Polynomial-Regression-Co2.ipynb

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    "<center>\n",
    "    <img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork/labs/Module%202/images/IDSNlogo.png\" width=\"300\" alt=\"cognitiveclass.ai logo\"  />\n",
    "</center>\n",
    "\n",
    "# Polynomial Regression\n",
    "\n",
    "Estimated time needed: **15** minutes\n",
    "\n",
    "## Objectives\n",
    "\n",
    "After completing this lab you will be able to:\n",
    "\n",
    "*   Use scikit-learn to implement Polynomial Regression\n",
    "*   Create a model, train it, test it and use the model\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=\"https://#download_data\">Downloading Data</a></li>\n",
    "        <li><a href=\"https://#polynomial_regression\">Polynomial regression</a></li>\n",
    "        <li><a href=\"https://#evaluation\">Evaluation</a></li>\n",
    "        <li><a href=\"https://#practice\">Practice</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": [
    "<h2 id=\"download_data\">Downloading Data</h2>\n",
    "To download the data, we will use !wget to download it from IBM Object Storage.\n"
   ]
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      "--2021-09-22 06:52:36--  https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork/labs/Module%202/data/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 0.06s   \n",
      "\n",
      "2021-09-22 06:52:36 (1.08 MB/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-SkillsNetwork/labs/Module%202/data/FuelConsumptionCo2.csv"
   ]
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   "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](https://www.ibm.com/us-en/cloud/object-storage?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkML0101ENSkillsNetwork20718538-2021-01-01)\n"
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    "## Understanding the Data\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?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkML0101ENSkillsNetwork20718538-2021-01-01)\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\n"
   ]
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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",
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       "      <th>FUELCONSUMPTION_COMB_MPG</th>\n",
       "      <th>CO2EMISSIONS</th>\n",
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       "    <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",
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       "      <td>8.5</td>\n",
       "      <td>33</td>\n",
       "      <td>196</td>\n",
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       "      <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",
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       "    <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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   "source": [
    "df = pd.read_csv(\"FuelConsumption.csv\")\n",
    "\n",
    "# take a look at the dataset\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's select some features that we want to use for regression.\n"
   ]
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       "      <th>ENGINESIZE</th>\n",
       "      <th>CYLINDERS</th>\n",
       "      <th>FUELCONSUMPTION_COMB</th>\n",
       "      <th>CO2EMISSIONS</th>\n",
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       "      <th>0</th>\n",
       "      <td>2.0</td>\n",
       "      <td>4</td>\n",
       "      <td>8.5</td>\n",
       "      <td>196</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\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",
       "      <th>2</th>\n",
       "      <td>1.5</td>\n",
       "      <td>4</td>\n",
       "      <td>5.9</td>\n",
       "      <td>136</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3.5</td>\n",
       "      <td>6</td>\n",
       "      <td>11.1</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.5</td>\n",
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       "      <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",
       "      <td>6</td>\n",
       "      <td>10.1</td>\n",
       "      <td>232</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",
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       "   ENGINESIZE  CYLINDERS  FUELCONSUMPTION_COMB  CO2EMISSIONS\n",
       "0         2.0          4                   8.5           196\n",
       "1         2.4          4                   9.6           221\n",
       "2         1.5          4                   5.9           136\n",
       "3         3.5          6                  11.1           255\n",
       "4         3.5          6                  10.6           244\n",
       "5         3.5          6                  10.0           230\n",
       "6         3.5          6                  10.1           232\n",
       "7         3.7          6                  11.1           255\n",
       "8         3.7          6                  11.6           267"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cdf = df[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_COMB','CO2EMISSIONS']]\n",
    "cdf.head(9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot Emission values with respect to Engine size:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
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frbSVh4ZscSauF18MJnL3wOz0jW/ku3aUp57K1y+6m3nppxRmGbDDzPoJlM+N7n6zmX3WzM4nMA0dAK4AcPe9ZnYjsA84Blzp7ioQKDpGf3/yJN9w0I6OTi8gPzyczYRUR1WzhrknLda/YSaDYqUdk1ZSSlExO6ky+uhed3+Vu7/S3V/h7r8f9r/T3X8m7L/M3Q9Hxmxx97Pd/Tx3//uqZBOiQdSxnOWpf98+WLly6nPWqmad2m8QpeGPyBrrXzQjaZJpLalfdDfa0SwKk1aVrNtlaHYsN0gL24ymqm4OpUzia1/LLlcrTj45vn9gINkRnFVx5fVZiB4laQPDbGjavFYf3bDZqF0Z0jaOFUnnnHdM3vOLFqPJssGu8b3zUuR3EvVCi81rSognCtENCczalaHVk717+vE48kYw5b1HkQipZhorpGaiq4s8FPmdRL20HX0URhL9BzPbHm44u87MritXTDGb6IYEZu3KkLYxbHQ0/nhzf9SEtXBh/JiyNnoViZBqZtWqqf0KDfr6gv4iJG1uS+oX3U1Wn8IXgZcBu4C/izQxR+mGBGZZZGjlc0grOL9370wF0Bx91Jzm4plnZk64q1cnP4EnPWUn9ZdRjGbz5pmhsCdOTBW8iaMb/EeiQyTZlaINuDvLeZ1u8inUx2zwKWSRccOGKd9Cf3/+QvFJpSiz/i6d8ilEyVtCNO13TPPNiO6DFj6FrErhPwNrspzbySalUC/tTqhl0KrWcJYay+1c3z173eSkexaRsSpFVlRGOZpnH62UQlbz0VXAzWb2YzN7Omw/rGTpImYFExNBgrVonqAdO7rLrNCuz6HZNBRXxjKruSzpnlnqQDcT3eF87Fh+5/CaNfn6037HvCYw0eUkaYvZ0LRSqI8ynsLbJc2ssWhRvIyLFmW7fpbvuHOn+/z56SuF/v7k1UanV1x1rRTSVl2ic9Cu+Si4BpcBHw/bm7KOq7JJKdRHXrt0FvJOGlWbNbKM37nTfWAgXSkkKa648QMDrb973Pl5KNunkPV3ar6vmRRDXbStFICrgd3Ae8J2G3B1lrFVNimF+ih7pVDEcZ02uXVCKST9Do2VQZITtvE7DQ3FHx8aipcpSQHlUQxF/u1aKewsv1PSamr+/Oxyi/IoQyncC/RFPvcD92YZW2WTUqiPsqOP0ibXuJVDN6wU2lVMeWVs9zu5x5u85s8v/m+XZeVRhtyiPFophTy5j06OvH9ZYSeG6AnKLp+Y5Mw8fjyYOuKcvEWctGWTtleijH0FVRA82yV/zsP73pevX3Q5Sdoi2oC3AweB64EdwEPA2ixjq2xaKfQOWeL940wc7Zo1WpFlfLv29qpWCq2c11UECaQ5y7VS6C4oydG8jMDZfDnwr7KOq7JJKfQOO3e69/VlUwxZI3WymDVaKZXR0fjxo6MzZS+6VyLvZJnFp5C2wa2KIIE0Vq+Ov+fq1dXdUyRTWCkAPxW+vjqutRrbiSal0DskTWRZWpJiWLw4/vzFi4PjWWzrzYqhWSGkUUbkTjNp0UdJyrWvL9vvUhXNikEKoT7aUQrbw9evxrSvtBrbiSalUC9lxp0nRelkXTnEkTbh5o38yUrz77JhQ3UmrjjSrtlqF7b2EMwNSjEf5W3ASQQ1lu8B9gIfC/tPJQhpfTB8PSUyZhOwH3gAuDTtHlIK9VF29FFRhdBqAq2iXkIaeX+XOpRClt+z03msRGdppRQy1VMws7cCt7r702b2H0Pz0R+4+7dajDFgkbs/Y2YDwNcJ0mX8GvCUu19tZh8OlcLvmtko8DngQuB0goys53qLOs2qp1AfZddTSKoTkIWitQqqqAOQ93epQoa+vvixZkE21Ky/dSdrY4jO0nY9BeA/hQrhF4FLCSKQPtlqQKiQngk/DoTNCRzVO8L+HcCbw/eXAze4+/Pu/hDBiuHCjPKJDpNUrD5LEfs42qk3kDR28eLW/UND8ceT+rOQFFp78GB5aaejdaXnzQs+R0lSJo3+iy7Kdp9O1sYQ3UNWpdB4rngjsM3dvwjMTxtkZv1mdjfwBHCbu38TOM3dDwOEry8PTz8DeCQy/FDYJ7qQsuPv4wq/xLF48fRaxKtXwy23xE+4P/pR/DUa/ddcE9Q2jjIwEPTnITpJt3q6dw+Uw7vfXVwxNNeVPn48+NysGFqxf3+28zpZG0N0EUl2pWgDbgb+EvguwSa2BcA9WcaG408mcE6/Avh+07Hvha9/Abwj0n8t8G9irrUe2APsWbFiRXlGNpGLLLbwPI7orPsUYOqaQ0Mzo4eK5ORpx1leNGqq4cwu20+Sds2sqb7z+hSU7G52QQlpLgYJfAHnhJ+XAa/PMjZyjY8AHyRwIi+LXOeB8P0mYFPk/C8Br2l1TTma6yMtcqdMh2veVmae/4ULp49buHD68VZRU2kTcJbfMc/vVMZvWWRSL5LUT9RLK6WQ1dF8NnDI3Z83s4uAVwKfcffvtxizFHjR3b9vZguBLwP/FfgV4EmfcjSf6u4fMrOVwF8z5WjeHSohOZq7kLQC8mU6XPPScKgWceJu3Bik62jliF24EJ59dupere6Rdnzx4ngz16JFQWnPZrJ8p3Z+ywzTwQyWLIEnn5zZPzQER48Wl0VURxmO5s8Dx83sJwnMOmcRTOCtWAZ81czuBf6FwKdwM0HG1UvM7EHgkvAz7r4XuBHYB9wKXNlKIfQ6ZdfETXNO5iWtgHy7BW7aoagtvNlen8Rzz029b9e3kub3mA3EKYRW/aLLSVpCRBtwV/j6IeC3wvffyjK2ytar5qOy9wCUUde3mTQzRt78OmWZjtrZLZxnA13W3zbtGnllrNp8VISyryeqhxJ8Ct8kSIp3H3BW2HdflrFVtl5VCmUnLKuisHraRNBpn0IZu4WLTp6tksGl+QyqUAp5nPbRVjTtRFU7w0V1tFIKWc1H7wZeA2xx94fM7CxgZ3nrFRGlbNNLmqmnCspOrZ3GiROBr6Kq60dZuHD651WrYPny4HsuXx58blBW2GuDDRvS++NSijdMhxCYtk4/ffrx1ath165iMl1zDcxvClCfP7/4dxQ1k6QtZkPr1ZVC2U9eaQnSilC2yaCd3EdJ98z7O2YJ12z+zbKsiFqFaxbJHpqlpnP0nkNDM6ODyk5joZDU2QVFVwpmdmP4+m0zuzfSvh06kMUsoPnJNq2/DqpYtZx/fr5+9/Rrnjgx3Um/efNUJFKDZ5+FdeumggQgWMXErWbOPTf+Pkn9AFu3BhFe7sHr1q0zzxkfn7rn4sXw4oszZdy8OfkeeYner1MrNlENLUNSzWyZux82s+G44+5eMKlBOfRqSGpa7pq6r9cYm0SWybWZl7wkPgQzK3H3TAubzXp+q/FJv22UwcFk01leGWF62Gx/f5DmI04xNKji31/MbgqHpPpUOoqDoQL4HvB0pIkKSCvxWPf1qqCKEMy8vpSs+Zei47P8hq2eyvPKWCTNRSf+/csOoRY1kmRXijbgCuBx4ABBKc6HgP+bZWyVrVd9CmUXVm/X7h1H2T6FdvwJ0RYtglMk6ipqr09q0fFxv22e3yWvjEW+U9khzp2+vigfSghJfRBYkuXcTrZeVgplpw1oNekXuV8RpVC0nnJRxVBkf0ZUKSQ5npvHR79XFkXSfL88MhZVxlU6gquo+SyqpQylcCswmOXcTrZeVQqd/iMrEu2Ud3JqpyxlkdYgS6RO9NxW10wbX+R3yStjFXtO2qWOms+iPVophay5j14FfJpgE9vzEdPTb5dmxyqAHM3lUMRpnGXMxERgS3/44eA7xdnJG7mQysx9FJUhD2U4z/PmMsrLypWwb9/M/tFR2Lu3/esXoeyCS6J6ysh99JfAV4B/Bu6MNFEBzRuP0vq7kYmJwHF78GAwoSY5TosW5elWmsNT0/rz8sAD+fo7QdxmucHBoF/MPrIqhWPu/jvu/ml339FolUo2h4kmXMvS3y5VVCCLi9+Po2hRnlaMjpZ/zawkrSharTTyRO7UsTs9jU7vXhfVklUpfNXM1pvZMjM7tdEqlWwOk2QiqiqmvIo0BVlXAGVPZu2YUZLMR2WbtqJMTASV2BorqrTKbGVXvCsLbV7rHbIqhX9HUATnn5gyHfWeMb+HaH763Lgx+Wl0fByuu276k95117X3h511kmpnNRKl4d5sVgh5nsLf9758/WVw1VUzdxu/+GLQH0fSXop2alwLMY0kD/RsaL0afVQ07LBBltj5vr72whLTZMwaJZQlW2iWlhRqmzd+Pk8kUJHfpd3zy5CxCpT7aHZB0ZBU4EOR929tOvaHrcZ2okkpxJM1dfKiRdXJmJSEr10lktaim/zqiJ/vhFLoNrR5bfbRSimkmY/WRt5vajr2hpIWK6KJdh2/We35VVb3yuP/6MtqxMzACy9MmV7qqP6W99+uCid/p0lKClhmwj3ROdL+HC3hfdzn6QfNzjSzr5rZ/Wa218yuCvs/amaPmtndYVsTGbPJzPab2QNmdmmub9JDzLX89MHCszwaZSDryPmU99+uF/6t6yy9KiogaQkRrDCCMpzN7+M+x4xdBrw6fP8S4P8Ao8BHgQ/GnD8K3AMsIKgB/V2gv9U9etV85N6ejTarqSVaG6Ds3EdZahNU2RrfqQ6zRt7fcrbb45XmYvZBC/PRvBSd8bNm9kOCVcHC8D3h55NSlM1hoJFl9Wkzux84o8WQy4Eb3P154CEz2w9cCNyeIqMoyBVXBK+NjWYNE8DBg1PRLEUjkMp++i9CQ/bGruoVK4INVVWHS46P57tH3vO7jS1bpv//AW1em9UkaYsyGzACPAy8lGClcAC4F7gOOCU8578D74iMuRb49VbX7dWVws6dM5+0zbI/QaY9RTdHrBR50kt7Sk/Kp9TJlcJcptOrj9m+2plr0G7uo3Yws8XAPxDUd/6CmZ0GHAUc+ANgmbu/x8z+Arjd3XeG464FbnH3zzddbz2wHmDFihUXHOy1PAnAggWBw7SZ+fPh+edn9jeTN4dPkVxLafdYsmTKtl8H3bBSqYvmlR+0LvQj5h5l5D4qeuMB4PPAhLt/AcDdH3f34+5+AvgrAhMRwCHgzMjw5cBjzdd09+3uPubuY0uXLq1S/NqIUwit+tulCofsU08VHyvaQ9FAoh0qUwpmZgQmoPvd/U8j/csip70FuC98fxOw1swWmNlZwDnAHVXJJ6aoIqHZqUqCUhuKBhLtUOVKYRXwTuB1TeGnf2Rm3zaze4HXAh8AcPe9wI3APoL6DVe6e41pvnoTs6AucLR8YycTmvX1VZtLSMyO8quie0mLPiqMu3+d+L0Mt7QYswVQzELFNOr6QuuC76046ST48Y/j+yHZfOQe+CmqVAyzaeNXFSgaSLRDpT4FUQ9ZU0dv3x68TkzAu941PVPnu97VOnncT/xE6/66nlYHBmbXxq8qUCpr0Q5SChWQJzNnFcRV5oqjkbb6iitmRhmdODG1jyHPPRr9a9bEH0/qb4fFi6cmv09/WpMfKJW1KE5l5qO5ShUbwaL09ZW/CSspB1I7uZFuSTASJvW3w3PPVVdrQoi5hlYKJVN1OGDDvLN+ffsrkCrt+p2MgKmz6pgQvYaUQsl0ajIsQ9FUucGrkz6FuquOCdFLSCmUTCcnw26OO0/b+1DmRK6qY0KUh5RCyXTSwdrNcedpETDnnVf82g2F0t8PGzYUD6sVQsyk8txHVTI2NuZ79nRXqeiknD9DQ3D0aLZrZLH1t8plk8dX4F5N7qM05s0r5gvImv9JCJFMbbmP5iJJSeDKSg5XRdx5HQXrizqHf+mXypVDCDEdhaTOMqoIvWyYX7ZvDybr/v7ATl+lWaa/v5hi+NrXShdFCBFBK4Ua2LgxMJ/E5SGqi61b4dixwPRz7Fj1dvqizmGFnwpRLVoplIxZsn0eAgXQyDsE5eQhqoO075lG8+okKwo/FaJatFIoQKs0FklO1kZ/I99QM0n9nSLv6uWnfzpffxzR1cnpp2cbo/BTIapFK4WctJvGIumpuE6zSJHVy/335+tPY2Cg9fFO+DmEEApJzc3ISKAImhkeDhKPpYVqJoVi9vcHT83Qfrhn3pDULDLluUeR/1JlX08IkYxCUkskqSR01lLRF12Ur79KFi4MXrth9ZLkK5APQYjOIqWQk3Ynr7vvztdfJc89F7wW+U6LF+frT6MbFJMQotoazWea2VfN7H4z22tmV4X9p5rZbWb2YPh6SmTMJjPbb2YPmNmlVcnWDu1OXlVvbitCkvO2lVP3k58MzE5R5s0L+oswPJyvXwhRDVWuFI4B/97dfxr4BeBKMxsFPgzsdvdzgN3hZ8Jja4GVwBuArWbWdcaD2TB5nXxyvvO3bg1yCOXJKTQ+DtdfPz230fXXF99l3cmcUUKIZCpTCu5+2N3vCt8/DdwPnAFcDuwIT9sBvDl8fzlwg7s/7+4PAfuBC6uSryizYfL6/vfzjymyea3M6l6dLMojhEimIz4FMxsBXgV8EzjN3Q9DoDiAl4ennQE8Ehl2KOzrKpImqe3bg30LohidLMojhEim8mnMzBYDnwfe7+4/bHVqTN+MYEQzW29me8xsz5EjR8oSMzNJUUbHj3cmdLKuus9V08k6FEKIZCpVCmY2QKAQJtz9C2H342a2LDy+DHgi7D8EnBkZvhx4rPma7r7d3cfcfWzp0qXVCZ9A3SGSZZbj7CbSivIIITpDldFHBlwL3O/ufxo5dBOwLny/DvhipH+tmS0ws7OAc4A7qpKvKN0SIllm3eeitEr3kZfxcVi3brqze9268tKDCyGyUeVKYRXwTuB1ZnZ32NYAVwOXmNmDwCXhZ9x9L3AjsA+4FbjS3btkCu5OkuztixZlG59n53MzjXQfBw+Ws3qZmAjCWRtK9/jx4HMvrYaEmA0ozUVO2plI3bOlc8h6j0ZqjWYuvhh2704fv2gRPPNMtns1k5buIy8nnRRfUW3BAvjxj/NfTwiRjNJc9CCt7O1f+Uq2a/zoR8XvX3a0UFKJTZXeFKKzSCnMMrKU4+zE4k/RQkL0JkqdPcuoohxnEbZsmZ5CHBQtJEQvoJVCD9KO3yMr4+PBaiWa5qLV6iWN1avz9QshqkGO5pzU7Wgus57C0BAcPZrt3E7Q7CBfvRp27apPHiF6FTma5xhZk/O97W3VypGXc8+dvk/h3HPrlUeIuYiUQg8Stzs4js98pnpZstIoCRrdp7BtW3qtaCFEuUgp9CDN9v4k2glJLZvt2/P1CyGqQUqhR4mmtZ4NqPKaEN2BlEKHSUpBEe0vOxInabXQiSglIcTsQkqhQzSqoWWZoPfvjz8nqV8IIcpCSqFDvOxlwWtSrqFof1LNhqT+NJLCWLspGnk2lDkVYi4gpdAhVEGsNaqnIER3IKUQw8aNMG9eYNKZN6+csMhTT23/Gr1M2TukhRDFUO6jJhrx8g0a8fKQrZh9N7J6dXwq7W5LITE+LiUgRN1opdBEWrz80FCx6z71VLFxZbBr10wFoBQSQog4pBSaSIuXL5oaou6U0rt2BY7lRpNCEELEUWWN5uvM7Akzuy/S91Eze7SpPGfj2CYz229mD5jZpVXJBa1rCzdy7zTT6L/llvz3GxiYcphmCUmdPz/+nKR+IYQoiypXCtcDb4jp/zN3Pz9stwCY2SiwFlgZjtlqZgnTc3uk1RZevz5+XKO/SBRRdMLPEh563XUzlYdZ0C+EEFVSmVJw938EslrSLwducPfn3f0hYD9wYRVybd48vTAMBJ83bw7eb90KGzZMz9a5YcOUkznJDNTfH0zccSuNF16Yun6WePzxcfjsZ6dH4nz2s3LCCiGqpw6fwm+a2b2heemUsO8M4JHIOYfCvtLJUlt41SpYvjyYkJcvDz43SIqn37EjyDOUlGuocf2s8fjR3EUHDkghCCE6Q6eVwjbgbOB84DDwJ2F/nKU91tBiZuvNbI+Z7Tly5EhuAZJSSjf608xLcfH069YFK4G+vqDF0VhhZI3Hb+X3yEK744UQcxR3r6wBI8B9aceATcCmyLEvAa9Ju/4FF1zgeenri8bgTLW+vuD48HD88f5+d7Pg+M6dU9fbudN9cDB+TKMNDk4fk0bcNfNcY+dO9/nzp4+fPz+fDEKI3gXY4wnzaqXlOM1sBLjZ3V8Rfl7m7ofD9x8Aft7d15rZSuCvCfwIpwO7gXPcvWXi5CLlONNKXfb1pecEGhycerofGYnPSdTfH5h+VqwITEN5zD9J1xweDkxJaSxZAk8+ObO/28pvCiHqoZZynGb2OeB24DwzO2Rm7wX+yMy+bWb3Aq8FPgDg7nuBG4F9wK3AlWkKoShpIadZ9hNEHdNJPoqGf6GIPyCL36MVcQqh0V9m6g4hRO9RZfTR2919mbsPuPtyd7/W3d/p7j/j7q9098saq4bw/C3ufra7n+fuf1+VXGkhp2vWxB9vpjFBJymRdjarJeVJKit/kkpdCiGSmHM7mtNCTrNuTmtM+klKJKtyqYKsqThU6lII0cycUwoQKIBjxwLfwbFj0xPdZTHRRENIk5RIkZ3PDZLyJGXNn3TNNcEu6jRU6lII0cycVAqtSNuc1hxC2q79P48MWU1S4+Pw6U9Phb0mkeRfEULMXaQUmkjbnNbsOC4ygaftISij4Ex081tSiuyLLsp+PSHE3EBKoYm8xV7yTuBpm+OKyJCGaj4LIbIipRBDnhQTeSfwtNxLVVCFiUsI0ZtIKRSg2fwD2ZVI3Ka05v4sq4k8VBE2K4ToTaQUctLuhJ22eQ7KX02U4aMQQswNpBRy0u6EnVbZDco395TtoxBC9C7z6hZgttHuhD08nJzXqMGKFfHntGPuGR+XEhBCpKOVQk7atc9nMeXI3COEqAsphZy0O2FnMeXI3COEqItKU2dXTZHU2WUwMRH4EB5+uFhqbCGEqJNaUmf3Mu2WysxSFU2V04QQdSClUAJ5JvAsIa1l71MQQoisyHzUJo0JPBqmGq3M1kyWqmrtVl4TQohWtDIfSSm0Sd4JPKncp1lgjsp6jhBCFKWucpzXmdkTZnZfpO9UM7vNzB4MX0+JHNtkZvvN7AEzu7Qqucom776FLCGtSkshhKiLKn0K1wNvaOr7MLDb3c8BdoefMbNRYC2wMhyz1cxmRbb/vBO49ikIIbqZKms0/yPQXCvscmBH+H4H8OZI/w3u/ry7PwTsBy6sSrYyyTuBa5+CEKKb6XSai9Pc/TCAux82s5eH/WcA/xw571DY1/U0Juo8+xaypJxQWgohRB10S+6juKKRsR5wM1sPrAdY0SVGdk3gQoheodP7FB43s2UA4esTYf8h4MzIecuBx+Iu4O7b3X3M3ceWLl1aqbBCCDHX6LRSuAlYF75fB3wx0r/WzBaY2VnAOcAdHZZNCCHmPJWZj8zsc8BFwBIzOwR8BLgauNHM3gs8DLwVwN33mtmNwD7gGHCluydUHhBCCFEVlSkFd397wqHVCedvARR0KYQQNaLcR0IIISaZ1WkuzOwIEJNkIjNLgKMliVMVkrEcJGM5SMZyqFvGYXePjdSZ1UqhXcxsT1L+j25BMpaDZCwHyVgO3SyjzEdCCCEmkVIQQggxyVxXCtvrFiADkrEcJGM5SMZy6FoZ57RPQQghxHTm+kpBCCFEhDmnFOKK/3QbZnammX3VzO43s71mdlXdMjVjZieZ2R1mdk8o48fqlikJM+s3s2+Z2c11y5KEmR0ws2+b2d1mVm85wQTM7GQz+xsz+074f/M1dcsUxczOC3+/Rvuhmb2/brmaMbMPhH8z95nZ58zspLplijLnzEdm9svAM8Bn3P0VdcsTR5gscJm732VmLwHuBN7s7vtqFm0SMzNgkbs/Y2YDwNeBq9z9n1OGdhwz+x1gDHipu7+pbnniMLMDwJi7d218vZntAP63u3/KzOYDg+7+/ZrFiiUs0vUo8PPu3s5eplIxszMI/lZG3f25ML3PLe5+fb2STTHnVgoJxX+6Cnc/7O53he+fBu6ny+pLeMAz4ceBsHXdE4aZLQfeCHyqbllmM2b2UuCXgWsB3P2FblUIIauB73aTQogwD1hoZvOAQRIyQtfFnFMKsw0zGwFeBXyzZlFmEJpl7iZIgX6bu3edjMAngA8BJ2qWIw0Hvmxmd4Y1Q7qNnwCOAJ8OTXGfMrNFdQvVgrXA5+oWohl3fxT4OEFC0MPAD9z9y/VKNR0phS7GzBYDnwfe7+4/rFueZtz9uLufT1D/4kIz6ypznJm9CXjC3e+sW5YMrHL3VwO/ClwZmjm7iXnAq4Ft7v4q4EeENda7jdC0dRnwP+uWpRkzO4Wg/PBZwOnAIjN7R71STUdKoUsJ7fSfBybc/Qt1y9OK0IzwNeAN9Uoyg1XAZaG9/gbgdWa2s16R4nH3x8LXJ4C/pftqlB8CDkVWg39DoCS6kV8F7nL3x+sWJIaLgYfc/Yi7vwh8AfjXNcs0DSmFLiR04l4L3O/uf1q3PHGY2VIzOzl8v5DgP/t3ahWqCXff5O7L3X2EwJzwFXfvqqcyADNbFAYUEJpkXg90VXScu/8/4BEzOy/sWk1Q/6QbeTtdaDoKeRj4BTMbDP/OVxP4DLuGOacUwuI/twPnmdmhsOBPt7EKeCfBk20jvG5N3UI1sQz4qpndC/wLgU+ha0M+u5zTgK+b2T0EFQf/zt1vrVmmOH4LmAj/zc8H/rBecWZiZoPAJQRP4F1HuNL6G+Au4NsEc3BX7W6ecyGpQgghkplzKwUhhBDJSCkIIYSYREpBCCHEJFIKQgghJpFSEEIIMYmUgpgzmNnxpiyahXfkmtk/lSlb07XHzOzPq7q+EK1QSKqYM5jZM+6+uG45hOhmtFIQc56wlsHHzOyusKbBT4X9S83strD/L83soJktCY89E75eZGZfi9QZmAh3qmJmF5jZP4RJ7r4UpkRvvvdbw7z695jZP0aueXP4/pbIyuYHZrYuTET4x2b2L2Z2r5ld0anfSvQ+UgpiLrGwyXz0byPHjoYJ6bYBHwz7PkKQGuPVBPmIViRc91XA+4FRgmyiq8LcVf8N+HV3vwC4DtgSM/b3gEvd/WcJkrhNw93XhEkH3wscBP5X+P4H7v5zwM8Bv2FmZ2X8DYRoyby6BRCigzwXTrBxNNIi3An8Wvj+F4G3ALj7rWb2vYSxd7j7IYAwlfgI8H3gFcBt4cKhnyBVcjPfAK4Pi63EpmYIVyefBd7m7j8ws9cDrzSzXw9PeRlwDvBQgnxCZEZKQYiA58PX40z9XVjOsdHxBux195YlK939fWb28wSFgO42s/Ojx8MKYjcAv+/ujSR5BvyWu38po3xCZEbmIyGS+TrwNoDw6fyUHGMfAJZaWMfYzAbMbGXzSWZ2trt/091/DzgKnNl0ytXAve5+Q6TvS8CG0ESFmZ3b5QVvxCxCKwUxl1gYmnca3OrurcJSPwZ8LvQ9/AOB+efpLDdy9xdC886fm9nLCP7WPgHsbTr1j83sHIKn/93APcCvRI5/ENgbkfv3CEqLjgB3hU7tI8Cbs8glRBoKSRUiATNbABx392PhE/+2Fj4JIXoCrRSESGYFcKOZ9QEvAL9RszxCVI5WCkIIISaRo1kIIcQkUgpCCCEmkVIQQggxiZSCEEKISaQUhBBCTCKlIIQQYpL/D/ZoRF15citXAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(cdf.ENGINESIZE, cdf.CO2EMISSIONS,  color='blue')\n",
    "plt.xlabel(\"Engine size\")\n",
    "plt.ylabel(\"Emission\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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=\"polynomial_regression\">Polynomial regression</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "Sometimes, the trend of data is not really linear, and looks curvy. In this case we can use Polynomial regression methods. In fact, many different regressions exist that can be used to fit whatever the dataset looks like, such as quadratic, cubic, and so on, and it can go on and on to infinite degrees.\n",
    "\n",
    "In essence, we can call all of these, polynomial regression, where the relationship between the independent variable x and the dependent variable y is modeled as an nth degree polynomial in x. Lets say you want to have a polynomial regression (let's make 2 degree polynomial):\n",
    "\n",
    "$$y = b + \\theta\\_1  x + \\theta\\_2 x^2$$\n",
    "\n",
    "Now, the question is: how we can fit our data on this equation while we have only x values, such as **Engine Size**?\n",
    "Well, we can create a few additional features: 1, $x$, and $x^2$.\n",
    "\n",
    "**PolynomialFeatures()** function in Scikit-learn library, drives a new feature sets from the original feature set. That is, a matrix will be generated consisting of all polynomial combinations of the features with degree less than or equal to the specified degree. For example, lets say the original feature set has only one feature, *ENGINESIZE*. Now, if we select the degree of the polynomial to be 2, then it generates 3 features, degree=0, degree=1 and degree=2:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.  ,  2.  ,  4.  ],\n",
       "       [ 1.  ,  2.4 ,  5.76],\n",
       "       [ 1.  ,  1.5 ,  2.25],\n",
       "       ...,\n",
       "       [ 1.  ,  3.2 , 10.24],\n",
       "       [ 1.  ,  3.2 , 10.24],\n",
       "       [ 1.  ,  3.2 , 10.24]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn import linear_model\n",
    "train_x = np.asanyarray(train[['ENGINESIZE']])\n",
    "train_y = np.asanyarray(train[['CO2EMISSIONS']])\n",
    "\n",
    "test_x = np.asanyarray(test[['ENGINESIZE']])\n",
    "test_y = np.asanyarray(test[['CO2EMISSIONS']])\n",
    "\n",
    "\n",
    "poly = PolynomialFeatures(degree=2)\n",
    "train_x_poly = poly.fit_transform(train_x)\n",
    "train_x_poly"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**fit_transform** takes our x values, and output a list of our data raised from power of 0 to power of 2 (since we set the degree of our polynomial to 2).\n",
    "\n",
    "The equation and the sample example is displayed below.\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "v\\_1\\\\\\\\\n",
    "v\\_2\\\\\\\\\n",
    "\\vdots\\\\\\\\\n",
    "v_n\n",
    "\\end{bmatrix}\\longrightarrow \\begin{bmatrix}\n",
    "\\[ 1 & v\\_1 & v\\_1^2]\\\\\\\\\n",
    "\\[ 1 & v\\_2 & v\\_2^2]\\\\\\\\\n",
    "\\vdots & \\vdots & \\vdots\\\\\\\\\n",
    "\\[ 1 & v_n & v_n^2]\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "2.\\\\\\\\\n",
    "2.4\\\\\\\\\n",
    "1.5\\\\\\\\\n",
    "\\vdots\n",
    "\\end{bmatrix} \\longrightarrow \\begin{bmatrix}\n",
    "\\[ 1 & 2. & 4.]\\\\\\\\\n",
    "\\[ 1 & 2.4 & 5.76]\\\\\\\\\n",
    "\\[ 1 & 1.5 & 2.25]\\\\\\\\\n",
    "\\vdots & \\vdots & \\vdots\\\\\\\\\n",
    "\\end{bmatrix}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It looks like feature sets for multiple linear regression analysis, right? Yes. It Does.\n",
    "Indeed, Polynomial regression is a special case of linear regression, with the main idea of how do you select your features. Just consider replacing the  $x$ with $x\\_1$, $x\\_1^2$ with $x\\_2$, and so on. Then the degree 2 equation would be turn into:\n",
    "\n",
    "$$y = b + \\theta\\_1  x\\_1 + \\theta\\_2 x\\_2$$\n",
    "\n",
    "Now, we can deal with it as 'linear regression' problem. Therefore, this polynomial regression is considered to be a special case of traditional multiple linear regression. So, you can use the same mechanism as linear regression to solve such a problems.\n",
    "\n",
    "so we can use **LinearRegression()** function to solve it:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients:  [[ 0.         49.76104156 -1.36458607]]\n",
      "Intercept:  [107.91670838]\n"
     ]
    }
   ],
   "source": [
    "clf = linear_model.LinearRegression()\n",
    "train_y_ = clf.fit(train_x_poly, train_y)\n",
    "# The coefficients\n",
    "print ('Coefficients: ', clf.coef_)\n",
    "print ('Intercept: ',clf.intercept_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As mentioned before, **Coefficient** and **Intercept** , are the parameters of the fit curvy line.\n",
    "Given that it is a typical multiple linear regression, with 3 parameters, and knowing that the parameters are the intercept and coefficients of hyperplane, sklearn has estimated them from our new set of feature sets. Lets plot it:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Emission')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(train.ENGINESIZE, train.CO2EMISSIONS,  color='blue')\n",
    "XX = np.arange(0.0, 10.0, 0.1)\n",
    "yy = clf.intercept_[0]+ clf.coef_[0][1]*XX+ clf.coef_[0][2]*np.power(XX, 2)\n",
    "plt.plot(XX, yy, '-r' )\n",
    "plt.xlabel(\"Engine size\")\n",
    "plt.ylabel(\"Emission\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "<h2 id=\"evaluation\">Evaluation</h2>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean absolute error: 22.15\n",
      "Residual sum of squares (MSE): 888.11\n",
      "R2-score: 0.76\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import r2_score\n",
    "\n",
    "test_x_poly = poly.fit_transform(test_x)\n",
    "test_y_ = clf.predict(test_x_poly)\n",
    "\n",
    "print(\"Mean absolute error: %.2f\" % np.mean(np.absolute(test_y_ - test_y)))\n",
    "print(\"Residual sum of squares (MSE): %.2f\" % np.mean((test_y_ - test_y) ** 2))\n",
    "print(\"R2-score: %.2f\" % r2_score(test_y,test_y_ ) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"practice\">Practice</h2>\n",
    "Try to use a polynomial regression with the dataset but this time with degree three (cubic). Does it result in better accuracy?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients:  [[ 0.         24.54620384  5.55976164 -0.57088268]]\n",
      "Intercept:  [134.67759623]\n",
      "Mean absolute error: 22.29\n",
      "Residual sum of squares (MSE): 894.37\n",
      "R2-score: 0.75\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "poly3 = PolynomialFeatures(degree=3)\n",
    "train_x_poly3 = poly3.fit_transform(train_x)\n",
    "clf3 = linear_model.LinearRegression()\n",
    "train_y3_ = clf3.fit(train_x_poly3, train_y)\n",
    "\n",
    "# The coefficients\n",
    "print ('Coefficients: ', clf3.coef_)\n",
    "print ('Intercept: ',clf3.intercept_)\n",
    "plt.scatter(train.ENGINESIZE, train.CO2EMISSIONS,  color='blue')\n",
    "XX = np.arange(0.0, 10.0, 0.1)\n",
    "yy = clf3.intercept_[0]+ clf3.coef_[0][1]*XX + clf3.coef_[0][2]*np.power(XX, 2) + clf3.coef_[0][3]*np.power(XX, 3)\n",
    "plt.plot(XX, yy, '-r' )\n",
    "plt.xlabel(\"Engine size\")\n",
    "plt.ylabel(\"Emission\")\n",
    "test_x_poly3 = poly3.fit_transform(test_x)\n",
    "test_y3_ = clf3.predict(test_x_poly3)\n",
    "print(\"Mean absolute error: %.2f\" % np.mean(np.absolute(test_y3_ - test_y)))\n",
    "print(\"Residual sum of squares (MSE): %.2f\" % np.mean((test_y3_ - test_y) ** 2))\n",
    "print(\"R2-score: %.2f\" % r2_score(test_y,test_y3_ ) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "poly3 = PolynomialFeatures(degree=3)\n",
    "train_x_poly3 = poly3.fit_transform(train_x)\n",
    "clf3 = linear_model.LinearRegression()\n",
    "train_y3_ = clf3.fit(train_x_poly3, train_y)\n",
    "\n",
    "# The coefficients\n",
    "print ('Coefficients: ', clf3.coef_)\n",
    "print ('Intercept: ',clf3.intercept_)\n",
    "plt.scatter(train.ENGINESIZE, train.CO2EMISSIONS,  color='blue')\n",
    "XX = np.arange(0.0, 10.0, 0.1)\n",
    "yy = clf3.intercept_[0]+ clf3.coef_[0][1]*XX + clf3.coef_[0][2]*np.power(XX, 2) + clf3.coef_[0][3]*np.power(XX, 3)\n",
    "plt.plot(XX, yy, '-r' )\n",
    "plt.xlabel(\"Engine size\")\n",
    "plt.ylabel(\"Emission\")\n",
    "test_x_poly3 = poly3.fit_transform(test_x)\n",
    "test_y3_ = clf3.predict(test_x_poly3)\n",
    "print(\"Mean absolute error: %.2f\" % np.mean(np.absolute(test_y3_ - test_y)))\n",
    "print(\"Residual sum of squares (MSE): %.2f\" % np.mean((test_y3_ - test_y) ** 2))\n",
    "print(\"R2-score: %.2f\" % r2_score(test_y,test_y3_ ) )\n",
    "\n",
    "```\n",
    "\n",
    "</details>\n"
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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=\"https://www.ibm.com/analytics/spss-statistics-software?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkML0101ENSkillsNetwork20718538-2021-01-01\">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://www.ibm.com/cloud/watson-studio?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkML0101ENSkillsNetwork20718538-2021-01-01\">Watson Studio</a>\n"
   ]
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   "source": [
    "### Thank you for completing this lab!\n",
    "\n",
    "## Author\n",
    "\n",
    "Saeed Aghabozorgi\n",
    "\n",
    "### Other Contributors\n",
    "\n",
    "<a href=\"https://www.linkedin.com/in/joseph-s-50398b136/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkML0101ENSkillsNetwork20718538-2021-01-01\" target=\"_blank\">Joseph Santarcangelo</a>\n",
    "\n",
    "## Change Log\n",
    "\n",
    "| Date (YYYY-MM-DD) | Version | Changed By | Change Description                                    |\n",
    "| ----------------- | ------- | ---------- | ----------------------------------------------------- |\n",
    "| 2021-01-11        | 2.3     | Lakshmi    | Changed R2-score calculation in polynomial regression |\n",
    "| 2020-11-04        | 2.2     | Lakshmi    | Made changes in markdown of equations                 |\n",
    "| 2020-11-03        | 2.1     | Lakshmi    | Made changes in URL                                   |\n",
    "| 2020-08-27        | 2.0     | Lavanya    | Moved lab to course repo in GitLab                    |\n",
    "|                   |         |            |                                                       |\n",
    "|                   |         |            |                                                       |\n",
    "\n",
    "## <h3 align=\"center\"> © IBM Corporation 2020. All rights reserved. <h3/>\n"
   ]
  }
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