{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"text-align:center\">\n",
    "    <a href=\"https://skills.network\" target=\"_blank\">\n",
    "    <img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/assets/logos/SN_web_lightmode.png\" width=\"200\" alt=\"Skills Network Logo\">\n",
    "    </a>\n",
    "</p>\n",
    "\n",
    "\n",
    "# Polynomial Regression\n",
    "\n",
    "\n",
    "Estimated time needed: **15** minutes\n",
    "    \n",
    "\n",
    "## Objectives\n",
    "\n",
    "After completing this lab you will be able to:\n",
    "\n",
    "* Use scikit-learn to implement Polynomial Regression\n",
    "* Create a model, train it, test it and use the model\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Table of contents</h1>\n",
    "\n",
    "<div class=\"alert alert-block alert-info\" style=\"margin-top: 20px\">\n",
    "    <ol>\n",
    "        <li><a href=\"#download_data\">Downloading Data</a></li>\n",
    "        <li><a href=\"#polynomial_regression\">Polynomial regression</a></li>\n",
    "        <li><a href=\"#evaluation\">Evaluation</a></li>\n",
    "        <li><a href=\"#practice\">Practice</a></li>\n",
    "    </ol>\n",
    "</div>\n",
    "<br>\n",
    "<hr>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Importing Needed packages\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import pylab as pl\n",
    "import numpy as np\n",
    "%matplotlib inline\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"download_data\">Downloading Data</h2>\n",
    "To download the data, we will use !wget to download it from IBM Object Storage.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--2025-10-20 11:51:40--  https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork/labs/Module%202/data/FuelConsumptionCo2.csv\n",
      "Resolving cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud (cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud)... 169.63.118.104, 169.63.118.104\n",
      "Connecting to cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud (cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud)|169.63.118.104|:443... connected.\n",
      "HTTP request sent, awaiting response... 200 OK\n",
      "Length: 72629 (71K) [text/csv]\n",
      "Saving to: ‘FuelConsumption.csv’\n",
      "\n",
      "FuelConsumption.csv 100%[===================>]  70.93K  --.-KB/s    in 0.002s  \n",
      "\n",
      "2025-10-20 11:51:40 (41.7 MB/s) - ‘FuelConsumption.csv’ saved [72629/72629]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "!wget -O FuelConsumption.csv https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork/labs/Module%202/data/FuelConsumptionCo2.csv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Did you know?__ When it comes to Machine Learning, you will likely be working with large datasets. As a business, where can you host your data? IBM is offering a unique opportunity for businesses, with 10 Tb of IBM Cloud Object Storage: [Sign up now for free](https://www.ibm.com/us-en/cloud/object-storage?utm_source=skills_network&utm_content=in_lab_content_link&utm_id=Lab-IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## Understanding the Data\n",
    "\n",
    "### `FuelConsumption.csv`:\n",
    "We have downloaded a fuel consumption dataset, **`FuelConsumption.csv`**, which contains model-specific fuel consumption ratings and estimated carbon dioxide emissions for new light-duty vehicles for retail sale in Canada. [Dataset source](http://open.canada.ca/data/en/dataset/98f1a129-f628-4ce4-b24d-6f16bf24dd64)\n",
    "\n",
    "- **MODELYEAR** e.g. 2014\n",
    "- **MAKE** e.g. Acura\n",
    "- **MODEL** e.g. ILX\n",
    "- **VEHICLE CLASS** e.g. SUV\n",
    "- **ENGINE SIZE** e.g. 4.7\n",
    "- **CYLINDERS** e.g 6\n",
    "- **TRANSMISSION** e.g. A6\n",
    "- **FUEL CONSUMPTION in CITY(L/100 km)** e.g. 9.9\n",
    "- **FUEL CONSUMPTION in HWY (L/100 km)** e.g. 8.9\n",
    "- **FUEL CONSUMPTION COMB (L/100 km)** e.g. 9.2\n",
    "- **CO2 EMISSIONS (g/km)** e.g. 182   --> low --> 0\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reading the data in\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\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>MODELYEAR</th>\n",
       "      <th>MAKE</th>\n",
       "      <th>MODEL</th>\n",
       "      <th>VEHICLECLASS</th>\n",
       "      <th>ENGINESIZE</th>\n",
       "      <th>CYLINDERS</th>\n",
       "      <th>TRANSMISSION</th>\n",
       "      <th>FUELTYPE</th>\n",
       "      <th>FUELCONSUMPTION_CITY</th>\n",
       "      <th>FUELCONSUMPTION_HWY</th>\n",
       "      <th>FUELCONSUMPTION_COMB</th>\n",
       "      <th>FUELCONSUMPTION_COMB_MPG</th>\n",
       "      <th>CO2EMISSIONS</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2014</td>\n",
       "      <td>ACURA</td>\n",
       "      <td>ILX</td>\n",
       "      <td>COMPACT</td>\n",
       "      <td>2.0</td>\n",
       "      <td>4</td>\n",
       "      <td>AS5</td>\n",
       "      <td>Z</td>\n",
       "      <td>9.9</td>\n",
       "      <td>6.7</td>\n",
       "      <td>8.5</td>\n",
       "      <td>33</td>\n",
       "      <td>196</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2014</td>\n",
       "      <td>ACURA</td>\n",
       "      <td>ILX</td>\n",
       "      <td>COMPACT</td>\n",
       "      <td>2.4</td>\n",
       "      <td>4</td>\n",
       "      <td>M6</td>\n",
       "      <td>Z</td>\n",
       "      <td>11.2</td>\n",
       "      <td>7.7</td>\n",
       "      <td>9.6</td>\n",
       "      <td>29</td>\n",
       "      <td>221</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2014</td>\n",
       "      <td>ACURA</td>\n",
       "      <td>ILX HYBRID</td>\n",
       "      <td>COMPACT</td>\n",
       "      <td>1.5</td>\n",
       "      <td>4</td>\n",
       "      <td>AV7</td>\n",
       "      <td>Z</td>\n",
       "      <td>6.0</td>\n",
       "      <td>5.8</td>\n",
       "      <td>5.9</td>\n",
       "      <td>48</td>\n",
       "      <td>136</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2014</td>\n",
       "      <td>ACURA</td>\n",
       "      <td>MDX 4WD</td>\n",
       "      <td>SUV - SMALL</td>\n",
       "      <td>3.5</td>\n",
       "      <td>6</td>\n",
       "      <td>AS6</td>\n",
       "      <td>Z</td>\n",
       "      <td>12.7</td>\n",
       "      <td>9.1</td>\n",
       "      <td>11.1</td>\n",
       "      <td>25</td>\n",
       "      <td>255</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2014</td>\n",
       "      <td>ACURA</td>\n",
       "      <td>RDX AWD</td>\n",
       "      <td>SUV - SMALL</td>\n",
       "      <td>3.5</td>\n",
       "      <td>6</td>\n",
       "      <td>AS6</td>\n",
       "      <td>Z</td>\n",
       "      <td>12.1</td>\n",
       "      <td>8.7</td>\n",
       "      <td>10.6</td>\n",
       "      <td>27</td>\n",
       "      <td>244</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   MODELYEAR   MAKE       MODEL VEHICLECLASS  ENGINESIZE  CYLINDERS  \\\n",
       "0       2014  ACURA         ILX      COMPACT         2.0          4   \n",
       "1       2014  ACURA         ILX      COMPACT         2.4          4   \n",
       "2       2014  ACURA  ILX HYBRID      COMPACT         1.5          4   \n",
       "3       2014  ACURA     MDX 4WD  SUV - SMALL         3.5          6   \n",
       "4       2014  ACURA     RDX AWD  SUV - SMALL         3.5          6   \n",
       "\n",
       "  TRANSMISSION FUELTYPE  FUELCONSUMPTION_CITY  FUELCONSUMPTION_HWY  \\\n",
       "0          AS5        Z                   9.9                  6.7   \n",
       "1           M6        Z                  11.2                  7.7   \n",
       "2          AV7        Z                   6.0                  5.8   \n",
       "3          AS6        Z                  12.7                  9.1   \n",
       "4          AS6        Z                  12.1                  8.7   \n",
       "\n",
       "   FUELCONSUMPTION_COMB  FUELCONSUMPTION_COMB_MPG  CO2EMISSIONS  \n",
       "0                   8.5                        33           196  \n",
       "1                   9.6                        29           221  \n",
       "2                   5.9                        48           136  \n",
       "3                  11.1                        25           255  \n",
       "4                  10.6                        27           244  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(\"FuelConsumption.csv\")\n",
    "\n",
    "# take a look at the dataset\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's select some features that we want to use for regression.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\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>ENGINESIZE</th>\n",
       "      <th>CYLINDERS</th>\n",
       "      <th>FUELCONSUMPTION_COMB</th>\n",
       "      <th>CO2EMISSIONS</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.0</td>\n",
       "      <td>4</td>\n",
       "      <td>8.5</td>\n",
       "      <td>196</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.4</td>\n",
       "      <td>4</td>\n",
       "      <td>9.6</td>\n",
       "      <td>221</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.5</td>\n",
       "      <td>4</td>\n",
       "      <td>5.9</td>\n",
       "      <td>136</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3.5</td>\n",
       "      <td>6</td>\n",
       "      <td>11.1</td>\n",
       "      <td>255</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.5</td>\n",
       "      <td>6</td>\n",
       "      <td>10.6</td>\n",
       "      <td>244</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>3.5</td>\n",
       "      <td>6</td>\n",
       "      <td>10.0</td>\n",
       "      <td>230</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3.5</td>\n",
       "      <td>6</td>\n",
       "      <td>10.1</td>\n",
       "      <td>232</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>3.7</td>\n",
       "      <td>6</td>\n",
       "      <td>11.1</td>\n",
       "      <td>255</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>3.7</td>\n",
       "      <td>6</td>\n",
       "      <td>11.6</td>\n",
       "      <td>267</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   ENGINESIZE  CYLINDERS  FUELCONSUMPTION_COMB  CO2EMISSIONS\n",
       "0         2.0          4                   8.5           196\n",
       "1         2.4          4                   9.6           221\n",
       "2         1.5          4                   5.9           136\n",
       "3         3.5          6                  11.1           255\n",
       "4         3.5          6                  10.6           244\n",
       "5         3.5          6                  10.0           230\n",
       "6         3.5          6                  10.1           232\n",
       "7         3.7          6                  11.1           255\n",
       "8         3.7          6                  11.6           267"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cdf = df[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_COMB','CO2EMISSIONS']]\n",
    "cdf.head(9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot Emission values with respect to Engine size:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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vF4WFhWhtbcXGjRvx4osvYunSpfjlL38Z65dARH466tyP6mrgrbdCt7tcYrtVTTGffFLM2Xn1VdGywalkwsn5RUSGKA47fvy4MmTIEGX16tXKD37wA2XmzJmKoijKsWPHlC5duiivv/66L/af//ynAkDZtGmToiiK8s477yidOnVSGhoafDFLlixRPB6P0tLSIn0OjY2NCgClsbHRoldFRIqiKGVliuJ2K4r42BM3t1tsTzZtbYqSkxP4Wv1vLpei5OaKOK3n1tQoSlWVuG9rU5Tly0P3l5sr3rvg7Tk5Ij7WqqrCv17/W1VV7M+NOgbZz2/HR3ZKSkpQWFiIsWPHBmzfsmULzpw5E7B96NChGDBgADZt2gQA2LRpE/Ly8pCVleWLGT9+PJqamrBz586wx2xpaUFTU1PAjYisZ2TuR6IzO8oRbnIvAHz+uWiiWVUl7hcuBH796/iZHxMP84uIZDjaG+u1117D1q1bsXnz5pDHGhoakJKSgl69egVsz8rKQkNDgy/GP9FRH1cfC2f+/Pl45JFHoj19IpKgzv1IdmZWUamTe4PnvKjJi39RPrX+Trj5MS6XeJ+LimJX30adX3TwoPZ5qTWB2C6CnObYyM7+/fsxc+ZMLFu2DF27do3psefOnYvGxkbfbf/+/TE9PhElH6OjHEYn98bj/Jh4aBfR3AzcdBMwYoS4b26271iUuBxLdrZs2YIjR47g0ksvRefOndG5c2esX78ev/3tb9G5c2dkZWWhtbUVx44dC3je4cOHkf1NY5bs7OyQ1Vnqz9kRmrykpqbC4/EE3IiIomF0FZXR5MXp+jvhONku4nvfA3r2BFasAHbsEPc9e4rtRP4cS3bGjBmDHTt2YNu2bb7bd7/7Xdx2222+f3fp0gVr1671PWf37t2oq6tDQUEBAKCgoAA7duzAkSNHfDGrV6+Gx+PBsGHDYv6aiKjjMjrKYTR5ief5McXFofOL9u2zP9HRmAEBQGxnwkP+HJuz07NnTwwfPjxgW/fu3ZGRkeHbfuedd2L27Nno06cPPB4PZsyYgYKCAlxxxRUAgHHjxmHYsGGYMmUKKioq0NDQgIceegglJSVITU2N+Wsioo5NHeWYOTNw1CYnRyQ6/h/+RpOXeJ8f43YDo0fH5ljNzeETHdXmzSKuR4/YnBNps6MPnRmOr8aKpLKyEtdffz0mTpyIUaNGITs7G9V+yw3cbjdWrVoFt9uNgoICTJ48GVOnTsW8efMcPGsi6shkRzmMXvaKh/kx8WLKFGvjyB7l5aKxbGmpaJJbWip+Li+P/bmw6znY9ZyInKGuxgICR2vU5EVrzkt1dejIUW5u6MhRMhsxQszR0ZOXB2zfbv/5UKjycuCJJ8I/Hq7PmlGyn99MdsBkhyjReb1iIm99vbjsM3Jk4oxwmEleEvn1WuGmm8RkZD0TJgBvvmn/+VCg1lYxghOpsrfbLWpuRXtJi8mOAUx2iBKXVrKQkyMu+STKSEdHT16Mam4Wq670HD/OOTtOWLRIXLLSU1kZfQ0u2c9vR4sKEhFFw0hRvnhm1eTejpI09egB5OdHnqScn89Exym1tdbGWSGuJygTEYXDjtuBwrWdiHULiVj5+GOR0GjJzxePkzMGD7Y2zgq8jAVexiJKROvWiQ90PTU1sVsSbVa0IzLhRrgiTXS2WnOzWP2kLjF++eXYjKw4dVwKLx7n7PAyFhElpHitKBxJXR1w8cXif/JpacDOncAnnxifc+SfHGVmRh7hMtsz69QpsWJmzx5gyBCxsqZbN+3Y4AJ/O3aIOTWxGGHp0YOTkONNSgowe3bk1VizZ8e23g5HdsCRHaJElGgjO126AG1tcrFGl57LMPI+TJgArFwZur2oKHQVVKRKxgAvKXVk5eXAwoWBIzxut0h0rFh2DnA1liFMdogSj9oFXK+i8L59zk/SNZLoqLTOP9zlKhlVVcCkSfpx4RIdlX/Cw1VRpMfuCsqyn9+coExECSlRKgrX1RlPdIDQRqCRJmTLyMzUjzl1KnKiA4jHT50S/548We7YsnGUfFJSxGXUxYvFvROtIgAmO0SUwJzsuC3r4ouje74650ivS7oVysqMxclWJ2YVY3IaJygTUUIrLhaXVuK1vszJk9E9X20EGu1E6yNH9GP27JHblxqXkSEus+nJyJDbL5FdOLJDRAlPLco3aZK4j5dEBxCrrswIbgQq2yU9HJnnDxkity817r/+Sy5eNo7ILkx2iCjheb1iddarr4r7eCokuHOn8edozTnS65IeaV/+SVMkkZYKa8Xt3SsXLxtHZBcmO0SU0OK9cvCAAUBngxMGtOYcRZqQHYmiyE/U7tZNXBKMpKiovd6OzCUsI3FEdmGyQ0RxxcgojboUO3jirtobK14SnjNnwic8nTuL1Vo1NWJ5eE2NSA60JleHm5Bt5ZyYFSvCJzzBdXbisS0AkRbW2QHr7BDFCyMdzNU6O+FWKMVTnR2VVgXlAQOM7ye4gvIdd1j/PshUUI5lWwAiLSwqaACTHSLnGe3vlGgVlCOJpvCa0+9DeXnkuT5lZdZUy7W7OB0lJhYVJKKEYaaDeSL2xtJSXi5GR0pLgaeeEvdpaWK7DKffh4oKkdAEjxq53dYlOtG+R0Sss0NEjtMrmOdfTVgdnZBdih3tkm0rBY9O7N8vegcF83rbR0v0koV4eB8qKoBHHpFvHGpEuJEjI+8RES9jgZexiJz26qtiJZUe//5OiTZfRKspoh6Z84+HHmFG5loZkWi/Y4o9XsYiooRhZnRi40b9xMHrFXFOU0cnjNb/8XpFh+hIK9Oc7hFmdkWczKq7Z56R+x0/84yZM6eOhMkOETlOr2CeVmE8p+eqyGpt1b5UJevpp/XrBznVI8zMXCtAvjZSba3cecjGUcfFOTtE5Dh1dOLmm0Vi4//hGW50Ih7mqoTjvzT8b3+zrqKzOlqilcA40SNMdq7V4sVAVpY4p6++An7849AESeu1sY4PWYVzdsA5O0TxQmvuR26uSHTC1dlxcq6KFq3XYKV4qh8kO9fKn9sdPvkLfm2cs0N6OGeHiBJOcTHw+edy1YRl5qo8+aQYfYhVz6xw81es5D9aYsXrOnUKmD4dGD9e3J86Jf9cM6Nmkc7Vf9UdIBKY2bMj72/2bCY6pI8jO+DIDlEiCzcadMstIhmweoVQOHoVne1k9nVNmACsXBm6PbgtRDinTpnv6h6J/6o7IPrzpOTFkR0i6hC0RoMWLgR+/evY9szSm79iJzOvK1wCAYjtEybo7+PZZ+WPZ4T/iFF1NfDWW6ExLpfYHi/9zyi+cWQHHNkhSiZO9cwyM3/FSi6XWI21dClw5EjkCcqyIzL//d/islK49gwzZoiKxlYJ/t0kYv8zii2O7BBRh2SkGrOs1lYxSXrGDHHf2hoa43SlZkURr3vsWP2l6mVlcvt84IHI7RmsXAWlterOjt8ldUxMdogoqVhdf0e2L5NaKyieHDgATJwYmvDs2WN8X2p7Bv/XPW2a+RGV4Odp1QRKlFpKFP+Y7BBRUrGy/k64ysdaH/xuN3DZZfLnGUt33x34GoYMMb+vhQvbR7ZSUoBLLzX2fJdL3F59VX/VXTzXUqLEwjk74JwdomQiOx/l5MnIjSqN1niRiQeAG24QE6oHDwb+3/8DJk8W2+3+P/GaNcCYMeLf0a6iqqwUlZFlX7O/cHWTtMRrLSWKH5yzQ0Qdhn+fJdn5KHoriYz2ZZKJB4BrrgG2bwfefFPMrdFq82CHdeva/92tm1i2bZbankH2NZeU6NdN0uJ03y9KHo4mO0uWLMGIESPg8Xjg8XhQUFCAv/zlL77HR48eDZfLFXC75557AvZRV1eHwsJCpKWlITMzE2VlZWhra4v1SyEihwT3WXr6abnn6c1bMdqXyWwfp+Cl85WVcvuJ1ooV5hMedWKy7NwfRRF1c0aPNp6YONX3i5KLo72xcnJysGDBAgwZMgSKouDFF19EUVER/vd//xcXX3wxAOCuu+7CvHnzfM9J8xt79Xq9KCwsRHZ2NjZu3Ij6+npMnToVXbp0weOPPx7z10NEsaVWLDZzCShc01GV0b5M0fRxcrtFIgCIkZInn4x86cZ/iXl9PTBnjv5x1f37W7FCXNIqKxOJy3nnAf/zP8DZs+H343aLicnquciQjQvHib5flGSUONO7d2/l+eefVxRFUX7wgx8oM2fODBv7zjvvKJ06dVIaGhp825YsWaJ4PB6lpaVF+piNjY0KAKWxsdH8iRORIS0tilJZqSjTp4t7A//JKoqiKG1tipKToygiJTB+W7pU//zc7sj7cLvbz9tofKT34o9/VBSXS9z8n69uW7488H3IyIh83IwMESejrCzyvsrK2mNfeknuvX7pJbljExkl+/kdN3N2vF4vXnvtNZw4cQIFBQW+7cuWLcM555yD4cOHY+7cuTh58qTvsU2bNiEvLw9ZWVm+bePHj0dTUxN27twZ9lgtLS1oamoKuBFR7Mgu544k2orF//535MeN9mUy28dJ67249VbgxhvDX7opKmqfo7RhA/C730U+7nPPyY+CVFSIkZ7geLdbbK+oaN+Wmyu3T9k4Irs4ehkLAHbs2IGCggKcPn0aPXr0wJtvvolhw4YBAG699VYMHDgQ/fv3x/bt2/HAAw9g9+7dqP6maERDQ0NAogPA93NDQ0PYY86fPx+PPPKITa+IiCJRl3MHU5dzA4EfqOFEW1ulb9/onq9FPe+FCwMn7rrdItF58EEgLw84dAjo319cWtKqQOz1ipYNc+YA118feOlm5crQqsI5OSIRqaoSl7/8t5vpmVVRATz2mJiAXFsbvoLyyJFARgZw9Gj4fWVkiDgiJzm+9Ly1tRV1dXVobGzEG2+8geeffx7r16/3JTz+PvjgA4wZMwZ79+7F4MGDcffdd+OLL77Ae++954s5efIkunfvjnfeeQfXXnut5jFbWlrQ0tLi+7mpqQm5ublcek5kM6PLuSNZu1ZUCzbLfym2ltZWsWop0vyVTp3EnJfgc21tDU0UBgwADh82do7B70W4OUrqnJg//lEkcbGa1+L1AllZ+snO4cOcX0P2SJil5ykpKTj//PNx2WWXYf78+fj2t7+N36hrDYNcfvnlAIC9e/cCALKzs3E46P8e6s/Z2dlhj5mamupbAabeiMh+RpdzO2nx4siJDiAeX7w4dHtKiqhDs3ixuDeT6ACB74XXK7q7a309VbfNmSMSHLMrn4zasCFyogOIx9nOgZzmeLIT7OzZswGjLv62bdsGAOj3TbnMgoIC7NixA0eOHPHFrF69Gh6PR3NkiIicZXZ5tha//+xN0Xv+hx/K7Ucv7uuvzSU6KvW9iMc+UWznQInC0Tk7c+fOxbXXXosBAwbg+PHjqKqqwrp16/Dee++htrYWVVVVuO6665CRkYHt27ejtLQUo0aNwogRIwAA48aNw7BhwzBlyhRUVFSgoaEBDz30EEpKSpCamurkSyMiDdEszw4WbYsAved37y63H724H/xAbj/hqO+FbMLw+98Dy5eHn2djJbZzoIQRk7VhYfzsZz9TBg4cqKSkpCh9+/ZVxowZo7z//vuKoihKXV2dMmrUKKVPnz5Kamqqcv755ytlZWUhy8s+//xz5dprr1W6deumnHPOOcqcOXOUM2fOGDoPLj0nio1olmcHU5eeBy/P1ru5XIqSm6u/FPvxx+X29/jjkffTp4/55fH+70VNjbnn+y8Vt5rM8n+Z95rILNnPb0dHdn7/+9+HfSw3Nxfr16/X3cfAgQPxzjvvWHlaRGQTdXm21mos1fTpwE9+0j659+WXgR49QuPUVgI33ywm6MostTDSYiBC9QpDcf37i0tZZvgvVVe7qocrNqjF6Ao3o9xuQG8QPSWFk5PJeXE3Z4eIkktrq0guZswQ9489Fr6OS1aWSGBWrAB27BD3PXsC3/ue9r7DtRLIzQXy80PjFUXUr5FZit3cLPf69OIkvrOF0KppE6lPlB7/TuVWam7Wn19VWyv/XhLZhckOEdkmXPFAQCyprqwUIzmVlcAll4SfyLt5c+SEx7+3VE0N8OMfi+doWblSrnihVfNR+vQRSVwkmZmB78XJk9ojMeGSOz12rXCbMsXaOCK7OF5nJx7IrtMnCok/3xQAACAASURBVOb1Jn6/HrteQ7jigSr/kYvmZjGCo+f4ce1LWv6squXz4ovAHXfon9PSpcDtt+vHZWdrJ3NZWUCEGqia/H9nf/qTGAHTM3269jL5aAwfLne57+KLgU8/tfbYREAC1dkhSlTB3bavvlr8/E2B74Rg12tobRWXTiLxv7Ri5QiBVbV8vvxS7pxk46ZONbY9ErVx6KRJ8qu9ZFfCGRGrRqBE0WKyQ2SCWsk2uO7JwYNieyIkPHa+BqMJh5X1d6za1zdlvXTJxEUa5XriCWM9wYJNm6Y/EuffqdxKV15pbRyRXZjsEBkkU8l21iz9D3sn2f0ajCYcVtbfsWpfVk1QNjrKZZTZBqRWuOgia+OI7MJkh8igeKxka5Tdr8FowvHyy3LxMnFWjXT07y93TnpxsWiRUVEhOqFrKSqyZ9k54OyoEpERTHaIDEqGEvl2vwajH4I9emgvFfeXnx9+crLXC6xbB7z6KrBxoxiVikRmpKOgIPLjsnFWXqILp7oaeOst7cfeesu+y6pOjioRGcFkh8igZCiRH81r8E8s1q3THrUw8yH48cfhE578fPG4Fq1J1n/8oxjR6BT0f7hOnULr14Rj1ciOlZfotES6JKkyc0lS5vcMiPcy0u/NrlElIkNiUs85zrFdBBmh16ZAth2Bk8y+huXLQ9sD5OSI7VrKykLbQ+i1MDh+XFEmTFCUvDxxf/x4+Njly7Vfg7otuFXDueeGP9dga9bItWRYsybyfqxskaFFto1ETY38Po38nsvKIh/XznYVRLKf30x2FCY7ZJz6IRv8Qatuk/1AdZLR1xApsYj0mltaFKWyUlGmTxf3Zj/Ug8n0ZTJ6rv6qquT2WVWlvy87EwIrz1NRjP2e7U7kiPQw2TGAyQ6ZsXy5GCmQHeWIR1rf4HNzQ1+DXmJh5WhWW5sYhaiqEvfh9mmmMaaRc7V6xMTMKJcMK8/T6O+5slLu2JWV0b1GonBkP785Z4coColeLE2r1cK+faG9o2K1As1IkUOzk6dlz1VtvBnud+xyiR5cI0fKHbeiIrRFRri2EEao5xmJ7Hka/T3HYvI1kRVMdz0/duwYPv74Yxw5cgRnz54NeGyqmZKgRAlELcinKIHb1YJ8b7wh12wyUcRiBZrR9zTaCeB65xqpq7qR7un+UlL0V4oZ5XaLSsqRWnPccovceRr9Pds9+ZrIKqZ6Y7399tu47bbb0NzcDI/HA5ffVx+Xy4Wvv/7a0pO0G3tjkRFerxhtCPcN2OUS37T37Yv/PlnV1WIlj/9ryckRH/L+icW6dWKURU9NjWhjYJSZ91R9zsGDoQmSjMpK0ZdKrx+Y7HvkFL33DhAjOzJ/j0Z/z9H0NEuGvnLkPFt7Y82ZMwc/+9nP0NzcjGPHjuHf//6375ZoiQ6RUclQVBAw1i5i5Ej9Bpw9eshf0glm5j1VR17MJDput+jALtsPLPgYZo5pF733DpD/ezR66e755+XOMTguGfrKUWIxlewcPHgQ9913H9LS0qw+H6K4lwxFBY22i/B69dsiNDebby8R6/c0+DzD9QNTE8KDB+XinWDle6cmkEBowqN16W73brlj+8clQ185Sjymkp3x48fjk08+sfpciBJCvBQVlC36psXoSIr6AahHNi5YZqbxODVhiyT4ski4yyThErxIxfoUxXixvoYGIDsb6NpV3Dc0yD83HKv/HouLxfyoc88N3J6TEzpvSvb81bhk6CtHicnUBOXCwkKUlZVh165dyMvLQ5cuXQIev/HGGy05OaJ4pA71h5sros4vMXtJR0a080iMjgasXCkXv3KlqFAcCzKXb7ze9rk5hw+LS1fh+Cd4o0cbuzwkM0+pe3ex+kp1+LBIQNLSgBMn9J8fjh1/j8XFogK13pwao4mWkSTbzNwvonBMJTt33XUXAGDevHkhj7lcLniZllMSs2OVjhFWrASLl9Ep1ZEjxuNkE7asLLFa6dVX5eLV/QZfugpHJi440fF38qR43GzCY9ffo9utn3BccIHcvtS4ZLgETInJ1GWss2fPhr0x0aGOwMhQv5WsugxgdCJquI7awWTjgvXqZTzOaMJmNP7LL+Xi9eIaGsInOqqTJ6O7pOXU36PRhq9mfs9EVmBRQSKTZAvyWUn2MsDixZHn8hidiKo3N0YlGxfs2WeNxxlN2EaOBDIyIu8/I6M9vm9fuXPSi7vkErn9yMaFU1wsivf5Fy3cu9fev0ejDV/DdWYPJhtHJMt0srN+/XrccMMNOP/883H++efjxhtvxIZ4X2tLZDF1qH/SJHFvd50Q2eF9mWXVRkcD9KpFR1NN+rPPjMcZTdiMsmoU4tgxuf3IxoVTXS2K95WWAk89Je4HD7Z/dVNFhZinpTUZPLjDvJnfM5EVTCU7r7zyCsaOHYu0tDTcd999uO+++9CtWzeMGTMGVVVVVp8jEX3DzByaSEt6ZUennnlGv7aMoog4M8xW4jWSsG3YABw9Gnn/R4+2r0B77jm5c9KLiyZpam0VCduMGeK+tVX7uU4v55ZthTFkiNz+ZOOIpJlpvDV06FBl4cKFIduffPJJZejQoWZ26Sg2AqVEoTZq1OpKbUXzy3CmT5c7zvTp5vZ//Ljc/o8fD/++6DUPNdodPC9PLj4vL/Jrq6+X2099feDzZBuHxrJJa7ROnpR7L06edPpMKVHY2gj0s88+ww033BCy/cYbb8S+ffuiTL+IKBz/SzdGqHN5Zs7UHyXQEk0PJJl6QD16APn5kfednx++irPM5USjE5St6vuUnS2Wl0eSlibiVOXlotdV8Hvl9Yrt5eXt2xKpone3bvqT2IuKRByRpcxkUoMHD1Z+97vfhWxfsmSJcv7555vZpaM4skOJpqjI2MiO1k1rlCAcs9/Ily8PHXXIyRHbteTna+83Pz+690tR9EfFgkdAjh6Ve81Hj8odPy1N+/lpaYFxLS2hIzpav7uWFhFvdMQqHoT7+y0qcvrMKNHYOrIzZ84c3Hfffbj33nvx8ssv4+WXX8Y999yDWbNm4f7777c2GyOiAOXl8kX+ItEaJQjn73+X26d/nJl5JB9/LJpGTpgA5OWJ++PHxfZoGZ3Q/NJLcvuVjTtxQkwwz8oCUlPFfX19aH2dZ57RLx3g9bbPj4q3mkkyVqwQc3pKSoBx48T9yZNiO5EtzGZT1dXVylVXXaX06dNH6dOnj3LVVVcpK1asMLs7R3FkhxKFzLd+MyM86ihBOEZHD/TmkQDOzSPRGm3KzQ0dbbJ7nlI406bJHXfaNBHPeTDUkcl+fpuqoAwAN910E2666Sbrsi6iBOT16pfUt5LMt36j1FGCWbPCx1jdFgCITVsArd+PbCsEq+bsGCW7hF+Nk61RtGQJcOmlsftbJYonppMdoo4u2v5UZtTWOrPfK68UH4yREi23W8QB1rZaMEvv96OXZN1yS+ReWv5xVrr8cuDpp+XiAPm/iV/9KrBzvd1/q0TxRHrOTp8+ffDVV18BAHr37o0+ffqEvRElu3DzUQ4csLeuidWjCLL73bhRbh7Jxo3i31a1WjDLirozP/yh3LFk42Tl5hqLk/2b8E90gNjV4CGKBy5FURSZwBdffBG33HILUlNTsXTpUrgijLXefvvtlp1gLDQ1NSE9PR2NjY3weDxOnw7FOa9XVCWOdJkmN1cU57P6MkFrq1imbOWlLLdbTA5VS/prefVVUZFZT1WVWP69bBkwebJ+/CuvALfdJn+uMvR+P2oXcL3fT0YG8PXX+sfr00e/WKERMr9j/99ZNH8Tsu8FUbyS/fyWvozln8DccccdUZ0cUSJzcj6K2ovoiSes26d/76JwjM7ZCa5oHI5snBFG+odlZYWfv+LxyCU7Rr4ftbaK+VG1tWJEZtq00PfeyCja6NHi+ddfb26Fnvpe2D13ishpppaeb926FTt27PD9vHLlSkyYMAG/+MUv0GqgUtmSJUswYsQIeDweeDweFBQU4C9/+Yvv8dOnT6OkpAQZGRno0aMHJk6ciMOHDwfso66uDoWFhUhLS0NmZibKysrQ1tZm5mURSXF6PkpFhfnu4v60eheFo84PkY1Tm3RG4t+k00pW9Q978EG5/cjGlZeLERj/3lVpaaFL//fvl9ufGuf1Alu2yD0nHNn3jChRmUp2fv7zn+Nf//oXAFFN+Sc/+QnS0tLw+uuvo1ymaMc3cnJysGDBAmzZsgWffPIJrrnmGhQVFWHnzp0AgNLSUrz99tt4/fXXsX79ehw6dAjFfrPpvF4vCgsL0draio0bN+LFF1/E0qVL8ctf/tLMyyKSEg/zUcx2hS4pCe1dJFPh2GhXcrWmTaSO5NE06Qzm30Pqb38z/nytuVanTsk9VybOSEVkozWNZEYa9cRTDR4iW5hZ1+7xeJS9e/cqiqIoCxYsUMaNG6coiqJ8+OGHSk5Ojpld+vTu3Vt5/vnnlWPHjildunRRXn/9dd9j//znPxUAyqZNmxRFUZR33nlH6dSpk9LQ0OCLWbJkieLxeJSWCIVDTp8+rTQ2Nvpu+/fvZ50dkvbKK3J1TV55xfpjy9SvMVJFV7bCsdmaM7I1baKh1UPK7M2/9o9Vv2ejFZGN1tmRrYGkdYunvllEZthaQVlRFJw9exYAsGbNGlx33XUAgNzcXN+KLaO8Xi9ee+01nDhxAgUFBdiyZQvOnDmDsWPH+mKGDh2KAQMGYNOmTQCATZs2IS8vD1lZWb6Y8ePHo6mpyTc6pGX+/PlIT0/33XJllz8QIbr5KDKjKJFE+y3+8OH2Y7/xhvyKpWi6kst0VTcr3IiJWf49pKyad2S0IrJsx2+XS/wug67sS9OqGh2NaP+2iWxlJpO6+uqrlalTpyovvfSS0qVLF2XPnj2KoijKunXrlIEDBxra1/bt25Xu3bsrbrdbSU9PV/785z8riqIoy5YtU1JSUkLi8/PzlfLyckVRFOWuu+7yjSqpTpw4oQBQ3nnnnbDH5MgORcNsdWCjfaK0RPMtXms0QfYb/5Ejcvs8csS691mPHdWk/UdqrKoCbXRUTLYDvOzvElCUjAx7R9is+NsmMsPWkZ1FixZh69atmD59Ov7zP/8T559/PgDgjTfewJVqVTFJF154IbZt24a///3vuPfee3H77bdj165dZk5LWmpqqm9StHojkuV2i+XVkdxyS+C3ZSvqvgDWzq2I9M1bUQJHOWSLpVtRVP3LL4HzzhMdzs87L/zcJ9lq0iUlYlSppET++IC537MWo6Nizz8vF+9P73341rfsG2FzquYUkSFWZlinTp1SWltbo9rHmDFjlLvvvltZu3atAkD597//HfD4gAEDlIULFyqKoij/9V//pXz7298OePyzzz5TAChbt26VPiZ7Y5ERRr/x68UbmTdh5lt/NDd1jk9urlx8bm507216uvZ+09NDY42OmLz0klz8Sy+Z+z2H88UXcsf94gtjr8vozY7eWPHcA406BltHdvbv348Dfmn8xx9/jFmzZuGll15Cly5dokq+zp49i5aWFlx22WXo0qUL1q5d63ts9+7dqKurQ0FBAQCgoKAAO3bswJEjR3wxq1evhsfjwbBhw6I6D6JwjNTZkYkPHkWJRHaZs1XUkaQBA+TiZeOAwBVUixaJejWNjdqxjY1Ar16B24yOmMgW/lPjjP6ew/ne9+SOq8bZVSW7rMz6fVr1HhHZzkwm9f3vf1956ZuvP/X19YrH41EKCgqUc845R3nkkUek9/Pggw8q69evV/bt26ds375defDBBxWXy6W8//77iqIoyj333KMMGDBA+eCDD5RPPvlEKSgoUAoKCnzPb2trU4YPH66MGzdO2bZtm/Luu+8qffv2VebOnWvo9XBkh4xYulTum/TSpSLeaMfwSH74w9iM6ASPNh09Kve8o0fl3kOzK6j85wQZXeVkdGTHqtVYqaly+0lNFfGyXcyN3oKmN1rCyZWJRIpi88jOp59+iu998zXkT3/6E4YPH46NGzdi2bJlWLp0qfR+jhw5gqlTp+LCCy/EmDFjsHnzZrz33nv44TfNZiorK3H99ddj4sSJGDVqFLKzs1HtdwHY7XZj1apVcLvdKCgowOTJkzF16lTMmzfPzMuiKDm5GiN4lMBAbUvDVqwwFme0+nAk3bvL7SsaWqt0tm+Xe65MXDQrqPxHSdRq0pH4V4c2OrJjVT0l2cFuNU62zo5Rsqu8jHC65hSRNDOZVPfu3ZV9+/YpiqIoN9xwg7JgwQJFURTliy++ULp27Wpml47iyE70nFyNoTVK4HaL7XaQHV354Q9FvDqvweWSG0WJRHZUKZqb1iqdWNaciXTr3j10n7K/f6Ov4Q9/kIv/wx8iv+apU+X2M3WqiLdyxZ3/zY45OxzZIafZOrJz8cUX43e/+x02bNiA1atX40c/+hEA4NChQ8jIyLAwFaNEYNVKIzOMVKa1ygUXGItTqwkDoRWFjdY6GThQ7thGVVZGXqVj1Td42RVU4fTtG7qtokJUg66sDK0O7c9o3RzZKtV6cd/5jtx+1Dg7qhkXFQHdulm/Xyd7oBEZYiaTqqmpUXr16qV06tRJ+elPf+rbPnfuXOWmm24ys0tHcWTHPCtXGhlldM6GVWTnVAR/k7aimrBdtWXUeSrhGJ3vEk60K42iqeNjdOWQ0RG8cIz+neqNBKrxweedn68dW1Rk/j2z+j0lspqtIzujR4/GV199ha+++gp/+MMffNvvvvtu/O53v7MoDaNEYOVKI6OMVqa1SrduQOfOkWM6dw79Jm1FNWGZjthm6M0TMTrfJZxoVhqlp2uP7ABy88WM9usyOoIXjtG5RXojgS6X+PvxH8nauxf4+GMxolVSAowbJ+5PnpSfY2aG/3sa7lyt7IFGZFqMkq+4xpEd86xcaWSU2X5N0XKymrDsHAmjN7XPUrTH1ZubYbZOkFadHZXR+WKyI2xmR/DCMTq3LNx5lpXFX7XiWPRAI9Ii+/mt8/203aWXXoq1a9eid+/e+M53vgNXuK9HALZu3WpBGkaJwMqVRkaZ7dcULSN1U/bts/bYdq1q0VupY9XcDNnqwF27Am1tQM+ewI4d4ferzhdTlMDt6nyxN94IHTkrLhZzWDZsAOrrxd/myJGhow/duom4lSvDn6eRuTAVFcBjj4mRxtpa8Xc5bVr7iE4wrfP88kvgJz8x9npjQfY9JXKKS1GC/7PR9sgjj6CsrAxpaWl45JFHIsb+6le/suTkYqWpqQnp6elobGxk6wiDWluBtLTIl1bcbjGcHu5/6madOiWOrefkSWsnZ3bvLvapJy0NOHHCuuMCwLJlwOTJ1u4TEJef+vQJ/7jXCwwaFPmSZW6uSO4ifcDNmAE89ZSxc3O7xWWe4AnHeufkcgE5OfrnpGfCBO2Ep6jI3ktEwWL1eokSieznt/TIjn8Ck2jJDNlHZg6J1yviRo+29tiy9Uj+/ndrj52aKpfspKZad0yVXata7rwTePPN8I+73cBll0VOdi691Lo+Uf7UlXVAYMJjZL5YNL//Cy4QiYT/10KXS35Oj1Vi9XqJkpGpCcr+mpub0dTUFHCjjqO+3tq4RDj29ddbG2fEyJHi27vV9uyJ/HhrK7BqVeSYVav0izlOm2Z+1GHhwsD9y/5e1641X+hSLW0QPP6tKOZKG0RT/NLJ/9aIEp2pZGffvn0oLCxE9+7dkZ6ejt69e6N3797o1asXevfubfU5Uhxzcs6OU8f+7DNr44zwX6ljJb3LbVatfJNZmSS7f9nf62OPAbfeClx9tahTJFv3qbVVJFiRBCdgkZSXi0ubpaXiUl5pqfhZNmFy8r81GU5WUCfSI30Zy9/kyZOhKAr+8Ic/ICsrK+JkZUpu6kjDwYOh336B9nkEI0cmz7Fl5//YUcQNAD76yPp9futbkR+vrZXbj0yceilq4ULjH4j++9f7/Ws5eBCYOBFYvlx/Iq+RBG/WrMhx6giR1vO1LtFpcfK/NT3V1cDMmYGX2XJyRGLuxIRpohBmlnp1795d+b//+z8zT41LXHoeneXLRQG04CJo6jY7l5+aPXZbm6LU1Igl8TU1xoqe/exnckuSf/YzK15hoJaWyMXmzN4GDVKUvDxFmTBBLA8PVlkpt5/KSmOvpbJSlAaYMMHc/sP9/vVuGRn6v3OrShtYWfzSyf/W9M4p+DU5eU7Ucch+fptKdkaPHq2sXr3a1InFIyY70Yt1fyp/Rmt8RNvH64or5D4Er7jCuteoqqiwPtHRuuXnBx7X7mrV0exf6/cpc1uzJvI5WZXgWZ0oxlNNGycrqBMpis3Jzt69e5WxY8cqS5cuVT755BPlH//4R8At0TDZiU64b3bq/+xi8T9h2ZEaK76Fyn6w5uRY+QqFq66KTbKjlfCUlUWOjzaxjWb//r//yZPlXt9DD0U+H6sSPDuKX0YzMmmlmhq511ZT48z5UfKzvKigvy+//BK1tbX46U9/6tvmcrmgKApcLhe8nJnWYXi94lq9ooSPmTVL1CSxs/aH262/3DbSuSqKmPMgc66ypZiMlGzyeuOvINvmzUBzM9Cjh/g53FybcHVw9LS2BhbYe+wx8/v3//3v2mXsPMJRJ1NrzbVR+bd5CMeO4pcyf++xwBVilDDMZFIXXXSRUlxcrHz00UfKvn37lM8//zzglmg4smNeIn2zs+pcZ8+W28/s2XLnZeSy2t13x25kBxBzaYL5z7WprDR36SrSZc9o979mjdxr07uMJXOuMpxqWBsLifTfPyUnW0d2vvjiC7z11ls4//zzrc28KOEk0jc7q85VpmqzbJzRdgff/z7w3HNyx7eC1uqqlBT91UeRWLEyKZLRo4GMjMhNSTMy5EdGjLZ5CGbVCFE8iucVYkT+TNXZueaaa/CPf/zD6nOhBBTvtT/8ZWZaE3fllXL70Yrzr0Wydm3ky2qASCr8L+mcc47csa1idV8xq2vXaHG79RPC554zdplQTfAWLxb3iZiY2EGvQzvArucUH0yN7Nxwww0oLS3Fjh07kJeXhy5dugQ8fuONN1pychT/1G92ej2TkumbneyckF27gGuvbf9ZqxZJJIoSWv7/rbcMnWrUXn7Z2v1ZWbsmEr1aRB99FLv6L7IJ3mOPJWYSVVwsRiC16uwsWsQ6OxQfTCU799xzDwBg3rx5IY9xgnLHYlXPpFg4csSauM8/l9uPf1y4y1Uy/C+ryRb3s0J+fvvkZKvs3m1tnJbWVuDJJyPHPPlk7JKLWCV4TmLXc4p3ppKds2fPWn0elKCM9Exy+lurVZfcBg6U248aJ7NiLRL/y2pdu5rbh1H5+cDHH1u/34YGa+O0LF4M6P0v6uxZETdnjtw+o1ktZ2X16XgWLyvEiLQYmrNz3XXXobGx0ffzggULcOzYMd/PR48exbBhw6w7O4p7VvVMigX1klu47iYulz2X3PS6VRtx0UXW7CdYjx5AXh4wYQJw/Lg9iQ4QmzleH35obVx1NTBokOitpfbYGjRIvseWHUvPicgYQ8nOe++9h5aWFt/Pjz/+OL7++mvfz21tbdgdzfgzJZxE+tZq1WTKL76QO54aF+1KNP/Lap1NjcXq698f2L4dePNN6y9d+bvgAmvjtMiev0ycevkxOFk9cEBsl0l4ZDq9u90ijojsYSjZUYLG4YN/po5n0CBr4+ymTqY899zA7Tk5ocu8w8nNlTuWGie7Ciwc/1EOuxKRWI0qxOKD/9ZbrYnTu/yoKKGr5bTIdHpP1KXnRInCpu+J1FHk5Vkbpyfc3AkjcyqinUy5b5+1cZFkZAReVvvgg+j3qeX0afnYaOavxKLmjJH6N5HIXH4MXi0XjtXVp4nIGEPJjsvlgito/D/4Z+pYvvzS2rhItJZu5+QAkyYBy5YBhw61b+/fX0xADTdSE81kyr17jcXJrgKT4TdFzlIHDojaP3rJS7jfwW9+I7/E2O4PfqsmQR88KLcf2bhoixPGu3hseUKkMpTsKIqCO+64A6mpqQCA06dP45577kH37t0BIGA+D3UMsUp2wi3dPnBAe5Tg0CFg4kRg+XLr63ycOmUsLprJtkePBo4c5OcDn3xifn/h7NnTflknXPJitNpzJHZ+8Fv1N2nH33a01afjlRVJMJGdDM3Zuf3225GZmYn09HSkp6dj8uTJ6N+/v+/nzMxMTJ061a5zpTjUt6+1cVqiWbp9++36cyqMGjLEWNyVVwKdTNUqF/wnOKvNMu2kJi/+k2/1mqgCcvNX/NlVldiqv8lY/G0ng3CTuLX+joicYmhk54UXXrDrPChBBU/0jTZOSzRLt5ubRVuGcePMHz/Y//2fsbgNG/TrvkTiP8H5F78wvx9ZWh3g9X4HWtWenWLV32Qs/rYTnV4SHPx3ROSUKL5vErXXrokk2to10S7dtrrlgdE5O+vWWXfsmhrr9hWJf/ICJFbDV6v+JmPxt53ojCTBRE5iskNRUWvXuFzatWtcrugbAUbbRLS5ObrnB5O9VGPV5bOGhvbmodE0yDRDTV4SqeGrVX+TsfjbTnSJlARTx8Zkh6JmRe2aSL7zneie//3vh27z7z6+bp2xxMRo1/NoL+uUlrZX75Xty2UV9RKaU9WnzbLqb9Luv+1El0hJMHVsLoWVAdHU1IT09HQ0NjbC4/E4fToJy66lpzfdBKxYYe65nTqJVVH+k1+jXTny3/8NPPigftyCBcADD4j3pVcv60eYYmHNGmDMGPFvdSIqEDhHQ02A4vHD36q/SS6r1ub1ioKhBw9qz9txucR/W/v28f0ie8h+frOoIFnGrkaAsnNktMyZE5roRLt82kzX89TUxEx2/GsXqaMcWoniokXxl+gA1v1NssmlNvVS3803i8RGKwnu6Jf6KD44ehlr/vz5yM/PR8+ePZGZmYkJEyaE9NYaPXq0r5ihervnnnsCYurq6lBYWIi0tDRkZmairKwMbW1tsXwphOguDUViZrDN7QbKygIL1Fm1fHrbNrlzUOM2bBD1chLRpk2BPxcXiySupgaomJSevgAAIABJREFUqhL3+/bFZ6JDscFLfZQIHB3ZWb9+PUpKSpCfn4+2tjb84he/wLhx47Br1y5foUIAuOuuuzBv3jzfz2lpab5/e71eFBYWIjs7Gxs3bkR9fT2mTp2KLl264PHHH4/p6+nI7CwqdtVVwMaN+nFXXw1cfHH4AnVWLZ+WTVzUuESenOk/sqPiKAcFi7YFC5HdHE123n333YCfly5diszMTGzZsgWjRo3ybU9LS0N2drbmPt5//33s2rULa9asQVZWFi655BI8+uijeOCBB/Dwww8jRaNSWUtLS0C156amJoteUccUqbqx0cq6Wr4p2K3rqquARx8N/7hVK0dkz0eNS+TJmZzC5qxEmivEJJjiWVytxmpsbAQA9OnTJ2D7smXLcM4552D48OGYO3cuTp486Xts06ZNyMvLQ1ZWlm/b+PHj0dTUhJ07d2oeZ/78+b6qz+np6ciVbWNNIazqDB2J7P9A9eKsWjkyebLcftS4K6+M3w8oPZMmOX0GHVd1tZj8q67Eu/pq8TMrEhMZFzfJztmzZzFr1ixcddVVGD58uG/7rbfeildeeQU1NTWYO3cuXn75ZUz2+7RpaGgISHQA+H5uCNPpb+7cuWhsbPTd9u/fb8Mr6hiMdIY2a/RooGvXyDFdu+onO1Ytny4tjfx4cNzGjda3rIiVf/7T6TPomNiCgchacbMaq6SkBJ9++ik+/PDDgO1333237995eXno168fxowZg9raWgwePNjUsVJTU33NTCk6X3xhbZwWr1e/mF5rq4iLNIJi1coRo0UFE3nOTm2t02fQ8bAFA5H14mJkZ/r06Vi1ahVqamqQo1Of/fLLLwcA7P1mPXJ2djYOHz4cEKP+HG6eD1lHtv6N2To5gOiMrddb6uxZEafHipUjZWX6Mf5xZubs+M3Pd1S4UTCyD1swEFnP0WRHURRMnz4db775Jj744AOcd955us/Z9s163n7ffIIUFBRgx44dOHLkiC9m9erV8Hg8GDZsmD0nTj4nTlgbp+Vf/7I2Ltrl00bPZ+RIICMjcmyfPqKAn3o+slWa7Zaf7/QZdDxswUBkPUcvY5WUlKCqqgorV65Ez549fXNs0tPT0a1bN9TW1qKqqgrXXXcdMjIysH37dpSWlmLUqFEYMWIEAGDcuHEYNmwYpkyZgoqKCjQ0NOChhx5CSUkJL1XFwKBB1sZpkf2f+oYNwIwZ4Zee+4tm5YjsqIuR0RmXS5yPelniT38CVq82fGqW+/e/nT6DjoctGIis5+jIzpIlS9DY2IjRo0ejX79+vtsf//hHAEBKSgrWrFmDcePGYejQoZgzZw4mTpyIt99+27cPt9uNVatWwe12o6CgAJMnT8bUqVMD6vKQfWSbjUTTlET2auSnnwJPPSUmBqelAeXl5o8ZyYQJxuJkigoePRp4WeLGG82dm9X69nX6DDqeROtDRpQIHB3Z0WvLlZubi/Xr1+vuZ+DAgXjnnXesOi0yoK7O2jgtF15o/DleL/DEE+Lf/lWU/R83W79k4EBjcWYuS8TLiErw3CayH1swEFkvLiYoU+L61resjdMybZr5/7EvXBi6kiva+iXqN+9I/L95m7ksoTfHJxY4euActmAgshaTHYqK7OWWaC7LpKQAl15q7rleb+AqrXD1S9RqzzIJj9utn8BkZ7cnaGYuS+zYoX8ednK5OHrgNPYhI7IOkx2KyldfWRunpbUV2LrV/PPVWjFWVXs+dQrYvDlyzObNIg5ovywR6bjBicVnn0Xev1UGDw4dpcrN5ehBvFAn0k+aFDiBnYiMYbLTgdjRlfzvf7c2Tsszz0R3rmrtSauqPRuts2NGrOrb1NYCP/kJRw+IKLkx2ekg7Oqz49emzJI4Lbt3m3+u2y3m/AAikZGhF2e0zo46ohSOWhHXP6H7pnZmTCxaJOr6cPSAiJIVk50OwM4+OzU1cnHvvGN+RCma+SuXXtpeb8eqUSijdXbMVMSNZW/a4HlNRETJhslOktPrswNE15Vcr2eV6vBh8yNK0dSG3Lq1/Rytqgl03XVy+1HjzCw9j+XIDsAeWESU3JjsJDm7++yYSZKMjii1tBg/hsp/1GLIELnn6MXJlnRS48wsPX/2WbnnWMVkT10iooTAZCfJ2d1nRzaB8Gd0RCmaGj1A+6jFz38uF68X19Qktx81zszS81iOtPjPayIiSkZMdpKc3X129uwx9zwjI0qrVpk7hkodtbBqzo5fz1mpOHXpORCa8ISriBvLkZbZsyP3ESMiSnRMdpKc0Wq/sSYzonT6dHTH+I//EPdWrcY65xy5/fjHGa2IG03VaFlut1ger9VOg4gomTDZSXJut1hSHMktt5j/YD1xwtzzVDIjSl27RneM558X91aN7MjOIQqOM1IRN5qq0ZEMGQJMnw5UVopyAEx0iKgjcLQRKNnP6xVLviN57TVg/nxzCU/37kBzs/HnuVxiVENmRKmwEHjlFePHUO3cKe6tWo0l27dKK06tiKsn2qrR4fzmN8C111q/XyKieMaRnSRnVdXgcMy0gTDaufnDD40fw99HH4l7q1ZjeTxy+5GN0xJt1WgtXbsC48ZZu08iokTAZCfJHTxobVywTib+gox2bj5zxvgx/LW1iXuZeTAyK5N69pQ7rmycFjtWY40fz+rIRNQxMdlJcl9+aW1csB495OPM9l4aNMjUqfmoI1spKWLlUSQyK5NkE4ZoEgs7VmOtWiVfBJKIKJkw2Uly0cwvkTF3rlzcL39pvvfSW28ZPq0Anf1mplVUiBVIwedgZGXSeefJHVc2Tosdq7HYFoKIOiomO0nu6FHzca2tYl7NjBniXmtUQPbDM5oP2e3bzT8XCG03UVEhViJVVsbvyiSZUSgz2BaCiDoirsZKcn37mosrLwcWLgycJHv//eID2D8pMFpN2Ayz1Z1VhYWh21JSRAVnM774wtq4cNT3Ofj3EA22hSCijogjO0kuO9t4XHk58MQToR+wXq/YXl7evs3uCs0A0KuX+ecCwNCh0T0/mGzCYEViETwKNXy4+X2xLQQRdVRMdpKc7IiAGtfaKkYSIlm4sP2S1oQJcvuXjdPy+uvmnwtEv5ormFWrumSpo1CLFwObNpnfD9tCEFFHxWQngXm9wLp1omjgunXaiY1s/Rw1Tqa+i/9E12XL5PYvG6dl+XLzzwW0iyrKzEcKJyUFuP76yDHXX29PYtGjh/ERI7aFIKKOjnN2ElR1NTBzZmDBwJwcUSHXf1n32bNy+1PjZCewqnEnT8rFy8ZpiXa+SnAiIzsfKdL56BU6/PBDEWfHiiq9dhU5OUBpqVjiP3iwGGHiiA4RdWQc2UlA1dXAzTeHVkY+eFBsr65u39anj9w+1Tij81Fikezk5Zl/LgBcc037v43MRwpn3Tr9VW5Hj4o4q8lUxD5wQPTVWrxYXP5iokNEHR2TnQTj9YoRHa3+Teq2WbPaP8yNTlCO9XwUGdHW2VHnIBmdjxTOBx/IHVc2zgjZlWnRrmAjIkomTHYSjN43e0UJ7HV17rly+1XjjFYZVlsx6JGN0xLNfJ+iIqBbN/Fvo/ORwqmrkzu2bJwRsVj9RkSUbJjsJBij3+xHjtSvjpyREdh9vKJCJAlaiooC57UYvUxmhtlCeOnpwIoVxvejFzdggNx+ZOOMMPP7JCLq6JjsJBgz3+z//e/IscGPV1drXzpyucR2/zlBZosWGtG/v7nnNTYC3/te+89W1cfxnwNkRRwREdnLpShasz86lqamJqSnp6OxsREej8fp04motRVIS4t8OcbtFhOCU1KAlSvlatysWCFGbbxe0Xgz0qWy3Fyx0sftFgmQLLN/aTfeCLz9trnnAsDx42LJttH3LhyvF8jKijxJOSMDOHzY+tVY69YBV1+tH1dTI/qQERElM9nPb47sJJiNG+XmnWzcKP5dVia3XzVOZrWP/5ygWPj88+ieP2WKuLey6/lzz0WOee456xMdgBOUiYjMYLKTYIx+2B07Jhevxh08KBcvG2eFaNsu7NnT/m8rup4DopbR8uWipo2/nByx3b/WkZU4QZmIyDgWFUwwRj/s+vYFvvxSP16dUyMT6x83eLDcxN9oEpaXXwZ69jT//BMnAn+uqAAee0ysuqqtNV94r7hYXPrbsEEkl/36iYnBdozoqEaOFAmV3mVGTlAmImrHZCfBqB92Bw9qz4FxucTj6ofd7NnAf/yH/n7VyztGJxzPnSu3/7lz5farpUcPMUfm8GFzzz/vvNBt0XQ99+d2x3ZujNsNTJokCiCGc8st9iZcRESJxtHLWPPnz0d+fj569uyJzMxMTJgwAbt37w6IOX36NEpKSpCRkYEePXpg4sSJOBz0qVdXV4fCwkKkpaUhMzMTZWVlaIumsEscc7tFS4hwk30VRfR6Uj/sBg2S268aZ7QIYWamXLxsnJbWVuCrr8w/3+qu507yerV7ffl77bXoW2wQESUTR5Od9evXo6SkBB999BFWr16NM2fOYNy4cTjhd92htLQUb7/9Nl5//XWsX78ehw4dQrHfhAiv14vCwkK0trZi48aNePHFF7F06VL88pe/dOIldTgLFlgbp0WmGGAkN95o/rnxJh4nkBMRxTtHL2O9++67AT8vXboUmZmZ2LJlC0aNGoXGxkb8/ve/R1VVFa75pmjJCy+8gIsuuggfffQRrrjiCrz//vvYtWsX1qxZg6ysLFxyySV49NFH8cADD+Dhhx9GSpI1BlLbRYTjconH09OBI0eAbdvk9qt+gB46JBevxsmulIpmRdU//2n+uYB+naFEwtVYRETGxdVqrMbGRgBAn2/K7W7ZsgVnzpzB2LFjfTFDhw7FgAEDsGnTJgDApk2bkJeXh6ysLF/M+PHj0dTUhJ07d2oep6WlBU1NTQG3RCHTLuLAAWDsWODWW+VXF6mFAv/2N7l4Nc7oai8ztm83/1wgusnN8YarsYiIjIubZOfs2bOYNWsWrrrqKgwfPhwA0NDQgJSUFPTq1SsgNisrCw0NDb4Y/0RHfVx9TMv8+fORnp7uu+Xm5lr9cmxj1zd2dSn5p5/Kxatxp0/LxZ88KeaarFtn/JKUXodxPXo1cRKJOkE9XDFHl4ursYiIgsVNslNSUoJPP/0Ur732mu3Hmjt3LhobG323/fv3235Mq0Qz0TeSHj3EvWyVYzXu7Fn5Y9x6q6j+O2hQYMsJPdFeidy3L7rnxxN1gjoQmvCoP/tPUCciojhJdqZPn45Vq1ahpqYGOX5V2rKzs9Ha2opjQddADh8+jOxvlgNlZ2eHrM5Sf84Os7QoNTUVHo8n4NbRHTki7vWaTKpk47QcPAjcfLN8wnPlleaPBYj5S8mkuBh4443QjvY5OWK7XQUNiYgSlaPJjqIomD59Ot5880188MEHOC+oIMpll12GLl26YO3atb5tu3fvRl1dHQoKCgAABQUF2LFjB46on9YAVq9eDY/Hg2HDhsXmhcSQ38u01PHj4j74AzQc2Tgt6qjQrFlyl7SivSRz553RPT8Sr1dcmjN7ic6s4mJRELGyEpg+Xdzv3ctEh4hIi6OrsUpKSlBVVYWVK1eiZ8+evjk26enp6NatG9LT03HnnXdi9uzZ6NOnDzweD2bMmIGCggJcccUVAIBx48Zh2LBhmDJlCioqKtDQ0ICHHnoIJSUlSE1NdfLl2SKaEZVIBg4U9xdeKBevxqWmAi0txo+nKO1LpPWK8kU7pUqrqKAVqqvFyjf/CeM5OeIyk91JR3U1MGNG4Oq5J54AFi9mwkNEFEJxEADN2wsvvOCLOXXqlDJt2jSld+/eSlpamnLTTTcp9fX1Afv5/PPPlWuvvVbp1q2bcs455yhz5sxRzpw5I30ejY2NCgClsbHRqpdmm1//WlFEqmDt7dgxsf+WFrn4lhYR36VLdMetqtJ/zW1tipKTY27/GRni+VZbvlxRXK7Q47lc4rZ8ufXH9D92pNds57GJiOKJ7Oe3S1Fkp6QmL9kW8fFg2jRgyRLr91tfL6oinzoFpKXpx588CXTrBnTqJD+pWUtNjVy7hQkTgJUrje+/Rw+x7N3KCbter5hkHa4EgNqyY98+6ycKe73iNUVaBde1K9DczEnKRJT8ZD+/42KCMsmza+n5JZeI++nT5eLVuM4mL4QaWSLd2gqsWmXuOM3NYi6NlWRqHdlVxXj1av3l/qdPizgiIhKY7CQY2d5VRqkL3t56Sy5ejZOd4+PP6BLpaNtFWJ3sOFnFeOFCa+OIiDoCJjsJxkxyIUOt2yhbN0eN+9a3jB/L6BLp2lrjx7CTk1WMZVtfJFOLDCKiaDHZSTA//7k9+/34Y3H/zYp+XWrc974nF3/HHUBVlZijs2+fsRVD0a6mGjUquucHc7KKcX6+tXFERB0Bk50E8/e/27NftcCfbAFrNU72fI4eBSZNEpORjU6czcszFh+sk8V/5U5WMX7ySWvjiIg6AiY7CcauzhZqd3TZ1gxqnOwlpmguRX31lfnnAkCYFmlRcaqKcbduQFFR5JiiIhFHREQCk50E89e/2rPfqipxv2iRXLwaJ9ukM5pmntH2A/vyy+ieH05xMfD55+LSnNlLdGasWBE+4SkqEo8TEVE7Rysok3Fr1tiz37Y2cf/yy3LxL78MlJcDffoAQa3JNPXpY/7cotW3r337drvl6gRZbcUKUROprAzYswcYMkRUUOaIDhFRKCY7CcZMawYZ3buL+9ZWuXg1TnZeSjTzV6LtBxZNH6941q0b8NRTTp8FEVH842WsBBPtZN1w1F6rsqMUapxajFCPbJyWaJZw27UqioiIEgeTnQRj1wTlG28U9zfdJBevxqkTm/XIxmnRW+odyS23JG/bhNZWMXdqxgxxLzsqR0TU0TDZSTAy82PMUIvQGZ1wbLQIoRmRlnrree216Kovx6vyctHDrLRUXMoqLRU/l5c7fWZERPGHyU6CsatPqZoQyK5cUuNka9hEW+sm3FJvPXb1qHJSebmYjBycxHm9YjsTHiKiQEx2EswvfmHPftXVUhkZcvFq3JVXysXLxkUSvNT7wQflnmfXpT8ntLbq971auJCXtIiI/DHZSTBmelHJOHVK3Bu9jHXRRXLxsnF61KXekyYBx4/LPceuqtNOkGmK6vWKOCIiEpjsJBi75p+ol8dka9KocdOm6U8AdrtFnNUUxdq4RLBnj7VxREQdAZOdBGPX/BO12absnBg1LiUFuP76yLHXXy/fhsKIIUOsjUsEshO0zaxcIyJKVkx2CADw5z+L+yuvlBupUefgeL3Ali2R47dutWdESrYDvF2d4p1w+eXWxhERdQRMdhKMHa0JsrKA9HTx740b5eaEbNwo/r1hA3DgQOR4u1ZEyc7FSaY5O7m51sYREXUETHYSjBWrmoKlpLQnOAcPyj1Hjauvl4uXjTPiiy+sjUsEaoHFSFg1mogoEJOdBPPss9bv03/kxWidHdlWDtG0fAhHtrt3MnUBVwsshpuT43KJasrJWjWaiMgMJjsJxq5VNurIi9E6O9/9rly8bJwRJ05YG5co1AKLwSM8ublie3GxM+dFRBSvmOwkGLtW2agjL0br7JSVycXLxhlxwQXWxiWS4AKLNTXAvn1MdIiItHR2+gTImPx86/fpP8fD6MjOBx/IxcvGGfHEE8DTT8vFJSO1wCIREUXGkZ04ItPFWm3YaSX/zuBGR3Zk2xLY0b6gWzegqChyTFGRiCMioo6LyU6ckO1iLVvh2Aj/zuC9e8s9R40bOFAuXjbOqBUrwic8RUXJNTmZiIjMYbITB4x0sTba9VuG/2qszZvlnqPGdZa8ECobZ8aKFcDJk0BJCTBunLg/eZKJDhERCZyz4zDZLtaPPSbq4ah1VvQK+RmlrsaSrXSsxnXvLhcvG2dWt25iRIyIiCgYR3YcZrSLtdstOn5bTV2NJVufRY3r318uXjaOiIjIakx2HFZbayzO6wVefdW647tcgauxZFd7qXGyFZ3tqPxMREQkg5exbOT1irkw9fVi5GTkyNCRk8GD5falxsn0ojLKv+Ku7GovNY69moiIKN5xZMcm1dXAoEHA1VcDt94q7gcNEtv9TZsm12V82jTxbyt7TLndwP33Bxaik13tpcaxVxMREcU7Jjs2qK4Gbr45dATm4EGx3T/hSUkBZs+OvL/Zs0UcYG2PqbNngV//OvB8ZFd7qXHs1URERPHO0WTnr3/9K2644Qb0798fLpcLK4LWCt9xxx1wuVwBtx/96EcBMV9//TVuu+02eDwe9OrVC3feeSeam5tj+TICeL3AzJmAooQ+pm6bNStwUnJFhWinEJwQuN1ie0VF+zZ1JCVS2wit/WjROh8zIzXs1URERPHM0WTnxIkT+Pa3v42nI9T8/9GPfoT6+nrf7dWg2bm33XYbdu7cidWrV2PVqlX461//irvvvtvuUw9Lb06NogTWtVFVVADHjwfWijl+PDDRAdpHUoDQhMflErdXX23vmVRZGXm1V/D5mB2pYa8mIiKKW0qcAKC8+eabAdtuv/12paio6P+3d/dRUZV5HMC/w5CALC+i8jLxIqQJoriYLKGuSuAKtqSZFR7cxeRUuwsJmi+p6wsFYnWOndpV0HYPuK3Y8SiaS0mmhiSaDhYWuYfEKMlCd5d4kxVz5u4fs0wODDADc+fOXL6fc+6hufPMvb+L1fx8nt/zPL1+5tKlSwIAQa1W688dPXpUUCgUwrVr10y+d0tLiwBAaGlpMT/wboqLBUGXQvR9FBcbfu7gQUHw9zds4++vO2+MsfYBAT3bWzIeY9cnIiKSiqnf3zY/G6u8vBze3t4YMWIEHnroIeTk5GDk/3ehPHv2LDw9PTF16lR9+/j4eDg4OODcuXN49NFHjV6zs7MTnZ2d+tetra0Wi9fUmpq723XV+HQf+uqq8TE2FLRwoW47BGOzve6eBXb9+sDi7uv6vTFl9tlgWeMeREQkLzad7CQkJGDhwoUIDg7GlStXsH79eiQmJuLs2bNQKpVobGyEt7e3wWccHR3h5eWFxsbGXq+bl5eH7OxsUWKOjjavXX81PgqFrqZm/nzjtTjdd70uKdFd7+6htK4EyBiFQldrY2y2lDm7ahu7r7+/bkjMUkNZ1rgHERHJj03PxkpOTsYjjzyCSZMmYcGCBSgtLYVarUZ5efmgrrtu3Tq0tLToj4aGBssEDGDXLvPamVrj86c/6Wpxyst7T1x6mwXWV6IDDH62lDmzz2z5HkREJE82nex0FxISglGjRqGurg4A4Ovrixs3bhi0uXPnDpqamuDr69vrdZycnODu7m5wWIq5KyKbum7OihV9r9fTVw9Rl+4Jjb//4GdLDWT2maXvIQiDvwcREcmXXSU73377Lf7zn//A7/8FJjExMWhubsaFCxf0bU6ePAmtVotoU8eTLMzcFZEHsm6Osd4MU1ZW1mh0s7MsOVtqoLPPLHkPYPD3ICIi+ZI02Wlvb0d1dTWqq6sBAPX19aiursbVq1fR3t6O1atX4+OPP8bXX3+NEydOYP78+Rg7dizmzp0LAAgLC0NCQgKefvppnD9/HpWVlcjIyEBycjJUEu08ae6KyKasm9OdsR4TU3uIfHx0G4nOnm2Zwl5T7zuYlZ+vXbNsOyIiGlokTXaqqqoQGRmJyMhIAMDKlSsRGRmJTZs2QalU4rPPPsMjjzyC+++/H2lpaXjggQfw0UcfwcnJSX+NvXv3IjQ0FHFxcZg3bx5mzJiB3bt3S/VIZq+I3Ne6OX3p3mMykFlglmCN+/7rX6a1O3AAeO45XQ3S7dsDvx8REcmLQhD6qvIYGlpbW+Hh4YGWlhaL1e+sWQNs325YR6JU6hKd7gsF9tbeFMXFup4ajUZXy3PtmvHalq5ZV/X1lp2q3XXfvoaZAgIGd9+9e4ElS8z7TF+/ayIikgdTv7/tqmbHnrzyCtDRoauRycjQ/ezoMP7lW1Ki26NqIAW2XT0m/a2sDIizR5VSqUu2+pKcPLj7mrpf1900GuDVV3VJJBERDW3s2YE4PTumMqVnxJjeemrM7VEaLGv07Az0dwTo7tnR8dOwIRERyQd7duyEKTONuuutp6a3HiKNpufu5pZijZlS/e3X1ReNBti5c+D3JiIi+8dkR2IDmaVkbH0cU9bZEWMtGmvMxgJ631ndFKaufURERPJk09tFDAWmzlJ67TXdtPHe9oMyZ70bU7eAMIU1Z4F136+rshLYsaP/z5m69hEREckTa3ZgGzU7g51FtW+fboXl/nTN3rIUqWaBAbrp5cOH991bxZodIiL5Ys2OnbDULCoxelg0Gt1eXH3tySXVLDDA/DWNiIhoaGKyYwO66lG6T7E2Z++q/lZiVih0s6KM7W5uTEmJrscmNrbvPbksFf9APfjg4N4nIiL54zAWpB3GuptG81M9Sm+1OX3p2hkcMBxS6kqATE08uq7T/d+M/q4z2PjN1d+UdDGH0IiISHocxrJDSqWueHige1dZoofFGruYW4o1NiElIiL7x9lYMtN9xpK5PSwDndVVUqJLku7+rL+/rp5HrGEsa017JyIi+8Zkx471NmzU1UM0EANJIHob9rp2TXderLodqTY/JSIi+8JhLDtlTgGxOby9zWsn5bCXpYuyiYhInpjs2KGunpTuw01dPSlibAvRGynrZqSc9k5ERPaDyY6dEbsn5cYN89pJXTcj5bR3IiKyD6zZsTNibwthbh2MLdTNDLYom4iI5I3Jjp0Ruyelqw6mv+0fuupgzG0vlsEUZRMRkbxxGMvOiN2TYm4dDOtmiIjI1jHZsTPWmIFkbh0M62aIiMiWcbsI2M52Eaay1LYQ/TF3+wdrbxdBRERDm6nf30x2YH/JDmB8xeKAAN2QEXtSiIhoKDD1+5sFynaKM5CIiIhMw2THjnEGEhERUf+Y7FCvWLNDRERywGSHjDJ3F3Mpdj0nIiIyBaeey5BGA5SXA/v26X6au3WEuXtv2dJeXURERN1xNhbsczZWbwbbw6Isz+lqAAAQk0lEQVTR6HZP721Liq4VkevrdUNU5rYnIiKyFFO/v9mzIyOW6GExdxdzKXc9JyIiMgWTHZmw1G7o5u69JfWu50RERP1hsiMTluphscddz4mIiPrCZEcmLNXDYu7eW9bYq4uIiGgwmOzIhKV6WLjrORERyQ2THZmwZA8Ldz0nIiI5kTTZqaioQFJSElQqFRQKBQ4fPmzwviAI2LRpE/z8/ODi4oL4+HhcvnzZoE1TUxNSUlLg7u4OT09PpKWlob293ZqPYRMs3cOycCHw9dfAhx8CxcW6n/X1vScu5rYnIiKyFkmTnZs3b2Ly5MnYsWOH0fdfeeUVvPHGGygoKMC5c+fg6uqKuXPn4tatW/o2KSkp+OKLL/DBBx+gtLQUFRUVeOaZZ6z1CDbF0j0sXXtvLV6s+9lfomRueyIiImuwmUUFFQoFDh06hAULFgDQ9eqoVCo8//zzWLVqFQCgpaUFPj4+KCoqQnJyMv75z39iwoQJUKvVmDp1KgCgrKwM8+bNw7fffguVSmXSveW0qCDAPaqIiGhosPtFBevr69HY2Ij4+Hj9OQ8PD0RHR+Ps2bMAgLNnz8LT01Of6ABAfHw8HBwccO7cuV6v3dnZidbWVoNDTtjDQkRE9BObTXYaGxsBAD4+PgbnfXx89O81NjbC29vb4H1HR0d4eXnp2xiTl5cHDw8P/REQEGDh6ImIiMhW2GyyI6Z169ahpaVFfzQ0NEgdEhEREYnEZpMdX19fAMD169cNzl+/fl3/nq+vL27cuGHw/p07d9DU1KRvY4yTkxPc3d0NDiIiIpInm012goOD4evrixMnTujPtba24ty5c4iJiQEAxMTEoLm5GRcuXNC3OXnyJLRaLaKjo60eMxEREdkeRylv3t7ejrq6Ov3r+vp6VFdXw8vLC4GBgcjKykJOTg7GjRuH4OBgbNy4ESqVSj9jKywsDAkJCXj66adRUFCAH3/8ERkZGUhOTjZ5JhYRERHJm6TJTlVVFWJjY/WvV65cCQBITU1FUVER1qxZg5s3b+KZZ55Bc3MzZsyYgbKyMjg7O+s/s3fvXmRkZCAuLg4ODg547LHH8MYbb1j9WYiIiMg22cw6O1KS2zo7REREQ4Hdr7NDREREZAlMdoiIiEjWJK3ZsRVdI3lyW0mZiIhIzrq+t/uryGGyA6CtrQ0AuJIyERGRHWpra4OHh0ev77NAGYBWq8V3330HNzc3KBQKi167tbUVAQEBaGhoGBLFz0PteQE+M59ZvvjM8n9me39eQRDQ1tYGlUoFB4feK3PYswPAwcEB/v7+ot5jqK3UPNSeF+AzDxV85qFhqD2zPT9vXz06XVigTERERLLGZIeIiIhkTblly5YtUgchd0qlErNnz4aj49AYNRxqzwvwmYcKPvPQMNSeeSg8LwuUiYiISNY4jEVERESyxmSHiIiIZI3JDhEREckakx0iIiKSNSY7IqmoqEBSUhJUKhUUCgUOHz4sdUiiysvLQ1RUFNzc3ODt7Y0FCxagtrZW6rBElZ+fj4iICP1iXDExMTh69KjUYVnNtm3boFAokJWVJXUootqyZQsUCoXBERoaKnVYorp27RqWLFmCkSNHwsXFBZMmTUJVVZXUYYlmzJgxPf6MFQoF0tPTpQ5NNBqNBhs3bkRwcDBcXFxw33334aWXXup3jyl7Jd95ZhK7efMmJk+ejGXLlmHhwoVShyO6U6dOIT09HVFRUbhz5w7Wr1+PX/3qV7h06RJcXV2lDk8U/v7+2LZtG8aNGwdBELBnzx7Mnz8fn376KcLDw6UOT1RqtRq7du1CRESE1KFYRXh4OI4fP65/Lecpuj/88AOmT5+O2NhYHD16FKNHj8bly5cxYsQIqUMTjVqthkaj0b+uqanBnDlz8Pjjj0sYlbhefvll5OfnY8+ePQgPD0dVVRWeeuopeHh4YPny5VKHZ3Hy/S9WYomJiUhMTJQ6DKspKyszeF1UVARvb29cuHABM2fOlCgqcSUlJRm8zs3NRX5+Pj7++GNZJzvt7e1ISUnBm2++iZycHKnDsQpHR0f4+vpKHYZVvPzyywgICEBhYaH+XHBwsIQRiW/06NEGr7dt24b77rsPs2bNkigi8Z05cwbz58/Hww8/DEDXu7Vv3z6cP39e4sjEwWEsEkVLSwsAwMvLS+JIrEOj0eDtt9/GzZs3ERMTI3U4okpPT8fDDz+M+Ph4qUOxmsuXL0OlUiEkJAQpKSm4evWq1CGJ5siRI5g6dSoef/xxeHt7IzIyEm+++abUYVnN7du38fe//x3Lli2z+MbQtmTatGk4ceIEvvzySwDAxYsXcfr0adn+JZ09O2RxWq0WWVlZmD59OiZOnCh1OKL6/PPPERMTg1u3buFnP/sZDh06hAkTJkgdlmjefvttfPLJJ1Cr1VKHYjXR0dEoKirC+PHj8f333yM7Oxu//OUvUVNTAzc3N6nDs7ivvvoK+fn5WLlyJdavXw+1Wo3ly5dj2LBhSE1NlTo80R0+fBjNzc1YunSp1KGI6oUXXkBraytCQ0OhVCqh0WiQm5uLlJQUqUMTBZMdsrj09HTU1NTg9OnTUociuvHjx6O6uhotLS04cOAAUlNTcerUKVkmPA0NDcjMzMQHH3wAZ2dnqcOxmrv/phsREYHo6GgEBQVh//79SEtLkzAycWi1WkydOhVbt24FAERGRqKmpgYFBQVDItn561//isTERKhUKqlDEdX+/fuxd+9eFBcXIzw8HNXV1cjKyoJKpZLlnzOTHbKojIwMlJaWoqKiAv7+/lKHI7phw4Zh7NixAIAHHngAarUar7/+Onbt2iVxZJZ34cIF3LhxA1OmTNGf02g0qKiowJ///Gd0dnZCqVRKGKF1eHp64v7770ddXZ3UoYjCz8+vR7IeFhaGgwcPShSR9XzzzTc4fvw4SkpKpA5FdKtXr8YLL7yA5ORkAMCkSZPwzTffIC8vj8kOUW8EQcBzzz2HQ4cOoby8XPYFjb3RarXo7OyUOgxRxMXF4fPPPzc499RTTyE0NBRr164dEokOoCvQvnLlCn7zm99IHYoopk+f3mPZiC+//BJBQUESRWQ9hYWF8Pb21hftyllHRwccHAzLdpVKJbRarUQRiYvJjkja29sN/uZXX1+P6upqeHl5ITAwUMLIxJGeno7i4mK88847cHNzQ2NjIwDAw8MDLi4uEkcnjnXr1iExMRGBgYFoa2tDcXExysvL8f7770sdmijc3Nx61GC5urpi5MiRsq7NWrVqFZKSkhAUFITvvvsOmzdvhlKpxOLFi6UOTRQrVqzAtGnTsHXrVjzxxBM4f/48du/ejd27d0sdmqi0Wi0KCwuRmpoq66UFuiQlJSE3NxeBgYEIDw/Hp59+iu3bt2PZsmVShyYOgUTx4YcfCgB6HKmpqVKHJgpjzwpAKCwslDo00SxbtkwICgoShg0bJowePVqIi4sTjh07JnVYVjVr1iwhMzNT6jBE9eSTTwp+fn7CsGHDhHvvvVd48sknhbq6OqnDEtU//vEPYeLEiYKTk5MQGhoq7N69W+qQRPf+++8LAITa2lqpQ7GK1tZWITMzUwgMDBScnZ2FkJAQYcOGDUJnZ6fUoYlCIQgyXS6RiIiICFxnh4iIiGSOyQ4RERHJGpMdIiIikjUmO0RERCRrTHaIiIhI1pjsEBERkawx2SEiIiJZY7JDREREssZkh4jsSlFRETw9PSWNYfbs2cjKypI0BiIyHVdQJiKLWLp0Kfbs2dPj/Ny5c1FWVmax+/z3v/9FW1sbvL29LXZNczU1NeGee+6Bm5ubZDEQkenkv9sZEVlNQkICCgsLDc45OTlZ9B4uLi6Sby7r5eUl6f2JyDwcxiIii3FycoKvr6/BMWLECP37CoUCf/nLX/Doo49i+PDhGDduHI4cOWJwjSNHjmDcuHFwdnZGbGws9uzZA4VCgebmZgA9h7G2bNmCn//853jrrbcwZswYeHh4IDk5GW1tbfo2Wq0WeXl5CA4OhouLCyZPnowDBw70+Sw7d+7Ux+Hj44NFixbp37t7GKu8vBwKhaLHsXTpUn37d955B1OmTIGzszNCQkKQnZ2NO3fumP8LJqIBYbJDRFaVnZ2NJ554Ap999hnmzZuHlJQUNDU1AQDq6+uxaNEiLFiwABcvXsSzzz6LDRs29HvNK1eu4PDhwygtLUVpaSlOnTqFbdu26d/Py8vD3/72NxQUFOCLL77AihUrsGTJEpw6dcro9aqqqrB8+XK8+OKLqK2tRVlZGWbOnGm07bRp0/D999/rj5MnT8LZ2Vnf/qOPPsJvf/tbZGZm4tKlS9i1axeKioqQm5tr7q+OiAZK2k3XiUguUlNTBaVSKbi6uhocubm5+jYAhD/+8Y/61+3t7QIA4ejRo4IgCMLatWuFiRMnGlx3w4YNAgDhhx9+EARBEAoLCwUPDw/9+5s3bxaGDx8utLa26s+tXr1aiI6OFgRBEG7duiUMHz5cOHPmjMF109LShMWLFxt9loMHDwru7u4G17zbrFmzhMzMzB7n//3vfwshISHCH/7wB/25uLg4YevWrQbt3nrrLcHPz8/otYnI8lizQ0QWExsbi/z8fINz3etbIiIi9P/s6uoKd3d33LhxAwBQW1uLqKgog/a/+MUv+r3vmDFjDIqF/fz89Nesq6tDR0cH5syZY/CZ27dvIzIy0uj15syZg6CgIISEhCAhIQEJCQn6obfe/Pjjj3jssccQFBSE119/XX/+4sWLqKysNOjJ0Wg0uHXrFjo6Ovq8JhFZBpMdIrIYV1dXjB07ts8299xzj8FrhUIBrVY7qPv2dc329nYAwLvvvot7773XoF1vxdNubm745JNPUF5ejmPHjmHTpk3YsmUL1Gp1r9Pef//736OhoQHnz5+Ho+NP/2ttb29HdnY2Fi5c2OMzzs7Opj8kEQ0Ykx0ishnjx4/He++9Z3BOrVYP6poTJkyAk5MTrl69ilmzZpn8OUdHR8THxyM+Ph6bN2+Gp6cnTp48aTRp2b59O/bv348zZ85g5MiRBu9NmTIFtbW1/SaBRCQeJjtEZDGdnZ1obGw0OOfo6IhRo0aZ9Plnn30W27dvx9q1a5GWlobq6moUFRUB0PXWDISbmxtWrVqFFStWQKvVYsaMGWhpaUFlZSXc3d2Rmpra4zOlpaX46quvMHPmTIwYMQLvvfcetFotxo8f36Pt8ePHsWbNGuzYsQOjRo3SP7+Liws8PDywadMm/PrXv0ZgYCAWLVoEBwcHXLx4ETU1NcjJyRnQMxGReTgbi4gspqysDH5+fgbHjBkzTP58cHAwDhw4gJKSEkRERCA/P18/G2sw6/W89NJL2LhxI/Ly8hAWFoaEhAS8++67CA4ONtre09MTJSUleOihhxAWFoaCggLs27cP4eHhPdqePn0aGo0Gv/vd7wyeOzMzE4BuUcXS0lIcO3YMUVFRePDBB/Haa68hKChowM9DRObhCspEZNNyc3NRUFCAhoYGqUMhIjvFYSwisik7d+5EVFQURo4cicrKSrz66qvIyMiQOiwismNMdojIply+fBk5OTloampCYGAgnn/+eaxbt07qsIjIjnEYi4iIiGSNBcpEREQka0x2iIiISNaY7BAREZGsMdkhIiIiWWOyQ0RERLLGZIeIiIhkjckOERERyRqTHSIiIpK1/wGbPyDGnMHL5AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(cdf.ENGINESIZE, cdf.CO2EMISSIONS,  color='blue')\n",
    "plt.xlabel(\"Engine size\")\n",
    "plt.ylabel(\"Emission\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Creating train and test dataset\n",
    "Train/Test Split involves splitting the dataset into training and testing sets respectively, which are mutually exclusive. After which, you train with the training set and test with the testing set.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "msk = np.random.rand(len(df)) < 0.8\n",
    "train = cdf[msk]\n",
    "test = cdf[~msk]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"polynomial_regression\">Polynomial regression</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sometimes, the trend of data is not really linear, and looks curvy. In this case we can use Polynomial regression methods. In fact, many different regressions exist that can be used to fit whatever the dataset looks like, such as quadratic, cubic, and so on, and it can go on and on to infinite degrees.\n",
    "\n",
    "In essence, we can call all of these, polynomial regression, where the relationship between the independent variable x and the dependent variable y is modeled as an nth degree polynomial in x. Lets say you want to have a polynomial regression (let's make 2 degree polynomial):\n",
    "\n",
    "\n",
    "$$y = b + \\theta_1  x + \\theta_2 x^2$$\n",
    "\n",
    "\n",
    "\n",
    "Now, the question is: how we can fit our data on this equation while we have only x values, such as __Engine Size__? \n",
    "Well, we can create a few additional features: 1, $x$, and $x^2$.\n",
    "\n",
    "\n",
    "\n",
    "__PolynomialFeatures()__ function in Scikit-learn library, drives a new feature sets from the original feature set. That is, a matrix will be generated consisting of all polynomial combinations of the features with degree less than or equal to the specified degree. For example, lets say the original feature set has only one feature, _ENGINESIZE_. Now, if we select the degree of the polynomial to be 2, then it generates 3 features, degree=0, degree=1 and degree=2: \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.  ,  2.  ,  4.  ],\n",
       "       [ 1.  ,  2.4 ,  5.76],\n",
       "       [ 1.  ,  1.5 ,  2.25],\n",
       "       ...,\n",
       "       [ 1.  ,  3.2 , 10.24],\n",
       "       [ 1.  ,  3.  ,  9.  ],\n",
       "       [ 1.  ,  3.2 , 10.24]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn import linear_model\n",
    "train_x = np.asanyarray(train[['ENGINESIZE']])\n",
    "train_y = np.asanyarray(train[['CO2EMISSIONS']])\n",
    "\n",
    "test_x = np.asanyarray(test[['ENGINESIZE']])\n",
    "test_y = np.asanyarray(test[['CO2EMISSIONS']])\n",
    "\n",
    "\n",
    "poly = PolynomialFeatures(degree=2)\n",
    "train_x_poly = poly.fit_transform(train_x)\n",
    "train_x_poly"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**fit_transform** takes our x values, and output a list of our data raised from power of 0 to power of 2 (since we set the degree of our polynomial to 2).   \n",
    "\n",
    "The equation and the sample example is displayed below.   \n",
    "\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "    v_1\\\\\\\\\\\\\n",
    "    v_2\\\\\\\\\n",
    "    \\vdots\\\\\\\\\n",
    "    v_n\n",
    "\\end{bmatrix}\\longrightarrow \\begin{bmatrix}\n",
    "    [ 1 & v_1 & v_1^2]\\\\\\\\\n",
    "    [ 1 & v_2 & v_2^2]\\\\\\\\\n",
    "    \\vdots & \\vdots & \\vdots\\\\\\\\\n",
    "    [ 1 & v_n & v_n^2]\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "    2.\\\\\\\\\n",
    "    2.4\\\\\\\\\n",
    "    1.5\\\\\\\\\n",
    "    \\vdots\n",
    "\\end{bmatrix} \\longrightarrow \\begin{bmatrix}\n",
    "    [ 1 & 2. & 4.]\\\\\\\\\n",
    "    [ 1 & 2.4 & 5.76]\\\\\\\\\n",
    "    [ 1 & 1.5 & 2.25]\\\\\\\\\n",
    "    \\vdots & \\vdots & \\vdots\\\\\\\\\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It looks like feature sets for multiple linear regression analysis, right? Yes. It Does. \n",
    "Indeed, Polynomial regression is a special case of linear regression, with the main idea of how do you select your features. Just consider replacing the  $x$ with $x_1$, $x_1^2$ with $x_2$, and so on. Then the 2nd degree equation would be turn into:\n",
    "\n",
    "$$y = b + \\theta_1  x_1 + \\theta_2 x_2$$\n",
    "\n",
    "Now, we can deal with it as a 'linear regression' problem. Therefore, this polynomial regression is considered to be a special case of traditional multiple linear regression. So, you can use the same mechanism as linear regression to solve such problems. \n",
    "\n",
    "\n",
    "\n",
    "so we can use __LinearRegression()__ function to solve it:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients:  [[ 0.         47.33765502 -1.04483635]]\n",
      "Intercept:  [112.41683927]\n"
     ]
    }
   ],
   "source": [
    "clf = linear_model.LinearRegression()\n",
    "train_y_ = clf.fit(train_x_poly, train_y)\n",
    "# The coefficients\n",
    "print ('Coefficients: ', clf.coef_)\n",
    "print ('Intercept: ',clf.intercept_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As mentioned before, __Coefficient__ and __Intercept__ , are the parameters of the fit curvy line. \n",
    "Given that it is a typical multiple linear regression, with 3 parameters, and knowing that the parameters are the intercept and coefficients of hyperplane, sklearn has estimated them from our new set of feature sets. Lets plot it:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Emission')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(train.ENGINESIZE, train.CO2EMISSIONS,  color='blue')\n",
    "XX = np.arange(0.0, 10.0, 0.1)\n",
    "yy = clf.intercept_[0]+ clf.coef_[0][1]*XX+ clf.coef_[0][2]*np.power(XX, 2)\n",
    "plt.plot(XX, yy, '-r' )\n",
    "plt.xlabel(\"Engine size\")\n",
    "plt.ylabel(\"Emission\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"evaluation\">Evaluation</h2>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean absolute error: 23.79\n",
      "Residual sum of squares (MSE): 971.85\n",
      "R2-score: 0.74\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import r2_score\n",
    "\n",
    "test_x_poly = poly.transform(test_x)\n",
    "test_y_ = clf.predict(test_x_poly)\n",
    "\n",
    "print(\"Mean absolute error: %.2f\" % np.mean(np.absolute(test_y_ - test_y)))\n",
    "print(\"Residual sum of squares (MSE): %.2f\" % np.mean((test_y_ - test_y) ** 2))\n",
    "print(\"R2-score: %.2f\" % r2_score(test_y,test_y_ ) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"practice\">Practice</h2>\n",
    "Try to use a polynomial regression with the dataset but this time with degree three (cubic). Does it result in better accuracy?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients:  [[ 0.         33.77909491  2.89825903 -0.34550049]]\n",
      "Intercept:  [126.13710244]\n",
      "Mean absolute error: 23.52\n",
      "Residual sum of squares (MSE): 953.26\n",
      "R2-score: 0.74\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "poly3 = PolynomialFeatures(degree=3)\n",
    "train_x_poly3 = poly3.fit_transform(train_x)\n",
    "clf3 = linear_model.LinearRegression()\n",
    "train_y3_ = clf3.fit(train_x_poly3, train_y)\n",
    "\n",
    "# The coefficients\n",
    "print ('Coefficients: ', clf3.coef_)\n",
    "print ('Intercept: ',clf3.intercept_)\n",
    "plt.scatter(train.ENGINESIZE, train.CO2EMISSIONS,  color='blue')\n",
    "XX = np.arange(0.0, 10.0, 0.1)\n",
    "yy = clf3.intercept_[0]+ clf3.coef_[0][1]*XX + clf3.coef_[0][2]*np.power(XX, 2) + clf3.coef_[0][3]*np.power(XX, 3)\n",
    "plt.plot(XX, yy, '-r' )\n",
    "plt.xlabel(\"Engine size\")\n",
    "plt.ylabel(\"Emission\")\n",
    "test_x_poly3 = poly3.transform(test_x)\n",
    "test_y3_ = clf3.predict(test_x_poly3)\n",
    "print(\"Mean absolute error: %.2f\" % np.mean(np.absolute(test_y3_ - test_y)))\n",
    "print(\"Residual sum of squares (MSE): %.2f\" % np.mean((test_y3_ - test_y) ** 2))\n",
    "print(\"R2-score: %.2f\" % r2_score(test_y,test_y3_ ) )\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python    \n",
    "poly3 = PolynomialFeatures(degree=3)\n",
    "train_x_poly3 = poly3.fit_transform(train_x)\n",
    "clf3 = linear_model.LinearRegression()\n",
    "train_y3_ = clf3.fit(train_x_poly3, train_y)\n",
    "\n",
    "# The coefficients\n",
    "print ('Coefficients: ', clf3.coef_)\n",
    "print ('Intercept: ',clf3.intercept_)\n",
    "plt.scatter(train.ENGINESIZE, train.CO2EMISSIONS,  color='blue')\n",
    "XX = np.arange(0.0, 10.0, 0.1)\n",
    "yy = clf3.intercept_[0]+ clf3.coef_[0][1]*XX + clf3.coef_[0][2]*np.power(XX, 2) + clf3.coef_[0][3]*np.power(XX, 3)\n",
    "plt.plot(XX, yy, '-r' )\n",
    "plt.xlabel(\"Engine size\")\n",
    "plt.ylabel(\"Emission\")\n",
    "test_x_poly3 = poly3.transform(test_x)\n",
    "test_y3_ = clf3.predict(test_x_poly3)\n",
    "print(\"Mean absolute error: %.2f\" % np.mean(np.absolute(test_y3_ - test_y)))\n",
    "print(\"Residual sum of squares (MSE): %.2f\" % np.mean((test_y3_ - test_y) ** 2))\n",
    "print(\"R2-score: %.2f\" % r2_score(test_y,test_y3_ ) )\n",
    "\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "<h2>Want to learn more?</h2>\n",
    "\n",
    "IBM SPSS Modeler is a comprehensive analytics platform that has many machine learning algorithms. It has been designed to bring predictive intelligence to decisions made by individuals, by groups, by systems – by your enterprise as a whole. A free trial is available through this course, available here: <a href=\"https://www.ibm.com/analytics/spss-statistics-software?utm_source=skills_network&utm_content=in_lab_content_link&utm_id=Lab-IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork\">SPSS Modeler</a>\n",
    "\n",
    "Also, you can use Watson Studio to run these notebooks faster with bigger datasets. Watson Studio is IBM's leading cloud solution for data scientists, built by data scientists. With Jupyter notebooks, RStudio, Apache Spark and popular libraries pre-packaged in the cloud, Watson Studio enables data scientists to collaborate on their projects without having to install anything. Join the fast-growing community of Watson Studio users today with a free account at <a href=\"https://www.ibm.com/cloud/watson-studio?utm_source=skills_network&utm_content=in_lab_content_link&utm_id=Lab-IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork\">Watson Studio</a>\n",
    "\n"
   ]
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    "### Thank you for completing this lab!\n",
    "\n",
    "\n",
    "## Author\n",
    "\n",
    "Saeed Aghabozorgi\n",
    "\n",
    "\n",
    "### Other Contributors\n",
    "\n",
    "<a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a>\n",
    "\n",
    "\n",
    "## <h3 align=\"center\"> © IBM Corporation 2020. All rights reserved. <h3/>\n",
    "\n",
    "\n",
    "<!--## Change Log\n",
    "\n",
    "\n",
    "|  Date (YYYY-MM-DD) |  Version | Changed By  |  Change Description |\n",
    "|---|---|---|---|\n",
    "| 2021-01-11  | 2.3  | Lakshmi  |  Changed R2-score calculation in polynomial regression |\n",
    "| 2020-11-04  | 2.2  | Lakshmi  |  Made changes in markdown of equations |\n",
    "| 2020-11-03  | 2.1  | Lakshmi  |  Made changes in URL |\n",
    "| 2020-08-27  | 2.0  | Lavanya  |  Moved lab to course repo in GitLab |\n",
    "|   |   |   |   |\n",
    "|   |   |   |   | --!>\n",
    "\n",
    "\n"
   ]
  }
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