Polynomial-Regression-Co2-py-v1.ipynb

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    "<a href=\"https://www.bigdatauniversity.com\"><img src=\"https://ibm.box.com/shared/static/cw2c7r3o20w9zn8gkecaeyjhgw3xdgbj.png\" width=\"400\" align=\"center\"></a>\n",
    "\n",
    "<h1><center>Polynomial Regression</center></h1>\n",
    "\n",
    "<h4>About this Notebook</h4>\n",
    "In this notebook, we learn how to use scikit-learn for Polynomial regression. We download a dataset that is related to fuel consumption and Carbon dioxide emission of cars. Then, we split our data into training and test sets, create a model using training set, evaluate our model using test set, and finally use model to predict unknown value."
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   "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>"
   ]
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   "source": [
    "### Importing Needed packages"
   ]
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   "source": [
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import pylab as pl\n",
    "import numpy as np\n",
    "%matplotlib inline"
   ]
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   "source": [
    "<h2 id=\"download_data\">Downloading Data</h2>\n",
    "To download the data, we will use !wget to download it from IBM Object Storage."
   ]
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     "text": [
      "--2020-01-04 11:23:41--  https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/ML0101ENv3/labs/FuelConsumptionCo2.csv\n",
      "Resolving s3-api.us-geo.objectstorage.softlayer.net (s3-api.us-geo.objectstorage.softlayer.net)... 67.228.254.196\n",
      "Connecting to s3-api.us-geo.objectstorage.softlayer.net (s3-api.us-geo.objectstorage.softlayer.net)|67.228.254.196|: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 0.05s   \n",
      "\n",
      "2020-01-04 11:23:41 (1.49 MB/s) - ‘FuelConsumption.csv’ saved [72629/72629]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "!wget -O FuelConsumption.csv https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/ML0101ENv3/labs/FuelConsumptionCo2.csv"
   ]
  },
  {
   "cell_type": "markdown",
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   "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](http://cocl.us/ML0101EN-IBM-Offer-CC)"
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    "\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"
   ]
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   "source": [
    "## Reading the data in"
   ]
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       "  <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",
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       "      <th>FUELCONSUMPTION_HWY</th>\n",
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       "      <th>FUELCONSUMPTION_COMB_MPG</th>\n",
       "      <th>CO2EMISSIONS</th>\n",
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       "      <th>0</th>\n",
       "      <td>2014</td>\n",
       "      <td>ACURA</td>\n",
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       "      <td>2.0</td>\n",
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       "      <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",
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       "      <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",
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       "      <th>3</th>\n",
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       "      <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",
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       "      <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",
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      "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  "
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     "execution_count": 3,
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   "source": [
    "df = pd.read_csv(\"FuelConsumption.csv\")\n",
    "\n",
    "# take a look at the dataset\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets select some features that we want to use for regression."
   ]
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       "      <th>ENGINESIZE</th>\n",
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       "      <th>CO2EMISSIONS</th>\n",
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      "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,
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   ],
   "source": [
    "cdf = df[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_COMB','CO2EMISSIONS']]\n",
    "cdf.head(9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets plot Emission values with respect to Engine size:"
   ]
  },
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "msk = np.random.rand(len(df)) < 0.8\n",
    "train = cdf[msk]\n",
    "test = cdf[~msk]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "<h2 id=\"polynomial_regression\">Polynomial regression</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "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",
    "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",
    "__PloynomialFeatures()__ 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: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "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",
    "$\n",
    "\\begin{bmatrix}\n",
    "    v_1\\\\\n",
    "    v_2\\\\\n",
    "    \\vdots\\\\\n",
    "    v_n\n",
    "\\end{bmatrix}\n",
    "$\n",
    "$\\longrightarrow$\n",
    "$\n",
    "\\begin{bmatrix}\n",
    "    [ 1 & v_1 & v_1^2]\\\\\n",
    "    [ 1 & v_2 & v_2^2]\\\\\n",
    "    \\vdots & \\vdots & \\vdots\\\\\n",
    "    [ 1 & v_n & v_n^2]\n",
    "\\end{bmatrix}\n",
    "$\n",
    "\n",
    "in our example\n",
    "\n",
    "$\n",
    "\\begin{bmatrix}\n",
    "    2.\\\\\n",
    "    2.4\\\\\n",
    "    1.5\\\\\n",
    "    \\vdots\n",
    "\\end{bmatrix}\n",
    "$\n",
    "$\\longrightarrow$\n",
    "$\n",
    "\\begin{bmatrix}\n",
    "    [ 1 & 2. & 4.]\\\\\n",
    "    [ 1 & 2.4 & 5.76]\\\\\n",
    "    [ 1 & 1.5 & 2.25]\\\\\n",
    "    \\vdots & \\vdots & \\vdots\\\\\n",
    "\\end{bmatrix}\n",
    "$"
   ]
  },
  {
   "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 degree 2 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 '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 a problems. \n",
    "\n",
    "\n",
    "\n",
    "so we can use __LinearRegression()__ function to solve it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients:  [[ 0.         49.17475677 -1.34150031]]\n",
      "Intercept:  [108.4220867]\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:"
   ]
  },
  {
   "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 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "<h2 id=\"evaluation\">Evaluation</h2>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean absolute error: 23.94\n",
      "Residual sum of squares (MSE): 1018.30\n",
      "R2-score: 0.67\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import r2_score\n",
    "\n",
    "test_x_poly = poly.fit_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?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients:  [[ 0.         26.9289451   4.91395054 -0.53052354]]\n",
      "Intercept:  [131.65659228]\n",
      "Mean absolute error: 23.76\n",
      "Residual sum of squares (MSE): 1014.20\n",
      "R2-score: 0.67\n"
     ]
    },
    {
     "data": {
      "image/png": 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rjJIcRJdpAZy6Orj3dzs5n/tZyDEs4GSOYSHXcC2DeI2vMYMlHN7u2KBBcI88UpjfYPJUVdV+9aVCnTqWsxrTySRXLQuaRiK9wB8/3s1DJOJex4+PvoRmNmvXwle/Gvx9V7Zzyto7OPbfh3I/F/IpNtPAbxjEa/yEa9jEXr7H1dQEz59UqMBmOq7YgoKIdBeRhSKyRESWi8iPvfRrReQNEVnsbaenHDNJRFaJyEoROTWuvBmTq549s6cnZypNFqzNze5z0LH58FtnpgdbmcAt/JP9uIMG3tU+nF/1Bw7kJe6gge20n9siGeySS4QGPRUVOrCZjifORXa2Ayer6hYR6QL8VUT+7H33S1W9OXVnERkGjAIOAvYB5onI/mrrNJsOZMuW7OnJNRDSrVgR7Vo1NTB2LMycmX3qbICebOEybudK/pO92cgCTuLfuZt5jISW4Jnyamv9Zwj1m1o6l7WhTXmJ7UnBa89I/lPp4m2a4ZCzgdmqul1VVwOrgGPiyp8xcYk6dbWIa8ZtbHQFtMiuO/apUzPfuYN7Mrj9szezmsHczJUs5nBO5P84mQXM4xQg89Spa9a0Dwip7Sip+Sn22tCm+GJtUxCRhIgsBjYCj6vqs95X3xKRpSIyQ0T6eGkDgNdTDl/npRkTq0LPgBp1ptJsVTLJ9oz0GVO7sY0J3MJq2Y9LV11Jv1OP4tFrn+G8mrn8jRNb98u1PTJ53ZYW/8BhOqmgbkmF3IDewALgYGBvIIELSFOAGd4+vwbGpBxzJ/CvPudqAJqApkGDBuXcJcsY1eijhDN110waNsz/+332ydy1NX2QXPqAtWR6NTv0G/xGX2eAKuibB41Q/dvf2vym9AFu3bv7X7N79zj/uqajoiOMUwCuAb6XllYHLPPeTwImpXw3Fzg+0zltnILJV9T5hNKnn05uVVXh9ok6orlv312BRGjWC7lPX+EzqqDPdTtBH/vBglC/M675m0x5yhQU4ux91E9EenvvewAjgZdFpH/KbucCy7z3c4BRItJNRAYDQ4CFceXPGAjuYhmUHjQbaWp6pn2SVTJhvfOOa+w9hcdoop7ZXMRH9OQMHuK4T/7KA++dFOo8774bLd1UrjjbFPoDC0RkKfAcrk3hIeAmEXnRS/8C8B0AVV0O3A+sAB4FvqnW88jELKg+X3XX+IJUQQ2+cc0ifRiLmcu/8Bin0of3GMM9HMELPMIZNLcI06a1z6OfMF1pjQFsmgtTmcJMW+03tUPQ7Kap+4Rpd8h2zQG8ro2JS7QZ0bfZQyfwS+3KNt99E4nsvzdMnkzlwKa5MKUU9/rGUc+fPrgsm9RxB0HTPESd/mHECP/0Pl228BOu5hXZn1FVv+flM77HIT1e5VauYAfdfI+J2gXWmIyCokU5bPak0PHFsb5xvucP+4TgdzcdZhrtMOdpbEw7nmYdy136Ue/+LmHUKNXVq1v3zdQ4bU8KJio6Qu+jODYLCh1fXOsb53P+qAEhtdANc70wBXDqeU7gr7qQelXQ57seq/rMM775DlN1FaSQa0KY8pcpKISqPvJ6Ev1ARKZ7A85miMiMeJ9hTGcQtXdPMc4fdXBZQ8OuKqq1a9tPipfL9A+vvQb78Ab3MIa/cSL9Wc9oGqnf8TQcd5zvMcOHuyqyVFVVLj2byy6Llm4qV9g2hQeBTwHzgIdTNmMyCurdU6iJ1bKd36+9oaHB/5hx49yWDBqJhPs8fLg7Zu1al67afgK51NG+vXr5n781fft2bvjUz1jJAXyZP/BTJnMAK7mX0exbG/xPcvLk9t1dW1raT9sddxuO6eSCHiFSN2BxmP2KvVn1UcdXyjaFTN+l9j5KJDJXwUStompsVK2ubrtvdbX3m//8Z9UhQ1RB/zdxrg7m1dB/lzBVQEG/OejYMO0RpvMh3zYF4KfA6WH2LeZmQaE8RCmAcxG0bnEu7Q1+58qlPj79PA/cskb1nHPcgfvvrzp3buT1lsP8nlxWdzOVpxBB4UOgBdjmvf8Q+CDMsXFuFhQ6vrifFJLX8CtcoxbmQXkNmiIiVGP59u2q11+v2qOHO9nPfqa6bVtOvzNMQ3PQbw7arKG5MuUdFDrqZkGh44u791GmoNOzp/+1e/aMltfU+YciBbYnnlAdOtQdcN55qmvX5vVb43pSiPrEYspfQYICcBZws7edGfa4ODcLCh1f3F0hMxWUUa9dsIJzwwbViy92B+63n+rDD/vu1qVL22t06ZL5t+bTppDtaSH9swWGzi1TUAjbJfUGYAJuXqIVwAQvzZiM4u59lKlLqruXaS8oPZOgtQVSe/oMrm3h71//LQwdyieNs7mOH9Ljn8uQM05n5Mi25+vaFT75pG3aJ5+49CBh/pZBi+Nkkv73UM289rPp5IKiReoGLAWqUj4ngKVhjo1zsyeFjq+QbQp+d+uZnhQy3R37ibp/6m8bygr9Cyeqgj5b83kdyop25xgxIvdrJa/XtWvbfbt2Dfe37NUr8zWj5MOUPwo091HvlPefKlhUMp1aoZZ1TI4vWLvWFVlr17rPp5/efmWxYq0lPHky7Ny6nWu5hiUcxkEs56vcybFbF/AyB7bbf/78/K/pd1cfxu23u1lfU6V/NgYI/aRwEbAWuBuYCawGRoU5Ns7NnhQqR6YngqD6/rifFE7k/3QFriG5kX/TfmwIffedbZ+oT0Vh+J3TnhQqEwVqaO6Pa2w+G/h02OPi3CwodH5hprgOaviN2tActIzmsGFpO27erHrZZaqgq6nVU/lz5CqZ9Ebm5NalS3A1UdA582m0HzHC/5ypVV2m88kUFDJWH4nIUO/1SC8orANeB/bx0oyJTdgprpNVSenTOURdWGb5chg2rG3asGEuvdWf/uQSp0/npdOu4Jgey5jLaa1fp1dlBdmxA7p0aZvWpYtLnzDBvabvHySfhXLmzWs/jfeIES7dVCZxQSPgS5HpqtogIgt8vlZVPTm+rGVXX1+vTU1NpcyCiVF1dbS1Ampr2y51mT5xXaoM/9v727TJldb33cf7Aw9m7M47+dOGY9hjD/f1u++6XkBTpsCYMfldN1O+g9TWumtHbasxlUlEFqlqve93mYJCnhftDvwF6AZUA39Q1WtEZA/g90AdsAa4QFXf846ZBHwNaAa+rapzM13DgkLnFrVwFGk7YVxQUEkkYOfOkCdVhd//Hi6/HDZvZumXJvO5P09i88e7+o7W1LRtPM83GOUSFPzyYUyQTEEh7DiF80VkN+/9D0XkjyJyRJbDtgMnq+phwOHAaSJyHDARmK+qQ4D53mdEZBgwCjgIOA2YKiIRJzk2HVGus3ZGneI6vR9/0FNG6KeP9evh3HPhootg8GB4/nnOWnRNm4AAsHVr+5lK85E+PXZYhc6HqUxh//f7kap+KCInAqfieiDdnukArz1ji/exi7cprqF6ppc+EzjHe382MFtVt6vqamAVcEzoX2I6pKCupGECQ9AU1378uqH27eu/b1B6K1W45x446CB49FG46SZ4+mk4+OCCrg8xfrx7mhFxr+PHu/T06bGjKNQ6FaZyhQ0KyXurM4BpqvogkGHspSMiCRFZDGwEHlfVZ4G9VXU9gPe6l7f7AFwjdtI6L82UscmT3R1sqrB3tH6Lyvjp2xd69ICLLy7A+gFvvglnnQWXXAIHHghLlsCVVzL+29VUVwdX/6hGu3Z6I3pzs/s8fnz0J6RUhRopbipYULek1A14CPgN8CpuEFs3YEmYY73jewMLgIOB99O+e897/TUwJiX9TuBffc7VADQBTYMGDSpQBy0Tl3zmPgo7uVv6NZIjpiP1wW9pUf3d71R791bt3l315z9X3blTVYNnJ/XbMnUdTb1uUDfbXNaPTv/dxmRDAUY0XwDMBU5T1feBPYArIwSe94EncW0FG0SkP4D3utHbbR2wb8phA4E3fc41XVXrVbW+X79+YbNgSiTZOydseqrkSmfZpN+9R65bf+stOOccuOQSnvlgGPtvW4J89z+Q6kRr421YO3YENxSnVlvl3d6RJsxIcVuRzYQRNij0Bx5W1VdE5CTgfGBhpgO8dZ17e+97ACOBl4E5wFhvt7G4pT7x0keJSDcRGQwMyXYN0/F9+GG09EIJXbf++9+zfchBbJ8zl+9yMye2/IVX2L/1648/jl5QB1UxbdsW7TxhVVW1naTPTz5tO6ayhA0K/wM0i8hncdU6g4F7sxzTH1ggIkuB53BtCg8BNwCniMgrwCneZ1R1OXA/bhbWR4FvqmqO900mXanuEoMGXWUajFUIWevW334bLrgARo1i6dbPchiL+QXfpYX4Orx99FE85w3TMJ1P246pMEH1Sqkb8Lz3ehVwuff+hTDHxrnZNBfhFGP1syCR6vUjHBumbj2oPeMsHlTday/VLl30xt7Xa4JPcr5W1C3f3xbUDpFN3OtamPJCAdoUPhGRi4BLcI3O4LqYmjJQSXeJqXXrmlaNszubmcFXeJCzoX9/aGpi4uZJNJN9utBx43b1Ckok3OesXVtzVFsbbf8wXXfjXtfCdB5hg8JXgOOBKaq62qvzb4wvW6aQ8u1bn0/VU1D3yny6XWYSVLd+EgtYyqFcwu+Ywg9g4UI49NBQcxX16OG6xw4c6BqRBw50n2+91X/+ojAaA/71NDa68RZB+UptxE4Gp6lTs1/P75zFmmLclJmgR4hy2Kz6KJyghef79s1+bL5VT/lUH+XSPTP9d3dnq/6CK1RBVzJEj+WZNr+7qirz+aqqMv8N/KajDjvzaKYlPlOnyg7qchuVrcVsksh16mzgfu/1Rdzqa8ntRWzltbKRT1DIdw7/fIJCPnX2qqrXf7lJl3OgKuhtfEt78JGCG3cQ5RqZVi3zK1z92jNyXfc437+/MX7yCQr9vddavy3TscXYLCiEk08jY74NlPkEhaBglvWcn3yi+pOf6A6q9XUG6EgeCyxQ8xksFnTnHrYgD3Pnbg3EJg6ZgkLGNgXdNR3FWlVdC7wHfJiymTKQTyNj2TVQvvIKnHgiXH01/835HMKLzOOUNruktqVEmV8pSHqjfZg2nLDjBsru72/KX1C0SN2AS4ENuKmuV3vbP8McG+dmTwrh5LPge7Y2hWx3u8WrPmrRb/Ab3UKNvl/VW/Xee0PfsWdb3U2k/d8g0517mOtGeZooVXdi03mR73KcwCvAnmH2LeZmQSGcxsb2yz8ml30Me7xfwR/mvMUICnvxls7hTFXQxxmhA3hdhw0LX6BmCwrjxmVeIzm9MA9z3SjVQtZAbAqtEEHhUaAmzL7F3CwohBNXY2WYBuy4g8KZzNEN9NOP6aYT+KUKzW3On61AzTTZXSLRtlE6eb70AJJI+Dc2Z7quNSCbUipEUDgCWIybKfW25Bbm2Dg3CwrhxNVYGabADxsU/ArRTMfWsEVvp0EV9AUO04N4MXLQyeVvExRE0oNHNoU6jzG5yBQUQi3HKSILgb/iuqK2zrSiqjMDDyoCW44znLo6/xlH09c0jirMspNh9kk2uqaOuq6paT8KO+loFtLIGD7LKm7me/yI69hBt8DzZxJ16cxEwn+uoaqqaBPnxfXfxJgw8l6OE9ipqv+hqnep6szkVsA8mhhNmQJd05ZE6to1/9GsOa9s5kmOlB4zxn8ajnQJdvJDruNpTqA72ziZJ/g+N/kGhGHDwuUhqqDJ59LTs40CL+QKbsYUUtigsEBEGkSkv4jskdxizZkpqPSF6kMvXJ/Brbf6B5tbbw13fLJLZhh1rOZJTuI6ruZ+LuBQlvIUJ/nuO2wYLF8e7ry9ekVLDyNMd1Pramo6rKB6pdSNXd1QUzfrklomchnRnFrH37ev2zJNx5BLl9RwW4uO4Xe6md30fXbXi5gVqfE6W/4aG1Wrq9ueo7o6uIdPmGuHaUS2rqamlMi3obmjbhYUwolSiKr6F1ipW5TurPkEhN68q/dxoSroU/w/HcSarMekd5kNU/BG6fIZ5m8ZtvG62F1NrWurSco5KABXpbw/P+276zMdW4zNgkI4UYNCmLWRw8yblO3ambbP8aSuZV/dQbVO5HqtYmfoY5MD8+Lo9lmoJ4VisycTkypTUMjWpjAq5f2ktO9Oy7PmyhRJ1AbhMPX877yTe34y6cIOrmcSC/gC2+jOCTzNDUyKtCLajh0wYTJXsjUAABh0SURBVEI8jblh/pYdcZrqSlpTw+QnW1CQgPd+n9t+KbKviCwQkZdEZLmITPDSrxWRN0RksbednnLMJBFZJSIrReTUSL/EBMq3QbhY9mclT3MCk7iBO/kaR/I8TRyd07neeSeextwwf8vRo91CP7W1rstr6sI/pWK9nUxoQY8Q7gnDLcOZ/t7vs8+x/YEjvfe7Af8AhgHXAt/z2X8YsATohlsD+lUgkekaVn0UXqHqzeOpPmrRrzNdt1Cjb7OHnsMfc652St3iqjIpx7r5jlilZUqHPKqPDhORD0TkQ+BQ733y8yFZgs16VX3ee/8h8BIwIMMhZwOzVXW7qq4GVgHHZMmfKYFCPmX05W3+yHncQQNPcwKHspT/5dyCnDuuO/bRo90As5aW4JXeOpqOWKVlOqigaFHIDagDXgN2xz0prMEt1jMD6OPt81/AmJRj7gS+nOm89qQQTtj5epIy3X1HvTPOdK6RPKZv0F+300X/g5vbzFtUiK2cxfE0Uo5POCYelLJLKtALWASc533eG0jg2jOmADO89F/7BIV/9TlfA9AENA0aNCjOv1un0bOnf6HZs6f//oUsaH17B7FNb+Y/VEGXc6AezvOtVTtBS1lWUlCwnkImbpmCQtgRzTkRkS7A/wCzVPWPAKq6QVWbVbUFuINdVUTrgH1TDh8IvJl+TlWdrqr1qlrfr1+/OLPfaXz0UbT0OA3lJf7OcXyXX/DUQeM5tqqJxRxBIgFjx8KqVcXPU0djPYVMKcUWFEREcHf7L6nqL1LS+6fsdi6wzHs/BxglIt1EZDAwBFgYV/5MsSmXMY3nOZKBrONLzOH01b9mS4ur6G5uhpkzw097kU2mie46OuspZEopzieF4cDFwMlp3U9vEpEXRWQp8AXgOwCquhy4H1iBW7/hm6oaYd5JUwzV1TB+fLRj+rGRBzmbaYznKT7PIbzIQ3zJ9244EX44QkauprE82bxIppSq4zqxqv4V/7EMj2Q4ZgquncF0UM3NMG2aez91avb9z+n+KNO2/Tu9eZ8J3MKvuJxMtZZRpp/OpLa2MOcphSlT/KcSt55CphhibVMw5WncuOz7TJ/uXsePd08PImlPEdu2wYQJPLDti2yiH0fzHLcxoTUgVAfcjlQV4P/Ici9AO+LgN1M5LCiUqWzz9efjH//Ivk9zswsA06bturtPPkX89MIX4eij4bbbuI3LOYaFLEsb1rJzp3+/+aD1CsLqLAVoOY6FMJ1EULekctgqdZxC1C6LUccdhO3y2X6x+xa9nFv1Y7qp7r236iOPZDw+6hKcYfJjjMmOfJfj7KgqdTnOqEs5ZuuJU1PT9u46TM8dkbaNuXvzFnfxFb7Io/yJM/nShjthr70iL3eZb6+hMv7f2ZiiKcRynKYDKXSXxVz6wKcWvl9iDi9yCJ/nKcYxlbOYA3vtlVtm8lConkvGVDILCmUoji6LuQSUGj5iGpcxh7N5nX05ikXczjiyTKCbUT4Fe0ND7scaYxwLCmXo9NOjpYcRNaAcRRPPcyQNTOcmruR4nuFlDsw9A54DDoh+TCLhekyF6SJrjMnMgkIZuv/+aOnZROnCWUUzk7ieZzieGrYygvl8n5vYQbfWffJpF1i5Mtr+PXu6nkwWEIwpDAsKZSho1bNcVkOL0oWzljU8yUlcz2T+yHnc8tWlPMkX2u132WXR85EUdfDaccflfi1jTHuxjWg25cGvt1J7yhga+S++BcAY7mEWo9E7hY+7uaDS3OyqcRoa8rtrTySiBYYnn8z9WsaY9uxJoZMJHGGcoz68y++5kHu4hCUcxmEsYRZjSDYmT53qqm9UC1ONE7WxuFDTYhhjHAsKZShTnb3fCONcjWAeL3II5/IAE/kZX2ABa6mLdI5evaKlT53qGo3D9kKybqjGFJYFhQ7ObzqLuAdodedjfskVzOMUPmB3juVZbmQiLbQvgbM9mdx+e/sgJuLSgySfPvbZJ3terRuqMYVlbQod2KxZbWfLXLu2CIXgCy/QxBgOYgW3cTkTuYGPqfHdNTn3UVLQDKpdusCOHW0/h5Fpv0K0Xxhj2rNpLjqwoOksCqn1P//OnXDTTXDNNby5sx9f4S4e49TA46qq3B2/X51+IuFOB9Gn5EgVdYoMY0w4Ns1FmYo7ILR69VX4/OfdXBfnncfBLMsYEAB23z24kTc1PZ8pOYLaC6wdwZj4WFDowHIp/NLXKQhat8BR+M1v4LDDYPlyV181ezbvsUfW67z/frhCO58pOcIEHWNMYcW5RvO+IrJARF4SkeUiMsFL30NEHheRV7zXPinHTBKRVSKyUkQy36pWgFwKv2S1TdDnpE+znoc5w400O/54WLYM/u3fQCT0iOSg9o3U9ClT/NdNCDOCOmj1tHJeVc2YDi9oTu18N6A/cKT3fjfgH8Aw4CZgopc+EbjRez8MWAJ0AwYDrwKJTNfo7Osp1Nbmt75A0HYh9+k79NGP6KH6q1+pNje3ue6wYeHOo6o6btyudRUSCfc5nd+6CWFEXTfCGBMOGdZTiC0otLsQPAicAqwE+uuuwLHSez8JmJSy/1zg+Ezn7OxBYdy4wgaDPXhbZ3OBKugzHKv787LvdcOerxhyDSjGmGCZgkJRuqSKSB1wBPAssLeqrgdQ1fUikpx4fwDw95TD1nlpFeuRRwp3rjP5E9NpoC/v8AOmcBNX0VwGPZJHj7alKI0pptgbmkWkF/A/wBWq+kGmXX3S2nU8FJEGEWkSkaZNmzYVKpsdUiF6H+3OZmbwFf7EWWxkL45hIT/jB60BodDrOxtjylusQUFEuuACwixV/aOXvEFE+nvf9wc2eunrgH1TDh8IvJl+TlWdrqr1qlrfr1+/+DLfAeTb9fIUHmMZB3Mx9/BTJnM0z7GEw9vskxwQZ4HBGAPx9j4S4E7gJVX9RcpXc4Cx3vuxuLaGZPooEekmIoOBIcDCuPJXDnLterkbHzCdb/AYp/Ihu3ECT/MjfsondPXdP5flOKPwm6qjGMcaY3IQ1NiQ7waciKv+WQos9rbTgb7AfOAV73WPlGMm43odrQS+mO0anb2hOZfG5JE8pmsYpDup0hu4SrvxcajjRHZdt2fP7Pt37RruN+TTg6ixcVfPpuSWSFhjszH5IkNDs01z0YFFWcFsNz7gZr5HA3fwMgfwFe7i7xwf+vjUaSdGjoT58zPv37MnbNmS/bz5THPRqxd89FHu1zbG+LNpLspUVcj/OqfyKMs4mK9xJzdyFUfwQqSAkD6Y7Iknsh/jV1j7yWeai6BrhL22MSY6CwodWLag0Jv3mMFXeJQvsoVenMDTTORGttEj9DX8luMs5MNjPtNcGGOKz4JCBxY0RQXAOTzACoZxMfdwHT/kCF5gIcdGvsaaNfGOA8hnmougoBj2CcoYE5398yoze/MW93M+D3Aeb/FpjuY5ruY6dtCtYNcI05bRt2+4c40e7Z5Eamvdef2eTIJcemm0dGNM/jr+kFbjUf6du/k536WGrUzkZ/yc77KTkCvWRLlSluqjRAJuvTX8+XIdlZxcQGf6dNc91xbWMSZ+9qRQBvbjVR7nFO7iqyzjYA5jCTcyMZaAANlnIbWpq43pvCwodGDVfMJV3MiLHMLRPMel3M5JPMk/OCDW6/q1A6QrRhVOcrnPZBBKLveZvg60MaZwLCh0VAsX0kQ9NzKRuZzKMFYwnUvRIvwnS20HCFKMbqHTp0dLN8bkz4JCR7N5M1x+ORx3HH15h3N4gPN4gDdjmDA206pso0dnH1wWN1t5zZjis6DQUajC/ffDgQe6ltRvfYthrOBBzsn71F39pzziG9/IfmxQT6Qoo62NMeXDgkJHsGoVfPGLcOGF0L8/PPss3HYbH7J7QU7/ySf+6YVcr8EY0zlYUCilbdvgxz+Ggw+Gp5+GW25xAaHed0qSnAV1MQ2zXkPQscWYMsvWaDam+CwolMrDD8NBB8G118K558LKlTBhQuaK/gqTz2hoY0xuLCgU2+rVcPbZcOaZrrL/8ccZ3+c+qvftj4iLCdbl0slnNLQxJjd2W1osW7fCDTfATTe5obk33ghXXMH4K7oybdqu3ZJ98TuKESP8p9EeMaI417c1mo0pLntSiJsq/OEPrlfRddfBeee5qqKrroKuXTP2xQ87v1Cc5s1rHwBGjHDpxpjOx4JCnBYvhi98Ac4/H3r3hqeegnvvhYEDW3fJ1Bf/gguKlM8s5s1ru+6aBQRjOq8412ieISIbRWRZStq1IvKGiCz2ttNTvpskIqtEZKWInBpXvopiwwY3D8RRR8GyZXD77fD88/C5z7XbNZHwP0UiEa3LaJcu0L17tGwGjV8wxlSuOJ8U7gZO80n/paoe7m2PAIjIMGAUcJB3zFQRCSguO7Bt21y7wZAhMGMGfPvb8MorLkAElP4NDf6namgItzpZkoi7fKbv0z/PmBH+/MaYyhBbUFDVvwDvhtz9bGC2qm5X1dXAKuCYuPJWcC0tMGsWDB0Kkya5KqPly+GXv4Q+fTIeOnUqjBu3K2YkEu7z1KnRVifbsSP4qaO2Fu65p20vnnvusQZcY0x7pWhT+JaILPWql5Il5gDg9ZR91nlpHd+CBXD00TBmDOyxh+uq8+CDsP/+7XYdP951OU3vejp8uGtmEHGvw4e79KB++kGam4P79SfnMmppiX+1NWNM+Sp2UJgGfAY4HFgP/NxL95tJx3fMrIg0iEiTiDRt2rQpnlyGsWSJm5ri5JNh0yZ3693U5D77CJoGeuRIV1W0dq1rxF271n2eNat9P/2+faFHhuWXk/34/fr1z5oFdXVuKcu6OvfZGGPaUdXYNqAOWJbtO2ASMCnlu7nA8dnOf9RRR2nRrVqlOnq0qohqnz6qN9+s+vHHWQ9LJFL772TfEgl3idpa1cZGt9XUBO9fU+P28eN3bKb9k8fU1rbNgzGmcwCaNKjcDvqiEFt6UAD6p7z/Dq4dAVwD8xKgGzAY+CeQyHb+ogaFN95QHTdOtbpatUcP1e9/X/W990IfHiUg+BX4ffsGf5+t0K6tDT7OTy5BxBhTPjIFBXHfF56I3AecBOwJbACu8T4fjqsaWgNcqqrrvf0nA18FdgJXqOqfs12jvr5em5qaYsh9io0b3ejjqVNh505Xt/PDH7rZTCOoro5nHQAR106QSVWV/wR2QcfW1QVPlmfrJBtT/kRkkar6zrwZ2zQXqnqRT/KdGfafAnScqc42bYKf/xx+9SvX1/OSS+BHP4L99svpdA0N/tNXDBsGK1bkns0wPZT22APeecc/3U+mrrCp03BYYDCm87ERzek2bnRTUNTVuXmKzjkHXnoJ7ror54AAwV1Pwy5r2auXf/rpp/un5yNMoLElMY3pnGKrPiqGglYfrVsHN9/sSrvt2+Gii1w10dChhTl/gKCqnVQ1Na7Xkd/dfm1t9mUzo1YfzZrlnmy2bs183jL+X8eYipap+sieFF55xZWA++0H//VfbsKhFSugsTH2gADBd+WJRNtupe8GDAMMM+o56BpB6aldYYMEDZQzxpS3yg0Kzz0HX/4yHHAA/O538PWvu2Ux777bpRVJ0AC1mTPbDjQLW7D7jUfIZbGa5GC3oCmyTzop+FhjTPmqzKAwfz4cc4yb7nPiRFf6TZ3qStEiC7uQTJiCPVntkz4QDnJfrGbVqmjpxpjyVplB4aSTXBB47TW4/nr49KdLmp0wU1CECR6TJ7dvB9i61aXnKqh6KspkfcaY8mENzZ1Ipkbrmpq2AaOmJtzTQtCYhTAN3MaYjskamitEpkbrXJ8gcmmPMMaULwsKnUhQAR40kjpMFVDYNg9jTOdgQaETCSrAg7qWhl2vwabdNqZyxDbNhSmN0aP9C+30wWhWBWSM8WNPChXAqoCMMWHZk0KFCHqCMMaYVPak0MkErbBmK68ZY8KwoFBGshXsQSOax48PXvLTGGNS2eC1MuE3c2n6ALSggWaJhH+3VBuAZkxlssFrnUCYKSyCxh3kM07BGFNZYgsKIjJDRDaKyLKUtD1E5HERecV77ZPy3SQRWSUiK0Xk1LjyVa7CzEGUaUSzn7DjFIwxlSPOJ4W7gdPS0iYC81V1CDDf+4yIDANGAQd5x0wVEZuxP0WYqbODRjQ3NNhUFcaYcGILCqr6FyB9aZizgZne+5nAOSnps1V1u6quBlYBx8SVt3IUZg6ioPEIU6faOAVjTDjFHqewt6quB1DV9SKyl5c+APh7yn7rvDTjSRbgkye7KqNBg1xASC/Yg8Yj2DgFY0wYHWXwmvik+XaLEpEGoAFgUIVVilvBboyJW7F7H20Qkf4A3utGL30dsG/KfgOBN/1OoKrTVbVeVev79esXa2aNMabSFDsozAHGeu/HAg+mpI8SkW4iMhgYAiwsct6MMabixVZ9JCL3AScBe4rIOuAa4AbgfhH5GvAacD6Aqi4XkfuBFcBO4JuqGtC73hhjTFxiCwqqelHAVyMC9p8CWCdJY4wpIRvRbIwxplVZz30kIpsAn9l+QtsTeLtA2SkXlfiboTJ/t/3myhH1d9eqqm9PnbIOCvkSkaagSaE6q0r8zVCZv9t+c+Uo5O+26iNjjDGtLCgYY4xpVelBYXqpM1AClfiboTJ/t/3mylGw313RbQrGGGPaqvQnBWOMMSkqMiiIyGneYj6rRGRiqfNTDCKyr4gsEJGXRGS5iEwodZ6KRUQSIvKCiDxU6rwUi4j0FpE/iMjL3n/z40udp7iJyHe8/7eXich9ItK91HmKQ9QFzKKquKDgLd7za+CLwDDgIm+Rn85uJ/BdVT0QOA74ZoX8boAJwEulzkSR3Qo8qqpDgcPo5L9fRAYA3wbqVfVgIIFbuKszupuQC5jlouKCAm7xnlWq+k9V3QHMxi3y06mp6npVfd57/yGukOj0a1aIyEDgDOC3pc5LsYjI7sDngDsBVHWHqr5f2lwVRTXQQ0SqgRoCZloudxEXMIusEoPCAOD1lM8Vt6CPiNQBRwDPljYnRXELcBXQUuqMFNF+wCbgLq/a7Lci0rPUmYqTqr4B3IybaHM9sFlVHyttroqqzQJmwF5Z9g9UiUEh9II+nZGI9AL+B7hCVT8odX7iJCJnAhtVdVGp81Jk1cCRwDRVPQL4iDyqE8qBV4d+NjAY2AfoKSJjSpur8lSJQSH0gj6djYh0wQWEWar6x1LnpwiGA2eJyBpcNeHJItJY2iwVxTpgnaomnwT/gAsSndlIYLWqblLVT4A/AieUOE/FFLSAWWSVGBSeA4aIyGAR6YprjJpT4jzFTkQEV8f8kqr+otT5KQZVnaSqA1W1Dvff+QlV7fR3j6r6FvC6iBzgJY3ArVXSmb0GHCciNd7/6yPo5I3raYIWMIuso6zRXDSqulNEvgXMxfVQmKGqy0ucrWIYDlwMvCgii720H6jqIyXMk4nP5cAs78bnn8BXSpyfWKnqsyLyB+B5XE+7F+iko5ujLGCW0/ltRLMxxpikSqw+MsYYE8CCgjHGmFYWFIwxxrSyoGCMMaaVBQVjjDGtLCiYiiEizSKyOGXLeZSviDxdyLylnbteRG6L6/zGZGJdUk3FEJEtqtqr1PkwpiOzJwVT8URkjYj8WESeF5EXRWSol97Pm5v+eRH5jYisFZE9ve+2eK8niciTKWsXzPJG1CIiR4nIUyKySETmJqchSLv2+d78/0tE5C8p53zIe/9IypPNZhEZ660P8Z8i8pyILBWRS4v1tzKdnwUFU0l6pFUfXZjy3duqeiQwDfiel3YNbmqMI4EHgEEB5z0CuAK3Psd+wHBvnqlfAV9W1aOAGcAUn2OvBk5V1cOAs9K/VNXTVfVw4GvAWuB/vfebVfVo4GjgGyIyOPyfwZhgFTfNhaloH3sFrJ/kBIGLgPO89ycC5wKo6qMi8l7AsQtVdR2AN4VIHfA+cDDwuPfgkMBN6Zzub8DdInJ/Sh7a8J5O7gEuUNXNIvIvwKEi8mVvl08BQ4DVAfkzJjQLCsY4273XZnb9u/CbZj3TsanHC7BcVTMug6mql4nIsbiFgBaLSJug5a0UOBv4iaoml18U4HJVnRsyf8aEZtVHxgT7K3ABgHd3HmXd25VAv+TayCLSRUQOSt9JRD6jqs+q6tXA27Sd1h3cRGdLVXV2StpcYJxXRYWI7N/ZF9ExxWNPCqaS9EiZIRbcGsaZuqX+GLjPa3t4Clf982GYC6nqDq965zYR+RTu39otQPqMvP8pIkNwd//zgSXA51O+/x6wPCXfV+OWFq0DnvcatTeRx/KLxqSyLqnGBBCRbkCzN9368biVzILaJIzpFOxJwZhgg3Bz1FcBO4BvlDg/xsTOnhSMMca0soZmY4wxrSwoGGOMaWVBwRhjTCsLCsYYY1pZUDDGGNPKgoIxxphW/x/zizCEVeY9nwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# write your code here\n",
    "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=3)\n",
    "train_x_poly = poly.fit_transform(train_x)\n",
    "train_x_poly\n",
    "\n",
    "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_)\n",
    "\n",
    "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)+ clf.coef_[0][3]*np.power(XX, 3)\n",
    "plt.plot(XX, yy, '-r' )\n",
    "plt.xlabel(\"Engine size\")\n",
    "plt.ylabel(\"Emission\")\n",
    "\n",
    "from sklearn.metrics import r2_score\n",
    "\n",
    "test_x_poly = poly.fit_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": [
    "Double-click __here__ for the solution.\n",
    "\n",
    "<!-- Your answer is below:\n",
    "\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",
    "# 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.fit_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_y3_ , test_y) )\n",
    "\n",
    "\n",
    "-->"
   ]
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    "<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=\"http://cocl.us/ML0101EN-SPSSModeler\">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://cocl.us/ML0101EN_DSX\">Watson Studio</a>\n",
    "\n",
    "<h3>Thanks for completing this lesson!</h3>\n",
    "\n",
    "<h4>Author:  <a href=\"https://ca.linkedin.com/in/saeedaghabozorgi\">Saeed Aghabozorgi</a></h4>\n",
    "<p><a href=\"https://ca.linkedin.com/in/saeedaghabozorgi\">Saeed Aghabozorgi</a>, PhD is a Data Scientist in IBM with a track record of developing enterprise level applications that substantially increases clients’ ability to turn data into actionable knowledge. He is a researcher in data mining field and expert in developing advanced analytic methods like machine learning and statistical modelling on large datasets.</p>\n",
    "\n",
    "<hr>\n",
    "\n",
    "<p>Copyright &copy; 2018 <a href=\"https://cocl.us/DX0108EN_CC\">Cognitive Class</a>. This notebook and its source code are released under the terms of the <a href=\"https://bigdatauniversity.com/mit-license/\">MIT License</a>.</p>"
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