ML0101EN-Reg-Simple-Linear-Regression-Co2-py-v1.ipynb

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   "source": [
    "<a href=\"https://www.bigdatauniversity.com\"><img src = \"https://ibm.box.com/shared/static/cw2c7r3o20w9zn8gkecaeyjhgw3xdgbj.png\" width = 400, align = \"center\"></a>\n",
    "\n",
    "# <center>Simple Linear Regression</center>\n",
    "\n",
    "\n",
    "#### About this Notebook\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": [
    "### 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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   "metadata": {
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   },
   "source": [
    "### Downloading Data\n",
    "To download the data, we will use !wget to download it from IBM Object Storage."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: wget in c:\\users\\lenovo\\anaconda3\\lib\\site-packages (3.2)\n",
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "pip install wget"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
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   "source": [
    "FuelConsumption = \"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)"
   ]
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   "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"
   ]
  },
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   },
   "source": [
    "## Reading the data in"
   ]
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>MODELYEAR</th>\n",
       "      <th>MAKE</th>\n",
       "      <th>MODEL</th>\n",
       "      <th>VEHICLECLASS</th>\n",
       "      <th>ENGINESIZE</th>\n",
       "      <th>CYLINDERS</th>\n",
       "      <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",
       "      <td>0</td>\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",
       "      <td>1</td>\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",
       "      <td>2</td>\n",
       "      <td>2014</td>\n",
       "      <td>ACURA</td>\n",
       "      <td>ILX HYBRID</td>\n",
       "      <td>COMPACT</td>\n",
       "      <td>1.5</td>\n",
       "      <td>4</td>\n",
       "      <td>AV7</td>\n",
       "      <td>Z</td>\n",
       "      <td>6.0</td>\n",
       "      <td>5.8</td>\n",
       "      <td>5.9</td>\n",
       "      <td>48</td>\n",
       "      <td>136</td>\n",
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       "    <tr>\n",
       "      <td>3</td>\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",
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       "      <td>4</td>\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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       "   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": 13,
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   "source": [
    "df = pd.read_csv(FuelConsumption)\n",
    "\n",
    "# take a look at the dataset\n",
    "df.head()\n",
    "\n"
   ]
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   "source": [
    "### Data Exploration\n",
    "Lets first have a descriptive exploration on our data."
   ]
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       "      <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",
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       "      <td>count</td>\n",
       "      <td>1067.0</td>\n",
       "      <td>1067.000000</td>\n",
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       "      <td>1067.000000</td>\n",
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       "      <td>1067.000000</td>\n",
       "      <td>1067.000000</td>\n",
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       "    <tr>\n",
       "      <td>mean</td>\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",
       "      <td>std</td>\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",
       "      <td>min</td>\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",
       "      <td>25%</td>\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",
       "      <td>50%</td>\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",
       "      <td>75%</td>\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",
       "      <td>max</td>\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  "
      ]
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     "execution_count": 14,
     "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",
   "execution_count": 15,
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       "      <th></th>\n",
       "      <th>ENGINESIZE</th>\n",
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       "      <td>0</td>\n",
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       "      <td>1</td>\n",
       "      <td>2.4</td>\n",
       "      <td>4</td>\n",
       "      <td>9.6</td>\n",
       "      <td>221</td>\n",
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       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>1.5</td>\n",
       "      <td>4</td>\n",
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       "      <td>3</td>\n",
       "      <td>3.5</td>\n",
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       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>3.5</td>\n",
       "      <td>6</td>\n",
       "      <td>10.6</td>\n",
       "      <td>244</td>\n",
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       "      <td>5</td>\n",
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       "      <td>6</td>\n",
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       "      <td>230</td>\n",
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       "      <td>6</td>\n",
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       "      <td>7</td>\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",
       "      <td>8</td>\n",
       "      <td>3.7</td>\n",
       "      <td>6</td>\n",
       "      <td>11.6</td>\n",
       "      <td>267</td>\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": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cdf = df[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_COMB','CO2EMISSIONS']]\n",
    "cdf.head(9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can plot each of these fearues:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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jwG9mVjIO/GZmJePAb2ZWMg78ZmYl48BvZlYyDvxmZiXjwG9mVjIO/GZmJePAb2ZWMg78ZmYl48BvZlYyDvxmZiXjwG9mVjIO/GZmJeP++G0jzfThP2/a+k1eTu9+/M36h0v8ZmYl48BvZlYyDvxmZiXjwG9mVjIO/GZmJePAb2ZWMg78ZmYl0/Pt+JtpV25mZs3r+cBv/aGVH2g/9GXWHa7qMTMrGZf4zczGSK9cGXekxC/pUEkPSFom6YxOrMOs1/i4t37R9hK/pC2Bi4FDgBXATyQtjIiftXtdZr2iH4/7YumzVsd7ZdJsSby4n/r5HlUnqnoOAJZFxK8AJH0NmAX07Alg1gZtO+7dks06TRHR3gVKRwOHRsT78vjxwOsi4pSq+eYCc/PovsADbc1I+0wCHu12JnpMr+6TF0fEC7ux4maO+x4/5nvxf+o8NdbSMd+JEr9qpG3y6xIR84H5HVh/W0m6MyKmdzsfvcT7pKaGx30vH/O9+D91njqnEzd3VwB7Fsb3AB7uwHrMeomPe+sbnQj8PwGmStpb0jbAscDCDqzHrJf4uLe+0faqnohYL+kU4HvAlsClEXF/u9czhnry0rzLvE+qjIPjvhf/p85Th7T95q6ZmfU2d9lgZlYyDvxmZiVT6sAvaU9Jt0haIul+Safm9ImSbpa0NP/dJadL0kX5kfx7JL26u1vQOZK2lPRfkr6dx/eWdEfeJ1/PNzCRtG0eX5anD3Qz3zYyScsl3Svpbkl31pg+pse4pH1zXirDOkmnVc0zKGltYZ6zOpCPSyWtlnRfIa1mHKjx3dl5nqWSZrc7b51Q6sAPrAfmRcTLgBnAyZL2A84AFkXEVGBRHgc4DJiah7nAF8c+y2PmVGBJYfzTwGfzPnkCOCmnnwQ8ERH7AJ/N81lve3NEvLJOe/QxPcYj4oGcl1cCrwGeBr5ZY9YfVuaLiH/sQFYuAw6tSqsXBzaQNBE4G3gd6ents+v9QPSSUgf+iFgZEXflz0+SAt3upEftL8+zXQ4cmT/PAq6I5HZggqQpY5ztjpO0B3A48OU8LuAtwDV5lup9UtlX1wAH5fmtP3XzGD8I+GVE/GaM1rdBRNwKPF6VXC8OFL0NuDkiHo+IJ4Cb2fQHpOeUOvAX5SqKVwF3AJMjYiWkHwdg1zzb7sBDha+tyGnjzeeAjwHP5vEXAGsiYn0eL273hn2Sp6/N81tvCuAmSYtzFxLVunmMHwtcVWfa6yX9VNJ3Je0/RvmpFweK+jImOPADknYErgVOi4h1I81aI21ctYeVdASwOiIWF5NrzBpNTLPec2BEvJpUpXOypDdWTe/K/zPfM3oH8I0ak+8i9Unz58Dnges7nZ9R6Mvjv/SBX9LWpKC/ICKuy8mrKpe3+e/qnF6Gx/IPBN4haTnwNVIVz+dIl/yVB/6K271hn+TpO7PpJbP1iIh4OP9dTapLP6Bqlm4d44cBd0XEquoJEbEuIobz5xuBrSVNGoM81YsDRX0ZE0od+HNd9CXAkoi4oDBpITA7B78Hgb0lDQMnAOdJmiMpgO0rl4J5eSskDRbGp0r6mqTf5dYKSyV9PtehV1orrCjMPyTp95L2LKQdnPNRGV8u6RlJw4XhC3naNpLOz/kYlvRrSZ+t+u7B+fP9VcsYlvQH4PSI2AOYQ7q03YZU1zkBGJb0emA2cENxX+XPRwM/CD8V2JMk7SBpp8pn4K3AfVWzLQROyK17ZgBri8d4B72bOtU8knar3DeSdAApbj02BnkqHtvFY77oe8BbJe2Sb+q+Naf1togo7QC8gXRZdg9wdx5mkuqoFwF/JF1mTszzi/SyjdWkFkFrgOcXlrcCGMyf9yGVfC8A9shpuwKnAcfm8UFgReH7Q6QDen4h7WBgeWF8OXBwne05G/gP4EU5rwPACU1+d0fSze1zC3n7HfDtPP4S4MfAMtLl+LY5fbs8vixPf0m3/6+9NOR9/gwwXBjeU/y/V/3/35c/n5OPv+L31hTmDWCfOuucQirQrASeBH4OnAvsD/w0D4+Quhd+Jh+n/xfYtnCMr8vrmF1Y7j4pZGwY3x+4idTKaw2wGJiZp80BbquzPw7Ony/L6zg6H/c75/TP5fTL8/hX8vifSOfdL4AjgOMK++YZ0j2pDfur1jFPKpEvyOt7Kh+zR5B+dFbmfR6kc3kSKQ4sBX4NfDUvYzrw5cIy35uP/2XA+/L/bmle/nLgUmCgMP8Reb1P5XwsIMeIwr4L4IKqfXdkTr8sjw/k8co2rwL+Fdi64XHZ7ROjl4fqg6bqH3Mb8C3g7EJ6MfBfCXyrwfIH2TTwn006WffJaaMJ/N8m3acY1fbkaV8jncRb1Mqbh/YdQ/X2LZsG/itHWG7NwA9MzOv8aiXYkKoiLgRekcc/nwPT60n9de2fA9ENheVcloPSTYW06sD/K+CjpKvCbUjVhG/I0+bQXOB/ALi2MH0r4LekIDqnelmk0v4HSc0+JzaxT4vrq+ybfwd2A7YnXWmsA46u2rePAe8ppH2SHHAb/L8XkgqLr83bsjNwMnBSnn50Xt9xef27kX4YlgO7FLZ3Wd4PWxWWfV3eX5fl8YGc163y+K7AfzFCDKgMpa7qaYN/AD6U2/JWO5h072C0fgt8iXTij9btwIclfUDStGabVUr6e9JJ+56IeLbR/NbTPkwqOPxNRCwHiIiHIuLUiLhH0lTgA8BxEfGfEbE+UmdyRwGHSnpLYVmXA6+Q9KbqleQ69r2BL0XEf+fhRxFx2yjz+y3gwELb90NJV+CP1Jo5H5+XkoLmS0a5rg+RSsYnRcQjEfFMRFwFfAo4v+p8+QxwbuG+VkO5GvUQYFZE/CTv27URcXFEXJKXfz7wyYhYkNf/COkqYTjnr+IR4F5Sc9HK8wJ/wQg9vka6b3MzsF+jvDrwN3a9pDWF4W8rEyLiblIp+fQa35tE4eCVdEr+/rCkLzVY5z8Dbx+h2Vq9PP0z6QGq44A7gd82epIw1+P+E3BMRFS/WehFVetZk+uGrXcdDFw3wg/4QaSS8Y+LiRHxEKngcEgh+WnSsfGpGst5jFQqvVLSkZImt5jf35OC2bF5/ATginoz50BcCZRLR7muQ0hXF9X75mpgL+DPCmnXkUrmc0ax/IOBH+d9Wcu+eT0btVzK+bmWjfc9pP1wQv58LOkewx/qrVzSi0g/FLc3yqgDf2NHRsSEwlAdtM8C3i9pt6r0x0h1rQBExBciYgKp/nLrkVYYEb8DvgDUe0KxZp4i4k+5dHEg6Wbsp4BLJb2s1kJyqe0bwMcjPaxT7eGq9UyIiKdGyrvVVPyhHk1TxHdV/eje0sR3XkCqq65n0gjTV+bpRf8H2EvSYcXESHULbyZVUZwPrJR0a76iGK0rSDeUdwbeRO3mmjMkrSEVpt4NvDMi1o5yPfW2fWVhekWQrujPkrRtk8tvZt9TZ55a+/6bwGDeLyP9ID6a981vSfcNrqkz3wYO/JspIn5OKh18omrSIuCvNmPR/0I6sV7TYr6eiYiLSTfeNrn0k7QFqR74RxHx+c3IpzVW/KE+knSDstaP/9akm4sVV1f96L65iXVtVOCo4dERpk+h6n2yEfEH4H/lQVXTVkTEKRHxUuDFpKBTCU7NbiO5euiFwJmkxgTP1Pje7XkfTIqIGRHx/RG2sZ562z6lML2YrxtJrfpqPehWSzP7njrz1Nr3zwDfIe2XSRHxozrLnZQLlc8DfkS6UT8iB/72OBc4kVTKrjgH+EtJF0jaHTaUsGuWvqtFxBpSSepjzWZC0mm5iej2krbK1Tw7kW74VDuHdNPvfc0u39rmQWCS0oODwIamxS8GNre7gu8D78w/7LX8ANgzN4vcIDchnkEqsFT7d9JNynfWW2mu3rgYeHlOepB0pbDhx0LS80g3IGtt45XAPEao5mmD7wNH1dg37yI9ffuLGt85E/ifpKDazPIPqDTXruEBUgOQY4qJOT9HUXvfX0HaL19ptPL8Q3EZ6SnnEZ9zcOBv7FtVbd036UAqIn5N+sfsUEj7BelE2gP4qaQnSb/GD5MuIZtxIakJW7N5eob0Y1FpqncycFRE/KrGMs4k3Rx7pEZ7/r3yPC+qMe2oJvNudUTEg6SuQT4tacdclfBRUim5Yf1swTaStisMW5KaDz8fuFzSiwEk7Z4LIK/Ix+W/AQskzVDqhXV/Uh3z92uVpCN1xXEOhXtZud36uZL2kbRFDjTvLeT/DlL9/Rk5bzsA55HuPdUK/BeR6rhvHcX2j9ZnSfvmEqVnA7aT9G5SYP9orr7aSEQMkW6yNux1M++7m4FvSnpNLnztJOnvJL03L/8jwJmS3pMLaLuR+sR6fs5ftf8g7ZeGV+X5ODqedP6P/JxDo2Y/Hjx4aH2gfpPgPUn3Vyo/0t8D9itMP4dN2/EPA7vm6VFjqDQFfRGp5csjPNeO/2zgeXn6FqQgvoxUWHiI1Iplu8L6LyO1PqHwnfvYUL3PDqRWP8tzvh4htYXfvfCd/fJ2PUpqY34NsGe9dVTtn9uo0ZxzhP08SIPmnHl8r5zPx0lVUz8htcIpfmejprKknjc3tJ9vkI9tSDUAy/Lyf0MK7HsV5pmV1/tUzsdVVful7vZSaFbKpu3415B+KF7bKJ9+9aKZWcm4qsfMrGQc+M3MmiTpuBr3vYYl3d/tvI2Gq3rMzEqm6ceRO2nSpEkxMDDQ7Wzw1FNPscMO/fNgar/lFzqb58WLFz8aES/syMLbrFeO+Xr68dhql37a9laP+Z4I/AMDA9x55ybvfR5zQ0NDDA4OdjsbTeu3/EJn8yypLa/sk7QdqVnhtqRz5JqIOFvS3qTO7CaSOuI6PiL+Ozeju4L0sN1jwF9H7iennl455uvpx2OrXfpp21s95l3Hb7apPwBvifTGp1eSOi+bgV84b+OEA79ZlUiG8+jWeQj8wnkbJ3qiqses1+SnYBeT+qC/GPglTb5wXlLlhfOPVi1zLrnfl8mTJzM0NNThrWjd8PBwT+evk8qw7eMy8A+c8Z1Rf2f5eYd3ICfWryLiT8ArJU0g9ZJYq4+lSpO4pl64HRHzgfkA06dPj27XI490nsyb9ifOv612R6zj/Vzppzr+Vrmqx2wEkTrLGyL1u+QXztu44MBvVkXSC3NJH0nbk16wsQS4hfTqPPAL562PjcuqHrPNNIXUu+WWpMLR1RHxbUk/A74m6ZOkrq4vyfNfAnxF0jJSSf/YWgs16xUO/GZVIuIe4FU10n8FHFAj/fdU9bFu1ssc+DdDKzeRYfzfHDOz3uY6fjOzknHgNzMrGQd+M7OSceA3MysZB34zs5Jx4DczKxkHfjOzknHgNzMrGQd+M7OSceA3MysZB34zs5JpGPgl7SnpFklLJN0v6dScPlHSzZKW5r+75HRJukjSMkn3SHp1pzfCzMya10wnbeuBeRFxl6SdgMWSbgbmAIsi4jxJZwBnAKcDhwFT8/A64Iv5r5mNA37DXf9rWOKPiJURcVf+/CTphRS7s/ELpqtfPH1FfmH17aS3Fk1pe87NzKwlo+qWWdIAqZ/yO4DJEbES0o+DpF3zbBtePJ1VXkq9smpZHXvx9Lxp6xvPVGVoaGjUL1luZT2VdbVDP74Uuh/zbDbeNB34Je0IXAucFhHrpFrvl06z1kgb0xdPz2nlUvS4wVG/ZLmV9VTW1Q79+FLofsxzP2j13RBWTk216pG0NSnoL4iI63LyqkoVTv67OqdvePF0VnwptZmZdVkzrXpEeqfokoi4oDCp+ILp6hdPn5Bb98wA1laqhMzMrPuaqeo5EDgeuFfS3TntE8B5wNWSTgIe5Ll3jt4IzASWAU8DJ7Y1x2ZmtlkaBv6IuI3a9fYAB9WYP4CTNzNfZmbWIX5y16yKH1q08c6B32xTlYcWXwbMAE6WtB/pIcVFETEVWJTHYeOHFueSHlo061kO/GZV/NCijXejeoDLrGzG80OLI5m8fXuX2U8P7ZXhIUMHfrM6xvtDiyOZN20959/bvvDQrocWx0IZHjJ0VY9ZDX5o0cYzB36zKn5o0cY7V/WYbcoPLdq45sBvVsUPLdp456oeM7OSceA3MysZV/VkA2d8h3nT1re9WZyZWa9xid/MrGQc+M3MSsaB38ysZBz4zcxKxoHfzKxkHPjNzCKmy+oAAAcHSURBVErGgd/MrGTcjr9PDNR4vqDRcwfLzzu8k1kysz7lEr+ZWck48JuZlYwDv5lZyTjwm5mVTM/f3K11U9PMzFrnEr+ZWck0DPySLpW0WtJ9hbSJkm6WtDT/3SWnS9JFkpZJukfSqzuZeTMzG71mSvyXAYdWpZ0BLIqIqcCiPA5wGDA1D3OBL7Ynm2Zm1i4NA39E3Ao8XpU8C7g8f74cOLKQfkUktwMTJE1pV2bNzGzztXpzd3JErASIiJWSds3puwMPFeZbkdNWVi9A0lzSVQGTJ09maGio5ormTVvfYhZHb/L2Y7O+ets6klr5apTfVtbTacPDwz2ZL+usVhpp+Mnzzml3qx7VSItaM0bEfGA+wPTp02NwcLDmAsfyVYjzpq3n/Hs739Bp+XGDo/5Orf3QKL+trKfThoaGqPe/7iWSLgWOAFZHxMtz2kTg68AAsBx4V0Q8IUnAhcBM4GlgTkTc1Y18mzWj1VY9qypVOPnv6py+AtizMN8ewMOtZ8+say7D97ZsnGo18C8EZufPs4EbCukn5NY9M4C1lSohs37ie1s2njWs15B0FTAITJK0AjgbOA+4WtJJwIPAMXn2G0mXu8tIl7wndiDPZt2yWfe2mr2v1Yp235saq/tdI+nWvaAy3IdqGPgj4t11Jh1UY94ATt7cTJn1mabubTV7X6sV7b4XNlb3u0bSrXtU/XIfanP0fJcNZj1klaQpubTve1sd5pZAneMuG8ya53tbNi64xG9Wg+9t2XjmwG9Wg+9t2Xjmqh4zs5Jxib8L/I4BM+sml/jNzErGgd/MrGQc+M3MSsaB38ysZHxzdxzzk49mVotL/GZmJeMSv22k1aamvlIw6x8u8ZuZlYwDv5lZyTjwm5mVjAO/mVnJOPCbmZWMW/WY2bjhVmnNcYnfzKxkXOI36zHutts6zSV+M7OSceA3MysZV/WYWekVq9fmTVvPnCaq2/r5hrBL/GZmJeMSv5lZC/q52/OOlPglHSrpAUnLJJ3RiXWY9Rof99Yv2l7il7QlcDFwCLAC+ImkhRHxs3avy6xX+Li3ZvTKVUInqnoOAJZFxK8AJH0NmAX4BLCN9MpJ0CY+7q1vdCLw7w48VBhfAbyueiZJc4G5eXRY0gMdyMuo/D1MAh7tdj6a1Uv51aebnnWz8txgPS9udblt0PC478Vjvp5eOrbGWq9teyeO+U4EftVIi00SIuYD8zuw/pZJujMipnc7H83qt/xCf+a5SQ2P+1485usZx/+nhsqw7Z24ubsC2LMwvgfwcAfWY9ZLfNxb3+hE4P8JMFXS3pK2AY4FFnZgPWa9xMe99Y22V/VExHpJpwDfA7YELo2I+9u9ng7pi8vwgn7LL/Rnnhvq8+O+lnH5f2rSuN92RWxS/W5mZuOYu2wwMysZB34zs5IpVeCXtKekWyQtkXS/pFNrzDMoaa2ku/NwVjfyWpWn5ZLuzfm5s8Z0SboodxVwj6RXdyOfhfzsW9h/d0taJ+m0qnl6bj+XlaRLJa2WdF8hbaKkmyUtzX936WYeO6FePCjFtpepjl/SFGBKRNwlaSdgMXBk8bF6SYPARyLiiC5lcxOSlgPTI6LmQyWSZgIfBGaSHhq6MCI2eWiuG3JXBr8FXhcRvymkD9Jj+7msJL0RGAauiIiX57TPAI9HxHm536FdIuL0buaz3erFA2AO43zbS1Xij4iVEXFX/vwksIT0xGW/m0U6aSMibgcm5IO6FxwE/LIY9K23RMStwONVybOAy/Pny0kBcVwZIR6M+20vVeAvkjQAvAq4o8bk10v6qaTvStp/TDNWWwA3SVqcH/uvVqu7gF75QTsWuKrOtF7bz/acyRGxElKABHbtcn46qioejPttL2V//JJ2BK4FTouIdVWT7wJeHBHDuQrlemDqWOexyoER8bCkXYGbJf08l9IqmuomY6zlB5neAXy8xuRe3M9WQtXxQKp1Oo0vpSvxS9qa9E9eEBHXVU+PiHURMZw/3whsLWnSGGezOk8P57+rgW+SeoIs6tXuAg4D7oqIVdUTenE/20ZWVaoL89/VXc5PR9SJB+N+20sV+JV+yi8BlkTEBXXm2S3Ph6QDSPvosbHL5Sb52SHfeELSDsBbgfuqZlsInJBb98wA1lYuVbvs3dSp5um1/WybWAjMzp9nAzd0MS8dMUI8GP/bXrJWPW8AfgjcCzybkz8B7AUQEf+WH7t/P7AeeAb4cET8vy5kFwBJLyGV8iFVzX01Ij4l6e9gQ54FfAE4FHgaODEiNmn2OZYkPY903+ElEbE2pxXz3FP7ucwkXQUMkrojXgWcTap6u5p0bjwIHBMR1TeA+9oI8eAOxvu2lynwm5lZyap6zMzMgd/MrHQc+M3MSsaB38ysZBz4zcxKxoHfzKxkHPjNzErm/wOG2gkMgP0tKwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "viz = cdf[['CYLINDERS','ENGINESIZE','CO2EMISSIONS','FUELCONSUMPTION_COMB']]\n",
    "viz.hist()\n",
    "plt.show()"
   ]
  },
  {
   "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": 17,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "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.FUELCONSUMPTION_COMB, cdf.CO2EMISSIONS,  color='blue')\n",
    "plt.xlabel(\"FUELCONSUMPTION_COMB\")\n",
    "plt.ylabel(\"Emission\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "button": false,
    "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": {},
   "source": [
    "## Practice\n",
    "plot __CYLINDER__ vs the Emission, to see how linear is their relation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "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": [
    "# write your code here\n",
    "plt.scatter(cdf.CYLINDERS, cdf.CO2EMISSIONS,  color='blue')\n",
    "plt.xlabel(\"cYLINDERS\")\n",
    "plt.ylabel(\"Emission\")\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click __here__ for the solution.\n",
    "\n",
    "<!-- Your answer is below:\n",
    "    \n",
    "plt.scatter(cdf.CYLINDERS, cdf.CO2EMISSIONS, color='blue')\n",
    "plt.xlabel(\"Cylinders\")\n",
    "plt.ylabel(\"Emission\")\n",
    "plt.show()\n",
    "\n",
    "-->"
   ]
  },
  {
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "button": false,
    "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": [
    "### Simple Regression Model\n",
    "Linear Regression fits a linear model with coefficients B = (B1, ..., Bn) 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": 21,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "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(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": 22,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients:  [[38.73060141]]\n",
      "Intercept:  [125.63195942]\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": 23,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Emission')"
      ]
     },
     "execution_count": 23,
     "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",
    "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",
    "    - 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.\n",
    "    - 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.\n",
    "    - Root Mean Squared Error (RMSE).\n",
    "    - 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).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean absolute error: 22.29\n",
      "Residual sum of squares (MSE): 795.56\n",
      "R2-score: 0.73\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_ = regr.predict(test_x)\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) )"
   ]
  },
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    "## Want to learn more?\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: [SPSS Modeler](http://cocl.us/ML0101EN-SPSSModeler).\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 [Watson Studio](https://cocl.us/ML0101EN_DSX)\n",
    "\n",
    "### Thanks for completing this lesson!\n",
    "\n",
    "Notebook created by: <a href = \"https://ca.linkedin.com/in/saeedaghabozorgi\">Saeed Aghabozorgi</a>\n",
    "\n",
    "<hr>\n",
    "Copyright &copy; 2018 [Cognitive Class](https://cocl.us/DX0108EN_CC). This notebook and its source code are released under the terms of the [MIT License](https://bigdatauniversity.com/mit-license/).​"
   ]
  }
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