AISaturday-Simple-Linear-AssSol.ipynb

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    "<h1><center>Simple Linear Regression</center></h1>\n",
    "\n",
    "\n",
    "<h4>About this Notebook</h4>\n",
    "In this notebook, we learn how to use scikit-learn to implement simple linear 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 your model using test set, and finally use model to predict unknown value.\n"
   ]
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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=\"#understanding_data\">Understanding the Data</a></li>\n",
    "        <li><a href=\"#reading_data\">Reading the data in</a></li>\n",
    "        <li><a href=\"#data_exploration\">Data Exploration</a></li>\n",
    "        <li><a href=\"#simple_regression\">Simple Regression Model</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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    "\n",
    "<h2 id=\"understanding_data\">Understanding the Data</h2>\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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    "<h2 id=\"reading_data\">Reading the data in</h2>"
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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",
       "      <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",
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       "    <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",
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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": 15,
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   "source": [
    "df = pd.read_csv(\"FuelConsumption.csv\")\n",
    "\n",
    "# take a look at the dataset\n",
    "df.head()\n",
    "\n"
   ]
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   "source": [
    "<h2 id=\"data_exploration\">Data Exploration</h2>\n",
    "Lets first have a descriptive exploration on our data."
   ]
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>MODELYEAR</th>\n",
       "      <th>ENGINESIZE</th>\n",
       "      <th>CYLINDERS</th>\n",
       "      <th>FUELCONSUMPTION_CITY</th>\n",
       "      <th>FUELCONSUMPTION_HWY</th>\n",
       "      <th>FUELCONSUMPTION_COMB</th>\n",
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       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1067.0</td>\n",
       "      <td>1067.000000</td>\n",
       "      <td>1067.000000</td>\n",
       "      <td>1067.000000</td>\n",
       "      <td>1067.000000</td>\n",
       "      <td>1067.000000</td>\n",
       "      <td>1067.000000</td>\n",
       "      <td>1067.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>2014.0</td>\n",
       "      <td>3.346298</td>\n",
       "      <td>5.794752</td>\n",
       "      <td>13.296532</td>\n",
       "      <td>9.474602</td>\n",
       "      <td>11.580881</td>\n",
       "      <td>26.441425</td>\n",
       "      <td>256.228679</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.415895</td>\n",
       "      <td>1.797447</td>\n",
       "      <td>4.101253</td>\n",
       "      <td>2.794510</td>\n",
       "      <td>3.485595</td>\n",
       "      <td>7.468702</td>\n",
       "      <td>63.372304</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>2014.0</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>4.600000</td>\n",
       "      <td>4.900000</td>\n",
       "      <td>4.700000</td>\n",
       "      <td>11.000000</td>\n",
       "      <td>108.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>2014.0</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>10.250000</td>\n",
       "      <td>7.500000</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>21.000000</td>\n",
       "      <td>207.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>2014.0</td>\n",
       "      <td>3.400000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>12.600000</td>\n",
       "      <td>8.800000</td>\n",
       "      <td>10.900000</td>\n",
       "      <td>26.000000</td>\n",
       "      <td>251.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>2014.0</td>\n",
       "      <td>4.300000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>15.550000</td>\n",
       "      <td>10.850000</td>\n",
       "      <td>13.350000</td>\n",
       "      <td>31.000000</td>\n",
       "      <td>294.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>2014.0</td>\n",
       "      <td>8.400000</td>\n",
       "      <td>12.000000</td>\n",
       "      <td>30.200000</td>\n",
       "      <td>20.500000</td>\n",
       "      <td>25.800000</td>\n",
       "      <td>60.000000</td>\n",
       "      <td>488.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "       MODELYEAR   ENGINESIZE    CYLINDERS  FUELCONSUMPTION_CITY  \\\n",
       "count     1067.0  1067.000000  1067.000000           1067.000000   \n",
       "mean      2014.0     3.346298     5.794752             13.296532   \n",
       "std          0.0     1.415895     1.797447              4.101253   \n",
       "min       2014.0     1.000000     3.000000              4.600000   \n",
       "25%       2014.0     2.000000     4.000000             10.250000   \n",
       "50%       2014.0     3.400000     6.000000             12.600000   \n",
       "75%       2014.0     4.300000     8.000000             15.550000   \n",
       "max       2014.0     8.400000    12.000000             30.200000   \n",
       "\n",
       "       FUELCONSUMPTION_HWY  FUELCONSUMPTION_COMB  FUELCONSUMPTION_COMB_MPG  \\\n",
       "count          1067.000000           1067.000000               1067.000000   \n",
       "mean              9.474602             11.580881                 26.441425   \n",
       "std               2.794510              3.485595                  7.468702   \n",
       "min               4.900000              4.700000                 11.000000   \n",
       "25%               7.500000              9.000000                 21.000000   \n",
       "50%               8.800000             10.900000                 26.000000   \n",
       "75%              10.850000             13.350000                 31.000000   \n",
       "max              20.500000             25.800000                 60.000000   \n",
       "\n",
       "       CO2EMISSIONS  \n",
       "count   1067.000000  \n",
       "mean     256.228679  \n",
       "std       63.372304  \n",
       "min      108.000000  \n",
       "25%      207.000000  \n",
       "50%      251.000000  \n",
       "75%      294.000000  \n",
       "max      488.000000  "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# summarize the data\n",
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets select some features to explore more."
   ]
  },
  {
   "cell_type": "code",
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       "      <td>2.4</td>\n",
       "      <td>4</td>\n",
       "      <td>9.6</td>\n",
       "      <td>221</td>\n",
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       "      <th>2</th>\n",
       "      <td>1.5</td>\n",
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       "      <td>136</td>\n",
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       "      <th>3</th>\n",
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       "      <th>4</th>\n",
       "      <td>3.5</td>\n",
       "      <td>6</td>\n",
       "      <td>10.6</td>\n",
       "      <td>244</td>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>3.5</td>\n",
       "      <td>6</td>\n",
       "      <td>10.0</td>\n",
       "      <td>230</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3.5</td>\n",
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       "      <th>7</th>\n",
       "      <td>3.7</td>\n",
       "      <td>6</td>\n",
       "      <td>11.1</td>\n",
       "      <td>255</td>\n",
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       "    <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",
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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": 17,
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   ],
   "source": [
    "cdf = df[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_COMB','CO2EMISSIONS']]\n",
    "cdf.head(9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can plot each of these features:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "button": false,
    "jupyter": {
     "outputs_hidden": true
    },
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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wjzR5raQ3VuSH0qM8h7rcecA8gOnTp0er25ZrnStzpr3EBXdWH8B1tJ8rndTm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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xd34a3ec320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "viz = cdf[['CYLINDERS','ENGINESIZE','CO2EMISSIONS','FUELCONSUMPTION_COMB']]\n",
    "viz.hist()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, lets plot each of these features vs the Emission, to see how linear is their relation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "button": false,
    "jupyter": {
     "outputs_hidden": true
    },
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6k2rxxj1mg6UTYxDvkPRw2gU1Jy2bDzydOWd/WtaTxseTv7LztAjWrSu+PmZm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\nIMzMrCoHCDMzq+r/AwMXuHi/0t2HAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xd34a1ec128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(cdf.FUELCONSUMPTION_COMB, cdf.CO2EMISSIONS,  color='blue')\n",
    "plt.xlabel(\"FUELCONSUMPTION_COMB\")\n",
    "plt.ylabel(\"Emission\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "button": false,
    "jupyter": {
     "outputs_hidden": true
    },
    "new_sheet": false,
    "run_control": {
     "read_only": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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8o9X79msLYseO2d/AzbJ/s0z7dh038yXvt8C0b+9JuZ062YKYyzrdKun1VtBc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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xd349e98da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(cdf.ENGINESIZE, cdf.CO2EMISSIONS,  color='blue')\n",
    "plt.xlabel(\"Engine size\")\n",
    "plt.ylabel(\"Emission\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Practice\n",
    "plot __CYLINDER__ vs the Emission, to see how linear is their relation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "button": false,
    "jupyter": {
     "outputs_hidden": true
    },
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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fVsOv57Tj78OyJmlnRHRMtl+tPYhfSLoO+AQwOlHQaW81OatcHCaKm5k1Wq0F4veAlcCm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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xd34a0743c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# write your code here\n",
    "plt.scatter(cdf.CYLINDERS, cdf.CO2EMISSIONS,  color='blue')\n",
    "plt.xlabel(\"Cylinder\")\n",
    "plt.ylabel(\"Emission\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "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. \n",
    "This will provide a more accurate evaluation on out-of-sample accuracy because the testing dataset is not part of the dataset that have been used to train the data. It is more realistic for real world problems.\n",
    "\n",
    "This means that we know the outcome of each data point in this dataset, making it great to test with! And since this data has not been used to train the model, the model has no knowledge of the outcome of these data points. So, in essence, it is truly an out-of-sample testing.\n",
    "\n",
    "Lets split our dataset into train and test sets, 80% of the entire data for training, and the 20% for testing. We create a mask to select random rows using __np.random.rand()__ function: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "button": false,
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": 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,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "<h2 id=\"simple_regression\">Simple Regression Model</h2>\n",
    "Linear Regression fits a linear model with coefficients $\\theta = (\\theta_1, ..., \\theta_n)$ to minimize the 'residual sum of squares' between the independent x in the dataset, and the dependent y by the linear approximation. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "#### Train data distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "button": false,
    "jupyter": {
     "outputs_hidden": true
    },
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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MsN3qWjsw0Lp6SjpXRfde6U9zyjqxu3+L+LESt7c4ZgugSYI7tHBh6ymqG9OH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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xd34a0394a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(train.ENGINESIZE, train.CO2EMISSIONS,  color='blue')\n",
    "plt.xlabel(\"Engine size\")\n",
    "plt.ylabel(\"Emission\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "#### Modeling\n",
    "Using sklearn package to model data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "button": false,
    "jupyter": {
     "outputs_hidden": true
    },
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients:  [[ 39.74520968]]\n",
      "Intercept:  [ 124.07234227]\n"
     ]
    }
   ],
   "source": [
    "from sklearn import linear_model\n",
    "regr = linear_model.LinearRegression()\n",
    "train_x = np.asanyarray(train[['ENGINESIZE']])\n",
    "train_y = np.asanyarray(train[['CO2EMISSIONS']])\n",
    "regr.fit (train_x, train_y)\n",
    "# The coefficients\n",
    "print ('Coefficients: ', regr.coef_)\n",
    "print ('Intercept: ',regr.intercept_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As mentioned before, __Coefficient__ and __Intercept__ in the simple linear regression, are the parameters of the fit line. \n",
    "Given that it is a simple linear regression, with only 2 parameters, and knowing that the parameters are the intercept and slope of the line, sklearn can estimate them directly from our data. \n",
    "Notice that all of the data must be available to traverse and calculate the parameters.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "#### Plot outputs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can plot the fit line over the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "button": false,
    "jupyter": {
     "outputs_hidden": true
    },
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0xd34c18fda0>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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IY3DpNi4HPl/ZfNrmuZmByI60HVva65PextMbhsHYk/WMVD3Wrx9ez7mjI93b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\nI+Bo4BHgM2lvICKLRaRfRPp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      "text/plain": [
       "<matplotlib.figure.Figure at 0xd34a43fe80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(train.ENGINESIZE, train.CO2EMISSIONS,  color='blue')\n",
    "plt.plot(train_x, regr.coef_[0][0]*train_x + regr.intercept_[0], '-r')\n",
    "plt.xlabel(\"Engine size\")\n",
    "plt.ylabel(\"Emission\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "#### Evaluation\n",
    "we compare the actual values and predicted values to calculate the accuracy of a regression model. Evaluation metrics provide a key role in the development of a model, as it provides insight to areas that require improvement.\n",
    "\n",
    "There are different model evaluation metrics, lets use MSE here to calculate the accuracy of our model based on the test set: \n",
    "<ul>\n",
    "    <li> Mean absolute error: It is the mean of the absolute value of the errors. This is the easiest of the metrics to understand since it’s just average error.</li>\n",
    "    <li> Mean Squared Error (MSE): Mean Squared Error (MSE) is the mean of the squared error. It’s more popular than Mean absolute error because the focus is geared more towards large errors. This is due to the squared term exponentially increasing larger errors in comparison to smaller ones.</li>\n",
    "    <li> Root Mean Squared Error (RMSE): This is the square root of the Mean Square Error. </li>\n",
    "    <li> R-squared is not error, but is a popular metric for accuracy of your model. It represents how close the data are to the fitted regression line. The higher the R-squared, the better the model fits your data. Best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse).</li>\n",
    "</ul>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "button": false,
    "jupyter": {
     "outputs_hidden": true
    },
    "new_sheet": false,
    "run_control": {
     "read_only": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean absolute error: 24.38\n",
      "Residual sum of squares (MSE): 1005.14\n",
      "R2-score: 0.67\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import r2_score\n",
    "\n",
    "test_x = np.asanyarray(test[['ENGINESIZE']])\n",
    "test_y = np.asanyarray(test[['CO2EMISSIONS']])\n",
    "test_y_hat = regr.predict(test_x)\n",
    "\n",
    "print(\"Mean absolute error: %.2f\" % np.mean(np.absolute(test_y_hat - test_y)))\n",
    "print(\"Residual sum of squares (MSE): %.2f\" % np.mean((test_y_hat - test_y) ** 2))\n",
    "print(\"R2-score: %.2f\" % r2_score(test_y_hat , test_y) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  },
  "widgets": {
   "state": {},
   "version": "1.1.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}