Week 2/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": [
      "--2020-04-22 08:10:40--  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 0.04s   \n",
      "\n",
      "2020-04-22 08:10:40 (1.59 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": 7,
   "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": 8,
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.  ,  2.4 ,  5.76],\n",
       "       [ 1.  ,  1.5 ,  2.25],\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": 8,
     "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": 9,
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients:  [[ 0.         52.73973959 -1.83588949]]\n",
      "Intercept:  [104.17336424]\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": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Emission')"
      ]
     },
     "execution_count": 11,
     "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": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean absolute error: 24.58\n",
      "Residual sum of squares (MSE): 1016.90\n",
      "R2-score: 0.64\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": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients:  [[ 0.         27.06124482  5.19888782 -0.58000393]]\n",
      "Intercept:  [131.56564155]\n",
      "Mean absolute error: 24.60\n",
      "Residual sum of squares (MSE): 1022.02\n",
      "R2-score: 0.64\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "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": {},
   "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",
    "-->"
   ]
  },
  {
   "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": "3.6.10"
  },
  "widgets": {
   "state": {},
   "version": "1.1.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}