ML0101EN-Reg-Polynomial-Regression-Co2-py-v1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "<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."
   ]
  },
  {
   "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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "### Importing Needed packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "<h2 id=\"download_data\">Downloading Data</h2>\n",
    "To download the data, we will use !wget to download it from IBM Object Storage."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--2020-04-04 23:03:36--  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 0.06s   \n",
      "\n",
      "2020-04-04 23:03:36 (1.10 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",
   "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](http://cocl.us/ML0101EN-IBM-Offer-CC)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "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": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "## Reading the data in"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\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>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": [
    "Lets select some features that we want to use for regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\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": [
    "Lets plot Emission values with respect to Engine size:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "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(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.  ,  3.5 , 12.25],\n",
       "       ...,\n",
       "       [ 1.  ,  3.  ,  9.  ],\n",
       "       [ 1.  ,  3.2 , 10.24],\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.         45.56117905 -0.84002507]]\n",
      "Intercept:  [114.87522834]\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: 24.01\n",
      "Residual sum of squares (MSE): 1043.70\n",
      "R2-score: 0.70\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": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients:  [[ 0.         32.74090956  2.89288981 -0.32818323]]\n",
      "Intercept:  [127.86512273]\n",
      "Mean absolute error: 23.76\n",
      "Residual sum of squares (MSE): 1022.97\n",
      "R2-score: 0.70\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEHCAYAAABBW1qbAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjAsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+17YcXAAAgAElEQVR4nO3deZwU5ZnA8d8zByhgFAZ0QXRQgwd4IEwwBteoeAWzaoxxNSMx6mYUNFETN4Fg1ByYw8QrLkSionHG4JVE1xiNslE2aNABQUBEWTkkEkE88CDAzDz7x1s9U9PT1V3V3dU9Pf18P5/6dPfbVdVvj1JP13s8r6gqxhhjDEBFsStgjDGm+7CgYIwxpp0FBWOMMe0sKBhjjGlnQcEYY0w7CwrGGGPaVcV5chFZA3wAtAItqlonIgOA+4BhwBrgLFV919t/KnCht/83VPWJdOcfOHCgDhs2LK7qG2NMj7Rw4cK3VXVQqvdiDQqeY1X1bd/rKcBcVf2JiEzxXn9HREYAZwMjgSHAUyKyv6q2Bp142LBhNDc3x1l3Y4zpcURkbdB7xWg+Og2423t+N3C6r3yOqm5T1dXAKmBsEepnjDFlK+6goMCfRWShiDR4ZXuo6gYA73F3r3xP4A3fseu9MmOMMQUSd/PROFV9U0R2B54UkVfS7Cspyrrk4PCCSwPA3nvvnZ9aGmOMAWK+U1DVN73HjcDvcc1Bb4nIYADvcaO3+3pgL9/hQ4E3U5xzlqrWqWrdoEEp+0mMMcZkKbagICJ9RWSXxHPgRGAZ8AhwnrfbecDD3vNHgLNFpLeI7AMMB56Pq37GGGO6ivNOYQ/gryKyBHdx/6OqPg78BDhBRF4DTvBeo6rLgfuBl4HHgUvSjTwyxhRPUxMMGwYVFe6xqanYNTL5IqWcOruurk5tSKoxhdXUBA0N8PHHHWV9+sCsWVBfX7x6mfBEZKGq1qV6z2Y0G2MimTatc0AA93ratOLUx+SXBQVjTCTr1kUrN6XFgoIxJpKgkeA2QrxnsKBgjIlk+nTXh+DXp48rN6XPgoIxJpL6etepXFsLIu7ROpl7jkIkxDPG9DD19RYEeiq7UzDGGNPOgoIxxph2FhSMMca0s6BgjDGmnQUFY4wx7SwoGGOMaWdBwRhjTDsLCsYYY9pZUDDGGNPOgoIxxph2FhSMMca0iz0oiEiliLwoIo96r68Vkb+LyGJvm+Dbd6qIrBKRlSJyUtx1M8YY01khEuJdBqwAPuEru1FVf+7fSURGAGcDI4EhwFMisr+t02yMMYUT652CiAwFTgFuD7H7acAcVd2mqquBVcDYOOtnjDGms7ibj24Cvg20JZVfKiIvicidItLfK9sTeMO3z3qvzBhjTIHEFhRE5PPARlVdmPTWTGA/YBSwAfhF4pAUp9EU520QkWYRad60aVM+q2yMMWUvzjuFccCpIrIGmAMcJyKNqvqWqraqahvwazqaiNYDe/mOHwq8mXxSVZ2lqnWqWjdo0KAYq2+MMeUntqCgqlNVdaiqDsN1IP+Pqp4rIoN9u30BWOY9fwQ4W0R6i8g+wHDg+bjqZ4wxpqtiLMf5MxEZhWsaWgNcBKCqy0XkfuBloAW4xEYeGWNMYRVk8pqqPq2qn/eeT1TVQ1T1UFU9VVU3+Pabrqr7qeoBqvqnQtTNGBNdUxMMGwYVFe6xqanYNTL5YjOajelhJk+GqioQcY+TJ+f3/E1N0NAAa9eCqntsaLDA0FNYUDCmB5k8GWbOhFav4bW11b3OZ2CYNg0+/rhz2ccfu3JT+kS1y6jPklFXV6fNzc3FroYx3UZFhfv1nkwE2pJnC3XjzzDxEpGFqlqX6j27UzCmBwn6jZfP33577x2t3JQWCwrGmEimT4c+fTqX9enjyk3ps6BgjImkvh5mzYLaWtdkVFvrXtfXF7tmJh8sKBjTg0yaFK08W/X1sGaN60NYs8YCQk9iQcGYbiIfY/9nzHABoLLSva6sdK9nzMhnTU1PZkHBmBzka05AqrH/Eye680YNEDNmQEuLO09LiwUEE00x0lwY0yMk5gQkJOYEQPQLcaqx/4kRQ4nJYWDNNCZ+Nk/BmCxVVXVMEvOrrHS/0KMIGvvvV1vr2u9NN6YK778P77wDW7Z0bFu3um3bNvc/R0uL65CpqOjYeveGnXZyW79+8IlPwC67QP/+UFPj3s+TdPMU7E7BmCylCgjpytPZe293R5DOunXhzjV5shsN1NrqAlRDg7tzaWpydyTr1rnPmz7d7jwi2boVXn/dReY33nB/yPXr4R//cNtbb8Hmzdn9DxBGv36w++4weLDbjjsu/yMIsKBgTNYqKlLP4K3Ioqdu+nR38U5uQvILMzksqEnr1Vfhuec6zm9NUgFU4e9/h2XL4OWXYeVKeOUVWLUK3kxa3qWqCoYMcRfo/faDI4+EgQPdNmAA7Lqr+7Xfr5+byJG4C6iqclvi9rCtzd05bN8O//yn2z78sOMu4913XbB5+20XeDZsgKVLYY89YvkTWPORMVnq1w8++qhred++7t90Kul+rSfeW7vWdTD7/2n26RNuLkBQk1aQsm6SammB5cth0SJ48UVYvNhdbN97r2Ofmho48EAYPtxd+Pfbz/X819a6i3JimFeJSdd8ZEHBlKV8NKVEzQGUGGHkvxsIutgHNQFlIqkWtc2wf9nkK9qwAZ591m3PPw8LF7omIXCR/LDD3HbIIXDwwXDQQe5Xfw9kQcEYnygX53SGDUvdDxD06zvs/rnUz+4UPKqwejU884zb5s1zr8F12I4ZA5/6lNvq6uCTnyzZX/3ZSBcUUNWS3caMGaPGRFVbq+quGp232tpo52lsVO3Tp/M5+vRx5amIpP5ckfzVb9Kk1MeOHx+triVp40bVe+9VveCCzn/EmhrVL3xB9Re/UP3b31S3bSt2TYsOaNaA62rsF26gEngReNR7PQB4EnjNe+zv23cqsApYCZyU6dwWFEw2wl6cw2hsdNcfEfeY7iIb9mKfa/0mTVKtrHTHVFa61+nKS1ZLi+qzz6pedZVqXV3HH2633VwQuPVW1WXLVFtbi13TbqfYQeGbwL2+oPAzYIr3fArwU+/5CGAJ0BvYB/g/oDLduS0omGzk604hqsZG1erqzp9ZXd01kMRRv6h3Nd3WBx+oPvig6sSJqgMHdkS4ceNUf/AD1QULXLAwaaULCrGmuRCRocApwO2+4tOAu73ndwOn+8rnqOo2VV2Nu2MYG2f9THkqZurn5I7gVB3Dqeon4vojss2JVNKrpb3zDsyeDf/2b67j98wz4Y9/hJNOgt/+FjZtgr/+Fb73PRg7tqz6BmIRFC3ysQEPAmOAY+i4U3gvaZ93vcdbgXN95XcAZ6Y7v90pmGxFafbJl0x3AP461dS4LdFslOsv/Hw2mRXE5s2qt9+ueuKJqlVVHX+oyy9Xffpp1R07il3DkkaaO4XYJq+JyOeBjaq6UESOCXNIirIuQ6NEpAFoANjblnoyWaqvL/ykraAZyevWdR1xtHmzu1uoqXHP/RK/8KPUP2jGdLf6J/TRR/Dww+7X/xNPwI4dbl7AlVe6u4PRo6OPuTWRxdl8NA44VUTWAHOA40SkEXhLRAYDeI8bvf3XA3v5jh8KJE0hBFWdpap1qlo3aNCgGKtvTH6lW8YyqHknOSAkhE15kZCPJrORI901ObGNHBmtDim1tsKf/+xSwu6xh4t0S5bA5Ze7eQSvvQY//rEbQmoBoTCCbiHyudG5+eh6Onc0/8x7PpLOHc2vYx3NpgdJ19kb1LwTtGXT6ZxLk9mIEanrMWJE9Hqoquorr6hOmaK6557aPmKooUF13jwbLVQAFHP0kXYNCjXAXNyQ1LnAAN9+03CjjlYCn8t0XgsKptQEXZiD+htqarrHqKF0ASq0Dz9UnT1b9aijtH3U0CmnqN5/v+rWrXFV3aRQ9KAQ12ZBwRRK3B3T6e4iitEpniynoLB4sZsUscsu7oD991f96U9V33wz9nqb1CwoGJODQo3xD3PxL1aAiBwUtm5Vvece1SOPdDv17q167rmueaitrTCVNoHSBQVbjtOYDLrLGP9US3Y2NISft5DL0qEjRoQsX7cOpk6FvfZyncebN8MNN7h01PfcA//6r9Zh3M1ZQjxjMoiaDTWsysr0xyeS4EFHSu1UkpPaHX88zJ3b8Xr8eNh//87rLCRMmhR+6dCRI90SAwkjRrjM06i6yWO33AK//717feqpcMklbiGYbBaYMLGyLKnG5CBqNtQwMgWEhJoal9053eI70BG0kgNCJjkFtu3b4YEH3J3AokVu2civfc3dgtTWZnlSUwjpgoKFcGMyiCMtRtgL8ebNmQOCP6tDlIAAqe+AMnr/fbj+eth3Xzj3XFfBX/3KLU35059aQChxthynMRkkZg531/WN41oSuIv16+HGG+HXv4YPPnBNQ7NmwcknWxNRD2JBwZgQipEWo08f2Hnn4FnNCbH/MF+xwt0ZNDa6W5yzznKpJ0aPjvmDTTFYeDemCNL9sBZxF/pZs+Dmm7s2XfklN2ONH5+/OrJoEXzxi66Hec4cuOgit4D9vfdaQOjBLCgY49PU5DqWKyqyT1MdRmtr18CQGOXU1uY6sBN3J7NmuSAh4jqea2o6Bw7/HcxTT3UNDOPHB2eTTln+3HMwYYLLNzR3Lnz3u66n/Ze/dH8U07MFTWAohc0mr5l8KvZCNHGujBa0TGenz5g3T/X4490bAwfqH8ZO1/4V78VSH1Nc2IxmYzIr9Ips/tnJffuGuGjnKDDozJunetxx7o099lD9+c/1sv/4MPb6mOJJFxRsnoIxnrgmqaWSvH5COrW1MY12eu45t1rZ3LkubfWUKa5SffpQVZV6VFNlJbS05LkepuBsnoIxIaRb7yBfEn0WieH9YURNZxEkkeZijCzkTzIBPvMZ3pq7lB/2/wVzrnvdrWHg9WoHDXMt2PBXUzQWFIzxhJ2klm1ntD93UVQff+wCSdDnZcprNHkyPD3zZe5r/SILqWMsC/gOP2FfXufqd7/JhV/v0+m8kTqmTc8S1K5UCpv1KZh8y5SFNJfO6KA+i6hb8udl7ERes0bvkvO0hQp9n130aq7VXXg/bd9JqI5pU7KwjmZj8iOXzuioq6tl2hJBK9F5nLzVsElv3+VybanqpVvprdfzLa1hU+D5RDrXN87RUKa40gUFaz4yJoKgtZGTy1M1MeWzbwJcM9QFF3Rt5+/DR0zjR7zOvnz1g1u4Ryeyv6ziP/k5mxkYeL7k+s2Y4TqVVd1j2GyqprTFFhREZCcReV5ElojIchH5vld+rYj8XUQWe9sE3zFTRWSViKwUkZPiqpsx2erbN3N50LoHQcfmYvv2jueVtHAht/Maw/kR32Mu4zmYZZzfejtvVQ9Ne55cE/yZniPOO4VtwHGqehgwCjhZRD7tvXejqo7ytscARGQEcDYwEjgZmCEi1q1luoXEL/8PP0z9vr88aFEe/1oEqWS/9ozyOR5jCYdxO19jNfvwGeZzBr/nFQ4COgePZKlmRpvyFVtQ8JquEv9Uqr0t3aSI04A5qrpNVVcDq4CxcdXPmLCijhoKamJKR9UtTBY1ud1hLOZJTuAxTqEX2zmDhziKv/Icnwl9jkRKDWMg5iGpIlIpIouBjcCTqrrAe+tSEXlJRO4Ukf5e2Z7AG77D13tlxsQq03DOVL/804nad5AY5jl/vstOnUqfPp2bn/6FDdzOhSxiNKPlRbj5ZoZvW84XG8+gTx/pcqwxYcUaFFS1VVVHAUOBsSJyMDAT2A/XpLQB+IW3e6qb5y53FiLSICLNItK8adOmmGpuysXkyW6ZykRnbWure+0PDFHnFUyYkLo8aJ3j1lYXkPz18Es079x2G/Sr+idTuY5X2Z+J3MPNFVcw91er4BvfgF69uiTQSxzbr1/qzw4qN2UsaFhSvjfgGuDKpLJhwDLv+VRgqu+9J4Aj053ThqSaXAUN56yszLyPf6uo6Ni/piZgiGhN52GeYbb2erS1qT7wgH4waJgq6O84XY8e8lroZH3p6mTKD8UYkioig0RkN+/5zsDxwCsiMti32xeAZd7zR4CzRaS3iOwDDAeej6t+xkC4dA5hUjv4cyMFLYqzeXPHMM9I9VuyBI49Fr70JXbs/AnO2X0uX5Tfs7b6k6HP88470cpN+Ypz5bXBwN3eCKIK4H5VfVRE7hGRUbimoTXARQCqulxE7gdeBlqAS1TVMq2YWFVWBl/0RdxaBLW1mZuQ4lj9bACb+ZF8D0bfBv378/z5Mzl+zn/wwVb3zzYx1BUydxT37Zt65FQcw2RNabMsqaYsNTW5DuQw/QUjRrgROuk6m8ePdwvcQPqhpYl/bun2qaCVi7iNH3EVu8oWKi+dDN//PsMO75+yvrW1rn7phKmTKR+WJdX0aFET1EUdYvryyx2dt0GefjpkZT277Za6/DPMp5k6ZnAJm4aMovKlxXDLLdC/f+jZ1MbkwoKCKWlBs4fTBYaoQ0zBNc+k+zUeNaX0rbd2fr07b3EX5zGfozh86Ntw330csH4uHHxw+z6FSO1tjAUFU9KCZg9PmxZ8TC6/rPOVUjpRv0pauIRbWckBnMNvmfGJKfDKK3DWWV3afMKm9k4lqPko+1nUpqcKFRS8kUTfFZFZ3oSzO0XkzrgrZ0wm2TSpBP2y7tUrdfn48R3PEx27yYLKg6xbB0fwN17gU9zK13mesRzCUi794MeBvb9BcxDCzEa++OJo5aZ8hb1TeBjYFXgK+KNvM6aoMjWppOpvCPrFfeednQMAdO5ABjekNNU+/gyiGSeKbd5MY98G/saRDGITX+J+TuIJXuWAjE1BiWastrbg9BSpvvO4cV3vZiorXbkxnQRNYPBvwOIw+xV6s8lrJt2iN5neS7eYTjaf59+nqqrzPlVVqo33tKnOnq1aU6OtFZV6U9W3tB9bAs+Tz79H0OS1MOtAmJ6HXBfZAX4ETAizbyE3CwqlIdsLcK7nz2VBnCBhz5lcp0d+ulz16KPdzuPGqb70UlZ/l0zHRF3dLXlhHVMe8hEUPgDagH96zz8AtoQ5Ns7NgkL3l8vylVE+I9WFMmils1wuhJHP+fHHqtOmqVZXqw4YoHr77aqtrVl9dpi/ZdTV3fr1y6oqpsTlHBS662ZBofuL49e6X7oLZd++qT+7b9/058v2l7h//8ZG1S/v/qS+xn6qoP931FdUN27M6buG+Vtmsw503HdypvvJS1AATgV+7m2fD3tcnJsFhe4vjl/rfukulOkuhKk0Nnatr0jX/oLkIJQckP7zqxv13spzVUFXMlyPZW7Ku6Pq6s7HVlen/65h/pZBQTJTE1K672x6nnw0H/0EmAtc4G1PAj8Jc2ycmwWF7i/uO4V0F8qoQSG5czixVVV13i/xy7rrvm36Fe7Stxmg26jWH3CV9mZryu+cHBDCBIZs+zMaG9P/LVJtvXpF/S9hSkk+gsJLQIXvdSXwUphj49wsKHR/+exTSHWxy+edQi7778sqfZLxqqD/yzg9iOVpzxP1sxLfv1evrhfvMH/LqH0N6ephSl+6oBBlRrM/W8uuEY4zZSyXCVd+QeksJkzIfpZvrior3YzkK7mepRzCp3iBi5nJ0cxjBQEr6uTI/SYLfh3EJqmZ0IKihX8DzgHWAncBdwOrgbPDHBvnZncK5SPdHUFQR2ncdwqjWKQLOVwV9PecpkNYH/rXd6Z9/IvxVFa617k2xaU6p90plCfy1NE8GNfZfBrwL2GPi3OzoNDzpWsiSmyJC1yydP0NqQLJiBGp9x8xIunEH3+s+p3v6A4qdQN76Bk8qNAWqUkmXZ9Cpot1qu+TrfHjU59z/Pjsz2m6v6yDAnCg9zg61Zbu2EJsFhR6tkwjfZK35MDQr1/q/XbaKbhtPjkwdAkIzzyjOny4Kuhrn71Ah+z8Tqf9M9XXL2j0UUVFtKCQ61yD5MBgAaHnyyUozPIe/5Ji+590xxZis6BQGrIdBx91zL1/XWXV6J2radcr3rJFdfJkVdAtg/bRL+/+pIq4Y2pqwo/0CSNKnRObzS8wUeSl+SjqBuyEW2N5CbAc+L5XPgA3pPU177G/75ipwCpgJXBSps+woND95TL6KNcRM9lM5Erp8cdV995bVURfPvlyHbjzh2m/TzGCQpS/qzHpgkLY1NlfEpFdvOdXicjvROTwDIdtA45T1cOAUcDJIvJpYAowV1WH4+Y+TPHOOwI4GxgJnAzM8NZ3NiUsm/UOEqIuHpOcBXT6dKhKWoU8+XVa774L558PJ5/shjTNn8/nVtzI21s7p7YO+33CynaNg3zXw5SnsENSv6eqH4jIUcBJuBFIv0p3gBeQEkuFV3ub4jqq7/bK7wZO956fBsxR1W2quhp3xzA29Dcx3VLQkpdhlsKcPj14jYNUktc0mD8fWlo6l7W0BJ+zpsb34r//G0aOhHvugalT4cUX4cgjA9dpWLs23FKgfkHLiLqb5uzY0pwmV2GDQmKxwVOAmar6MJDxn6uIVIrIYmAj8KSqLgD2UNUNAN7j7t7uewJv+A5f75WZEpbrSmVhLpCVlTBpUuc1DcDNh0ilpQWqqzuXVVfDzTcDmzfDuefCqafCwIGwYAFcdx2Tv7kTVVXp67N2rbuxCCObZUTDsKU5Ta7CBoW/i8htwFnAYyLSO8yxqtqqqqOAocBYETk4ze6pbpq7/BMUkQYRaRaR5k2bNoWsvimWoLWLW1uDfyknTJsGO3Zk/oyhQ1MvFhP02W1tMHt25wl1s2dDfd8/uLuD++6Dq6+G5mYYM4bJk2HmzHDrMIepL+TWrBYk06S9TH9vY4BwHc1AH+AMYLj3ejBwYphjfee4BrgS14k82HeeldrRyTzVt/8TwJHpzmkdzd1f0OIufftm7oDOtZM1dIfv22+rnnOOKujSqlF6GC+27zdkSMeEr1w3/+imfJwvyuijxsbUQ2CtY7o8kaajWTTE/bmI7AesV9VtInIMcCjwG1V9L80xg4AdqvqeiOwM/Bn4KfBZYLOq/kREpgADVPXbIjISuBfXjzAE1wk9XFUDf5/V1dVpc3Nzxvqb4unXDz76qGu5SOqmmNpat8xkYp8o/MdmOr79sx9+mK3nXUTl++/wI67ix0ylhergA3PQty98+GHmukVVUZH5LmbgQNcylqymBt5+O391MaVBRBaqal2q98I2Hz0EtIrIJ4E7gH1wF/B0BgN/EZGXgBdwfQqP4jKuniAirwEneK9R1eXA/cDLwOPAJekCgokml6aDXI5NFRAguG0+l47SSMe+847rOzj9dF7dMpg6mvkhV8cWECD4b5GstjbaedvaMu+TKiCkKzdlLOgWwr8Bi7zHbwNf956/GObYODdrPgonl7kCuWY5zaYZJNtjk2f2Bu13Cv+t+i//olpVpTfseq1WsT3vzTmZmq3S7RN1JnfypL2o/x1M+SEPWVJ3iMg5wFeAR72y+H5SmbzKpVMz1w7Rvn1Tl/fqlf/sppl+ie/Ke8zmqzzKv8Huu8MLL/CtLdeEujuYNKljxFRitFPUX/Rh+TPLQuampuShuKl0Gm4botyUsaBo4d+AEcAtwDne632AKWGOjXOzO4Vwcln9LNeV06ImpfPL5Zd48vEn8ISuY6juoFJ/yDTVbdtUNXjJTv82ZEjq75bNKmcJQUnvUiX28/+d+vXr+JsGJQIMqmu2azGYngdbo7m8BY0ASpvrJw/Hqoa/gKeSzaif5Lr3Y4vO5CJV0OUcpHU836numZLP7bxz+jqmCmxhM4+mSmUdJ1uL2SSkCwppm49E5H7vcamIvOTblnodyMbEJsy8gHQm1s5jCYfRwCyu50pGs4hmPsWoUR37ZOqk3boVJk/uXObveJ82zTV5tbW5kU/19bD//qnPlVw+Y4abSKfqHpMn3+Vbfb2ro7+uxnQRFC1cMGmfT1Cbakt3bCE2u1MIp5jNR7ncKQSlvs54zo8/Vr3iCm1FdBX76jj+t9M+/o7ZMHcj/v3DdLwHnTO5Q7jQdwrGJJDtnYJ2pKNYq6prgXeBD3ybKQFBqQ/CpETI5dhchR3C2UlzM4weDTfeyEwmcRhLmM9RnXbx34GE6aT17x+m4z3dLO6E5FnSra3udfJdST7ZjGYTSlC08G/ARcBbwBrcUpyrgdfDHBvnZncK4eTSyZjpl3EuncWZRLlDqGK7XsM1uoNK3dh7T9U//zmrX+yZ9g/zfcJ8bti65UuuQ4tNz0KuHc24tQ8Ghtm3kJsFhXByTXEQdOEPc6EJGxRSfUbYgHAQy/UFxqiC3s1E3ZV3dfz48CN8Mi356d8/zMU8zOfmEiyzkev6zqZnyUdQeBzoE2bfQm4WFMKJ64IQ5rxhLn7ZDO0EVaFVL+cG3Upv3chA/QIPdTl/pnb7xsb0F/rk/cNezDN9bqHvFHLtGzI9S7qgEDb30eHAbGABbvGcRNPTN/LWjpUFy30UTkWFuwQkEwmXIiGX86abeNXY6Nriw6ytkKyWNdzFVzmGZ3iYU2lgFhvZo9M+If7XDszN5M9T5DdsWOr6JuddymTkSHj55a7lI0bA8uXhzxNWvupteoZ85D66Dfgf4G/AQt9mSsCAAdHKw8q1EzqxnkA0yleZzUscymgWcQF3cDp/6BIQwgrqzA4qnz49PzOxV66MVp6rfNXblIGgWwj/BjwbZr9Cb9Z8FE6uE9CChOlTyDQ5LMo2iLf095ymCvo0R2stqwP3TZ4oFiSbtv0wQ0nj7IDPlk1eMwnkoU9hOtCAy3w6ILGFOTbOzYJCOHG2J2e60ATN7o26ncof9C0G6T/ppd/k5yq05hwQVIODVkVF8PfN1GkfZp9C9ykY45ePoLA6xWZDUktENncK/ot9TY3bsvmFmc0ENP+2C+/r7VygCvoih+lIlub1V3aUHESq4f6WYfaJ+rnG5FPOQaG7bhYUwokaFDKlbq6oiC91tn87inn6OsO0hQqdzlStZlvGY7IRZWZxmM8OWz+b0WyKJV1QSDv6SES+rao/855/SVUf8L13nap+N89dHJHY6KNwoo4+Chqp4hc0OifVZ0TVi218n2v4Nj9jNfvwFX7Ds6RYhDmFNP8750WY1dxCrfhmTBHlMvrobN/zqUnvnZxTrUzBRB0lFGZEUFYpKEIYyTIWcL4A4KQAABiMSURBVART+Cl3cCGjWBw6IABUVcWbKiLMugS2doEpZZmCggQ8T/W685sie4nIX0RkhYgsF5HLvPJrReTvIrLY2yb4jpkqIqtEZKWInBTpm5hApTAcUWjjCm5gIWMYzAb+jUdo4Nd8yC6RzhN3DqGbb3YLBPn16uXKo+xjTLcV1K7kNSstSvU81esUxw4GRnvPdwFexS3Wcy1wZYr9RwBLgN64RXz+D6hM9xnWpxBelOGIYdr7E6Nz8rFQzl6s1bkcqwr6e07TgWzMqS8i0UYflzB/Sxv+aboz0vQpVGWIGYeJyBbcXcHO3nO81ztlCDYbgESW1Q9EZAWwZ5pDTgPmqOo2YLWIrALGAs9lqKMpgosuclk2Gxo6soauXduRdTRcrn6lniZu5VIqaeV87uQuvkqGm9BQcl2LIZ36+szfL8w+xnRHmVJnV6rqJ1R1F1Wt8p4nXodeo1lEhgGH49JkAFzqLdZzp4j098r2BN7wHbae9EHEhNTUBBMnuou2qnucODG71MmJ9YlnzMht/eb+vMN9/DuNTGQZB3MYS7iL88lHQOgJLM21KZawaS6yJiL9gIeAy1V1CzAT2A8YhbuT+EVi1xSHdxmrISINItIsIs2bNm2KqdY9ywUXdB31ourKo/KvELZuXep9gsoTjudJlnIIp/MHpvBjPsszrGbf6JXpoRJ3YP4g3tBggcEURqxBQUSqcQGhSVV/B6Cqb6lqq6q2Ab/GNRGBuzPYy3f4UODN5HOq6ixVrVPVukGDBsVZ/R5j+/Zo5UFDKpPLo45q2omt3Mw3eJITeZ9dOYIF/JQptFGZ+oAylcsdmDG5ii0oiIgAdwArVPUGX/lg325fAJZ5zx8BzhaR3iKyDzAceD6u+plgQWPpk8ujjGo6nEUsYjTf4JfcxGWMYSGLOTw/Fe5hsr0DMyYf4rxTGAdMBI5LGn76MxFZKiIvAccCVwCo6nLgfuBl3PoNl6hqjN2FJhv+9u36epg1y6VfFnGPs2Z17mCtoJWpXMcCjuATbOEE/swV3MQ/2blLQMlmoltPVMwlUI2JLSio6l9VVVT1UFUd5W2PqepEVT3EKz/VG6WUOGa6qu6nqgeo6p/iqptJryLN/xWR2rdff52/ytFcxzR+xxkcwlKe4gQAdtqpa0C555781B9Ke6JYKcwrMT1XpiGppgwdeGDqBWAS/O3b558PO3a452vXuteoUr99Nlx2GSOlki9rE7/lHPxjCfaNsV+5urq0J4ol7rSmTXNNRnvv7QKCDXE1BRE0gaEUtnKevJavyWhR909sieypyeUD2aiPVp/uXhx7rO7F2sBzZLMEZ6bNJooZkxk5TF4z3VDuk8ZyN2AAbN7cuWwCf+QOLqT/jnfhF7+Ayy/njcrgtqhUI2xyUVlpS0sak6vY5ymY/OtuQxb78BEzuZg/8nneYg/qaIZvfjN950QM4pzFbEy5sKBQgrrDkMXEXcJYFvAih9PALH7GfzKW51nGIYWriE+lTXcwJmcWFEpQdxiyWMUOruUa5jOO3mzjWP7Cd/gZ2+kd+hypRtjkMiw10YRmjMmeBYUSNGFCtPJ825+VzGcc1/ADmqjnUF5iHp+NfJ5UcxyOOy56ffz5mIwxuUm78lp3V64rrw0c2LWTF9zY/Lff7loedSWw4P2VSczk51zJVnbmYm7jQc5MeXxiRbfqapcvKVlVVcdQVr8wq775hV0BzhjTIZeV10w3lCogpCvPh8G8yZ/4HDO4hHkczSEsZdCkrgEB4OKLO56nCgjpyqP2i3zlK9H2N8akZ0HBZHQmD7CUQziaeUzmv/gcf2IDQ5gxwzXbJDp489GME7Vf5LHHsv8sY0xXFhR6mHzm4d+V9/gNE3mAs1jFJzmcF5nJZPwzk2fMcL/6VTun1c5WqhQP6ViSOGPyy4JCCUrXR5AqD382jmMuSzmEc/gtV/N9xjGfVzkgb3UNKvcn2QvDksQZk18WFLq5VL/8040NyHmW8Nat3MjlzOV4PqIvR/IcP+RqWgMmv0+e7DqNRdzj5Mmd3z/ooNQfE1QOLjCsWQMjRqSvqiWJMyYGQfkvSmHr6bmPGhvjyQ8UmPuouVn1oINUQW/m67ozH6U9dtKk4PIEkeDcSZnU1lqOI2PiQJrcRzYktRuLOjwzG6q4zoDrroMf/hD22IMT/j67PcV1OpWVqVNLVFZ2jC6KOhzWL5djjTHBbEhqiYo7IACwciWMGwfXXANnnQVLl4YKCLvtFpxrKF85iILSVlg6C2PiY0GhG4vz4ie0cSm/hFGjYNUquO8+12HRv3+o4997L9xFu1+/1PsElfvFHXSMMV3FuUbzXiLyFxFZISLLReQyr3yAiDwpIq95j/19x0wVkVUislJEToqrbqUirovfXqzjz5zIL/mGyyuxbJm7S4goaGSTv/xXv3Id0H5VVa48k6ARSGFHJhljoovzTqEF+JaqHgR8GrhEREYAU4C5qjocmOu9xnvvbGAkcDIwQ0TKuqEg/xc/5SvczVIO4QgW8DVmwaOPwuDBnfYaMiTc2cJMXquvh7vu6pzj6K67wq37UOwcT8aUo4J1NIvIw8Ct3naMqm4QkcHA06p6gIhMBVDVH3v7PwFcq6rPBZ2zp3c0T54MM2fm51y78xa3cRGn8zDPcDTnM5vV7Bsx91Fncf+vE9TRXltri+kYk4uidzSLyDDgcGABsIeqbgDwHnf3dtsTeMN32HqvrGzlK4XDGTzEMg7mZB7nW/ycY/kLq4lxkeQ86Q7rRhhTbmIPCiLSD3gIuFxVt6TbNUVZl9+iItIgIs0i0rxp06Z8VbNbynX0UX/eoZF6HuJM1lLLaBZxA99Cff/Zc02FEafusG6EMeUm1qAgItW4gNCkqr/zit/ymo3wHjd65euBvXyHDwXeTD6nqs5S1TpVrRs0aFB8le8Gchl99DkeYxkHcxb3cw3XciTPsYKuU4QTqTC6Y2BIlQfJZjEbE684Rx8JcAewQlVv8L31CHCe9/w84GFf+dki0ltE9gGGA8/HVb9SkM3oo13Ywq/5Dx7jFDZTwxEs4AdcQwvVgcfEvb5ztkn6/HmQ/AvxhOmkNsZkJ847hXHAROA4EVnsbROAnwAniMhrwAnea1R1OXA/8DLwOHCJqtqI9AjG8xTLOJjzmc1P+A51NPMio0Md62+n79s38/69eoWrU1NT6iR9YQPD/Pmwfr07dv1699oYE6Og/BelsPX03Edh8xf15QP9L1wiohUcoEfwXOQcSLW1HZ8blNMoKL9ROkH5i/yfFyRMbiVjTHRY7qPSFGZo6DH8hTu5gFrWchOXM43p/JOdI31Onz6dm2WClvv0C1r6M1lFRfCSn4klO4NUVWXOrWSMia7oQ1JNdtJ1NPflQ27h6/yF42ihiqOZx7e4IXJASNVOH2ZZz7BLf+YygsjSXBhTeBYUurGgi99neZqXOJRL+C9u4jIOYwnzOSqrz1izJt6O21xGEFlCPGMKz4JCCUncHTzNsbRRwWd5hiu4ia1EWL8yhJqa/J0rlxFEYXIrGWPyy4JCiUgsj5m4OziUl/gr/xrLZ918c+bRRVECR2Iltba2aHcmYXIrGWPyy4JCN7cLW5jJxczleHZQzdHMi+XuwK++Hu68M31CviySqhpjSoAFhW7sZP7EckbyNX7N9VyZU99BVIlf90FzFn7zm/jrkEgImOhbaW11r5PXgTbG5I8Fhe7onXfgq1/lT0zgA3bhMzzLt7k+8siiTCpC/Nf/6KNo5fk0a1a0cmNM7iwodDcPPQQjRkBjIz9iGofzIs9zRCwfddFFsZw2b2xIqjGFZ0Ghu/jHP+DMM902ZAg0N/M9fsR2eud86l69ut4VVFS4pZkzCZpAF3bNBWNMabGgUGyqrlf3oIPcKmg//jEsWODWTs6THTu6zh5ua4s3CZ4xpjRZUCim11+HE06ACy+EQw6BJUtgyhSoDs5omo2gTCZh1msIOrYQ2VFsjWZjCs+CQjG0tMD118PBB8Pzz7shNU8/DQccUOyadSu2noIxhWdBodAWLYKxY+Hb34YTT4QVK2ja5WKG7VsReb2Bns7WUzCm8KqKXYGy8eGHcM01cNNNsPvu8OCDcMYZNN0rNDS4hW6gY72B7mL8eJg7N3V5IdTXWxAwppDsTqEQHnvMNRXdcAN87WuwYgV88YsgwrRpHQEhIbESWj5zEGXrqae6BoDx4125MabnsaAQpzffdPkgTjnFNYb/7//Cr34Fu+3Wvot/xTO/deu6TyqJp57qvMyNBQRjeq4412i+U0Q2isgyX9m1IvL3pOU5E+9NFZFVIrJSRE6Kq14F0drqsrYddBA88gj88IeweDFNa4/qslZxuvUGHnss/EdmM2CpO9yJGGO6lzjvFO4CTk5RfqOqjvK2xwBEZARwNjDSO2aGiJRm1vxFi+DII+GSS+BTn4KlS+Gqq2h6oFfKtYonTAgeYRN0F5FKpslkyVlPe/Vy2VCNMcYvtqCgqvOAd0LufhowR1W3qepqYBUwNq66xWLLFrj8chcI1q51twFPPgnDhwME9h089ljwCJswq5MlbN8evPhMbW1H1tPEZ9x5p3XgGmO6KkafwqUi8pLXvNTfK9sTeMO3z3qvrPtThfvugwMPhFtucT//X3kFvvzlTj/f0/UdBAkapx+ktTX4riPbNQ2MMeWl0EFhJrAfMArYAPzCK0/V+JFyzqyINIhIs4g0b9q0KZ5ahrVypZtrcPbZMHgw/O1vbiJa//5ddg26mFdXk7JZqamp6zj9mhrYOU2i1MRdRqq7jqYmuvRnpBN1f2NMD6GqsW3AMGBZpveAqcBU33tPAEdmOv+YMWO0KD78UHXqVNXqatVdd1X95S9VW1rSHlJR4R+/k3mrre18fGOjap8+wfv36eP2SSXVsZn279Wr8/69egXvb4wpLUCzBl23g97Ix5YcFIDBvudX4PoRwHUwLwF6A/sArwOVmc5f8KDQ1qb6wAOqe+3l/nTnnaf6j3+EOjRKQABVkc7H19amDyDpLthBxyYHnoSamtT719SE+qrGmG4uXVCIbUaziPwWOAYYKCLrgWuAY0RkFK5paA1wEYCqLheR+4GXgRbgElXtXlnzV6yAr3/dTe899FDXnvKv4ddIrqyMtg5AcidzUN+DiOsjSCdqf8bmzcHlw4Z19FEYY3qeOEcfnaOqg1W1WlWHquodqjpRVQ9R1UNV9VRV3eDbf7qq7qeqB6jqn+KqV2Tvvw/f/KYLBAsXwq23uscIAQGCU1eMGJG6fMKEzq/TzWfIZMCAaOXp+Ps8jDE9j81oDtLWBrNnw/77u3xF558Pr77q5h9URb/BmjEDJk3qGDZaWeleBy1rmTxxrZAZQzNNakuk4TDG9DwWFFJ59lmXyfSCC2C//eCFF9wwnkGDcjrtjBkua7aqe5wxI3zTTi4ZQ98JmC0SVH7zzZlnSEeZWGeMKR0WFPzWrXNX2XHj3PKYjY0wfz6MGRPbR0ZpFsp2rkHUpqf6eneTlG4xmygT64wxpcOCAri01t/7nlvk5ne/g6uucnMQ6utjX4w4381CqeYXZPMZiQA0aVLq95P7PIwxPUTQsKRS2HIektrSonrHHaqDB7sxl+eco7p2bW7nzEJjoxseKpJ5eGmm8wTNR8j2M6IOZzXGdH+kGZJavncKc+e6ZqELL3RtIc8+C/feW5R2kXyloEi3NkO2sknPYYwpXeUZFJ56Co4/3g03nTMHnnvOZTbthqKkm1i7Nrg8KJVGJrkMhTXGlJ7yDArHHQd33OEmpP37v8feb5CtpqZoF/OgLKmQ/R1EIYfCGmOKT1zzUmmqq6vT5ubmYlcjNsOGpf71X1ubehZz1Ngm4pqsMmlqcgFk3Tp3h2Azmo0pbSKyUFXrUr0XW5oLk7uo7fm1tamDSFCKjbBNQPX1FgSMKRfl2XxUIqK25wc19TQ0WBOQMSYcCwrdWNT2/KBZzzNmZD8b2hhTXqxPoZuz9nxjTL6l61OwO4VuLl9zGGwlNWNMGBYUSki2F/aoQ1uNMeXLgkKJyOXCHsdMZ2NMz2RBoUTkcmG3VBXGmLBiCwoicqeIbBSRZb6yASLypIi85j329703VURWichKETkprnqVqlwu7JaqwhgTVpx3CncBJyeVTQHmqupwYK73GhEZAZwNjPSOmSEiaZI2lJ9cLuyWqsIYE1acazTPA5LX9joNuNt7fjdwuq98jqpuU9XVwCpgbFx1K0W5XNhzWbXNGFNeCp3mYg9V3QCgqhtEZHevfE/gb7791ntlxpO4gGc7Z8FSVRhjwuguuY9SpXJLOatORBqABoC9y6xR3C7sxpi4FXr00VsiMhjAe9zola8H9vLtNxR4M9UJVHWWqtapat2gQYNirawxxpSbQgeFR4DzvOfnAQ/7ys8Wkd4isg8wHHi+wHUzxpiyF1vzkYj8FjgGGCgi64FrgJ8A94vIhcA64EsAqrpcRO4HXgZagEtUNUWyZ2OMMXGKLSio6jkBb40P2H86YIMkjTGmiGxGszHGmHYlnTpbRDYBAcvVhzIQeDtP1SkV5fidoTy/t33n8hH1e9eqasqROiUdFHIlIs1BOcV7qnL8zlCe39u+c/nI5/e25iNjjDHtLCgYY4xpV+5BYVaxK1AE5fidoTy/t33n8pG3713WfQrGGGM6K/c7BWOMMT5lGRRE5GRvMZ9VIjKl2PUpBBHZS0T+IiIrRGS5iFxW7DoViohUisiLIvJosetSKCKym4g8KCKveP/Njyx2neImIld4/28vE5HfishOxa5THKIuYBZV2QUFb/Ge/wI+B4wAzvEW+enpWoBvqepBwKeBS8rkewNcBqwodiUK7GbgcVU9EDiMHv79RWRP4BtAnaoeDFTiFu7qie4i5AJm2Si7oIBbvGeVqr6uqtuBObhFfno0Vd2gqou85x/gLhI9fs0KERkKnALcXuy6FIqIfAI4GrgDQFW3q+p7xa1VQVQBO4tIFdCHgEzLpS7iAmaRlWNQ2BN4w/e67Bb0EZFhwOHAguLWpCBuAr4NtBW7IgW0L7AJmO01m90uIn2LXak4qerfgZ/jEm1uAN5X1T8Xt1YF1WkBM2D3DPsHKsegEHpBn55IRPoBDwGXq+qWYtcnTiLyeWCjqi4sdl0KrAoYDcxU1cOBj8ihOaEUeG3opwH7AEOAviJybnFrVZrKMSiEXtCnpxGRalxAaFLV3xW7PgUwDjhVRNbgmgmPE5HG4lapINYD61U1cSf4IC5I9GTHA6tVdZOq7gB+B3ymyHUqpKAFzCIrx6DwAjBcRPYRkV64zqhHilyn2ImI4NqYV6jqDcWuTyGo6lRVHaqqw3D/nf9HVXv8r0dV/Qfwhogc4BWNx61V0pOtAz4tIn28/9fH08M715MELWAWWXdZo7lgVLVFRC4FnsCNULhTVZcXuVqFMA6YCCwVkcVe2XdV9bEi1snE5+tAk/fD53Xg/CLXJ1aqukBEHgQW4UbavUgPnd0cZQGzrM5vM5qNMcYklGPzkTHGmAAWFIwxxrSzoGCMMaadBQVjjDHtLCgYY4xpZ0HBlA0RaRWRxb4t61m+IvJsPuuWdO46EbklrvMbk44NSTVlQ0Q+VNV+xa6HMd2Z3SmYsicia0Tk+yKySESWisiBXvkgLzf9IhG5TUTWishA770PvcdjRORp39oFTd6MWkRkjIg8IyILReSJRBqCpM/+kpf/f4mIzPOd81Hv+WO+O5v3ReQ8b32I60XkBRF5SUQuKtTfyvR8FhRMOdk5qfno333vva2qo4GZwJVe2TW41Bijgd8Dewec93Dgctz6HPsC47w8U78EzlTVMcCdwPQUx14NnKSqhwGnJr+pqhNUdRRwIbAW+IP3/H1V/RTwKeBrIrJP+D+DMcHKLs2FKWtbvQtsKokEgQuBM7znRwFfAFDVx0Xk3YBjn1fV9QBeCpFhwHvAwcCT3o1DJS6lc7L5wF0icr+vDp14dyf3AGep6vsiciJwqIic6e2yKzAcWB1QP2NCs6BgjLPNe2yl499FqjTr6Y71Hy/AclVNuwymql4sIkfgFgJaLCKdgpa3UuAc4Aeqmlh+UYCvq+oTIetnTGjWfGRMsL8CZwF4v86jrHu7EhiUWBtZRKpFZGTyTiKyn6ouUNWrgbfpnNYdXKKzl1R1jq/sCWCS10SFiOzf0xfRMYVjdwqmnOzsyxALbg3jdMNSvw/81ut7eAbX/PNBmA9S1e1e884tIrIr7t/aTUByRt7rRWQ47tf/XGAJ8Fnf+1cCy331vhq3tOgwYJHXqb2JHJZfNMbPhqQaE0BEegOtXrr1I3ErmQX1SRjTI9idgjHB9sblqK8AtgNfK3J9jImd3SkYY4xpZx3Nxhhj2llQMMYY086CgjHGmHYWFIwxxrSzoGCMMaadBQVjjDHt/h/AIW9kfPxqdwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# write your code here\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) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "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=\"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>"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python",
   "language": "python",
   "name": "conda-env-python-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
  },
  "widgets": {
   "state": {},
   "version": "1.1.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}