ML0101EN-Reg-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=\"#download_data\">Downloading Data</a></li>\n",
    "        <li><a href=\"#polynomial_regression\">Polynomial regression</a></li>\n",
    "        <li><a href=\"#evaluation\">Evaluation</a></li>\n",
    "        <li><a href=\"#practice\">Practice</a></li>\n",
    "    </ol>\n",
    "</div>\n",
    "<br>\n",
    "<hr>\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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      "--2021-07-13 05:15:29--  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 0.01s   \n",
      "\n",
      "2021-07-13 05:15:29 (7.14 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",
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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",
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       "      <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",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2014</td>\n",
       "      <td>ACURA</td>\n",
       "      <td>MDX 4WD</td>\n",
       "      <td>SUV - SMALL</td>\n",
       "      <td>3.5</td>\n",
       "      <td>6</td>\n",
       "      <td>AS6</td>\n",
       "      <td>Z</td>\n",
       "      <td>12.7</td>\n",
       "      <td>9.1</td>\n",
       "      <td>11.1</td>\n",
       "      <td>25</td>\n",
       "      <td>255</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2014</td>\n",
       "      <td>ACURA</td>\n",
       "      <td>RDX AWD</td>\n",
       "      <td>SUV - SMALL</td>\n",
       "      <td>3.5</td>\n",
       "      <td>6</td>\n",
       "      <td>AS6</td>\n",
       "      <td>Z</td>\n",
       "      <td>12.1</td>\n",
       "      <td>8.7</td>\n",
       "      <td>10.6</td>\n",
       "      <td>27</td>\n",
       "      <td>244</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "   MODELYEAR   MAKE       MODEL VEHICLECLASS  ENGINESIZE  CYLINDERS  \\\n",
       "0       2014  ACURA         ILX      COMPACT         2.0          4   \n",
       "1       2014  ACURA         ILX      COMPACT         2.4          4   \n",
       "2       2014  ACURA  ILX HYBRID      COMPACT         1.5          4   \n",
       "3       2014  ACURA     MDX 4WD  SUV - SMALL         3.5          6   \n",
       "4       2014  ACURA     RDX AWD  SUV - SMALL         3.5          6   \n",
       "\n",
       "  TRANSMISSION FUELTYPE  FUELCONSUMPTION_CITY  FUELCONSUMPTION_HWY  \\\n",
       "0          AS5        Z                   9.9                  6.7   \n",
       "1           M6        Z                  11.2                  7.7   \n",
       "2          AV7        Z                   6.0                  5.8   \n",
       "3          AS6        Z                  12.7                  9.1   \n",
       "4          AS6        Z                  12.1                  8.7   \n",
       "\n",
       "   FUELCONSUMPTION_COMB  FUELCONSUMPTION_COMB_MPG  CO2EMISSIONS  \n",
       "0                   8.5                        33           196  \n",
       "1                   9.6                        29           221  \n",
       "2                   5.9                        48           136  \n",
       "3                  11.1                        25           255  \n",
       "4                  10.6                        27           244  "
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     "execution_count": 3,
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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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       "      <th>1</th>\n",
       "      <td>2.4</td>\n",
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       "      <td>9.6</td>\n",
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       "      <th>2</th>\n",
       "      <td>1.5</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3.5</td>\n",
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       "      <th>5</th>\n",
       "      <td>3.5</td>\n",
       "      <td>6</td>\n",
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       "      <td>230</td>\n",
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       "      <th>6</th>\n",
       "      <td>3.5</td>\n",
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       "      <th>7</th>\n",
       "      <td>3.7</td>\n",
       "      <td>6</td>\n",
       "      <td>11.1</td>\n",
       "      <td>255</td>\n",
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       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>3.7</td>\n",
       "      <td>6</td>\n",
       "      <td>11.6</td>\n",
       "      <td>267</td>\n",
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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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\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.  ,  9.  ],\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.         48.42824092 -1.1979177 ]]\n",
      "Intercept:  [110.20331477]\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": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean absolute error: 22.30\n",
      "Residual sum of squares (MSE): 854.88\n",
      "R2-score: 0.77\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": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients:  [[ 0.         26.08915091  5.05704084 -0.52823787]]\n",
      "Intercept:  [133.59451609]\n",
      "Mean absolute error: 22.23\n",
      "Residual sum of squares (MSE): 849.78\n"
     ]
    },
    {
     "ename": "NameError",
     "evalue": "name 'r2_score' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-11-78216ae87c46>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     18\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Mean absolute error: %.2f\"\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmean\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mabsolute\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtest_y3_\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mtest_y\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     19\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Residual sum of squares (MSE): %.2f\"\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmean\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtest_y3_\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mtest_y\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m**\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 20\u001b[0;31m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"R2-score: %.2f\"\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0mr2_score\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtest_y\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mtest_y3_\u001b[0m \u001b[0;34m)\u001b[0m \u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'r2_score' is not defined"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# write your code here\n",
    "poly3 = PolynomialFeatures(degree=3)\n",
    "train_x_poly3 = poly3.fit_transform(train_x)\n",
    "clf3 = linear_model.LinearRegression()\n",
    "train_y3_ = clf3.fit(train_x_poly3, train_y)\n",
    "\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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