ML0101EN-Reg-Polynomial-Regression-Co2-py-v1.ipynb

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   "source": [
    "<a href=\"https://www.bigdatauniversity.com\"><img src=\"https://ibm.box.com/shared/static/cw2c7r3o20w9zn8gkecaeyjhgw3xdgbj.png\" width=\"400\" align=\"center\"></a>\n",
    "\n",
    "<h1><center>Polynomial Regression</center></h1>\n",
    "\n",
    "<h4>About this Notebook</h4>\n",
    "In this notebook, we learn how to use scikit-learn for Polynomial regression. We download a dataset that is related to fuel consumption and Carbon dioxide emission of cars. Then, we split our data into training and test sets, create a model using training set, evaluate our model using test set, and finally use model to predict unknown value."
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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>"
   ]
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   "source": [
    "### Importing Needed packages"
   ]
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   "source": [
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import pylab as pl\n",
    "import numpy as np\n",
    "%matplotlib inline"
   ]
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   "source": [
    "<h2 id=\"download_data\">Downloading Data</h2>\n",
    "To download the data, we will use !wget to download it from IBM Object Storage."
   ]
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     "text": [
      "--2020-04-11 13:45:05--  https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/ML0101ENv3/labs/FuelConsumptionCo2.csv\n",
      "Resolving s3-api.us-geo.objectstorage.softlayer.net (s3-api.us-geo.objectstorage.softlayer.net)... 67.228.254.196\n",
      "Connecting to s3-api.us-geo.objectstorage.softlayer.net (s3-api.us-geo.objectstorage.softlayer.net)|67.228.254.196|: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",
      "2020-04-11 13:45:05 (1.10 MB/s) - ‘FuelConsumption.csv’ saved [72629/72629]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "!wget -O FuelConsumption.csv https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/ML0101ENv3/labs/FuelConsumptionCo2.csv"
   ]
  },
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   "cell_type": "markdown",
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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](http://cocl.us/ML0101EN-IBM-Offer-CC)"
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    "\n",
    "## Understanding the Data\n",
    "\n",
    "### `FuelConsumption.csv`:\n",
    "We have downloaded a fuel consumption dataset, **`FuelConsumption.csv`**, which contains model-specific fuel consumption ratings and estimated carbon dioxide emissions for new light-duty vehicles for retail sale in Canada. [Dataset source](http://open.canada.ca/data/en/dataset/98f1a129-f628-4ce4-b24d-6f16bf24dd64)\n",
    "\n",
    "- **MODELYEAR** e.g. 2014\n",
    "- **MAKE** e.g. Acura\n",
    "- **MODEL** e.g. ILX\n",
    "- **VEHICLE CLASS** e.g. SUV\n",
    "- **ENGINE SIZE** e.g. 4.7\n",
    "- **CYLINDERS** e.g 6\n",
    "- **TRANSMISSION** e.g. A6\n",
    "- **FUEL CONSUMPTION in CITY(L/100 km)** e.g. 9.9\n",
    "- **FUEL CONSUMPTION in HWY (L/100 km)** e.g. 8.9\n",
    "- **FUEL CONSUMPTION COMB (L/100 km)** e.g. 9.2\n",
    "- **CO2 EMISSIONS (g/km)** e.g. 182   --> low --> 0\n"
   ]
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   "source": [
    "## Reading the data in"
   ]
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>MODELYEAR</th>\n",
       "      <th>MAKE</th>\n",
       "      <th>MODEL</th>\n",
       "      <th>VEHICLECLASS</th>\n",
       "      <th>ENGINESIZE</th>\n",
       "      <th>CYLINDERS</th>\n",
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       "      <th>FUELCONSUMPTION_COMB_MPG</th>\n",
       "      <th>CO2EMISSIONS</th>\n",
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       "      <th>0</th>\n",
       "      <td>2014</td>\n",
       "      <td>ACURA</td>\n",
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       "      <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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       "      <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",
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       "      <td>ACURA</td>\n",
       "      <td>MDX 4WD</td>\n",
       "      <td>SUV - SMALL</td>\n",
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       "      <td>6</td>\n",
       "      <td>AS6</td>\n",
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       "      <td>12.7</td>\n",
       "      <td>9.1</td>\n",
       "      <td>11.1</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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      "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": [
    "Lets select some features that we want to use for regression."
   ]
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       "      <th>CO2EMISSIONS</th>\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,
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   ],
   "source": [
    "cdf = df[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_COMB','CO2EMISSIONS']]\n",
    "cdf.head(9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets plot Emission values with respect to Engine size:"
   ]
  },
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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,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "#### Creating train and test dataset\n",
    "Train/Test Split involves splitting the dataset into training and testing sets respectively, which are mutually exclusive. After which, you train with the training set and test with the testing set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "button": false,
    "deletable": true,
    "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,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "<h2 id=\"polynomial_regression\">Polynomial regression</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "deletable": true,
    "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",
    "\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",
    "\n",
    "\n",
    "__PloynomialFeatures()__ 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: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.  ,  2.  ,  4.  ],\n",
       "       [ 1.  ,  2.4 ,  5.76],\n",
       "       [ 1.  ,  3.5 , 12.25],\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",
    "$\n",
    "\\begin{bmatrix}\n",
    "    v_1\\\\\n",
    "    v_2\\\\\n",
    "    \\vdots\\\\\n",
    "    v_n\n",
    "\\end{bmatrix}\n",
    "$\n",
    "$\\longrightarrow$\n",
    "$\n",
    "\\begin{bmatrix}\n",
    "    [ 1 & v_1 & v_1^2]\\\\\n",
    "    [ 1 & v_2 & v_2^2]\\\\\n",
    "    \\vdots & \\vdots & \\vdots\\\\\n",
    "    [ 1 & v_n & v_n^2]\n",
    "\\end{bmatrix}\n",
    "$\n",
    "\n",
    "in our example\n",
    "\n",
    "$\n",
    "\\begin{bmatrix}\n",
    "    2.\\\\\n",
    "    2.4\\\\\n",
    "    1.5\\\\\n",
    "    \\vdots\n",
    "\\end{bmatrix}\n",
    "$\n",
    "$\\longrightarrow$\n",
    "$\n",
    "\\begin{bmatrix}\n",
    "    [ 1 & 2. & 4.]\\\\\n",
    "    [ 1 & 2.4 & 5.76]\\\\\n",
    "    [ 1 & 1.5 & 2.25]\\\\\n",
    "    \\vdots & \\vdots & \\vdots\\\\\n",
    "\\end{bmatrix}\n",
    "$"
   ]
  },
  {
   "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",
    "\n",
    "\n",
    "so we can use __LinearRegression()__ function to solve it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients:  [[ 0.         47.86099788 -1.17509286]]\n",
      "Intercept:  [112.62551831]\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:"
   ]
  },
  {
   "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,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "<h2 id=\"evaluation\">Evaluation</h2>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean absolute error: 23.03\n",
      "Residual sum of squares (MSE): 944.67\n",
      "R2-score: 0.67\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?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "# write your code here\n",
    "msk = np.random.rand(len(cdf)) < 0.8\n",
    "train1 = cdf[msk]\n",
    "test1 = cdf[~msk]\n",
    "\n",
    "train1_x = np.asanyarray(train1[['ENGINESIZE']])\n",
    "train1_y = np.asanyarray(train1[['CO2EMISSIONS']])\n",
    "\n",
    "test_x = np.asanyarray(test[['ENGINESIZE']])\n",
    "test_y = np.asanyarray(test[['CO2EMISSIONS']])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coeff:  [[ 0.         27.32662937  5.17957072 -0.57331487]]\n",
      "Intercept:  [130.63527049]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn import linear_model\n",
    "\n",
    "clf = PolynomialFeatures(degree=3)\n",
    "train_poly_x = clf.fit_transform(train1_x)\n",
    "train_poly_x\n",
    "regr = linear_model.LinearRegression()\n",
    "train_poly_y = regr.fit(train_poly_x,train1_y)\n",
    "\n",
    "print(\"Coeff: \",train_poly_y.coef_)\n",
    "print(\"Intercept: \",train_poly_y.intercept_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(train1_x,train1_y,color='red')\n",
    "plt.xlabel(\"ENGINESIZE\")\n",
    "plt.ylabel(\"CO2EMISSIONS\")\n",
    "xx = np.arange(0.0,10.0,0.1)\n",
    "yy = train_poly_y.intercept_[0]+train_poly_y.coef_[0][1]*xx+train_poly_y.coef_[0][2]*np.power(xx,2)\n",
    "plt.plot(xx,yy,color='blue')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MAE:  1.0785433713411694\n",
      "MSE: 918.00\n",
      "R2_score:  0.9994427882556282\n"
     ]
    }
   ],
   "source": [
    "test1_x = test[['ENGINESIZE']]\n",
    "test1_x_ploy = clf.fit_transform(test1_x)\n",
    "y_hat = regr.predict(test1_x_ploy)\n",
    "\n",
    "print(\"MAE: \",np.mean(np.absolute(y_hat-test1_y)))\n",
    "print(\"MSE: %.2f\" %np.mean((y_hat-test_y)**2))\n",
    "print(\"R2_score: \",r2_score(y_hat,test1_y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click __here__ for the solution.\n",
    "\n",
    "<!-- Your answer is below:\n",
    "\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",
    "# 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_y3_ , test_y) )\n",
    "\n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients:  [[ 0.         27.32662937  5.17957072 -0.57331487]]\n",
      "Intercept:  [130.63527049]\n",
      "Mean absolute error: 1.08\n",
      "Residual sum of squares (MSE): 1.60\n",
      "R2-score: 1.00\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(train1_x)\n",
    "clf3 = linear_model.LinearRegression()\n",
    "train_y3_ = clf3.fit(train_x_poly3, train1_y)\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(test1_x)\n",
    "test_y3_ = clf3.predict(test_x_poly3)\n",
    "print(\"Mean absolute error: %.2f\" % np.mean(np.absolute(test_y3_ - test1_y)))\n",
    "print(\"Residual sum of squares (MSE): %.2f\" % np.mean((test_y3_ - test1_y) ** 2))\n",
    "print(\"R2-score: %.2f\" % r2_score(test_y3_ , test1_y) )\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "<h2>Want to learn more?</h2>\n",
    "\n",
    "IBM SPSS Modeler is a comprehensive analytics platform that has many machine learning algorithms. It has been designed to bring predictive intelligence to decisions made by individuals, by groups, by systems – by your enterprise as a whole. A free trial is available through this course, available here: <a href=\"http://cocl.us/ML0101EN-SPSSModeler\">SPSS Modeler</a>\n",
    "\n",
    "Also, you can use Watson Studio to run these notebooks faster with bigger datasets. Watson Studio is IBM's leading cloud solution for data scientists, built by data scientists. With Jupyter notebooks, RStudio, Apache Spark and popular libraries pre-packaged in the cloud, Watson Studio enables data scientists to collaborate on their projects without having to install anything. Join the fast-growing community of Watson Studio users today with a free account at <a href=\"https://cocl.us/ML0101EN_DSX\">Watson Studio</a>\n",
    "\n",
    "<h3>Thanks for completing this lesson!</h3>\n",
    "\n",
    "<h4>Author:  <a href=\"https://ca.linkedin.com/in/saeedaghabozorgi\">Saeed Aghabozorgi</a></h4>\n",
    "<p><a href=\"https://ca.linkedin.com/in/saeedaghabozorgi\">Saeed Aghabozorgi</a>, PhD is a Data Scientist in IBM with a track record of developing enterprise level applications that substantially increases clients’ ability to turn data into actionable knowledge. He is a researcher in data mining field and expert in developing advanced analytic methods like machine learning and statistical modelling on large datasets.</p>\n",
    "\n",
    "<hr>\n",
    "\n",
    "<p>Copyright &copy; 2018 <a href=\"https://cocl.us/DX0108EN_CC\">Cognitive Class</a>. This notebook and its source code are released under the terms of the <a href=\"https://bigdatauniversity.com/mit-license/\">MIT License</a>.</p>"
   ]
  }
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