boston-housing-regression-notebook.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from pandas import DataFrame,Series\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline \n",
    "from sklearn.linear_model import LinearRegression, Lasso, Ridge, ElasticNet, SGDRegressor\n",
    "from sklearn.datasets import load_boston\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.model_selection import train_test_split\n",
    "import statsmodels.api as sm\n",
    "from scipy import stats\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "#from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pretty_print_linear(coefs, names = None, sort = False):\n",
    "    if names is None:\n",
    "        names = [\"X%s\" % x for x in range(len(coefs))]\n",
    "    lst = zip(coefs, names)\n",
    "    if sort:\n",
    "        lst = sorted(lst, key = lambda x:-np.abs(x[0]))\n",
    "    return \" + \".join(\"%s * %s\" % (round(coef, 3), name) for coef, name in lst)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def load_data():\n",
    "    boston = load_boston()\n",
    "    print (boston.DESCR)\n",
    "    X = boston[\"data\"]\n",
    "    Y = boston[\"target\"]\n",
    "    names = boston[\"feature_names\"]\n",
    "    return X,Y,names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def scale_data(X):\n",
    "    scaler = StandardScaler()\n",
    "    X = scaler.fit_transform(X)\n",
    "    return X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def split_data(X,Y):\n",
    "    X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size=0.33, random_state=42)\n",
    "    return X_train, X_test, Y_train, Y_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def root_mean_square_error(y_pred,y_test):\n",
    "    rmse_train = np.sqrt(np.dot(abs(y_pred-y_test),abs(y_pred-y_test))/len(y_test))\n",
    "    return rmse_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_real_vs_predicted(y_pred,y_test):\n",
    "    plt.plot(y_pred,y_test,'ro')\n",
    "    plt.plot([0,50],[0,50], 'g-')\n",
    "    plt.xlabel('predicted')\n",
    "    plt.ylabel('real')\n",
    "    plt.show()\n",
    "    return plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_regression_values(model, X, y):\n",
    "    params = np.append(model.intercept_, model.coef_)\n",
    "    predictions = model.predict(X)\n",
    "    newX = pd.DataFrame({\"Constant\": np.ones(len(X))}).join(pd.DataFrame(X))\n",
    "    MSE = (sum((y - predictions) ** 2)) / (len(newX) - len(newX.columns))\n",
    "\n",
    "    # Note if you don't want to use a DataFrame replace the two lines above with\n",
    "    # newX = np.append(np.ones((len(X),1)), X, axis=1)\n",
    "    # MSE = (sum((y-predictions)**2))/(len(newX)-len(newX[0]))\n",
    "\n",
    "    var_b = MSE * (np.linalg.inv(np.dot(newX.T, newX)).diagonal())\n",
    "    sd_b = np.sqrt(var_b)\n",
    "    ts_b = params / sd_b\n",
    "\n",
    "    p_values = [2 * (1 - stats.t.cdf(np.abs(i), (len(newX) - 1))) for i in ts_b]\n",
    "\n",
    "    sd_b = np.round(sd_b, 3)\n",
    "    ts_b = np.round(ts_b, 3)\n",
    "    p_values = np.round(p_values, 3)\n",
    "    params = np.round(params, 4)\n",
    "\n",
    "    myDF3 = pd.DataFrame()\n",
    "    myDF3[\"Coefficients\"], myDF3[\"Standard Errors\"], myDF3[\"t values\"], myDF3[\n",
    "        \"Probabilites\"\n",
    "    ] = [params, sd_b, ts_b, p_values]\n",
    "    print(myDF3)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "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": [
    "X,Y,names = load_data()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.set_printoptions(precision=2, linewidth=100, suppress=True, edgeitems=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0.01,  18.  ,   2.31,   0.  ,   0.54,   6.58,  65.2 ,   4.09,   1.  , 296.  ,  15.3 ,\n",
       "        396.9 ,   4.98],\n",
       "       [  0.03,   0.  ,   7.07,   0.  ,   0.47,   6.42,  78.9 ,   4.97,   2.  , 242.  ,  17.8 ,\n",
       "        396.9 ,   9.14],\n",
       "       [  0.03,   0.  ,   7.07,   0.  ,   0.47,   7.18,  61.1 ,   4.97,   2.  , 242.  ,  17.8 ,\n",
       "        392.83,   4.03],\n",
       "       [  0.03,   0.  ,   2.18,   0.  ,   0.46,   7.  ,  45.8 ,   6.06,   3.  , 222.  ,  18.7 ,\n",
       "        394.63,   2.94],\n",
       "       [  0.07,   0.  ,   2.18,   0.  ,   0.46,   7.15,  54.2 ,   6.06,   3.  , 222.  ,  18.7 ,\n",
       "        396.9 ,   5.33]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[0:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = scale_data(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, Y_train, Y_test = split_data(X,Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Let's try Linear Regression:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Linear model:  -3.906 * LSTAT + -2.992 * DIS + 2.739 * RM + 2.043 * RAD + -2.009 * PTRATIO + -1.872 * NOX + -1.383 * TAX + -1.106 * CRIM + 1.073 * B + 0.881 * ZN + 0.822 * CHAS + 0.399 * INDUS + -0.361 * AGE\n",
      "Root Mean Square Error: 4.552364598463066\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<module 'matplotlib.pyplot' from '/anaconda3/lib/python3.6/site-packages/matplotlib/pyplot.py'>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create linear regression object\n",
    "linreg = LinearRegression()\n",
    "\n",
    "# Train the model using the training sets\n",
    "linreg.fit(X_train,Y_train)\n",
    "\n",
    "print (\"Linear model: \", pretty_print_linear(linreg.coef_, names, sort = True))\n",
    "\n",
    "# Predict the values using the model\n",
    "Y_lin_predict = linreg.predict(X_test)\n",
    "\n",
    "# Print the root mean square error \n",
    "print (\"Root Mean Square Error: {}\".format(root_mean_square_error(Y_lin_predict,Y_test)))\n",
    "plot_real_vs_predicted(Y_test,Y_lin_predict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    Coefficients  Standard Errors  t values  Probabilites\n",
      "0        22.4660            0.383    58.584         0.000\n",
      "1        -1.1064            0.431    -2.570         0.011\n",
      "2         0.8813            0.534     1.649         0.101\n",
      "3         0.3990            0.856     0.466         0.642\n",
      "4         0.8218            0.449     1.830         0.069\n",
      "5        -1.8719            0.776    -2.413         0.017\n",
      "6         2.7389            0.570     4.809         0.000\n",
      "7        -0.3614            0.705    -0.513         0.609\n",
      "8        -2.9918            0.770    -3.885         0.000\n",
      "9         2.0429            1.025     1.993         0.048\n",
      "10       -1.3829            1.170    -1.182         0.239\n",
      "11       -2.0086            0.572    -3.511         0.001\n",
      "12        1.0734            0.438     2.451         0.015\n",
      "13       -3.9063            0.783    -4.990         0.000\n"
     ]
    }
   ],
   "source": [
    "generate_regression_values(linreg, X_test, Y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Let's try Lasso Regression:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lasso model:  -4.01 * LSTAT + 2.858 * RM + -1.611 * PTRATIO + -0.91 * DIS + 0.802 * B + 0.736 * CHAS + -0.423 * NOX + -0.296 * CRIM + 0.0 * ZN + -0.0 * INDUS + -0.0 * AGE + 0.0 * RAD + -0.0 * TAX\n",
      "Root Mean Square Error:  4.845345289310666\n"
     ]
    },
    {
     "data": {
      "image/png": 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IjC+8uAl6cO6VG1fq+f8+XxmEthzVUj8/Osx+hUuo4hKOn8nQlJrbROBl0dBeoJ2qngy0AC4UkTOAx4FnVLUxsAXo5mEMxpScH+3YC4uDwpWjw0Hrd+/fzf2z7+ekkScxb808nuv4HPNvmc/pv6aH3zc9zPriWvFEmmMXbOiHZOImW5R2ATKAL4HTgY1AucD6M4H3i9vf3giML+L9RhDu6Tt0CRTvTPlmih4z9BhlEHr9W9fr2m1r/zjOeeeF3/e88w49p0j4bUWii9PeEhISCfBGgIiki8hiYD0wA/ge2Kqq+YFNfgGOjrBvdxFZICILNmzY4GWYxoQX74rNcE/nIX6ucoArx1/JRa9dRPm08sy6cRZ5f8mjbrW6f2z03Xfhdw63PlLb/6L6BNjQD0nH00SgqgdUtQVQDzgNaBpuswj7jlbVbFXNrl3bhsE1PohULOJVO/Yiipz2p8GTraBpL2Hqt1N5tN2jfJX7Fe0atXN/nHDrS5LsbOiHpBOXDmWqulVEPgTOAKqLSLnAW0E9YG08YjCmRHJy4teBKcKQCp80gNyLYVkduCSjBcNueZuG1RtGfZywT/kl6bRlQz8kHc/eCESktohUD/xcGWgPLAdmA1cFNusCTPQqBmOKlEhj3eflwY4dB61aXwVuuhzO6Qo7Kqczse4dTPrHl+GTQPC17Njh9P4NVtRTfk5OdH0CrC9A8nFTkVCSBWgOLAK+ApYC9wfWH4PTrPQ74D9AxeKOZZXFJuYSqcIzJJZ8QUdmo9X7iZYflK79Z/bXHXt3uN5fQbVCBdXMTO/a6ltfgDIBl5XFNsSESU2JNNRBUCwL6zrFQPOPhrbrKjL84UU0rR2uai38/gexYRtSng0xYUxRiqvwjGex0erVbK0EvTrCabfA6sMh7y2YNXpv8UkgOGa3640JYYnApKaimk3m5UHXrgfPwNW1qyfJQFXJa1OTJrfBiFOh53xY8TxcvwSkZqa7ZFSSJqDGBLFEYFJTURWevXsfPMQyON97945pCMs3LKfdv9txw7mbyNqWxvwXYdhUqL4HZ5jnbdvcTQdplbemlCwRmNRUVB+BTZvC7xNpfZR27ttJ/5n9OXnUySz+dTGjOo3i09b/x58rBMVSrRrs33/wjpE6bcW7v4NJPm5qlP1erNWQ8Uy41i9FDfFQ1H4uTFg+QRs800AZhN404Sb9bcdv4WOKdP6ihn4wJgQuWw3ZDGUmdRXWBRQWAxXWBVSpAjt3Hrp9ZqazT+/eB78dRJp3Ny/vfx21fmxWl95djuDdXYs4sc6JfHzTx7TOah0+psJjhWPl/sYDlghM6opUFxC6DpwK26uvhptvPrTIBpximxtvdH7OyfnfDX3v3l08dTY8cs5a0rau5Z91r+f27v9H+fTyhx4Dih5vyMr9jUcsEZjUFU2Zf0EBjBxZ/DZduzo/DxjArCN20bMTrKwFV34Nz0yD+jXmwm0RkgAU3eTTyv2NR6yy2PgjkYZ3iKV9+1j3yD1cn72K9l2cweKmjIU3x0P9bRTftj9S0U9WliUB4xlLBKb0or2pF5aDu2ka6aXMzJgeLj8NnjsNmly+hreawQMfwtIR0DF49OfiyvjLalPQZE3sqcJNjbLfi7UaSmAlGbPHzykggxXXQiiK5fOj0ZZ/RxmEdrilkn7z8j9LPpZRWRvHJ5HGbTIHwe85i2O5WCJIYCW5qZdkVqySKu6mWsoEsKky2v1iVB5Aj+qLjm9eTgtefdXduWN9LX5JlMRuDhGTRAD8pajFzQlisVgiSGAluamX5sZR1M0w9He5ucU/qZYwARwQ9OUWaK1/oOn3o307oNtqVPHu5pzIT93xTOwmKm4TQXGthi4pqlQJeLuUJVOmrCvJJCWDBzt1AsHNJN2UgxfWLRTuF9x+Hw793ahRzi0pWHDv3BJOrbikjjNC6NwG0Go1jJwMzTObweZlJTqeK0VND+l3JbJNVFP2uckWfi/2RpDASvqkWpJijszMyG8Skd4yIi3FTRIfZtlWAb2zg/MGkHm380ZwQIK2yc0t/b9nJIn81J3IbyspjljPRyAinYATgEpBSeQhb9LTwWw+ggQX1IPW1VSHJT3HDTeE/53IoU/+RUlPhwMHXG+uwFvNoM+FsOYwuGUhPDYTMneHOW5+vvs4opHocw7E42/ARC2m8xGIyCjgGqAXIEBnIKtUEZrkETrVIcS+KWFRxTg1azrJwK0oksB3NaHjDdD5aqi9Ez57CUa/GyYJRHncqCV6s9Jop7s0CcVtP4JWqnojsEVVHwTOBOp7F5Yps7zqI1BUR6wtW6J7I4iUNDIz/9e3YE85GNSxMif2SufTBsLQqTD/RTjjlyKOm57uPoZo2QijqSXe/TLclB8B8wKfnwNHARWBb93sG4vF6gjKEC+aEo4dq5qeHnWZfpFLaJl7UJn21G+n6rFDj1UGode+ea2u2bbGXR2El3UEidp01MReDOtciGU/AmAgUB24EvgVWAc87GbfWCyWCMqQWFdqhvufIlZLyI315/8bqld1yVAGocfdUU5njO5X/HWBk6S8TgJWGZs6Yvgw5TYRRD15vYhUBCqp6u+xeScpnlUWlyGxrtSMdLzSCopn/4H9DLvnXB6o+BkHBO77GO76FCpWzPij+MXPytpEryg2sZWWFr6oU8Spg4lCrCuLM0RkoIi8qKp7gToicnFUEZnUEOtKTS8mYA+KZ87qOZzyxLHcVe0z2vwEXw+HAZ9AxQMc3OfAz8pam5w+tfgwB7XbyuJXgL04lcQAvwCPeBKRKdtiXanpxR9/5cpsOLCNrhO70vqV1vy+eS0TxsG7r0GjrSHbFt5s/aystcnpU4sfDx1uyo8IlDMBi4LW/dfNvrFYrI4ghbmpIyiq/D5kOSDoC6egNe5Byz2Qpv3+cpjuKF9MPYLfrI4g9cSocQAxnqpyn4hUxulbg4gci/OGYIy3Cp+4BwyIXFfgsp5r0ZFw68XwRT1o8yMMn1JAsw3bIu8gkhjt9IP/DazDVmrIyYnrf99ii4ZERIBRwDSgvojkAbOAuz2OzSSzaNpJF3ZWysoq0al+rwi3d4Ts7vBTdXj1bfhgDDTbUMROInDrrYlzs7UOW8ZDxb4RqKqKSG+gA3AGTs/i3qq60evgTBKKZvL3UIMHRx5mIligU5hu2sS4k+DODvBbVegxHx75AKrvcRFnzZpw1lkuNjSm7HNbWfw5cIyqTlbV9ywJmBIp7HUcbq7g4BY6ofvUquU8obtJAgCbN7NixRzaj2lHzpVQb1c6X7wIz09xmQTAidGPWdOM8YHbRNAW+ExEvheRr0RkiYh8VdQOIlJfRGaLyHIRWRZ4q0BEaorIDBH5NvBZo7QXYRJYcBFQly6HDqUcLLQ5ZF6eMxl8FJPM7yoPA9oqzYc1ZeGqzxlx0Qg+f+EA2WtLEHuk5GRMknGbCDoCxwLtcOYouJii5yoAyAfuVNWmOEVKPUWkGdAPmKWqjXHqGvqVJHDjsViMdRI67lBxg7KFNofs3Rv27XN9unePg2Y94dFz4LolsHKYkvvNYaTXL6ZuoagB66ytvkkFbpoWxWIBJgLnAyuBuoF1dYGVxe1rzUfjLFbNFaOZIyD4+GPHRp57IMzyY3X00mud+YKb9UA/zApp/jl2bOQmpoXNQ226RZOEcNl81O0bQamISEOgJTAPOEJV1wWS0DqgTjxiMFEoajasQm7eGKJ5mq5c+Y/j3nyzq+Kgfekw5GznLWDmMfDEdFg8Cs4NbmW6erVTAX3rrYc++Qd30kn0YZ6N8ZKbbFGaBagKLCQwxzGwNeT3WyLs1x1YACxo0KCBN+nShFfcwHFu3xhKMmtYlSqutv2gIdqkp/MWcMU16KrDI2wb/ERfXCcdG+HTJBliOfpoSRegPPA+0DdonRUNJarCG2FxvWzdFqOMHataoUJ0yaCYZV1VNOcvTgJo1Bt9r3Ex+2Rm2g3dpCy3icBtz+KoBTqi/QtYrqpPB/1qEtAFGBL4nOhVDCYKoRPDhwouJolmEDR11+u3OAcERp4mDGir7CkHAz+C/p9A5dCZIUOnrSxsBgrWCcuYCLysIzgL+CvQTkQWB5aLcBLA+SLyLU7l8RAPYzBuhasXKBQ6wJrbQdAGDID9+8NvG8XUkl8cDafdAr06KqftrsmSiUfx0OwwSQDCJ55EawYa79mnjCmGZ28EqjoHpxdyOOd5dV5TQpGe8kUOHvM+Lw927Dh0u3AVq0VVFt96K4wcWWRIWyrBvefBC9lw5A54/T9w9bLNSG4ubJsS3TwFidIMNPTNy22vamM8FJdWQ8ZHbp8+i3rKLzxGYe/e0BY9mZnhh2SOdMysLGf4hrTwf34KjDkZju8Fo0+B3p/DiufhmmWBJ4vRoyO38gkML+H6+uLNTYssY+LNTUWC34tVFpdQNP0BIm2bm1v8MNBVqkR3/iKOuaQO2vpmpzL4zG7ooiMjnLPw+KGtfBJ9yOZYT+VpTBFIhFZDsVosEZRQtJ2kwt1Y3TYBDb7RBh8nM9NZijnm9groP85Hyw1Ea96NvtTSmTsg7LnS04uOOzc3cZuBWsc1E0eWCExsnj7dTvpSeMMN1yM49Ik86JgFoG81Revd4bwFdLsU3ZAR2C9Sn4LgieIT/Q0gVFmL15RplghM5KfPzEz3T8zRdAorKmkEP/EGjvldDbRjjpMAmt+Kzq0ftH358k5cubnOG0Dhm0BwEigqvkR+wraOayZOLBGY8E+f5csf2smrqCdSN1NFuk0SAbv//bI+2L68VrwPrdoffeYMdH9aSKJy2+vXytyNichtIrBWQ8ks3ITrhx126IieRbVaCT1GlSoliyXQamf699NpvvUxHjh7P5evzmDFcOizLoty/x77x21848aDWyCFjmJa2OQyL8+ZQKaI8xljiidO0khs2dnZumDBAr/DSA5pac7NNJSIMw2iG3l5f8yfW7Nm8QPEZWSwZsQQ+laZw/hl42lcszHDLxrO+cee7+58DRuG7zOQlubEHTq8dfny8Mor1i7fpDwRWaiq2cVtZ28EZV20vVTd9gouSvD8uVWrFrlpfq2aPPPEFTRZey+TVk7i4bYPsyR3ifskAJE7gxUUhJ/j4LDDLAkYEwVLBGVZUUUmkcR6uOUieuzOvf1yTnm4Hn035tG6QWuW9VjGfefcR8VyFf+IvzSd3SLZvDm67Y1JdW4qEvxerLI4gpK2mHHTasVty5YwMWzIQLt2rqgMQus9XU/f/vptLSgoOPT40XR2i2YU00RuMWRMHOGystjqCMqyWJT3hxNuJNIKFZyy9507ne9VqkClSk79QGDEzwKBl1vCPefDtsrp9G11JwPPHUjVCmGKjyKV+2dl/TG2UWFdRDRjCmVkhB/uwpgU5LaOwLNB50wcNGgQ/iZZ2hYz4cbD2bfv4NZGO3f+kRRUWXwk5HaCz+vDOZWaMOLmNzmhzgmRz1HcUNbFDYtdqEIFqFbNKQ5q0MAp4rIkYExUrI6gLPNqesUoRurcVhH6XAindIfva6Ux5vIxfHj310UnASi+0rqoYbGD7dvnVFi/+qrzJmFJwJioWSIoy8L1E4hFsYiLNwoFXj8RmtwGw06Hvy+ElcMKuPHkGxE3cw0Ul8SiGTbaTSW5MSYiSwRlXXBTzlg9EYe7SQf5JhM6/BWuuwqO2g7zXoQRk6FGnSz35yguiUVbvGVDORtTYpYIzKFCb9KBMf53l4OBbeGkXJh/NDw/2UkCp66lZEVSRSWxcMmouDeNRJl8pjg2Q5lJMJYIzB+Cb1ADBjg344IC2LiRyb0v4oSe8Mi5cPUyZ6KYnvMhXYldkVSwcG8Mr77qtJLKivDmURaGlShJ3w9jPGbNR40jXCudjAxWD3+U3pU/ZMKKCTQtfxQjJh2gzRfr/W2hEyHWMtFs1E2zWWNixG3zUUsExhFyg9qXDs+cAQ+1EciozP3n3M8dZ95BhfQK/sUYLHi8o7LUbNSrvh/GhGH9CEx0gsrXP8qCHp3g6zpw2Qpl6MivyaoeRUVwPOTklI0bfyiv+n4YUwpWR2AcNWvyWxW48QpoczPsKg+TXoMJMzITLwmUZV71/TCmFCwRJAIvW5G4OPaBggOMOGkPx/dy+gYM+BiWjYBLvvH2vKXavqzyqu+O8h5AAAAPhklEQVSHMaXhZkAiv5ekHnTOyzlsXRx7/pr5mj06WxmEtrsRXZEZYRC3aKZVjPaabB5fYzyBTVXpk2jno/Vyzt0ijr1512bt8V4PlUGiR/7zSH2tTS0tcDMPsZsbdLTXVBbnHTamDHCbCKxoKJZK0ka8uMHXSiPMMRR4tfoqmgxvwqiFo+h1Wi9W9FzBdX97FgnXgUtDWri46cHr9poKi4MijS5aVjqIGVPGWSKIpXADpRV344zFjGEuj72sNrS5yakQblS9EQtuWcDQjkM5vNLh4cuuQ5NAoeJu0G6uKThpRnscY0xMWSKIpZI83XvZiiRw7J3loV97aHErLDkCRtfuxqfdPqVl3ZYHbx865ENJe/C6uabiRhe1ljTGxI+b8qOSLMDLwHpgadC6msAM4NvAZw03xyozdQRezhhWgm0LCgr0nVF9tP5d6cogtOv1VXT9mBHuj1WaStzijh1a9xD672UVxcaUGn5XFgPnAH8OSQRPAP0CP/cDHndzrDKTCLxu/RLF8b/f/L12yuukDEJPGnGSzlk1p2THirby2y2rIDbGc74nAicGGoYkgpVA3cDPdYGVbo5TZhKBqnc3TlVXN889+/fowx89rJUeqaRVH62qT336lO7L31eiY3nKmowa4zm3icDTsYZEpCHwnqqeGPi+VVWrB/1+i6rWKO44NtZQQKRhmAPj1Mz8YSY9p/Tkm03f0LlZZ56+4GnqHVYv/D6JMOZNWR0vyJgyosyPNSQi3YHuAA2s9Yhz0wzXnBNYW786fbtU4Y1jdvGnbeWYdvzdXND58aKPlwhj3pTV8YKMSTLxbjX0m4jUBQh8ro+0oaqOVtVsVc2uXbt23AJMWAMGHJIE8tNg6OnQJGcLExrs4sHZsGRYPhfc8XzxQzTYmDfGmIB4J4JJQJfAz12AiXE+f9kV8vT+WT3I7g59OkKrn2HpCLj/I6iUj7tOXzbmjTEmwLOiIREZB7QBaonIL8ADwBBgvIh0A1YDnb06f1IJKhbaVNnpE/DSKXD0NnjzDfjLcjik9sBNr1wrmjHG4GEiUNXrIvzqPK/OmbQGDKAA5ZWWcM/5sLUS3DUX7v8YqlXNBDYduo/VqxhjXLKexWXAV3tW0fpm+Ntl0HQDLBoFT86AanuBoUOtrN8YUyqWCBLY9r3b6ft+X/78d/gmE16ZAB+/AicVVrFnZVlZvzGm1CwRxFoMJlhRVcYvG0+T4U149vNn+Vv1dqz8V2VuWhxUFxD81B86RpAlAWNMFCwRxFJJhqEO8e2mb7kw70KuefMajqhyBJ91+4xRd8yi5rAX3T/1p8psX8aYmPC0Z3GslJmexZHG1s/Kcp7Ui7B7/26GzBnCkLlDqFSuEoPbDSY3O5f0tPToYihMRsEje2ZkWHGRMSnIbc9iSwSxVMJhG6Z+O5Xbpt7GD1t+4PqTruef5/+TutXqliyGUiQjY0xyKfNDTJRJUQ7b8PPvP9Pn/T68vfxtjs88nlk3zqJdo3ali8HLGc+MMUnJ6ghiyeWwDfsP7OfJuU/SdHhTpn47lUfbPcpXuV+VPgmAtzOeGWOSkiWCWHLRlPOTVZ/Q8oWW3D3zbto1asfXPb+mf+v+VEivEJsYbAwhY0yUrGgo1iIM27B+53runnE3Y/47hqzDs5h47UQuPf5Sb2KoXPmPyuLMTKfTmVUUG2MisETgsQMFB3jxyxfpP6s/O/ftpP/Z/RnQegBVKlSJ/cnCtRjavTv25zHGJBVrNeShhWsX0mNKD75Y8wVtG7Zl+EXDaVq7qXcntBZDxpgg1mrIR1v3bGXgBwMZsWAEtTNqk/eXPK478Tok0gxjsWIthowxJWCJIIZUldeWvMad0+9kw64N9Dy1Jw+1fYjqlaoXv3MsJMKsY8aYMsdaDcXI8g3Laffvdtzwzg1kVc9i/i3zGdZxWPySAFiLIWNMidgbQSnt3LeTRz5+hKc+e4oqFaowqtMo/vbnv0U/NEQsFLYMsgnhjTFRsERQChNXTOT2abez+vfV3NTiJh5v/zh1qtTxNyibdcwYEyVLBCXw45Yf6T2tN+9+8y4n1jmRj2/6mNZZrf0OyxhjSsQSQRT25u/lqc+e4pGPHyFN0njy/CfpfXpvyqeX9zs0Y4wpMUsELs36YRY9p/Rk5aaVXNn0Sp654BnqH17f77CMMabULBEUY932ddw5/U7GLR3HMTWOYcr1U+jYuKPfYRljTMxYIoggvyCfkfNHct/s+9iTv4cHzn2Ae866h8rlK/sdmjHGxJQlgjDm/TKP3Mm5LPp1ER2O7cDzHZ+ncWZjv8MyxhhPWCIIsnn3ZvrP7M+LX75I3Wp1GX/VeK5qdpX3Q0MYY4yPLBEABVrAmMVjuHvm3WzZvYU7zriDQW0GUa1iNb9DM8YYz6V8Iljy2xJyJ+cy9+e5tKrfipGdRtL8iOZ+h2WMMXGTsolg+97tPPjRgzz7+bNUr1Sdly99mS4tupAmNvySMSa1pFwiUFXeWv4Wfab1Yc32Ndzy51t47LzHyMzI9Ds0Y4zxhS+PvyJyoYisFJHvRKRfvM773ebv6JjXkc7/6UztKrX5rNtnjL5ktCUBY0xKi/sbgYikA8OB84FfgPkiMklVv/bqnHvy9/D4nMd5bM5jVEivwNALh9Lj1B6US0u5FyJjjDmEH3fC04DvVPUHABF5HbgM8CQRTPtuGrdNuY3vt3zPtSdey1MdnuKoakd5cSpjjCmT/CgaOhr4Oej7L4F1MXfThJvomNeR9LR0Zvx1BuOuHGdJIJHl5TnzLqelOZ95eX5HZExK8OONIFzvLD1kI5HuQHeABiWcarHlkS1pXLMxd7W6i4rlKpboGCZO8vKge3fYtcv5vmqV8x1sfgVjPCaqh9yDvT2hyJnAIFW9IPC9P4CqPhZpn+zsbF2wYEGcIjS+aNgw/HzLWVnw00/xjsaYpCAiC1U1u7jt/Cgamg80FpFGIlIBuBaY5EMcJpGsXh3demNMzMQ9EahqPnAb8D6wHBivqsviHYdJMJGK/0pYLGiMcc+XfgSqOkVVj1PVY1V1sB8xmAQzeDBkZBy8LiPDWW+M8ZSNp2ASQ04OjB7t1AmIOJ+jR1tFsTFxYD2qTOLIybEbvzE+sDcCY4xJcZYIjDEmxVkiSATWo9YY4yOrI/Cb9ag1xvjM3gj8NmDAH0mg0K5dznpjjIkDSwR+sx61xhifWSLwm/WoNcb4zBKB36xHrTHGZ5YI/GY9ao0xPrNWQ4nAetQaY3xkbwTGGJPiLBEYY0yKs0RgjDEpzhKBMcakOEsExhiT4uI+eX1JiMgGIMzM5q7UAjbGMJyywK45Ndg1J7/SXm+WqtYubqMykQhKQ0QWqGq233HEk11zarBrTn7xul4rGjLGmBRnicAYY1JcKiSC0X4H4AO75tRg15z84nK9SV9HYIwxpmip8EZgjDGmCEmdCETkQhFZKSLfiUg/v+Pxgoi8LCLrRWRp0LqaIjJDRL4NfNbwM8ZYEpH6IjJbRJaLyDIR6R1Yn8zXXElEvhCR/wau+cHA+kYiMi9wzW+ISAW/Y401EUkXkUUi8l7ge1Jfs4j8JCJLRGSxiCwIrPP8bztpE4GIpAPDgY5AM+A6EWnmb1Se+D/gwpB1/YBZqtoYmBX4nizygTtVtSlwBtAz8N81ma95L9BOVU8GWgAXisgZwOPAM4Fr3gJ08zFGr/QGlgd9T4VrbquqLYKajXr+t520iQA4DfhOVX9Q1X3A68BlPscUc6r6MbA5ZPVlwJjAz2OAy+MalIdUdZ2qfhn4eTvOTeJokvuaVVV3BL6WDywKtAPeDKxPqmsGEJF6QCfgpcB3IcmvOQLP/7aTOREcDfwc9P2XwLpUcISqrgPnxgnU8TkeT4hIQ6AlMI8kv+ZAEcliYD0wA/ge2Kqq+YFNkvHv+1ngbqAg8D2T5L9mBaaLyEIR6R5Y5/nfdjJPTCNh1lkTqSQhIlWBt4A+qrrNeVhMXqp6AGghItWBd4Cm4TaLb1TeEZGLgfWqulBE2hSuDrNp0lxzwFmqulZE6gAzRGRFPE6azG8EvwD1g77XA9b6FEu8/SYidQECn+t9jiemRKQ8ThLIU9W3A6uT+poLqepW4EOc+pHqIlL4MJdsf99nAZeKyE84xbrtcN4QkvmaUdW1gc/1OAn/NOLwt53MiWA+0DjQyqACcC0wyeeY4mUS0CXwcxdgoo+xxFSgnPhfwHJVfTroV8l8zbUDbwKISGWgPU7dyGzgqsBmSXXNqtpfVeupakOc/3c/UNUckviaRaSKiFQr/BnoACwlDn/bSd2hTEQuwnmKSAdeVtXBPocUcyIyDmiDM0rhb8ADwARgPNAAWA10VtXQCuUySUTOBj4BlvBH2fG9OPUEyXrNzXEqCdNxHt7Gq+pDInIMztNyTWARcIOq7vUvUm8EiobuUtWLk/maA9f2TuBrOeA1VR0sIpl4/Led1InAGGNM8ZK5aMgYY4wLlgiMMSbFWSIwxpgUZ4nAGGNSnCUCY4xJcZYIjImSiOwIfB4lIm8Ws20fEcmI8vhtCkfbNCYeLBEYw/9Gq42Kqq5V1auK2awPEFUiMCbeLBGYpCciDUVkhYiMEZGvRORNEckIjP1+v4jMATqLyLEiMi0w4NcnItIksH8jEflMROaLyMMhx10a+DldRP4ZGEv+KxHpJSK3A0cBs0VkdmC7DoFjfSki/wmMmVQ4d8aKQCx/ife/kUltlghMqjgeGK2qzYFtQI/A+j2qeraqvo4zP2wvVT0FuAsYEdhmKDBSVU8Ffo1w/O5AI6Bl4Bx5qjoMZyyctqraVkRqAfcB7VX1z8ACoK+IVAJeBC4BWgNHxvTKjSlGMo8+akywn1V1buDnscDtgZ/fgP+NZtoK+E/QSKYVA59nAVcGfn4VZ3KUUO2BUYVDJEcYAuAMnEmS5gbOUQH4DGgC/Kiq3wZiGYuTWIyJC0sEJlWEjqVS+H1n4DMNZ6z7Fi73DyUut5mhqtcdtFKkhYt9jfGMFQ2ZVNFARM4M/HwdMCf4l6q6DfhRRDqDM8qpiJwc+PVcnBEwAXIiHH86cGvhEMkiUjOwfjtQLfDz58BZIvKnwDYZInIcsAJoJCLHBsVnTNxYIjCpYjnQRUS+whm5cmSYbXKAbiLyX2AZf0xt2htnbuT5wOERjv8SzsiQXwX2vz6wfjQwVURmq+oG4CZgXCCOz4EmqroHpyhocqCyeFXpLtWY6NjooybpBaa0fE9VT/Q5FGMSkr0RGGNMirM3AmOMSXH2RmCMMSnOEoExxqQ4SwTGGJPiLBEYY0yKs0RgjDEpzhKBMcakuP8H1jwz9e0vl1AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<module 'matplotlib.pyplot' from '/anaconda3/lib/python3.6/site-packages/matplotlib/pyplot.py'>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create lasso regression object\n",
    "lasso = Lasso(alpha=.3)\n",
    "\n",
    "# Train the model using the training sets\n",
    "lasso.fit(X_train, Y_train) \n",
    "\n",
    "print (\"Lasso model: \", pretty_print_linear(lasso.coef_, names, sort = True))\n",
    "\n",
    "# Predict the values using the model\n",
    "Y_lasso_predict = lasso.predict(X_test)\n",
    "\n",
    "# Print the root mean square error \n",
    "print (\"Root Mean Square Error: \", root_mean_square_error(Y_lasso_predict,Y_test))\n",
    "plot_real_vs_predicted(Y_test,Y_lasso_predict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    Coefficients  Standard Errors  t values  Probabilites\n",
      "0        22.5150            0.408    55.162         0.000\n",
      "1        -0.2961            0.458    -0.646         0.519\n",
      "2         0.0000            0.569     0.000         1.000\n",
      "3        -0.0000            0.911    -0.000         1.000\n",
      "4         0.7361            0.478     1.540         0.125\n",
      "5        -0.4230            0.826    -0.512         0.609\n",
      "6         2.8582            0.606     4.715         0.000\n",
      "7        -0.0000            0.750    -0.000         1.000\n",
      "8        -0.9101            0.820    -1.110         0.268\n",
      "9         0.0000            1.091     0.000         1.000\n",
      "10       -0.0000            1.245    -0.000         1.000\n",
      "11       -1.6107            0.609    -2.645         0.009\n",
      "12        0.8023            0.466     1.721         0.087\n",
      "13       -4.0096            0.833    -4.813         0.000\n"
     ]
    }
   ],
   "source": [
    "generate_regression_values(lasso, X_test, Y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Let's try Ridge Regression:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ridge model:  -3.902 * LSTAT + -2.979 * DIS + 2.741 * RM + 2.017 * RAD + -2.005 * PTRATIO + -1.86 * NOX + -1.361 * TAX + -1.101 * CRIM + 1.073 * B + 0.874 * ZN + 0.824 * CHAS + 0.39 * INDUS + -0.362 * AGE\n",
      "Root Mean Square Error:  4.553273945771453\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<module 'matplotlib.pyplot' from '/anaconda3/lib/python3.6/site-packages/matplotlib/pyplot.py'>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge = Ridge(fit_intercept=True, alpha=.3)\n",
    "              \n",
    "# Train the model using the training sets\n",
    "ridge.fit(X_train, Y_train) \n",
    "\n",
    "print (\"Ridge model: \", pretty_print_linear(ridge.coef_, names, sort = True))\n",
    "\n",
    "# Predict the values using the model\n",
    "Y_ridge_predict = ridge.predict(X_test)\n",
    "\n",
    "# Print the root mean square error \n",
    "print (\"Root Mean Square Error: \", root_mean_square_error(Y_ridge_predict,Y_test))\n",
    "plot_real_vs_predicted(Y_test,Y_ridge_predict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    Coefficients  Standard Errors  t values  Probabilites\n",
      "0        22.4663            0.384    58.573         0.000\n",
      "1        -1.1014            0.431    -2.558         0.011\n",
      "2         0.8743            0.535     1.636         0.104\n",
      "3         0.3900            0.856     0.456         0.649\n",
      "4         0.8235            0.449     1.834         0.068\n",
      "5        -1.8605            0.776    -2.398         0.018\n",
      "6         2.7413            0.570     4.812         0.000\n",
      "7        -0.3622            0.705    -0.514         0.608\n",
      "8        -2.9790            0.770    -3.867         0.000\n",
      "9         2.0169            1.025     1.968         0.051\n",
      "10       -1.3605            1.170    -1.163         0.246\n",
      "11       -2.0051            0.572    -3.504         0.001\n",
      "12        1.0726            0.438     2.448         0.015\n",
      "13       -3.9017            0.783    -4.984         0.000\n"
     ]
    }
   ],
   "source": [
    "generate_regression_values(ridge, X_test, Y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Now let's try to do regression via Elastic Net."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elastic Net model:  -3.337 * LSTAT + 2.801 * RM + -1.574 * PTRATIO + -1.142 * DIS + 0.851 * CHAS + 0.845 * B + -0.701 * NOX + -0.513 * CRIM + 0.196 * ZN + -0.163 * AGE + -0.052 * TAX + -0.039 * INDUS + 0.0 * RAD\n",
      "Root Mean Square Error:  4.810461359302996\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<module 'matplotlib.pyplot' from '/anaconda3/lib/python3.6/site-packages/matplotlib/pyplot.py'>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "elnet = ElasticNet(fit_intercept=True, alpha=.3)\n",
    "              \n",
    "# Train the model using the training sets\n",
    "elnet.fit(X_train, Y_train) \n",
    "\n",
    "print (\"Elastic Net model: \", pretty_print_linear(elnet.coef_, names, sort = True))\n",
    "\n",
    "# Predict the values using the model\n",
    "Y_elnet_predict = elnet.predict(X_test)\n",
    "\n",
    "# Print the root mean square error \n",
    "print (\"Root Mean Square Error: \", root_mean_square_error(Y_elnet_predict,Y_test))\n",
    "plot_real_vs_predicted(Y_test,Y_elnet_predict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Now let's try to do regression via Stochastic Gradient Descent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stochastic Gradient Descent model:  -3.33 * LSTAT + 2.788 * RM + -1.793 * DIS + -1.677 * PTRATIO + -0.981 * NOX + 0.959 * B + 0.927 * CHAS + -0.758 * CRIM + 0.595 * RAD + 0.454 * ZN + -0.432 * TAX + -0.363 * AGE + -0.111 * INDUS\n",
      "Root Mean Square Error:  4.679374006096742\n"
     ]
    },
    {
     "data": {
      "image/png": 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x8UTumissGw1XLwPJv2F8fOAH99VVdOzY4g30ioHZvkoj16qGRESA8qq6W0QSgTnAAGAgMElV3xaRscBPqvpCYceyqiETFqEaOJXHV7VJfgWqhub/OZ/eU3uTtT6Li/4qw+hJB6i/uZD9A/3/3VedvjdWvRNxwl415Gm03u1ZTPS8FGgBvO9ZPwFo71YZjCmRUA2cAifo7N5d9HaeLppb927l5k9upsn4Jvy5cSVvfZzErBeLCALFeSIIpM++DfQqtVxtIxCReBFZBGwCZgK/ATtUNduzyTrAUhuayBSqka15Tx5btxa+XXIyuUMeZfzC8Zwy6hRe/vFlbmt6G8snVOS6hQePrAbyJifH9/l9VX95q9MXH2eygV6llquBQFVzVLUhUAs4B6jvbTNv+4pITxHJEpGszZsL+5ljjEtCNbLVVyNxSsoRdek/Pn8vzQ6MoccnPTi16qn8ePOPPNP6GSr9ts6/86SlHb2uqAFe3ur0b7nFGnyjjT+DDYLxAh4E7gS2AAmedecC04va1waUGVcUNVippIO6/CXifZCVZ6DV9rJo344VNe4h0WpPVdPXF72uubm5h/f3NUjLn3IHOsArjw30KhXwc0CZmzf+qkBlz+dywGzgMuA94DrP+rFA76KOZYHABJ2/N/lQ3PB83IxzBZ1wJlrtDjTuAbTv5Qm6fcKL/l1LUpJqSkrR5fYVhESCf50m5CIhEDQAfgQWA0uABzzrawM/ACs9QaFMUceyQGCCrri/hN3g5Ua+uDp6/o0oD6FNu6MLjy+ifMUNWJH072CCLuyBIJgvCwQm6Ir6JRzqqg/P+f4ug97aoaLGP4CmDELHn4XmiIu/1ENV/WXCwt9AYHMWm9iUmuq9z35qqtNQ2q0bHDzorFu92lkG1wY+aefOvN0gjttn3M6G3RvoubwCj03eTZV9XsoXTAFMam+il6WYMLGpsFQHAwYcDgJ5Dh501ucJ4ojjXzb/wsWvX0znSZ2pWakm39/0PWMvG0sVCVHPnIwMZyBYbq7zbkEg9vjz2BDul1UNGVf4qv4prPdN3n5BqE7ZdWCXDpoxSBMeSdBjnzhWX5j/gmbnZBddPmP8hKWhNqaYfA2YAue2X8IMmqrKB8s+4Lbpt7Fu5zq6NezGEy2foGr5qsUusjHehD3FhDGlgrcqnpQU79vmrfc1stiP7J7/2/o/2mS2ocN7HUgpl8LcbnN5+YqXLQiYsLJAYGJXZibceOORo2q7dIGGDSEx8chtExNh5Ejns68GWxGfbQV7D+3lvi/u44wXzuC7dd/xXJvnyOqZxXknnhfECzKmeCwQmNg1YAAcOnT0+lmzICnJeQLIS6vw6quHG1GHDvVefaR6ZEK6zEw0PY3J9YVT76nE0NlDufa0a1nRdwX9mvQjIS6KOu2FMl23CToLBCZ2FZbkbc8e2LbNubnv3u0Ejbg4qFABrr/ed2rmvOqhzEx+v/MmLm+2hvbXQYV9OXz9Zhle39ua4yscX3i5SttNNZAJ6U1EssZiE7sKaxQuwTH3T3iZYR/cxuNn/E1iDjz8FfT7HhJzKbpBOdRzIASDTT8ZsWzOYmOKctxxRad+DtC0f0G//yTwW6Vsrl0Cz0yHmrvybVDUnMOl8aZqE9JHLOs1ZCKbG9UfgR5z5MigPRWsPgauvBbadoHEA9l8/lk13n6/QBCAokcGh2oOhGAKVbpu4xoLBCb0SlKn7OtmX9gxfe2TkVHoZPD+OBAPj10A9fvCjJPhiZnw09RULu47vHg5+wu7qUZq24FNSF/6+TPqLNwvG1kc4QIdAVuSHPhJSUfuk5R0+PzejlmhwtEJ5vKPAi5sLoAiXjNro3X7OhlCr+6Irj6mwLGLMzLY16jlXr0iOzmcjYKOSARjZLGIXFVEEJkU7MDkjbURRLDiNG4Wt07ZV51+SsrhHj7+yqtz92fC+ALWVYLbL4F3T4d/bYXnp0GblZ5yjBxZ8kbdzMyjk8ANHlz62g5M2AWlsVhEXi1kX1XVbsUpXKAsEESw4jRuFrdBtLD6/LS0gG/o/+wj4lcQORQHI5vCQ80hR+De2XDnt1C2Zpr7GTutQdYUg7+BoNARLap6Y/CKZKJScRo3hw71/hRRkjplb8csjMjhwOFHEPgqHfq0hV+qweUrYOQ0OGlH8YsbsCpVvD8NWYOsCQK/hzaKSDvgNKBs3jpVfcSNQplSpLC8/r4UJwd+YQ2jKSmH9x0wwL8uod5u/uXLO4Ek39/+qgB3XgKZDSB9O3z8Jlz+vwL75TVM57+2YMrMhF0Fux/hpL2wBlkTBH6NIxCRsUAycBEwHrgG+EFVu7tbPIdVDUWwUA2AKqwuPyUlOOMBRGDiRBg8mOy1qxnd+lgeaLiD/fHKXXPhntlQLruQ/d2qr/d17SkpsGVL8M9nokawxxGcp6r/Bbar6sPAucCJJSmgiRIZGc5NPy3tcF4eN0bBFlbVFGgQiI/3vj41FTIymPtNJmePbsCtTbZz7lplyRh45MsigkBRZSwJX8fdts2d85nwC3FXYX8DQd6EeXtF5ATgEHCSO0UypU7BGa4g+F/iYNaF5+QcvS45mU0PD+LGyTdy/qvns33fdj7o+AHTZqdSx9/7bQnHJPhkA7ZiSzhyN/nTxxS4H6gMXA1sAP4CHvVn32C8bBxBKeLWZOjexhCU9OUZQ5At6Ojm5bXyI8ma+Eii3j3zbt19YLfv6/H1Skkp+b+fr2uP5DEEJriKO87GC/wcRxDwTRkoAxwT6H4leVkgKEWC+CX+R2EDxkr4+r4menZPZ1BYi66iy/5V+ehBUQUHSxUWWNxiA7Zih69BjsX4fvkbCPxtLE4GbgdSVbWHiNQBTlHVT914SinIGotLkWD3d/fWGB0EW8vBPS1hfCOosQuGT4eOS+GIkQpJSfDKK0e3d5TGxHCm9Aji9yvYjcWvAgdwGokB1gFDAiqRiQ3Brs8ePDioQSBXnJv/Kf3glbNg4DxYPgquLRgEAA4edLqjFmS5dYybwvD98jcQnKyqT+I0EqOq+/Dy/40xQf8SB7EnzsIacF536PEfOG0TLBoLT8+AigcL2clbj6RQ9ZQysSkM3y9/A8FBESkHKICInIzzhGDMkYr6EgfaLS4IPXG2l3VGBTfuCasqw8RJ8NVrcPqmEhy0YE8pCwImmEL8/SpyZLGICDAW+Aw4UUQygWbADa6WzJReGRnev7gF6/uLGpHra0StnxR4/UxnZPDWctD3B2c8QOX9+TaKj/fenTRPSkqxz29MaVFkIHAasWUAcAnQFKdKaICq2pBGExhv9f1790LXrs7ngsFg8GCnnr4YFld3ngLmpMG5a2HGFGi4wcuGubmFJ50bObJY5zemNPE319B3QG1VneLvgUXkROB14HggFxinqiNFpArwDpAOrAI6qur2QAptSilf9f05Od6fDIrRPrCzDDzYHJ5vKhy7V3l5MtzwkxCX6+NGn9eI7SuFg1X5mBjgbxvBRcA8EflNRBaLyM8isriIfbKB21W1Ps6TRB8RORW4G5ilqnWAWZ5lE63ytwnEFfJ127vXeQLIv48fXZvzKPDmGXBKXydVdI/GN7Pi4a10W6jE5eRCr15Hp7HOa8T21cBtTwMmVvgz2ABI8/byZ998x5gMtAJWADU862oAK4ra1waUhUEwBjAFMio3b8BMoPuALq2KNu/qDApr3AP9YfzDgV+TDdgyUYhgDigrKRFJB74BTgfWqGrlfH/brqrHFra/DSgLsWBlFA109q+0NOfdz312J8EjF8KIpk4X0Mc/h5sWCfG5+Jfa2pgoF5QZyoJUkArA18BQVZ0kIjv8CQQi0hPoCZCamnr26kBnnzLFF6yRjb5GGYMzardgQ7Cf6aQVeP9UuK0N/FkJui90gkDVguPO3EiHbUwpEuyRxcUtRCLwAZCph+c33igiNTx/rwF47c2tquNUtbGqNq5ataqbxTQF+TPrmD/jAQobTawKFSocuc6PILAiBVpfDx07QtU98O14GP+xlyAAR7Y7GGN8ci0QeMYfvAwsU9Xh+f70MeDpL0hXnLYDE0mKShPhb5rcoUOdX/7eHDoE+/Z5/5sXexNhcAs4ozf8UBOenwpZ4+DcdUXs6NYcAcZEETefCJoB1wMtRGSR59UWeAJoJSK/4jQeP+FiGUwg8n7l503onl/+NBG+xgN4+/VdWNVjYQO58nYHPqoH9fvAY/8H1y2BFc87g8Pi/anVjMSc/SGedMSYIvnTohzul/UaKgF/e8N4662Tlw634H7+psktKnW0r+N4XiuPRdt2dnoDnd4L/TrN/55E/7xSUiKrB5DNLWBCCLfmIwjHywJBMQVy0/F3HoE33lCNj/dv28Ju9ImJqgkJXv+2NwF9sDla5j60wj3o8KbowTg/bvrly6tWqHD0+ki60boxX4MxPvgbCELSfbSkrPtoMQXS+8efeQQyM6FbN+9pH7z10PF1/vh4KFsW9uw56k9T60C/S+H3KtDpZyc76AmBpBvylS4iUuYKCPZ8DcYUIiJ6DZkw86f3T57CGojz6rS7dPEeBOLivHfT9DVit2fPo4LA6mOg/XXQLgOScmDWBHjzgwCDAPhuk4iURmObf9hEIAsE0SyQm46vm3bbtod7CPmSm+sEgbyAIQIJCU7gKFfOGR+QPyX11Kn/7HogHh67AOr3hZm14YmZ8NNYaPEHUL58wJfsU6TcaG1SGxOJ/Kk/CvfL2giKKdCGSW8Ny/7OFdyrl+82gYLn9Gw3ozZat6/TGHx1R3RNpQL1/fnLBKpxcf6VJZLbCFQtnYUJGayNwADOr/TBg52qkeKkXShsdHAg8tXRrzu1FgNP/5P3ToM6W50xAa1/K7B9wbYJb/MWly/vtZ3hiGNYqgkTw/xtI/A3DbUprXxNEuOv1NTA8gX5smYNB3MOMvK7kTx83RZyDsKjX8Cdc6GMt+EE+atyfM1bfNxxTqOztxHJkdI4bEwpYG0EpnDe6rSL4atzqtFwbEMGfT6Ii+u2Ztm/RnDf6jQnCBQ2eA0Kb/QeOdLq3I0pIQsEsSiQka0F5yCOjw/oVH9VgIyO8Vx06Ub2Z+/nk06fMPm6yaTfcKvzi10VJk4sfKJuX/MWV6liE8kbEwz+NCSE+2WNxUFU0pGt3vZPSnIGiOVbdygOHdEUrXivaJmHE/WBLx7QvQf3Hn0sfxpNU1K8NwKnpJTkX8KYqIeNLDZeBTKCOP9NulevI2/I+XsIlS/vvDzLs0+vpGc8dqLyENrmjTb669Zfjy5HIAGpsBHK1vPGGJ/8DQTWayjW+DuC2FsvnSJsKg+DWsGEhnBiQgojr3qJ9vXaIwXbAMC/Uc95PZ78aay2uQeMOYqNLI4VgWay9GeQma9eOj7kCIz5tzNf8JtnwD2zYdmryVxZ/0rvQQCKHvWcP9W1P2zuAWOKzQJBaebvvAD5+TOyNYB0DN/XhHN6QJ92cPZfsPgFeGwWlP+9iIkCigpIAQYjIHLSSBhTylggKM0CmRcgjz+9bPxIx7AlGXpcDk17wIYK8M57MPN1qLfFz2MUFZB83dTzyuxNpKSRMKaUsUBQmgWSVC6/jAynHj4313n3J1mcR67AS42caqDXGsIdc2H5KOi4FP6pBPKnH39RAamwJwbL12NMUFkgKM3cymTp7SZdoQILasC53aHnf+D0TbBoLDw1EypWTDk6sRwU3XZRWEAq7GZvYweMCS5/uhaF+2XdR30I0WxX2/Zu094jWqo8iFa/A53YAM0t7FzBKpclZzOmRLBxBDEimDfLAsfKmfi6vvrjq1r1yaoa93Cc9h9xie7414lFn8tm4SqcBTgTIv4GAhtHYByZmXDjjXDoEAA/VYc+lwlzT1TOO/E8xrQdw5nHn+nfsWwWLt+8jdGwMRDGJTaOwARmwAA4dIi/y8CtbaDRzbCiivLK5+WZfeNs/4MA+N92EegYiGhQnJ5exrjMAoEBQLduJfMMqNcXnmsCNy+AFaPgxjl7iDupdmA3a3969XgbA3H99c5TQzQHheL29DLGRRYIIoGbv4z9OPbSTUu56AbocjWcuBN+eAnGTIEq+zwbBDJgDfzr1ePtl3FedZK/5ymNbM5iE4n8aUgI9yuqG4vd7PlTxLF37t+pd0y/QxMeSdAqd4mWD9bVAAAPeklEQVS+eDaaI14aed1o9C0skVw0Ny6HqKeXMarWWFx6+JN8LcjH1rRU3pvyFAOnD+TPXX/S/azuPLGjMcf1GAAHDxZ93GA0+vq67mCfJxKVdPpQY/zkb2OxBYJwc7OHjZdjr0iBfm1h5slwVpk0xnxwgKYLNjo3pLZtYerUwzeo3bvdmwbSnwynNt2kMSVivYZKCzfrjPMdY08i3HsxnNEbfqgljDquK/OHbKJp1obD9f8TJji/TvNG+ro5DWT+dgQoerpKY4xrLBCEm5t5c4YORZPL8VE9OLUPPH4BdP4lnhWnjKLPU18Rv2ffkdsX7MbodiqHvBQT6sd0lcYY17hWNSQirwCXAZtU9XTPuirAO0A6sAroqKrbizpWVFcNgWt1xr9t+41+L1/NtL0/ccZGGL2gOhf0f8Y5tg36MibqRULV0GtAmwLr7gZmqWodYJZn2RSVDbQoBbqI7pv4Kg9++SCnjTmNOdm/M/yS4SwcdYgLvt/gX3ZPY0xMSXDrwKr6jYikF1h9BdDc83kC8BVwl1tliAkFGl2nJK2m/4Lu/P670un0Tjx9ydOcUPGEo/cbOtR7qgOrlzcm5oS6jaC6qv4F4Hmv5mtDEekpIlkikrV58+aQFbDU8QzMWlUZ2l8Hl2VAmWzli2nVefPqN70HAbBUzsaYf0RsY7GqjlPVxqrauGrVquEuTmTwMkr4wJ+rGXqB0xj8eW0YNtOZJ+CiHzYVfbySVkkZY6JCqAPBRhGpAeB59+NuVcq4lS7CS26eGY9154w+cdx3MbT7HywbBYPmQlIOVtdvjPFbqAPBx0BXz+euwOQQn99dxZlM3l/5cvOsqwQdOkDrjgcA+OzdMrz3npMnCLC6fmNMQFwLBCLyFjAPOEVE1olId+AJoJWI/Aq08ixHDzdTDK9Zw8F4eLKZkyF0Sl0YMgt+Hp1L63tftrp+Y0yxWYqJYHKxb/6XZx5Dnwt2sqwqXLEcnv0M0ndgaRiMMT5FwjiC2ONC3/z1u9bT+ZnzaHHVTvYnwKeZ8NHbniCQmGhVQMaYErNAEExBTBeRnZvNiHkjqDeqHpN2zOPBr2DpaGj3a76NKlWyKiBjTIlZIAimjAzo2hXi453l+HhnOcCb9Zw1c2j0YiMGzhjI+anns2QMPPQVlMsusOG2bUEptjEmtlkgCKbMTCeDZ06Os5yT4yz72Wto4+6NdP2oKxe8egF/H/ibD6/9kCmdp/Cvimned7AuosaYILBAEEzF7DWUk5vDqB9GccqoU3jr57e49/x7+aX3L7Sv1x4RCbzKKRYnhTfGFJtruYZiUjEmJv9u3Xf0ntKbHzf8SMvaLRl16ShOOe6UIzfKq1oaPNgZmxAff2SAyV/11Ls3jB179Py/BbczxhgPeyIIpgB6DW3Zu4UeH/fg3JfPZeOejbxzzTvM6DLj6CCQJyPj8JNBXtVTwQFrmZlHBoE8wRrLYIyJShYIgsmPKpxczWXcgnGcMuoUXvvpNe449w6W91lOx9M6OtVAhSmq6mnwYO/jGKDQpxJjTGyzqqFgyl+F42WSmaz1WfSe0pv56+dzYdqFjG47mtOqneb/8YuqeirsZm8Ny8YYHywQBFtGxlF18dv3bWfwF4MZmzWW6hWqk3lVJp1O71T0E0BBqalOdZC39YX9Pa/B2RhjvLCqIRflai6v/vgqdUfV5cUFL9K/SX+W91lO5zM6Bx4EoOiqJ29/F4FbbrGGYmOMTxYIXLJowyIuePUCun3cjbopdVnYcyHPtnmWY8oeU/yDFjWZjLe/T5wIY8YE56KMMVHJks4F2d/7/+aBLx9g1PxRpJRL4clWT/LfM/9LnFjMNcaElr9J56yNIEhUlcyfM7ljxh1s2rOJXo17MaTFEI4td2y4i2aMMYWyQBAESzctpc/UPny9+mvOqXkOUzpP4ewTzg53sYwxxi8WCEpg14FdPPz1w4z8fiSVylRi3GXj6N6ou1UDGWNKFQsExaCqvLv0XQbOGMj6Xevp0agHj138GMclHxfuohljTMAsEARo+Zbl9JvWj89//5xGNRoxqeMkmtRqEu5iGWNMsVkg8NOeg3sY8s0Qnpn3DMmJyYxuO5qbz76Z+Lj4cBfNGGNKxAJBEVSVj5Z/xK3Tb2XN32voemZXnmz1JNXKVwt30YwxJigsEBRi5baV9J/Wn2krp9GgegMyr8rk/NTzw10sY4wJKgsEXuw7tI8n5jzBsLnDSIpP4tnWz9LnnD4kxNk/lzEm+tidrYBP//cp/af1548df9D5jM483eppalSsEe5iGWOMaywQePyx/Q8GfDaAT/73CfWPq88X//2Ci066KNzFMsYY18V8IDiQfYCnvn2KobOHEi/xPNnySQY0HUBSfFK4i2aMMSER04Fg+srp9J3Wl5XbVtLh1A4Mbz2cWpVqhbtYxhgTUjGZC2Ht32u55t1raJPZhjiJY3qX6bzb4V0LAuGWmQnp6RAX57znzcVsjHFVWJ4IRKQNMBKIB8ar6hOhOO/BnIOMmDeCR755BFVlaIuh3H7u7ZRJKBOK05vCZGZCz56H52RevdpZBptUxxiXhXw+AhGJB/4HtALWAfOBTqr6i699gjEfwRd/fEHfqX1ZtmUZ7eu1Z0TrEaRXTi/RMU0Qpad7n2YzLQ1WrQp1aYyJCpE8H8E5wEpV/R1ARN4GrgB8BoKSWL9rPbfPuJ23l7xN7WNr82mnT2lXt50bpzIlsWZNYOuNMUETjkBQE1ibb3kd4ErWtme/e5b7v7yfQzmHeOjChxjUbBDlEsu5cSpTUqmp3p8IUlNDXxZjYkw4Gou9zdp+VP2UiPQUkSwRydq8eXOxTvTL5l/4v7T/Y2nvpTzY/EELApFs6FBITj5yXXKys94Y46pwPBGsA07Mt1wLWF9wI1UdB4wDp42gOCca1XYUiXGJiHiLPSai5DUIDx7sVAelpjpBwBqKjXFdOALBfKCOiJwE/AlcB3R240Q2KKyUyciwG78xYRDyQKCq2SLSF5iO0330FVVdGupyGGOMcYRlHIGqTgWmhuPcxhhjjhSTI4uNMcYcZoHAGGNinAUCY4yJcRYIjDEmxlkgMMaYGGeBwBhjYpwFgkhgefiNMWEU0zOURQTLw2+MCTN7Igi3wYMPB4E8e/c6640xJgQsEISb5eE3xoSZBYJw85Vv3/LwG2NCxAJBuFkefmNMmFkgCLeMDBg3zpmbV8R5HzfOGoqNMSFjvYYigeXhN8aEkT0RGGNMjLNAYIwxMc4CgTHGxDgLBMYYE+MsEBhjTIwTVQ13GYokIpuB1cXc/ThgSxCLUxrYNccGu+boV9LrTVPVqkVtVCoCQUmISJaqNg53OULJrjk22DVHv1Bdr1UNGWNMjLNAYIwxMS4WAsG4cBcgDOyaY4Ndc/QLyfVGfRuBMcaYwsXCE4ExxphCRHUgEJE2IrJCRFaKyN3hLo8bROQVEdkkIkvyrasiIjNF5FfP+7HhLGMwiciJIvKliCwTkaUiMsCzPpqvuayI/CAiP3mu+WHP+pNE5HvPNb8jIknhLmuwiUi8iPwoIp96lqP6mkVklYj8LCKLRCTLs87173bUBgIRiQdGA5cCpwKdROTU8JbKFa8BbQqsuxuYpap1gFme5WiRDdyuqvWBpkAfz3/XaL7mA0ALVT0TaAi0EZGmwDBghOeatwPdw1hGtwwAluVbjoVrvkhVG+brNur6dztqAwFwDrBSVX9X1YPA28AVYS5T0KnqN8C2AquvACZ4Pk8A2oe0UC5S1b9UdaHn8y6cm0RNovuaVVV3exYTPS8FWgDve9ZH1TUDiEgtoB0w3rMsRPk1++D6dzuaA0FNYG2+5XWedbGguqr+Bc6NE6gW5vK4QkTSgbOA74nya/ZUkSwCNgEzgd+AHaqa7dkkGr/fzwKDgFzPcgrRf80KzBCRBSLS07PO9e92NE9MI17WWRepKCEiFYAPgFtVdafzYzF6qWoO0FBEKgMfAvW9bRbaUrlHRC4DNqnqAhFpnrfay6ZRc80ezVR1vYhUA2aKyPJQnDSanwjWASfmW64FrA9TWUJto4jUAPC8bwpzeYJKRBJxgkCmqk7yrI7qa86jqjuAr3DaRyqLSN6PuWj7fjcD/iMiq3CqdVvgPCFE8zWjqus975twAv45hOC7Hc2BYD5Qx9PLIAm4Dvg4zGUKlY+Brp7PXYHJYSxLUHnqiV8Glqnq8Hx/iuZrrup5EkBEygEtcdpGvgSu8WwWVdesqveoai1VTcf5f/cLVc0giq9ZRMqLSMW8z8AlwBJC8N2O6gFlItIW51dEPPCKqg4Nc5GCTkTeAprjZCncCDwIfAS8C6QCa4AOqlqwQblUEpHzgdnAzxyuO74Xp50gWq+5AU4jYTzOj7d3VfUREamN82u5CvAj0EVVD4SvpO7wVA3doaqXRfM1e67tQ89iAvCmqg4VkRRc/m5HdSAwxhhTtGiuGjLGGOMHCwTGGBPjLBAYY0yMs0BgjDExzgKBMcbEOAsExgRIRHZ73k8QkfeL2PZWEUkO8PjN87JtGhMKFgiM4Z9stQFR1fWqek0Rm90KBBQIjAk1CwQm6olIuogsF5EJIrJYRN4XkWRP7vcHRGQO0EFEThaRzzwJv2aLSD3P/ieJyDwRmS8ijxY47hLP53gRedqTS36xiPQTkf7ACcCXIvKlZ7tLPMdaKCLveXIm5c2dsdxTlqtC/W9kYpsFAhMrTgHGqWoDYCfQ27N+v6qer6pv48wP209VzwbuAMZ4thkJvKCq/wY2+Dh+T+Ak4CzPOTJV9TmcXDgXqepFInIccB/QUlUbAVnAQBEpC7wEXA5cABwf1Cs3pgjRnH3UmPzWqupcz+c3gP6ez+/AP9lMzwPey5fJtIznvRlwtefzRJzJUQpqCYzNS5HsIwVAU5xJkuZ6zpEEzAPqAX+o6q+esryBE1iMCQkLBCZWFMylkre8x/Meh5PrvqGf+xckfm4zU1U7HbFSpKEf+xrjGqsaMrEiVUTO9XzuBMzJ/0dV3Qn8ISIdwMlyKiJnev48FycDJkCGj+PPAG7JS5EsIlU863cBFT2fvwOaici/PNski0hdYDlwkoicnK98xoSMBQITK5YBXUVkMU7myhe8bJMBdBeRn4ClHJ7adADO3MjzgWN8HH88TmbIxZ79O3vWjwOmiciXqroZuAF4y1OO74B6qrofpypoiqexeHXJLtWYwFj2URP1PFNafqqqp4e5KMZEJHsiMMaYGGdPBMYYE+PsicAYY2KcBQJjjIlxFgiMMSbGWSAwxpgYZ4HAGGNinAUCY4yJcf8PbIE3+5l6bzAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<module 'matplotlib.pyplot' from '/anaconda3/lib/python3.6/site-packages/matplotlib/pyplot.py'>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgdreg = SGDRegressor(penalty='l2', alpha=0.15, n_iter=200)\n",
    "\n",
    "# Train the model using the training sets\n",
    "sgdreg.fit(X_train, Y_train) \n",
    "\n",
    "print (\"Stochastic Gradient Descent model: \", pretty_print_linear(sgdreg.coef_, names, sort = True))\n",
    "\n",
    "# Predict the values using the model\n",
    "Y_sgdreg_predict = sgdreg.predict(X_test)\n",
    "\n",
    "# Print the root mean square error \n",
    "print (\"Root Mean Square Error: \", root_mean_square_error(Y_sgdreg_predict,Y_test))\n",
    "plot_real_vs_predicted(Y_test,Y_sgdreg_predict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}