machine_learning_regression_algorithms_for_beginners.ipynb

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        "<a href=\"https://colab.research.google.com/github/clizarraga-UAD7/Notebooks/blob/main/machine_learning_regression_algorithms_for_beginners.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tIiJ8_Xf_QYc"
      },
      "source": [
        "#Machine Learning Algorithms for Beginners Code Examples\n",
        "\n",
        "Tutorial: https://towardsai.net/p/machine-learning/machine-learning-algorithms-for-beginners-with-python-code-examples-ml-19c6afd60daa\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QVc-KJWMAD6J"
      },
      "source": [
        "# Linear Regression Example"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Import required libraries:\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn import linear_model\n",
        "\n",
        "\n",
        "# Read the CSV file :\n",
        "data = pd.read_csv(\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/ML0101ENv3/labs/FuelConsumptionCo2.csv\")\n",
        "\n",
        "data.head()\n"
      ],
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      "execution_count": 1,
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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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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>MODELYEAR</th>\n",
              "      <th>MAKE</th>\n",
              "      <th>MODEL</th>\n",
              "      <th>VEHICLECLASS</th>\n",
              "      <th>ENGINESIZE</th>\n",
              "      <th>CYLINDERS</th>\n",
              "      <th>TRANSMISSION</th>\n",
              "      <th>FUELTYPE</th>\n",
              "      <th>FUELCONSUMPTION_CITY</th>\n",
              "      <th>FUELCONSUMPTION_HWY</th>\n",
              "      <th>FUELCONSUMPTION_COMB</th>\n",
              "      <th>FUELCONSUMPTION_COMB_MPG</th>\n",
              "      <th>CO2EMISSIONS</th>\n",
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              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>2014</td>\n",
              "      <td>ACURA</td>\n",
              "      <td>ILX</td>\n",
              "      <td>COMPACT</td>\n",
              "      <td>2.0</td>\n",
              "      <td>4</td>\n",
              "      <td>AS5</td>\n",
              "      <td>Z</td>\n",
              "      <td>9.9</td>\n",
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              "      <td>33</td>\n",
              "      <td>196</td>\n",
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              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>2014</td>\n",
              "      <td>ACURA</td>\n",
              "      <td>ILX</td>\n",
              "      <td>COMPACT</td>\n",
              "      <td>2.4</td>\n",
              "      <td>4</td>\n",
              "      <td>M6</td>\n",
              "      <td>Z</td>\n",
              "      <td>11.2</td>\n",
              "      <td>7.7</td>\n",
              "      <td>9.6</td>\n",
              "      <td>29</td>\n",
              "      <td>221</td>\n",
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              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>2014</td>\n",
              "      <td>ACURA</td>\n",
              "      <td>ILX HYBRID</td>\n",
              "      <td>COMPACT</td>\n",
              "      <td>1.5</td>\n",
              "      <td>4</td>\n",
              "      <td>AV7</td>\n",
              "      <td>Z</td>\n",
              "      <td>6.0</td>\n",
              "      <td>5.8</td>\n",
              "      <td>5.9</td>\n",
              "      <td>48</td>\n",
              "      <td>136</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>2014</td>\n",
              "      <td>ACURA</td>\n",
              "      <td>MDX 4WD</td>\n",
              "      <td>SUV - SMALL</td>\n",
              "      <td>3.5</td>\n",
              "      <td>6</td>\n",
              "      <td>AS6</td>\n",
              "      <td>Z</td>\n",
              "      <td>12.7</td>\n",
              "      <td>9.1</td>\n",
              "      <td>11.1</td>\n",
              "      <td>25</td>\n",
              "      <td>255</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>2014</td>\n",
              "      <td>ACURA</td>\n",
              "      <td>RDX AWD</td>\n",
              "      <td>SUV - SMALL</td>\n",
              "      <td>3.5</td>\n",
              "      <td>6</td>\n",
              "      <td>AS6</td>\n",
              "      <td>Z</td>\n",
              "      <td>12.1</td>\n",
              "      <td>8.7</td>\n",
              "      <td>10.6</td>\n",
              "      <td>27</td>\n",
              "      <td>244</td>\n",
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        "data.info()"
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        "id": "C7ZzmygxXRi-",
        "outputId": "5e05615f-b78b-4092-f805-0d69f23437ad"
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      "execution_count": 2,
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          "text": [
            "<class 'pandas.core.frame.DataFrame'>\n",
            "RangeIndex: 1067 entries, 0 to 1066\n",
            "Data columns (total 13 columns):\n",
            " #   Column                    Non-Null Count  Dtype  \n",
            "---  ------                    --------------  -----  \n",
            " 0   MODELYEAR                 1067 non-null   int64  \n",
            " 1   MAKE                      1067 non-null   object \n",
            " 2   MODEL                     1067 non-null   object \n",
            " 3   VEHICLECLASS              1067 non-null   object \n",
            " 4   ENGINESIZE                1067 non-null   float64\n",
            " 5   CYLINDERS                 1067 non-null   int64  \n",
            " 6   TRANSMISSION              1067 non-null   object \n",
            " 7   FUELTYPE                  1067 non-null   object \n",
            " 8   FUELCONSUMPTION_CITY      1067 non-null   float64\n",
            " 9   FUELCONSUMPTION_HWY       1067 non-null   float64\n",
            " 10  FUELCONSUMPTION_COMB      1067 non-null   float64\n",
            " 11  FUELCONSUMPTION_COMB_MPG  1067 non-null   int64  \n",
            " 12  CO2EMISSIONS              1067 non-null   int64  \n",
            "dtypes: float64(4), int64(4), object(5)\n",
            "memory usage: 108.5+ KB\n"
          ]
        }
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    {
      "cell_type": "code",
      "source": [
        "# Let's select some features to explore more :\n",
        "data = data[[\"ENGINESIZE\",\"CO2EMISSIONS\"]]\n",
        "\n",
        "# ENGINESIZE vs CO2EMISSIONS:\n",
        "plt.scatter(data[\"ENGINESIZE\"] , data[\"CO2EMISSIONS\"] , color=\"blue\")\n",
        "plt.xlabel(\"ENGINESIZE\")\n",
        "plt.ylabel(\"CO2EMISSIONS\")\n",
        "plt.show()\n"
      ],
      "metadata": {
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          "height": 300
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        "id": "6WRk3M8wXglf",
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      "execution_count": 3,
      "outputs": [
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          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
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            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Generating training and testing data from our data:\n",
        "# We are using 80% data for training.\n",
        "train = data[:(int((len(data)*0.8)))] # The first 80% of data [0:852]\n",
        "test = data[(int((len(data)*0.8))):]  # The rest after the first 80% of data [853:1066]\n",
        "\n",
        "# Modeling:\n",
        "# Using sklearn package to model data :\n",
        "regr = linear_model.LinearRegression()     # Linear fit\n",
        "train_x = np.array(train[[\"ENGINESIZE\"]])  # Train data 1st. column\n",
        "train_y = np.array(train[[\"CO2EMISSIONS\"]]) # Train data 2nd. column\n",
        "regr.fit(train_x,train_y) # Fit using training data. Returns coeffs linear fit\n",
        "\n",
        "# The coefficients:\n",
        "print (\"coefficients : \",regr.coef_) #Slope\n",
        "print (\"Intercept : \",regr.intercept_) #Intercept\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fdpzzQJmX-Fp",
        "outputId": "69bb3107-c444-48f4-bdb2-eab29553a6b7"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "coefficients :  [[38.79512384]]\n",
            "Intercept :  [127.16989951]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "(int((len(data)*0.8)))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dEIpQF4VYKou",
        "outputId": "ebeffc54-bd60-4a9e-d92a-cfb024e8dde6"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "853"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Plotting the regression line:\n",
        "plt.scatter(train[\"ENGINESIZE\"], train[\"CO2EMISSIONS\"], color='blue')\n",
        "plt.plot(train_x, regr.coef_*train_x + regr.intercept_, '-r')\n",
        "plt.xlabel(\"Engine size\")\n",
        "plt.ylabel(\"Emission\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 318
        },
        "id": "d4M59bXKYPRd",
        "outputId": "fd98eeb6-74ff-4c50-f166-b78d84e3f00d"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'Emission')"
            ]
          },
          "metadata": {},
          "execution_count": 8
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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TkSqccQaIcOedw9/zn3/eVc1PMe6XYmP0aP/nCZLXJEFDiCQLMBa4B9gJ2BxnIhoFzAPO8865Cdg7r85dwPRS1zXzkdEI5JLEjWTa8CPI/BJUmppGvmZTU7S6fonuxo4dXrdw1bRc8UuKV2gS+xi3+le+4YaRHyYi48f732r8+MRvlSpUwnxUoHhe85TCx1V1pdeud4GfArt7pz0PbJVXbbInM4yGJmgGcJiZwUHmlyDChFwGnRMkv/RS6O933Wd/v8sV99prw89Zv96/rp/z+txzYfTal7mVg1CE2/j40MFjj3XebVU4/PCRHyYi1Zg2JGnSjD6aKCJjve0xwIHAX3N+AhER4DDgCa/KjcCxXhTSnsDrqroyrfYZRq0QxS5fSJD5ZepU//OD5ElSqBBKMUzxqcLll/PMcuFlJnAQtwPwBpvwYR5GUDr+MI+mjdtTyzNUDWlD0qYlxWtvDswTkWac8lmgqjeJyN0iMhFnQloEnOKdfwsuAmkZsBY4IcW2GUbN0N3tfAiFbLLJ8Dj4adNg8eLi87q6/J2exx/v3txztLRUXwx9czPw5JMwcyYsWzbs2P/jf5jNueQMHiJD8yxyeYYgWYdv0IgmSF6TBNmVaqGYT8GoN4IWmimUF9rkc2XatPD3CWvDLyROOOtI9Qf9JazXCziz+MDOO+sNFy2vWJ6huM9eLVDCp1Dxjj1OMaVQn9RKvHfS7YzSUcftnOI4r+PeO0ihtbaqfrTp/7QfH0/2NdcMu0bhdx/UnqRXmDOlUOXFlEL9EXaZyUqTRjujdNRpvq2nWVe1WPltwuu6gCOKL/bpT6u+9lqoa8ae5BaSRlAKobKkej6A/wQ6yPNDqOqJ6Ri1wmFZUuuPsMtMVpo02lkqr07hv2mUc/1oafGPXmpuHu5n8COpex/NtVyLj8H/3nthn31GvlAeubkchSS9nGfcZ68WksiS+ltgU+BO4Oa8YhiJUivLTKbRzihRRtOm+Z8bJC8kyqSyRHnuOR4a2A1FhimE7/FlWlnnetaICgHglluiyf0IkyMq7vdeEwQNIfILsCjMeVkXMx/VH1mZAeKSRjujOn+nTRt+Xlgns6ozc7W0DK/f0hLO/BXZhDIwoPqtbxWdvIxtdDv+FsmfEUSQozmsTyGsOTCOL6aaIK5PAfgWMDPMuVkWUwr1x/z5xbNbW1sbw6egGhx9FNSGch3dcZRa6Fm9Cxf6epWv/cilChtCK7+0nydK/UbwKYRVCmuADcA73vYa4I0wddMsphTqj/nz3dKG+f9sbW3VpxRUo3XKSUcqxVVKcd6sS/5Ga9eqnnBC8YUPOEB19erBa0RRfmHI6vuIOyKpFmIrhWotphTqj1oxH0UhDUUX5XtKIyV1Yad+6cd/63/Bm28u/yEjksXIKepIoVrDqxNRCsCngO975ZCw9dIsphTqj3p5E8snjSRqYTunoDfoWbPKf7POmfgm8qLey0eLG9Ddrfr22+U/XAUIO9KIohSqObw6CfPRBbispSd65Q7gO2HqpllMKdQfWY8UsniTS8MOHdbhWer7LOvZN2zQs9svKrrgKiboRzddFLr9fn6jShPm+4jyW1bzqDcJpfAY0JS33ww8FqZumsWUQv2R5dtVVvdKQymEvWZiI68lS1QnTy660JlcoMJApOcJSpNdDYphJKJ8n2n87klRSilEyZI6Nm970wj1DCM0QVk901jFKmhVsnPPTfY+QYvXx13UPgyxsnquWwenneZ+iGnTYMUKAB5id7ZkBYLyXc4iagb+Wk4qd8op0eQ1SZC2yC/A0cBy3PrK84Cngf8IUzfNYiMFIw5Z+S+q0adQcjR0113+F77++kj3jtv2HElHKsUlbHtqdaQQugPGpcL+lFfeF7ZemsWUghGHIJvvRhsV/9PH6ZiiKJ+wdv4oHU6oa77yiuohhxRf7OijVdesKfvecdseZUJftSmPulQKwA7e565+pVTdLIopBSMOnZ2l/3FHKmE7nbAOxyihq4WzmXMlyqxmVVW96qrii4wapfrAA4FV4nZ2UXwKYZf+jJMKPC2C/r46OyvXphxxlMJc7/Men3J3qbpZFFMK9UlWsd1BETxhS9jUBmFNOFHNTGWnuXjqKV+t8tihX1Pt7x+xehJvwGGjj8LeK+i3zP0NVWqeQKFiqAaFoBpDKVR7MaVQf2QZfRRHIUTtBJMOd4xMf7/q175WdOEnmKZb849I33Oq7SzzXmF/r2qZJ1BpSimFUGEDIvIZEdnE2/6aiNwgIruMUGe0iDwsIo+KyGIR+YYn31pEHhKRZSJyvYi0efJR3v4y73hHmLYZ9UVWEUEQbo3jNOtnwoMPwpgxLl/1t741KP7K+CsRlJ1YzNNsA6T3PcchKFV1oTzsb1GNz1hthI0l+3+qukZE9gYOAK4ELhuhzrvA/qr6IWBn4OMisifwv8CFqrot8Cpwknf+ScCrnvxC7zyjwfBbo6CUPA5x00SHrd/b685dvty9r+bWDy5MzTx+vH/9IHkgb74Jn/2s6zn32gveecfJDzkEXnkFVPnBK/5LoWSVorynx+kpEffZ0+N/nmo4+b77hr93taVhrzbCKoXcchyfwPkZbgbaSlXwRilverutXlFgf+CXnnwecJi3fai3j3e8U6TUkhZGPRJlTYG4zJjhcufn09RUnBu/s9Mt1pJrQ3Oz258xY+T8+xB+9HPxxdDaOlzW2urkofjFL1wvu8kmcN11Q9f95J20NCty0+9ombgZPT0x5y/EJLcgTm6Rn4EBtx+kGMKwbFn4c7N4xpomyK6UX4CbgMuBp3CT2EYBj4ao1wwsAt7EvflPAJblHd8KeMLbfgKYnHfsH8CEUtc3n0L9kaW9OigqqDCE1M8OHcX3EeWZIjvZn39edY89ii/8hS+ovvtuYFROZ2f5vpu4v1Eay44Ghf2aT8EfEkhz0Q58GtjO298c+FiYut75Y3ERS3vHVQpAN9AH9E2ZMiXlr87ImizzxYTtSMBFAOV31kGRQn7tTFzRbdigesEFxRebPFl18eJhp5bqgMuN8or7G0X5PkqdG+b3KPzdklAI1Zr5NApJKIX3A6O87X2BLwBjw9TNu8Z5wFeAl4AWT7YXcJu3fRuwl7fd4p0npa5pI4X6I8t488I5AUmUVHPgLFqkOmFC0UW+wEUKG3TMmBTvnUfc3ygppVD4vfvJI8/bGIFaWQRqJEophbA+hV8BAyKyLTDXe8O/tlQFEZkoImO97THAgcBSb8RwhHfacbj1nwFu9Pbxjt/tNd5oIK68Mpo8DuvWJX9NP3t12AgaX955B04+2Z28887w0ksA/IGPMokXEJRLOA0Q3n4b2tuHV0/DR7NgQTR5HMJ6FYN6iiVLkmsLuFRQhTma1q938nohrFLYoKr9OBPSj1T1KzgTUik2B+4RkceAPwN3qOpNwFnAF0VkGTAeF8mE9znek38R+Gq0R2lcwiw4XisEddRpdOBJ094Os2cXy0eN8j8/SA7A73/vesQxY1xGQI9D+Q2Csi9/YBWTiqq9/fbw/aAIqTiRVy+/HE0ehyySBkYhy2evGEFDiPwCPIRLivcEsLUneyJM3TSLmY+qeyGPckjD3FHOvcKWRPMUrV7tlq0sOOkqOUFHszZ0mwpJOidQ3N8oSv0ofp8s/m6y/PtMExIwH52As//PVtWnRWRr4GfJqygjKllO9qqnEUlSPPMMbNjgPstK763q4jFFYOJEuPNOJ990U+jrA1VO1Kt4hzFlt3HGDJg82d1i8mS3XyuEDR8NMjN1dibXFkhwLkk1E6QtaqHYSCG7N5daXpCmnHsl+RbqV287/qbL2Kb4wDe/qTowUHY7C53Nafxucb+PKI5qv/a3tRUnymttLU7nlEaeoTTW264ExEiIt8D7fBy3+lquPI6tvFYVRIn5jkNWoaJZKoWgZ0paKeQ6kWbW63f5cvFFdt1V9dlnA+tHaU9hx5rG75ZE9s8oJq3CENAo4cBp0NAhqcDm3udUv1KqbhbFlEJ2nWhWC9JkqRTmzw9OzZykUthH/uBbuUt6Q9WPks218GWg1O9WbudW6TTVWf0t1jOllEJJn4KqrvQ+l6vqclyuojV5xagwU6dGk5dLJdMipMX99zt/QCq88QZ8+tMgwr26z6D4FxzBe3gdQenVz4a6VJRIoVzqiBxBv8+4cXDCCcPzMZ1wQjg/UV4wVCi5H2FzH/lR6b/FuvetBWmL/AKcDLwAPINbivNp4KkwddMsNlLIzsZZjz6FVCJbfvazopP6adK9+eOIb/WlKDS3hB0pBP1uG23kXz/MEqFxf6O4I41KRtzVS7QfCcxofpIR8hBVophSyHaGZRa21CyVQlyFMGhDX75c9UMfKj7hzDNV169PxdwS1Vlb+LvF+Z7j+rGS8INVyq6fZRqWNElCKdwKtIc5N8tiSqF+/khzJKEUkljneKSy478OqJ5/fvGBbbdV/fvfi+4Vd66AX/0414zzPWeZ5qLaqBd/RhJKYRdcttPLgUtyJUzdNIsphfr5I80Rt8NIKntpUNmNP+sbbFx84LLLXKK6FEhjpBF16U+/NpWrkGr5b7ZeXsJKKYWwk9cuB+4GHgQW5hWjwlTa6ZY0UScHFTr9Tjst+cl8Y1jL1RyHIvTxYTbBLRNyZ/PHXC4i1aH8RCkwZ040eRh23jmavJBLL4X+fvfo/f1uPyzuPTO8vJqYPbs4v1RQepOaJUhb5BfgL2HOy7rYSKHy4YFJEyUG3m9UEGWkMdL5h/Jr3wMf49ZMzR1pmFuCQnGbmsLVj2PTr2XzkWr9z1MQDaGeReTbuMij3+GW2cwplFfSUVXhmD59uvb19VWyCRVnwgT/ZFzjxw8m1KwpWlqKwyrBZfXs7x8u6+gIv0ynX32/F/v38iK/5Ag+wn3D5JcyizO4kHUMz2KXxdttqQFIufePc83eXhe+mp8ttLUVfvrTcKk+ovzGRjqIyEJVne53LKz56GjgbOABhkxHjd0bVwlpZW30i8XOIj7br7MIkkdZazfoug7lDH6IIrzI+wYVwgtM4oM8iqCcyqVFCiEKcb67WKm3UyBu+ug0MrcaCRI0hKiFYuajdIbifmaZ1tbi+RCVnqcQJU2FX7jjPtzje/KX+J7ChrJMUn7EjW1Pw0QY55mS+JtLOnOrEQ1ipLk4M2/7MwXHvl2qbhbFlEI6SiFKZ1vJ3Edl+RTWrlXdxicRHej7+Gfoa0X5jpOIWKmm9Ndp/M3VEvXuUxhJKTzit+23X4liSiF+aKEfUWb6Vjr3UeE/6MY+0aKgesZGl/seOJdvRlYEhR37SJ1DNYZgxvm7SeNvrlZohBnNI/kUJGDbb9+oABdfDG1tw2VtbU5eLlGWaqy20Ff3vuLYnH+iCIrww7dOHjrQ3g6vvoqgzOZrse6Xnzuou9vfV1CNYcNx/m7S+JurFbJcv6RiBGkLjTlSwK3jfA+wBFgMnObJzweex02GWwTMzKtzNrAM+BtwUKnrq40UBkl6OBv2LbnSPoUg89GP6fG/wK9+VdZzRh05hGlnNbxdxvm7qQcTSjlU46ivHIhhPhoA3sBlRO33tnP760eouzmwq7e9CfB3YJqnFL7sc/404FFgFLA18A+gudQ9TCmkQ1xzSVr3LiTfVr8bf/at9Ac+os2s9zVtpKEUgjqHRu1E642Gn9Gsqs2q+h5V3URVW7zt3H7rCHVXquoj3vYaYCmwZYkqhwI/V9V3VfVpb8Swe6l7GI4sU/nGXn4yQf65fD0PsfvgTON8duERBGUf/sgALZm1Kcgk1NVVXd+dUR6NMKM57DyFWIhIBy5/0kOe6L9E5DERuUpENvNkWwLP5VVbQWklYuAUwIknDrdtn3hiHeZ4z+f660GEdbSxO38eFF/EaZ4HQVnELsOqvJLBNMt66xyqhWpav6Cry60bMXWqmycydarbryslHzSESKoAG+Mmu33a258ENOMU0mzgKk/+Y+BzefWuBI7wuV43buJc35QpUxIeVNUeaUSCFM5HyJW2tuTaHUSQWWYcLwUadCexsixbf1xTUVubmYTSplr9MbUOCSTEKwsRaQV+BfSq6g2eEnpRVQdUdQPwE4ZMRM/jnNM5JnuyYajqXFWdrqrTJ06cmGbza4I0ZjSvWxdNnibf4I/CsC4AABWaSURBVDwU4WUmuD4hx5VX0iRuVPAi7yt5jbTe4NetM5NQ2jREtE+VkZpSEBHBve0vVdUf5sk3zzvtcOAJb/tG4CgRGSUiWwPbAQ+n1T6jPMpdQjEKO7B0MJT0PL6Zd2AHePttpxxOPJFx4/zrb7RRnQ/vG4igVCZRUpwY0UjTAzcDOAZ4XEQWebJzgKNFZGdAcUn2TgZQ1cUisgAXwtoPnKqqJTPWGNmTyyE0MDCUujlK2uRANmyAQw5B+X3RoY/wR+7jI+jScJcaPdq9uRu1z5Qp/kkPq21+TD0RKktqtWJZUrPPoFlI7MyWt94KBx9cJJ5PF8fwM3JzJEePdoOEfJqa/J9RxOmYkYibUM6yeqZPb6+bFJhvQmpvt9FfXJLIkmo0ENOmhT+3dPbRAN58EyZNcr1ygUI4cNunEZRjmE/+pPlttim+TKVnCltWz/RpiGifKsOUQsZUU3hdEEuWhD83SkoMLrrI/WdvsgmsWjUk//73B4NL7lzWEbpNjRAzbtgcj6wxpZAhuaFwmHw5SZCF8hnxbXn5cqcIROCMM4bkEybAG2+4L+JLXyrr3pV+i5w7N5v7GEaWmE8hQ4JWCps6tXzHaFi7eBQ7bNhrdnbCnXf6HFCF44+Ha64pPnbzzTBzZln3TvpPNYlFamr438doYMynUCVUMrwujdjuP/2pYARy//2up21qGq4QDj7YOR9USyqEWiOS6cwwagRTChlSacdo0spn7Vr4xjnvwk47OWWw997DT1i82CmCW25xiqLOMEezUY/U339qFRP0kpzVy3OSyudY5qEIf392tOv8c5xzzlBGgihhTDVAbmTQ3AyzZiU0P8Mwqozs0kcaLFgQLE+7g0kiKue9vOifUkIEVq+G8ePj3aCKEbE5CUZjYCOFDEkjT1EpkorK+T5fQpEihXA01yKoixWsY4UAyTilDaMWsJFCldLT4zrygQFnrujujj6aiJPq4YM8yqPsXCT/M9P5Nx6gn5LLadQdYWZIG0Y9YEqhCunpGcorBCnkGQqivx86O1H+WHRodx7izw285pFFGhmNgpmPqpCgSVGpTZb6zW+cfaS1Ff44pBAu42SEDQiamUII6nzT6JSjXNMijYxGwZRCAiSduiIon1BZeYaCeO01l2NaBA4/fNihLVmBoMziMvLzD2XB9ttHk8dh33395VtsYZFGRuNiSiEmUVJXBIXqF8pTfVuePdspgs02G556cs6cwVDSf0ZYBXXq1ATalMfSgPTYQfI4LFvmL29tdZY0VfdpCsFoJEwpxCTKylBBzspCeZCpomwTxpNPDuUf+trXhuRbbw1vveV6v1NOiXzZtrbkk88FpY1II52EX8qRUnLDaARMKcQkjY5lxozi0UNTk5OHR+Hf/90pgn/5l+GH7rrL9bJPPVWcZjQClVieM0my9F8YRq1gSiEmaXQsp51WPHrYsMHJR2I/7vaWsmyCG24YOnDEEe4iqrD//uU3roCTT07sUgBsvHE0eRwy8d0YRo2R5hrNW4nIPSKyREQWi8hpnnyciNwhIk96n5t5chGRS0RkmYg8JiK7ptW2JEmjY4k6yW0U7/A0HSjC3XQOP/jkk04R/OIXqczAeuutZK932WVu/ed8WlqcPGmC/CFJ+0kMo5ZIc6TQD3xJVacBewKnisg04KvAXaq6HXCXtw9wMLCdV7qBOcWXrD4q2rHcfjuK8A5j6GDIXnU233YzjVVh220jX3bs2CQbGY2uLrj66uGzsa++Op01Eiqdi8owqpHUlIKqrlTVR7ztNcBSYEvgUGCed9o84DBv+1DgGnU8CIwVkc3Tal9SpNGxBL3Qi+CGCwcd5HYOOmjw2APsxaa8hqBcwNnl3xwXrRqWNJKfZrXS1i23RJMbRiOQiU9BRDqAXYCHgEmqutI79AIwydveEngur9oKT1bVlOpYCucvhKU40kbp5nI2qLgVy26/3Yk33pgP8zCCMoMHeINNoz9ATPbbL/NbJkYl17cwjGoldaUgIhsDvwJOV9U38o+pW/YtUrChiHSLSJ+I9K1evTrBlpZHqeijwvkLYcmZnt7PMv7OdihNXE5eyOj557sA+jVr6OPDgdfJYjnORYvSuW4WVHp9C8OoRlJVCiLSilMIvaqaC4V5MWcW8j5zK7g/D2yVV32yJxuGqs5V1emqOn3ixInpNT4kpaKMCucvhKK/n5s/cBaKsIzt2A43w+px+SC/uegZp2G+/vVQ4U1ZrAWdVobXLJg9uzgiN4kU44ZRy6QZfSTAlcBSVf1h3qEbgeO87eOA3+bJj/WikPYEXs8zM1UtiYUv3nef6+hbW9nxpu8Oio9lHoJy1L8+ymGnle+9TmM5zrRIOm1IEF1dLp9UUinGDaMeSHOkMAM4BthfRBZ5ZSZwAXCgiDwJHODtA9wCPAUsA34C9KTYtqpgY9awgM+gCHzkI4OTE/5v4uGDTuOfcSwAS5bAAQfEu19YW/lGG4W/ZtLLKERJG5IE998PK1a4e61Y4fYNo6FR1Zotu+22m1aaobUni0trq7/8KK71P3DvvSNeM8r9C8vUqeGeqbMz3PWamlTnz0/uu1R1bYzT9ijMmuV/r1mzkr+XYVQTQJ8G9Ks2ozlF8kNLJ/McfeyGIlzHZwfl3+PLtLLO9Uf77JNaW6LYyu++O9x5aYSjZhkRlHmKcsOoAUwppMj6dRs4h9kownNMYTceAeAfbMP2/BVBOZPvpbaKWbm28rDJ5/r7w6XeiEKWEUGW5sIwirGV11JgFx7hLjrZjOGzwGZxKZdxClmtURBnOc6wJB19NHu28yHkR26lFRHU3OyvACwhntHI2EghIUbzNldyIorwCLsNKoQ7OIAJrEZQLmMWWS9aUw6VXKQ+y4igxFOUG0YdYCOFmHySG7mRQ4vkM7mZ25pm1uSC71HWLkg6+gicAsgiLDS3eM7cuW7E0NzsFIItqmM0MjZSKIdVq5xTWGSYQricbkbzNoLye8pXCCVzH2VAlGR+Rx6ZXjsMw8geUwphUYWLL3Y986RJgwvcr2YCO/MXBOUULuddRse+VdByBwkug1ASv5m+QVxzTbptSZOeHrcKac6vMDDg9nvqfoaMYQRjSmEkli6FrbZy8Zennz4kv+ACGBjgvazmUXZO9JZBawcHyZPGz64fRNLrKWTJ5ZdHkxtGI2BKwY9161yspQhMm+amugLsvvvQ9NezzkonUJ9osfpBs4+jzEr2ozB9dT0Sds1sw2gkTCnkc/fdThGMGgWXXDIkv/56pwgeegi2TD+bd5RY/WOP9T83SF4ulfZzGIaRDaYUXnsNPvlJ17t15i1ledRRsGaNUwYpe1MLVzqbPRva2obL2tr8Y/VtoZjySWuUZRi1TOMqhXnznCLYbDO46SYna2uDBx5wiuC669JZLd6HTX3WxikMCw0KEy21nkOSBN0/SvhqtXH55cUWwKYm8ykYjU1jKoXHH4fjjx/aP+ccl7Ph3Xdhr70yb06hr+Dcc2H9+uGy9etrJ/V1rdDV5aKn8h3q11xjqbONxqYxlcL227vYw3/8w73qzp7tm9ugpwdaWlyH0dISPVSx0AQUxLhxw/ezevs3slsP2jBqhcZUCm1tcMopsM02gackEcNermklKPdOJXPy5LtbwsgNw6hNGlMphCBsWuWgNA9NTcUmoCBeeWX4fjVm77zzzmIF0Nnp5IZh1A+mFAII2zEHBSZFiXUvDDUNmiwWJf1EGtx55/DlaEwhGEb9keYazVeJyCoReSJPdr6IPF+wPGfu2NkiskxE/iYiB6XVrrDr/4Y14QSFfgbVL4zr90sLHWVB+SC/RVh/hmEYRj5pjhSuBj7uI79QVXf2yi0AIjINOArY0atzqYgkbkGPsv5v2LTKQbOPBwb8O/ZTThk5LXSU9NFXXVWsaESc3DAMIzJB63QmUYAO4Im8/fOBL/ucdzZwdt7+bcBeI10/6hrNUdf/nTVLtbnZndPc7L92b6lrzp/vPkWG9tMgq/sYhlEfUGVrNP+XiDzmmZc282RbAs/lnbPCkyVK1PV/Z8yAyZPdm/fkyW6/kFKmnqzCHS2s0jCMpMhaKcwB3g/sDKwEfhD1AiLSLSJ9ItK3evXqSHWj5BQKa2oqZeoJ67+ISxr3yarthmFUGUFDiCQKBeajoGNkZD6aP1+1vX24mae93d/cEtXUFOdecUjjPvPnq7a1Db9mW5uZpQyjXqCE+Ug0xeQ1ItIB3KSqO3n7m6vqSm/7DGAPVT1KRHYErgV2B7YA7gK2U9WSkfnTp0/Xvr6+SG3q7XXpIp591o0QcmaeQpqa/CefiYQLN+3o8J+BPHVqsqmo07jPhAnw8svF8vHj4aWXyrumYRjVg4gsVNXpfsfSDEm9DvgTsL2IrBCRk4DvisjjIvIYsB9wBoCqLgYWAEuAW4FTR1II5RLW/h7F1ORHVP9FuaRxHz+FkJObSckw6puWtC6sqkf7iK8scf5swCcSvzLMnOnSWvjJwzBliv8bfFilEpZx4/w78cJ8SkmRe6acjwXMsW0Y9YTNaA4g7joFQcojrFKpJEGpOwpZu9YytxpGvWFKIYC4ZpmsFr8pzJs0kjwMF18Mra3hzk3aHGYYRmUxpRBArfgU4rbTj64u+OlPh4fZBo0ekjaHGYZRWUwpBBAl/5AfcTvrsPME4rYziEKH/MUXp3MfwzCqjKBY1VooUecpRCVO+og48wei1rV0GoZhRIES8xRSiz6qB7q6yo+sydULMyeikHPPdU7cfHJO3UpG+sT5PgzDqA1SnbyWNuVMXqsFokycy6XjyFci7e3BWVUNwzAqMnnNKJ8o/ohSowrDMIyomFKoQqI4j7OKcjIMozEwpVCFRFlkJ42QVMMwGhdTClVK2BxNaYWkGobRmJhSqHGijCoMwzBGwkJS6wALFTUMIylspFAH2CpphmEkhY0UapzCeQqW0towjDjYSKHGsXkKhmEkiSmFGsfmKRiGkSRpLsd5lYisEpEn8mTjROQOEXnS+9zMk4uIXCIiy0TkMRHZNa121Rs2T8EwjCRJc6RwNfDxAtlXgbtUdTvgLm8f4GBgO690Az4LYRp+2DwFwzCSJDWloKp/BArX/zoUmOdtzwMOy5Nf42V1fRAYKyKbp9W2esLmKRiGkSRZRx9NUtWV3vYLwCRve0vgubzzVniylRgjYvMUDMNIioo5mr2FHiLn7RaRbhHpE5G+1atXp9AywzCMxiVrpfBizizkfa7y5M8DW+WdN9mTFaGqc1V1uqpOnzhxYqqNNQzDaDSyVgo3Asd528cBv82TH+tFIe0JvJ5nZjIMwzAyIjWfgohcB+wLTBCRFcDXgQuABSJyErAcONI7/RZgJrAMWAuckFa7DMMwjGBSUwqqenTAoU6fcxU4Na22GIZhGOGo6TWaRWQ1bsRRDhOAlxJsTjVQb89Ub88D9fdM9fY8UH/P5Pc8U1XV1ylb00ohDiLSF7Rwda1Sb89Ub88D9fdM9fY8UH/PFPV5LPeRYRiGMYgpBcMwDGOQRlYKcyvdgBSot2eqt+eB+numenseqL9nivQ8DetTMAzDMIpp5JGCYRiGUUDDKQW/dR5qGRHZSkTuEZElIrJYRE6rdJviIiKjReRhEXnUe6ZvVLpNSSAizSLyFxG5qdJtSQIReUZEHheRRSLSV+n2xEVExorIL0XkryKyVET2qnSb4iAi23u/Ta68ISKnj1iv0cxHIvJR4E1cqu6dKt2euHg5pDZX1UdEZBNgIXCYqi6pcNPKRkQE2EhV3xSRVuA+4DQvrXrNIiJfBKYD71HVQyrdnriIyDPAdFWti5h+EZkH/J+qXiEibUC7qr5W6XYlgYg04/LJ7aGqJed2NdxIIWCdh5pFVVeq6iPe9hpgKS7teM3iravxprfb6pWafnsRkcnAJ4ArKt0WoxgR2RT4KHAlgKquqxeF4NEJ/GMkhQANqBTqGRHpAHYBHqpsS+LjmVoW4TLp3qGqtf5MFwFnAhsq3ZAEUeB2EVkoIt2VbkxMtgZWAz/1THxXiMhGlW5UghwFXBfmRFMKdYKIbAz8CjhdVd+odHvioqoDqrozLo367iJSs6Y+ETkEWKWqCyvdloTZW1V3xS2ne6pnmq1VWoBdgTmqugvwFkPLBdc0ninsU8AvwpxvSqEO8OzuvwJ6VfWGSrcnSbwh/D0Ur/ddS8wAPuXZ4H8O7C8i8yvbpPio6vPe5yrg18DulW1RLFYAK/JGpL/EKYl64GDgEVV9MczJphRqHM8peyWwVFV/WOn2JIGITBSRsd72GOBA4K+VbVX5qOrZqjpZVTtww/i7VfVzFW5WLERkIy+wAc/M8jGgZiP6VPUF4DkR2d4TdQI1G6xRwNGENB1B9ms0Vxy/dR5U9crKtioWM4BjgMc9GzzAOap6SwXbFJfNgXlexEQTsEBV6yKMs46YBPzavZPQAlyrqrdWtkmx+W+g1zO3PEUdrOviKewDgZND12m0kFTDMAwjGDMfGYZhGIOYUjAMwzAGMaVgGIZhDGJKwTAMwxjElIJhGIYxiCkFo2EQkYGCrJFlz1gVkQeSbFvBtaeLyCVpXd8wSmEhqUbDICJvqurGlW6HYVQzNlIwGh5vXYBviMgj3voAO3jyiSJyh7emwxUislxEJnjH3vQ+9xWRe/Py8Pd6s8wRkd1E5A9ewrjbvDTnhff+jIg84a0d8ce8a97kbd+SN7J5XUSO85IFfk9E/iwij4lI6IlJhjESphSMRmJMgfnoP/KOveQld5sDfNmTfR2XkmJHXC6cKQHX3QU4HZgGbAPM8PJR/Qg4QlV3A64CZvvUPQ84SFU/hEtaNgxVneklBjwJWA78xtt+XVU/DHwY+E8R2Tr812AYwTRcmgujoXnb62D9yCUSXAh82tveGzgcQFVvFZFXA+o+rKorALxUIx3Aa8BOwB3ewKEZWOlT937gahFZkNeGYXijk58BR6rq6yLyMeCDInKEd8qmwHbA0wHtM4zQmFIwDMe73ucA0f8v3s3bztUXYLGqllzSUVVPEZE9cAvwLBSR3fKPe/mffg78j6rmEs4J8N+qelvEdhrGiJj5yDCCuR84EsB7O98sQt2/ARNz6/yKSKuI7Fh4koi8X1UfUtXzcIu8bFVwygXAY6r68zzZbcAsz0SFiPxLnS0IY1QQGykYjcSYvEyyALeqaqmw1G8A14nIMcCfgBeANWFupKrrPPPOJd5Sjy241dcWF5z6PRHZDvf2fxfwKLBP3vEvA4vz2n0ebknPDuARz6m9GjgsTLsMYyQsJNUwAhCRUcCAqvZ7b/xzSvgkDKMusJGCYQQzBVggIk3AOuA/K9wew0gdGykYhmEYg5ij2TAMwxjElIJhGIYxiCkFwzAMYxBTCoZhGMYgphQMwzCMQUwpGIZhGIP8fzFpmoRSDVCXAAAAAElFTkSuQmCC\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Regression \n",
        "# Predicting values:\n",
        "# Function for predicting future values :\n",
        "def get_regression_predictions(input_features,intercept,slope):\n",
        " predicted_values = input_features*slope + intercept\n",
        " return predicted_values\n",
        "\n",
        "# Predicting emission for future car:\n",
        "my_engine_size = 3.5\n",
        "estimatd_emission = get_regression_predictions(my_engine_size,regr.intercept_[0],regr.coef_[0][0])\n",
        "print (\"Estimated Emission :\",estimatd_emission)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dobIvOkUbZeT",
        "outputId": "676fe255-6637-42b2-8254-ee7c66c6ce44"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Estimated Emission : 262.9528329350173\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "w33IafvU41nP",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "24c912cf-3276-4cef-db05-ba7318eaa0c5"
      },
      "source": [
        "# Evaluation of Regression\n",
        "# Checking various accuracy:\n",
        "from sklearn.metrics import r2_score\n",
        "test_x = np.array(test[['ENGINESIZE']])\n",
        "test_y = np.array(test[['CO2EMISSIONS']])\n",
        "test_y_ = regr.predict(test_x)\n",
        "\n",
        "print(\"Mean absolute error: %.2f\" % np.mean(np.absolute(test_y_ - test_y)))\n",
        "print(\"Mean sum of squares (MSE): %.2f\" % np.mean((test_y_ - test_y) ** 2))\n",
        "print(\"R2-score: %.2f\" % r2_score(test_y_ , test_y) )\n"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mean absolute error: 20.60\n",
            "Mean sum of squares (MSE): 746.45\n",
            "R2-score: 0.71\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sTVcjiI_AX2X"
      },
      "source": [
        "# Multivariable Linear Regression"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Import the required libraries:\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn import linear_model\n",
        "\n",
        "# Read the CSV file:\n",
        "data = pd.read_csv(\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/ML0101ENv3/labs/FuelConsumptionCo2.csv\")\n",
        "data.head()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 324
        },
        "id": "bBUTpvicbp9B",
        "outputId": "143dc993-f1c6-4cef-9ef8-7231e9732487"
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "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  "
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-a36ce34b-ab30-4a9c-8abf-3b3397e24a80\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
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              "        vertical-align: middle;\n",
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              "\n",
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>MODELYEAR</th>\n",
              "      <th>MAKE</th>\n",
              "      <th>MODEL</th>\n",
              "      <th>VEHICLECLASS</th>\n",
              "      <th>ENGINESIZE</th>\n",
              "      <th>CYLINDERS</th>\n",
              "      <th>TRANSMISSION</th>\n",
              "      <th>FUELTYPE</th>\n",
              "      <th>FUELCONSUMPTION_CITY</th>\n",
              "      <th>FUELCONSUMPTION_HWY</th>\n",
              "      <th>FUELCONSUMPTION_COMB</th>\n",
              "      <th>FUELCONSUMPTION_COMB_MPG</th>\n",
              "      <th>CO2EMISSIONS</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>2014</td>\n",
              "      <td>ACURA</td>\n",
              "      <td>ILX</td>\n",
              "      <td>COMPACT</td>\n",
              "      <td>2.0</td>\n",
              "      <td>4</td>\n",
              "      <td>AS5</td>\n",
              "      <td>Z</td>\n",
              "      <td>9.9</td>\n",
              "      <td>6.7</td>\n",
              "      <td>8.5</td>\n",
              "      <td>33</td>\n",
              "      <td>196</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>2014</td>\n",
              "      <td>ACURA</td>\n",
              "      <td>ILX</td>\n",
              "      <td>COMPACT</td>\n",
              "      <td>2.4</td>\n",
              "      <td>4</td>\n",
              "      <td>M6</td>\n",
              "      <td>Z</td>\n",
              "      <td>11.2</td>\n",
              "      <td>7.7</td>\n",
              "      <td>9.6</td>\n",
              "      <td>29</td>\n",
              "      <td>221</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>2014</td>\n",
              "      <td>ACURA</td>\n",
              "      <td>ILX HYBRID</td>\n",
              "      <td>COMPACT</td>\n",
              "      <td>1.5</td>\n",
              "      <td>4</td>\n",
              "      <td>AV7</td>\n",
              "      <td>Z</td>\n",
              "      <td>6.0</td>\n",
              "      <td>5.8</td>\n",
              "      <td>5.9</td>\n",
              "      <td>48</td>\n",
              "      <td>136</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>2014</td>\n",
              "      <td>ACURA</td>\n",
              "      <td>MDX 4WD</td>\n",
              "      <td>SUV - SMALL</td>\n",
              "      <td>3.5</td>\n",
              "      <td>6</td>\n",
              "      <td>AS6</td>\n",
              "      <td>Z</td>\n",
              "      <td>12.7</td>\n",
              "      <td>9.1</td>\n",
              "      <td>11.1</td>\n",
              "      <td>25</td>\n",
              "      <td>255</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>2014</td>\n",
              "      <td>ACURA</td>\n",
              "      <td>RDX AWD</td>\n",
              "      <td>SUV - SMALL</td>\n",
              "      <td>3.5</td>\n",
              "      <td>6</td>\n",
              "      <td>AS6</td>\n",
              "      <td>Z</td>\n",
              "      <td>12.1</td>\n",
              "      <td>8.7</td>\n",
              "      <td>10.6</td>\n",
              "      <td>27</td>\n",
              "      <td>244</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
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              "  "
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Consider features we want to work on:\n",
        "X = data[[ 'ENGINESIZE', 'CYLINDERS', 'FUELCONSUMPTION_CITY','FUELCONSUMPTION_HWY', \n",
        " 'FUELCONSUMPTION_COMB','FUELCONSUMPTION_COMB_MPG']]\n",
        "Y = data[\"CO2EMISSIONS\"]\n",
        "\n",
        "# Generating training and testing data from our data:\n",
        "# We are using 80% data for training.\n",
        "train = data[:(int((len(data)*0.8)))]\n",
        "test = data[(int((len(data)*0.8))):]\n"
      ],
      "metadata": {
        "id": "32kZKPUzbxMp"
      },
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "test"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 544
        },
        "id": "sWV621QAcIPJ",
        "outputId": "e1594710-efaf-4ef4-85c1-234957f9aaa6"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "      MODELYEAR    MAKE                  MODEL    VEHICLECLASS  ENGINESIZE  \\\n",
              "853        2014  NISSAN  PATHFINDER HYBRID 4WD  SUV - STANDARD         2.5   \n",
              "854        2014  NISSAN                  QUEST         MINIVAN         3.5   \n",
              "855        2014  NISSAN                  ROGUE     SUV - SMALL         2.5   \n",
              "856        2014  NISSAN              ROGUE AWD     SUV - SMALL         2.5   \n",
              "857        2014  NISSAN                 SENTRA        MID-SIZE         1.8   \n",
              "...         ...     ...                    ...             ...         ...   \n",
              "1062       2014   VOLVO               XC60 AWD     SUV - SMALL         3.0   \n",
              "1063       2014   VOLVO               XC60 AWD     SUV - SMALL         3.2   \n",
              "1064       2014   VOLVO               XC70 AWD     SUV - SMALL         3.0   \n",
              "1065       2014   VOLVO               XC70 AWD     SUV - SMALL         3.2   \n",
              "1066       2014   VOLVO               XC90 AWD  SUV - STANDARD         3.2   \n",
              "\n",
              "      CYLINDERS TRANSMISSION FUELTYPE  FUELCONSUMPTION_CITY  \\\n",
              "853           4           AV        X                   9.1   \n",
              "854           6           AV        X                  12.5   \n",
              "855           4           AV        X                   9.2   \n",
              "856           4           AV        X                   9.5   \n",
              "857           4           AV        X                   7.8   \n",
              "...         ...          ...      ...                   ...   \n",
              "1062          6          AS6        X                  13.4   \n",
              "1063          6          AS6        X                  13.2   \n",
              "1064          6          AS6        X                  13.4   \n",
              "1065          6          AS6        X                  12.9   \n",
              "1066          6          AS6        X                  14.9   \n",
              "\n",
              "      FUELCONSUMPTION_HWY  FUELCONSUMPTION_COMB  FUELCONSUMPTION_COMB_MPG  \\\n",
              "853                   8.5                   8.8                        32   \n",
              "854                   9.5                  11.1                        25   \n",
              "855                   7.2                   8.3                        34   \n",
              "856                   7.4                   8.6                        33   \n",
              "857                   6.0                   7.0                        40   \n",
              "...                   ...                   ...                       ...   \n",
              "1062                  9.8                  11.8                        24   \n",
              "1063                  9.5                  11.5                        25   \n",
              "1064                  9.8                  11.8                        24   \n",
              "1065                  9.3                  11.3                        25   \n",
              "1066                 10.2                  12.8                        22   \n",
              "\n",
              "      CO2EMISSIONS  \n",
              "853            202  \n",
              "854            255  \n",
              "855            191  \n",
              "856            198  \n",
              "857            161  \n",
              "...            ...  \n",
              "1062           271  \n",
              "1063           264  \n",
              "1064           271  \n",
              "1065           260  \n",
              "1066           294  \n",
              "\n",
              "[214 rows x 13 columns]"
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              "      <th></th>\n",
              "      <th>MODELYEAR</th>\n",
              "      <th>MAKE</th>\n",
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              "      <th>VEHICLECLASS</th>\n",
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              "      <th>853</th>\n",
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              "      <td>9.2</td>\n",
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              "      <td>33</td>\n",
              "      <td>198</td>\n",
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              "    <tr>\n",
              "      <th>857</th>\n",
              "      <td>2014</td>\n",
              "      <td>NISSAN</td>\n",
              "      <td>SENTRA</td>\n",
              "      <td>MID-SIZE</td>\n",
              "      <td>1.8</td>\n",
              "      <td>4</td>\n",
              "      <td>AV</td>\n",
              "      <td>X</td>\n",
              "      <td>7.8</td>\n",
              "      <td>6.0</td>\n",
              "      <td>7.0</td>\n",
              "      <td>40</td>\n",
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              "      <th>1062</th>\n",
              "      <td>2014</td>\n",
              "      <td>VOLVO</td>\n",
              "      <td>XC60 AWD</td>\n",
              "      <td>SUV - SMALL</td>\n",
              "      <td>3.0</td>\n",
              "      <td>6</td>\n",
              "      <td>AS6</td>\n",
              "      <td>X</td>\n",
              "      <td>13.4</td>\n",
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              "      <td>271</td>\n",
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              "      <td>2014</td>\n",
              "      <td>VOLVO</td>\n",
              "      <td>XC60 AWD</td>\n",
              "      <td>SUV - SMALL</td>\n",
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              "      <td>6</td>\n",
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              "      <td>264</td>\n",
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              "      <th>1064</th>\n",
              "      <td>2014</td>\n",
              "      <td>VOLVO</td>\n",
              "      <td>XC70 AWD</td>\n",
              "      <td>SUV - SMALL</td>\n",
              "      <td>3.0</td>\n",
              "      <td>6</td>\n",
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              "      <td>24</td>\n",
              "      <td>271</td>\n",
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              "      <td>2014</td>\n",
              "      <td>VOLVO</td>\n",
              "      <td>XC70 AWD</td>\n",
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              "      <td>260</td>\n",
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              "      <td>2014</td>\n",
              "      <td>VOLVO</td>\n",
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              "      <td>3.2</td>\n",
              "      <td>6</td>\n",
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              "      <td>14.9</td>\n",
              "      <td>10.2</td>\n",
              "      <td>12.8</td>\n",
              "      <td>22</td>\n",
              "      <td>294</td>\n",
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              "<p>214 rows × 13 columns</p>\n",
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              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
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              "\n",
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              "\n",
              "    .colab-df-convert:hover {\n",
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              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
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              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
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              "    }\n",
              "  </style>\n",
              "\n",
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              "          document.querySelector('#df-290cf62d-0802-4309-b522-cc640f9a6943 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-290cf62d-0802-4309-b522-cc640f9a6943');\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",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "#Modeling:\n",
        "#Using sklearn package to model data :\n",
        "regr = linear_model.LinearRegression()\n",
        "train_x = np.array(train[[ 'ENGINESIZE', 'CYLINDERS', 'FUELCONSUMPTION_CITY',\n",
        " 'FUELCONSUMPTION_HWY', 'FUELCONSUMPTION_COMB','FUELCONSUMPTION_COMB_MPG']])\n",
        "train_y = np.array(train[\"CO2EMISSIONS\"])\n",
        "\n",
        "regr.fit(train_x,train_y)\n",
        "\n",
        "test_x = np.array(test[[ 'ENGINESIZE', 'CYLINDERS', 'FUELCONSUMPTION_CITY',\n",
        " 'FUELCONSUMPTION_HWY', 'FUELCONSUMPTION_COMB','FUELCONSUMPTION_COMB_MPG']])\n",
        "test_y = np.array(test[\"CO2EMISSIONS\"])\n",
        "\n",
        "# print the coefficient values:\n",
        "coeff_data = pd.DataFrame(regr.coef_ , X.columns , columns=[\"Coefficients\"])\n",
        "coeff_data\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 260
        },
        "id": "SbeQCd77cf-m",
        "outputId": "ad76798b-407a-42c1-b588-3cb8f84dacde"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "                          Coefficients\n",
              "ENGINESIZE                    7.873147\n",
              "CYLINDERS                     8.408908\n",
              "FUELCONSUMPTION_CITY         -3.368325\n",
              "FUELCONSUMPTION_HWY           2.742498\n",
              "FUELCONSUMPTION_COMB          3.851251\n",
              "FUELCONSUMPTION_COMB_MPG     -4.082913"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-fa0b5527-3935-4cdd-98cf-7d4b24614103\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Coefficients</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>ENGINESIZE</th>\n",
              "      <td>7.873147</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>CYLINDERS</th>\n",
              "      <td>8.408908</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>FUELCONSUMPTION_CITY</th>\n",
              "      <td>-3.368325</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>FUELCONSUMPTION_HWY</th>\n",
              "      <td>2.742498</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>FUELCONSUMPTION_COMB</th>\n",
              "      <td>3.851251</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>FUELCONSUMPTION_COMB_MPG</th>\n",
              "      <td>-4.082913</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
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              "              title=\"Convert this dataframe to an interactive table.\"\n",
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              "        \n",
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              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
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              "      gap: 12px;\n",
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              "\n",
              "    .colab-df-convert {\n",
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              "      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-fa0b5527-3935-4cdd-98cf-7d4b24614103 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-fa0b5527-3935-4cdd-98cf-7d4b24614103');\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",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eQfVWFlrAbl3",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "611114ea-2921-401d-b75f-a01d41a5754f"
      },
      "source": [
        "\n",
        "#Now let's do prediction of data:\n",
        "Y_pred = regr.predict(test_x)\n",
        "\n",
        "# Check accuracy:\n",
        "from sklearn.metrics import r2_score\n",
        "R = r2_score(test_y , Y_pred)\n",
        "print (\"R² :\",R)\n"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "R² : 0.9362912548588906\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OnN44asuAo_m"
      },
      "source": [
        "# Polynomial Regression"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Least Squares Linear Regression \n",
        "\n",
        "Suppose we have $(n+1)$ points $(x_0, y_0), (x_1,y_1), \\ldots , (x_n, y_n)$ in a plane and we want to fit a curve  $y = a_0 + a_1 x$ which \"best fits\" to the set of data.\n",
        "\n",
        "This is the [Linear Regression Method](https://en.wikipedia.org/wiki/Linear_regression), that minimizes the sum of squares errors $SSE$. \n",
        "\n",
        "\\begin{equation*}\n",
        "SSE = \\sum_i (y_i - (a_0 + a_1 x_i))^2\n",
        "\\end{equation*}\n",
        "\n",
        "In matrix form, the linear regression can be written as \n",
        "\n",
        "\\begin{equation*}\n",
        "X = \n",
        "\\begin{bmatrix}\n",
        "1 & x_1 \\\\\n",
        "1 & x_2 \\\\\n",
        "\\vdots & \\vdots \\\\\n",
        "1 & x_n \\\\\n",
        "\\end{bmatrix}, \\vec{y} = \n",
        "\\begin{bmatrix}\n",
        " y_1 \\\\\n",
        " y_2 \\\\\n",
        "\\vdots \\\\\n",
        " y_n \\\\\n",
        "\\end{bmatrix}, \\vec{a} = \n",
        "\\begin{bmatrix}\n",
        "a_0 \\\\\n",
        "a_1 \\\\\n",
        "\\end{bmatrix}\n",
        "\\end{equation*}\n",
        "\n",
        "from which the $SSE$ can be rewritten as  \n",
        "\\begin{equation*}\n",
        "SSE = || \\vec{y} - X \\vec{a} ||^2\n",
        "\\end{equation*}\n",
        "\n",
        "The vectors $\\vec{a}$ that minimize the previous equation, have a unique solution if and only if the columns of the $X$ matrix are linear independent. Then matrix $X^T X$ is symmetric and therefore diagonalizable. Multiplying the above equation by the left, we get\n",
        "\n",
        "\\begin{eqnarray*}\n",
        "(\\vec{y} - X \\vec{a}) & = & 0 \\\\\n",
        "X^T (\\vec{y} - X \\vec{a}) & = & 0 \\\\\n",
        "X^T \\vec{y} - (X^T X) \\vec{a} & = & 0 \\\\\n",
        "(X^T X) \\vec{a} & = & X^T \\vec{y}\n",
        "\\end{eqnarray*}\n",
        "\n",
        "This last equation must be solved for the vector $\\vec{a}$.\n"
      ],
      "metadata": {
        "id": "LrzPrQG94EH0"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Import required libraries:\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Generate datapoints:\n",
        "x = np.arange(-5,5,0.1)\n",
        "y_noise = 20 * np.random.normal(size = len(x))\n",
        "y = 1*(x**3) + 1*(x**2) + 1*x + 3+y_noise\n",
        "plt.scatter(x,y);\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        },
        "id": "ihdY1I0Ecwf-",
        "outputId": "74fdc7c1-3129-47be-d546-00b9bf5659c6"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "# Make polynomial data:\n",
        "x1 = x                  # One dimensional arrays\n",
        "x2 = np.power(x1,2)\n",
        "x3 = np.power(x1,3)\n",
        "n = len(x1)\n",
        "\n",
        "# Reshaping data:\n",
        "x1_new = np.reshape(x1,(n,1))  # Array of n rows and 1 column\n",
        "x2_new = np.reshape(x2,(n,1))\n",
        "x3_new = np.reshape(x3,(n,1))\n"
      ],
      "metadata": {
        "id": "KMSVZOB_dVwN"
      },
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "# First column of matrix X:\n",
        "x_bias = np.ones((n,1))\n",
        "\n",
        "# Form the complete x matrix:\n",
        "x_new = np.append(x_bias,x1_new,axis=1)\n",
        "x_new = np.append(x_new,x2_new,axis=1)\n",
        "x_new = np.append(x_new,x3_new,axis=1)\n",
        "\n"
      ],
      "metadata": {
        "id": "EMX4Wojsdimu"
      },
      "execution_count": 26,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "# Finding transpose:\n",
        "x_new_transpose = np.transpose(x_new)\n",
        "\n",
        "# Finding dot product of original and transposed matrix :\n",
        "x_new_transpose_dot_x_new = x_new_transpose.dot(x_new)\n",
        "\n",
        "# Finding Inverse:\n",
        "temp_1 = np.linalg.inv(x_new_transpose_dot_x_new)# Finding the dot product of transposed x and y :\n",
        "temp_2 = x_new_transpose.dot(y)\n",
        "\n",
        "# Finding coefficients:\n",
        "theta = temp_1.dot(temp_2)\n",
        "theta\n",
        "\n",
        "# Store coefficient values in different variables:\n",
        "beta_0 = theta[0]\n",
        "beta_1 = theta[1]\n",
        "beta_2 = theta[2]\n",
        "beta_3 = theta[3]\n",
        "\n",
        "# Plot the polynomial curve:\n",
        "plt.scatter(x,y)\n",
        "plt.plot(x,beta_0 + beta_1*x1 + beta_2*x2 + beta_3*x3,c=\"red\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 303
        },
        "id": "rYfuwifgeUwC",
        "outputId": "d5e0620f-9e5d-40aa-de80-1502a8339584"
      },
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f4b6fe81750>]"
            ]
          },
          "metadata": {},
          "execution_count": 30
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "theta"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dEtW9pk2ez-o",
        "outputId": "7a92876e-dfd1-47ff-fce3-e07728fc80c7"
      },
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([5.34486175, 2.53229519, 1.08575696, 0.98237323])"
            ]
          },
          "metadata": {},
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KPl85hmJAroZ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "73b773bc-77b3-4d48-d966-220a2166b20b"
      },
      "source": [
        "\n",
        "# Prediction function:\n",
        "def prediction(x1,x2,x3,beta_0,beta_1,beta_2,beta_3):\n",
        " y_pred = beta_0 + beta_1*x1 + beta_2*x2 + beta_3*x3\n",
        " return y_pred\n",
        " \n",
        "# Making predictions:\n",
        "pred = prediction(x1,x2,x3,beta_0,beta_1,beta_2,beta_3)\n",
        " \n",
        "# Calculate accuracy of model:\n",
        "def err(y_pred,y):\n",
        " var = (y - y_pred)\n",
        " var = var*var\n",
        " n = len(var)\n",
        " MSE = var.sum()\n",
        " MSE = MSE/n\n",
        " \n",
        " return MSE\n",
        "# Calculating the error:\n",
        "error = err(pred,y)\n",
        "error\n"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "381.02069120586765"
            ]
          },
          "metadata": {},
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "88fKkYqqcwsF"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UF__r1KUCp30"
      },
      "source": [
        "# Exponential Regression"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Import required libraries:\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.optimize import curve_fit\n",
        "\n",
        "# Dataset values :\n",
        "day = np.arange(0,8)\n",
        "weight = np.array([251,209,157,129,103,81,66,49])\n",
        "\n",
        "# Exponential Function :\n",
        "def expo_func(x, a, b):\n",
        " return a * b ** x"
      ],
      "metadata": {
        "id": "t-G6RgBMfWr7"
      },
      "execution_count": 32,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "#popt :Optimal values for the parameters\n",
        "#pcov :The estimated covariance of popt\n",
        "popt, pcov = curve_fit(expo_func, day, weight)\n",
        "weight_pred = expo_func(day,popt[0],popt[1])\n"
      ],
      "metadata": {
        "id": "gqUvDVZNfXA3"
      },
      "execution_count": 35,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q-w2fW-uDKHK",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 333
        },
        "outputId": "f0d0a586-0bc7-4f28-8733-eab3ebfcc114"
      },
      "source": [
        "\n",
        "# Plotting the data\n",
        "plt.plot(day, weight_pred, 'r-')\n",
        "plt.scatter(day,weight,label='Day vs Weight')\n",
        "plt.title(\"Day vs Weight a*b^x\")\n",
        "plt.xlabel('Day')\n",
        "plt.ylabel('Weight')\n",
        "plt.legend()\n",
        "plt.show()\n",
        "\n",
        "# Equation\n",
        "a=popt[0].round(4)\n",
        "b=popt[1].round(4)\n",
        "print(f'The equation of regression line is y={a}*{b}^x')\n"
      ],
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The equation of regression line is y=254.0486*0.7964^x\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "85GQobzgDz7X"
      },
      "source": [
        "# Sinusoidal Regression"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Import required libraries:\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.optimize import curve_fit\n",
        "from sklearn.metrics import r2_score\n",
        "\n",
        "# Generating dataset:\n",
        "# Y = A*sin(B(X + C)) + D\n",
        "# A = Amplitude\n",
        "# Period = 2*pi/B\n",
        "# Period = Length of One Cycle\n",
        "# C = Phase Shift (In Radian)\n",
        "# D = Vertical Shift\n",
        "\n",
        "X = np.linspace(0,1,100) #(Start,End,Points)\n",
        "\n",
        "# Here…\n",
        "# A = 1\n",
        "# B= 2*pi\n",
        "# B = 2*pi/Period\n",
        "# Period = 1\n",
        "# C = 0\n",
        "# D = 0\n",
        "\n",
        "Y = 1*np.sin(2*np.pi*X)\n",
        "\n",
        "# Adding some Noise :\n",
        "Noise = 0.4*np.random.normal(size=100)\n",
        "Y_data = Y + Noise\n",
        "\n",
        "plt.scatter(X,Y_data,c=\"r\");\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 288
        },
        "id": "eJ8BlW3Nf8yt",
        "outputId": "fd620603-1af1-484f-c498-7d6edd09b909"
      },
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "# Calculate the value:\n",
        "def calc_sine(x,a,b,c,d):\n",
        " return a * np.sin(b* ( x + np.radians(c))) + d\n",
        "\n",
        "# Finding optimal parameters :\n",
        "popt,pcov = curve_fit(calc_sine,X,Y_data)\n"
      ],
      "metadata": {
        "id": "VVAEfXMlgQFk"
      },
      "execution_count": 39,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "# Plot the main data :\n",
        "plt.scatter(X,Y_data)# Plot the best fit curve :\n",
        "plt.plot(X,calc_sine(X,*popt),c=\"r\")\n",
        "plt.show();\n",
        "\n",
        "# Check the accuracy :\n",
        "Accuracy =r2_score(Y_data,calc_sine(X,*popt))\n",
        "print ('Accuracy =', Accuracy)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 306
        },
        "id": "5tb4GrgIgdIa",
        "outputId": "a888e9fd-d8d9-4817-8774-5700c47aea53"
      },
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Accuracy = 0.7629648684021527\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "# Function to calculate the value :\n",
        "def calc_line(X,m,b):\n",
        " return b + X*m\n",
        "\n",
        "# It returns optimized parametes for our function :\n",
        "# popt stores optimal parameters\n",
        "# pcov stores the covarience between each parameters.\n",
        "popt,pcov = curve_fit(calc_line,X,Y_data)\n"
      ],
      "metadata": {
        "id": "XIMswaWWgopw"
      },
      "execution_count": 42,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vPU_9qhzD2Z4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 306
        },
        "outputId": "f601556d-3870-4503-eb34-e5c3431e9b3e"
      },
      "source": [
        "\n",
        "# Plot the main data :\n",
        "plt.scatter(X,Y_data)\n",
        "\n",
        "# Plot the best fit line :\n",
        "plt.plot(X,calc_line(X,*popt),c=\"r\")\n",
        "plt.show()\n",
        "\n",
        "# Check the accuracy of model :\n",
        "Accuracy =r2_score(Y_data,calc_line(X,*popt))\n",
        "print (\"Accuracy of Linear Model : \",Accuracy)\n"
      ],
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Accuracy of Linear Model :  0.4052551559366674\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bS2qLvX-EiNX"
      },
      "source": [
        "# Logarithmic Regression"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Import required libraries:\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn.metrics import r2_score\n",
        "\n",
        "# Dataset:\n",
        "# Y = a + b*ln(X)\n",
        "X = np.arange(1,50,0.5)\n",
        "Y = 10 + 2*np.log(X)\n",
        "\n",
        "#Adding some noise to calculate error!\n",
        "Y_noise = np.random.rand(len(Y))\n",
        "Y = Y +Y_noise\n",
        "\n",
        "plt.scatter(X,Y);"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        },
        "id": "3FBZ4F6og0IK",
        "outputId": "ca040c84-2ca6-4098-c4f2-82d14072500c"
      },
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# 1st column of our X matrix should be 1:\n",
        "n = len(X)\n",
        "x_bias = np.ones((n,1))\n",
        "print (X.shape)\n",
        "print (x_bias.shape)\n",
        "\n",
        "# Reshaping X :\n",
        "X = np.reshape(X,(n,1))\n",
        "print (X.shape)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fAeWV6MVg0V0",
        "outputId": "2bb3ae51-0046-4539-8502-6394d6d251ed"
      },
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(98,)\n",
            "(98, 1)\n",
            "(98, 1)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-FNHHye-Ek9P",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 303
        },
        "outputId": "53d38155-238b-46fe-fb79-bca771a72b85"
      },
      "source": [
        "\n",
        "# Going with the formula:\n",
        "# Y = a + b*ln(X)\n",
        "X_log = np.log(X)\n",
        "\n",
        "# Append the X_log to X_bias:\n",
        "x_new = np.append(x_bias,X_log,axis=1)\n",
        "\n",
        "# Transpose of a matrix:\n",
        "x_new_transpose = np.transpose(x_new)\n",
        "\n",
        "# Matrix multiplication:\n",
        "x_new_transpose_dot_x_new = x_new_transpose.dot(x_new)\n",
        "\n",
        "# Find inverse:\n",
        "temp_1 = np.linalg.inv(x_new_transpose_dot_x_new)\n",
        "\n",
        "# Matrix Multiplication:\n",
        "temp_2 = x_new_transpose.dot(Y)\n",
        "\n",
        "# Find the coefficient values:\n",
        "theta = temp_1.dot(temp_2)\n",
        "\n",
        "# Plot the data:\n",
        "a = theta[0]\n",
        "b = theta[1]\n",
        "Y_plot = a + b*np.log(X)\n",
        "plt.scatter(X,Y)\n",
        "plt.plot(X,Y_plot,c=\"r\")\n",
        "\n",
        "# Check the accuracy:\n",
        "Accuracy = r2_score(Y,Y_plot)\n",
        "print ('Accuracy =', Accuracy)\n"
      ],
      "execution_count": 46,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Accuracy = 0.9730083222502734\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "E3ckwyLPhUwr"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}