Polynomial Regression.ipynb

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    "\n",
    "# Polynomial Regression\n",
    "\n",
    "\n",
    "\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\n"
   ]
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   "source": [
    "<h2 id=\"download_data\">Downloading Data</h2>\n",
    "For downloading the data, we will use !wget to download it from IBM Object Storage.\n"
   ]
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      "--2021-12-11 01:37:09--  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 0.001s  \n",
      "\n",
      "2021-12-11 01:37:10 (109 MB/s) - ‘FuelConsumption.csv’ saved [72629/72629]\n",
      "\n"
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   "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": [
    "## 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 \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",
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       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2014</td>\n",
       "      <td>ACURA</td>\n",
       "      <td>ILX</td>\n",
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       "      <td>2.0</td>\n",
       "      <td>4</td>\n",
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       "      <td>ACURA</td>\n",
       "      <td>ILX</td>\n",
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       "      <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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       "      <th>2</th>\n",
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       "      <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",
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       "      <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",
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       "   MODELYEAR   MAKE       MODEL VEHICLECLASS  ENGINESIZE  CYLINDERS  \\\n",
       "0       2014  ACURA         ILX      COMPACT         2.0          4   \n",
       "1       2014  ACURA         ILX      COMPACT         2.4          4   \n",
       "2       2014  ACURA  ILX HYBRID      COMPACT         1.5          4   \n",
       "3       2014  ACURA     MDX 4WD  SUV - SMALL         3.5          6   \n",
       "4       2014  ACURA     RDX AWD  SUV - SMALL         3.5          6   \n",
       "\n",
       "  TRANSMISSION FUELTYPE  FUELCONSUMPTION_CITY  FUELCONSUMPTION_HWY  \\\n",
       "0          AS5        Z                   9.9                  6.7   \n",
       "1           M6        Z                  11.2                  7.7   \n",
       "2          AV7        Z                   6.0                  5.8   \n",
       "3          AS6        Z                  12.7                  9.1   \n",
       "4          AS6        Z                  12.1                  8.7   \n",
       "\n",
       "   FUELCONSUMPTION_COMB  FUELCONSUMPTION_COMB_MPG  CO2EMISSIONS  \n",
       "0                   8.5                        33           196  \n",
       "1                   9.6                        29           221  \n",
       "2                   5.9                        48           136  \n",
       "3                  11.1                        25           255  \n",
       "4                  10.6                        27           244  "
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   "source": [
    "df = pd.read_csv(\"FuelConsumption.csv\")\n",
    "\n",
    "# take a look at the dataset\n",
    "df.head()"
   ]
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   "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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       "      <td>3.7</td>\n",
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      "text/plain": [
       "   ENGINESIZE  CYLINDERS  FUELCONSUMPTION_COMB  CO2EMISSIONS\n",
       "0         2.0          4                   8.5           196\n",
       "1         2.4          4                   9.6           221\n",
       "2         1.5          4                   5.9           136\n",
       "3         3.5          6                  11.1           255\n",
       "4         3.5          6                  10.6           244\n",
       "5         3.5          6                  10.0           230\n",
       "6         3.5          6                  10.1           232\n",
       "7         3.7          6                  11.1           255\n",
       "8         3.7          6                  11.6           267"
      ]
     },
     "execution_count": 4,
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   ],
   "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"
   ]
  },
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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, we 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": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/least_angle.py:35: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  eps=np.finfo(np.float).eps,\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/least_angle.py:597: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  eps=np.finfo(np.float).eps, copy_X=True, fit_path=True,\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/least_angle.py:836: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  eps=np.finfo(np.float).eps, copy_X=True, fit_path=True,\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/least_angle.py:862: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  eps=np.finfo(np.float).eps, positive=False):\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/least_angle.py:1097: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  max_n_alphas=1000, n_jobs=None, eps=np.finfo(np.float).eps,\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/least_angle.py:1344: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  max_n_alphas=1000, n_jobs=None, eps=np.finfo(np.float).eps,\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/least_angle.py:1480: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  eps=np.finfo(np.float).eps, copy_X=True, positive=False):\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/randomized_l1.py:152: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  precompute=False, eps=np.finfo(np.float).eps,\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/randomized_l1.py:320: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  eps=np.finfo(np.float).eps, random_state=None,\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/randomized_l1.py:580: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  eps=4 * np.finfo(np.float).eps, n_jobs=None,\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[ 1.  ,  2.  ,  4.  ],\n",
       "       [ 1.  ,  1.5 ,  2.25],\n",
       "       [ 1.  ,  3.5 , 12.25],\n",
       "       ...,\n",
       "       [ 1.  ,  3.2 , 10.24],\n",
       "       [ 1.  ,  3.  ,  9.  ],\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 we select our features. Just consider replacing the  $x$ with $x\\_1$, $x\\_1^2$ with $x\\_2$, and so on. Then the 2nd degree 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 a 'linear regression' problem. Therefore, this polynomial regression is considered to be a special case of traditional multiple linear regression. So, we can use the same mechanism as linear regression to solve such 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.         51.47535133 -1.62190874]]\n",
      "Intercept:  [105.95053731]\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: 22.62\n",
      "Residual sum of squares (MSE): 853.54\n",
      "R2-score: 0.73\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import r2_score\n",
    "\n",
    "test_x_poly = poly.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": [
    "\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.         32.316066    3.63953436 -0.43408934]]\n",
      "Intercept:  [126.26673178]\n",
      "Mean absolute error: 22.51\n",
      "Residual sum of squares (MSE): 848.57\n",
      "R2-score: 0.74\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.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"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  },
  "widgets": {
   "state": {},
   "version": "1.1.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}