3_done_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=\"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\n"
      ]
    },
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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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            "--2022-02-22 06:09:18--  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 0.004s  \n",
            "\n",
            "2022-02-22 06:09:18 (19.7 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": [
        "**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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      "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 in\n"
      ]
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              "      <th></th>\n",
              "      <th>MODELYEAR</th>\n",
              "      <th>MAKE</th>\n",
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              "      <th>ENGINESIZE</th>\n",
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              "      <th>FUELTYPE</th>\n",
              "      <th>FUELCONSUMPTION_CITY</th>\n",
              "      <th>FUELCONSUMPTION_HWY</th>\n",
              "      <th>FUELCONSUMPTION_COMB</th>\n",
              "      <th>FUELCONSUMPTION_COMB_MPG</th>\n",
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              "      <th>0</th>\n",
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              "      <td>2.0</td>\n",
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              "      <td>Z</td>\n",
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              "      <td>4</td>\n",
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              "      <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",
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              "   MODELYEAR   MAKE  ... FUELCONSUMPTION_COMB_MPG CO2EMISSIONS\n",
              "0       2014  ACURA  ...                       33          196\n",
              "1       2014  ACURA  ...                       29          221\n",
              "2       2014  ACURA  ...                       48          136\n",
              "3       2014  ACURA  ...                       25          255\n",
              "4       2014  ACURA  ...                       27          244\n",
              "\n",
              "[5 rows x 13 columns]"
            ]
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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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      "source": [
        "Let's select some features that we want to use for regression.\n"
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              "      <td>3.7</td>\n",
              "      <td>6</td>\n",
              "      <td>11.1</td>\n",
              "      <td>255</td>\n",
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              "      <th>8</th>\n",
              "      <td>3.7</td>\n",
              "      <td>6</td>\n",
              "      <td>11.6</td>\n",
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              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-ba562853-5632-4c30-94f5-363b9f8ebe19 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-ba562853-5632-4c30-94f5-363b9f8ebe19');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "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"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ],
      "source": [
        "cdf = df[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_COMB','CO2EMISSIONS']]\n",
        "cdf.head(9)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GlX89XFXJ_7K"
      },
      "source": [
        "Let's plot Emission values with respect to Engine size:\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "button": false,
        "new_sheet": false,
        "run_control": {
          "read_only": false
        },
        "scrolled": true,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 280
        },
        "id": "Ym0Yk1SYJ_7K",
        "outputId": "018d0aaa-a675-4625-d97a-775aa16c94d3"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "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
        },
        "id": "0RZBL9SkJ_7L"
      },
      "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": 11,
      "metadata": {
        "button": false,
        "new_sheet": false,
        "run_control": {
          "read_only": false
        },
        "id": "wuAffcAyJ_7L"
      },
      "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
        },
        "id": "bvnh3eTuJ_7L"
      },
      "source": [
        "<h2 id=\"polynomial_regression\">Polynomial regression</h2>\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "button": false,
        "new_sheet": false,
        "run_control": {
          "read_only": false
        },
        "id": "t3JYyjaQJ_7L"
      },
      "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": 12,
      "metadata": {
        "button": false,
        "new_sheet": false,
        "run_control": {
          "read_only": false
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ixIkmXlTJ_7M",
        "outputId": "a4c9d2b7-9fc9-4dc0-c488-a3408e28640f"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1.  ,  2.  ,  4.  ],\n",
              "       [ 1.  ,  2.4 ,  5.76],\n",
              "       [ 1.  ,  3.5 , 12.25],\n",
              "       ...,\n",
              "       [ 1.  ,  3.  ,  9.  ],\n",
              "       [ 1.  ,  3.  ,  9.  ],\n",
              "       [ 1.  ,  3.2 , 10.24]])"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ],
      "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\n",
        "#train_x.tail\n",
        "#type(train_x_poly)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "train_x_polytr = poly.transform(train_x)\n",
        "train_x_polytr"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GyUKJX5R316v",
        "outputId": "84590b82-8742-4f8b-f768-4d62eee49000"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1.  ,  2.  ,  4.  ],\n",
              "       [ 1.  ,  2.4 ,  5.76],\n",
              "       [ 1.  ,  3.5 , 12.25],\n",
              "       ...,\n",
              "       [ 1.  ,  3.  ,  9.  ],\n",
              "       [ 1.  ,  3.  ,  9.  ],\n",
              "       [ 1.  ,  3.2 , 10.24]])"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PMaq3RU2J_7M"
      },
      "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": {
        "id": "AkiEMkqeJ_7M"
      },
      "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 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, you 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": 14,
      "metadata": {
        "button": false,
        "new_sheet": false,
        "run_control": {
          "read_only": false
        },
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Fo-96T9-J_7M",
        "outputId": "8965afac-e76e-42d1-9795-ff338e70c868"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Coefficients:  [[ 0.         51.99903023 -1.76148181]]\n",
            "Intercept:  [105.18546137]\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": {
        "id": "zboUrCXsJ_7N"
      },
      "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",
      "source": [
        "aaa = [1, 3, 2]\n",
        "aaa.sort()\n",
        "aaa\n",
        "train_x_me = train_x\n",
        "train_x_me.sort()\n",
        "train_x_me_sorted = sorted(train_x_me)"
      ],
      "metadata": {
        "id": "ZVXlvWTktHld"
      },
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# My try\n",
        "plt.scatter(train.ENGINESIZE, train.CO2EMISSIONS,  color='blue')\n",
        "plt.plot(np.asanyarray(train_x_me_sorted), clf.coef_[0][2]*np.power(np.asanyarray(train_x_me_sorted), 2) + clf.coef_[0][1]*np.asanyarray(train_x_me_sorted) + clf.intercept_[0], '-r')\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 284
        },
        "id": "CgsS3VKwSaUC",
        "outputId": "8f6491c0-86e2-4a8b-8d16-6ff847b1ea1a"
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f0f83ec6350>]"
            ]
          },
          "metadata": {},
          "execution_count": 16
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 298
        },
        "id": "-w7JPlEEJ_7N",
        "outputId": "e3fa267f-a9de-47f4-8781-2c3c4f4425a9"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'Emission')"
            ]
          },
          "metadata": {},
          "execution_count": 17
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "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
        },
        "id": "GEbk_ObZJ_7N"
      },
      "source": [
        "<h2 id=\"evaluation\">Evaluation</h2>\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BuEQHjsmJ_7N",
        "outputId": "3da91889-6045-489e-90b0-0b19de2dccb6"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mean absolute error: 26.45\n",
            "Residual sum of squares (MSE): 1154.57\n",
            "R2-score: 0.76\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": {
        "id": "sY1qU2xUJ_7N"
      },
      "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": 19,
      "metadata": {
        "id": "UXMMOmRQJ_7N",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 533
        },
        "outputId": "4b15d602-1a36-4a19-d60b-6dfa0409b03b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "--2022-02-22 06:09:20--  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: ‘Lab3practice.csv’\n",
            "\n",
            "Lab3practice.csv    100%[===================>]  70.93K  --.-KB/s    in 0.004s  \n",
            "\n",
            "2022-02-22 06:09:21 (15.5 MB/s) - ‘Lab3practice.csv’ saved [72629/72629]\n",
            "\n",
            "Coefs and Intercept:  [[ 0.         32.68390396  3.40276051 -0.40650962]] [125.98031747]\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'CO2')"
            ]
          },
          "metadata": {},
          "execution_count": 19
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "# importing libs\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import pylab as pl\n",
        "%matplotlib inline\n",
        "\n",
        "from sklearn.preprocessing import PolynomialFeatures\n",
        "from sklearn import linear_model\n",
        "\n",
        "# Downloading data\n",
        "!wget -O Lab3practice.csv https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork/labs/Module%202/data/FuelConsumptionCo2.csv\n",
        "# picking data\n",
        "dframe = pd.read_csv(\"Lab3practice.csv\")\n",
        "culdframe = dframe[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_COMB','CO2EMISSIONS']]\n",
        "# creating train and test data set\n",
        "selecting = np.random.rand(len(dframe)) < 0.8\n",
        "train = culdframe[selecting]\n",
        "train_x = np.asanyarray(train[[\"ENGINESIZE\"]])\n",
        "train_y = np.asanyarray(train[[\"CO2EMISSIONS\"]])\n",
        "\n",
        "test = culdframe[~selecting]\n",
        "test_x = np.asanyarray(test[[\"ENGINESIZE\"]])\n",
        "test_y = np.asanyarray(test[[\"CO2EMISSIONS\"]])\n",
        "\n",
        "# poly features\n",
        "poly = PolynomialFeatures(degree=3)\n",
        "poly_train_x = poly.fit_transform(train_x)\n",
        "\n",
        "# linear regression\n",
        "clf = linear_model.LinearRegression()\n",
        "y_hat_train = clf.fit(poly_train_x, train_y)\n",
        "print(\"Coefs and Intercept: \", clf.coef_, clf.intercept_)\n",
        "\n",
        "# plot\n",
        "plt.scatter(train.ENGINESIZE, train.CO2EMISSIONS, color='blue')\n",
        "xax = np.arange(0.0, 10.0, 0.1)\n",
        "yax = clf.intercept_[0]+clf.coef_[0][1]*xax+clf.coef_[0][2]*xax*xax+clf.coef_[0][3]*xax*xax*xax\n",
        "plt.plot(xax, yax, '-r')\n",
        "plt.xlabel('Eng size')\n",
        "plt.ylabel('CO2')\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5EG_ogAhJ_7O"
      },
      "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.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"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {
        "button": false,
        "new_sheet": false,
        "run_control": {
          "read_only": false
        },
        "id": "bszQH3sbJ_7O",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "086984a1-44c5-45c5-811a-4af773cf8c98"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "MAE:  24.99041236746178\n",
            "RSS:  1069.9999725651592\n",
            "R2 score:  0.7425386958821668\n",
            "Increasing poly degree was not helpful. \n"
          ]
        }
      ],
      "source": [
        "# Eval\n",
        "from sklearn.metrics import r2_score\n",
        "poly_test_x = poly.transform(test_x)\n",
        "y_hat_test = clf.predict(poly_test_x)\n",
        "print(\"MAE: \", np.mean(np.absolute(y_hat_test - test_y)))\n",
        "print(\"RSS: \", np.mean((y_hat_test - test_y)**2))\n",
        "print(\"R2 score: \", r2_score(test_y, y_hat_test))\n",
        "print (\"Increasing poly degree was not helpful. \")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "U0PDGzMOJ_7O"
      },
      "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=\"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"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4qIScovrJ_7O"
      },
      "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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