zM93r8xxmSTiKxQ1and3PY1Vf1EtmPqDdZW7WftlDGm0KTbVqVMsApJXzRaC1fW8d1HXk84hCJWMOCnpMhHY3PnCvbeVcFUKoMB5p/Zs8YrUeMaDPg5+9hqXnh7a8ohI/H76WqIiTHG9FQPE6xlqnpCtmPqDdZWdYwzG+2Uty9rq4wxvS3dtqqrIYLG5TUEXTU44IwhLw34Ol39S3Y1MF5jcyijdUdSNSy3PLuWusbm9mEe9y/7sP1qZVfrm/TFeijGGNNTiZIrdw7xbOBcVT2676PKjUJrq26aOalH7ZS3X2urjDH5pKsy7QeV2EpK8WXNk41TT6ZxX6hDyfTqyiCfGD0g7e1TrTsSG+fk655j7h9fp66xuVO1wERVmuKb3FTH6Yv1UIwxJltEpEpELhWRV4A1gB8nyTqgHEhtFdCjdgqsrTLG5B/rwXJ1dQUs00m3lWWBDlfqxgwO8tL7OzLaR6Kx6fFxJhraEVuFKZ3GNtOJxjYB2RiTT0TkP3ESqZHAI8A3gD+p6nV9cOzpwB04ydyvVbW2N493ILZV3s+ppHpd1lYZY/JNV2XaXyC9BeHvVdXfZyek3OiqXOwhlcGEjYgARX4hFNl/mgJ+oaklzM59ToNS19iccNuuJFooMt2rk17Dkk4Dk2x9k2SveUAw0OU+jTGmD90F/AM4T1WXA4hIr08wFhG/e+zPAZuAV0Vkkaq+2VvHPFDbqq6kWofL2ipjTL7pqgfra2nup7GHcfTYO++8w8UXX8xRRx3FUUcdxcSJExk8eHDa23d1BWzuaUd0mowrwJdPGN1prZG9reGEV+sy5Q2XWLiyjuueXNPeCKbDa4ySNTyeVOubzD3tCOY++jqhaMfPKXvbwu1DEI0xJg8cgrNe4m0iMhynF6svPl0fD7ynqusAROQh4CwgaYK1YftebvrzW3xsWDnjhlcwblg5/UrSH0ySr22VN7/Km0uVzhww2N9WdbedAmurjDH5J+W7uqp+0FeB9FQkEuGee+6hqWl/Vflhw4a1J1uxidfQoUM7bZ8sEfHe/GdMqWb5Bzs6TL5V4LEVnVecz0aD5Zl83XPsaQ0TiaZ/MTa2MUrU2Hq6KrU7Y0p1wsQuFFFbCNIYkzdUdRtwN3C3iIwEzgUaROQt4AlVvaqXDl0NbIy5vQn4ZPyTROSbwDcByqoO556XNtAWie7fSWWQjw0rZ/zwcsYNq+Bjw8sZN6ycitLOOWK+tlWx5d7TTa5i26pk7ZRfhLOPTb3Ol7VVxph8c8DMwTryyCN59dVX2bhxI2+++Wb715o1a7jvvvvYvXt3+3OHDBnSIeE66qij+MaxA7n5xVZawvsbvfirZi+8vTXh5Nv4ikfZlGkDWB1XRdBrbB94+UPic7SWUDTBHuKOn6TXzMa2G2PyhYicoKrLAFR1E3ArcKuIHIGTbPXaoRPc1ym7UNVfAr8Ep0z7sutP48Md+3i3oYn3Gpp4t34P79Q3sWzddlpj2qCqAaVOT9ewCif5Gl7ORScfzg+feqtT1b9ct1WZjseMb6sA5i9a06nNi6jy2Io6ph46KGWiZG2VMSafHDAJFoCIMHr0aEaPHs306dPb71dVNm/ezJo1azokXw899BCNjftHN5YPqEQGjkQHjGToqMM59/QTOX64oKqISNIGKV9WEjv/hNHcMGNSh/sWrqzjsRV1nZIr6DhuP5murpYaY0we+AXQaaFhVV0L9Gahi03AqJjbI4HNXW1U5Pdx2NByDhtazmkT998fiSqbdu7jnfom3m3Yw3v1Tbzb0MSDr3zYIaEaEAwQVaU1HKUyGOD/t3fucXKVZZ7/PlVd3elLku5O59pJJ8EEQriFgMgMoiKCrHjhoiLjrIyzu87sjDuiM6ywuGtwZInDKOqMMyOOOs6IEBQNKINBDOo6ytUkkAsxEXLrkHs6pDuddHX3s3+cU9VV1XXqnKo+VXWq+/l+Pvmk6lyfevvU+6vnfZ/3eT70e/N5yxkjkRm1qFVAlnOZiWmVYRi1hl+SiwtTC4ZrGRGhs7OTzs5OrrzyyvR2VWXfvn3pma6RWa9neGXDj1nxo6+w4r9Da2srS5cu5UjfZOqmzSPR0UViWhfxydOQPIt7q8WTLx0ctc1vobHf6F6+EEO/ePhcolAAMgo2GIYx7ngWWCwiC4FunNmyPyj1YvGYMH9aM/OnNXPF0pnp7cPDSndPP9sOODNd2/b3sv3AcbYd6KWnP8mX127ny2u309HSwOkzWxCi40zlw7Qqmvc3DCM8/GawviYiLcD9wAPlzIxUDUSE2bNnM3v2bC6//PL0dlXlwIEDWWGGmzdvpm/bUwxvWDNyfn0TiY55JKZ1Ue/+n5jeRXzy9Ko4Xt09/VkLelev6/YNA5namOCSlWs9O/TMgsWldPpRKAAZBRsMwygrp4nII147VfXd5bipqg6KyEeBNThp2r+hqpvCvk8sJsxrb2JeexNvXZLteO091u+EGu7v5bf7Hacrys4VmFZF8f6GYYSLqM9i1IwY9huAAUacrUglwLjwwgv1uefKO9l2ycq17Nq7j+ShXSQP7yZ5aCcDh3aTPLyL4b6RUEOpbyQxbS6JafMdB6yji8S0edRNnYFI8bWdEzEZlR3Ji8xsUV6LhjOvi5CVtrcxEeeu684JrUO/ZOXavMIZF2FYNbAIjmVkz8uGztZG/uPWtwb7IIZhlBUReV5VLyzx3G04ta/yoqo/L9mwkKmEVv3+XT9l77GTZb1HPoqZOUvEhbvfex7gneAifWwVtQryrxfzolStMp0yjNogqFb5rsHKiGG/Q0TOw3G21orIPlW9ZOym1g5OCMIA/U1TmdTlxI8n4sLQkJLsfy3D8dpF8tAuTu74DX0bn0ifL4kGEtPmOf865qdnv+paZ3o6XnERbrhoHk++dDDQomQFvv3UrrxJLTIR1/YTOYkuvGLdSxUNr7COVJapIKN0Yx3ZsyKUhjHu6Y2SE1Vt/udVS0Y5LYm4MDikZZvdiotw4xuCa1VySLl51XrflO7V1ioIrjlj0SrTKcMYXwROciGOBzADmAk0A6ODqMc5uSEIUxsTHDuZRIF44xTi885m0ryzs84ZOtlL8pAz25Vyvk7ufIG+TU+mj5G6BnfGy53tSs14tc5iKBbnoee7uf6CTlY9szvwTJbfYQqjBCtFd08/l6xcy2VLpqfFMnNkshjR8KvDBf4LmP0Ka/phi58NY9zzSrUNiBKFtKpcpLL9Le+ayt6e/sD38kvpHhWtCqI5Y9Eq0ynDGF8ECRG8FLgRuAbYCDwAPKSqx8pvXnAqEXaRSe5IlRcxye/sDJ/qI3loNwOHdpE8vMtxwg7vYui1DL81nnAdry6mzFoA7XOJtc2jrm02EouH+4FKxC90Img7gTNSmW/EceGtj+YVawFeWXm173Xz2RB2eEm5sEXPxkRhjCGCrwd2q+o+9/2HgOuBncAKVT0SnqVjI6paNZ6Ji/D5959X1OyTF52tjZ798Vi0qpZ1CkyrjIlDKCGCIrIb2IXjVN2hqvtDsq/m8ct4lIqbXnjro3n3xxqaaehcQkPnkqztw6dOODNdGaGGp/a+xL4tGdEv8ToSbZ1Zs131HfMdxyte2cz7fiOEuSOpsQLhIOpxvbGO7I118XMlyCdOgC16NoxgfBV4G4CIvAlYCfwPYBlO/an3Vs+06hJUqxZ4aNV4YEjVt+/M1AmvmSxhJAV+2FpVCzoFplWGEZSCM1giMj9qySy8qPSooNdIFWSPOhVaOFsMwwP9JA/vGZntckMOB3v2kw6IiMVdx2sklXyiYx6J9k4knsh73bamBKrFFzTOJehC3GJGCVPXCzKyV8ujZ16fb1IixtE8xTNt0bMxHhnjDNYGVT3Pff0V4KCqrnDfr1fVZeFZOjbGu1aVizC0aiw65ZXAw7TKtMqYWIQyg6WqO0XkJuBjQKqYxBbgy6r6r2M3s3bxGqmKi2R1pvlqc5RCrL6RhtmLaZi9OGv7cPKk63iNzHgNHHiZE1t/RVoOJEZd2xzqM2a8Eh1dTJ7ZxdXndvHQ891jsg2CL8TNHaXzEv7M6/mN7NV6eluvuH2vZ8YWPRvGKOIiUqeqg8DlwEcy9lV2Wj9iVFqrysGkuhhXnzt7zFpVqk4VWp9lWmVaZRj58AsR/BBwM/AJ4Dc4gzjLgbtFhInsZHkVNcyNlw4SdjAWYolJNMxaRMOsRVnbh5OnGDza7Thc7vqugUM7ObHtKVBnwfD+WIzPt89B2uaS6OhyHLBpXdS1dxJLNBRlRzELca85vzPdLl6jprnXyzwnl7Emwag2xYqQLXo2jFHcD/xcRA4B/cD/AxCRRUCk1gtXmqho1VgYHFYeeGY3gwGTPHlRqk6BaRWYVhlGMfiN7P0ZcK2q7sjYtlZErsdZlzVhHazckapWN3zh46vWc/earVmjVqkOd/W6bm5etb4i9sUSDdTPOI36GafRnLFdB5Mkj3Zz42Kh+cQ+Pr/qpyQP76b/d8/CsNvxS4y61pm0zlnIwOQ5bqhhF4lpc4klJo26lwCXLZmetS1oGISX+Kfiur3IvH6hWbBaCMfwGh1tbUxwanC46LYxjImGqt4pIj8FZgOP60jsewz4aPUsqz5R16pCfOJtpzO7dRLbD/Ty1V+87HlcQ12MU4P5Mw1m0ndqMKvAMZhWFYNplWEEx28N1mZVXVrsvmpQ6bj2TIrJ/rPsjsfHvN4pDFKx0ed/5nGOnkiiQ0mSR/amCyinshomj+yF4UH3LKFu6oyM5BruGq9p82hubkl/3k+tfpH7ntqVJSaZBZBzReS5nUe4/+ndDKmma6l89ppzPG0Puo7Lq9OPWlamQs8PRH/Rs2GEwVjWYPlcd5eqdoV93VIxrQpOW1OCdf/nSoC0Vo2VzM9rWlUcplWGEVyr/Bys51X1gmL3VYNqilYxFdjzdejVICUi335qV8HjdGiQwaOvMnB4V3qNV/LwbpJH9sDQYPq4+JQZJDrmMXnWQoandqbXesUamrKul4gLySHNeo+SVd+rkLCsXtfNXz64wbd2SiLmZCvMF1GSKdphE3QUMve4VB0XE6fqUAujx+OdMjpYu1V1XtjXLZVa0io/fagEX7xhGSse2RS6s3d25xQ2dr/mub9SWuWVPAPKlySimP7OtCpamFZVn7AcrBPA9ny7gNNUtTnPvlAQkauALwFx4J9VdWWh46spWkFrX0TFuQoDHR5i8Oir6ayGaQfs8B4YGhHC+OTp6VmuRMd86t0Mh7EG/0cn7qZ0T/3f2pigb2AwS/RyEWBqgOO+eMOy0DulfKN7ibjQXF/Hsf6kZ0pbiOZo5USh1uvPjBdsBqv8BNGq1eu6ueOHm0KZLZooiEDqp1RrY4J3nuck5PCbuSrkXKXYEaDWYzF49XfXX9A5ynEC06ooYVoVDULJIgicGZI9RSEiceArwBXAHuBZEXlEVTdXwx4/gtS+WL2ue9w4VwASi7tFkOfC6SPbdXiIwWP7s2e7Du2id/dGdHAgfVy8ZVpWRsPUv/iklvQxqZG/1P9BRzCPnxz0HTUstKi41BGifAuYk0OatjuVMWpSIlbTC53HG7W+8NwAEfmE1y6gxWPfhMNPq6wocWlkyk1PfzLwzJ/f74G4SMH9pWiVV3+X+fvEtCqamFbVFn4OVqOqvgQgIg2qeiq1Q0QuBspVI+siYLuqvuze6wHgPUAkHawgi1/vXrN13DhXhZBYnETbHBJtc2DxxentOjzE4GsHMxwvZ+ar94U1aDL9WBFvbssqoJx2vBqnBLq/gq9zBYz6kZESqu6e/qxRxSBpdDPP9aOSKW0tlCAYXu1uKYZriskF9n2pYlZEHD+t8itKbFSWIVXPpBzFapWfTuWqpmlV9DCtqi38HKzv4KRlB/h1xmuAf8h5HyadwO6M93uAN+QeJCIfwa130tVVvQiQIBXYJ/oXQGJxEq2zSLTOgkUXpberDjPkOl4Dh3anna/eF59AB0baLNbUSqJjXjqVvFNMeT7xpqml2QNp4codtc0nNF4jRGGO+IaZ0rbW661UkiAz0Ea0UdU7qm1DLeCnVRNdp6JIZr9dqlaFPTNpWlUdTKtqCz8HSzxe53sfJvmuPWpaQlXvBe4FJ669jPb4Uqj2BXh/MSY6IjHqps6kbupMGl/3+vR2VWXo+EEnm+GhXQykHK+NT6IDJ9LHxRqnjJrxqp/WRay5FSkQXqHAHT/cFHjmyeuHRykjvpVIaRtGKMFEGVUsNf2yYdQihbTKdCp69CeHxqxVpc5M1oJWTRSdAtOqWsPPwVKP1/neh8keIDPr01xgbxnvV3byfTEMb0SEuikzqJsyg8bTRpJVOo7X4XSIYdJNrtG3+efoqb70cbFJk93kGl1ZDli8pT3teB09kQy8kFuBBbc+SmcII77vPG82P9rwavpZaGtK8Ol3nRWKKPiFgQS1dyKNKgaZgTaMiYDpVDQZq1aVolOJuEReqyaSToFpVa3h52DNFZEv48wopV7jvi/nX/RZYLGILAS6gQ8Af1DG+5WdfF+MVLrT3FjqsfLFG5Zx+w9epG9g/Imk43h1UDelg8aFIxGqqspQ39GcNV67OLH1lwxv6E0fF2toHp1cY1oX8cnTCs54pcjswJ/beaSkv9mqZ3Znpfo9mfQvkBmEIGEgQUMJgowqjqeRQ78ZaMOYCFRSp8BJQ24zZuUhU6saEzFOFKszqqMyIUZNq4LOfplWGdXAz8G6JeN1bl7ZsuWZVdVBEfkosAYnTfs3VHVTue5XKQp9MVav6+bmVes9zxXIKnbolaWos7UxfZ8Ftz4ahtk1gYhQ19JOXUs7jQuWpberKsMnepxU8od2prMantj2FMMvPD5yfn1Tesar3l3fleiYR3zy9FGOV39yiFu+u55StSaZU5wrrCxAfmEgiZgEDiXwW0w70UYOjdpCRK5Q1Z9U245axE+n/ELVUlp12ZLpPPrCq54zL5k1nqKgVX8YoC5krTEWrUoOQ3K4PBnrwtKqIEkfTKuMalHQwVLVb1XKkDz3/nfg36t1/0pzzfmdnsKVW2zwmvM7uXB+u28sbhRGBxMxGBwubzxpIUSEeHMb8eY2Js0/N2vf0IljGankdzJwaDf9Lz9L34sjv8ukvtFNRz/fTazRRX1HFzplOiKx0OwMY3G53zVaJtUFFhS/xbS1kC52PI1a5mO8f74x8jnAHKyQSTlfQQsWf/aaczxr92RqVWtjIvRCwoZDSJNOaaKkVUGSPphWVZ/x/vm8KOhgicgjhfar6rvDNWdiU8wCxiCxuLe8/YyCs2KVYFCr51z5EW+aSrzrHCZ1nZO1faj/tawaXslDuzi54zf0bXwifYwkGpwww2kjs12JaV3Utc4syfHKrZlWSmfkt0C9p4jCoX7PYqnpYoN8tjA64/E+ajneP58RbcLWqgDR2WXn/qd3+x9kREqrgjyHplXVZbx/vkL4hQj+Hk669PuBpylv5sAJT7ELGP1ica85v7NoB6u5Ph7q2q0AJakiR7xxCvF5ZzNp3tlZ24dO9o4qoHxy5wv0bXoyfYzUNbgzXvOykmvUtc5CYnHPex7pO8Xqdd0Anp0R+DvUt3xvA8mh/I1eTCpXv2exlHSxQTrasDrj8Z6ZqhZGZSuNiHwTZzxHgC4R+UZqn6r+cdUMG4eErVXFDP6kWDyjmW0H+vwPDEiQ+okG9J0aLKhVz+08wpMvHSz4XISlVUGeQ9Oq6jKRtcrPwZoFXAHciJNk4lHg/vGwHiqqhL2A0S9MUCTbCeobGCIRF8+Or1jiIuNGuOKTWojPXcqkuUuztg+f6hup4+VmNzy5exN9m3+WcXLCdby6sup51bXNRmJx+pPD3PLdDbRMqsvbGd3xw02cTA4X7MyvOb+TFY9syhtqI1B0KtdCz2Ip6WKDdLRhJdcYS0HGWhhxs4KTefmXjNdvBKoW4j4RCFOrSkkPv+foSZpKSd7gwXjSqnLS05/ktu+/yKRELG9ffd9Tu3yLH4epVX7PoWlVdZnIWuW3BmsI+DHwYxFpwHG0fiYin1HVv6uEgcbYKJR2tzERp6EuNqqTSw4pbU2JrB/0ucQEhgNo0Y1vmDcqE1GYpESxtTFB38BgaI4hOGlqB4fUN8Qx1tBMQ+eZNHSembV9+NSJkTBD9/9Te1/ixJafZ3yAOhJtnenZrp5p86jvmO84XvGRr2e+heL5RoGOeaxjCPtnQynpYoN0tGEl1xhLQcZaGHGzgpOjUdX0F0tEjme+N6KNX3r4fNkL+5NDtDUlUCTrvERcqIsJ/a7jFTTzYbm1Cpw051efOzvU+zQm4izvmsp//O5IKNcLQn9yyNP+oMWPTascTKvGL34zWLiO1dU4ztUC4MvA98trlhEWmZ1Ld09/2iFJ1cj4uEcIYc+JJPfcsMyzUwqSTaqtKcFnrzmHC+e385cPbijL6OCsqZPSdvllYvQjERea6+s41p9kTmsjC6Y1jkm0Yg1NNMw5g4Y52SNlwwP9JA/vSaeSTx7axcC+bZx46Zek5SUWz3C8Mup5tc9B4on0tbp7+rlk5dp0GxQaCQ57ZKvYEewgHW1rUyKvM9na5HzmoIJS7Khl5kij11MapRE3Kzjpy0BYFxKRu4F3udf8HfBhVe1x990G/BdgCPgLVV0T1n0nErk/gqc2JhBxdKhQn+anU+B8t+/44aaCdaQqoVWZdakunN8+Jq1KOY2dbrbGVc9Ee/1Yd08/C299NOvvY1rlYFo1fhEt0JGIyLeAs4HHgAdUdWOlDCuWCy+8UJ97rmyZ48ctQbNBZRKkhkVjIs5d152T7kgW3vpo2ZJdZN7L6/P4XyPGpEQ8LeiXLZle8ZS9w8mTDB7ZA0e76dv/SrqQ8uDRfaQdL4lR1zbHCTHMqOc1eWYXn3u/U5C50N+m0N81H34hDsXEf3tlE8t8Tpbd8XjesJHWxgTrP31lweeos7Uxyw4INmoZ5HlOXT/VdlGIe//U6he5/+ndDKkSF+Hi09rYcbi/ojaF2Q4i8ryqXhiyiWNGRK4E1rrlQz4HoKqfFJGlOOuTLwLmAE8Ap7uRH56YVhVPKToF41OrWnOczyN9p9KzdZWmlOUEk+pirLzeyehrWmVaNZ61ys/BGgZSq0gzDxRAVXVKSdaVAROt0gjSkeTiJQxxEYZV8z68pYpJUFIdyup13Xx81fqiBTLMdWdj5Ys3LMsacR1OnmLwSDfJw+46L7ee1+DRV0FdYZUYDe1zaJ45n8GpnSNrvNo7iSUa0tcW4JWVVweyY/W6bj6xaj2Z0h0DvnDDsvSM4S3f3ZBV1ysRE+5+33m+dXS8OrlCoiRALOA6Cb9nOJMgz2bm9VrKOzMAAB1qSURBVEr5zoRNKT8cK2HDWO4ZVQcrExG5Fnivqn7Qnb1CVe9y960BVqjqrwtdw7SqeEp91kyrykuuVgUlJtBQFy/Yf5lWjca0KjwbKqFVBR2sWsJEq3SK9ey9OpZCHWK+BzwRk1FFdzOvVcyTmXnvT61+MWuhbS0SZMG1DiZJHu0meXCkgPLAoV0MHt2b5XjVtc5MJ9eY2bWIBz75PpYsWUJTU1P6WpnPQCo8p5BoptKJ5rMwNYJXCmH+uAk6AuonlLnfiVJH08MkaDuV06aw26FGHKwfAqtU9dsi8vfAU6r6bXff14HHVPV7ec77CPARgK6urgt27txZSbPHBaWMQFdCq4plImpVKbQ31bPqTy5m/rRm6utGSp9kLk9I3bvQ7wXTKtOqammVXx2sFlXtHesxRrQpR3xyvnvA6Gnw53YeGSUwjYk411/QyZMvHQzcgWXeOxVLn3svoOp1wYISRLCkLkH99AXUT1+QtV2HkiSP7HWTa+xKhxr2v/w8rz01yAUPrkREWLBgAWeddRaJafN46kgj2jaPxLS59ASwr5B1Pf1JFt766Kh1FEF+EPktdk+RGoEuNEoYNA7d63n26nyjkBUp6L3KaVMU2iEsROQJnKy5udyuqg+7x9wODAL3pU7Lc3zeh1FV7wXuBWcwcMwGT0BKyVpYbq1KxISWSXX0nEgGnrGYiFpVCkdODHDFPb+gLiYs7Ghm8cwWhoaVtS8dSM/gpe5dyALTqtLvFwYTWav8klw8LCLrgYeB51W1D0BETgMuA94PfA0YNWJnRIsw409LXbSYTyBTC34LJdMIMr2ce28vMS4lnKHWkHiC+unzqZ8+P2u7Dg3y4z8+nc2bN7Np0yY2b97M5s2b2fjYGnRopE3iU2aMWuOVmDaPWENT7q08UciKTw+aPjb3x42XOA6r8srKq1l466Oe1wqSpWj1um76Tg2O2l7oeY5CVqSgaa3LaVMU2iEsVPVthfaLyE3AO4HLdSTsYw8wL+OwucDe8lg4MQh7vYhpVe3yo//xRrYf6OW3+4+z7UAvW149ziuHwqt7lsK0qrxMZK3yS9N+uYi8A/gT4BIRaQeSwFacmlg3qeq+slpojJmwayWUkvbU73pe5+a712VLpvsWMoT8Yn31ubPzJq8Imna+lqmrS7D15BSuv/56rr/++vT2Bf/zEZJHX03Pdg24M1/9OzdApuM1ebqT0dBd31Xvvo41NAe6f9D0sZnPg9fUfqpj9Oo4g9RS8fpB1NaU4NPvOivUGmBhE2T0tNw2RaEdUojIcfIPVo95vbCIXAV8Enizqp7I2PUI8B0R+QJOkovFwDOl3meiU46aPqZVtUlchO0Heke11YICTkqYmFaFx0TWKluDNQGIQhxupfFa1DgpEcs7KthcH+dkcji0cIdUmKNfvZOg8eupFL9hhI3kZkzsOzWYNxuSDg8x2LNvVC2v5OHd6OBIFux4y7Ts2S73X3xSy6hrFrtwOd8ort8iXgE+eHFXwdFmKD2DplfJg0pnZsr9URb0x1w5bRinWQS3Aw3AYXfTU6r6p+6+24E/xgkdvFlVH/O7nmlVfiaiTkF0tOo7T+/ydNw6XSch6FqaSmtVOaiUVv3+69p9M+qZVoVvQyW0yrcOlnsxAT4ILFTVvxaRLmCWqtpoXQ0QhTjcSuNVg8LL2ekbCF70MREXLlrQVrBGVmZ2mlR60lyCOmGZnahf7bEg9CeH02l9u3v6ScQl7yJuicVJtHeSaO+ExRent+vwEIOvHXSyGbrru5KHdtH7who0eSp9XLylPSvEMNHRRddpp6f3F+rwvEbsWhsTrHj3yIid1wg14DsaXuz3ItemIdX0KFg1ijqWsiZlPNqQDxGZAUxKvVfVkmsuqOqiAvvuBO4s9drGCBNRp6C8WuU325U7A5LPycoc6febiaiWVpWDWVOd7iNI+vdSteqyJdOz9N9r1ta0qjZtCORgAf8ADANvBf4aOA48BLy+THYZIRKFONxKE4Yo58tQlClIC297lHyDiHGR9IjVQ893ZzlXmQUiM4tOeolR7jR2vqnuYjMu5pIcUtqaEjTV140q8plvYa7E4iRaZ5FonQWL3pDerjrM0GsH09kMU85X74tPoAPOZ9sPzLx3BjO6FrGHacTa5pLo6GLXiS5u+74zK3bN+Z15f3QANDfU5V0bkW/Ez6/IY7Hfi6CFI43qISLvBj6PE7J3AJgPbAHOqqZdhj8TUaeg/FpVyNFpqq/L0qpcvyXXSQBvx6nSWpU7MxP27Narx05y/mce51h/Mt0u3T393PrQC0C2w1SqVgXRKTCtqlWCOlhvUNXlIrIOQFWPikh9Ge0yQiQKcbiVxqtDam1McGpw2DfzDziLU3cUCBHwitBIOST5OrmUc5U5rZ/Z6eabSr/jh5vS4RatjYl0hsWUM5QcGi5qVDMfPSeSaTFO3fvT73J+kwbJlAQgEqNu6kzqps6k8XWvT4d3HO0boEOO8465Q0w9tZ/Nmzfz4E9+Td/+9ejAyJKWWOMUbrpvAR+86hK2bBsm0dFFfUcXsaZWnEn0kR8jfqOKQUb8iv1eRGGEPQpFIyPOXwMXA0+o6vkichlwY5VtMgIwEXUKKqNVXuF6qb4rqJNQqlYFTakehFyt6vSIWiiG1ozSJDMmN/DOc2fT3lzPV5783Sin8+TgMH/54Aa+v64bwTtsMohWBdUU06raJKiDlRSROO73QkSmA9UpHW4UTdgLfWsBrw5pxbsdpyGzLbxGvvxGTjsLpEyF0jq5XAG75XsbsopK9vQnWfXMbu5+33lA6YKSS2tTIm9I3V3XncNd151TYkYr8VyAu/bWR2lXZej44ZFU8od2curwbr71b/dxove19LGxSZOd5BrTupg+73Xc8U/H+beXhkg2TEVE8oZVBBnx8wrZuHvNVj6+av2o70lrUyJvG7Q2JYpsl9IoRxKAcUhSVQ+LSExEYqr6pIh8rtpGGf5MRJ2C8mvVNed3suKRTQXPK6dW3XDRvKwwuLEG94WtVam2zvecff7x3+Y9Z0iVlw/2sueod/tMbUzwhce3cu8vXubk4EiYY2afHXRmKve7kYoy+fiq9dy9Zuuo74lpVTQI6mB9GfgBMENE7gTeC3yqbFYZoROFGNhK4ifWfjHUQUZO/UaVxhrycvearVmClSI5rPzlgxs8Fzmn6m6kHIZHX3i1oOA0JuKo4hlS8B+3vjUdRpK7aLYQhUISUm1TN6WDuikdNC5cDjgjiU31cXbt6c5IquGs8Tqx9Ze8suHHrPjRVwCINTRnrO+az+3dL3DhZ/6Azs5O379N7ujaPTcsAwqv2/L6uD0nkqxe1+35/QprJK/SYR81OgLZIyItwC+A+0TkAE4CCqMGmGg6BZXRqhXvPqtqWpUvEyKQFZZeTq3ymzELolO5tDYmPPUgRU9/ki+v3Z73fp99dDNvPn16oJmp3H74gxd3+a7bMq2KhlYFziIoIkuAy3HCaH+qqlvKaVixWGYmYyyU+gUtNlFDZlYhPwpVbS9EvuxHmXbmK6r48VXrPXNc58uklG/EMqgt6fO/u2HUYuVEXDyvqao884nXc97NX3dTybsO2KFdDPePzHhNmTKFpUuX0jxzPtuTrfQ3z2HeaYu5/f2Xcu3yuUVn7UqFdBb6e3j9Xcf6DGTidf9isl0FJUy7gxJGFkERaQZO4iaTBKYC96nq4YInVhDTKmMsjBetKqQNYWlVkNpkfrYUq1MAX3j/ebx+QTuX/s2TBe/b0VJPa1M9r/b00zcwREdzPR9722L+8+8t8LTfy2HMXHpgWhUNrQo6g4WqvgS8NCarDCOilDpyWmxdlGJGVoIW6Mt3XjF2pmwsdhGtn3NV6Pxrzu/MG8qRHFLP2bG5bU3MnDmT1513Md0952XtGzpxjKkn9/NnyxrSBZRf/PWTHDhwAHCyHXzoKy0sXbqUV4baSE6ek17jFZ8ynf7k6FHRFN09/axe113w7+E1OhfmSF4lkwDU6iJpVc2sRPqtqhliGGVivGhVIW0IS6u81pYVY0uxOtXZ2sh1y+emX+ezdVpzPf/9La9j2/5eth04zn53jfGhvgH+98ObuOeJbSya0cKm7mN513Hno7unn0tWruWWt59hWhURrQrsYBmGUTxjCXm55e1nBJolyqTUReFhLaItxpYej1CQVErZ3FG7lIDkprYFaJnazmc//OZRbX3o0CG2bNnC5s2b2bRpE5s3b+bI088y1DuSYl8SDRnp5LvcYsrzqZs6A5EY4IQO+qXUz9cmYS42rmQSgCgski6FnILD9UAC6BtLoWHDmAhUUqvG0m8V0w9WU6duefsZnrb+73cuzWprVWX/a6fYduA4v93fy/YDx9m2v7fo5FWpcEHTqmholTlYhhFRUh1w5ghaoXjysRQRzB3BbG1yYsy9FtF6jVBlrv/ys8XrGqnPkS+Gvrunn4ee787KpFjoXh0dHVx66aVceuml6W2XrFzLrlcPZIUYJg/vZmDnC/RtXJs+TuoaSEybm3a+Htq5iMsuPp9HdwwjsXjezxP0M5YyklfJJAC1mjJbVSdnvheRa4CLqmSOYUwIitGquMiYwrcy+8HUeuDUjEXmfqiuTmUm3vDrs0WEWVMnMWvqJC5dPD29/ffv+il7j50M2jSAM3vz2Iv7uOrsmfxg3V7PzxT0c5pWlU7gNVhRx+LajYlAJeKNg9wjDDuCXKOUCvZjuW/f8WP81df+nYGMAsrJQ7sZOn5w5ALxhOt4ObNd9R1dtMxayN0fvoLrXz+/6M8YRaIc117CdZ9S1Yv9j6wMplXGRKDcfch416lC975u+Rx+uuUg+14rzvkCaKiLsfK6c7jWDWP0u5dp1WhCX4NlGEb1qcTIUJCY5jDsCHKNckz/F75vJ//wq31095yZdc7wqRMMHdnNqYMjyTVOdW/hxJafA3AQ+IOv13PGGWewdOlSli5dyllnncXSpUv563ct4Z61L0cuw1EhajVltohcl/E2BlzI2DNDG4ZRJOXuQ8a7Tvnd+85rvR27GN51lE4NDvOp1Rv5l1/tYNGMyZw+s4XFM1u4YH4bd157Np9//Lc11edHWauqNoMlIncD7wIGgN8BH1bVHnffbcB/AYaAv1DVNX7Xs1FBwwiHSmYA8qNcI4OF8BoRyxfPPjzQz+DhPdz11rZ0co3NmzfzyiuvkOpb6+rqOP3009MOV8r5Wrx4MfX1Vq89RUhZBL+Z8XYQ2AF8TVUPjOW6YWJaZRhjZ6LrFBSnVSnuvPZstu3vZfuBXn67/zgHjp/KOnfRjBYWz2hh0cwWTp8xmcUzW5jb1kQ8JmX7HLVGLcxg/QS4TVUH3UKQtwGfFJGlwAeAs4A5wBMicrqqjr2aqmEYvkQpprmSi2VTeI2I5cteFatvZOGZ53LTTdki2tfXx9atW7OSa6xbt47vfe97accrHo+zePHirNmupUuXcsYZZ9DQ0FC2zzeeUdUPV9sGwzDKz0TXKShOq8Bx+D74huww9mMnkmw/6CTXSGU1/NXvDvP9dd3pYxrqYmnHa/HMyen/u9rN8SpE1RwsVX084+1TOMWLAd4DPKCqp4BXRGQ7ziLlX1fYRMOYkFRLLPJRrel/r4xaQdulubmZ5cuXs3z58qzt/f39accr5Xxt3LiR1atXMzzsBHXEYjEWLVqU1/FqbKz+wt0oIiJ/R4FQQFX9iwqaYxhGmTGdGrn3WLRqalOCC+a3c8H89qztr51Msv1AL9v3OzNd2w708uyOo6xeP5I4o74uxmkdzZyedrocx2t+exN18ViIn7I2iUSSCxH5IbBKVb8tIn8PPKWq33b3fR14TFW/53ONg8DOMpvaARwq8z3KQa3aDbVre03bHWuc0h5vae+UeF29Dg0ODPUe6R7uf+2I79nVpextXqZ2qdVnBcK1fb6qTvc/bDQicpP78hJgKbDKff8+4HlV/XgI9oWCm0p+a7XtKJFafVbN7spj/XFlybK7xjS81to8kFaVdQZLRJ4AZuXZdbuqPuwecztOrPx9qdPyHJ/XCxSRjwAfybjmvWOzuDAi8lw5slyVm1q1G2rXdrO78tSq7bVqN0THdlX9lmvPHwGXqWrSff9PwOMFTq0GW6PQZqUQlb93sZjdladWbTe7K08t216IsjpYqvq2QvvdUcd3ApfryFTaHmBexmFzgbzJ/F2HqqxOlWEYhlEzzAEmA6mR2hZ3m2EYhmFUjKqtwRKRq4BPAm9W1RMZux4BviMiX8ARxsXAM1Uw0TAMw6gtVgLrRORJ9/2bgRXVM8cwDMOYiFQzi+DfAw3AT0QEnHVXf6qqm0TkQWAzTujgn0cog2CtzpbVqt1Qu7ab3ZWnVm2vVbshYrar6jdF5DHgDe6mW1V1XzVtykOk2qxIatV2s7vy1KrtZnflqWXbPYlEkgvDMAzDKBURWaKqL4nI8nz7VfU3lbbJMAzDmLiYg2UYhmHUNCJyr6p+JCM0MBNV1fJV+zQMwzCMHMzBMgzDMAzDMAzDCAmrBBYAEXmfiGwSkWERuTBn320isl1EtorI26tlox8iskJEukVkvfvvHdW2qRAicpXbpttF5NZq21MMIrJDRF502/m5atvjhYh8Q0QOiMjGjG3tIvITEdnm/t9WTRu98LA98s+4iMwTkSdFZIvbp3zM3R7pdi9gd6Ta3O2rJ7uvPyUi3xeR86tpUya12q/VSp8GtduvWZ9WWWqlT8uHiEwSkWdEZINr+x3u9oUi8rTb5qtEpL7atmZSwO5/EZFXMtp8WbVtDQObwQqAiJwJDANfBf5KVZ9zty8F7gcuwsl4+ARweoSScqQRkRVAr6r+bbVt8UNE4sBvgStw0vY/C9yoqpuralhARGQHcKGqRrpwnoi8CegF/lVVz3a3/Q1wRFVXuj8A21T1k9W0Mx8etq8g4s+4iMwGZqvqb1xH4HngGuCPiHC7F7D7/USozUXkBVU9V0TeCNwF/C3wv1T1DT6nlp1a7tdqpU+D2u3XrE+rLLXSp+VDRARoVtVeEUkAvwQ+BnwC+L6qPiBODcANqvqP1bQ1kwJ2/ynwI1X9XlUNDBmbwQqAqm5R1a15dr0HeEBVT6nqK8B2HGfLGBsXAdtV9WVVHQAewGlrI0RU9ReM1AtK8R7gW+7rb+EITuTwsD3yqOqrqYQLqnoc2AJ0EvF2L2B31EgNbl0N/KNb0D4qo7jWr1WAWu3XrE+rLDXUp41CHXrdtwn3nwJvBVJOShTb3MvucYk5WGOjE9id8X4P0f6CflREXnBDESI1XZ9DrbVrLgo8LiLPi8hHqm1MkcxU1VfBESBgRpXtKZZaecYRkQXA+cDT1FC759gN0WrzbhH5Ks4o9L+LSAPR0bla7tdquU+DGvp+5SFK36+CWJ9WOUQkLiLrgQPAT4DfAT2qOugeEsn+JdduVU21+Z1um9/j9ts1T1SEp+qIyBMisjHPv0IjjJJnW9W8cZ/P8I/A64BlwKvA56tlZwAi1a4lcImqLgf+E/DnbuiHUX5q5hkXkRbgIeBmVX2t2vYEJY/dUWvz9wNrgKtUtQdoB26prklparlfsz6tOkTt++WJ9WmVRVWHVHUZMBdndvzMfIdV1ip/cu0WkbOB24AlwOtx+uzIhJKOhWoWGo4Uqvq2Ek7bA8zLeD8X2BuORcUT9DOIyNeAH5XZnLEQqXYtFlXd6/5/QER+gNP5/aK6VgVmv4jMVtVX3Rj1A9U2KCiquj/1OsrPuBt7/hBwn6p+390c+XbPZ3fU2lxVT4jIAeCNwDacYvXbqmlTBjXbr9V4nwY18P3KR9S+X15Yn1Y9VLVHRH4GXAy0ikidO4sV6f4lw+6rMta7nRKRbwJ/VT3LwsNmsMbGI8AHRKRBRBYCi4FnqmxTXtwOLsW1wEavYyPAs8BicTLi1AMfwGnryCMizTKSxawZuJJot3UujwA3ua9vAh6uoi1FUQvPuLvI9+vAFlX9QsauSLe7l91Ra3MR+TTO6Odt7qYE8O3qWZRFTfZr46BPg4h/v7yI2vcrH9anVR4RmS4ire7rRuBtOGvIngTe6x4WxTbPZ/dLqTZ3/ybXEME2LwXLIhgAEbkW+DtgOtADrFfVt7v7bgf+GGek9GZVfaxqhhZARP4NZ8pbgR3An6Tio6OIOKlRvwjEgW+o6p1VNikQInIa8AP3bR3wnajaLiL3A28BOoD9wKeB1cCDQBewC3ifqkZu4bWH7W8h4s+4ONnt/h/wIk5mUoD/hRP7H9l2L2D3jUSozd3Y/vOB36jq+e62F1T13GrZlEkt9mu11KdB7fZr1qdVllrp0/IhIufiJLGI40yUPKiqn3G/qw/ghNmtA/5QVU9Vz9JsCti9Fuf3tQDrgT/NSIZRs5iDZRiGYYwLROQZVb1IRH6jqsvdGZdfR8XBMgzDMCYGFiJoGIZhjBcedLMItorIf8OpTfjPVbbJMAzDmGDYDJZhGIYxbhCRK3DWCQmwRlV/UmWTDMMwjAmGOViGYRjGuERE4sAHVPW+attiGIZhTBwsRNAwDMOoaURkiojcJiJ/LyJXisNHgZdxamMZhmEYRsWwGSzDMAyjphGRh4GjwK+By4E2oB74mKqur6ZthmEYxsTDHCzDMAyjphGRF1X1HPd1HDgEdKnq8epaZhi1iYj0qmpLzrYzgK8CrUADTprzh4DPuYcsArqBfuAFVf2Qe96XcOozzVPVYRH5MPAx95ylwFZgCPixqt5a1g9mGBXCQgQNIyTcsKS1IjLFfT+qjoOInCEiPxOR9SKyRUTuFZG3u+/Xi0iviGx1X/9rxnlfEpFuEYm57z+ccc6AiLzovl6Z55478myLi8jzIvKmjG2Pi8j73NdPiEhbKA1jGOUnmXqhqkPAK+ZcGUbofBm4R1WXqeqZwN+p6hr3/TLgOeCD7vuUcxXDKdi7G3gTgKp+M+OcvcBl7ntzroxxQ121DTCMccQ7gA2q+lqBY1IC9TCAiJyjqi8Ca9z3PwP+SlWfS52QR6B+pqrfBL7p7t+BI1CHghqqqkMi8mfAP4vIcpzRRVXV77qH/BvwZ0BkC4oaRgbniUjqeydAo/tecJ7rKdUzzTDGDbOBPak3rnb5cRmwEViFU8T3Z2WxzDAihs1gGUaRiMgfisgz7ozRV92QJIAPAg/7nD4WgfpHHIEKBVV9GvgVsAL4v8CfZ+x+JMx7GUY5UdW4qk5x/01W1bqM1+ZcGUY43AOsFZHHROTjItIa4JwbgfuBHwDvFJFEWS00jIhgDpZhFIGInAncAFzihjcM4ThWAJcAz/tcImoCdRtwM/AdVd2e2qiqR4EGEZkW4r0MwzCMGsWNnDgT+C7wFuApEWnwOl5E6nEiO1a7kR1P49SoM4xxjzlYhlEclwMXAM+KyHr3/Wnuvna/dR8RFKg3AceAs/PsOwDMCfFehmEYRg2jqntV9Ruq+h5gkPzakeIqYCrwohvK/kYsMsKYIJiDZRjFIcC3Ugt0VfUMVV3h7htMJaEoRFQESkSagb8B3gpMF5F35BwyCScblGEYhjHBEZGrUhEUIjILmIaTNdCLG4H/qqoLVHUBsBC4UkSaym6sYVQZc7AMozh+CrxXRGYAiEi7iMx3921lZDYrLxETqP8DPKiqL+EktLhHRCa5tgkwC9gRwn0MwzCM2qJJRPZk/PsETvTERhHZgJOY6RZV3ZfvZFej3g48mtqmqn3AL4F3ld98w6gulkXQMIpAVTeLyKeAx93ZqiROcoidOELyFiC1lqlJRPZknP4FYC7wJRE56W4LIlB/knH/PhFJCdSqUj+HiCzFyUx4nnvd9SKyBvgkcAdOGORTqjpY6j0MwzCM2kRVvQbgP1HgnLdkvD4BtOc55rqc9wtKs9Awoo0VGjaMkBCR2cC/quoV1bYlExHZUayIuYUhH1HVn5bHKsMwDMMwjPGJhQgaRkio6qvA11KFhmucjeZcGYZhGIZhFI/NYBnGOEdEblbVL1bbDsMwDMMwjImAOViGYRiGYRiGYRghYSGChmEYhmEYhmEYIWEOlmEYhmEYhmEYRkiYg2UYhmEYhmEYhhES5mAZhmEYhmEYhmGExP8HSNfKDZ+GEGwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 864x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from statsmodels.graphics.regressionplots import plot_regress_exog\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "fig = plt.figure(figsize=(12,4))\n",
    "print(plot_regress_exog(lm1, 'LSTAT', fig=fig))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Ďalšia diagnostika (na čo si dať pozor)\n",
    "\n",
    "Pozorovania s vysokým vplyvom, vychýlené hodnoty, kolinearita, nekonštantná variancia chýb (heteroscedascita), korelované chyby, ...\n",
    "\n",
    "https://www.statsmodels.org/stable/diagnostic.html\n",
    "\n",
    "http://www.statsmodels.org/devel/examples/notebooks/generated/regression_diagnostics.html\n",
    "\n",
    "https://www.statsmodels.org/dev/examples/notebooks/generated/regression_plots.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Lineárna regresia v praxi\n",
    "\n",
    "<img src=\"img/seer.jpg\" alt=\"Veštenie z gule\" style=\"margin-left: auto; margin-right: auto; width:600px\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Predikcia: IFP Kalkulačka hodnoty bytov\n",
    "\n",
    "http://www.institutfinancnejpolitiky.sk/kalkulacky/nehnutelnosti/\n",
    "\n",
    "Atribúty ako obec, ulica, obytná plocha, balkón, poschodie, a pod."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "### Porozumenie vzťahu: Kto volil Kotlebu?\n",
    "\n",
    "https://dennikn.sk/402526/obraz-kotlebovej-podpory-zatial-velmi-povrchny-nieco-dolezite-unika/?cst=1324f9abaa007e30565f85fa6ace469f92e99f9f\n",
    "\n",
    "Dáta z: výsledkov volieb, sčítania obyvateľstva, atlas rómskych komunít, štatistiky nezamestnanosti"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Logistická regresia"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Mohli by sme na klasifikáciu použiť lineárnu regresiu?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "*Áno* - majme povedzme dve triedy (0/1); zvolíme si hranicu, dokedy predikujeme 0, a odkedy už predikujeme 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Problém, ako interpretovať, keď nám vráti hodnotu menšiu ako 0 alebo väčšiu ako 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Nebude fungovať pre viacero tried (napr. 0, 1, 2) - zaniesli by sme umelo poradie, ktoré vo väčšine prípadov nemá zmysel."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Aj na klasifikáciu teda môžeme použiť regresnú metódu, ale chceli by sme funkciu, ktorá vracia hodnoty z intervalu <0,1> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "... *Logistická regresia*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Logistická funkcia\n",
    "\n",
    "\n",
    "$$p(Y=1|X) = p(X) = \\frac{e^{\\beta_0+\\beta_1X}}{1 + e^{\\beta_0+\\beta_1X}}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<img src=\"img/logistic-curve.svg\" alt=\"Logistická krivka\" style=\"margin-left: auto; margin-right: auto; width:600px\"/>\n",
    "\n",
    "Zdroj: https://en.wikipedia.org/wiki/Logistic_function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Úpravou funkcie dostávame:\n",
    "\n",
    "$$ \\frac{p(X)}{1-p(X)} = e^{\\beta_0+\\beta_1X} $$\n",
    "\n",
    "kde ľavá strana predstavuje šancu (angl. *odds*)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$$ \\log{\\left(\\frac{p(X)}{1-p(X)}\\right)} = \\beta_0+\\beta_1X $$\n",
    "\n",
    "kde výraz na ľavej strane sa označuje ako *log-odds* alebo *logit*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Trénovanie modelu = odhad koeficientov $\\hat{\\beta_i}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Algoritmus *Maximum Likelihood Estimation (MLE)* - cieľom je nájsť také hodnoty koeficientov, aby pozorovania s triedou 0 mali pravdepodobnosť čo najbližšiu nule a naopak. Optimalizuje sa (*maximalizuje sa*) nasledovná funkcia:\n",
    "\n",
    "$$ l(\\beta_0, \\beta_1) = \\prod_{i:y_i=1}{p(x_i)} \\prod_{i':y_{i'}=0}{(1-p(x_{i'}))} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Viacnásobná logistická regresia\n",
    "\n",
    "Zovšeobecnenie analogické k tomu, ako to bolo pri lineárnej regresii."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_breast_cancer\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "data = load_breast_cancer()\n",
    "label_names = data['target_names']\n",
    "labels = data['target']\n",
    "feature_names = data['feature_names']\n",
    "features = data['data']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['malignant' 'benign']\n"
     ]
    }
   ],
   "source": [
    "print(label_names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
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       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean radius</th>\n",
       "      <th>mean texture</th>\n",
       "      <th>mean perimeter</th>\n",
       "      <th>mean area</th>\n",
       "      <th>mean smoothness</th>\n",
       "      <th>mean compactness</th>\n",
       "      <th>mean concavity</th>\n",
       "      <th>mean concave points</th>\n",
       "      <th>mean symmetry</th>\n",
       "      <th>mean fractal dimension</th>\n",
       "      <th>...</th>\n",
       "      <th>worst texture</th>\n",
       "      <th>worst perimeter</th>\n",
       "      <th>worst area</th>\n",
       "      <th>worst smoothness</th>\n",
       "      <th>worst compactness</th>\n",
       "      <th>worst concavity</th>\n",
       "      <th>worst concave points</th>\n",
       "      <th>worst symmetry</th>\n",
       "      <th>worst fractal dimension</th>\n",
       "      <th>target</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>17.99</td>\n",
       "      <td>10.38</td>\n",
       "      <td>122.80</td>\n",
       "      <td>1001.0</td>\n",
       "      <td>0.11840</td>\n",
       "      <td>0.27760</td>\n",
       "      <td>0.3001</td>\n",
       "      <td>0.14710</td>\n",
       "      <td>0.2419</td>\n",
       "      <td>0.07871</td>\n",
       "      <td>...</td>\n",
       "      <td>17.33</td>\n",
       "      <td>184.60</td>\n",
       "      <td>2019.0</td>\n",
       "      <td>0.1622</td>\n",
       "      <td>0.6656</td>\n",
       "      <td>0.7119</td>\n",
       "      <td>0.2654</td>\n",
       "      <td>0.4601</td>\n",
       "      <td>0.11890</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>20.57</td>\n",
       "      <td>17.77</td>\n",
       "      <td>132.90</td>\n",
       "      <td>1326.0</td>\n",
       "      <td>0.08474</td>\n",
       "      <td>0.07864</td>\n",
       "      <td>0.0869</td>\n",
       "      <td>0.07017</td>\n",
       "      <td>0.1812</td>\n",
       "      <td>0.05667</td>\n",
       "      <td>...</td>\n",
       "      <td>23.41</td>\n",
       "      <td>158.80</td>\n",
       "      <td>1956.0</td>\n",
       "      <td>0.1238</td>\n",
       "      <td>0.1866</td>\n",
       "      <td>0.2416</td>\n",
       "      <td>0.1860</td>\n",
       "      <td>0.2750</td>\n",
       "      <td>0.08902</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>19.69</td>\n",
       "      <td>21.25</td>\n",
       "      <td>130.00</td>\n",
       "      <td>1203.0</td>\n",
       "      <td>0.10960</td>\n",
       "      <td>0.15990</td>\n",
       "      <td>0.1974</td>\n",
       "      <td>0.12790</td>\n",
       "      <td>0.2069</td>\n",
       "      <td>0.05999</td>\n",
       "      <td>...</td>\n",
       "      <td>25.53</td>\n",
       "      <td>152.50</td>\n",
       "      <td>1709.0</td>\n",
       "      <td>0.1444</td>\n",
       "      <td>0.4245</td>\n",
       "      <td>0.4504</td>\n",
       "      <td>0.2430</td>\n",
       "      <td>0.3613</td>\n",
       "      <td>0.08758</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>11.42</td>\n",
       "      <td>20.38</td>\n",
       "      <td>77.58</td>\n",
       "      <td>386.1</td>\n",
       "      <td>0.14250</td>\n",
       "      <td>0.28390</td>\n",
       "      <td>0.2414</td>\n",
       "      <td>0.10520</td>\n",
       "      <td>0.2597</td>\n",
       "      <td>0.09744</td>\n",
       "      <td>...</td>\n",
       "      <td>26.50</td>\n",
       "      <td>98.87</td>\n",
       "      <td>567.7</td>\n",
       "      <td>0.2098</td>\n",
       "      <td>0.8663</td>\n",
       "      <td>0.6869</td>\n",
       "      <td>0.2575</td>\n",
       "      <td>0.6638</td>\n",
       "      <td>0.17300</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>20.29</td>\n",
       "      <td>14.34</td>\n",
       "      <td>135.10</td>\n",
       "      <td>1297.0</td>\n",
       "      <td>0.10030</td>\n",
       "      <td>0.13280</td>\n",
       "      <td>0.1980</td>\n",
       "      <td>0.10430</td>\n",
       "      <td>0.1809</td>\n",
       "      <td>0.05883</td>\n",
       "      <td>...</td>\n",
       "      <td>16.67</td>\n",
       "      <td>152.20</td>\n",
       "      <td>1575.0</td>\n",
       "      <td>0.1374</td>\n",
       "      <td>0.2050</td>\n",
       "      <td>0.4000</td>\n",
       "      <td>0.1625</td>\n",
       "      <td>0.2364</td>\n",
       "      <td>0.07678</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 31 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   mean radius  mean texture  mean perimeter  mean area  mean smoothness  \\\n",
       "0        17.99         10.38          122.80     1001.0          0.11840   \n",
       "1        20.57         17.77          132.90     1326.0          0.08474   \n",
       "2        19.69         21.25          130.00     1203.0          0.10960   \n",
       "3        11.42         20.38           77.58      386.1          0.14250   \n",
       "4        20.29         14.34          135.10     1297.0          0.10030   \n",
       "\n",
       "   mean compactness  mean concavity  mean concave points  mean symmetry  \\\n",
       "0           0.27760          0.3001              0.14710         0.2419   \n",
       "1           0.07864          0.0869              0.07017         0.1812   \n",
       "2           0.15990          0.1974              0.12790         0.2069   \n",
       "3           0.28390          0.2414              0.10520         0.2597   \n",
       "4           0.13280          0.1980              0.10430         0.1809   \n",
       "\n",
       "   mean fractal dimension   ...    worst texture  worst perimeter  worst area  \\\n",
       "0                 0.07871   ...            17.33           184.60      2019.0   \n",
       "1                 0.05667   ...            23.41           158.80      1956.0   \n",
       "2                 0.05999   ...            25.53           152.50      1709.0   \n",
       "3                 0.09744   ...            26.50            98.87       567.7   \n",
       "4                 0.05883   ...            16.67           152.20      1575.0   \n",
       "\n",
       "   worst smoothness  worst compactness  worst concavity  worst concave points  \\\n",
       "0            0.1622             0.6656           0.7119                0.2654   \n",
       "1            0.1238             0.1866           0.2416                0.1860   \n",
       "2            0.1444             0.4245           0.4504                0.2430   \n",
       "3            0.2098             0.8663           0.6869                0.2575   \n",
       "4            0.1374             0.2050           0.4000                0.1625   \n",
       "\n",
       "   worst symmetry  worst fractal dimension  target  \n",
       "0          0.4601                  0.11890       0  \n",
       "1          0.2750                  0.08902       0  \n",
       "2          0.3613                  0.08758       0  \n",
       "3          0.6638                  0.17300       0  \n",
       "4          0.2364                  0.07678       0  \n",
       "\n",
       "[5 rows x 31 columns]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame(features)\n",
    "df.columns = feature_names\n",
    "df['target'] = labels\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean radius</th>\n",
       "      <th>mean texture</th>\n",
       "      <th>mean perimeter</th>\n",
       "      <th>mean area</th>\n",
       "      <th>mean smoothness</th>\n",
       "      <th>mean compactness</th>\n",
       "      <th>mean concavity</th>\n",
       "      <th>mean concave points</th>\n",
       "      <th>mean symmetry</th>\n",
       "      <th>mean fractal dimension</th>\n",
       "      <th>...</th>\n",
       "      <th>worst texture</th>\n",
       "      <th>worst perimeter</th>\n",
       "      <th>worst area</th>\n",
       "      <th>worst smoothness</th>\n",
       "      <th>worst compactness</th>\n",
       "      <th>worst concavity</th>\n",
       "      <th>worst concave points</th>\n",
       "      <th>worst symmetry</th>\n",
       "      <th>worst fractal dimension</th>\n",
       "      <th>target</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
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       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
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       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>14.127292</td>\n",
       "      <td>19.289649</td>\n",
       "      <td>91.969033</td>\n",
       "      <td>654.889104</td>\n",
       "      <td>0.096360</td>\n",
       "      <td>0.104341</td>\n",
       "      <td>0.088799</td>\n",
       "      <td>0.048919</td>\n",
       "      <td>0.181162</td>\n",
       "      <td>0.062798</td>\n",
       "      <td>...</td>\n",
       "      <td>25.677223</td>\n",
       "      <td>107.261213</td>\n",
       "      <td>880.583128</td>\n",
       "      <td>0.132369</td>\n",
       "      <td>0.254265</td>\n",
       "      <td>0.272188</td>\n",
       "      <td>0.114606</td>\n",
       "      <td>0.290076</td>\n",
       "      <td>0.083946</td>\n",
       "      <td>0.627417</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>3.524049</td>\n",
       "      <td>4.301036</td>\n",
       "      <td>24.298981</td>\n",
       "      <td>351.914129</td>\n",
       "      <td>0.014064</td>\n",
       "      <td>0.052813</td>\n",
       "      <td>0.079720</td>\n",
       "      <td>0.038803</td>\n",
       "      <td>0.027414</td>\n",
       "      <td>0.007060</td>\n",
       "      <td>...</td>\n",
       "      <td>6.146258</td>\n",
       "      <td>33.602542</td>\n",
       "      <td>569.356993</td>\n",
       "      <td>0.022832</td>\n",
       "      <td>0.157336</td>\n",
       "      <td>0.208624</td>\n",
       "      <td>0.065732</td>\n",
       "      <td>0.061867</td>\n",
       "      <td>0.018061</td>\n",
       "      <td>0.483918</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>6.981000</td>\n",
       "      <td>9.710000</td>\n",
       "      <td>43.790000</td>\n",
       "      <td>143.500000</td>\n",
       "      <td>0.052630</td>\n",
       "      <td>0.019380</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.106000</td>\n",
       "      <td>0.049960</td>\n",
       "      <td>...</td>\n",
       "      <td>12.020000</td>\n",
       "      <td>50.410000</td>\n",
       "      <td>185.200000</td>\n",
       "      <td>0.071170</td>\n",
       "      <td>0.027290</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.156500</td>\n",
       "      <td>0.055040</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>11.700000</td>\n",
       "      <td>16.170000</td>\n",
       "      <td>75.170000</td>\n",
       "      <td>420.300000</td>\n",
       "      <td>0.086370</td>\n",
       "      <td>0.064920</td>\n",
       "      <td>0.029560</td>\n",
       "      <td>0.020310</td>\n",
       "      <td>0.161900</td>\n",
       "      <td>0.057700</td>\n",
       "      <td>...</td>\n",
       "      <td>21.080000</td>\n",
       "      <td>84.110000</td>\n",
       "      <td>515.300000</td>\n",
       "      <td>0.116600</td>\n",
       "      <td>0.147200</td>\n",
       "      <td>0.114500</td>\n",
       "      <td>0.064930</td>\n",
       "      <td>0.250400</td>\n",
       "      <td>0.071460</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>13.370000</td>\n",
       "      <td>18.840000</td>\n",
       "      <td>86.240000</td>\n",
       "      <td>551.100000</td>\n",
       "      <td>0.095870</td>\n",
       "      <td>0.092630</td>\n",
       "      <td>0.061540</td>\n",
       "      <td>0.033500</td>\n",
       "      <td>0.179200</td>\n",
       "      <td>0.061540</td>\n",
       "      <td>...</td>\n",
       "      <td>25.410000</td>\n",
       "      <td>97.660000</td>\n",
       "      <td>686.500000</td>\n",
       "      <td>0.131300</td>\n",
       "      <td>0.211900</td>\n",
       "      <td>0.226700</td>\n",
       "      <td>0.099930</td>\n",
       "      <td>0.282200</td>\n",
       "      <td>0.080040</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>15.780000</td>\n",
       "      <td>21.800000</td>\n",
       "      <td>104.100000</td>\n",
       "      <td>782.700000</td>\n",
       "      <td>0.105300</td>\n",
       "      <td>0.130400</td>\n",
       "      <td>0.130700</td>\n",
       "      <td>0.074000</td>\n",
       "      <td>0.195700</td>\n",
       "      <td>0.066120</td>\n",
       "      <td>...</td>\n",
       "      <td>29.720000</td>\n",
       "      <td>125.400000</td>\n",
       "      <td>1084.000000</td>\n",
       "      <td>0.146000</td>\n",
       "      <td>0.339100</td>\n",
       "      <td>0.382900</td>\n",
       "      <td>0.161400</td>\n",
       "      <td>0.317900</td>\n",
       "      <td>0.092080</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>28.110000</td>\n",
       "      <td>39.280000</td>\n",
       "      <td>188.500000</td>\n",
       "      <td>2501.000000</td>\n",
       "      <td>0.163400</td>\n",
       "      <td>0.345400</td>\n",
       "      <td>0.426800</td>\n",
       "      <td>0.201200</td>\n",
       "      <td>0.304000</td>\n",
       "      <td>0.097440</td>\n",
       "      <td>...</td>\n",
       "      <td>49.540000</td>\n",
       "      <td>251.200000</td>\n",
       "      <td>4254.000000</td>\n",
       "      <td>0.222600</td>\n",
       "      <td>1.058000</td>\n",
       "      <td>1.252000</td>\n",
       "      <td>0.291000</td>\n",
       "      <td>0.663800</td>\n",
       "      <td>0.207500</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 31 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       mean radius  mean texture  mean perimeter    mean area  \\\n",
       "count   569.000000    569.000000      569.000000   569.000000   \n",
       "mean     14.127292     19.289649       91.969033   654.889104   \n",
       "std       3.524049      4.301036       24.298981   351.914129   \n",
       "min       6.981000      9.710000       43.790000   143.500000   \n",
       "25%      11.700000     16.170000       75.170000   420.300000   \n",
       "50%      13.370000     18.840000       86.240000   551.100000   \n",
       "75%      15.780000     21.800000      104.100000   782.700000   \n",
       "max      28.110000     39.280000      188.500000  2501.000000   \n",
       "\n",
       "       mean smoothness  mean compactness  mean concavity  mean concave points  \\\n",
       "count       569.000000        569.000000      569.000000           569.000000   \n",
       "mean          0.096360          0.104341        0.088799             0.048919   \n",
       "std           0.014064          0.052813        0.079720             0.038803   \n",
       "min           0.052630          0.019380        0.000000             0.000000   \n",
       "25%           0.086370          0.064920        0.029560             0.020310   \n",
       "50%           0.095870          0.092630        0.061540             0.033500   \n",
       "75%           0.105300          0.130400        0.130700             0.074000   \n",
       "max           0.163400          0.345400        0.426800             0.201200   \n",
       "\n",
       "       mean symmetry  mean fractal dimension     ...      worst texture  \\\n",
       "count     569.000000              569.000000     ...         569.000000   \n",
       "mean        0.181162                0.062798     ...          25.677223   \n",
       "std         0.027414                0.007060     ...           6.146258   \n",
       "min         0.106000                0.049960     ...          12.020000   \n",
       "25%         0.161900                0.057700     ...          21.080000   \n",
       "50%         0.179200                0.061540     ...          25.410000   \n",
       "75%         0.195700                0.066120     ...          29.720000   \n",
       "max         0.304000                0.097440     ...          49.540000   \n",
       "\n",
       "       worst perimeter   worst area  worst smoothness  worst compactness  \\\n",
       "count       569.000000   569.000000        569.000000         569.000000   \n",
       "mean        107.261213   880.583128          0.132369           0.254265   \n",
       "std          33.602542   569.356993          0.022832           0.157336   \n",
       "min          50.410000   185.200000          0.071170           0.027290   \n",
       "25%          84.110000   515.300000          0.116600           0.147200   \n",
       "50%          97.660000   686.500000          0.131300           0.211900   \n",
       "75%         125.400000  1084.000000          0.146000           0.339100   \n",
       "max         251.200000  4254.000000          0.222600           1.058000   \n",
       "\n",
       "       worst concavity  worst concave points  worst symmetry  \\\n",
       "count       569.000000            569.000000      569.000000   \n",
       "mean          0.272188              0.114606        0.290076   \n",
       "std           0.208624              0.065732        0.061867   \n",
       "min           0.000000              0.000000        0.156500   \n",
       "25%           0.114500              0.064930        0.250400   \n",
       "50%           0.226700              0.099930        0.282200   \n",
       "75%           0.382900              0.161400        0.317900   \n",
       "max           1.252000              0.291000        0.663800   \n",
       "\n",
       "       worst fractal dimension      target  \n",
       "count               569.000000  569.000000  \n",
       "mean                  0.083946    0.627417  \n",
       "std                   0.018061    0.483918  \n",
       "min                   0.055040    0.000000  \n",
       "25%                   0.071460    0.000000  \n",
       "50%                   0.080040    1.000000  \n",
       "75%                   0.092080    1.000000  \n",
       "max                   0.207500    1.000000  \n",
       "\n",
       "[8 rows x 31 columns]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "train, test, train_labels, test_labels = train_test_split(df[feature_names], df['target'], test_size=0.33, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "scaler = StandardScaler()\n",
    "scaler.fit(train)\n",
    "\n",
    "train = scaler.transform(train)\n",
    "test = scaler.transform(test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 0, 1, 1, 0, 0, 0, 1, 1])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logit = LogisticRegression(solver='lbfgs')\n",
    "logit.fit(train, train_labels)\n",
    "preds = logit.predict(test)\n",
    "preds[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.36048257, -0.37928706, -0.34239942, -0.40981403, -0.0701941 ,\n",
       "         0.6382286 , -0.79808635, -1.0985293 ,  0.15315188,  0.11908427,\n",
       "        -1.17747141,  0.22238149, -0.70866434, -0.81444289, -0.20651383,\n",
       "         0.53205463,  0.04447138, -0.43698303,  0.49799868,  0.59437411,\n",
       "        -0.76099683, -1.28013819, -0.56382538, -0.71579019, -0.5415975 ,\n",
       "         0.09222063, -0.97554811, -0.74688349, -1.16159623, -0.11296927]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logit.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9787234042553191"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logit.score(test, test_labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 66,   1],\n",
       "       [  3, 118]], dtype=int64)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import confusion_matrix\n",
    "from sklearn.metrics import precision_score\n",
    "from sklearn.metrics import recall_score\n",
    "\n",
    "confusion_matrix(test_labels, preds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9915966386554622"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "precision_score(test_labels, preds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9752066115702479"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "recall_score(test_labels, preds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              precision    recall  f1-score   support\n",
      "\n",
      "           0    0.95652   0.98507   0.97059        67\n",
      "           1    0.99160   0.97521   0.98333       121\n",
      "\n",
      "   micro avg    0.97872   0.97872   0.97872       188\n",
      "   macro avg    0.97406   0.98014   0.97696       188\n",
      "weighted avg    0.97910   0.97872   0.97879       188\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import classification_report\n",
    "print(classification_report(test_labels, preds, digits=5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import roc_curve, auc\n",
    "\n",
    "probs = logit.predict_proba(test)\n",
    "\n",
    "fpr, tpr, _ = roc_curve(test_labels, probs[:, 1]) # z pravdepodobnosti vypocitam body roc krivky\n",
    "roc_auc = auc(fpr, tpr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(fpr, tpr, lw=2, label='ROC (area = %0.2f)' % (roc_auc))\n",
    "\n",
    "plt.plot([0, 1], [0, 1], linestyle='--', lw=2, color='k', # nahodny klasifikator by spravil rovnu ciaru\n",
    "         label='Luck')\n",
    "\n",
    "plt.xlim([-0.05, 1.05])\n",
    "plt.ylim([-0.05, 1.05])\n",
    "plt.xlabel('False Positive Rate')\n",
    "plt.ylabel('True Positive Rate')\n",
    "plt.title('Receiver operating characteristic example')\n",
    "plt.legend(loc=\"lower right\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9972862957937585"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import roc_auc_score\n",
    "roc_auc_score(test_labels, probs[:, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Logarithmic loss (Logloss)\n",
    "\n",
    "Používa sa v prípade, ak máme algoritmus, ktorý predikuje pravdepodobnosť toho, že nejaké pozorovanie patrí do triedy (ako napr. logistická regresia). Vieme vtedy penalizovať model proporčne k tomu, ako si je istý svojou predikciou.\n",
    "\n",
    "Penalizácia za nesprávne zaradenie do triedy závisí od toho, ako veľmi sme si istí, že to tam patrí.\n",
    "\n",
    "$$log loss = -\\frac{1}{N}\\sum_{i=1}^N {(y_i\\log(p_i) + (1 - y_i)\\log(1 - p_i))}$$\n",
    "\n",
    "https://towardsdatascience.com/understanding-binary-cross-entropy-log-loss-a-visual-explanation-a3ac6025181a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.09569674356226468, 0.09754065232344436)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.model_selection import cross_val_score\n",
    "\n",
    "model = LogisticRegression(solver='lbfgs')\n",
    "results = cross_val_score(model, train, train_labels, cv=10, scoring='neg_log_loss')\n",
    "(results.mean(), results.std()) # cim mensia hodnota, tym lepsie"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Klasifikácia do viacerých tried (multiclass classification)\n",
    "\n",
    "Ide o prípad, že mám viac ako 2 triedy. Nemýliť si s multi-label klasifikáciou (pri nej jedno pozorovanie môžem priradiť naraz do viacerých tried)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "##  Ako zovšeobecniť binárny klasifikátor na klasifikáciu do viacerých tried?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### One-vs-rest (one-vs-all)\n",
    "\n",
    "Trénujeme $k$ klasifikátorov, v ktorých pozorovania z $i$-tej triedy sú považované za pozitívne, pozorovania z ostatných za negatívne. Pri predikcii zoberieme výsledok klasifikátora s najvyššou istotou."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "### One-vs-one\n",
    "\n",
    "Trénujeme $k(k-1)/2$ klasifikátorov pre všetky dvojice tried. Pri predikcii zoberiem výsledok hlasovania všetkých natrénovaných klasifikátorov (triedu, ktorá vyjde najčastejšie)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Pre viac info pozrite: https://en.wikipedia.org/wiki/Multiclass_classification"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Vzťah medzi logistickou regresiou a neurónovými sieťami\n",
    "\n",
    "<img src=\"img/logit-neural.png\" alt=\"Schéma logistickej funkcie\" style=\"margin-left: auto; margin-right: auto; width:800px\"/>\n",
    "\n",
    "Zdroje:\n",
    "\n",
    "https://sebastianraschka.com/faq/docs/logisticregr-neuralnet.html\n",
    "\n",
    "https://stats.stackexchange.com/questions/43538/difference-between-logistic-regression-and-neural-networks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Čo si odniesť z prednášky\n",
    "\n",
    "Nezavrhujte jednoduché modely\n",
    "* Prekvapivo úspešné na reálnych dátach\n",
    "* Častou výhodou nižšie výpočtové nároky a jednoduchšia interpretovateľnosť\n",
    "\n",
    "Pozor na kliatbu dimenzionality (príliš veľa prediktorov) \n",
    "* Nabudúce sa preto ešte pozrieme na **výber atribútov**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Zdroje\n",
    "\n",
    "G. James, D. Witten, T. Hastie, R. Tibshirani (2017). Introduction to Statistical Learning with Applications in R. https://www-bcf.usc.edu/~gareth/ISL/ (hlavne kap. 3 a 4)\n",
    "\n",
    "V Pythone: \n",
    "* https://github.com/JWarmenhoven/ISLR-python \n",
    "* https://github.com/sujitpal/statlearning-notebooks\n",
    "* https://github.com/mscaudill/IntroStatLearn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<img src=\"img/linear-regression-xkcd.png\" alt=\"Lineárna regresia na XKCD\" style=\"margin-left: auto; margin-right: auto; width:800px\"/>\n",
    "\n",
    "Zdroj: https://xkcd.com/1725/"
   ]
  }
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