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",
    "<h1><center>Simple Linear Regression</center></h1>\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>\n"
   ]
  },
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   "source": [
    "### Importing Needed packages\n"
   ]
  },
  {
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   "source": [
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import pylab as pl\n",
    "import numpy as np\n",
    "%matplotlib inline"
   ]
  },
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   "source": [
    "### Downloading Data\n",
    "\n",
    "To download the data, we will use !wget to download it from IBM Object Storage.\n"
   ]
  },
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     "text": [
      "--2021-02-25 04:48:16--  https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-ML0101EN-Coursera/labs/Data_files/FuelConsumptionCo2.csv\n",
      "Resolving cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud (cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud)... 169.63.118.104\n",
      "Connecting to cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud (cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud)|169.63.118.104|: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 0.08s   \n",
      "\n",
      "2021-02-25 04:48:16 (938 KB/s) - ‘FuelConsumption.csv’ saved [72629/72629]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "!wget -O FuelConsumption.csv https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-ML0101EN-Coursera/labs/Data_files/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)\n"
   ]
  },
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   "source": [
    "<h2 id=\"understanding_data\">Understanding the Data</h2>\n",
    "\n",
    "### `FuelConsumption.csv`:\n",
    "\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?cm_mmc=Email_Newsletter-_-Developer_Ed%2BTech-_-WW_WW-_-SkillsNetwork-Courses-IBMDeveloperSkillsNetwork-ML0101EN-Coursera-20231514&cm_mmca1=000026UJ&cm_mmca2=10006555&cm_mmca3=M12345678&cvosrc=email.Newsletter.M12345678&cvo_campaign=000026UJ&cm_mmc=Email_Newsletter-_-Developer_Ed%2BTech-_-WW_WW-_-SkillsNetwork-Courses-IBMDeveloperSkillsNetwork-ML0101EN-Coursera-20231514&cm_mmca1=000026UJ&cm_mmca2=10006555&cm_mmca3=M12345678&cvosrc=email.Newsletter.M12345678&cvo_campaign=000026UJ&cm_mmc=Email_Newsletter-_-Developer_Ed%2BTech-_-WW_WW-_-SkillsNetwork-Courses-IBMDeveloperSkillsNetwork-ML0101EN-Coursera-20231514&cm_mmca1=000026UJ&cm_mmca2=10006555&cm_mmca3=M12345678&cvosrc=email.Newsletter.M12345678&cvo_campaign=000026UJ&cm_mmc=Email_Newsletter-_-Developer_Ed%2BTech-_-WW_WW-_-SkillsNetwork-Courses-IBMDeveloperSkillsNetwork-ML0101EN-Coursera-20231514&cm_mmca1=000026UJ&cm_mmca2=10006555&cm_mmca3=M12345678&cvosrc=email.Newsletter.M12345678&cvo_campaign=000026UJ)\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": [
    "<h2 id=\"reading_data\">Reading the data in</h2>\n"
   ]
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       "<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()\n",
    "\n"
   ]
  },
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   "source": [
    "<h2 id=\"data_exploration\">Data Exploration</h2>\n",
    "Lets first have a descriptive exploration on our data.\n"
   ]
  },
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   "execution_count": 4,
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       "  <thead>\n",
       "    <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",
       "      <th>FUELCONSUMPTION_COMB_MPG</th>\n",
       "      <th>CO2EMISSIONS</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <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",
       "</table>\n",
       "</div>"
      ],
      "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": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# summarize the data\n",
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets select some features to explore more.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
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       "  <thead>\n",
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       "      <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": 5,
     "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 features:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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 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:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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3EFqVt4UwY4azmfaqXEEhIj4n6X7gX5IEhQ9GxP8tsmJm7dTqHghOpzA9IyONA4ME117rYNDLGnYfSfrx9PbNJJvm7AWeAualZWY9zwGhcxp1By1aBHfc4YDQ65q1FH4NWAl8rMZzAbyt7TUya5NWuoucsqI9Kl/4GzYkLYaRkSRQOBD0j9zrFFp+Yel1wNeA40mCz59FxIclnQZ8niTj6i7gPRHxYnrOGuAakqR774+Iv2r0Hl6nYPW0EhCcQsGGTTvWKbxb0snp/d+S9EVJR221WeVV4G0R8UZgKXCRpH8N3ABsiYglwJb0MZLGgOXAOMmU15vT/Z3NWpY3IMyb54BglpV3Sup/iYjvS3oLcCFwO3BLoxMisT99OCv9CeDS9HzS23el9y8F7oyIVyPiSWAncF7eX8QMkoR2rYwhPP10cXUx60d5g0JlPsE7gPURcRdwXLOTJI1I2gY8D9wbEd8AzoyIZwHS2zPSw+eTDGJX7E3LzHKRvCmO2bHKGxSelnQr8B7gy5KOz3NuRByMiKXAAuA8SW9ocHitv++O+m8raaWkrZK27tu3L1/treM6mfpaaq11MGuWA0K14447fB2l5LENp7xB4T3AXwEXRcRLwGnAb+Z9k/Sc+0nGCp6TNBcgvX0+PWwvsDBz2gLgqJ7hiNgQERMRMTE6Opq3CtZBnUx9PZ3ppt7c/UjHHQevvXZk2WuvOTAMq7xBYS7wFxHxHUkXAO8GHmx0gqRRSaem908AJoFvA3cDV6WHXUWy1Sdp+XJJx0s6G1jS7D2sN3Ui9XWrrQNIWgiWyLbkqgNCRb1yG2x501x8AZiQ9Hrg0yRf4J+lcVK8ucDt6QyiGcCmiLhH0gPAJknXAHtIAgwRsV3SJpIsrAeA6yLCORT7UL2tFfNsuZhHq8EAkoDgFkLzVNZmeYPCoYg4IOnfATdFxB9K+majEyLiEeCoaasR8Y/AsjrnrAPalAvTOqlcTloCe/bU38i+Hamv509j6oG/ABOVDKZmjeQNCq9Juhz4JeDn0zI3xg04PIZQ6TKqFRDalfq6lYR24IBQMTmZb+/pLHe3Dae8Ywq/DPw0sC4inkz7/DcWVy3rJ7XGECBJcdCu1NetjiFEOCBUTDcguLttOBWW5qITnOaiu0qlwzluamnX9plOaHds8ly/2bO9J/IwmXaai3TgF0mPSnok8/OopEeKqKz1hzw7bLVjDKGVnbncOkhkt8OcmaOD+KSTHBDssGYfmevT20uKroj1j3K5+YBlO8YQjjsuf0tj2INBvS6iZpveOBmgVWsYFDLpKHYDSDql2Tk22CpTGhtZtCgJCMc6hpDXsA+ITmfMAJKd5RwQrFquL3hJq4DfBn7A4dQTAfxoQfWyHlQuN5/jPjICu3ZN/z1GRlobh/CA6PQDgrcatVry/tX/G8B4RLxQZGWst61d27yb5lg2YveAcn7NBvmrjYzAgQPF1skGQ96g8A+A96Uacs1WJB9L/3QrAaHe4rhBNz7eWhbYrGMJ1jZc8gaFNcDfSvoGyeY5AETE+wuplfWMPCuVpWTv3emMIUwnf9Ewdhe1spNcNY8dWCvyBoVbga8CjwJtmHlu/SDPSmUJrr22MwEBhjMglMvTCwjtGPC34ZM3KByIiF8rtCbWcxqtVD50KFmHMN0vnVKpteOHscuo1e4ijxtYO+QNCvdJWgn8OUd2H323kFpZT6g3hnDo0LGtVPaAcnPTGT/wuIG1Q96g8Ivp7ZpMmaekDrizzko2yKlVPl0OCLVNd61BxdiYxw2sPXIlxIuIs2v8OCAMuHXrkpXJWdNdqdxqQrsTTnBAyGNkJJn1tX17e+tkw6tZ7qMPZO6/u+q53y2qUtYbVqxI5sIvWnRs2U6n0zqoNZYxiMrl1gPCokWwcWNynQ4ccAvB2qthllRJD0fEm6vv13rcDc6S2h/cZXS0UgluvbX1sZmxMbcK7NhNO0sqoDr3az2uftOFku6T9Lik7ZKuT8s/IulpSdvSn4sz56yRtFPSE5IubFI363HT2Ud5WALC+vUOCNabmg00R537tR5XOwD8ekQ8LOlk4CFJ96bPfSIiPpo9WNIYsBwYB+YBmyWd632a+5ODwZGmM27g/ETWDc2CwhslfY+kVXBCep/08esanZhmWK1kWf2+pMeBRjvsXgrcGRGvAk9K2gmcBzzQ/NewXuKAcCQHBOsnDbuPImIkIk6JiJMjYmZ6v/I4d8JiSYuBNwHfSIvel27Wc5ukOWnZfOCpzGl7aRxEbBrKZVi8OFkMtnhx8rhdvGVmba0EhNmzk0FkBwTrlrx7NE+bpJOALwC/EhHfA9YD5wBLSVoSH6scWuP0o74yJK2UtFXS1n379hVT6QFVSVuxe3fyZbx7d/K4HYFhOikr7Egnnugd0Kz7Cg0KkmaRBIRyRHwRICKei4iDEXEI+BRJFxEkLYOFmdMXAEdlfImIDRExERETo6OjRVZ/4NRKW/HKK0n5dE1nMBmGo4WQV2Wtwf79DgjWfYUFBUkCPg08HhEfz5TPzRx2GfBYev9uYLmk4yWdDSwBHiyqfsOoXtqKZimx65luMBi2gLBsWf3nVq/2WgPrLUVurXk+cCXwqKRtadmHgMslLSXpGtoFrAKIiO2SNgE7SGYuXeeZR+1VRNqKVgxbMKjYvLn2YLP3R7Ze1HDxWq/z4rXWVKfChmRgs9V+bO+BcOTOZyMjyXX1F7z1i2NZvGYDpB1pK6Yz3XQQA8L69YdTeR88mDxuNR24WS9yS8Fy8/qDxMyZtfd28H4G1i8atRSKHFOwAdLq+oNBVm+zn2HbBMgGk7uPBkiplPwVKyW37erOGNY1CKXS4Sm3lZ/JyaRFUEu9crN+4pbCgKie3VLp54ZjGwAd1i6jyrhBtS1bYN682nsme+czGwRuKQyARjn5N2yY3msOe8qKRtftmWeS6aSVlkFl8ZlnH9kgcFDoc6USXHFF/een0889rK2DbF6oZtft5puTQWVvdGODxt1HfaxeF0dWK/3cw5quolSCW24ZjN/F7Fg5KPSxPF1Defu5hzkgNAus1RqlrTDrd+4+6mPNujiWLSuuW2MQAgK0PubifQ5s0Lml0MdGRuoHho0b861UHtYWQkWzwLpoEeza1ZGqmPUEtxT6SPUGORdcUPu41auLCQiDNsMIGo+5zJ4N69Z1ri5mvcBBoU/U2iDngQeS7oxWp0a2Ot101qzBCwYV9cZcTjrJG97YcHL3UZ+ot0HOzp2t5dsZ1umm9VQCqDOemiWcEK9PzJhR+wtagkOH8r2GU16bGTh19kCotxFOURvkOCCYDScHhT6xbl0y8JmVdyB0zpzWU1Y4IJgNpyL3aF4o6T5Jj0vaLun6tPw0SfdK+k56OydzzhpJOyU9IenCourWj6a7QY4EL72U7z3qdVGZ2fAobExB0lxgbkQ8LOlk4CHgXcDVwHcj4kZJNwBzIuKDksaAzwHnAfOAzcC5jfZpHqYxhVZ5QNnM6unKmEJEPBsRD6f3vw88DswHLgVuTw+7nSRQkJbfGRGvRsSTwE6SAGEtckAws+nqyJiCpMXAm4BvAGdGxLOQBA7gjPSw+cBTmdP2pmVDoR0b5LS6/sDMrFrhQUHSScAXgF+JiO81OrRG2VF/w0paKWmrpK379u1rVzW7anz82DeCn24w6IdWQvVK7nK52zUyG1yFBgVJs0gCQjkivpgWP5eON1TGHZ5Py/cCCzOnLwCO2t8qIjZExERETIyOjhZX+Q4olZIvuh07aj8/3Q1y8uiXlBW1VnKvXOnAYFaUImcfCfg08HhEfDzz1N3AVen9q4C7MuXLJR0v6WxgCfBgUfXrtkrK5kZfzHk2yJlOl1E/BIOKeiu5167tTn3MBl2RaS7OB64EHpW0LS37EHAjsEnSNcAe4N0AEbFd0iZgB3AAuK7RzKN+l6cV0GyDnEEOBhV79rRWbmbHprCgEBF/Q+1xAoCa25RExDpgoPNSTk7W30+5WqMNcoYhIECyYnv37trlZtZ+XtHcQePj+QPC2FjtpGytdhf1y9hBPceyktvMWueg0CHlcv0B5WqrV8P27UeXD+N00+mu5Daz6XHq7A7Isw9wESmb+7mFkLVihYOAWac4KBQs78bwjfZEGJbxAzPrPncfFSzPLKNlNYfdEw4IZtZJDgoFa7bWYGwMNm8+urzVAeUTTnBAMLNj56BQsEZrDTZubM+AcsTRC7zMzKbDQaFg9dYarF5de/C01fQNs2a1Xiczs3ocFAp2881JAKi0GEZGkse1ZhlNTsIVV+R/7V7aMtNJ68wGQ2Gb7HTCIG2y088DypWkddkurNmzvZ7ArFd1ZZMdy6/fAkL13g/XXuukdWaDwkGhi8bH+y9lRWXdRXbvh/37ax/rpHVm/ceL17pkZAQOHcp/fKO1DJ1QLid/+ddKTlePk9aZ9R+3FDps/vykddBqQKi1lqFTshvd5OWkdWb9yS2FDpo/H545ai+5xrrdXQS1N7qpJiUtgz17ktt16zzIbNaPHBQ6qB8DAuQbG7j22vYm8zOz7nD3UYeUSvmPnTevdwICNB4baLTuwsz6T5F7NN8m6XlJj2XKPiLpaUnb0p+LM8+tkbRT0hOSLiyqXp1Wmb6ZJ1PqjBlJMHj66eLr1Yp6G91s3Jhkd3VAMBscRbYUPgNcVKP8ExGxNP35MoCkMWA5MJ6ec7OkJjsU977q6ZuNzJuX77hu8EY3ZsOjyD2avyZpcc7DLwXujIhXgScl7QTOAx4oqn6dkCdtNvRWV1E93ujGbDh0Y0zhfZIeSbuX5qRl84GnMsfsTcv60uRk8hd1nr/8V68uvj5mZnl1OiisB84BlgLPAh9Ly2ut663597OklZK2Stq6b9++Qip5LObMgS1bmh/nAVoz60UdDQoR8VxEHIyIQ8CnSLqIIGkZLMwcugCoOYEzIjZExERETIyOjhZb4RaUSknr4KWXmh+7erUHaM2sN3U0KEiam3l4GVCZmXQ3sFzS8ZLOBpYAD3aybsci7z7Mbh2YWa8rbKBZ0ueAC4DTJe0FPgxcIGkpSdfQLmAVQERsl7QJ2AEcAK6LiB6di3PY+Djs2JH/+AMHiquLmVk7FDn76PIaxZ9ucPw6oG+y5bSasqLbCe3MzPLwiuZpKJdbCwinntrdhHZmZnk5KExDK5vHLFsGL75YXF3MzNrJQaEFlX2Im6WQrgwoR7iFYGb9xVlScyqV4JZbmq8+HhuD7ds7Uyczs3ZzSyGHcjlfQJg3zwHBzPqbg0ITpRJccUXjgLBoUZIxtNeym5qZtcrdRw1MTjZPWbFoEeza1ZHqmJkVzi2FOsrl5gFB8j7EZjZYHBTqaDbtVEq2oHQ6aTMbJO4+qqPZvsR33OGAYGaDxy2FOhrtS7x6tQOCmQ0mB4U6au1LDMkKZWc5NbNB5aBQR619iTdu9AplMxtsQxsUSiWYOTP5wp85M3lcbcWKZLrpoUPJrbuMzGzQDeVAc/X6g4MHD2+S464hMxtmQ9dSaLT+YMOGztbFzKzXDF1QaLT+4GDP7/VmZlaswoKCpNskPS/psUzZaZLulfSd9HZO5rk1knZKekLShUXVq9H6g5GRot7VzKw/FNlS+AxwUVXZDcCWiFgCbEkfI2kMWA6Mp+fcLKmQr+hG6w9WriziHc3M+kdhQSEivgZ8t6r4UuD29P7twLsy5XdGxKsR8SSwEziviHp5/YGZWX2dHlM4MyKeBUhvz0jL5wNPZY7bm5a1ndcfmJnV1ytTUlWjrOYOBpJWAisBzmrUF9TAihVec2BmVkunWwrPSZoLkN4+n5bvBRZmjlsAPFPrBSJiQ0RMRMTE6OhooZU1Mxs2nQ4KdwNXpfevAu7KlC+XdLyks4ElwIMdrpuZ2dArrPtI0ueAC4DTJe0FPgzcCGySdA2wB3g3QERsl7QJ2AEcAK6LCK8aMDPrsMKCQkRcXuepZXWOXwd4HzMzsy4auhXNZmZWnyJqTvLpC5L2Abvb+JKnAy+08fUGja9PY74+jfn6NNbJ67MoImrO1OnroNBukrZGxES369GrfH0a8/VpzNensV65Pu4+MjOzKQ4KZmY2xUHhSN5RoTFfn8Z8fRrz9WmsJ66PxxTMzGyKWwpmZjbFQQGQtEvSo5K2Sdra7fr0glY3SRo2da7PRyQ9nX6Otkm6uJt17CZJCyXdJ+lxSdslXZ+W+zNEw+vT9c+Qu49IggIwERGeQ52S9FZgP/CnEfGGtOz3ge9GxI2SbgDmRMQHu1nPbqlzfT4C7I+Ij3azbr0gTXg5NyIelnQy8BDJ/ilX489Qo+vzHrr8GXJLwWpqcZOkoVPn+lgqIp6NiIfT+98HHifZI8WfIRpen65zUEgE8NeSHkr3a7Da6m2SZIe9T9IjaffSUHaNVJO0GHgT8A38GTpK1fWBLn+GHBQS50fEm4F/C1yXdg2YtWo9cA6wFHgW+FhXa9MDJJ0EfAH4lYj4Xrfr02tqXJ+uf4YcFICIeCa9fR74EgXtDz0A6m2SZEBEPBcRByPiEPAphvxzJGkWyRdeOSK+mBb7M5SqdX164TM09EFB0onpQA+STgR+Dnis8VlDq94mScbUl1zFZQzx50iSgE8Dj0fExzNP+TNE/evTC5+hoZ99JOlHSVoHkOwv8dl0b4ehlt0kCXiOZJOk/wlsAs4i3SQpIoZysLXO9bmApNkfwC5gVaX/fNhIegvwdeBR4FBa/CGSfvOh/ww1uD6X0+XP0NAHBTMzO2zou4/MzOwwBwUzM5vioGBmZlMcFMzMbIqDgpmZTXFQMDOzKQ4K1laSDmbS/m6TtFjS1ZL+qOq4+yVNpPezqcu3SfqDtPwzkn6hxnucK+nLknamqYc3STozfe4tkh6U9O30Z2XmvI9IekXSGZmy/Zn7a9M0xo+k9fhXmfqdnjnuAkn3pPevlhSSlmWevywt+4XM7/qEpG9J+l+SfkzSl9L32CnpnzK/+89UXZsfkvSnkv4h/flTST+UPrc4fZ//nHnvP5J0dZN/o99Ir81jaZ1+KS0/TtJN6ft8R9JdkhZkzgtJd2Qez5S0r+pa7Et/j+2S/kzS7EZ1sd7joGDt9oOIWJr52ZXzvJ/NnPP+egdJeh3wF8D6iHh9RPwLknwxo5J+BPgscG1E/DjwFmCVpHdkXuIF4NdrvO5PA5cAb46InwQmgady1v1RkkVHFcuBb1UdsyIi3kiSGfS/R8RlEbEU+I/A1zO/+99Wnfdp4P9ExDkRcQ7wJPAnmeefB66XdFyeikq6Fng7cF6a8vutgNKnfxc4GTg3IpaQLFb8Yrr6FuBl4A2STkgfvx14uuotPp/+HuPAPwPvzVMv6x0OCtZvfhF4ICL+vFIQEfdFxGPAdcBnMimJXwA+ANyQOf824L2STqt63bnACxHxauXcSk6sHL4OnCdplpIEZ68HttU59mvp801Jej3wU8DvZIp/G5iQdE76eB+whcOpI5r5EFCqJKeLiH+KiNvTv+h/GfjViDiYPvc/gFeBt2XO/wpQCbKXA5+rU/eZwInAiznrZT3CQcHa7YRMV8iXmh8+5b7Meb/a4Lg3kGxIUst4jee2puUV+0kCw/VVx/01sFDS30u6WdK/aaHuAWwGLiTZL+DuBsf+PEnLIo8xYFvlSxogvb+NI3+nG4FflzTS6MWU5Pg6OSL+ocbTrwf21MhkWn397gSWpy22n+RwuueK90raRtKCOA34c6yvOChYu2W7jy5Ly+rlUsmWZ7uPPjHN91ad96ou+wPgKkmnTB0QsZ/kr/KVJH99fz7TN5/nNe8k6TZaTu2/nsvpl+X5wG80/C0Oq/f7HFEeEU8CD5K0oqbzeq281yPAYpJWwpdrHP/5tFvsR0iC3282qZP1GAcF64R/BKo3CzmNpH+/VdtJvrzrPTdRVfZTwI5sQUS8RDL2UKoqPxgR90fEh4H3Af8+faq6/kfVPSIeJGnFnB4Rf1+jbivSgPeuiMg7VrEdeJOkqf+n6f03kuzUlfW7wAdp8H86bQW8rCQJZLWdwKK0NZH1ZqquH0lL6KPU6TpK3ytIWgnem6TPOChYJ/wdcH46EEw6s+Z48g/kZn0W+Jns4LGkiyT9BPDHwNWSlqblPwz8N+D3a7zOx4FVJJlxSWcELck8vxTYnd6/H7gyPW4EuAK4r8ZrriHps2+LiNgJfBP4rUzxbwEPp89lj/02yZf3JU1e9veAP660kiSdImllRLxMMgj+8Uo3VDoraTbw1arXuA347Yho1g32FqBWV5X1sJndroANvoh4TtL1wJfTv3T3A5enG4lU3Cep0nf+SET8Unr/Vkk3pfefioiflnQJcFNa/hrwCHB9+j5XAJ9K/+IVcFN2UDpTpxfSMY/K+MVJwB9KOhU4QPKXc2U66+8A6yV9K33NvwQ21njNr7R2ZXK5Jq3XzvS9H0jLallHEkQaWU/yu/6dpNdIrl9ld681JC2Av5d0CPg2cFlUpVKOiL3AJ+u8/nuVpIWeAewFrm5SH+sxTp1tZmZT3H1kZmZT3H1kNoAk/THJTKesT6ZrD8zqcveRmZlNcfeRmZlNcVAwM7MpDgpmZjbFQcHMzKY4KJiZ2ZT/D4SFrJqSvFbvAAAAAElFTkSuQmCC\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": 8,
   "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",
    "\n",
    "plot **CYLINDER** vs the Emission, to see how linear is their relation:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "# write your code here\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",
    "-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "#### Creating train and test dataset\n",
    "\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: \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True,  True, ...,  True,  True,  True])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "msk = np.random.rand(len(df)) < 0.8\n",
    "msk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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": [
    "<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. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "#### Train data distribution\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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",
    "\n",
    "Using sklearn package to model data.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients:  [[38.42224754]]\n",
      "Intercept:  [127.25550534]\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\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can plot the fit line over the data:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Emission')"
      ]
     },
     "execution_count": 13,
     "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",
    "\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",
    "\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>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean absolute error: 24.60\n",
      "Residual sum of squares (MSE): 1055.44\n",
      "R2-score: 0.64\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": "markdown",
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    "<h2>Want to learn more?</h2>\n",
    "\n",
    "IBM SPSS Modeler is a comprehensive analytics platform that has many machine learning algorithms. It has been designed to bring predictive intelligence to decisions made by individuals, by groups, by systems – by your enterprise as a whole. A free trial is available through this course, available here: <a href=\"http://cocl.us/ML0101EN-SPSSModeler\">SPSS Modeler</a>\n",
    "\n",
    "Also, you can use Watson Studio to run these notebooks faster with bigger datasets. Watson Studio is IBM's leading cloud solution for data scientists, built by data scientists. With Jupyter notebooks, RStudio, Apache Spark and popular libraries pre-packaged in the cloud, Watson Studio enables data scientists to collaborate on their projects without having to install anything. Join the fast-growing community of Watson Studio users today with a free account at <a href=\"https://cocl.us/ML0101EN_DSX\">Watson Studio</a>\n",
    "\n",
    "<h3>Thanks for completing this lesson!</h3>\n",
    "\n",
    "<h4>Author:  <a href=\"https://ca.linkedin.com/in/saeedaghabozorgi\">Saeed Aghabozorgi</a></h4>\n",
    "<p><a href=\"https://ca.linkedin.com/in/saeedaghabozorgi\">Saeed Aghabozorgi</a>, PhD is a Data Scientist in IBM with a track record of developing enterprise level applications that substantially increases clients’ ability to turn data into actionable knowledge. He is a researcher in data mining field and expert in developing advanced analytic methods like machine learning and statistical modelling on large datasets.</p>\n"
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    "| Date (YYYY-MM-DD) | Version | Changed By | Change Description    |\n",
    "| ----------------- | ------- | ---------- | --------------------- |\n",
    "| 2020-08-4         | 0       | Nayef      | Upload file to Gitlab |\n",
    "|                   |         |            |                       |\n"
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    "<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>\n"
   ]
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