10.01-Standardisation.ipynb

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    "## Feature Scaling\n",
    "\n",
    "We discussed previously that the scale of the features is an important consideration when building machine learning models. Briefly:\n",
    "\n",
    "\n",
    "### Feature magnitude matters because:\n",
    "\n",
    "- The regression coefficients of linear models are directly influenced by the scale of the variable.\n",
    "- Variables with bigger magnitude / larger value range dominate over those with smaller magnitude / value range\n",
    "- Gradient descent converges faster when features are on similar scales\n",
    "- Feature scaling helps decrease the time to find support vectors for SVMs\n",
    "- Euclidean distances are sensitive to feature magnitude.\n",
    "- Some algorithms, like PCA require the features to be centered at 0.\n",
    "\n",
    "\n",
    "### The machine learning models affected by the feature scale are:\n",
    "\n",
    "- Linear and Logistic Regression\n",
    "- Neural Networks\n",
    "- Support Vector Machines\n",
    "- KNN\n",
    "- K-means clustering\n",
    "- Linear Discriminant Analysis (LDA)\n",
    "- Principal Component Analysis (PCA)\n",
    "\n",
    "\n",
    "### Feature Scaling\n",
    "\n",
    "**Feature scaling** refers to the methods or techniques used to normalize the range of independent variables in our data, or in other words, the methods to set the feature value range within a similar scale. Feature scaling is generally the last step in the data preprocessing pipeline, performed **just before training the machine learning algorithms**.\n",
    "\n",
    "There are several Feature Scaling techniques, which we will discuss throughout this section:\n",
    "\n",
    "- Standardisation\n",
    "- Mean normalisation\n",
    "- Scaling to minimum and maximum values - MinMaxScaling\n",
    "- Scaling to maximum value - MaxAbsScaling\n",
    "- Scaling to quantiles and median - RobustScaling\n",
    "- Normalization to vector unit length\n",
    "\n",
    "In this notebook, we will discuss **Standardisation**.\n",
    "\n",
    "=================================================================\n",
    "\n",
    "## Standardisation\n",
    "\n",
    "\n",
    "Standardisation involves centering the variable at zero, and standardising the variance to 1. The procedure involves subtracting the mean of each observation and then dividing by the standard deviation:\n",
    "\n",
    "**z = (x - x_mean) /  std**\n",
    "\n",
    "The result of the above transformation is **z**, which is called the z-score, and represents how many standard deviations a given observation deviates from the mean. A z-score specifies the location of the observation within a distribution (in numbers of standard deviations respect to the mean of the distribution). The sign of the z-score (+ or - ) indicates whether the observation is above (+) or below ( - ) the mean.\n",
    "\n",
    "The shape of a standardised (or z-scored normalised) distribution will be identical to the original distribution of the variable. If the original distribution is normal, then the standardised distribution will be normal. But, if the original distribution is skewed, then the standardised distribution of the variable will also be skewed. In other words, **standardising a variable does not normalize the distribution of the data** and if this is the desired outcome, we should implement any of the techniques discussed in section 7 of the course.\n",
    "\n",
    "In a nutshell, standardisation:\n",
    "\n",
    "- centers the mean at 0\n",
    "- scales the variance at 1\n",
    "- preserves the shape of the original distribution\n",
    "- the minimum and maximum values of the different variables may vary\n",
    "- preserves outliers\n",
    "\n",
    "Good for algorithms that require features centered at zero.\n",
    "\n",
    "## In this demo\n",
    "\n",
    "We will perform standardisation using the Boston House Prices data set that comes with Scikit-learn"
   ]
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  {
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   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "\n",
    "# dataset for the demo\n",
    "from sklearn.datasets import load_boston\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "# the scaler - for standardisation\n",
    "from sklearn.preprocessing import StandardScaler"
   ]
  },
  {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "      <th>MEDV</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00632</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1.0</td>\n",
       "      <td>296.0</td>\n",
       "      <td>15.3</td>\n",
       "      <td>396.90</td>\n",
       "      <td>4.98</td>\n",
       "      <td>24.0</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.02731</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.421</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.14</td>\n",
       "      <td>21.6</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.02729</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
       "      <td>34.7</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.03237</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.63</td>\n",
       "      <td>2.94</td>\n",
       "      <td>33.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.06905</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.33</td>\n",
       "      <td>36.2</td>\n",
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      "text/plain": [
       "      CRIM    ZN  INDUS  CHAS    NOX     RM   AGE     DIS  RAD    TAX  \\\n",
       "0  0.00632  18.0   2.31   0.0  0.538  6.575  65.2  4.0900  1.0  296.0   \n",
       "1  0.02731   0.0   7.07   0.0  0.469  6.421  78.9  4.9671  2.0  242.0   \n",
       "2  0.02729   0.0   7.07   0.0  0.469  7.185  61.1  4.9671  2.0  242.0   \n",
       "3  0.03237   0.0   2.18   0.0  0.458  6.998  45.8  6.0622  3.0  222.0   \n",
       "4  0.06905   0.0   2.18   0.0  0.458  7.147  54.2  6.0622  3.0  222.0   \n",
       "\n",
       "   PTRATIO       B  LSTAT  MEDV  \n",
       "0     15.3  396.90   4.98  24.0  \n",
       "1     17.8  396.90   9.14  21.6  \n",
       "2     17.8  392.83   4.03  34.7  \n",
       "3     18.7  394.63   2.94  33.4  \n",
       "4     18.7  396.90   5.33  36.2  "
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   "source": [
    "# load the the Boston House price data\n",
    "\n",
    "# this is how we load the boston dataset from sklearn\n",
    "boston_dataset = load_boston()\n",
    "\n",
    "# create a dataframe with the independent variables\n",
    "data = pd.DataFrame(boston_dataset.data,\n",
    "                      columns=boston_dataset.feature_names)\n",
    "\n",
    "# add target\n",
    "data['MEDV'] = boston_dataset.target\n",
    "\n",
    "data.head()"
   ]
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   "cell_type": "code",
   "execution_count": 3,
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     "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": [
    "# Information about the boston house prince dataset\n",
    "# you will find details about the different variables\n",
    "\n",
    "# the aim is to predict the \"Median value of the houses\"\n",
    "# MEDV column in this dataset\n",
    "\n",
    "# and there are variables with characteristics about\n",
    "# the homes and the neighborhoods\n",
    "\n",
    "# print the dataset description\n",
    "print(boston_dataset.DESCR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
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       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "      <th>MEDV</th>\n",
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       "  </thead>\n",
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       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>3.613524</td>\n",
       "      <td>11.363636</td>\n",
       "      <td>11.136779</td>\n",
       "      <td>0.069170</td>\n",
       "      <td>0.554695</td>\n",
       "      <td>6.284634</td>\n",
       "      <td>68.574901</td>\n",
       "      <td>3.795043</td>\n",
       "      <td>9.549407</td>\n",
       "      <td>408.237154</td>\n",
       "      <td>18.455534</td>\n",
       "      <td>356.674032</td>\n",
       "      <td>12.653063</td>\n",
       "      <td>22.532806</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>8.601545</td>\n",
       "      <td>23.322453</td>\n",
       "      <td>6.860353</td>\n",
       "      <td>0.253994</td>\n",
       "      <td>0.115878</td>\n",
       "      <td>0.702617</td>\n",
       "      <td>28.148861</td>\n",
       "      <td>2.105710</td>\n",
       "      <td>8.707259</td>\n",
       "      <td>168.537116</td>\n",
       "      <td>2.164946</td>\n",
       "      <td>91.294864</td>\n",
       "      <td>7.141062</td>\n",
       "      <td>9.197104</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.006320</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.460000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.385000</td>\n",
       "      <td>3.561000</td>\n",
       "      <td>2.900000</td>\n",
       "      <td>1.129600</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>187.000000</td>\n",
       "      <td>12.600000</td>\n",
       "      <td>0.320000</td>\n",
       "      <td>1.730000</td>\n",
       "      <td>5.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.082045</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.190000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.449000</td>\n",
       "      <td>5.885500</td>\n",
       "      <td>45.025000</td>\n",
       "      <td>2.100175</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>279.000000</td>\n",
       "      <td>17.400000</td>\n",
       "      <td>375.377500</td>\n",
       "      <td>6.950000</td>\n",
       "      <td>17.025000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.256510</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>9.690000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.538000</td>\n",
       "      <td>6.208500</td>\n",
       "      <td>77.500000</td>\n",
       "      <td>3.207450</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>330.000000</td>\n",
       "      <td>19.050000</td>\n",
       "      <td>391.440000</td>\n",
       "      <td>11.360000</td>\n",
       "      <td>21.200000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>3.677083</td>\n",
       "      <td>12.500000</td>\n",
       "      <td>18.100000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.624000</td>\n",
       "      <td>6.623500</td>\n",
       "      <td>94.075000</td>\n",
       "      <td>5.188425</td>\n",
       "      <td>24.000000</td>\n",
       "      <td>666.000000</td>\n",
       "      <td>20.200000</td>\n",
       "      <td>396.225000</td>\n",
       "      <td>16.955000</td>\n",
       "      <td>25.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>88.976200</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>27.740000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.871000</td>\n",
       "      <td>8.780000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>12.126500</td>\n",
       "      <td>24.000000</td>\n",
       "      <td>711.000000</td>\n",
       "      <td>22.000000</td>\n",
       "      <td>396.900000</td>\n",
       "      <td>37.970000</td>\n",
       "      <td>50.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "             CRIM          ZN       INDUS        CHAS         NOX          RM  \\\n",
       "count  506.000000  506.000000  506.000000  506.000000  506.000000  506.000000   \n",
       "mean     3.613524   11.363636   11.136779    0.069170    0.554695    6.284634   \n",
       "std      8.601545   23.322453    6.860353    0.253994    0.115878    0.702617   \n",
       "min      0.006320    0.000000    0.460000    0.000000    0.385000    3.561000   \n",
       "25%      0.082045    0.000000    5.190000    0.000000    0.449000    5.885500   \n",
       "50%      0.256510    0.000000    9.690000    0.000000    0.538000    6.208500   \n",
       "75%      3.677083   12.500000   18.100000    0.000000    0.624000    6.623500   \n",
       "max     88.976200  100.000000   27.740000    1.000000    0.871000    8.780000   \n",
       "\n",
       "              AGE         DIS         RAD         TAX     PTRATIO           B  \\\n",
       "count  506.000000  506.000000  506.000000  506.000000  506.000000  506.000000   \n",
       "mean    68.574901    3.795043    9.549407  408.237154   18.455534  356.674032   \n",
       "std     28.148861    2.105710    8.707259  168.537116    2.164946   91.294864   \n",
       "min      2.900000    1.129600    1.000000  187.000000   12.600000    0.320000   \n",
       "25%     45.025000    2.100175    4.000000  279.000000   17.400000  375.377500   \n",
       "50%     77.500000    3.207450    5.000000  330.000000   19.050000  391.440000   \n",
       "75%     94.075000    5.188425   24.000000  666.000000   20.200000  396.225000   \n",
       "max    100.000000   12.126500   24.000000  711.000000   22.000000  396.900000   \n",
       "\n",
       "            LSTAT        MEDV  \n",
       "count  506.000000  506.000000  \n",
       "mean    12.653063   22.532806  \n",
       "std      7.141062    9.197104  \n",
       "min      1.730000    5.000000  \n",
       "25%      6.950000   17.025000  \n",
       "50%     11.360000   21.200000  \n",
       "75%     16.955000   25.000000  \n",
       "max     37.970000   50.000000  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's have a look at the main statistical parameters of the variables\n",
    "# to get an idea of the feature magnitudes\n",
    "\n",
    "data.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The different variables present different value ranges, mean, max, min, standard deviations, etc. In other words, they show different magnitudes or scales. Note for this demo, how **the mean values are not centered at zero, and the standard deviations are not scaled to 1**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When standardising the data set, we need to first identify the mean and standard deviation of the variables. These parameters need to be learned from the train set, stored, and then used to scale test and future data. Thus, we will first divide the data set into train and test, as we have done throughout the course."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((354, 13), (152, 13))"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's separate the data into training and testing set\n",
    "X_train, X_test, y_train, y_test = train_test_split(data.drop('MEDV', axis=1),\n",
    "                                                    data['MEDV'],\n",
    "                                                    test_size=0.3,\n",
    "                                                    random_state=0)\n",
    "\n",
    "X_train.shape, X_test.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Standardisation\n",
    "\n",
    "The StandardScaler from scikit-learn removes the mean and scales the data to unit variance. Plus, it learns and stores the parameters needed for scaling. Thus, it is top choice for this feature scaling technique.\n",
    "\n",
    "On the downside, you can't select which variables to scale directly, it will scale the entire data set, and it returns a NumPy array, without the variable values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# standardisation: with the StandardScaler from sklearn\n",
    "\n",
    "# set up the scaler\n",
    "scaler = StandardScaler()\n",
    "\n",
    "# fit the scaler to the train set, it will learn the parameters\n",
    "scaler.fit(X_train)\n",
    "\n",
    "# transform train and test sets\n",
    "X_train_scaled = scaler.transform(X_train)\n",
    "X_test_scaled = scaler.transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3.35828432e+00, 1.18093220e+01, 1.10787571e+01, 6.49717514e-02,\n",
       "       5.56098305e-01, 6.30842655e+00, 6.89940678e+01, 3.76245876e+00,\n",
       "       9.35310734e+00, 4.01782486e+02, 1.84734463e+01, 3.60601186e+02,\n",
       "       1.24406497e+01])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# the scaler stores the mean of the features, learned from train set\n",
    "\n",
    "scaler.mean_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([8.34141658e+00, 2.36196246e+01, 6.98393565e+00, 2.46476009e-01,\n",
       "       1.15437239e-01, 7.01016354e-01, 2.79987983e+01, 2.06473886e+00,\n",
       "       8.65974217e+00, 1.70351284e+02, 2.22166426e+00, 8.55009244e+01,\n",
       "       7.06848020e+00])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# the scaler stores the standard deviation deviation of the features,\n",
    "# learned from train set\n",
    "\n",
    "scaler.scale_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# let's transform the returned NumPy arrays to dataframes for the rest of\n",
    "# the demo\n",
    "\n",
    "X_train_scaled = pd.DataFrame(X_train_scaled, columns=X_train.columns)\n",
    "X_test_scaled = pd.DataFrame(X_test_scaled, columns=X_test.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .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>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>3.4</td>\n",
       "      <td>11.8</td>\n",
       "      <td>11.1</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.6</td>\n",
       "      <td>6.3</td>\n",
       "      <td>69.0</td>\n",
       "      <td>3.8</td>\n",
       "      <td>9.4</td>\n",
       "      <td>401.8</td>\n",
       "      <td>18.5</td>\n",
       "      <td>360.6</td>\n",
       "      <td>12.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>8.4</td>\n",
       "      <td>23.7</td>\n",
       "      <td>7.0</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.7</td>\n",
       "      <td>28.0</td>\n",
       "      <td>2.1</td>\n",
       "      <td>8.7</td>\n",
       "      <td>170.6</td>\n",
       "      <td>2.2</td>\n",
       "      <td>85.6</td>\n",
       "      <td>7.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.4</td>\n",
       "      <td>3.6</td>\n",
       "      <td>2.9</td>\n",
       "      <td>1.2</td>\n",
       "      <td>1.0</td>\n",
       "      <td>187.0</td>\n",
       "      <td>12.6</td>\n",
       "      <td>0.3</td>\n",
       "      <td>1.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.4</td>\n",
       "      <td>5.9</td>\n",
       "      <td>45.2</td>\n",
       "      <td>2.1</td>\n",
       "      <td>4.0</td>\n",
       "      <td>276.0</td>\n",
       "      <td>17.4</td>\n",
       "      <td>376.1</td>\n",
       "      <td>6.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.3</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8.6</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>6.2</td>\n",
       "      <td>79.4</td>\n",
       "      <td>3.2</td>\n",
       "      <td>5.0</td>\n",
       "      <td>311.0</td>\n",
       "      <td>19.1</td>\n",
       "      <td>391.6</td>\n",
       "      <td>11.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>3.1</td>\n",
       "      <td>20.0</td>\n",
       "      <td>18.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.6</td>\n",
       "      <td>6.6</td>\n",
       "      <td>93.8</td>\n",
       "      <td>5.1</td>\n",
       "      <td>24.0</td>\n",
       "      <td>666.0</td>\n",
       "      <td>20.2</td>\n",
       "      <td>395.7</td>\n",
       "      <td>16.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>89.0</td>\n",
       "      <td>100.0</td>\n",
       "      <td>27.7</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.9</td>\n",
       "      <td>8.8</td>\n",
       "      <td>100.0</td>\n",
       "      <td>12.1</td>\n",
       "      <td>24.0</td>\n",
       "      <td>711.0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>396.9</td>\n",
       "      <td>37.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        CRIM     ZN  INDUS   CHAS    NOX     RM    AGE    DIS    RAD    TAX  \\\n",
       "count  354.0  354.0  354.0  354.0  354.0  354.0  354.0  354.0  354.0  354.0   \n",
       "mean     3.4   11.8   11.1    0.1    0.6    6.3   69.0    3.8    9.4  401.8   \n",
       "std      8.4   23.7    7.0    0.2    0.1    0.7   28.0    2.1    8.7  170.6   \n",
       "min      0.0    0.0    0.5    0.0    0.4    3.6    2.9    1.2    1.0  187.0   \n",
       "25%      0.1    0.0    5.0    0.0    0.4    5.9   45.2    2.1    4.0  276.0   \n",
       "50%      0.3    0.0    8.6    0.0    0.5    6.2   79.4    3.2    5.0  311.0   \n",
       "75%      3.1   20.0   18.1    0.0    0.6    6.6   93.8    5.1   24.0  666.0   \n",
       "max     89.0  100.0   27.7    1.0    0.9    8.8  100.0   12.1   24.0  711.0   \n",
       "\n",
       "       PTRATIO      B  LSTAT  \n",
       "count    354.0  354.0  354.0  \n",
       "mean      18.5  360.6   12.4  \n",
       "std        2.2   85.6    7.1  \n",
       "min       12.6    0.3    1.7  \n",
       "25%       17.4  376.1    6.7  \n",
       "50%       19.1  391.6   11.2  \n",
       "75%       20.2  395.7   16.7  \n",
       "max       22.0  396.9   37.0  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's have a look at the original training dataset: mean and standard deviation\n",
    "# I use np.round to reduce the number of decimals to 1.\n",
    "\n",
    "np.round(X_train.describe(), 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
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       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-0.4</td>\n",
       "      <td>-0.5</td>\n",
       "      <td>-1.5</td>\n",
       "      <td>-0.3</td>\n",
       "      <td>-1.5</td>\n",
       "      <td>-3.9</td>\n",
       "      <td>-2.4</td>\n",
       "      <td>-1.3</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>-1.3</td>\n",
       "      <td>-2.6</td>\n",
       "      <td>-4.2</td>\n",
       "      <td>-1.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>-0.4</td>\n",
       "      <td>-0.5</td>\n",
       "      <td>-0.9</td>\n",
       "      <td>-0.3</td>\n",
       "      <td>-0.9</td>\n",
       "      <td>-0.6</td>\n",
       "      <td>-0.9</td>\n",
       "      <td>-0.8</td>\n",
       "      <td>-0.6</td>\n",
       "      <td>-0.7</td>\n",
       "      <td>-0.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>-0.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>-0.4</td>\n",
       "      <td>-0.5</td>\n",
       "      <td>-0.4</td>\n",
       "      <td>-0.3</td>\n",
       "      <td>-0.2</td>\n",
       "      <td>-0.1</td>\n",
       "      <td>0.4</td>\n",
       "      <td>-0.3</td>\n",
       "      <td>-0.5</td>\n",
       "      <td>-0.5</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.4</td>\n",
       "      <td>-0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>-0.0</td>\n",
       "      <td>0.3</td>\n",
       "      <td>1.0</td>\n",
       "      <td>-0.3</td>\n",
       "      <td>0.6</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.9</td>\n",
       "      <td>0.6</td>\n",
       "      <td>1.7</td>\n",
       "      <td>1.6</td>\n",
       "      <td>0.8</td>\n",
       "      <td>0.4</td>\n",
       "      <td>0.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>10.3</td>\n",
       "      <td>3.7</td>\n",
       "      <td>2.4</td>\n",
       "      <td>3.8</td>\n",
       "      <td>2.7</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.1</td>\n",
       "      <td>4.1</td>\n",
       "      <td>1.7</td>\n",
       "      <td>1.8</td>\n",
       "      <td>1.6</td>\n",
       "      <td>0.4</td>\n",
       "      <td>3.5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        CRIM     ZN  INDUS   CHAS    NOX     RM    AGE    DIS    RAD    TAX  \\\n",
       "count  354.0  354.0  354.0  354.0  354.0  354.0  354.0  354.0  354.0  354.0   \n",
       "mean     0.0    0.0   -0.0    0.0   -0.0   -0.0    0.0    0.0    0.0   -0.0   \n",
       "std      1.0    1.0    1.0    1.0    1.0    1.0    1.0    1.0    1.0    1.0   \n",
       "min     -0.4   -0.5   -1.5   -0.3   -1.5   -3.9   -2.4   -1.3   -1.0   -1.3   \n",
       "25%     -0.4   -0.5   -0.9   -0.3   -0.9   -0.6   -0.9   -0.8   -0.6   -0.7   \n",
       "50%     -0.4   -0.5   -0.4   -0.3   -0.2   -0.1    0.4   -0.3   -0.5   -0.5   \n",
       "75%     -0.0    0.3    1.0   -0.3    0.6    0.5    0.9    0.6    1.7    1.6   \n",
       "max     10.3    3.7    2.4    3.8    2.7    3.5    1.1    4.1    1.7    1.8   \n",
       "\n",
       "       PTRATIO      B  LSTAT  \n",
       "count    354.0  354.0  354.0  \n",
       "mean       0.0   -0.0   -0.0  \n",
       "std        1.0    1.0    1.0  \n",
       "min       -2.6   -4.2   -1.5  \n",
       "25%       -0.5    0.2   -0.8  \n",
       "50%        0.3    0.4   -0.2  \n",
       "75%        0.8    0.4    0.6  \n",
       "max        1.6    0.4    3.5  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's have a look at the scaled training dataset: mean and standard deviation\n",
    "# I use np.round to reduce the number of decimals to 1.\n",
    "\n",
    "np.round(X_train_scaled.describe(), 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected, the mean of each variable, which were not centered at zero, is now around zero and the standard deviation is set to 1. Note however, that the minimum and maximum values vary according to how spread the variable was to begin with and is highly influenced by the presence of outliers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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nd1+YjPFMYJm7v+7uzcA8gl2TOjIXuKUQg+ttIqneeM2JZJlHItL/7LPPPuy9997Mmzev1fEpU6Zw4okndvAskb4nkzFOKGMsfVdfnbPD1BhndkhKqQf2y3Wime0CTAAe6vnQep90KUVTXIGxSCls3ry51f277747c3vJkiXtzj/ppJM46aSTij0skaLKZIxVSiF9TCXM2WEyxqF2SEqZA9zu7jnbNvT1XZTSm6k0KzAWEZEiSSSDj9CmRFOZRyLS/4QJjDM7JKWMBd7p4Nw5dFJG0dd3UcqUUigwFhGRIsmuMRaR0goTGD8FTDKzCWZWTRD8zm97kpntDmwPPF7YIfYe6VIK1RiLiEixqMZYpHy6DIzdPQ6cASwAlgJ/dPcX2uyiBMGiu3mVvK2oSilERKTY0hljlVKIlF6oDT7c/V7g3jbHLmxz/+LCDauXSoX8CoxFRKRYlDEWKR9tCZ2HltTGHiqlEBGRYlGNsUj5KDDOQyKZmqyUMRYpiUGDBrU79vLLLzNr1iymT5/OnnvuyamnnsqCBQuYPn0606dPZ9CgQey+++5Mnz6dE044IfO8s846izFjxpBM/X/861//OvOc6upqpk6dyvTp0znvvHabe4qUVDpj3JRUKYX0LZUwZ4cqpZBAS2rnu3hSgbFIuZx55pl87WtfY/bsYJ+h559/nqlTp/KJT3wCgFmzZvHDH/6QGTNmZJ6TTCa58847GTduHP/4xz+YNWsWJ598MieffDIA48eP5+GHH2bEiBGlf0MibaQzxi2JljKPRKTn+tqcrYxxHuKpEopEsmLXF4r0eitWrGDs2LGZ+1OnTu3yOQ8//DB77bUXp512GrfcUpEbc0oF0eI7qSR9bc5WYJyHeCogjicUGIuUy9e+9jUOPvhgDj/8cK655hrWr1/f5XNuueUW5s6dy2c+8xnuueceWlqUiZPeSxt8SCXpa3O2SinykA6IlTGWfue+82Dl84W95qipcPgVeT/t5JNP5hOf+AT3338/d911FzfccAPPPvssNTU1Oc9vbm7m3nvv5ZprrmHw4MHst99+/PWvf+WII47o6TsQKQqVUkiPac7uNmWM85AOiOMKjEXKaqedduKLX/wid911F7FYjCVLlnR47v3338+GDRuYOnUq48eP57HHHlM5hfRqmcV3yhhLhehLc7YyxnloSS26S1TuHiYiuXUjS1As999/Px/72Meoqqpi5cqVrFmzhjFjxnR4/i233MIvfvEL5s6dC8CWLVuYMGECW7duZcCAAaUatkhomXZtSbVrk27SnN1tCozzkExlihOqMRYpia1bt7ZatHH22WdTX1/PWWedRW1tLQBXXnklo0aN6vD5CxYs4IYbbsgcGzhwIB/5yEe4++67OfbYY4v7BkS6QRt8SF9VCXO2AuM8pCsoVEohUhrJDlojXn311R0+55FHHsncHjBgAGvXrm13zh133NHq/vLly7s1PpFiUFcK6asqYc5WjXEekp5efKc+xiIiUhzKGIuUjwLjPChjLCIixaYtoUXKR4FxHjI1xgqMRUSkSDIZYy2+Eyk5BcZ5SJdSKGMsIiLFkq7TVI2xSOkpMM7DthpjBcYiIlIcqjEWKR8FxnlIty9WYCwiIsWiGmOR8lFgnAdljEVKa+XKlcyZM4eJEycyefJkPvnJT/LKK69QV1fH9OnTmTx5MieccAItLcHWuY888ghHHnkkADfddBNmxoMPPpi53p133omZcfvtt5fl/YiEoYyx9GV9fd5WYJwHdaUQKR135zOf+QyzZs3itdde48UXX+Syyy7j3XffZeLEiSxevJjnn3+e+vp6/vjHP+a8xtSpU1ttJTpv3jz23nvvUr0FkW7RznfSV1XCvK3AOA+JpPoYi5TKww8/TFVVFV/5ylcyx6ZPn864ceMy96PRKDNnzuTtt9/OeY2PfvSjPPnkk7S0tLB582aWLVvG9OnTiz52kZ7QBh/SV1XCvK3AOA+urhQiJbNkyRL23XffTs9pbGxk4cKFHHbYYTkfNzMOOeQQFixYwF133cVRRx1VjKGKFJRKKaSvqoR5W1tC5yGpxXfST33/ye/z0tqXCnrNPYbtwTdmfqNbz33ttdeYPn06r776KkcffTTTpk3r8Nw5c+Zw7bXXsmHDBq666iouu+yy7g5ZpCS0+E56qrfN2dB35m1ljPOQ6WOcUGAsUmxTpkzh6aefzvlYulZt2bJlPPHEE8yfP7/D68ycOZMlS5awevVqdtttt2INV6Rg0hljlVJIX1MJ87YyxnlIJ4rTAbJIf9GTLEF3HXzwwVxwwQX8/Oc/58tf/jIATz31FFu3bs2cM3r0aK644gouv/zyTr9uu/zyy6mtrS36mEUKIb3BR0uypcwjkb6qHHM2VMa8rYxxHlRjLFI6Zsadd97JAw88wMSJE5kyZQoXX3wxO+20U6vzPv3pT7N161YeffTRDq91+OGHc9BBBxV7yCIFkZ0xdiVipA+phHnbyvU/3YwZM3zRokVlee3umn7JX1m/tYVhA6t55tuHlns4IkW1dOlS9txzz3IPo+xy/R7M7Gl3n1GmIZVFX5yz+6oD5h3AuqZ1ADxz/DNURarKPCLpCzRnb9OTeVsZ4zwkk+kaY7VrE5HeyczGmdnDZrbUzF4ws7NynDPLzDaY2eLUz4XlGKvkls4YA7QkVE4hUkqqMc6DtoQWkT4gDpzj7s+Y2WDgaTN7wN1fbHPeo+5+ZBnGJ11IepKIRUh6kqZEEwOqBpR7SCL9RqiMsZkdZmYvm9kyMzuvg3M+Z2YvpjIUNxd2mL1DUjXGItLLufsKd38mdXsTsBQYU95RST4SnqAuVgeoZZtIqXUZGJtZFLgeOByYDMw1s8ltzpkEnA982N2nAF8twljLTn2Mpb/p7wt/+vr7N7PxwD7AwhwP729mz5rZfWY2paQDk04lPanAWLqlr89ZhdDT30GYjPFMYJm7v+7uzcA8YHabc74MXO/u61KDeq9Ho+qlEsoYSz9SW1vLmjVr+u1E6+6sWbOmz7Z5M7NBwJ+Ar7r7xjYPPwPs4u57Az8B/tzBNU41s0VmtmjVqlXFHbBkJDxBbTT47069jCWs/j5nQ2Hm7TA1xmOAt7Lu1wP7tTlnNwAz+ycQBS529/u7PapeKvs/tmTSiUSsjKMRKa6xY8dSX19Pfw6IamtrGTt2bLmHkTczqyIIiv/g7ne0fTw7UHb3e83s/8xshLuvbnPejcCNEHSlKPKwJSXpSeqqUhnjpDLGEo7m7EBP5+0wgXGu6K/tBBkDJgGzgLHAo2a2l7uvb3Uhs1OBUwF23nnnvAdbbtmJ4njSqVZgLBWsqqqKCRMmlHsYkiczM+CXwFJ3v7qDc0YB77q7m9lMgm8P15RwmNIBd1cphXSL5uzCCBMY1wPjsu6PBd7Jcc4T7t4C/MfMXiYIlJ/KPqmvZx+S7lRFjZaEa/c7EemtPgwcDzxvZotTxy4AdgZw958BRwOnmVkcaADmeH/+/rUXSXrQDrQuqsBYpBzCBMZPAZPMbALwNjAH+Hybc/4MzAVuMrMRBKUVrxdyoOXm7rhDVTRCSyKhOmMR6ZXc/TFyf9OXfc51wHWlGZHkIxMYpzLGqjEWKa0uF9+5exw4A1hA0Pbnj+7+gpldYmbpTa4XAGvM7EXgYeDr7l5RX8ulcymxVPmEOlOIiEihpTf3qI0Fi4eUMRYprVAbfLj7vcC9bY5dmHXbgbNTPxUp3ZGiOhb8LZFUYCwiIgXWNmOsxXcipaUtoUNK1xRXRYNfmUopRESk0NIZY5VSiJSHAuOQMqUU0aCUQovvRESk0NIZY5VSiJSHAuOQ2maMVWMsIiKF1jZjrMBYpLQUGIeUjoOrIgqMRUSkOBJJlVKIlJMC45AyGeOYulKIiEhxtMsYa/GdSEkpMA4p3YVCi+9ERKRY0jXGsUiMmMVUSiFSYgqMQ2pbSqHFdyIiUmjpjHHEIlRHqxUYi5SYAuOQVEohIiLFls4YRy1KdbRaNcYiJabAOKR0YBzT4jsRESmS7IxxLBIjnoyXeUQi/YsC45DSlRNq1yYiIsWSTG7LGEctmskgi0hpKDAOaVsf46CUQovvRESk0NIZ42gkCIzT90WkNBQYh5Ro05VCi+9ERKTQ0hniiEWIRhQYi5SaAuOQVEohIiLFlr34LmrRzIYfIlIaCoxDaltKocBYREQKLXvxnUopREpPgXFI6Tg4psBYRESKJDtjHIlElDEWKTEFxiFtyxirlEJERIqjVbs2i6krhUiJKTAOyRUYi4hIkbXKGFuEuKuPsUgpKTAOKZH6oz1TY6yuFCIiUmCtaowj6mMsUmoKjENSKYWIiBRbZoOPiLpSiJSDAuOQFBiLiEixqSuFSHkpMA5pWx9jdaUQEZHiaNfHWIGxSEkpMA4pnTGORZQxFhGR4mhbY6zAWKS0FBiHlI6Dq2KpwFiL70REpMDadqVQjbFIaSkwDimdIa5WKYWIiBSJ+hiLlJcC45BcpRQiIlJk6mMsUl4KjENqW0qRVCmFiIgUWLs+xklljEVKSYFxSJl2bZGglCKeUGAsIiKFpa4UIuUVKjA2s8PM7GUzW2Zm5+V4/CQzW2Vmi1M/pxR+qOXVto+xMsYiIlJo6cV2kYi6UoiUQ6yrE8wsClwPHArUA0+Z2Xx3f7HNqbe6+xlFGGOvkP42K5ZafBdXjbGIiBRYu4yxulKIlFSYjPFMYJm7v+7uzcA8YHZxh9X7pDPE1dr5TkREikQ734mUV5jAeAzwVtb9+tSxtj5rZs+Z2e1mNq4go+tFMqUU6cV3CoxFRKTA0hnjiEWCPsYKjEVKKkxgbDmOtY0K7wbGu/s04G/Ab3JeyOxUM1tkZotWrVqV30jLLF1SHIuolEJERIojHQhHLUosoj7GIqUWJjCuB7IzwGOBd7JPcPc17t6UuvtzYN9cF3L3G919hrvPGDlyZHfGWzbpjHE0YkRMi+9ERKTw2maM40n1MRYppTCB8VPAJDObYGbVwBxgfvYJZjY66+5RwNLCDbF3SCeII2ZEI6aMsYj0SmY2zsweNrOlZvaCmZ2V4xwzs2tTnYaeM7P3l2Os0l7bxXfKGIuUVpddKdw9bmZnAAuAKPArd3/BzC4BFrn7fOBMMzsKiANrgZOKOOaySC+2MwuCY9UYi0gvFQfOcfdnzGww8LSZPdCmk9DhwKTUz37AT1P/lDLT4juR8uoyMAZw93uBe9scuzDr9vnA+YUdWu/iWaUUsYipK4WI9EruvgJYkbq9ycyWEiyYzg6MZwO/9WBie8LMhprZ6NRzpYwyGeNINOhjrHZtIiWlne9Cyi6liKiUQkT6ADMbD+wDLGzzUNhuQ1JimQ0+lDEWKQsFxiGlF9tFLOhMocV3ItKbmdkg4E/AV919Y9uHczyl3aTWlzsJ9VWtaoxTO9+5Pm9ESkaBcUjpQNi0+E5EejkzqyIIiv/g7nfkOKXLbkPQtzsJ9VXZNcYRS/XN1wI8kZJRYBxS+g92Q4vvRKT3MjMDfgksdferOzhtPnBCqjvFB4ENqi/uHZKeJGpRAGIWyxwTkdIItfhOtnWl0OI7EenlPgwcDzxvZotTxy4AdgZw958RLKb+JLAM2AqcXIZxSg4JT2Qyxel/xj1OFVXlHJZIv6HAOKRtNcbB4jsFxiLSG7n7Y+SuIc4+x4HTSzMiyUerjHFEGWORUlMpRUjpUopIJKgxTmgxhIiIFFjOjLF2vxMpGQXGIWV3pdDiOxERKYbsjHH6n8oYi5SOAuOQWm0JrcV3IiJSBIlkgkgk+GhOB8bqZSxSOgqMQ9rWri3IGKvGWERECq1VxjiSCoy1+51IySgwDil78Z0CYxERKYbsGmNljEVKT4FxSOnSiahp8Z2IiBRH0pPbAuOIAmORUlNgHFKrGmNljEVEpAgSnshkitMBskopREpHgXFImRrjSJA1VmAsIiKFlp0x1s53IqWnwDgkV8ZYRESKLFfGOO7qYyxSKgqMQ0q06WOswFhERAotV42xMsYipaPAOKR2XSm0+E5ERAos1wYfqjEWKR0FxiG1LaXQBh8iIlJo2uBDpLwUGIeUDoQjFiy+05bQIiJSaDkzxgqMRUpGgXFIatcmIiLF1mqDD+18J1JyCoxD0pYTk4jmAAAgAElEQVTQIiJSbNkZ40wfY2WMRUpGgXFISXfMwMyIaPGdiIgUQXbGOBaJZY6JSGkoMA4p6U7UDICYFt+JiEgR5MwYq5RCpGQUGIeU9KC+GLT4TkREiqNVxlg734mUnALjkNKlFIDatYmISFHkyhhr5zuR0lFgHJJnZ4wjyhiLiEjh5epKoYyxSOkoMA4pmXQiqYxxJGKZLhUiIiKFkkwm22/woRpjkZJRYBxSwj2TMY6pXZuIiBRBwhPa4EOkjEIFxmZ2mJm9bGbLzOy8Ts472szczGYUboi9g3uQKYagpEKlFCIiUmitSikUGIuUXJeBsZlFgeuBw4HJwFwzm5zjvMHAmcDCQg+yN0j6tlIKLb4TEZFiaLUltHa+Eym5MBnjmcAyd3/d3ZuBecDsHOd9F/gB0FjA8fUayTalFMoYi4hIoWVnjLXznUjphQmMxwBvZd2vTx3LMLN9gHHufk8Bx9arJD3Y9Q60+E5ERIoj6clM/+L0znfqSiFSOmECY8txLBMVmlkEuAY4p8sLmZ1qZovMbNGqVavCj7IXyO5KocV3IiJSDIlkItOVItPHOKk+xiKlEiYwrgfGZd0fC7yTdX8wsBfwiJktBz4IzM+1AM/db3T3Ge4+Y+TIkd0fdRlkl1JEzEg6uLLGIiJSQK1qjE19jEVKLUxg/BQwycwmmFk1MAeYn37Q3Te4+wh3H+/u44EngKPcfVFRRlwmSQ8W3cG2fyprLCIihaSuFCLl1WVg7O5x4AxgAbAU+KO7v2Bml5jZUcUeYG/RdktoQAvwRESkoHJtCa3AWKR0YmFOcvd7gXvbHLuwg3Nn9XxYvU/bLaEBLcATEZGCys4YpxffqV2bSOlo57uQsvsYx1RKISIiRZD0pNq1iZSRAuOQEsnWi+/Sx0RERApFW0KLlJcC45Cyt4TW4jsRESmG7IyxmRGxiEopREpIgXFIbbeEBkioxlhERAooe/EdBFljZYxFSkeBcUjZfYyVMRaR3srMfmVm75nZkg4en2VmG8xsceon50JqKY/sDT4gCIzVx1ikdEJ1pZDWW0IrMBaRXuwm4Drgt52c86i7H1ma4Ug+2mWMI1HtfCdSQsoYh+TZpRRafCcivZS7/wNYW+5xSPdkt2uDoDOFMsYipaPAOKTsrhTKGItIH7e/mT1rZveZ2ZRyD0YC7o7jrTLGMYupxlikhFRKEVIyR1cKbfAhIn3QM8Au7r7ZzD4J/BmYlOtEMzsVOBVg5513Lt0I+6l0ANw2Y6zAWKR0lDEOKVdXCm0JLSJ9jbtvdPfNqdv3AlVmNqKDc2909xnuPmPkyJElHWd/lC6ZaFtjrHZtIqWjwDikXFtCq5RCRPoaMxtlqZXEZjaT4HNgTXlHJZA7Y6x2bSKl1W9KKS5feDljB4/l+MnHd+v5SS2+E5E+wMxuAWYBI8ysHrgIqAJw958BRwOnmVkcaADmuKsurDfImTFWYCxSUv0mMH7s7ccYN3hctwPjRNLVrk1Eej13n9vF49cRtHOTXiZnxjgSJZlUVwqRUuk3pRRNiSbWNna/g1FQShHc1uI7EREptHQAHI20zhjHXX2MRUql3wTGzYlm1jet7/bzk+6ZgDiz+C6hwFhERAqjo64U6mMsUjr9ppSiKdFEY6Kx28/P3hI6/c+EMsYiIlIguWqMYxH1MRYppX6VMW6IN9AQb+jW87O3hI5FVWMsIiKF1WEfY7VrEymZfhEYx5PxTI3W+sbulVNkbwkdUVcKEREpsJwZY4uplEKkhPpFYNycaM7cXte0rlvXSGSVUsS0+E5ERAosnRmORbZVOUYsosV3IiXU7wLj7maMk8n2G3xo8Z2IiBRKOgBuu/OdMsYipdMvAuPsRXdrm7rXsi2Zo5RCGWMRESmUdMa4bbs21RiLlE6/CIwLkTHO3hI6vfgurhpjEREpkPTiu5htK6XQzncipdUvAuOmRFPmdndrjJPuRFK/LS2+ExGRQsuUUmRljCMRdaUQKaV+ERi3WnzX2P3A2LT4TkREiiRTStGmK4UyxiKl0y8C4+yMcXd3v0u6Ft+JiEjxpAPgVhljiygwFimhfhUYRy3ao4xxNL34ThljEREpsHgyKKXIrjGORdTHWKSU+kVgnC6lGDlgZA8yxu37GGvxnYiIFEpHGeN0wCwixRcqMDazw8zsZTNbZmbn5Xj8K2b2vJktNrPHzGxy4YfafemM8agBo1jb2M12bcltW0Jn2rUpMBYRkQLJVWMcNfUxFimlLgNjM4sC1wOHA5OBuTkC35vdfaq7Twd+AFxd8JH2QDow3nHgjmxo2tCtSSZ7S+h0xlhdKUREpFAy7doiatcmUi5hMsYzgWXu/rq7NwPzgNnZJ7j7xqy7A4FeFTGmSyl2HLAjCU+wqXlT3tfI3hI6olIKEREpsHTJRNud7xQYi5ROrOtTGAO8lXW/Htiv7UlmdjpwNlANHFyQ0RVIJmM8YEcg6EwxpGZIXtdI+raAOKrFdyIiUmC5aoy1851IaYXJGFuOY+0iQne/3t0nAt8AvpXzQmanmtkiM1u0atWq/EbaA+mM8aiBo4Du9TLOXUpRmPGJiIikA2DtfCdSPmEC43pgXNb9scA7nZw/D/h0rgfc/UZ3n+HuM0aOHBl+lD2UXWMM3QuMs/sYb9v5TpGxiIgURs6d79THWKSkwgTGTwGTzGyCmVUDc4D52SeY2aSsu0cArxZuiD3XlGgialFG1I0AurfJRyLpmDLGIiJSJDl3vovESCoJI1IyXdYYu3vczM4AFgBR4Ffu/oKZXQIscvf5wBlmdgjQAqwDTizmoPPVnGimOlrN9jXbA3SrZVsy6Zna4khEGWMRESmsXF0pIhbJZJJFpPjCLL7D3e8F7m1z7MKs22cVeFwF1ZRooiZaQ12sjppoTfcyxu5EbVu5dTRiJLT4TkRECqSjrhTqYyxSOv1j57tkMzXRGsyMoTVDu1VjnMjKGEMqMNZcJSIiBaKuFCLl1y8C43TGGGD72u27lTFOumdKKACiZiqlEBGRgulo5zstvhMpnX4RGKdrjAGG1AxhXVM3M8ZZpRQxZYxFRKSAOtr5znGVU4iUSL8IjBvjjZmMcV2sjsZ4Y17Pd/dWG3wARKNGXBljEREpkI5qjAFljUVKpF8Exs2J5kxgXButzfQ1Diu983PrjHGEloQW34mISGHkqjGOWPAxrTpjkdLoF4FxU6IpU0pRG6vNO2OcSEXG0azfVnXUiKuWQkRECiRnH+PULngqpRApjX4TGKczxjXRGhoT+QXGyVRbtuxSiqpYhBYFxiIiUiBxjxOxSCZLDNsyxuplLFIa/SIwzl58VxutpSmeXylFOmMci7RefKdSChERKZREMtEqWwzbyiq0+51IafSLwDg7Y1wbq6Ux0YjnsTlHPBUYR7JqjKuiyhiLiEjhJDzRqiMFbCurUMZYpDT6RWDcavFdrDY4lmwO/fxkpsZ4W2BcrVIKEREpoHgy3nHGWDXGIiXRLwLjpuS2xXfpADmfBXjprZ+jKqUQEZEiSXiiVUcK2JYxVlcKkdLoF4FxroxxPoFxUqUUIiJSZDlrjE19jEVKqeIDY3dv3a4tGgTG+fQyzpUxVimFiPRWZvYrM3vPzJZ08LiZ2bVmtszMnjOz95d6jNJewhOZ9mxpmT7GCoxFSqLiA+O4x0l6slW7NoCGeEPoa2T6GJtKKUSkT7gJOKyTxw8HJqV+TgV+WoIxSRfiyXi7Uor0YjwFxiKlUfGBcXMiWGTXtpQin4xxuktOqz7GKqUQkV7K3f8BrO3klNnAbz3wBDDUzEaXZnTSkYS3L6XQzncipVXxgXE6AC5MKcW2Y9rgQ0T6sDHAW1n361PHpIwSyfbt2rTznUhpVXxg3DZjXBPrfilFq8V3KqUQkb7LchxrN6GZ2almtsjMFq1ataoEw+rf4t5xu7aWZEs5hiTS71R8YFyQjHFm57ttv66qaIS4MsYi0jfVA+Oy7o8F3ml7krvf6O4z3H3GyJEjSza4/iqRbN+uLf3ZlU7yiEhx9ZvAuCft2jKL79qUUjQrYywifdN84IRUd4oPAhvcfUW5B9Xf5aoxTn925ZPMEZHui3V9St/WrpQivcFHIo8+xt5RKYUyxiLS+5jZLcAsYISZ1QMXAVUA7v4z4F7gk8AyYCtwcnlGKtniHm9XY5z+zFIphUhpVHxg3GEpRTz/Uopom64UKqUQkd7I3ed28bgDp5doOBJSrg0+0p9dyhiLlEb/LaXII2Oc7krRql1bLKLFdyIiUjC5toRWKYVIaVV+YBxvnTHuziSTzLHBR1XEaE4kcVdwLCIiPZdItt/5Lv2ZpcV3IqVR+YFxMpUxjgSTi5lRE63p5uK71qUU2Y+JiIj0RNzb73ynUgqR0qr4wLjt4jsIyinyCoxzLb6LBb86lVOIiEgh5KoxVsZYpLQqPjBuu/gOgommO1tCZ2eMY6nbzVqAJyIiBZCrxrg6ooyxSClVfGCcM2Mc7V7GOLuPcXUqY6zOFCIiUgjxZLxdjXEsEsMwBcYiJRIqMDazw8zsZTNbZmbn5Xj8bDN70cyeM7MHzWyXwg+1ezJdKWJtSiny6UqRShlH2+x8ByqlEBGRwsiVMU6vi2lJqI+xSCl0GRibWRS4HjgcmAzMNbPJbU77NzDD3acBtwM/KPRAuytTShHZVkpRG63Nc0vo4J/ZXSnSpRTa5ENERAohV40xBKWAyhiLlEaYjPFMYJm7v+7uzcA8YHb2Ce7+sLtvTd19Ahhb2GF2X3OimVgk1uqv8JpY97pSRHKUUigwFhGRQkh4ot3Od5D/uhgR6b4wgfEY4K2s+/WpYx35EnBfTwZVSE2Jplb1xRBMMt3ZEjpXuzaVUoiISCHEk/EOM8bqSiFSGmG2hLYcx3JGg2Z2HDADOLCDx08FTgXYeeedQw6xZ5oTze0C47pYXfe2hFYphYiIFEmuGmNQxliklMJkjOuBcVn3xwLvtD3JzA4Bvgkc5e45/w929xvdfYa7zxg5cmR3xpu3pkRTq1Zt0P2McdstoUGBsYiIFEZHNcY10RpljEVKJExg/BQwycwmmFk1MAeYn32Cme0D3EAQFL9X+GF2X4elFN3Z+S4rY1ytUgoRESmguHdcSqGMsUhpdBkYu3scOANYACwF/ujuL5jZJWZ2VOq0K4FBwG1mttjM5ndwuZJrTjS3yxjXxery7ErRvsZYpRQiIlJIiWTuUgoFxiKlE6bGGHe/F7i3zbELs24fUuBxFUxToomaSGEW3+UqpdDOdyIiUggJT7Tb4AOCwHhDy4YyjEik/+kXO9+1qzGO1RBPxokn46GukY59Y5H2pRTNcQXGIiLScx1ljGsiNTQnVWMsUgoVHxjnqjGui9ZlHgsjvfNdJKvGuCamwFhERArD3TusMdbiO5HSqfjAOFe7tvT20GEX4OWqMa6JBZNXkwJjERHpoaQHnyWqMRYpr4oPjHO1a6uN1gKErjNON55o1ZVCGWMRESmQhCcActYYq4+xSOn0i8C4bca4NhYExmE3+Ujm2BI6XUrRFE8UYJQiItKfpde8dJQxVimFSGn0i8A41wYfkE/GuH0phTLGIiJSKOmMcUc1xsoYi5RGvwiM22WM06UUedYYR1RKISIiRZBIpkopIrnbtbUkWzJ1yCJSPJUfGMebMovt0jKL70JmjJMdbPARMS2+ExGRnot7qpSig53vAJVTiJRARQfGiWSC5mQzdbG6VsfzrTHOlFJkZYzNjOpYRBt8iIhIj6Uzxjn7GKe+9VQvY5Hiq+jAOJ0RTvctTsu3K0U84USs9c53ELRsa2rR4jsREemZrrpSgDLGIqVQ0YFxQ7wBoF3GOLP4LmSNcTzpxCLtf1XKGIuISCF0ljFOl1JoAZ5I8VV2YNySCoyrOiilCDnJxBNJYlFrd7w6GlGNsYiI9FhnNcbpZI4CY5Hiq+zAOBEExunSibR8u1IEGeP2gXFNlQJjERHpuTAZY5VSiBRfZQfGHZVS5NmVIp5MUhXNUUoRjahdm4iI9FiYGmNljEWKr18ExunSibSqSBUxi+VRSuGtWrWl1VRFlTEWEZEeC1NKoYyxSPFVdGCcLpUYEBvQ7rGaWE3oUoqWhOfMGNdEIzRrS2gREemhzkopqiJVgDLGIqVQ0YFxR6UUEPwFnk8pRc7FdzGVUoiISM+pXZtI71DRgXE6I9y2lAKCYDnsBh/xZAelFDEtvhMRkZ6LJ1OlFJ1t8KHAWKToKjow3hrfChQgY5xIUtVRH2MFxiIi0kPpjHFnW0KrlEKk+Co6MO6ylCJsu7aE5yylUMZYREQKIV1jHIuoK4VIOVV0YNwYb8SwzKSSrTZWG74rRdKJ5WrXpoyxiPRCZnaYmb1sZsvM7Lwcj59kZqvMbHHq55RyjFO2CZMxVimFSPG1/9O0gjTEG6iN1WLWPttbG61lS3xLqOvEk8mcG3xoS2gR6W3MLApcDxwK1ANPmdl8d3+xzam3uvsZJR+g5BSmxlgZY5Hiq+iMcUO8IWcZBeTfri3nznexKE0tatcmIr3KTGCZu7/u7s3APGB2mcckXUh6kGRRxlikvCo6Y9wYb+wwMK6N5lFKkUgyoLr9r0oZYxHphcYAb2Xdrwf2y3HeZ83sAOAV4Gvu/laOc6RE0ht8xCIxGlsS/N/Dy7hvyUo2NcaZOnYI0Tw2pRKR7uu3GeO6WB0NLQ2hrpPopF1bS8JJJr1H4xQRKaD2kxW0naTuBsa7+zTgb8Bvcl7I7FQzW2Rmi1atWlXgYUq29OK7TQ0Jjr3hca59aBk7bFfDhyYO599vriMej/LYaytJ6PNGpKgqOmPcEG+gNtq+hzHA0JqhrGtah7vnrEHOFux8l7vGGKA5kaQ2R12YiEgZ1APjsu6PBd7JPsHd12Td/Tnw/VwXcvcbgRsBZsyYoYisiNKL7y79y8ssXRnjZ8fty2F7jQJgS1OcA26t4fl31nDWvH/z4zn75EzWiEjPVX7GuCp3xnj72u1pSbawpaXrBXjB4rscXSlSnSqaWlROISK9xlPAJDObYGbVwBxgfvYJZjY66+5RwNISjk9ySGeMn16+ke/OnpIJigEG1sQYNmAA08YO5J7nVvDtu5bgrr9TRIqh8gPjDkoptq/dHoB1jeu6vE486URz9TGuCrLETQktwBOR3sHd48AZwAKCgPeP7v6CmV1iZkelTjvTzF4ws2eBM4GTyjNaSVu7NSjtm7Xbjhz7gZ3bPV4TrWHCDtWcNmsiNy98k98+/kaphyjSL4QKjEP0xDzAzJ4xs7iZHV34YXZPY6Kxw1KKYbXDAFjbtLbL68QTTlWuGuNUxli9jEWkN3H3e919N3ef6O7fSx270N3np26f7+5T3H1vdz/I3V8q74hlwQtBtcvXDtkj5+PV0WqaE818/eO7c8ieO/Lde17kmTe7TuyISH66DIyzemIeDkwG5prZ5DanvUmQcbi50APsiU4zxjV5ZIwTyZwbfNRWBxnjhmZljEVEJE/ukEzw1potLK4PkjS7DB+c89SaSA1NiSYiEePqY/dmx+1qOfvWxWxtjpdyxCIVL0zGuMuemO6+3N2fA3pV6rSQpRS5Ft8NrgnWLm5u0sQkIiIhbVkD958PV+0Blwxj2E8n85noP4DcfYxhW8YYYLvaKq763N68sXYrl92r8nCRQgoTGOfqiTmmOy9W6tY/nfUxzpRSNIYopeigXdugWgXGIiKShxXPwc8+DAtvgJ33o+FD57KgeW92ja4AIHrP2bD5vXZPq4nWtOpj/MFdh3PKRybw+yfe5JGX258vIt0TJjAO0xMzFHe/0d1nuPuMkSNHducSoSWSCZoSTZ32Ma6J1oTKGDfHk1RH2/8VPzgdGDcqMBYRkS6seQ1+OxssAqc+DJ/7Lb+vncvZzf/Nmn1PByC25A64fj94sVUjEQZUDWjXRemcj+/O7jsO5ht/eo6NjS0lexsilSxMYNxlT8zeqDERbPdcG8u9+M7M2L52e9Y1dR0YN8UT1Fa1/1UNSpVSbFJgLCIinWlphHlfADM48W4YvTfuzs1PvsmMXbZn++2CJE70K4/C0J3hj8fDnadB40YAdhywIyu3rGx1ydqqKFceM41Vm5q44j6tnxQphDCBcZc9MXujhnjQ+qajjDEEC/C6KqVIJJ2WhFMTy5ExrqkCYJNKKUREpDOPXA6rlsJnboThEwF4/LU1/Gf1Fr7wwZ1JJBMYRmSHPeGUv8EB58Jz8+CnH4bl/2SnQTuxuWUzm5o3tbrstLFD+dJHJnDzwjd54vU1uV5ZRPLQZWAcpiemmX3AzOqBY4AbzOyFYg46jDCB8bDaYV2WUjTFg44TuTLGA2uCYFmlFCIi0qHVr8Lj18H042DSIZnDf1j4JkMHVHH4XqNJeIJoegfVaBUc/E344gKIROGmIxj1WrA4b8WWFe0uf/ahu7PzsAGc96fnaGxRlySRngjVxzhET8yn3H2suw909+HuPqWYgw6jMd55KQUEnSnWN63v9DrpXe1qYu1/VbFohLqqKJtU2yUiIh154CKI1cEhF2UOvbepkQUvrOSYfcdSWxUlkUwQs1jr542bCV95DPY9kdEvBF/UrnjrX+0uX1cd5Yr/msryNVv50d9eLepbEal0FbvzXahSitquSykaMxnj3C10th9QxbqtCoxFRCSHlUvg5b/Ah86AQTtkDt+2qJ540pk7M9jlLu7xbRnjbDWD4FM/ZvSR1wOw4oFvwZ1fgfVvtTrtQ+8bwbEzxvHzR19nydsbivd+RCpcvw6Mh9UOoyHekMku55LJGOcopQAYMbiGVZubcj4mIiL93GPXQPUgmHlq5lAi6dzy5Jt8aOJwdh05KHUs0WEPY4Dhex1NVaSKFbt8AJbcAT/ZFxZ8E7aszpxzwSf3ZNjAas69/TlaEr1qWwGRPqNiA+N0sNvV4jvofJOPpni6lCL3hDViUA2rNykwFhGRNta8Bi/cAR/4EgwYljn8j1dXUb+ugS/st0vmWMITxCKxXFcBIGIRRg0cxYodJsH/WwR7/Rc88X/wo2nw4CXQsI4hA6r47uy9eHHFRn7+6OtFfWsilapiA+OwpRQAa5s6LqdIL2TItfgOYMSgalYrYywiIm3961qIVMEHT291+A9PvMmIQdUcOnnHzLF4Mt5pxhhg9MDRQcu2oTvDZ34G/7MQdvsEPHoV/GhveOT7HPa+ARy+1yh+9LdXeX3V5qK8LZFKVvGBcWeL79K733WWMU73KB6Uas3W1ohBNazZ0kwy2a09T0REpBI1rINnb4W958DgbQHwW2u38tBL7/K5GeOozlrU3aorRQdGDRzVuivFyN3gmF/DV/4J4z8Cj1wGP57GD8b9k4Ex57w/Pa/PJpE8VXxgHCZj3HlgHCysS+9y19bIwTUkks76Bi3AExGRlGfnQbwhKKPIctO/lhMx4/j9d2l1vKsaYwgyxu9tfY94sk2L0FF7wdyb4csPw+jpDH742zy03SVsfWMRNz/5ZkHejkh/ocAYOu1Mkd5mc7u6jjPGgMopREQk4A6LfgVjZsDovTOHNza2cOtTb3HktNGMHtL6synu8U5rjCEIjJOe5L2t7+U+Ycz74fg74ZjfMDS5jj/XXMR7913BivVbcp8vIu1UbGCc3hK6JlrT4TmDqwYTi8RClVJ0lDHOBMZagCciIgDLH4PVr7TLFv/xqbfY3BTnSx/Ztd1TwmaMIfcmHxlmMOXT2P88TvPEwzjbbmblT2cT39L5ZlYiEuj8z9M+rKGlgbpYHRHrOPY3M7av2Z51TR1PGBsbWjCDQdWpX5U7rHgW3vgXbHiLPbc28cVoM7y2GcZ8AuqGFvqtiIhIX7Lol1A7FKZ8JnMonkjy638uZ78Jw5g6dki7p4SpMR49KAiMz/37uQyoGkDUonxp6pf41MRPtT95wDAGHPcHnrnjaqY+9z02XDeL4afckdmOWkRyq9zAON7QaRlFWlebfGxsjDOoJkbECHpH/v0HwX73AFUDGQJcWLUFHv8dLIwFCyD2PCqYELPa84iISD+w6V1YejfM/G+o2vYZdN+Slby9voGLj8q9MWzOne/a2GW7XThuz+NY3bAax1m2bhmXPnEp+++0PyPqRrR/ghnv/+w53Lh5BEe/fgFNP/84NSf9GUZN7dFbFKlkFV1KURvtuCNF2va123daSrGxsYWxNQ1w87Fw+8nB11SfuhbOeRkueJvk+W+zb9PPuG3KT2H/02FDPfzlbLhqd5j3hWCCjKvMQkSkX/j3byEZhxknZw4lk871Dy9j1xED+dgeO+R8Wkuypcsa44hF+MbMb3DlgVfywwN/yI8P/jHNyWau+/d1nT7vhM8fx/lDr2Rdo5P49RHw5sL835dIP1GxgXHYjPGwmmGdBsZ1m5bzq5Zz4fWH4bArMvvWM3gUmBGNGPHa4SypngaHXgJnLIJT/w4fOAXeWgi3HhcEyfecDW89GZRiiIhI5Ukm4OnfwIQDYMSkzOF7l6zgpZWbOOuQSUQilvOp65vWM6SmfYlFZ3bZbhfm7jGXO169g5fXvtzhebVVUb514qc5JXopbzcPwH87G5b9La/XEukvKjYw3hrfGrqUosPAeM1rfP3trzLQG+Hk++CDp0GOGrChA6q2tWszg52mw2GXw9kvwRduh4kfg8V/gF8eCj95PzxwIbz+d2WSRUQqyasPwIa3YMa2RXfN8SRXP/AKu+04iCOn7dThU9c2rs301s/Hf0/7b7ar2Y4rF12Jd5J4GTdsAJed/Em+kLiY130UfvMcePGuvF9PpNJVbGDcGG/sdHOPtJ0G7cSmlk3BbkLZNq2E330G8wQ/GH01jJ3R4TWG1lWxfmuOPsbRGEw6FI7+JfzvqzD7ehgyDh7/P/jtUfD98fCHz8HCG2DVK8omi4j0ZU/9AgbtCHsckTn0m38t5/VVWzjv8D2IdpAtdnfWNq5leO3wvF9ySM0QTtv7NBauWMijbz/a6bnTxktFroUAABtHSURBVA7l0uM+xjENF/BK9H34bSfB4pvzfk2RSlaxgXHYUooDxh4AwENvPrTtYONG+P1nYctq/rf6m2wZ8r5OrzFkQDXrtzZ3/kK128E+x8GJ8+Eb/4G582D654OWPvedC9d/AK7ZC+46HZ6/Hbas7nLsIiLSS6x5DZY9APueDNGg7/17Gxv58YOvcvAeO3DwHjt2+NSt8a00JZq6lTEG+Nzun2P8duO54skr2Nqytf31W7Zy1aKr+Onin3LgbiP57pyPcsyWc1kcnQZ/Pg0W3tit1xWpRBUbGIfNGE8YMoFdh+y6LTB2h7v+B95bCsf+joVNEzrsYZw2tK4qv53vagbD7ofDEVfBWYvhzMVw5DVBc/ald8OfvgRXToRffjzILm94O/y1RUSk9J78OUSqWi26u+K+l2iOJ7nwyMmdPnVtQ9AZaVhd9wLjqkgVF+1/EfWb6vn+U99v9dgbG9/gmLuP4aYXbuKG525gdcNqjpg2mh+f8BFOaDybx2L7wX1fh4cuhWSyW68vUkkqNjAOmzEGOHjng1n07iI2NG2Af/44CE4P/Q7xCQexsTHO9gOqO33+0AEdlFKENWwCzPgiHPs7OPc/cMpDcNA3oWUrLDgfrpkMvz4ClvwJ4l1kpkVEpLSaNgfrSKZ8OliYDSxavpY7/v02Xz5gAuNHDOz06Wsa1wB0O2MMMGPUDE6Zegp3vHoH816aBwR1y6f97TQ2NW/iov0vIuEJ/vL6XwA4aI8d+MUXP8IZ8a/yZw6Cf1wJt50AzdolT/o3BcbAweMOJuEJ/v7MDfDgd2Dyp2H/MzJZ4GEDOw+Mhw2sZmNjC03xRI/HTSQKY/eFA88NOmCc8TQc9C3YWA+3fxF+tBc8fDlsWdPz1xIRkZ579hZo2gj7fQWAzU1xzrntWcYMreP0gzovxQMyvfR7EhgDnDb9NA4YewDfW/g9znzoTD7/l8/z3tb3+MnHfsLRux3NtJHT+POyP2cW6e2363DuOP0AfjLoLC6NH09y6V/wGw6Ed/7do3GI9GUVGxg3xhtDB8ZTRkxhh9rhPPTcr2H4JJh9HZixbkuQnd2+i8B44shBuMNr7xXhL+0R74MDvw7/79/w+dtg9HT4+/fhR1OD7habVxX+NUVEJJxEHB6/Dsbsm1mk/Z35L/DW2q1cc+x0BlR3vY9WoQLjqkgVPz7ox8zZfQ5Pv/s04waP49qDr2XvkXsDMHvibJatX8aLa17MPGfXkYO484yPsHzSiXyh+XzWrV+P/+IQePSqoP2cSD9TkTvfJT1JYyJ8YBxJtHDQlq3cURPluFE7w4OnAdDYbMQGTWXYgP06ff601PaeC/+zhsk7bdezwXc4yAjs9vHgZ9XL8I8fwr9+EiyamPFF+PCZma/wRESkRJ67FdYtD/rcA/c+v4Lbnq7n9IMmMnNCuEC3UIExQCwS45sf/Cbf/OA32z122ITDuOLJK7jvP/cxZcS2Hfi2q63ixuNn8IvHhnHI/eO5svYmPvbgJfDi/GAtTCddmUQqTUVmjNOrckMFxu5w37nMXfEaHxy6OwPqhjEgNoABsQGsaVxF3bjf8YfXLw/qjzuwy/CBTNphEA+99F6h3kLnRu4On/05nP5kUNO28Kfwo2nBJiLrlpdmDCIi/V0iHtTmjt4bdjuMN9Zs4fw7nmfa2CF89ZDdQl9mbeNaBlcNpjra+beTPbVd9Xb/v70zj4+quh7498xMksmekIWELCQsRRAxAYwguAAquEL9qQX1Jy1VqlXQFivV/tTiT2t/ta1aPipSxK2KtqiIWkS2VrDKJrJvYQnZ932ZZGbu7483gZBMIIGQGSb3m8/7vPfuu3lz7tx555y5c+85jO4zmlVZq9rEPDaZhJlX9Of1+67hKf85zLbPprY0BxZNMKIl6UhJmh6CTzrGB8oPAJASlnL6ypsXwdY36X/pLF6Z8iELr114fJuW8BdsxVfzTeEaJi+bfHJIt1ZcktqL7dkVOJ3dGIs4eiD8cIGRbS9tGmx7B/4yHD76mRFVQ6PRaDTnjp1/h/IjcOWvqWywM+PNzYjA/Gnp+Jk7bl7L6svOOCJFZ7mm7zXk1eadNJ2iJenJkbw0PY6sQVYyaubxceAtqO3vG8mpvnkZmhq6RU6NxlP4pGO8rchYOHBx7MWnrnjkK/ji1/CDSTD+iTaXj5XaCKiZxJIblhAdGM1D6x5i9trZZJZntqmblhhBVWMN7+z8hHnfzGPOv+ZQVNdNI8hR/eGml+Ch7UZ2vr3L4ZVR8Mb1sP0DaKrvHjk0Go2mp9BYB+t+B/EXU933aqYv3sSxsjpevXMEfaNOHYWiNWea9e5MGJc0DotY+DLrS7fXlx5YyszVd3PY+T6hFy7gt5LO9bbfcyRgEKx8HOaPgO/eMUbLNRofxCcd4++LvyclLOXUiqZgJ3xwF/TqD7f81W2q5/8cKuXixAgGRw1myQ1LeGj4Q2wu2Mwty29h1ppZfHroU3aX7uarnK/YUrOYkAG/44/fP8GKIytYn7ueGStndJ9zDBDWByY+Cw/vgglPQXU+fDwT/jQIlj0AB1bqNNQajUbTFaz/E1RmUzp2HtMWbWRXbiUv3zGc0f07n72utKGUyIDIcyBkW8IDwrk0/lJWZa3CqU6OW/x17tfM+2YeI+NGsvCahfQOjiI6ZTmDLkpjXOHD3Gd6kiLCYfmDMD8dvl1gJMTSaHwIn3OMlVJsL9pOWmxa+5WKD8DbU8A/BO78h5GVrhWHims4XFzLNUOMbEV+Zj/uuegeVtyyghlDZ7CnbA+Pb3icqZ9N5YE1D7AqZxmqbihXhDzFhqkbWHjNQkrqS5ixcgYl9d08Nys4Ci7/pRHqbfqnxoj43uXw3u3w/AD48B7YvQzqK7pXLo1Go/EFcr9DbXiBnOTJTPzYzpHiWhbePYJrLzyzBdBlDd03lQLgpv43kV2dzcqjK4+X1TXV8fQ3T5Mansr88fMZ3Wc0j17yKEX1hYwZfpTPZo2lKn4MGUWPc7/9EQ41hMIXc3E+PxC1dIYRZ1+HEdX4AD4XlSKrKotyWzlpMe04xvk7DAdRTHD3cojs67baF7sKALj2wpPTeEZYI3h4xMPMHj6bnSU7KakvISYwhuTQZH721l5yCpxYTBbSYtNYcPUCZq6ayYNrHmTxxMUE+QWdVv5KWyXVjdUkhCQgIp1rfGtMJki9wtjsNmPqyJ5PYN/nsPMfIGZIyoABE6D/BGMBiZuRc41Go9EY2KpLsL93Nw0SwfUHbiQ5wcqfb0/jB71Dz+h+DqeDCltFt02lAJiUMok3d7/Ji1tfZHzyePxN/jy36TnyavN4+7q3jy8CvKzPZQyLHsaiHYv47IdTeO/eUezNr+LvW1K57ftRJNn28F/m9dy8ayURuz4EoCqoL47eQwlPGY4p/iLofSGEJcDZ2jONppvwOce4eX5xemx624u7lxl54QMj4e6PjBjB7bBydwFpSRHEh7uPbGES0/HYkM2kJUfwxoaj2OwOAixm0mLTeP6K55m9bjZzv5rLC+NewGJq+5bbnXY+PPAhnx7+lJ0lO3EqJ+EB4YyOH83cjLlEB0Z34h1oB0sADLzG2G58EXK3wMFVkLnaSAW69hljBD1xJCRdCnHDjMV9kalgObcrpTUajcabKamxsW5fEV/vyeKuQ49wEfk8FvAMj065lKmXJGHpxEK71lQ2VuJUzm51jM0mM3NGzuHeL+9l7ldzCbIE8enhT7n3ontPsp0iwv1p93P/6vt5d++7/HjojxkcH8ZTN13IEzcM4VDxKLZmTeG57GwkZz99yjYxsPoQF9ZsIvLI58fv4wwIxxQ31HCS49MMOxM10Bi80Wi8jA45xiIyCXgJMAOLlFK/b3U9AHgbGAGUAj9SSh3tWlE7xvfF3xPmH0ZKeMqJwroyWPu/sGUxJGbA1HchJNbt/9c3OjhaWsuOnEp+NXFQp147LTGCRoeTffnVXJwUAcCVSVfyWMZjPLvxWaavmM4zY58hNTwVMEYKvs77mhe2vkBmRSaDew1m5rCZxATGsLt0N58f/pythVv5wxV/YGRcF8aRNFsgeZSxTXgCaorg8L8h+1vI3mSEH2qeeyZmCE+EkN7Ge3Z8Hwuh8ca85tA+EBSllZxG4yWcTzrbG7HZHWzNKmfDwRI2ZJawM7eSGFXO4sAXGSKH2DfmBV6dMB2z6exHQcvqjRjGUdbOz00+G0bFj+InQ3/CB/s+oM5ex4yhM5iVPqtNvTF9xnBV4lW8sv0Vrk25lj4hfXAqJztLd7ImZw3rctdxtOYoqX1TSb3qBvr3eYbteU28vv8oRZnfEVWbyQX2Y6Tn5DEg+28EOBcCoAJCkT7pRmKUhBGQMBLC4rv1PdBo3CGtYxm2qSBiBg4A1wA5wGZgmlJqT4s6PweGKaXuE5GpwA+VUj861X1HjhyptmzZcrbyt2Hysskkhiby8oSXofSQ4QxvWQz2Bhj1c5jwpDF62g73vLWF1XsLAfjn7Ms7lbAjr6Key36/lnk3X8j0y1JOurbiyAqe3fgsDfYGhsUMIzowmq2FWymqKyIhJIFfXfIrxieNP2n6xP6y/cz59xyOVR3j9kG3Myt9FuEB4cevNzmbKK4rJq8mj/zafApqC/Az+REXEkdqWCr9IvrhZ/LrsPzHsdVAyQEoOQilB43YyDVFxlZbBHVu5pGZ/Y0EI2EJJxzm5i3UtQ+OAT9r5+XRaLwMEdmqlPLKrAfnm87ubpRSNDQ5qW5ooryuidJaG2W1jZRU28gsrmFffjW786qob3JgMQkZSUHcG/IfLs9ZgNlpR255DQbf1GXybMrfxE+//CmvX/s6GfEZXXbfjmJz2MiqymJgxMB2p+/l1eQx5ZMpRAdGc0GvC9hetJ2i+iIsYuGSuEtIj01na+FWNhZspJe1F1cmXsnw3sOZlDKJnLIm1u0rZu2+IrYcLSFZ5ZEmh0gzZTLccphBZGHByLBXaYnmcHAiAUFJEJaMRCRjjUwgMCqB8JgkAsOjOzwlw+aw8cauN/g2/1vKGsq4deCtTBs87Yxsos1hI8Dcvt+gOTeU1JeglCImKKZL7tdRvd0Rx3g08Ful1ETX+WMASqnnWtRZ6arzjYhYgAIgRp3i5melZJUCRxM4GsHZZMRVrCulsuIIYzc+zkNBA7inINtw6sQMF90GY38BsRec8rZbjpZx64JvABiaEManD47t1DxfpRQZv1vDqH5RzJ/WdipHcV0xr25/lcyKTAprC+kf0Z/JAyYzLmlcu4Hda5tqmb9tPkv2LSHIEkRccBwB5gBK6ksori9us6q4Jf4mf5LDkom0RhIdGE1qeCr9wvvRL7wffcP6njaYvFIKp3JSbisnryaP3JpccmtyqWuspo8llATxJ9HhJM5Wh191IVTlGVu1a293E+/SHADWcGPBozX8+NbgH0yexcwR7GxpKmdHYwmVzkbqnXb6BsWSFjGIQZED6RcxgOCgGGw4KbNVkldXSFVTDSJmAv2CSAhJID4knsiASIL9ghER7E47RXVFJ32BMJvMhPmHEeofSph/GGEBYcbeVWYS3xj9VkpR1VhFQW0BhXWFFNQWUG+vx2q2EuofSkJoAnFBcQT6BWI1W/Ez+Z393PYupKUKUah2y1ofV9oqyanOIbs6m5zqHGqaaugb1peUsBQirZGEB4QTHhB+xsbOyx1j79PZLpxOhd2pcDgVdqeTRrsTm/3E3mZ3tDh30Gh3IiJYTILZJFhMJkwmsJhMx0dra2x2qhuaqGmwU91gHFe1OK5usFNta6Kq/sS5vVW8eTMOrDQSZVWkR0N6ZD2jQorob9uN3+E10FAJfccY09BiOp64oyOszlrNL//1Sz66+SMGRLY/vc/TrMlaw3v73iO/Np9BkYMYnzyeKxKvOGmwZlfJLhbuWMi2om1U2CqIDYxl2uBpTEyZSGxQLE6HmcMltRworOZYaT1ltTbKqyqwVG+i2rmBLP8s8gMaCXMorq2t5fraWi60NWJVChPQqCyUSSSVll7U+EXTYI2mMSgGZ1BvJCwWS3hv/EKt7LcdZGnuMrJqshkWPQyzmNlWvI2UsBTuGHwHsYGxHKw4yOqs1RTXF2M1W7ks4TImJE9gSNQQgv2CKagtYO2xtaw+tpodxTuIDYplROwIJqVOYljMMKKsUd2uK5sfz5a68Phxs/5z7aoaq/iu6DtWZ61mfe56rGYrfcP6MjFlIhlxGSSFJZ3ZwFkreRTqxL7lcYt9s3yt6zXfw4nz+DWH08H3xd/zxZEvWJe9DoVifNJ4xiWPY1j0MBJCEvAzn5ncXekY3wpMUkrd4zr/b+BSpdSDLersctXJcZ0fctVpNxzDGSnZBWOhaJ/hDLvhsJ+FJ6KjmFPTyPDYdCMaw6DrISLptLfefLSMO/+6kchgPz6ffTnB/hYC/Tu/EO03H+/k3Y3H+O1NQ/jxmNRO/3977Cvbx/v73qfCVkGDo4EoaxTxwfH0CelDXHAc8cHxxAXHYXfayavJ43DlYXaX7OZY9TEqbZUU1hWSV5N3kvMAxlxpEyZEBLOYERGUUtidduzKfZxKs5hxKEeb8jb3QgAnSjV/6J04Wz4kgDu3PsDpZKitkRiHA3+lyPT3Y7+/P45OKiFpfq3O/h+C1dKxkW13z0/r97hT9dyUuS/q+Ou6vWc7mMTk1lls1xltpajbyHHSoZu67dy3qwkwB2BztA1VaDVbeXrM01yXel2n7ufljrHX6OwnP9nFB5uzcTgVDqU4jbnpEkQgJMBCmNWPUKvFtZ183Hxt7P5n6Xt0KeJGnwHGr1+pV0L6nZBy+TlbQOZwOhARn/pCvqlgE6/teI3NBZuPlwtCgDnguJ1RqJOey2Exw7gq8Sr2lB5gfe6/sDlODK5YMGFShp5wNtuPU3RHYlMT/1Nazpj6BhSwLjCQ1yLC2WM9MSCUHtafgXEjKLeVsyF3A/X2tjH/h0QNYXT8aPJq8/g271vKbeWAy96JCWn+a6f/WjuGzcct96i2Ze5065kQHhDOuKRxmMTEjuIdZFacyMPQbLOPt8X1+W4eFGt2Ypvla+ncnmt6WXsxuf9kRISPD3580vt+xwV3MDdjbqfv2ZWO8W3AxFZKNkMpNatFnd2uOi2VbIZSqrTVvWYCM12ng4D9HW9SlxAN+Hpey57QRugZ7ewJbYTzs519lVJd8/teF+MjOtvbPhPeJg94n0xantPjbTL1NHk6pLc7svguB2g55JoI5LVTJ8f1s1w4UNb6RkqphcDCDrzmOUFEtnjrKE9X0RPaCD2jnT2hjdBz2tmNnPc629s+E94mD3ifTFqe0+NtMml53NOR3202AwNFJFVE/IGpwPJWdZYD013HtwJrTzVXTaPRaDTnDK2zNRqN5gw57YixUsouIg8CKzFC/yxWSu0WkaeBLUqp5cDrwDsikokx6jD1XAqt0Wg0Gvdona3RaDRnTofiGCul/gn8s1XZky2OG4Dbula0c4LHpnF0Iz2hjdAz2tkT2gg9p53dhg/obG/7THibPOB9Mml5To+3yaTlccNpF99pNBqNRqPRaDQ9Ad+IDaPRaDQajUaj0ZwlPcIxFpFJIrJfRDJF5NeelqerEJEkEVknIntFZLeIPOQq7yUiq0TkoGsf6WlZzxYRMYvINhH5zHWeKiIbXW38wLXI6LxGRCJEZKmI7HP16Whf60sR+YXrs7pLRJaIiNUX+1LTdYjIIyKiRCTaw3I873o2d4jIxyIS4SE5vMaetWeDvIHWNsPDsrTR7R6Wp40e9oAMi0WkyBVTvbnMK+ydzzvGYqRHfRm4DhgCTBORIZ6VqsuwA3OUUoOBUcADrrb9GlijlBoIrHGdn+88BOxtcf5/wAuuNpYDP/WIVF3LS8AXSqkLgIsx2uszfSkiCcBsYKRSaijGwrCp+GZfaroAEUnCSG19zNOyAKuAoUqpYRgptx/rbgG80J61Z4O8gdY2w5O40+0e4RR6uLt5E5jUqswr7J3PO8ZABpCplDqslGoE3gcme1imLkEpla+U+s51XI3xsCVgtO8tV7W3gCmekbBrEJFE4AZgketcgPHAUlcVX2hjGHAFRrQAlFKNSqkKfKwvMRb8Brpi5wYB+fhYX2q6lBeAR3Gb/7F7UUp9qdTxdKDfYsSH7m68yp6dwgZ5lNY2w8OytKfbPUlrPdw6zvk5Ryn1FW1jp3uFvesJjnECkN3iPAcveHC7GhFJAdKBjUBvpVQ+GIoLiPWcZF3CixjGsTmDdBRQ0cJI+UKf9gOKgTdcP/8tEpFgfKgvlVK5wB8xRv/ygUpgK77Xl5ouQERuBnKVUts9LYsbZgArPPC6XmvPWtkgT9PaZniS9nS7R3Cnh5VSX3pKnlZ4hb3rCY6xu2zqHh996EpEJAT4EHhYKVXlaXm6EhG5EShSSm1tWeym6vnepxZgOPCqUiodqOU8njbhDtd8sclAKtAHCMb4Sbg153tfajqIiKx2zXNsvU0GfgM8ebp7dKM8zXV+gzGF4N3ulK355d2Uefx58SYb1I7N8CRepdvd6WERuctT8ngjHYpjfJ7TkfSo5y0i4oehkN5VSn3kKi4UkXilVL6IxANFnpPwrBkD3Cwi1wNWIAxjNCBCRCyukUZf6NMcIEcp1TzashRDefpSX14NHFFKFQOIyEfAZfheX2o6iFLqanflInIRhuHebsycIhH4TkQylFIF3S1PC7mmAzcCEzyUKdDr7Fk7NsiTtLEZIvI3pZSnnL/2dLunaE8P/82DMjXjFfauJ4wYdyQ96nmJa67t68BepdSfW1xqme51OvBJd8vWVSilHlNKJSqlUjD6bq1S6k5gHUYqWzjP2wjgMvbZIjLIVTQB2IMP9SXGT3ejRCTI9dltbqNP9aXm7FFK7VRKxSqlUlzPfg4w/Fw6xadDRCYBc4GblVJ1HhLDq+zZKWyQx2jHZnhsRPQUut1TuNPD3rJI0SvsXY9I8OH65vgiJ9KjPuthkboEERkLrAd2cmIu1eMYc7z+DiRjPAS3KaVaT3I/7xCRq4BHlFI3ikg/jIUnvYBtwF1KKZsn5TtbRCQNY7GIP3AY+AnGl1ef6UsRmQf8COOn6G3APRhzJH2qLzVdi4gcxVhFX+JBGTKBAKDUVfStUuo+D8jhNfasPRvkyrzocVraDA/L0Ua3K6XKPShPGz3c3TpXRJYAVwHRQCHwFLAML7B3PcIx1mg0Go1Go9FoTkdPmEqh0Wg0Go1Go9GcFu0YazQajUaj0Wg0aMdYo9FoNBqNRqMBtGOs0Wg0Go1Go9EA2jHWaDQajUaj0WgA7RhrNBqNRqPRaDSAdow1Go1Go9FoNBpAO8YajUaj0Wg0Gg0A/w9Wo/NdUjVOYwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# let's compare the variable distributions before and after scaling\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(12, 5))\n",
    "\n",
    "# before scaling\n",
    "ax1.set_title('Before Scaling')\n",
    "sns.kdeplot(X_train['RM'], ax=ax1)\n",
    "sns.kdeplot(X_train['LSTAT'], ax=ax1)\n",
    "sns.kdeplot(X_train['CRIM'], ax=ax1)\n",
    "\n",
    "# after scaling\n",
    "ax2.set_title('After Standard Scaling')\n",
    "sns.kdeplot(X_train_scaled['RM'], ax=ax2)\n",
    "sns.kdeplot(X_train_scaled['LSTAT'], ax=ax2)\n",
    "sns.kdeplot(X_train_scaled['CRIM'], ax=ax2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note from the above plots how standardisation centered all the distributions at zero, but it preserved their original distribution. The value range is not identical, but it looks more homogeneous across the variables. \n",
    "\n",
    "Note something interesting in the following plot: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# let's compare the variable distributions before and after scaling\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(12, 5))\n",
    "\n",
    "# before scaling\n",
    "ax1.set_title('Before Scaling')\n",
    "sns.kdeplot(X_train['AGE'], ax=ax1)\n",
    "sns.kdeplot(X_train['DIS'], ax=ax1)\n",
    "sns.kdeplot(X_train['NOX'], ax=ax1)\n",
    "\n",
    "# after scaling\n",
    "ax2.set_title('After Standard Scaling')\n",
    "sns.kdeplot(X_train_scaled['AGE'], ax=ax2)\n",
    "sns.kdeplot(X_train_scaled['DIS'], ax=ax2)\n",
    "sns.kdeplot(X_train_scaled['NOX'], ax=ax2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.9, 100.0)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train['AGE'].min(), X_train['AGE'].max(), "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the above plot, we can see how, by scaling, the variable NOX, which varied across a very narrow range of values [0-1], and AGE which varied across [0-100], now spread over a more homogeneous range of values, so that we can compare them directly in one plot, whereas before it was difficult. In a linear model, AGE would dominate the output, but after standardisation, both variables will be able to have an input (assuming that they are both predictive).  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0xa9fba91be0>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X_train['AGE'], X_train['NOX'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0xa9fbaed1d0>"
      ]
     },
     "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": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X_train_scaled['AGE'], X_train_scaled['NOX'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "feml",
   "language": "python",
   "name": "feml"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  },
  "toc": {
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": "block",
   "toc_window_display": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}