coefficients_of_multiple_linear_regression.ipynb

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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
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      "source": [
        "<a href=\"https://colab.research.google.com/github/Blackman9t/Machine_Learning/blob/master/coefficients_of_multiple_linear_regression.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lghukHiPLn4E",
        "colab_type": "text"
      },
      "source": [
        "### <font color='khaki'>Getting to understand Multiple Linear Regression better by walking through it's internal workings and computation.\n",
        "\n",
        "[stattrek.com](https://stattrek.com/multiple-regression/regression-coefficients.aspx?Tutorial=reg)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QsSWslxGGGxn",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "B-Eo1ihpHJ8O",
        "colab_type": "text"
      },
      "source": [
        "## Defining the scores table  like on the website"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9PsvB8kOFRBB",
        "colab_type": "code",
        "outputId": "26125352-7242-416d-9332-b24a3ed708a1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 225
        }
      },
      "source": [
        "student_scores = pd.DataFrame({'Score':[100, 90, 80, 70, 60], 'IQ':[110, 120, 100, 90, 80,], 'Study_hours':[40, 30, 20, 0, 10]})\n",
        "\n",
        "student_scores.index.name='Student'\n",
        "\n",
        "student_scores.head()"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
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              "    }\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>Score</th>\n",
              "      <th>IQ</th>\n",
              "      <th>Study_hours</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Student</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>100</td>\n",
              "      <td>110</td>\n",
              "      <td>40</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>90</td>\n",
              "      <td>120</td>\n",
              "      <td>30</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>80</td>\n",
              "      <td>100</td>\n",
              "      <td>20</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>70</td>\n",
              "      <td>90</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>60</td>\n",
              "      <td>80</td>\n",
              "      <td>10</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "         Score   IQ  Study_hours\n",
              "Student                         \n",
              "0          100  110           40\n",
              "1           90  120           30\n",
              "2           80  100           20\n",
              "3           70   90            0\n",
              "4           60   80           10"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_G1CDfReHVk7",
        "colab_type": "text"
      },
      "source": [
        "## Defining Matrix $X$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8TzsNfgwHx6f",
        "colab_type": "code",
        "outputId": "c68fc9f8-1252-4d03-b924-ba6db9e58534",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 225
        }
      },
      "source": [
        "X = student_scores.loc[:, ['IQ',\"Study_hours\"]]\n",
        "\n",
        "ones = np.ones(len(student_scores), dtype=int)\n",
        "\n",
        "X.insert(0, 'ones', ones)\n",
        "\n",
        "X.head()"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
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              "    }\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>ones</th>\n",
              "      <th>IQ</th>\n",
              "      <th>Study_hours</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Student</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>110</td>\n",
              "      <td>40</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>120</td>\n",
              "      <td>30</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1</td>\n",
              "      <td>100</td>\n",
              "      <td>20</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1</td>\n",
              "      <td>90</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1</td>\n",
              "      <td>80</td>\n",
              "      <td>10</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "         ones   IQ  Study_hours\n",
              "Student                        \n",
              "0           1  110           40\n",
              "1           1  120           30\n",
              "2           1  100           20\n",
              "3           1   90            0\n",
              "4           1   80           10"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Tmo8PzCuKfM0",
        "colab_type": "code",
        "outputId": "93b0f214-f719-4d99-a6ef-8b690716226e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 101
        }
      },
      "source": [
        "# Next we convert X to a Numpy array from a Data frame\n",
        "\n",
        "X = X.values\n",
        "\n",
        "X"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[  1, 110,  40],\n",
              "       [  1, 120,  30],\n",
              "       [  1, 100,  20],\n",
              "       [  1,  90,   0],\n",
              "       [  1,  80,  10]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zmj2SJbRILRl",
        "colab_type": "text"
      },
      "source": [
        "## Defining $X'$ or X Transpose"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xV2mf89zIScK",
        "colab_type": "code",
        "outputId": "c21af384-155a-46ef-8c01-5124b032f326",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 67
        }
      },
      "source": [
        "X_tp = X.transpose()\n",
        "\n",
        "X_tp"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[  1,   1,   1,   1,   1],\n",
              "       [110, 120, 100,  90,  80],\n",
              "       [ 40,  30,  20,   0,  10]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4goHC6OtIj8B",
        "colab_type": "text"
      },
      "source": [
        "#### Print out the shape of X and X'."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1xAUFA3XItcL",
        "colab_type": "code",
        "outputId": "1441afa5-471c-48fe-92cf-d522e5596e56",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 50
        }
      },
      "source": [
        "print('X shape is',X.shape,'\\nX-tanspose shape is',X_tp.shape)"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "X shape is (5, 3) \n",
            "X-tanspose shape is (3, 5)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dCjaoHp3JFr7",
        "colab_type": "text"
      },
      "source": [
        "## Post-multiply $X'$ by $X$... using matrix multiplication"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DJzEcJ0nJE8Q",
        "colab_type": "code",
        "outputId": "7bab47d5-391a-466b-e8db-2c7fc2941cdb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 67
        }
      },
      "source": [
        "X_tp_X = np.matmul(X_tp, X)\n",
        "\n",
        "X_tp_X"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[    5,   500,   100],\n",
              "       [  500, 51000, 10800],\n",
              "       [  100, 10800,  3000]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bMi346K1LKoU",
        "colab_type": "text"
      },
      "source": [
        "Notice,  that so far we are getting exactly the same result as on the website [stattrek.com](https://stattrek.com/multiple-regression/regression-coefficients.aspx?Tutorial=reg)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RDBp4eGnMKsZ",
        "colab_type": "text"
      },
      "source": [
        "## Next we define the inverse of $X'X$, just like in the website"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4G8S-KPyJBeT",
        "colab_type": "code",
        "outputId": "1fa999ae-1321-4940-8984-c75dbbd6d232",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 67
        }
      },
      "source": [
        "from numpy.linalg import inv\n",
        "\n",
        "inverse = inv(X_tp_X)\n",
        "\n",
        "inverse"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 2.02000000e+01, -2.33333333e-01,  1.66666667e-01],\n",
              "       [-2.33333333e-01,  2.77777778e-03, -2.22222222e-03],\n",
              "       [ 1.66666667e-01, -2.22222222e-03,  2.77777778e-03]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RMfqQHFYMfod",
        "colab_type": "code",
        "outputId": "52cd23aa-ecf0-4c6b-f62e-2ae173bc4fc7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 67
        }
      },
      "source": [
        "# checking to make sure the same values as the website\n",
        "\n",
        "print(inverse[0,:])\n",
        "print(inverse[1,:])\n",
        "print(inverse[2,:])"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[20.2        -0.23333333  0.16666667]\n",
            "[-0.23333333  0.00277778 -0.00222222]\n",
            "[ 0.16666667 -0.00222222  0.00277778]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DM4J6tTeNKSt",
        "colab_type": "text"
      },
      "source": [
        "everything is perfect up to this point"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dki3abPhnDDz",
        "colab_type": "code",
        "outputId": "d165151f-3ce7-4a95-f0ef-4f077e09eb65",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "X_tp.shape"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(3, 5)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dLniC5yGnIep",
        "colab_type": "code",
        "outputId": "0b1cab35-6dbf-4d4d-bd55-5ae9b9a879ad",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "inverse.shape"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(3, 3)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MRVwhb4LsPSs",
        "colab_type": "text"
      },
      "source": [
        "## Next we post-multiply $(X'X)^{-1}$ by $X'$ "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RdLDdJ_ZltZG",
        "colab_type": "code",
        "outputId": "00675953-46cc-4873-e9ce-98b13dc60873",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 118
        }
      },
      "source": [
        "X_tp_inverse = np.matmul(inverse, X_tp)\n",
        "\n",
        "X_tp_inverse"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1.20000000e+00, -2.80000000e+00,  2.00000000e-01,\n",
              "        -8.00000000e-01,  3.20000000e+00],\n",
              "       [-1.66666667e-02,  3.33333333e-02,  1.73472348e-17,\n",
              "         1.66666667e-02, -3.33333333e-02],\n",
              "       [ 3.33333333e-02, -1.66666667e-02, -1.73472348e-17,\n",
              "        -3.33333333e-02,  1.66666667e-02]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EFPSxUQpnhqz",
        "colab_type": "code",
        "outputId": "9a1a3ec7-ecde-40f9-a69c-0c2d9e8b587a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "X_tp_inverse.shape"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(3, 5)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fnJ1bgmLNVpR",
        "colab_type": "text"
      },
      "source": [
        "## Next we define the $Y$ variable"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vtdORPdkNPAQ",
        "colab_type": "code",
        "outputId": "15bd7191-abcd-4b77-ac7a-75e030a10209",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "Y = student_scores.Score.values\n",
        "\n",
        "Y"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([100,  90,  80,  70,  60])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jZ57MBUNphKD",
        "colab_type": "code",
        "outputId": "23589382-1baa-4aae-80ef-fdecc3cbfad5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "Y.shape"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(5,)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rB5Waw2DOHpm",
        "colab_type": "text"
      },
      "source": [
        "## Calculating the slope or coefficients"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_V0F5xHONnFw",
        "colab_type": "text"
      },
      "source": [
        "<h2><font color='khaki'>$ b = (X'X)^{-1}X'Y $</h2>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9gdsAfBFPHoG",
        "colab_type": "text"
      },
      "source": [
        "## Finally we Post-multiply $(X'X)^{-1}X'$ by $Y$ to get the coefficients of the MLR model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "H-BpaLZBptV9",
        "colab_type": "code",
        "outputId": "523f5f38-034d-418d-e2b3-1c0e768ef28b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "coefficients = np.matmul(X_tp_inverse, Y)\n",
        "\n",
        "coefficients"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([20. ,  0.5,  0.5])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Uw-32wc6tddp",
        "colab_type": "text"
      },
      "source": [
        "## $y_{hat} = b0 + b1x1 + b2x2$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "W6M9mh_4t096",
        "colab_type": "text"
      },
      "source": [
        "which now means"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "J3NB9GMwt6DQ",
        "colab_type": "text"
      },
      "source": [
        "## $y_{hat} = 20 + 0.5x1 + 0.5x2$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bq0M3aONvoyi",
        "colab_type": "text"
      },
      "source": [
        "which now means"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IAMd0zRCvub_",
        "colab_type": "text"
      },
      "source": [
        "## $y_{hat} = 20 + 0.5(IQ) + 0.5(Study-hours)$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "d0w_im23eRwU",
        "colab_type": "text"
      },
      "source": [
        "# <font color='khaki'>Part Two\n",
        "\n",
        "# Real World Data"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6Wt-8B-dfTJz",
        "colab_type": "text"
      },
      "source": [
        "### Let's extrapolate on our learnings and apply these concepts to real live data"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IRPSJQxZgXRl",
        "colab_type": "text"
      },
      "source": [
        "Let's download the data set from Git-hub"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dI8g447-tZ5K",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Let's import our Data set\n",
        "data = \"https://raw.githubusercontent.com/Blackman9t/Machine_Learning/master/Original_2000_2014_Fuel_Consumption_Ratings.csv\"\n",
        "\n",
        "# Next let's define additional usual representation of null values to help us select and deal with null data\n",
        "missing_data = ['n/a','na','--','?']"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qG40elHRgh_o",
        "colab_type": "code",
        "outputId": "70fd30b3-2fe5-453f-f265-3136c711450a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 215
        }
      },
      "source": [
        "fuel_df = pd.read_csv(data, na_values=missing_data)\n",
        "\n",
        "fuel_df.head()"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<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>MODEL_YEAR</th>\n",
              "      <th>MAKE</th>\n",
              "      <th>MODEL</th>\n",
              "      <th>VEHICLE_CLASS</th>\n",
              "      <th>ENGINE_SIZE(L)</th>\n",
              "      <th>CYLINDERS</th>\n",
              "      <th>TRANSMISSION</th>\n",
              "      <th>FUEL_TYPE</th>\n",
              "      <th>FUEL_CONSUMPTION_CITY(L/100km)</th>\n",
              "      <th>HWY_(L/100km)</th>\n",
              "      <th>COMB_(L/100km)</th>\n",
              "      <th>COMB_(mpg)</th>\n",
              "      <th>CO2_EMISSIONS(g/km)</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>2000</td>\n",
              "      <td>ACURA</td>\n",
              "      <td>1.6EL</td>\n",
              "      <td>COMPACT</td>\n",
              "      <td>1.6</td>\n",
              "      <td>4</td>\n",
              "      <td>A4</td>\n",
              "      <td>X</td>\n",
              "      <td>9.2</td>\n",
              "      <td>6.7</td>\n",
              "      <td>8.1</td>\n",
              "      <td>35</td>\n",
              "      <td>186</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>2000</td>\n",
              "      <td>ACURA</td>\n",
              "      <td>1.6EL</td>\n",
              "      <td>COMPACT</td>\n",
              "      <td>1.6</td>\n",
              "      <td>4</td>\n",
              "      <td>M5</td>\n",
              "      <td>X</td>\n",
              "      <td>8.5</td>\n",
              "      <td>6.5</td>\n",
              "      <td>7.6</td>\n",
              "      <td>37</td>\n",
              "      <td>175</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>2000</td>\n",
              "      <td>ACURA</td>\n",
              "      <td>3.2TL</td>\n",
              "      <td>MID-SIZE</td>\n",
              "      <td>3.2</td>\n",
              "      <td>6</td>\n",
              "      <td>AS5</td>\n",
              "      <td>Z</td>\n",
              "      <td>12.2</td>\n",
              "      <td>7.4</td>\n",
              "      <td>10.0</td>\n",
              "      <td>28</td>\n",
              "      <td>230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>2000</td>\n",
              "      <td>ACURA</td>\n",
              "      <td>3.5RL</td>\n",
              "      <td>MID-SIZE</td>\n",
              "      <td>3.5</td>\n",
              "      <td>6</td>\n",
              "      <td>A4</td>\n",
              "      <td>Z</td>\n",
              "      <td>13.4</td>\n",
              "      <td>9.2</td>\n",
              "      <td>11.5</td>\n",
              "      <td>25</td>\n",
              "      <td>264</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>2000</td>\n",
              "      <td>ACURA</td>\n",
              "      <td>INTEGRA</td>\n",
              "      <td>SUBCOMPACT</td>\n",
              "      <td>1.8</td>\n",
              "      <td>4</td>\n",
              "      <td>A4</td>\n",
              "      <td>X</td>\n",
              "      <td>10.0</td>\n",
              "      <td>7.0</td>\n",
              "      <td>8.6</td>\n",
              "      <td>33</td>\n",
              "      <td>198</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   MODEL_YEAR   MAKE    MODEL  ... COMB_(L/100km)  COMB_(mpg)  CO2_EMISSIONS(g/km)\n",
              "0        2000  ACURA    1.6EL  ...            8.1          35                  186\n",
              "1        2000  ACURA    1.6EL  ...            7.6          37                  175\n",
              "2        2000  ACURA    3.2TL  ...           10.0          28                  230\n",
              "3        2000  ACURA    3.5RL  ...           11.5          25                  264\n",
              "4        2000  ACURA  INTEGRA  ...            8.6          33                  198\n",
              "\n",
              "[5 rows x 13 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qPWfIua8io4w",
        "colab_type": "text"
      },
      "source": [
        "let's explore the data "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3oNKBXJji4xW",
        "colab_type": "code",
        "outputId": "75e412a6-7841-445e-d70c-d1455d11d5dc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 252
        }
      },
      "source": [
        "# let's check the data types per column or attribute are correct\n",
        "fuel_df.dtypes"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "MODEL_YEAR                          int64\n",
              "MAKE                               object\n",
              "MODEL                              object\n",
              "VEHICLE_CLASS                      object\n",
              "ENGINE_SIZE(L)                    float64\n",
              "CYLINDERS                           int64\n",
              "TRANSMISSION                       object\n",
              "FUEL_TYPE                          object\n",
              "FUEL_CONSUMPTION_CITY(L/100km)    float64\n",
              "HWY_(L/100km)                     float64\n",
              "COMB_(L/100km)                    float64\n",
              "COMB_(mpg)                          int64\n",
              "CO2_EMISSIONS(g/km)                 int64\n",
              "dtype: object"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tL3TR8yDi8tz",
        "colab_type": "code",
        "outputId": "771d60dc-d1f8-4713-cb9f-23a515abb2bc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "# Let's confirm the shape of the data type\n",
        "fuel_df.shape"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(14343, 13)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Crfle784j0zo",
        "colab_type": "code",
        "outputId": "bf98548b-6f95-4379-e366-4394935b60b3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 252
        }
      },
      "source": [
        "# Let's check for missing values\n",
        "fuel_df.isna().sum()"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "MODEL_YEAR                        0\n",
              "MAKE                              0\n",
              "MODEL                             0\n",
              "VEHICLE_CLASS                     0\n",
              "ENGINE_SIZE(L)                    0\n",
              "CYLINDERS                         0\n",
              "TRANSMISSION                      0\n",
              "FUEL_TYPE                         0\n",
              "FUEL_CONSUMPTION_CITY(L/100km)    0\n",
              "HWY_(L/100km)                     0\n",
              "COMB_(L/100km)                    0\n",
              "COMB_(mpg)                        0\n",
              "CO2_EMISSIONS(g/km)               0\n",
              "dtype: int64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "veTRNCs1k9h5",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Let's rename some column names for brevity\n",
        "fuel_df.rename(columns={'FUEL_CONSUMPTION_CITY(L/100km)':'FUEL_CONS_CITY', \n",
        "                        'ENGINE_SIZE(L)':'ENGINE_SIZE',\n",
        "                       'HWY_(L/100km)':'HWY_L100km',\n",
        "                       'COMB_(L/100km)':'COMB_L100km',\n",
        "                       'COMB_(mpg)':'COMB_MPG',\n",
        "                       'CO2_EMISSIONS(g/km)':'CO2_EMISSIONS'},\n",
        "                       inplace=True)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Uodvyz1AmUpU",
        "colab_type": "code",
        "outputId": "80406601-b4c6-43b4-ff80-48d6aa894427",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 195
        }
      },
      "source": [
        "# Let's display the renamed data set\n",
        "fuel_df.head()"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<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>MODEL_YEAR</th>\n",
              "      <th>MAKE</th>\n",
              "      <th>MODEL</th>\n",
              "      <th>VEHICLE_CLASS</th>\n",
              "      <th>ENGINE_SIZE</th>\n",
              "      <th>CYLINDERS</th>\n",
              "      <th>TRANSMISSION</th>\n",
              "      <th>FUEL_TYPE</th>\n",
              "      <th>FUEL_CONS_CITY</th>\n",
              "      <th>HWY_L100km</th>\n",
              "      <th>COMB_L100km</th>\n",
              "      <th>COMB_MPG</th>\n",
              "      <th>CO2_EMISSIONS</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>2000</td>\n",
              "      <td>ACURA</td>\n",
              "      <td>1.6EL</td>\n",
              "      <td>COMPACT</td>\n",
              "      <td>1.6</td>\n",
              "      <td>4</td>\n",
              "      <td>A4</td>\n",
              "      <td>X</td>\n",
              "      <td>9.2</td>\n",
              "      <td>6.7</td>\n",
              "      <td>8.1</td>\n",
              "      <td>35</td>\n",
              "      <td>186</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>2000</td>\n",
              "      <td>ACURA</td>\n",
              "      <td>1.6EL</td>\n",
              "      <td>COMPACT</td>\n",
              "      <td>1.6</td>\n",
              "      <td>4</td>\n",
              "      <td>M5</td>\n",
              "      <td>X</td>\n",
              "      <td>8.5</td>\n",
              "      <td>6.5</td>\n",
              "      <td>7.6</td>\n",
              "      <td>37</td>\n",
              "      <td>175</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>2000</td>\n",
              "      <td>ACURA</td>\n",
              "      <td>3.2TL</td>\n",
              "      <td>MID-SIZE</td>\n",
              "      <td>3.2</td>\n",
              "      <td>6</td>\n",
              "      <td>AS5</td>\n",
              "      <td>Z</td>\n",
              "      <td>12.2</td>\n",
              "      <td>7.4</td>\n",
              "      <td>10.0</td>\n",
              "      <td>28</td>\n",
              "      <td>230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>2000</td>\n",
              "      <td>ACURA</td>\n",
              "      <td>3.5RL</td>\n",
              "      <td>MID-SIZE</td>\n",
              "      <td>3.5</td>\n",
              "      <td>6</td>\n",
              "      <td>A4</td>\n",
              "      <td>Z</td>\n",
              "      <td>13.4</td>\n",
              "      <td>9.2</td>\n",
              "      <td>11.5</td>\n",
              "      <td>25</td>\n",
              "      <td>264</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>2000</td>\n",
              "      <td>ACURA</td>\n",
              "      <td>INTEGRA</td>\n",
              "      <td>SUBCOMPACT</td>\n",
              "      <td>1.8</td>\n",
              "      <td>4</td>\n",
              "      <td>A4</td>\n",
              "      <td>X</td>\n",
              "      <td>10.0</td>\n",
              "      <td>7.0</td>\n",
              "      <td>8.6</td>\n",
              "      <td>33</td>\n",
              "      <td>198</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   MODEL_YEAR   MAKE    MODEL  ... COMB_L100km  COMB_MPG  CO2_EMISSIONS\n",
              "0        2000  ACURA    1.6EL  ...         8.1        35            186\n",
              "1        2000  ACURA    1.6EL  ...         7.6        37            175\n",
              "2        2000  ACURA    3.2TL  ...        10.0        28            230\n",
              "3        2000  ACURA    3.5RL  ...        11.5        25            264\n",
              "4        2000  ACURA  INTEGRA  ...         8.6        33            198\n",
              "\n",
              "[5 rows x 13 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CcAJmL6Tj7Mx",
        "colab_type": "code",
        "outputId": "0803d980-2a17-49cf-d64b-32026a341c80",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 453
        }
      },
      "source": [
        "# Let's plot the correlation of the data set using a heatmap from seaborn library\n",
        "corr_data = fuel_df.corr()\n",
        "\n",
        "plt.figure(figsize=(10, 6))\n",
        "sns.set_style('ticks')\n",
        "\n",
        "sns.heatmap(corr_data, annot=True)\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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jlrm37+It2jeogdF/zt2jxwkEhkYVuOnWnNpzxo9uLd04sGAsiz/rx5Tl23TO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9LjyOinWBQ307rGorgZS7zTxwG+SEzi8B/npHFy8S8SGTlzCaM83HC0e/cfuNxmaW5GZPR/r63I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\nRK5CYII=\n",
            "text/plain": [
              "<Figure size 720x432 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xGbt0H4cEhWc",
        "colab_type": "text"
      },
      "source": [
        "The Top correlated variables with CO2_EMISSIONS"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YmOOLn3J_TTb",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 225
        },
        "outputId": "f4055c47-e8d9-4734-9f9a-3d930727d56d"
      },
      "source": [
        "corrs = {'Variable_Name':['Engine_Size','Cylinders','Fuel_Cons_City','Hwy_L/100','Comb_L/100','Comb_mpg'],\n",
        "                'Corr_Amount':[round(fuel_df['ENGINE_SIZE'].corr(fuel_df.CO2_EMISSIONS),2),\n",
        "                               round(fuel_df['CYLINDERS'].corr(fuel_df.CO2_EMISSIONS),2),\n",
        "                               round(fuel_df['FUEL_CONS_CITY'].corr(fuel_df.CO2_EMISSIONS),2),\n",
        "                               round(fuel_df['HWY_L100km'].corr(fuel_df.CO2_EMISSIONS),2),\n",
        "                               round(fuel_df['COMB_L100km'].corr(fuel_df.CO2_EMISSIONS),2),\n",
        "                               round(fuel_df['COMB_MPG'].corr(fuel_df.CO2_EMISSIONS),2)],\n",
        "               'Description':['Strong Positive Correlation',\n",
        "                              'Strong Positive Correlation',\n",
        "                              'Strong Positive Correlation',\n",
        "                              'Strong Positive Correlation',\n",
        "                              'Strong Positive Correlation',\n",
        "                              'Strong Negative Correlation']}\n",
        "\n",
        "highest_corr = pd.DataFrame(highest_corr, index=[1,2,3,4,5,6])\n",
        "\n",
        "highest_corr"
      ],
      "execution_count": 65,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<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>Variable_Name</th>\n",
              "      <th>Corr_Amount</th>\n",
              "      <th>Description</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>Engine_Size</td>\n",
              "      <td>0.83</td>\n",
              "      <td>Strong Positive Correlation</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>Cylinders</td>\n",
              "      <td>0.80</td>\n",
              "      <td>Strong Positive Correlation</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Fuel_Cons_City</td>\n",
              "      <td>0.92</td>\n",
              "      <td>Strong Positive Correlation</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>Hwy_L/100</td>\n",
              "      <td>0.89</td>\n",
              "      <td>Strong Positive Correlation</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>Comb_L/100</td>\n",
              "      <td>0.92</td>\n",
              "      <td>Strong Positive Correlation</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>Comb_mpg</td>\n",
              "      <td>-0.90</td>\n",
              "      <td>Strong Negative Correlation</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "    Variable_Name  Corr_Amount                  Description\n",
              "1     Engine_Size         0.83  Strong Positive Correlation\n",
              "2       Cylinders         0.80  Strong Positive Correlation\n",
              "3  Fuel_Cons_City         0.92  Strong Positive Correlation\n",
              "4       Hwy_L/100         0.89  Strong Positive Correlation\n",
              "5      Comb_L/100         0.92  Strong Positive Correlation\n",
              "6        Comb_mpg        -0.90  Strong Negative Correlation"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 65
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lNxz2XDHBloA",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4lG6nEjKm6c4",
        "colab_type": "text"
      },
      "source": [
        "### Selecting our independent variables ($X$), an $m * n$ matrix and our dependent variable ($y$), a $m * 1$ vector"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "a8v4-1E42jQa",
        "colab_type": "text"
      },
      "source": [
        "#### Let's first compile the data into training and testing data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qJqP8jlWndXM",
        "colab_type": "code",
        "outputId": "fa2d0329-6369-4ea2-e0a6-349f8595433b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 195
        }
      },
      "source": [
        "data = fuel_df[['ENGINE_SIZE','CYLINDERS','FUEL_CONS_CITY','COMB_MPG', 'CO2_EMISSIONS']]\n",
        "\n",
        "data.head()"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<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>ENGINE_SIZE</th>\n",
              "      <th>CYLINDERS</th>\n",
              "      <th>FUEL_CONS_CITY</th>\n",
              "      <th>COMB_MPG</th>\n",
              "      <th>CO2_EMISSIONS</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1.6</td>\n",
              "      <td>4</td>\n",
              "      <td>9.2</td>\n",
              "      <td>35</td>\n",
              "      <td>186</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1.6</td>\n",
              "      <td>4</td>\n",
              "      <td>8.5</td>\n",
              "      <td>37</td>\n",
              "      <td>175</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>3.2</td>\n",
              "      <td>6</td>\n",
              "      <td>12.2</td>\n",
              "      <td>28</td>\n",
              "      <td>230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>3.5</td>\n",
              "      <td>6</td>\n",
              "      <td>13.4</td>\n",
              "      <td>25</td>\n",
              "      <td>264</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1.8</td>\n",
              "      <td>4</td>\n",
              "      <td>10.0</td>\n",
              "      <td>33</td>\n",
              "      <td>198</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   ENGINE_SIZE  CYLINDERS  FUEL_CONS_CITY  COMB_MPG  CO2_EMISSIONS\n",
              "0          1.6          4             9.2        35            186\n",
              "1          1.6          4             8.5        37            175\n",
              "2          3.2          6            12.2        28            230\n",
              "3          3.5          6            13.4        25            264\n",
              "4          1.8          4            10.0        33            198"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WPfArGhi3f_n",
        "colab_type": "text"
      },
      "source": [
        "next we define the training data by making it 73% of the data selected at random "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ATQv-lDO25CR",
        "colab_type": "code",
        "outputId": "456524b3-67b6-4d15-937c-ba58449f1699",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 136
        }
      },
      "source": [
        "training_data = data.sample(frac=0.73, random_state=47)\n",
        "\n",
        "training_data.head(3)"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>ENGINE_SIZE</th>\n",
              "      <th>CYLINDERS</th>\n",
              "      <th>FUEL_CONS_CITY</th>\n",
              "      <th>COMB_MPG</th>\n",
              "      <th>CO2_EMISSIONS</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>9054</th>\n",
              "      <td>3.0</td>\n",
              "      <td>6</td>\n",
              "      <td>11.9</td>\n",
              "      <td>28</td>\n",
              "      <td>232</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14088</th>\n",
              "      <td>1.6</td>\n",
              "      <td>4</td>\n",
              "      <td>8.7</td>\n",
              "      <td>37</td>\n",
              "      <td>177</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7891</th>\n",
              "      <td>3.5</td>\n",
              "      <td>6</td>\n",
              "      <td>11.6</td>\n",
              "      <td>29</td>\n",
              "      <td>223</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "       ENGINE_SIZE  CYLINDERS  FUEL_CONS_CITY  COMB_MPG  CO2_EMISSIONS\n",
              "9054           3.0          6            11.9        28            232\n",
              "14088          1.6          4             8.7        37            177\n",
              "7891           3.5          6            11.6        29            223"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "u2yVTc0S3t7g",
        "colab_type": "text"
      },
      "source": [
        "next we define the remaining 27% of the data as testing data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bMpkCG1F38tt",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Now to find the index of the remaining 20% of the data to use as our random test data,\n",
        "# we do the following to extract and cast it to a list:-\n",
        "# convert the entire index to a set and convert the training data index to a set too, \n",
        "# find the diff between the two and cast that difference to a list. \n",
        "\n",
        "testing_index = list(set(data.index.values).difference(set(training_data.index.values)))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cqncHW6_49lr",
        "colab_type": "code",
        "outputId": "db9aa5b2-f21e-4637-e56b-de30eaab9a9c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 136
        }
      },
      "source": [
        "# And now we simply create a testing data set with only the index not in the training data set\n",
        "\n",
        "testing_data = data.iloc[testing_index, :]\n",
        "\n",
        "testing_data.head(3)"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
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              "\n",
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              "    }\n",
              "\n",
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              "        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>ENGINE_SIZE</th>\n",
              "      <th>CYLINDERS</th>\n",
              "      <th>FUEL_CONS_CITY</th>\n",
              "      <th>COMB_MPG</th>\n",
              "      <th>CO2_EMISSIONS</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>3.5</td>\n",
              "      <td>6</td>\n",
              "      <td>13.4</td>\n",
              "      <td>25</td>\n",
              "      <td>264</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8195</th>\n",
              "      <td>2.0</td>\n",
              "      <td>4</td>\n",
              "      <td>9.0</td>\n",
              "      <td>34</td>\n",
              "      <td>191</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8197</th>\n",
              "      <td>3.5</td>\n",
              "      <td>6</td>\n",
              "      <td>12.2</td>\n",
              "      <td>27</td>\n",
              "      <td>237</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "      ENGINE_SIZE  CYLINDERS  FUEL_CONS_CITY  COMB_MPG  CO2_EMISSIONS\n",
              "3             3.5          6            13.4        25            264\n",
              "8195          2.0          4             9.0        34            191\n",
              "8197          3.5          6            12.2        27            237"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dIn1vtu35WuW",
        "colab_type": "text"
      },
      "source": [
        "Let's confirm the shapes of both training and testing data sets"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "laDpirzb5edh",
        "colab_type": "code",
        "outputId": "abdfd7c1-05ab-4eb1-8bcb-d5d8dc541c8e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 50
        }
      },
      "source": [
        "print('Training data shape is',training_data.shape)\n",
        "print('Testing data shape is',testing_data.shape)"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Training data shape is (10470, 5)\n",
            "Testing data shape is (3873, 5)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "N68vwtHn57_Q",
        "colab_type": "text"
      },
      "source": [
        "### Now let's define $X$ our $m * n$ matrix of the independent variables or features"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IHtpa7c17Q_n",
        "colab_type": "text"
      },
      "source": [
        "#### First the training data $X-train$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "p68LmnXD6SYb",
        "colab_type": "code",
        "outputId": "f8d1ed6a-b723-46db-8f60-fa6287ea3867",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 136
        }
      },
      "source": [
        "# The training data for our model\n",
        "\n",
        "X_train = training_data.iloc[:, :-1]\n",
        "X_train.head(3)"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
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              "    }\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>ENGINE_SIZE</th>\n",
              "      <th>CYLINDERS</th>\n",
              "      <th>FUEL_CONS_CITY</th>\n",
              "      <th>COMB_MPG</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>9054</th>\n",
              "      <td>3.0</td>\n",
              "      <td>6</td>\n",
              "      <td>11.9</td>\n",
              "      <td>28</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14088</th>\n",
              "      <td>1.6</td>\n",
              "      <td>4</td>\n",
              "      <td>8.7</td>\n",
              "      <td>37</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7891</th>\n",
              "      <td>3.5</td>\n",
              "      <td>6</td>\n",
              "      <td>11.6</td>\n",
              "      <td>29</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "       ENGINE_SIZE  CYLINDERS  FUEL_CONS_CITY  COMB_MPG\n",
              "9054           3.0          6            11.9        28\n",
              "14088          1.6          4             8.7        37\n",
              "7891           3.5          6            11.6        29"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 30
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zEPDbawOosG-",
        "colab_type": "text"
      },
      "source": [
        "next, adding a column of 1's as bias unit or intercept to $X-train$ to make $X-train$ a:  $1 + m * n$ matrix"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UmhjCI9EqErZ",
        "colab_type": "code",
        "outputId": "ffdbd31a-9d6b-45c0-d6a7-091ca75e9ba6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 136
        }
      },
      "source": [
        "ones = np.ones(len(X_train), dtype='int')\n",
        "\n",
        "X_train.insert(0, 'ones', ones)\n",
        "\n",
        "X_train.head(3)"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
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              "\n",
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              "    }\n",
              "</style>\n",
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>ones</th>\n",
              "      <th>ENGINE_SIZE</th>\n",
              "      <th>CYLINDERS</th>\n",
              "      <th>FUEL_CONS_CITY</th>\n",
              "      <th>COMB_MPG</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>9054</th>\n",
              "      <td>1</td>\n",
              "      <td>3.0</td>\n",
              "      <td>6</td>\n",
              "      <td>11.9</td>\n",
              "      <td>28</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14088</th>\n",
              "      <td>1</td>\n",
              "      <td>1.6</td>\n",
              "      <td>4</td>\n",
              "      <td>8.7</td>\n",
              "      <td>37</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7891</th>\n",
              "      <td>1</td>\n",
              "      <td>3.5</td>\n",
              "      <td>6</td>\n",
              "      <td>11.6</td>\n",
              "      <td>29</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "       ones  ENGINE_SIZE  CYLINDERS  FUEL_CONS_CITY  COMB_MPG\n",
              "9054      1          3.0          6            11.9        28\n",
              "14088     1          1.6          4             8.7        37\n",
              "7891      1          3.5          6            11.6        29"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BXbmZjVlqUPe",
        "colab_type": "text"
      },
      "source": [
        "next convert $X-train$ to a numpy array"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tCkwgsyEqTFU",
        "colab_type": "code",
        "outputId": "3769f591-cb0c-4ed2-cd75-4024bac7f855",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 134
        }
      },
      "source": [
        "X_train = X_train.values\n",
        "\n",
        "X_train"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1. ,  3. ,  6. , 11.9, 28. ],\n",
              "       [ 1. ,  1.6,  4. ,  8.7, 37. ],\n",
              "       [ 1. ,  3.5,  6. , 11.6, 29. ],\n",
              "       ...,\n",
              "       [ 1. ,  2.3,  6. , 12.2, 27. ],\n",
              "       [ 1. ,  1.8,  4. , 10.1, 31. ],\n",
              "       [ 1. ,  1.6,  4. ,  9.5, 34. ]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lffs4wtA8K0r",
        "colab_type": "text"
      },
      "source": [
        "#### Next we do the above steps to define the $X-test$ data we would use to test the model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5hmoCr9N-7mj",
        "colab_type": "code",
        "outputId": "43d4963d-7b05-4910-f456-0810acfe2f45",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 136
        }
      },
      "source": [
        "X_test = testing_data.iloc[:, :-1]\n",
        "X_test.head(3)"
      ],
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
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              "</style>\n",
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>ENGINE_SIZE</th>\n",
              "      <th>CYLINDERS</th>\n",
              "      <th>FUEL_CONS_CITY</th>\n",
              "      <th>COMB_MPG</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>3.5</td>\n",
              "      <td>6</td>\n",
              "      <td>13.4</td>\n",
              "      <td>25</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8195</th>\n",
              "      <td>2.0</td>\n",
              "      <td>4</td>\n",
              "      <td>9.0</td>\n",
              "      <td>34</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8197</th>\n",
              "      <td>3.5</td>\n",
              "      <td>6</td>\n",
              "      <td>12.2</td>\n",
              "      <td>27</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "      ENGINE_SIZE  CYLINDERS  FUEL_CONS_CITY  COMB_MPG\n",
              "3             3.5          6            13.4        25\n",
              "8195          2.0          4             9.0        34\n",
              "8197          3.5          6            12.2        27"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "H4gOANPe_L1n",
        "colab_type": "code",
        "outputId": "b5f4feb4-a80c-49f0-9e3f-6decdd7c048b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 136
        }
      },
      "source": [
        "# Adding a column of 1's as bias unit\n",
        "\n",
        "ones = np.ones(len(X_test), dtype='int')\n",
        "\n",
        "X_test.insert(0, 'ones', ones)\n",
        "\n",
        "X_test.head(3)"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<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>ones</th>\n",
              "      <th>ENGINE_SIZE</th>\n",
              "      <th>CYLINDERS</th>\n",
              "      <th>FUEL_CONS_CITY</th>\n",
              "      <th>COMB_MPG</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1</td>\n",
              "      <td>3.5</td>\n",
              "      <td>6</td>\n",
              "      <td>13.4</td>\n",
              "      <td>25</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8195</th>\n",
              "      <td>1</td>\n",
              "      <td>2.0</td>\n",
              "      <td>4</td>\n",
              "      <td>9.0</td>\n",
              "      <td>34</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8197</th>\n",
              "      <td>1</td>\n",
              "      <td>3.5</td>\n",
              "      <td>6</td>\n",
              "      <td>12.2</td>\n",
              "      <td>27</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "      ones  ENGINE_SIZE  CYLINDERS  FUEL_CONS_CITY  COMB_MPG\n",
              "3        1          3.5          6            13.4        25\n",
              "8195     1          2.0          4             9.0        34\n",
              "8197     1          3.5          6            12.2        27"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YuJmBnDw_had",
        "colab_type": "code",
        "outputId": "40fe46f6-afeb-4b10-ab94-dd150ae9b6e9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 134
        }
      },
      "source": [
        "# Now we convert X_test to an array\n",
        "\n",
        "X_test = X_test.values\n",
        "\n",
        "X_test"
      ],
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1. ,  3.5,  6. , 13.4, 25. ],\n",
              "       [ 1. ,  2. ,  4. ,  9. , 34. ],\n",
              "       [ 1. ,  3.5,  6. , 12.2, 27. ],\n",
              "       ...,\n",
              "       [ 1. ,  2.4,  4. ,  9.8, 32. ],\n",
              "       [ 1. ,  2.4,  4. , 10.3, 32. ],\n",
              "       [ 1. ,  2.4,  4. ,  9.7, 34. ]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 35
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_VxMkKTS_1gx",
        "colab_type": "text"
      },
      "source": [
        "### Now let's define $y$ our $m * 1$ column vector of the dependent variable or target"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IYwrYmRo_zpk",
        "colab_type": "code",
        "outputId": "d0ffb4ef-f698-448a-d5ed-e58493ea5fec",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 134
        }
      },
      "source": [
        "# first we define y_train\n",
        "\n",
        "y_train = training_data.iloc[:, -1:].values\n",
        "\n",
        "y_train"
      ],
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[232],\n",
              "       [177],\n",
              "       [223],\n",
              "       ...,\n",
              "       [237],\n",
              "       [207],\n",
              "       [189]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 36
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1U7jwoArAj9P",
        "colab_type": "code",
        "outputId": "fabd3e60-0c37-4bbb-fbe3-1dd3178f8b17",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 134
        }
      },
      "source": [
        "# next we define y_test\n",
        "\n",
        "y_test = testing_data.iloc[:, -1:].values\n",
        "\n",
        "y_test"
      ],
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[264],\n",
              "       [191],\n",
              "       [237],\n",
              "       ...,\n",
              "       [202],\n",
              "       [202],\n",
              "       [191]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 37
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "441iD5Ljelko",
        "colab_type": "text"
      },
      "source": [
        "## Model Development or Compiling-The-Model"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3BTb0yHbqlZQ",
        "colab_type": "text"
      },
      "source": [
        "next define $X'$ or $X$ transpose"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wTn7EemmpFkc",
        "colab_type": "code",
        "outputId": "941cb4b4-029c-4a33-cf46-6a6c6fdae11d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 101
        }
      },
      "source": [
        "X_trans = X_train.transpose()\n",
        "\n",
        "X_trans"
      ],
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1. ,  1. ,  1. , ...,  1. ,  1. ,  1. ],\n",
              "       [ 3. ,  1.6,  3.5, ...,  2.3,  1.8,  1.6],\n",
              "       [ 6. ,  4. ,  6. , ...,  6. ,  4. ,  4. ],\n",
              "       [11.9,  8.7, 11.6, ..., 12.2, 10.1,  9.5],\n",
              "       [28. , 37. , 29. , ..., 27. , 31. , 34. ]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 38
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XrnXO9SorElL",
        "colab_type": "text"
      },
      "source": [
        "Next post-multiply $X'$ by $X$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DfEMVpUYrMOi",
        "colab_type": "code",
        "outputId": "624f6cb4-28de-4cbc-ea1c-68991de159e7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 101
        }
      },
      "source": [
        "X_trans_X = np.matmul(X_trans, X_train)\n",
        "\n",
        "X_trans_X"
      ],
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[  10470.  ,   36336.7 ,   62725.  ,  135052.8 ,  286522.  ],\n",
              "       [  36336.7 ,  143975.85,  239737.3 ,  508132.51,  915467.6 ],\n",
              "       [  62725.  ,  239737.3 ,  409039.  ,  860567.7 , 1616006.  ],\n",
              "       [ 135052.8 ,  508132.51,  860567.7 , 1871908.76, 3440852.4 ],\n",
              "       [ 286522.  ,  915467.6 , 1616006.  , 3440852.4 , 8427362.  ]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 39
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BhBC9pHUrmRG",
        "colab_type": "text"
      },
      "source": [
        "Let's print out their corresponding shapes"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ni6plMgprqlK",
        "colab_type": "code",
        "outputId": "17ba75a9-b228-4be7-91bb-b7b0f2b823e3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 67
        }
      },
      "source": [
        "print('Shape of X is',X_train.shape)\n",
        "print('Shape of X transpose is',X_trans.shape)\n",
        "print('Shape of X transpose X is',X_trans_X.shape)"
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Shape of X is (10470, 5)\n",
            "Shape of X transpose is (5, 10470)\n",
            "Shape of X transpose X is (5, 5)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IT2qrHGmsPMd",
        "colab_type": "text"
      },
      "source": [
        "Next we define the inverse of $X'X$ written as $(X'X)^{-1}$ using the linear algebra library(linalg) from numpy"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mrlbFG7csWkQ",
        "colab_type": "code",
        "outputId": "167491c8-726a-479c-adac-abd2d7ea849b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 202
        }
      },
      "source": [
        "from numpy.linalg import inv\n",
        "\n",
        "X_trans_X_inv = inv(X_trans_X)\n",
        "\n",
        "print(\"Shape of inverse of X'X is\",X_trans_X_inv.shape)\n",
        "X_trans_X_inv"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Shape of inverse of X'X is (5, 5)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 3.38337058e-02, -8.01293531e-05, -1.55797930e-06,\n",
              "        -1.28516162e-03, -6.16583945e-04],\n",
              "       [-8.01293531e-05,  3.76575963e-04, -1.88406928e-04,\n",
              "        -2.42411229e-05,  7.84261804e-06],\n",
              "       [-1.55797930e-06, -1.88406928e-04,  1.72088451e-04,\n",
              "        -1.97154444e-05, -4.42976118e-06],\n",
              "       [-1.28516162e-03, -2.42411229e-05, -1.97154444e-05,\n",
              "         6.73073105e-05,  2.26268665e-05],\n",
              "       [-6.16583945e-04,  7.84261804e-06, -4.42976118e-06,\n",
              "         2.26268665e-05,  1.18409551e-05]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 41
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QGKgCwf3uzzv",
        "colab_type": "text"
      },
      "source": [
        "Next we post-multiply  $(X'X)^{-1}$ by $X'$ "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "X1L-n92vv80N",
        "colab_type": "code",
        "outputId": "2baf1960-0e51-47c0-e4dd-b0fdf02b31b8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 202
        }
      },
      "source": [
        "X_trans_X_inv_X_trans = np.matmul(X_trans_X_inv, X_trans)\n",
        "\n",
        "print(\"Shape of inverse of X'X by X' is\",X_trans_X_inv_X_trans.shape)\n",
        "X_trans_X_inv_X_trans"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Shape of inverse of X'X by X' is (5, 10470)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1.02619623e-03, -2.95245047e-04,  7.55096093e-04, ...,\n",
              "         1.31332224e-03,  1.58900649e-03,  5.26377494e-04],\n",
              "       [-1.49719089e-04, -1.51956426e-04,  5.36838477e-05, ...,\n",
              "        -4.28437218e-04, -1.57634514e-04, -1.94877178e-04],\n",
              "       [ 1.07104839e-04,  4.99192086e-05,  1.43862472e-05, ...,\n",
              "         2.37504817e-04,  1.12147679e-05,  4.74361366e-05],\n",
              "       [-4.16683948e-05,  1.99584706e-05, -5.13542830e-05, ...,\n",
              "        -2.71342821e-05, -2.64207181e-05,  5.92371961e-06],\n",
              "       [-1.88282036e-05,  1.32142768e-05, -9.85399940e-06, ...,\n",
              "        -2.93709314e-05, -2.45853172e-05, -4.20709539e-06]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 42
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4SnTNH_ufBT8",
        "colab_type": "text"
      },
      "source": [
        "## Model Training or Fitting-The-Model"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ucr6b14wyNob",
        "colab_type": "text"
      },
      "source": [
        "Finally we find our coefficients by post-multiplying $(X'X)^{-1}X'$ by $y-train$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YQQB_aLuyAy4",
        "colab_type": "code",
        "outputId": "466a0438-3f73-4707-e218-eb0ad451fd9c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 118
        }
      },
      "source": [
        "coefficients = np.matmul(X_trans_X_inv_X_trans, y_train)\n",
        "\n",
        "print('Final shape of coefficients is',coefficients.shape)\n",
        "coefficients"
      ],
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Final shape of coefficients is (5, 1)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[188.52046097],\n",
              "       [  5.33277744],\n",
              "       [  3.85299841],\n",
              "       [  7.08266566],\n",
              "       [ -2.66311109]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 43
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "q6acDCYay8oJ",
        "colab_type": "text"
      },
      "source": [
        "### Thus our Multiple Linear Regression Model Ideal Parameters are:- "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hCU4smeuC4QH",
        "colab_type": "code",
        "outputId": "b48af5cd-4562-4d2d-c8c7-e4e6d823da7d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 101
        }
      },
      "source": [
        "intercept = coefficients[0]\n",
        "\n",
        "b1 = coefficients[1]\n",
        "\n",
        "b2 = coefficients[2]\n",
        "\n",
        "b3 = coefficients[3]\n",
        "\n",
        "b4 = coefficients[4]\n",
        "\n",
        "print('Intercept or bias unit is:',intercept)\n",
        "print('b1 or slope for ENGINE_SIZE variable is:',b1)\n",
        "print('b2 or slope for CYLINDERS variable is:',b2)\n",
        "print('b3 or slope for FUEL_CONS_CITY variable is:',b3)\n",
        "print('b4 or slope for COMB_MPG variable is:',b4)"
      ],
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Intercept or bias unit is: [188.52046097]\n",
            "b1 or slope for ENGINE_SIZE variable is: [5.33277744]\n",
            "b2 or slope for CYLINDERS variable is: [3.85299841]\n",
            "b3 or slope for FUEL_CONS_CITY variable is: [7.08266566]\n",
            "b4 or slope for COMB_MPG variable is: [-2.66311109]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mxHbzurmQBeh",
        "colab_type": "text"
      },
      "source": [
        "## Model Evaluation"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "M77oKO7pQGgQ",
        "colab_type": "text"
      },
      "source": [
        "#### Let's define a simple method for prediction"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "c3ydmbaSGKnm",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def predict(x):\n",
        "    \"\"\" takes a row of test data and predicts it\n",
        "    and returns only the float value of the observation\"\"\"\n",
        "    x = list(x)\n",
        "    \n",
        "    x = x[0]*intercept + x[1]*b1 + x[2]*b2 + x[3]*b3 + x[4]*b4\n",
        "    \n",
        "    return x[0]  # returns the float of value of x"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ihljpoLLQoto",
        "colab_type": "text"
      },
      "source": [
        "Next let's convert the test data to a Data frame so we can apply the predict method on it"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7gZDiu7wIaBU",
        "colab_type": "code",
        "outputId": "cacc91a7-d59e-44e6-a7dc-c60cd3d4509c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 195
        }
      },
      "source": [
        "X_eval = pd.DataFrame(X_test)\n",
        "\n",
        "X_eval.head()"
      ],
      "execution_count": 46,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<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>0</th>\n",
              "      <th>1</th>\n",
              "      <th>2</th>\n",
              "      <th>3</th>\n",
              "      <th>4</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1.0</td>\n",
              "      <td>3.5</td>\n",
              "      <td>6.0</td>\n",
              "      <td>13.4</td>\n",
              "      <td>25.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1.0</td>\n",
              "      <td>2.0</td>\n",
              "      <td>4.0</td>\n",
              "      <td>9.0</td>\n",
              "      <td>34.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1.0</td>\n",
              "      <td>3.5</td>\n",
              "      <td>6.0</td>\n",
              "      <td>12.2</td>\n",
              "      <td>27.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1.0</td>\n",
              "      <td>1.8</td>\n",
              "      <td>4.0</td>\n",
              "      <td>9.4</td>\n",
              "      <td>34.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1.0</td>\n",
              "      <td>6.1</td>\n",
              "      <td>8.0</td>\n",
              "      <td>16.0</td>\n",
              "      <td>21.0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "     0    1    2     3     4\n",
              "0  1.0  3.5  6.0  13.4  25.0\n",
              "1  1.0  2.0  4.0   9.0  34.0\n",
              "2  1.0  3.5  6.0  12.2  27.0\n",
              "3  1.0  1.8  4.0   9.4  34.0\n",
              "4  1.0  6.1  8.0  16.0  21.0"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 46
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mKndu5mMQzSm",
        "colab_type": "text"
      },
      "source": [
        "Next let's apply the predict method and pass axis=1 so it's done along the columns<br>\n",
        "Then we convert it to a numpy ID array using the .values and assign it all to y_hat.<br>\n",
        "y_hat is then our model's prediction on the out-of-sample or test data set"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5d6OJXMALHxl",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "y_hat = X_eval.apply(predict, axis=1).values"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qwtwwNQNgGPE",
        "colab_type": "text"
      },
      "source": [
        "y_hat or our model prediction is now a numpy 1D array. This will be useful for plotting"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ME9eGBJYLPJV",
        "colab_type": "code",
        "outputId": "1fe97666-eac1-42dc-9c24-4d5ec62ea23f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 50
        }
      },
      "source": [
        "y_hat"
      ],
      "execution_count": 48,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([258.63311518, 187.79622351, 244.80769421, ..., 200.92168918,\n",
              "       204.46302201, 194.88720045])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 48
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hdO73AdjgCTN",
        "colab_type": "text"
      },
      "source": [
        "## Importing Metrics from Sklearn to evaluate the model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Wstoq2SDEw4Y",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from sklearn.metrics import mean_squared_error, r2_score"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WxixHWidTvQw",
        "colab_type": "text"
      },
      "source": [
        "Let's compute the Mean Squared Error"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GZJ3LkNNRMXT",
        "colab_type": "code",
        "outputId": "8720c1fb-eac2-4bbb-b2a9-90cebb767024",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "MSE = mean_squared_error(y_hat, y_test)\n",
        "MSE"
      ],
      "execution_count": 50,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "444.1983754997918"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 50
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hfGlx_UwT2k1",
        "colab_type": "text"
      },
      "source": [
        "Lets find the RMSE which is the square root of the MSE"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "J9cg-EZQT4cT",
        "colab_type": "code",
        "outputId": "0c85bb28-464a-4650-abaf-654a91e5d365",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "RMSE = MSE**0.5\n",
        "\n",
        "RMSE"
      ],
      "execution_count": 51,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "21.076014222328467"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 51
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7NnaePlVUI_K",
        "colab_type": "text"
      },
      "source": [
        "**Finding the RMSE as a percentage of the range of the target variable.\n",
        "The lower the percentage the better the model**\n",
        "\n",
        "First we find the range of the target variable"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xlNmV1DMUIA3",
        "colab_type": "code",
        "outputId": "2d063ca1-4a9e-4423-8da9-545df3e8bd7d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "y_range = y_test.max() - y_test.min()\n",
        "y_range"
      ],
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "439"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 52
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1lvurG8HVUM1",
        "colab_type": "text"
      },
      "source": [
        "Next we compute the RMSE as a percent of the range, the lower the error percent, the better the model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aVlbNnqCVGvd",
        "colab_type": "code",
        "outputId": "49616307-b961-44fb-a042-36d219c4e0c7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "error_margin = (RMSE / y_range) * 100\n",
        "\n",
        "error_margin"
      ],
      "execution_count": 53,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "4.800914401441565"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 53
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KdgcrIA9VkHA",
        "colab_type": "text"
      },
      "source": [
        "Finally let's compute the  R2  score or coefficient of determination of our model prediction.<br>\n",
        "This tells us how confident the model is on each prediction<br>\n",
        "The highest value is 1... So the closer to 1, the better the score"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Os1khJsSVk-H",
        "colab_type": "code",
        "outputId": "6622ee0a-f2eb-4390-d43a-f2e46204269b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "r2_score(y_test, y_hat)  # pass in the true values first, then the predicted values."
      ],
      "execution_count": 54,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.8724117885849141"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 54
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x2jPJtaDWnM1",
        "colab_type": "text"
      },
      "source": [
        "## Visualization"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zXUpdaDCWqln",
        "colab_type": "code",
        "outputId": "4e9ae2dc-e4c6-4d50-b224-b2e0689c7bca",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 497
        }
      },
      "source": [
        "fig = plt.figure(figsize=(20, 7))\n",
        "plt.suptitle('Distplot and Regplot for Predictions of MLR Linear Algebra Model on Test data set', fontsize=16)\n",
        "\n",
        "ax = fig.add_subplot(121)\n",
        "ax1 = fig.add_subplot(122)\n",
        "\n",
        "# plotting the Distplot\n",
        "sns.distplot(y_test.squeeze(), hist=False, label='Target', color='navy', ax=ax)\n",
        "sns.distplot(y_hat.squeeze(), hist=False, label='Prediction', color='red', ax=ax)\n",
        "ax.set_xlabel('CO2_EMISSIONS', fontsize=14)\n",
        "ax.set_title('Distplot showing Prediction VS Actual for our Linear Algebra Model')\n",
        "\n",
        "# plotting the Regplot\n",
        "sns.regplot(y_test.squeeze(), y_hat, scatter_kws={\"color\": \"navy\"}, line_kws={\"color\": \"red\" ,'linewidth':3}, ax=ax1)\n",
        "ax1.annotate('y_hat = {} + {}(Engine_Size) + {}(Cylinders) + {}(Fuel_Cons) + {}(Comb_L)'.format(np.round(intercept), \n",
        "                                                             np.round(b1[0]), \n",
        "                                                             np.round(b2[0]), \n",
        "                                                             np.round(b3[0]),\n",
        "                                                             np.round(b4[0])), \n",
        "                                                             xy=(140,420), \n",
        "                                                             rotation=32, \n",
        "                                                             fontsize=11.5, color='black')\n",
        "ax1.set_xlabel('CO2_EMISSIONS', fontsize=14)\n",
        "ax1.set_title('Regplot showing Prediction for our MLR Model')\n",
        "\n",
        "\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": 55,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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jRkBfXx88Hg9nzpzBxIkTkZSUxDYMzZs3D1FRUYiMjGTLU7du3QC8u/d88803bG/xq1ev\nYs6cOeDxeAK9KxuTts8AcOrUKUyfPh3u7u5YtWoV6uvr2eN6+PBh6OrqYuPGjQgMDESPHj0QFBQE\nANDW1m7KISKE/FsxhJD/pIMHDzIcDod5/PixyN8zMzMZDofDHDt2jGEYhsnLy2M4HA5z8OBBhmEY\nJjc3l+FwOMydO3fExrFu3TqGw+EwPB5PYDk/rK+//pqpq6tjl2dnZzMcDodJTk5ml7m6ujJz585l\n/w4NDWWsra2Z169fs8vevn3L2NraMlOmTGGX+fn5MSNHjpQlK4TU1tYyFRUVjJWVFbNt2zZ2OT/P\n1q5dK7D+5MmTmf79+7N/79u3j+FwOExOTg67rK6ujvnmm28YDofD5OXlSYx/7ty5jLOzM8Pj8Rge\nj8c8e/aMiYyMZCwtLZkbN24IrNuvXz9m7NixAsvevn3L2NnZMUuWLGEYhmFKS0sZKysrJiIiQmC9\nrVu3MhwOh1m3bh27jH/MEhMTBdZdsGABY2Vlxeb7lStXGA6Hw1y5coVhGIZ59eoVY2pqKnCsGIZh\nUlNTGQ6Hw5w5c4ZhmP879g2PsSTJyclCeXbu3DmBssg3f/58xtTUlHn58qVAGkNCQmSKi7/+xYsX\nGR6Px7x9+5Y5fvw4Y2VlxQwcOJBdz8/PjzEyMmJu374tsH1WVhbD4XCYQ4cOCSxPS0tjOBwOu35T\nykfj8j979mzGysqKefbsmdj9EFf2+eWXH/69e/eEjj/DMEx8fLzAuc0/Zn5+fgLrbd68meFwOGxa\nNm/ezNja2opNlziDBg1i3N3dBa4Tf//9N2NiYsIsW7aMXRYdHc1wOByZwnR1dWXCwsKY+vp6xtXV\nlS3PERERzIgRIxiGEZ1PHA6HiY6OFhsuPy/27t3L8Hg8pqKigrl06RLj7OzMhIaGNilt0uJoWL7n\nzp3LcDgc5vLly+yy6upqxs7Ojlm4cCG7bN68eYy9vT1TUlIiEGZAQAAzYMAAsXHyeDy2/N66dUso\n3tOnT8u0bwzDMBMnTmSsra2ZqqoqhmEYZtWqVQyHw2Hu378vsJ6fn59AmVq9ejVjamrKFBYWsssq\nKyuZnj17Chx3Wc+zpt5nLCwsmOLiYon7Vltby/B4PKZ///7Mjz/+KDUv+OWprKyMsbS0ZI4ePcrm\n0cyZM9m4G5aH5cuXM8bGxgL35traWqZ///6Mr68vu2zEiBFC+5aTkyN0rsbFxTFmZmbMo0ePBNK2\nYMECxs7Ojj3vGl8fRJH1Os/fd3d3d6ampoZddvz4cYbD4TC//fab+ExrRNw5+fr1a8bS0lLovvbw\n4UPG2NiY2b17N8Mw765njo6OEuMYNmwYM27cOJnSExUVxZibmwuUlTdv3jDW1taMmZmZ2O3q6uoY\nHo/HjB49mpk+fTq7PCMjg+FwOExWVpbEePnbz5o1ixk6dKjEdaXtc11dHdO7d29m4sSJAstfvXrF\nWFtbMytXrmSX9erVi5k/f77E+Agh/z00nI0QIhLT6OtsjXXu3BmtWrVCREQE0tLSZP4yUUMeHh4C\nby2tra3Z3gLiZGVloU+fPmjVqhW7TENDA25ubu/VsyA9PR3Dhg2DjY0NTExMYGVlhYqKCoEhNXx9\n+vQR+JvD4QgMY8nJyUH79u0F5nCQl5fH119/LXN6ioqKYGpqClNTU/Tu3Ru7du3CsmXLYGlpya7z\n+PFj/P333/Dx8UFtbS37T0VFBVwuF9nZ2QCAP//8ExUVFfD09BSIQ9LcSo3T6uXlhYqKCqFhcny/\n//47eDweBgwYILSdoqLiB+31kZWVBXl5eXh7ewssHzBgADvRcUPu7u5NCn/ChAkwNTWFtbU1pk+f\nDnt7e6HeAgYGBjA2NhZYdvHiRSgpKcHDw0PgeDg5ObHpBt6vfPz666/o06cP2rVr16R9EoWfnsbH\njP9342PWu3dvgb85HA4AsOe+ubk5Xr9+jVmzZuH8+fNSeyABQEVFBW7fvo2vv/5aoGdCx44d0aNH\nj/cuN3JycvDx8UFaWhpqampw/PjxDzJ57uLFi2FqagorKysEBASgbdu2bE/Aj0VVVZXtcQS8mz+m\nc+fOAteeixcvwsXFBS1bthQqg3fv3mWHHNXU1CAhIQGenp6wsLCAqakp21Po0aNHAvEqKSnB1dVV\npjQ+f/4cv/76Kzw9PdGiRQsAYPNb2tevbty4ASsrK+jp6bHLVFRU2J43DfdRlvOMT9b7jKWlpVCv\nU+D/hvzY29vDxMQEpqamePz4sVA+SaKuro5+/fohLS2NzSNx5TArKwuWlpYCcxUqKCjA29sbd+7c\nQVlZGerq6nDz5k2hfbOysmJ7UPFdvHgRlpaW6NChg1B+lZaW4v79+zLvR1Ov87169RLo7dX4mvE+\nsrOzUVlZKXT/69ixIzp27Mje/8zNzfH8+XOEh4cjIyNDaNhdU924cQM2NjYCZaVly5ZC10fgXX5N\nnDgRPXv2hLGxMUxNTZGdnS1z2Xnw4AGmT58OJycntuwdPnxY6vbS9vmvv/7Cs2fPMGDAAIG809DQ\ngLm5OZt3hBAiDg1nI4SIxJ/rRNyXnFq2bInt27dj/fr1+OGHH1BeXo5u3bohNDRU5omf27ZtK7RM\nW1tbaD6Dhl6/fi2yot+2bVuh+Txkde7cOcyYMQODBg3C1KlT0aZNG8jJyWHy5Mkihz/xhy7xKSsr\nC6z3/PlzkV2+m9INXFtbG4mJiWAYBn///TfWrFmD+fPnw8jICF26dAEAvHz5EgCwYMECLFiwQCgM\n/pdenj9/LjJ+UfkvLq38v0V12QeA0tJSABA6NoqKitDU1Gz2sRHl9evXaN26tdCkt/z9aRyXqPIi\nyeLFi2FhYQEVFRUYGBiI/HqSqDBfvnwJHo8ndgJYfh69T/koLS0VeMh+H/x8arwv/L8b52PjiZH5\n+c+fh8bOzg5r167Fzp07MXXqVADvJp0ODw9H9+7dRabhzZs3YBhG5HWmbdu2H2TSYV9fXyQkJCA+\nPh4VFRX45ptv3jvMb7/9Fn379kVVVRVOnDiBnTt34vvvv0dUVNR7hy1Ow4ZzvsbXnpKSEqSmpopt\nsHn16hU0NDQQHR2NnTt3IiQkBFwuF+rq6igqKsLUqVOF5hVq06aNyOHIohw+fBh1dXXo27cv24io\no6MDY2NjHD58GDNmzBA7Kfrz58/ZYTwNNb5OyXqeidseEH2fEXVO37p1C5MnT4aTkxOWLl0KHR0d\nyMvLY+HChU0eGuvr64ugoCAkJSVBS0tL7Pxsr1+/Fmqg5u8HwzB4/fo1qqqqwOPxRO5b42UlJSV4\n8uSJ2K9hNs4vSZp6nRd1rwQgcu6qpuLf/0aPHi3y9w4dOgAAnJ2dER0djV27drFDuB0cHBAeHi6y\nvElTXFwMa2troeWNr995eXkICAiAqakpIiIioKenBwUFBaxatUpiHYfvzZs3GD9+PFq3bo05c+ag\nQ4cOUFJSws8//4yTJ09K3FbaPpeUlAAAZs2ahVmzZglt37lzZ6npI4T8t1EjEiFEpAsXLqBFixYS\nP8NubGyM2NhY1NbW4ubNm0hMTMR3332HtLQ09o2jJC9evBBa9vLlS5EVaL7WrVuL3O7FixdCFVZZ\nHTt2DJ06dcLy5cvZZTwer9kNHzo6OiLf7vIrvbJQVFSEubk5AMDCwgImJiYYMGAAVqxYwU7iyX+o\nDwsLQ8+ePYXC4L8B5lf4X758KVBpFpWPDdPasPGEn3ZxjYr8tLx48UIgjtraWpSWljb72IjSunVr\nvH79WugrUfz9aRxXUydQNjQ0ZPNeHFFhampqokWLFti1a5fIbfh59z7lo02bNjI9gMiCn08vXrwQ\nmMuH3+jYnGPm6ekJT09PlJeX49q1a1i1ahUmTpyIzMxMkY0HrVq1gpycHBtnQy9evPggX/QyNDSE\npaUlNm7cCHd3d5GNMU1lYGDAlhFbW1uUl5cjJSUFo0aNgoWFxXuH31yampqwtrZmJ+ttjN+D7dix\nYxg4cKDAvGhXrlwRuU1Tzh9+41VwcLDI369cuSK28URHR4d9uG2o8XVK1vNM3PaA6PuMqP08deoU\nFBQUEBsbK9Cj5s2bN00uR7169YKWlha2bt2KgIAAsQ1zku5xcnJyaN26NVRVVaGkpCR2vYa9kTQ1\nNaGlpSXyRQMAgfmTpPmU13lp2rRpAwBYvXq1QK8tvoZzwXl5ecHLywtlZWW4cuUKVq5ciaCgIJw7\nd67J8erq6oq8VjdeduHCBXZ+t4ZfxayoqJApnuzsbBQVFSE+Pl7gflRbWyvT9pL2mX8cw8PDYWNj\nI7QtvxchIYSIQ8PZCCFCTp48iXPnzmHkyJFQVVWVur6ioiKsrKwwffp01NfXs1/34D/gV1VViY2n\n4Re/fvvtNzx79kzip3xtbW2RmZkp0D27rKwM58+fh52dHbtMWVlZ5redVVVVQhX6tLS0Zn/+m8vl\norCwUGC4RH19PY4fP96s8ADgq6++wpgxY5CRkcF+ie6rr76CgYEB/vrrL5ibmwv94/f+4HA4UFNT\nw4kTJwTCbPx3Q43TeuzYMaipqYmdSNbS0hJKSkpCX2FKT09HbW0te2yklQlZ2NnZob6+Xij9R44c\ngZKS0mf7FLSzszOqq6tRVlYm8njwH+Dfp3w4Ojri/PnzYnuEAbKXff6E+Y2PGf/rPw3Pp6ZSV1eH\nq6srRowYgefPn4vt7aCmpgZTU1OcOHFC4HzjT9L/PmloaOLEiXB1dYWfn98HCa+xsLAwqKiosF+k\n/FycnZ1x7949dOvWTWQZbHj+NZ7YWNrX7qS5desW/vzzT4wYMQLbt28X+LdlyxYoKyvj0KFDYre3\nsrLCjRs3BL74V1VVxX4lreE+ynKe8TXnPsNXWVkJeXl5gQamy5cvN+srfPLy8ggJCYGrqyuGDh0q\ndj1bW1v8/vvvAl+Qq6urQ3p6OkxMTKChoQEFBQWYmZkJ7dvvv/8u1HvP2dkZjx49gr6+vsj8kjTx\nfmOyXuc/BRsbG6ioqCAvL0/kfolqHNPQ0EC/fv0wdOhQ5Ofns/UIZWVlme9JVlZWyM7OFmj4fvv2\nrdDX8/hftm14nv3555+4efOmwHriemfx09Ow8fLly5dC54M0ovaZw+FAV1cXDx48EJl3DV8CNiVv\nCCH/HdQTiZD/uDt37uDVq1fg8XgoKCjAhQsXcOLECTg6OiIsLEzsdufPn8e+ffvQr18/dOjQAZWV\nldixYwfU1dXB5XIBgB12tW3bNvTu3Rvy8vICb9TKy8sREhKCkSNHoqSkBNHR0ejcubPEOUtCQkJw\n4cIFBAQEYNKkSZCTk8OmTZtQWVmJKVOmsOt16dIFu3fvRnp6Ojp27Ah1dXV89dVXIsN0dnbGmTNn\nsGzZMri6uuKPP/7Azp07m91jwdfXFxs3bsTUqVMxc+ZMaGtrY8+ePe89F8PkyZORnJyM9evXIyEh\nAXJycoiIiEBISAh4PB6+/vprtGnTBi9evEBOTg709fXZ7vBjx45FYmIi1NXV2a+zHTx4EIDoN/DJ\nycmor6+Hubk5fvnlF+zfvx+hoaFiv1qjqamJwMBAJCYmQlVVFS4uLnjw4AHWrFkDa2trdh6ptm3b\nQlNTE8eOHYORkRFUVVXRoUMH9q2yLHr37g1ra2tERESgpKQE3bp1Q0ZGBvbv34+goCCBt76fkr29\nPby9vTFt2jQEBATAwsIC8vLyyM/PR0ZGBmbNmgVDQ8P3Kh+hoaHIyMjAyJEjERwcjP/9738oKirC\nxYsXsWrVKgCyl30OhwNvb2/ExcWhrq4OXC4XOTk52LBhA7y9vWX+8hTf2rVr8fLlS9jb20NXVxfP\nnj3Djh07YGxsLPGYTJ8+HUFBQQgKCsLo0aNRUVGB2NhYaGhoYPz48U1Kgzj9+/dH//79ZVr30aNH\nIhtYRfX249PR0cHo0aOxdetW3Lx5U+grio0VFhaKjIN/7WyuadOmYdiwYRgzZgz8/PxgYGCAN2/e\n4M8//0ReXh473M7Z2RmpqangcDjo1KkTTp06xX5Zs7kOHToEOTk5TJo0CR07dhT6vV+/fjhz5gzK\ny8uhrq4u9HtAQAD27NmDCRMmYMqUKezX2ZSVlQWuUbKeZ3zNuc/wOTs74+eff0Z4eDiGDBmCR48e\nYf369c2ek2zUqFEYNWqUxHUCAgJw6NAhBAYGIjQ0FBoaGti9ezceP36MxMREdr1p06YhMDBQYN9i\nY2OFhpoFBAQgPT0do0ePRkDkTBEBAAAgAElEQVRAAAwNDVFZWYmHDx8iOzsbGzZskDn9sl7nPwVN\nTU2EhYVhxYoVKC4uhpOTEzss8+rVq+jduzc8PT2xatUqlJWVwc7ODjo6OigoKMCePXtgZWXFNqB1\n6dIFqampOHnyJPT19dGyZUuxQ7omTJiA5ORkNu8VFRWxceNGqKurCzQEOTk5ISYmBrNnz8bYsWPx\n7NkzxMbGsl9M5fvqq68gLy+P/fv3sz3MunTpAmtra6ipqWHx4sWYMmUKysrKEB8fj7Zt2wo0tIoi\nyz4vXrwY06dPR2VlJTw8PKCpqYkXL17g+vXr6Ny5M9vg3qVLF1y9ehUZGRnQ0tKCtrY2O1SeEPLf\nRY1IhPzHTZ8+HcC77sva2towMTFBdHQ0PD09JQ5j6NSpE1RUVLB+/Xo8f/4c6urqMDc3x7Zt29g5\nW1xdXTF69Gjs3r0b8fHxYBgG9+7dY8OYPHky/v77b4SHh6OyshL29vZYtGiRwJu3xrp3744dO3Yg\nJiYG4eHhYBgGlpaW2Llzp8C8K5MmTcKjR4+wYMECVFRUwM7Ojv0UeWPDhw9HYWEhDh48iH379sHc\n3BwJCQnsvC5NpaysjG3btiEyMhI//PADVFVV4e3tjT59+iAiIqJZYQLv5lzw9/dHYmIibt++DRMT\nE7i4uGDnzp1ISEjAwoULUVVVBR0dHVhaWgrM/TJt2jQAwIEDB7Bjxw5YWloiKioKo0aNEtkwtH79\nevz4449Yv349WrZsiW+//VZg6IsoM2bMgJaWFvbs2YM9e/ZAU1MTvr6+CAsLY4cyycvLY+nSpYiO\njsb48eNRW1uLqKgoiZ8rbkxeXh4bN25EdHQ0Nm/ejNLSUhgYGGDevHkYN26czOF8DCtXrsSOHTtw\n8OBBJCQkQFlZGQYGBnBycmLnKnmf8tGhQwckJydjzZo1WL16NSoqKtCuXTv20+1A08p+VFQUOnTo\ngIMHD2LDhg3Q1dXFxIkTm1X2LS0tsWPHDkRFRaG0tBTa2tpwdHRkrzHi9O7dG4mJiYiPj8d3330H\nJSUl2NnZYfbs2R9kAvGmOnnypMg5Rw4cOCCxsXPSpEnYt28f4uPjpT6YZ2dni5y8du3atVIboCTR\n19fHwYMHERsbi+joaLx69Qqampro1q2bQKPJwoULwTAM1qxZA+DdMVi9ejWGDRvWrHh5PB6OHj0K\ne3t7kQ1IADB06FCkp6fj5MmTIs93LS0tJCUlYcmSJZg7dy40NTUxcuRIvHr1CmlpaQLrynKe8TXn\nPsPn7OyMhQsXYtu2bTh16hS6deuGn376qUkNL03Vrl077N69G6tWrcL333+PmpoaGBsbIzExUWDy\n5l69emHVqlWIjY3F1KlT0alTJ8yfPx/bt28XCK9ly5bYu3cv4uPj2U/Rt2zZEoaGhjI3rDYky3X+\nUxk7diz09fWRlJSE1NRU1NfXo127drC1tWV701hZWWHXrl04ffo0Xr9+jbZt28LZ2VnguvTtt98i\nLy8P4eHhqKiogJOTE7Zs2SIyTh0dHSQlJWHZsmWYPXs2tLW1MWbMGLx58wY///wzu56JiQmWL1+O\n9evXIzg4GJ07d8a8efNw4sQJ3Llzh11PV1cXCxYswNatW+Hn54e6ujrs27cPVlZWWLduHVauXInQ\n0FDo6ekhICAABQUFAvGIIss+u7u7Y/v27UhISMCCBQvYugOXyxWYOH327NmIiIjAtGnTUFVVhREj\nRiAyMrJpB4oQ8q8jx0j7BBMhhHxgT58+Rd++fbFkyZJmP7SQ93fixAlMnz4du3btYudFiI2NRVxc\nHG7duiU03IUQQj6luro6DBo0CG3atJH64EwIIYSQT4OeEAgh5D/g999/x4ULF2BpaYkWLVrg5s2b\n2LRpE6ysrER+aYYQQj61NWvWoFOnTtDX10dpaSn279+Pe/fusR8TIIQQQsjnR41IhBDyH6Cmpobs\n7Gzs3r0bZWVl0NLSgqenJ8LCwpr89TJCCPkY5OTkEB8fj+LiYsjJycHIyAjx8fFwcXH53EkjhBBC\nyP9Hw9kIIYQQQgghhBBCiFSfdgY8QgghhBBCCCGEEPKPRI1IhBBCCCGEEEIIIUQqakQihBBCCCGE\nEEIIIVJRIxIhhBBCCCGEEEIIkYoakQghhBBCCCGEEEKIVNSIRAghhBBCCCGEEEKkokYkQgghhBBC\nCCGEECIVNSIRQgghhBBCCCGEEKmoEYkQQgghhBBCCCGESEWNSIQQQgghhBBCCCFEKmpEIoQQQggh\nhBBCCCFSUSMSIYQQQgghhBBCCJGKGpEIIYQQQgghhBBCiFTUiEQIIYQQQgghhBBCpKJGJEIIIYQQ\nQgghhBAiFTUiEUIIIYQQQgghhBCpqBGJEEIIIYQQQgghhEhFjUiEEEIIIYQQQgghRCpqRCKEEEII\nIYQQQgghUlEj0j/A4sWLER8f/8HDjY2NxaxZsz54uI25ubnh0qVLHy38goICcLlc1NXVfbQ4PpaG\neZOQkIAFCxY0KxwvLy9cvXr1QybtX01a2d+9ezd69eoFLpeLV69efcKUfVjvU6Y+tQ91PXr69CmM\njIxQW1v7AVL16aSkpGDUqFEyrRseHo6YmJiPnCJCCPk4jIyM8OTJk48aR1Ouqc31sernH1vjvOFy\nucjLy2tyOIcPH0ZgYOCHTBrr31IP+6ehugiRFTUifWZubm6wsLAAl8uFjY0NRo4ciT179qC+vp5d\nJzIyElOmTJEprI/VWPOxG4Leh76+PnJycqCgoPDBww4PD4eZmRm4XC7s7Owwfvx4PHjw4IPHAwDB\nwcFYunSpTGlqfNE+duwY7O3tP2h6Fi9ejDlz5ggtv3v3LszMzFBaWoo3b95g3rx5cHR0BJfLhYeH\nBzZu3Cgx3PLycnC5XEycOFHmtHyKyiAfj8fD8uXLsXXrVuTk5KBNmzafJN7mktRoImuZ+pTCw8Nh\nYmKC4uLiz52UZuHnt6+vr8DykpISmJmZwc3N7TOljBBCZNew/uno6Ijw8HCUl5d/7mQJ+JT3/uaQ\ntX7eVPz7DJfLBZfLhZubm9S61fvIyclBx44dZUpTw7rGgAEDsHXr1g+enn9qPUyWeoG456mrV6+i\ne/fu7DH38PDAwYMHP0ichHwM1Ij0BUhISEBOTg7Onz+PSZMmYdOmTf+Y3gP/BRMmTEBOTg4yMjKg\npaWFefPmiVzvn9bzQZpBgwbh9OnTqKioEFielpYGV1dXaGpqIioqChUVFUhPT8dvv/2G9evX43//\n+5/EcE+dOgVlZWVcunQJz58//5i70CwvX75EdXU1unbt2uRtGYYRaAD+0P4pZUxcr8CKigqcPHkS\nLVu2xOHDhz9xqkRrbp5WVlbizz//ZP8+evQoDAwMPlSyCCHko+PXP1NTU3H79u2P2lBBmi4rKws5\nOTlYvXo14uPjkZmZKbTOP6Ve0BT/1HrY+9YLdHV1kZOTg+vXr2P+/PlYtGgRHj58KHEbqouQz4Ua\nkb4gLVu2RN++fbFmzRocOnSIvSg07HlSUlKCoKAg2NjYwM7ODqNHj0Z9fT1mz56NgoICBAcHg8vl\nYtOmTWwr9b59++Dk5AQnJyds2bJFbPxnz56Fl5cXbGxs4O/vz/a4ERV2Y+LSxXfnzh34+PjA2toa\n3333Haqrq9nfkpOT4e7uDjs7OwQHB6OoqAgAsG7dOvz4448A3r2VsLKywooVKwAAVVVVMDc3R2lp\nqdDbEX9/f6xZswYjR44El8tFYGAgSkpK2PhSU1Ph6uoKe3t7xMfHy9zLSlVVFT4+Pvjrr78AvBt+\nM23aNMyaNQs9evTAoUOHUF9fj40bN6Jfv36wt7fH9OnTUVpaKjLuDRs2CITfeDhPdnY2Ro4cCRsb\nG7i4uCAlJQX79u3DkSNHsGXLFnC5XAQHBwMQfLNRU1ODpUuXssd86dKlqKmpAfDuTUfv3r2xdetW\n9OzZE05OTmLfdHC5XOjq6uLUqVPssrq6Ohw5cgQDBw4EAPzxxx/w8fFB69atIS8vjy5dusDT01Ni\nPh46dAgjR46EkZGRUENCYWEhpk6dCgcHB9jb2yMyMhIPHjxAREQEbty4wfbYA94d5/3797PbNn5j\nuWTJEri4uKBHjx4YPHgwsrOzJaYLAB49esSm39bWFmPHjgUAXL9+HUOGDIG1tTWGDBmC69evs9v4\n+/sjJiYGI0eOhKWlpcgu4Q8ePIC/vz9sbGzg5eWFs2fPCmwvaT+MjIywa9cu9O/fH/3795e6Dw01\nLFP88+TQoUPo06ePUBmUVnanTZsGR0dHWFtbY8yYMex5ALy7RkVERGDSpEmwsrISO7Ty1KlTaNWq\nFUJCQpCamiox7ZLOU2lpBYCDBw+KvO6JOm9zc3MxYsQI2NjYwMnJCZGRkew5I87AgQNx6NAhgfQ2\nfiMo6bi/evUKwcHB6NGjB4YOHYq///5baNvx48fDzs4OHh4eSE9Pl5geQghpLh0dHTg5OeHOnTvs\nspqaGqxYsQJ9+vRBr169sHjxYlRVVbG/b9q0ib3G7t+/X2CIWnh4OBYvXozx48eDy+XCz88P+fn5\nIuN++/Yt5syZAwcHB7i6umL9+vWor68Xe+9vLCUlBX379mV77DSuV6xYsQK2trZwc3NDRkYGu7yo\nqAjBwcGws7ODu7s7kpOTAQDV1dWwsLBg640bNmyAiYkJysrKAABr1qxhe/g2rJ9Lq181vOYPGTIE\nMTExMvey4nK56Nq1K3vfFVUvkHTPkHa/aXjsqqqqsHz5cri6usLa2hqjRo1CVVUV/Pz8ALyrG3G5\nXOTk5AjVV6TVlSTVzfn+yfUwWeoFspCTk4OLiwtat26Ne/fuSVyX6iLkc6FGpC+QhYUF9PT0RD70\nbtu2De3atcPly5fx66+/YubMmZCTk8PKlSuhr6/PvlWaNGkSu83Vq1dx6tQpbNmyBZs2bRLZYPLo\n0SOEhYVh/vz5uHz5Mnr37o3g4GDU1NRIDFtauviOHz+OzZs34+zZs7h37x5SUlIAAJcvX8bq1aux\nZs0a/PLLLzAwMMDMmTMBvLt5XLt2DcC7xoq2bduyeZKTkwNDQ0NoamqKzMOjR48iKioKly9fBo/H\nY7vb3r9/Hz/88ANWrlyJixcvoqysjG20kqa8vBxHjhyBsbExu+zs2bPw9PREdnY2fHx8sGPHDpw5\ncwY7d+7ExYsX0bp1a0RGRgrE/dNPP+HixYsoLS3Fs2fPRMaVn5+PSZMmwc/PD5cvX0ZqaiqMjY0x\nYsQI+Pj4sL2jEhIShLbdsGEDfv/9d6SlpeHw4cP4448/sH79evb3Fy9e4O3bt8jMzMTSpUsRGRmJ\n169fi0yHr6+vwMP+pUuXUFtbCxcXFwCApaUlYmJicPDgQTx+/FhqHubn5+PatWvw8fGBj4+PQNh1\ndXUICgqCvr4+zp07h8zMTHzzzTfo0qULfvjhB1hZWSEnJ0emxiAAMDc3R2pqKq5duwZvb29Mnz5d\noPFSFENDQxw9ehTAuzeA27dvR2lpKYKCguDv74+rV69i/PjxCAoKEhijn5aWhh9//BHXr1+Hvr6+\nQJg8Hg/BwcFwdHTEpUuXsHDhQsyaNUvq26WGzpw5g+Tk5A9y8/7tt99w4sQJ/Pzzz4iPj2cbiyWV\nXQDo3bs3Tp48icuXL8PExERo/qKjR48iODgY169fh7W1tci4Dx06BC8vL3h5eeHhw4e4efOmyPWk\nnafS0gpIvu41Pm/l5eUxb948XLlyBXv37sXly5exe/duifk4YMAApKeno66uDvfv30dFRQUsLS3Z\n36Ud98jISLRo0QK//PILli1bJvCwUVFRgcDAQHh7e+PSpUuIiYnBDz/8gPv370tMEyGENMezZ89w\n8eJFgZ7Eq1atwqNHj5CamopTp06huLiYnf8nMzMTSUlJ2LZtG06fPi3yxcGRI0cQEhLCDtMRN+fd\njz/+iLdv3+LMmTPYsWMH0tLScPDgQZnu/RUVFViyZAk2bdqEnJwc7N27V6COlpubC0NDQ1y5cgUT\nJ07EggULwDAMAGDmzJnQ09PDxYsXsW7dOkRHR+Py5cto0aIFzM3NkZWVBeBdXUBfXx+//fYb+7ed\nnZ3IfZFUv4qMjISqqip+/fVXrFixQuqLFD6GYfDbb7/h/v37MDExYZc3rBdIu2dIut80tmLFCty6\ndQt79+7FtWvXMHv2bMjLy2Pnzp3s/ufk5IDL5QpsJ0tdSVzdvKF/cj1MWr1AVvX19Th79ixevXqF\nTp06SVyX6iLkc6FGpC+Urq6uyAd7RUVFPH/+HAUFBVBSUoKNjY1AY40oU6ZMgZqaGoyMjDB48GD2\n4txQeno6XFxc4OjoCCUlJUyYMAFVVVXIycmRKb3S0uXv74927dpBU1MTrq6u7NuuI0eOYMiQITA1\nNYWysjJmzpyJGzdu4OnTp+ByuXj8+DFevXqF7OxsDB06FEVFRSgvL5d4EweAwYMHw9DQECoqKvD0\n9GTjO3HiBFxdXWFjYwNlZWVMmzZNav5t3boVNjY26N+/P8rLy7F8+XL2NysrK/Tr1w/y8vJQUVHB\n3r17MWPGDOjp6UFZWRlTp07FyZMnUVtbixMnTqBPnz6wtbWFsrIypk+fDnl50afg0aNH0atXL3h7\ne0NJSQlt2rQRqBhJcuTIEUyZMgXa2trQ0tLClClTBN7MKSoqYsqUKVBSUoKLiwvU1NTw6NEjkWEN\nHDgQWVlZbGNXamoqmyYAWLRoEXx8fLBr1y54eXnB3d1d4E1fY2lpaTAyMkLXrl3h5eWF+/fv4/bt\n2wDeVfaKi4sxZ84cqKmpoUWLFmLfPMpi4MCBaNOmDRQVFREYGIiamhqx+ynJhQsX0KlTJ/j6+kJR\nURHe3t746quvcP78eXadQYMGoVu3blBUVGTzhu/3339HRUUFJk+eDGVlZfTs2ROurq44duyYzGmY\nPHkyNDU1oaKi0uT0NzZ16lSoqKige/fu6N69O+7evQsAEssuAAwdOhQaGhpQVlZGaGgo7t69i7dv\n37Lh9u3bF9bW1pCXl0eLFi2E4i0oKMDVq1fh4+ODtm3bomfPnmIr0dLOU2lpBSRf9xqft2ZmZrCy\nsoKioiI6dOiAESNGsA8Q4ujp6cHQ0BCXLl1Camoq2zuPT9Jxr6urw6lTpzBt2jSoqamBw+Fg0KBB\n7LYXLlyAgYEBhgwZAkVFRZiYmMDDwwMnTpyQmCZCCGmKKVOmgMvlwsXFBVpaWpg2bRqAdw0XycnJ\nmD9/PjQ1NaGhoYGgoCD2vnX8+HEMHjwY3bp1g6qqKkJDQ4XCbljfmTFjBm7cuIHCwkKBderq6pCe\nno6wsDBoaGigQ4cOGD9+fJOGO8vLy+Ovv/5CVVUVdHV10a1bN/Y3fX19DB8+HAoKChg0aBCeP3+O\nFy9eoLCwENevX8esWbPQokULGBsbY9iwYUhLSwPw7iVmVlYWamtrce/ePfj7+yMrKwvV1dX4448/\nxNZNxNWv+Nf80NBQqKqqomvXrjL1UHFwcICdnR0WLlyIsLAw9OzZk/2tYb1A0j1D2v2mofr6ehw8\neBALFixAu3btoKCggB49ekBZWVlqWmWpK4mrm3+IsL+Eepi0eoE0xcXFsLGxgYWFBaZOncrOISkJ\n1UXI56L4uRNARCsqKkLr1q2Flk+YMAFxcXHs1xBGjBiByZMnSwyrffv27P8NDAwExs7yFRcXC7Tc\ny8vLo3379jL30pGWLh0dHfb/qqqq7KS6xcXFMDU1ZX9TV1eHpqYmioqK0KFDB5iZmSErKwtZWVkI\nDg7GnTt3cP36dWRlZbFda0VpHB9/Xp/i4mLo6ekJ/CauNxNfYGAgZsyYIfK3hmEB7x6Up0yZItA4\nJC8vj5cvXwrFraamJjbuwsJCqXMLidP4WOrr6wtMYqypqQlFxf879RvmT2P6+vqwsbHB4cOHMWbM\nGJw9e5Z9GwUAKioqCA4ORnBwMMrKyrBx40Z89913OH/+vMh9S0tLw7BhwwAA7dq1g62tLQ4dOgQT\nExMUFhZCX19fIG3vY8uWLThw4ACKi4shJyeHsrKyZn3ho3F+Au/ypeG50fAcE7W9np6eQJlovL00\nksJvqrZt27L/b3jsJZXdtm3bIiYmBidOnEBJSQm7zqtXr9CyZUuZ0piWloYuXbqwjaE+Pj5Yvnw5\n5s6dK1Thk3aeSkorn6TrXuPz9tGjR1i+fDlu3ryJyspK1NXVCVyXxPH19cWhQ4eQk5ODXbt2CfTG\nk3TcS0pKUFtbK5DGhmUsPz8fubm5Ag8qdXV1GDBggNQ0EUKIrOLj49GrVy9cu3YNYWFhePXqFVq1\naoWSkhJUVlZi8ODB7LoN55opLi6GmZkZ+5uo63/D66y6ujpat26N4uJigXVfvXoFHo8nVGeR9f6o\npqaGmJgYbN26FQsWLECPHj0wd+5cdOnSBYDw/Q5417uitLQUrVu3hoaGhkC8/N6xdnZ2iIqKwu3b\nt8HhcODo6IgFCxbgxo0b6NSpk9iJnsXVr0Rd82W5r1+5ckVsnajh9pLuGdLuNw29evUK1dXVUifZ\nFkWWupK4uvmHCPtLqYdJqhdIo6uri8zMTNTU1GDVqlW4cuUKAgIC3itOqouQj4Uakb5Aubm5KCoq\nEjkkRENDA+Hh4QgPD8eff/6JcePGwdzcXODtRGOFhYXsDbWgoAC6urpC6+jq6go8ZDEMg8LCQrRr\n106mNDcnXfx4G46T59/c+fHa2dnhypUruHPnDszNzWFnZ4dffvkFubm5sLW1lSltjeNr2BulqqpK\naC6Vpmjci0lPTw/Lli0Teex0dXUFvuxWWVkpNu727dsjNzdXpjhFxVNQUMC+jSssLBR5zGU1aNAg\nbNq0CTo6OmzDnij8N5WJiYl4+vSpUCPS9evX8fjxY2zcuBHbtm0D8G6I4F9//YW5c+eiffv2KCws\nRG1trVClSdQ+q6qqorKykv37xYsX7P+zs7OxefNmJCUloVu3bpCXl4etrS3bjb0p+PnZUGFhIZyd\nnSWmr+H2z549Q319PXsTLywsROfOnaXuhyzhfyiSym5qairOnj2Lbdu2oUOHDnj79m2T8zM1NRWF\nhYVwdHQE8G5yytLSUmRkZKBfv34C60o7TyWl9enTpwAkX/ca5+f3338PExMTrF69GhoaGkhKSsLJ\nkyel7lP//v0RGRkJU1NT6OvrC1TcJB13LS0tKCoqCqSx4Rv69u3bw9bWlj1PCCHkY7Kzs8PgwYOx\nYsUKrF+/Hm3atIGKigqOHTsmsh6oq6sr8ADeuIcRAIHh+uXl5Xj9+rVQXaRNmzZQUlJCQUEBO4ly\nw7qnLPc+Z2dnODs7o6qqCmvWrMGiRYukDkfm9/YvKytjG5IaxsvlcvHo0SOcPn0atra26Nq1KwoK\nCpCRkdGsuif/mv/s2TMYGhqy8b2Phnkj6Z5RV1cn8X7TUJs2bdCiRQvk5eWhe/fuYuMTRZa6UnP9\nk+phkuoFslJWVsasWbPg6emJM2fOCNWRmhIn1UXIx0LD2b4gZWVlOH/+PGbOnIkBAwbAyMhIaJ3z\n58/jyZMnYBgGLVu2hIKCAntha9u2rcjJ5NavX4/Kykr89ddfSElJwTfffCO0ztdff42MjAyBccrK\nysrsmGdxYcuSLkm8vb2RkpKCO3fuoKamBtHR0bCwsECHDh0AvOtSnJqaii5dukBZWRl2dnbYv38/\nOnToAC0tLanhN+bh4YFz587h+vXrqKmpQWxsbLMaFsQZNWoU1qxZwzaMlZSU4MyZM2zcFy5cQHZ2\nNmpqarBu3TqxX5Dw8fHBpUuXkJ6ejtraWrx69Yrt9qutrc0+KIvi5eWFDRs2oKSkBCUlJYiPj4eP\nj0+z96l///4oKChAbGysUPfr+Ph45ObmoqamBtXV1di+fTtatWrFVpIaSk1NhaOjI44dO4bU1FSk\npqbiyJEjqKqqQmZmJiwsLKCjo4PVq1ejoqIC1dXV7BwE2traKCoqEpjs2NjYGKdPn0ZlZSWePHmC\nAwcOsL+Vl5dDQUEBWlpaqK2tRVxcHDspZlO5uLjg8ePHOHLkCGpra5Geno779++jT58+Mm1vYWEB\nFRUVbN68GTweD1evXsW5c+fY81DSfjQF/xjw/zX16ySSym55eTmUlZXRpk0bVFZWIjo6uklh5+Tk\nIC8vD/v372eP/dGjR+Ht7c0OH2hI2nkqKa18slz3+MrLy6Gurg51dXU8ePAAe/bskWm/1NTU8PPP\nP7OTrDYk6bgrKCjA3d0dcXFxqKysxP379wUmxuzTpw8eP36M1NRU8Hg88Hg85ObmCjRCE0LIhzRu\n3DhcunQJd+/ehby8PIYNG4Zly5axPTyLiopw8eJFAICnpydSUlLw4MEDVFZWCsy7yJeRkcHWd9au\nXQtLS0uh3hwKCgrw9PRETEwMysrKkJ+fj23btrE9HUTd+xt68eIFzpw5g4qKCigrK0NNTU3sNAEN\ntW/fHlwuF9HR0aiursbdu3dx4MABNl5VVVWYmZlh165d7NQJXC4Xe/fubVYjUuNr/oMHD0Te+5pL\n0j1D2v2mIXl5eQwZMgRRUVEoKipCXV0dcnJyUFNTAy0tLcjLy4t9FnjfupIk/5R6GCC5XsDH4/EE\n6muivvimrKyMwMBAdh6y5sZJdRHysVAj0heA/9UzFxcXJCQkYPz48YiKihK57pMnT9ivXYwYMQKj\nRo2Cg4MDgHfjdTds2AAbGxuBrxHxvzwREBCAwMBAODk5CYX71VdfYeXKlfjxxx/h4OCA8+fPIyEh\ngR0HLS5sWdIlSa9evTB9+nSEhobCyckJeXl57JcugHc37erqavam3bVr1/eaK6dbt25YtGgRZs6c\nCWdnZ6ipqUFLS0um8d6yGDt2LNzc3BAYGAgul4vhw4ezPYq6deuGxYsXY9asWXB2dkarVq2EhtXw\n6evrY9OmTdi2bRvs7Ozg6+vLzl0zdOhQ3L9/HzY2NggJCRHaNiQkBGZmZhgwYAAGDBgAU1NTkevJ\nSk1NDR4eHnj27JlQY2INx+8AACAASURBVJScnBzmz58PBwcHODs749KlS0hMTIS6urrAetXV1Th+\n/Dj8/Pygo6PD/uvYsSMGDhyI1NRUKCgoICEhAU+ePIGrqyt69+6N48ePA3g3L0DXrl3h5OQEe3t7\nAO8qvEpKSujVqxfmzp0rkDYnJyc4OzvDw8MDbm5uaNGiRbOHhLVp0wYJCQnYtm0b7O3tsXnzZiQk\nJMjciKmsrIyEhARkZmbCwcGBnVyd/9ZH0n40BZfLhYWFBfvvypUrTdpeUtn19fWFvr4+nJ2d4eXl\nBSsrqyaFfejQIfTt2xdGRkYCx3/cuHE4f/68UI88aeeppLTyyXLd45s7dy6OHj2KHj16YNGiRRIb\nnBozNzcXOfRU2nFfvHgxKioq4OjoiPDwcIFhIxoaGtiyZQvS09Ph7OwMJycnrFq1SuoX4wghpLm0\ntLQwcOBA9qF19uzZ6NSpE4YPH44ePXogICCA7SHq4uICf39/jB07Fu7u7uxEvg3rUt7e3oiPj4e9\nvT1u3bqFlStXiox30aJFUFVVRb9+/TB69Gh4e3tjyJAhAETf+xuqr69HUlISnJ2dYWdnh6ysLHz/\n/fcy7W90dDTy8/Ph7OyMqVOnIjQ0FL169WJ/t7W1RW1tLSwsLAC8u6eUl5c3qxEJeHfNf/v2LRwd\nHTFnzhx4eXl9sLqntHuGpPtNY3PnzgWHw8HQoUNhZ2eHVatWob6+HqqqqggODsaoUaNgY2ODGzdu\nCGz3vnUlSf4p9TA+cfUCvsmTJwvU12JjY0WuN2TIEBQUFODcuXPNjpPqIuRjkWM+ZDcM8kV5+vQp\n+vbti1u3bn2weWb+bfgVgpMnTzZrDDgh5OOj85QQQr5cDx48gLe3N/744w8oKioiPDwc7dq1Ezuf\nJAFWrlyJFy9eYMWKFZ87KYQQ0mTUE4n855w7dw6VlZWoqKjAihUrwOFw2OFzhJAvA52nhBDy5Tp9\n+jRqamrw+vVrrFy5Eq6urvTCUoIHDx7g7t27YBgGubm5OHDgANzd3T93sgghpFnoak/+c86ePYs5\nc+aAYRiYmZkhOjr6k0xcTAiRHZ2nhBDy5dq7dy/Cw8OhoKAAW1tbREREfO4kfdHKy8sRFhaG4uJi\naGtrIzAwEH379v3cySKEkGah4WyEEEIIIYQQQgghRCoazkYIIYQQQgghhBBCpPpHDWezt7eHgYHB\n504GIYQQQj6S/Px8XL169XMngzRA9S9CCCHk30/WOtg/qhHJwMAAKSkpnzsZhBBCCPlIJH1+mnwe\nVP8ihBBC/v1krYPRcDZCCCGEEEIIIYQQIhU1IhFCCCGEEEIIIYQQqagRiRBCCCGEEEIIIYRI9Y+a\nE4kQQgj5HHg8Hp4+fYqqqqrPnZR/DRUVFXTo0AFKSkqfOymEEEIIIURG1IhECCGESPH06VO0bNkS\nnTt3hpyc3OdOzj8ewzB4+fIlnj59CkNDw8+dHEIIIYQQIiMazkYIIYRIUVVVBW1tbWpA+kDk5OSg\nra1NPbsIIYQQQv5hqBGJEEIIkQE1IH1YlJ+EEEIIIf88MjUiZWZmwsPDA+7u7ti4caPQ7zU1Nfju\nu+/g7u6OYcOG4enTp+xviYmJcHd3h4eHBy5evMguT0pKgpeXF7y9vTFz5kxUV1d/gN0hhBBCCCGE\nEEIIIR+D1DmR6urq/h97dx9fc90/cPx1bnY2m2EbNmMYbYWNEUW5nYa5n4h05+6qRCip33XJYqQk\npNx0uXShrpKrGqq5bXMXE5KbcM3tmGwHs9lstrNz8/vja+ds7A67O/N+Ph4exz7nc77nc6jNeZ/3\nDREREaxYsQJPT08GDx5McHAwDz30kHXPd999R40aNdi6dStRUVF8/PHHfPLJJ5w+fZqoqCiioqLQ\n6/WMHDmSzZs3c/XqVb788ks2bNiAk5MTEydOJCoqikGDBpXpixVCCCHsUUpKCiNGjADg6tWrqNVq\n3N3dAeVnsE6nK/XnPHbsGMnJyXTu3LnUry2EEEIIIexTsUGkI0eO0KhRI3x8fADo06cP0dHR+YJI\nMTExjB8/HoCePXsSERGBxWIhOjqaPn36oNPp8PHxoVGjRhw5cgRvb29MJhNZWVlotVqysrKoW7du\nGb1EIYQQwr65ubmxfv16AD777DOcnZ0ZPXp0iR9vMpnQaDR39ZzHjx/n5MmTEkQSQgghhBBWxQaR\n9Ho9Xl5e1q89PT05cuTIHXvq1aunXFCrxdXVlZSUFPR6Pa1atcr3WL1eT+vWrRk1ahTdunXD0dGR\nJ598ko4dO5bWaxJCCCEeGK+++iqXL18mOzubESNGMGTIEIxGI+3btycsLIy9e/cSERHBtWvX+Oij\nj3BxcaF169YkJiayZMkSMjIymDlzJqdPn8ZoNDJhwgSeeOIJFi9eTFZWFvv27WPs2LH06tWrol+q\nEEIIIYSoYMUGkcrC9evXiY6OJjo6GldXVyZOnMj69esZMGDAHXvXrFnDmjVrACWdXwghhKhIX355\nmH//+49SveaoUa158cVWxW8swIcffkitWrW4efMmTz/9ND169MDFxYX09HTatWvH1KlTuXnzJj17\n9mT16tV4e3szceJE6+MXL15Mp06d+PDDD7l+/TrPPPMMP/74I+PGjePkyZNMnTq1tF6mEEIIIYSw\nc8UGkTw9PUlKSrJ+rdfr8fT0vGNPYmIiXl5eGI1G0tPTcXNzK/Sxe/bsoUGDBtZ+Dj169OCPP/4o\nMIg0dOhQhg4dCiA9k4QQQojbrFy5kpiYGACSkpK4cOECzZo1w8HBgZCQEABOnz6Nr68v9evXB6Bv\n376sW7cOgN27d7Nr1y7r4Izs7GwuXbpUAa9ECCGEEEJUdsUGkQIDA4mPjychIQFPT0+ioqKYN29e\nvj3BwcGsXbuW1q1bs3nzZtq3b49KpSI4OJjJkyczcuRI9Ho98fHxtGzZErVazeHDh7l58yZOTk7E\nxsYSEBBQZi9SCCGEKC0vvtjqnrOGStuePXs4cOAA//3vf3FycuLZZ5+1Tjt1cnJCpVIVew2LxcLi\nxYtp2LBhvvUDBw6UyZmFEEIIIYT9Uhe3QavVEh4ezpgxY+jduzehoaH4+fmxcOFCoqOjARg8eDCp\nqamEhISwYsUK3nrrLQD8/PwIDQ2ld+/ejBkzhvDwcDQaDa1ataJnz56EhYXRr18/zGazNdtICCGE\nECWTnp5OzZo1cXJy4tSpUxw9erTAfQ899BDnzp0jMTERi8XChg0brPd17NiRr776yvr18ePHAXBx\ncSEjI6NsX4AQQgghhLArJeqJ1KVLF7p06ZJvLW8/BUdHRz799NMCHzt27FjGjh17x/qECROYMGHC\n3ZxVCFHerl+HPXugXTuoXbuiTyOEuE3Xrl3573//S+/evfH19c03zCKvatWqER4ezogRI3BxcSEg\nIMCasTR+/Hhmz55t/VCnYcOGLF26lPbt27N8+XIGDhzIq6++Ko21hRBCCCFExTTWFkLYifHj4T//\nUX7fogX07w8REaCVbx1CVJTXX3/d+ntHR0e++OKLAvfdXo7WoUMHNm/ejMViITw83FpG7uzszKxZ\ns+54vLu7O5GRkaV4ciGEEEIIUemYzXAXQ8yKLWcTQjyg/vwTvv4aXnoJ3n8f6tSBDz6AtWsr+mRC\niHuwevVqBgwYQO/evcnKyuKZZ56p6CMJIYQQQoiKdPkyTJ4MwcElfoikEwghCvbuu+DqCvPng7s7\nvPMO+PnBokUwZEhFn04IcZfGjBnDmDFjKvoYQgghhBCiomVnKwkD770HFy8qa02bluihkokkxAMo\nO9tIePg2vv76CGlp2Xdu+O03WL8epkxRAkgAGg2MHQs7d0IhzXuFEEIIIYQQQlRSZjPs2wc9e8Lo\n0bYA0l2QIJIQDxiLxcKrr0Yxc+ZOnn9+LXXrzmXgwG85cOCSbdM//qGUr+VpoA/AqFHg5ARLlpTv\noYUQQgghhBBC3Du9HiZMgI4dYccO23qtWlBAf8zCSBBJiAfMwoW/sXLlIaZN68zu3aN49dW27NmT\nQP/+q7l+PQuioyEmBqZOVcrZ8vLwgGHD4KuvlMltQgghhBBCCCEqr+xsWL4cWreGxYshJ0dZV6mU\n93abNsHQoSW+nASRhHiAbN16hsmTtxAW9gjTp3fliSd8+OSTXkRFDUevz+Af/4hWsoy8vOCVVwq+\nyLhxkJEBq1aV7+GFEEIIIYQQQpSMxaKUrnXvDn/7GyQm2u5r1Qq+/x5mzABvb+VXCUkQSYgHRHx8\nKkOHfk/z5nX48ssw1GqV9b527eozYcJjLFvyG8atv0CfPkrZWkHatoXHH1ei2GZzOZ1eCNGsWTMG\nDBhA3759mTBhAjdv3rzna/3222+8citQHB0dzbJlywrdm5aWxtdff239Wq/XM2HChHt+biGEEEII\nUcYuX1Y+/O/YEXbvtq27uSmTt7/9FoKCoG5daNAAnJ1LfGkJIgnxgFi0aB83bhhYv34Y1avr7rh/\n5sxgete9jjY9DWO37kVfbNw4OHkS9uwpo9MKIW7n5OTE+vXr+fnnn3FwcODbb7/Nd7/FYsF8D4Hd\n7t278/LLLxd6f1paGqtXr7Z+7enpyaeffnrXzyPKTnBwMP369WPAgAEMGjQIgNTUVEaOHEmPHj0Y\nOXIk12+VIFssFmbNmkVISAj9+vXj2LFjFXl0IYQQQpQmgwGWLVMyjZYutZWuqdXw3HOwebMyadvD\nAxo2VPohqVRFX/M2EkQS4gFgNltYs+YYvXo9RJMmbgXuqV5dx5ynwAx8drx60Rfs00e53b69VM8p\nhCiZtm3bcv78eS5evEjPnj15++236du3L4mJifz6668MHTqUsLAwJkyYQEZGBgA7d+6kV69ehIWF\nsXXrVuu1IiMjiYiIAODq1auMGzeO/v37079/fw4ePMi8efO4cOECAwYMYM6cOVy8eJG+ffsCkJ2d\nzd///nf69evHwIED2bt3r/Wa48ePZ/To0fTo0YOPPvqonP+EHjyrVq1i/fr1REZGArBs2TI6dOjA\nli1b6NChgzXbbOfOncTHx7NlyxZmzpzJ9OnTK/DUQgghhCgVFosyYbtrV6UtSVKS7b7WrSEyEt57\nD+rVAx8fZYiSVntPT3VvjxJC2JXduy9w8WIac+Y8VeS+RxL+4EytJrz7yVFGvR1CzZqFlLS5u0NA\nAOzaVQanFaKS+/JL+Pe/S/eao0bBiy+WaKvRaGTnzp106tQJgPPnzzNnzhyCgoK4du0aS5cuZcWK\nFTg7O7Ns2TJWrFjB3/72N6ZNm8aqVato1KgRkyZNKvDas2bNol27dixevBiTyURmZiaTJ0/m1KlT\nrF+/HoCLeUbB5pa5/fTTT5w5c4bRo0ezefNmAE6cOMG6devQ6XT06tWLF154gXr16t3zH5G4O9HR\n0Xz11VcADBw4kBdeeIEpU6YQHR3NwIEDUalUBAUFkZaWxuXLl6lbt24Fn1gIIYQQ9+TyZQgPhy++\nAKPRtu7hAVOmwIABSqsSD487ByfdA8lEEuIB8O23f1Ktmpb+/R8ufFN6OsTG4jKwN5mZOXz55eGi\nL9qpk1LOlvcblRCizGRlZTFgwACefvppvL29GTx4MADe3t4EBQUBcPjwYU6fPs2zzz7LgAEDWLdu\nHZcuXeLs2bM0aNCAxo0bo1Kp6N+/f4HPsXfvXoYPHw6ARqPBtZh/aPz+++/WazVt2hRvb2/OnTsH\nQIcOHXB1dcXR0ZGmTZvy119/lcqfgyjY6NGjGTRoEGvWrAEgOTnZGhiqU6cOycnJgNLTysvLy/o4\nLy8v9Hp9+R9YCCGEEPcnJwc+/xwCA+Gf/7S9L9NolA8nN22Cp59Wso58fEolgASSiSRElWc0mvnu\nu+P07etfYC8kq+3bwWjE68VBPHb8DEuXHmD8+MdQFVYj27mzUmd7+DA8+miZnF2ISunFF0ucNVSa\ncnsi3c45TyNEi8XCk08+yfz58/PtOXHiRJmf73Y6ne37jUajwWQylfsZHhSrV6/G09OT5ORkRo4c\nSZMmTfLdr1KpCv9eXog1a9ZYA1IpKSmldlYhhBBC3CeLBfbuhTfeUErY8mrbFqZNg2bNwMVFyT5y\ndCzVp5dMJCGquG3bznHlSibDhgUUvXHrVqUr/xNP8NprbTlx4io7dpwvfP+tUhp27iy9wwoh7ktQ\nUBAHDx7k/Hnl/93MzEzOnTtHkyZN+Ouvv7hw4QIAUVFRBT6+Q4cOfPPNNwCYTCbS09NxcXGx9lW6\nXdu2bfnpp58AOHfuHImJiXcEMETZ8/T0BMDDw4OQkBCOHDmCh4cHly9fBuDy5cu4u7tb9ybl6ZOQ\nlJRkfXxeQ4cOJTIyksjISNzcCu6lJ4QQQohyptfDyy8r78XyBpDq1IG5c+E//1GaaterB97epR5A\nAgkiCVHlrV79J66uOnr39it649atSnaRoyPPPNMCNzcnlizZX/j++vXB11f6IglRibi7u/PBBx/w\n5ptv0q9fP4YOHcrZs2dxdHQkIiKCl19+mbCwMGtA4XZTp07lt99+o1+/fgwaNIjTp0/j5uZGmzZt\n6Nu3L3PmzMm3f/jw4VgsFvr168cbb7zBBx98kC8DSZS9zMxMbty4Yf397t278fPzIzg4mHXr1gGw\nbt06undXpm7mrlssFg4dOoSrq6v0QxJCCCEqO6MRFi9W+tIuXw65Gd4aDYwcqZSuhYXZSteqFzMo\n6T6oLBaLpcyuXsoGDRpknToihChedrYRT8+PGTDgEVatGlj4xoQEZcTjvHnw5psAvPXWFhYu/I0L\nFyZRr14h9bMvvQQbNyoR8bsslRDCnpw4cYJmzZpV9DGqnIL+XOVn/d1JSEhg3LhxgJI91rdvX8aO\nHUtKSgqTJk0iMTERb29vPvnkE2rVqoXFYiEiIoJdu3ZRrVo1Zs+eTWBgYJHPIX8nQgghRAXavRsm\nTYIDB/KvP/aY0lDb31/pd+ThAQ4O9/w0Jf15Lz2RhKjCNm8+w/Xr2Qwb1qLojbnjvnv0sC698sqj\nzJsXy/LlB5k2rUvBj+vUSZlUFRcHjzxSSqcWQghRUj4+Pvz44493rLu5ubFq1ao71lUqFe+99155\nHE0IIYQQ9yMpCf7xD1i1Csxm23rduvB//we9eyvtSDw8lNtyIuVsQlRhP/xwAnf3ajz1VDE9Sn75\nRambbWELNvn5edCjR1OWLTuI0Wgu+HGdOyu30hdJCCGEEEIIIe5fTg589plSurZihS2ApNXCmDFK\n6dqAAeDpCQ0alGsACSSIJESV9uuvF+jatTEODpqiN8bGKllFt5Wkvfrqo1y8mMbWrWcKfpyfnxIJ\nl75I4gFgR9XfdkH+PIUQQgghbvPrr9C+PUyYAMnJtvUnnoAff4S331YCRw0bQq1aFdJSRIJIQlRR\nev0Nzp5NoUOHBkVvvHIF4uOhXbs77urd249atZxYs+ZYwY9VqZTgkwSRRBXn5OREcnKyBD5KicVi\nITk5GScnp4o+ihBCCCFExUtKghEjoEsXOHjQtl6vHixcqGQkBQYqTbPr1FGykiqI9EQSooqKjb0I\nwBNP+BS9MbdBWwFBJEdHLYMGPcL335/g88+NODkV8C2jUyf44QelObdPMc8lhJ1q0KABFy9e5MqV\nKxV9lCrDycmJBg2KCXILIYQQQlRluVPXZsyAlBTbuoMDjBoFr76qZBx5eCjNsysBCSIJUUXt2ZOA\ng4OaNm3qFb1x/34lo6hNmwLvHjYsgH//+xAbN54iLKyA6VSdOim3v/4Kzz57n6cWonJycHDA19e3\noo8hhBBCCCGqip07lbK1w4fzr3fsCO++C02bgpubEkTSFNOepBxJOZsQVVRs7EUefdS74OyhvPbv\nh2bNCo1sd+vmS506znz7bSElbYGBoNPBH3/c54mFEEIIIYQQoopLTIQXXoCuXfMHkLy9lYbaX3xh\nK13z8KhUASSQIJIQVZLBYGL//r+K74dksShBpAJK2XJptWqGDGnOTz/FceOG4c4NDg7KVLfbI+hC\nCCGEEEIIIRRGI8yfD82bw3/+o7wXA+X91NixsGED9OunBJO8vcHRsWLPWwgJIglRBR06lER2tqn4\nfkgXL4JeX2QQCZSStps3jfz0U1zBG4KC4NChezytEEIIIYQQQlRh27cr7UMmT4bUVNt6164QFaWs\n+/gov6pXr6hTlogEkYSogvbsSQAoPhNp/37ltpgg0pNPNqR+fdfCS9patYLLl5WpAkIIIYQQQggh\n4NIleO456NYNjh61rTdoAEuXwrJlSulaw4bg7g7qyh+iqfwnFELctdjYizRsWJP69WsUvXH/fiV9\nslWrIrep1SqGDm3Bxo2nSEm5eeeGoCDlVrKRhBBCCCGEEA86oxHmzlV6z37zjW3d0RFef13JPurd\nG+rXBy8v5T2ZnZAgkhBV0J49CcVnIYESRGrZskT1tsOGBZCTY2bduv/deWfLlsqtBJGEEEIIIYQQ\nD7KYGOVD+rffhrQ023pwsBI8mjRJyTzy8QFn54o75z2SIJIQVUxCwnUuXkwrvh+S2QwHDhRbypar\nbVtvGjWqSWRkAUEkNzdo1EiaawshhBBCCCEeTH/9BUOHQvfucPy4bb1hQ6Vs7fPPbaVrtWqBSlVx\nZ70Pxcz+FkLYm9jYi0AJ+iGdPg3Xr5c4iKRSqRg48BE+//wAN24YqF5dl39Dq1aSiSSEEEIIIYR4\nsOTkKFPX3n8f0tNt605O8MorMGaMEjSqXVtZs3OSiSREFRMbm0C1alqCgryK3ljCptp5DRz4CNnZ\nJjZtOn3nnUFBcPIkZGbexWmFEEIIIYQQwk798ovyYfr//V/+AFJICGzYYCtda9CgSgSQQIJIQlQ5\ne/ZcpG1bbxwcNEVv3L9fqcFt1qzE1+7YsSEeHtUK7ovUqpVSIvfnn3d5YiGEEEIIIYSwIxcvwpAh\nSrDoxAnbeuPG8K9/wZIlSt9YHx+oUcywIzsjQSQhqhCj0cyhQ0k89lj94jfv3w9t2oC25FWtWq2a\nfv0e5uefT2IwmPLfmTuhTfoiCSGEEEIIIaqinByYPVv5IP77723r1arBm2/Czz8rU9d8fMDDAzTF\nfLBvhySIJEQVcvJkMgaDiZYtPYveaDIp/YseffSunyMs7BGuX89mx474/Hc0bqxE2aUvkhBCCCGE\nEKKq2bIFAgJg6lS4ccO23rOnUro2YYIybMjbu0TTr+2VBJGEqEKOHtUDFB9Eyu1d1KbNXT9HSEgT\nnJ0dWLv2tpI2tVpJ2ZRMJCGEEEIIIURVceECDBqkBItOnrStN2kCK1bA4sW20rXq1SvunOVEgkhC\nVCFHj15Go1HRrFntojf+8Ydy27r1XT9HtWoO9Or1EOvXx2E2W/LfGRSkBJHM5ru+rhBCCCGEEEJU\nGgYDzJoFzZvD2rW2dWdnmDIFfvwRevVSGme7uysfqj8AHoxXKcQD4ujRy/j7e+DoWEyfo4MHlRTL\nRx65p+cZOPBhLl1K58CBS/nvaNVKSe08d+6eriuEEEIIIYQQFW7jRmjRAqZNg4wM23qfPrBpE7z+\nOvj6gpcXODhU3DkrQImCSDt37qRnz56EhISwbNmyO+43GAxMmjSJkJAQhgwZwsWLF633/fOf/yQk\nJISePXuya9cuAM6ePcuAAQOsv9q0acPKlStL5xUJ8QA7elRPYGAxpWygZCK1bHnP3/D69vVHo1Gx\ndu2J/HfkNteWvkhCCCGEEEIIe3P+PAwcqDTHPn3atv7QQ7BqFXz6KQQGQoMGSkbSA6jYIJLJZCIi\nIoLly5cTFRXFzz//zOm8f5jAd999R40aNdi6dSsjRozg448/BuD06dNERUURFRXF8uXLmTFjBiaT\niSZNmrB+/XrWr19PZGQk1apVIyQkpGxeoRAPiPT0bM6dSyUwsG7RGy0WJYh0D6VsudzcqtGlS2N+\n/PFk/jtatFDSOKUvkhBCCCGEEMJeZGfDjBnK1LX1623rLi7wf/+nrOWWrtWqBSpVxZ21ghUbRDpy\n5AiNGjXCx8cHnU5Hnz59iI6OzrcnJiaGsLAwAHr27ElsbCwWi4Xo6Gj69OmDTqfDx8eHRo0aceTI\nkXyPjY2NxcfHh/r1SzCSXAhRqGPHrgAUH0Q6fx5SUu4riATQp48fx49f4fz5VNtitWrg5wd//nlf\n1xZCCCGEEEKIcvHzz0rfo+nT4eZN23r//rB5M4wbpzTRrlsXtMW0DXkAFBtE0uv1eHl5Wb/29PRE\nr9ffsadevXoAaLVaXF1dSUlJKdFjo6Ki6Nu37329CCGEbTJbseVs99FUO6/evf0A2Lgxf2YiAQES\nRBJCCCGEEEJUbvHx0K+f8uvsWdu6vz98/TUsXGgrXXNyqrBjVjYV2ljbYDAQExNDr169Ct2zZs0a\nBg0axKBBg0hJSSnH0wlhX44evUz16joaN65V9MY//gCNRumJdB8eftgDX99abNhwKv8dAQFK/XDe\nKL4QQgghhBBCVAbZ2fDee0rp2s8/29arV4epU5XStR49wMcHatSouHNWUsUGkTw9PUlKSrJ+rdfr\n8fT0vGNPYmIiAEajkfT0dNzc3Ip97M6dO2nRogW1axc+jnzo0KFERkYSGRmJm5tbyV+ZEA+Yo0cv\nExBQF7W6mPrcgweVqWzVqt3X86lUKkJDHyI6+hxZWUbbHYGBSt+l48fv6/pCCCGEEEIIUarWr1eC\nRxERkJVlWw8Lgy1b4LXXlKlrtWsrH7yLOxQbRAoMDCQ+Pp6EhAQMBgNRUVEEBwfn2xMcHMzatWsB\n2Lx5M+3bt0elUhEcHExUVBQGg4GEhATi4+NpmSf7ISoqij59+pTySxLiwWOxWG5NZiumHxLcd1Pt\nvHr39iMzM4edO8/bFgMClFspaRNCCCGEEEJUBmfPQmioMnnt3DnberNm8M03sGCB8j7G2xscHSvu\nnHag2K5QWq2W8PBwxowZg8lk4umnn8bPz4+FCxcSEBBA9+7dGTx4MFOmTCEkJISaNWuyYMECAPz8\n/AgNDaV3795oyAMnEAAAIABJREFUNBrCw8PR3IrmZWZmsmfPHiIiIsr2FQrxAEhKukFy8s3ig0h6\nPVy6BG3alMrzduvmi6Ojho0bT9GjR1NlsWlT5RuvBJGEEEIIIYQQFenmTZg1C+bNU8rYctWoAZMm\nwfDhUKeOMnFNXaHdfuxGiVqLd+nShS5duuRbmzhxovX3jo6OfPrppwU+duzYsYwdO/aOdWdnZ377\n7be7OasQohBHj14Gyq+pdi5nZwe6dfNlw4bT3IodKxMLmjWTIJIQQgghhBCi4qxdqwSKLlzIv/70\n0zBlCjRqBO7uoNNVzPnslITahKgCbJPZislEyg0iBQWV2nP37v0QJ08mc/r0NdtiYKAEkYQQQggh\nhBDl7/Rp6NkTBg3KH0Bq0QLWrIH585X3K15eEkC6BxJEEqIKOHLkMvXqVcfDw7nojX/8oTSKq1XM\nBLe7EBrqB8DGjXmmtAUEwMWLIBMVhRBCCCGEEOUhMxP+/nflvciWLbb1mjVhxgwlMyl36ppzMe+b\nRKEkiCREFXD0qJ6WLYspZQNlMlsp9UPK9dBD7vj7e7Bhw2nbYm5z7WPHSvW5hBBCCCGEECIfiwV+\n+EGZQP3hh7beRyoVDB0KmzfDq6/aPkxXFTPNWhRJgkhC2Dmj0czx41eKL2VLTYUzZ0qtH1JeoaEP\nsW3bObKyjMqCTGgTQgghhBBClLW4OCW7aPBgSEiwrQcGwnffwccfQ6tWULeu0rv1Lm3ceIrg4FX4\n+i4kOHhV/uqLB5QEkYSwc2fOXCM721R8U+2DB5Xbdu1K/QxPPdWE7GwTsbG3vnH7+CgTDySIJIQQ\nQgghhChtGRnwzjvQsiX88ottvVYtmDkT1q2DkBBo0ACcnO7pKTZuPMX48RtJTEzH3d2JxMR0xo/f\n+MAHkiSIJISd+9//rgLQrFntojceOKDcPvpoqZ+hU6eGqNUqYmLOKQsqlZKNdPRoqT+XEEIIIYQQ\n4gFlsSgZRg8/DB99BAaDsq5SwbPPwtatSulao0bKh9r3Ye7cPeh0alxcdKhUKlxcdOh0aubO3VMK\nL8R+3X0+lxCiUomLSwbA39+j6I0HDih1wB7F7LsHNWs60batN9u2xdsWAwLg+++Vb/RSdyyEEEII\nIYS4H//7H7z2Gmzbln89KAjeew8ee0x5r+PoWCpPd+5cKu7u+bOYnJ0diI9PLZXr2yvJRBLCzsXF\nXcXT04WaNYtJ0zxwANq2LbNzdOvWmH37/iIj49anAQEBcO0aJCWV2XMKIYQQQgghqrgbN2DyZKV0\nLW8Ayd0dZs+GyEjo3h28vUstgATg61uLzMycfGuZmTk0blx6k67tkQSRhLBzcXHJPPxwMaVsyclw\n7lyZB5Fycszs3n2rL5I01xZCCCGEEELcK4sFVq8Gf3+YPx9ybgV01Gp4/nmldO2VV5TSNVfXUn/6\nKVOewGAwk5FhwGKxkJFhwGAwM2XKE6X+XPZEgkhC2LmTJ5N5+OFiStR+/125LcMgUseODdFq1ba+\nSBJEEkIIIYQQQtyLY8egSxcYPhwSE23rbdoomUdz5yrvN9zdlaBSGQgN9WPRolDq1XMlJSWLevVc\nWbQolNBQvzJ5PnshPZGEsGMpKTe5ciWz+CBSblPtNm3K7CwuLjoef7y+rS9SnTrg6SnNtYUQQggh\nhBAlk5YG4eGweDEYjbb12rVhyhQYOlR5n+HsXC7HCQ31e+CDRreTTCQh7FhuU+1iy9n27wc/P2Xk\nZRkKDvblwIFLXL+epSwEBEgmkhBCCCGEEKJoFgt89ZVSurZwoS2ApNHASy/BL7/Ayy9Dw4blFkAS\nBZMgkhB2LC7uKkDJMpHKsJQtV7dujTGbLezadUFZCAhQUlHN5jJ/biGEEEIIIYQdOnoUOnWCF18E\nvd623q4drFsHH30ELVooH4jL1OcKJ0EkIexYXFwyWq266AkBSUlw8WK5BJE6dPDB0VHDtm23+iIF\nBkJmJsTHl/lzCyGEEEIIIezI9evw+uvQujXs3m1br1MH5s2DH36Ap56CunVB++B24tm48RTBwavw\n9V1IcPAqNm48VaLHnTlzBgCLxVKq55EgkhB2LC4umaZN3XBw0BS+qRyaaudyctLyxBM+tr5I0lxb\nCCGEEEIIkZfFAitXKqVrixaByaSsa7UwahRER8OYMeDjA05OFXrUirZx4ynGj99IYmI67u5OJCam\nM378xiIDSSaTie+++46hQ4eyb98+MjMzgdILJkkQSQg7pkxmK6Yf0oEDStpn69blcqZu3Rpz6FAS\n167dhObNlUVpri2EEEIIIYQ4dAiefBJGjoTLl23rjz8OP/4Ic+Yo7yFq1Ki4M1Yic+fuQadT4+Ki\nQ6VS4eKiQ6dTM3funkIfo9FoGDJkCKNGjWLZsmVMnz4dAFUplQJKEEkIO2UymTl1Krlk/ZAeeQRc\nXcvlXF27NsZigV9/vaA8Z+PGkokkhBBCCCHEgywlBcaNg0cfhdhY27qnJ3zyiVK6FhysTGHTFFFl\n8YA5dy4VZ2eHfGvOzg7Ex6cW+pjcjKPXXnuNl19+mdjYWN599918990PCSIJYacuXLhOdrap6CCS\nxVJuTbVztW3rjVar5rffLioLgYESRBJCCCGEEOJBZDbDF18opWtLltgG7jg4KCVrMTFKCVv9+uDo\nWLFnrYR8fWuRmZmTby0zM+eOnrjJycnW3+fNOHrsscdYsGABs2fPZt++fahUqvsOJEkQSQg7FRen\nfKPw9y8iiHTxotJYuxyDSNWqORAU5MXevX8pCwEB8L//gcFQbmcQQgghhBBCVLDff4cOHZRg0dWr\ntvUnn4Sff1ZK18qxYqIyKq5p9pQpT2AwmMnIMGCxWMjIMGAwmJky5QnrnsjISN58800OHjwI5M82\nMpvNtGvXjokTJ/LKK68A91/WJkEkIexUXJzyjbjInki5Uw6eeKLwPWXg8cfrs2/fX5hMZiWIZDTC\nyZPlegYhhBBCCCFEBbh2DV55Bdq1g337bOv16sGnn8J330HXruDuDuoHNyRRkqbZoaF+LFoUSr16\nrqSkZFGvniuLFoUSGupn3ePr68vNmzeJiYkhMzMzX7ZRbsBo1qxZ3Lx5k6ioKOD+ytoe3L8xIexc\nXFwytWo5UaeOc+Gbdu8GZ2do1ar8Dga0b9+AGzcMHD9+RSa0CSGEEEII8SAwm2HZMvDzU25zAxUO\nDvDqq0rp2ujRSjBJp6vYs5ZQRMQO3NzmoNVG4OY2h4iIHaV27ZI2zQ4N9SMm5iXOnp1ITMxL+QJI\nAK1bt6Z79+78/vvvxMTEALbgUe6tTqfjxRdf5OitgUf3k40kQSQh7JQymc2j6G8Au3crkw4cHArf\nUwbat28AwN69F5UUVa1WgkhCCCGEEEJUVfv3w2OPKRlI167Z1jt1go0b4YMP4OGHlQ+47URExA5m\nztxJZqYBnU5NZqaBmTN3llog6V6aZt8uN6PohRdeoEaNGsTExHDu3DkAjEYj5ls9qBwcHHBwcOD6\n9esA1vV7IUEkIexUXFxy0aVs6elw+LBSc1zOmjZ1w8OjmhJE0umURnoSRBJCCCGEEFVAcX1sHihX\nryo9jx5/XOmBlKt+fVi8WCld69IFatWCUhoxX14WLNiLWg1arQaVSo1Wq0GtVtZLQ0mbZhdFpVJh\nNptxdnbm2Wef5cKFC2zatAmDwYBWq0WtVrNv3z4OHDhA9+7diY2NxWAwoL6PMkIJIglhhzIyDFy8\nmIa/v3vhm377TUkprYAgkkqlon37Bvmba0sQSQghhBBC2JmWLZegUs2w/mrceEGxfWweCCYTfP65\nUrr2xRe20jWdDl57DbZtg5EjwdNTqUqwQ+np2Wg0+QNfGo2KGzeyS+X6xTXNNtwaTJSTowSaCutj\nlBsQ6tq1K61btyY2NpazZ88CMGzYMDp06MClS5eoV68eCxcuRHefpYQSRBLCDp08qUxmK7aptkql\nTESoAO3bN+DEiStcv56lBJHOnoWMjAo5ixBCCCGEEHerZcslHD16Jd/a+fNpJCRcL7aPTZW2d6/S\nNHvsWEjNU3rVtSts2qSUrvn5QbVqFXbE0uDq6ojJlD9wYzJZqF7dsVSuX1DT7M8+60XLls689NJL\nbN++HVBK0QDS09MLvVZuedrIkSNRq9VMnDgRJycnrl27RmJiIv3796devXq0KoVeuRJEEsIOxcXl\nBpE8Ct+0e7cSvKlZs5xOlV/79g2wWGD//ksQGKh8OnH8eIWcRQghhBBCiLt1ewApV05O/n4yd9vH\nxm5dvqxkF3XoAH/8YVtv0EDJSvruO+jcGWrUKPejlUWJ4RtvtMdsBqPRhMVixmg0YTYr66Xl9qbZ\nvXv7U79+fVJTU9m0aROpqals27aN1q1bM2TIEBYvXszFixcBMJlM1uuo1WosFgve3t706dMHtVrN\n6tWr2bJlC3Xr1sVoNJbamSWIJIQdiou7ikoFDz1USDmbyaR8QtCxY/keLI927bxRqW4115YJbUII\nIYQQooq62z42dsdohEWLlMbYK1fa1h0dYcIEpXTtpZegdm3QaMr9eBs3niqTEsPw8C5Mm9YZZ2cd\nOTlmnJ11TJvWmfDwLqV08jvlBntmzJjBgQMH+Pbbb4mIiODtt98mLCyMXbt28frrrwOg0WgKLHEb\nMmQIGzduJCwsDIvFgslkQluKJYX2WZwoxAPu5MlrNGpUi2rVCpm6dvSo0li7Avoh5apZ04lmzeoo\nQaS/P6mks0oQSQghhBBCVAEZGQacnR3IzMzJ18emytm9W+lxdORI/vXu3eG99yAoCFxdK+Zst8yd\nuwedTo2Li9LrR7k1MHfuHkJD/e7r2uHhXco0aJTLYrFgsVjQarVYLBaCgoIICQlh6dKlNGnShGef\nfRaAbt26MWbMGBYvXsy4cePuuI7JZEJzK5BnsVhQqVTWr0uLZCIJYYfi4q7i719MKRtUaBAJoH37\n+uzdexGLWg3Nm9/5w0cIIYQQQohKKjCwToHrjRrVyNfHZtGi0PsOVlQ6er2SXdSxY/5/wzdqpDTS\nXrNGea9RwQEkgHPnUnF2zv/hur2VGKpUKtRqNUlJScTHxwPw9ttv06RJEwD++ksZWNS4cWOeeeYZ\nDh48SHZ2NqpbE++MRqM1YHT06FH++c9/kpaWViZnlSCSEHbGYrEQF5dcfD8kb2/lm3wFat++AcnJ\nNzlzJgXatFHGfhYyVUAIIYQQQojK5MiR1+4IJAUG1iE+/o18fWyqVADJaISFC8HfH7780rbu5ARv\nvAHbt8Pzz4OHB9zHmPjS5Otbi8zMnHxr9lBimNsMO9e7775L8+bNGThwIIsXL8bR0ZFx48Zx9epV\n9u3bh9FoxNHRkbS0NOvvTSaTNYMJYPLkybRq1YqbN29Ss4x640o5mxB2JjHxBjduGIoPIj35pDKd\nrQK1b98AUPoiPdS2LfzrXxAfD76+FXouIYQQQgghSuLIkdcq+gjlZ+dOGDfuzhYUPXtCeDi0agUu\nLhVztiJMmfIE48dvBOynxNBisaC+FYS7ckVp4J6dnc2ff/7Jr7/+yvTp03n44Yd56qmniIqKYsmS\nJZw5c4YXXniBzZs306WLUmKXW6r2008/8frrr9OkSRMSEhKoX79+mZ29coQOhRAlFhd3FYCHH65d\n8IaEBLhwocJL2QCaN6+Di4sD+/b9BY8+qiweOFCxhxJCCCGEEELYJCbCc89Bly75A0iNG8OKFbB6\ntTKRrYwDSPc6YS001I9Fi0LtqsRQpVKRlZVFnz596NGjB927dyctLQ1vb2+eeeYZevXqxeeff861\na9eYOnUqRqORL774glGjRtGyZUtmzpxpvda//vUvJkyYwMyZM4mJiSnTABJIEEkIuxMXlwxQeCZS\nTIxy27lzOZ2ocBqNmpYtPTl8WK9MaNPpJIgkhBBlwGQyMXDgQF555RUAEhISGDJkCCEhIUyaNAmD\nwQCAwWBg0qRJhISEMGTIEOuYYCGEEMWLiNiBm9sctNoI3NzmEBGxo6KPdH9ycmD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hhBBC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\nEREREbkuFZFEREREREREROS6/h+Z6WYyTD4AygAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 1440x504 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WSTzP3dQoM10",
        "colab_type": "text"
      },
      "source": [
        "## Summary"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CsyePOwxoNiX",
        "colab_type": "text"
      },
      "source": [
        "We have seen how Multiple Linear regression works step by step using Simple Linear Algebra.<br>\n",
        "\n",
        "We built a MLR Model from scratch by first determining correlated variables, selecting four of them  and shaping them into a 2D array.<br>\n",
        "Then using pandas library to split the data into training and testing sets.<br>\n",
        "Then training the model with the tarining data set using the Matrix Multiplication,<br>\n",
        "And using the model to make predictions on the test data set that is not yet known to the model(out of sample data set)<br>\n",
        "Finally evaluating the model using MSE, RMSE and $R^2$ score."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MqrtOXHzo9QH",
        "colab_type": "text"
      },
      "source": [
        "Our Model performed quite good on the out-of-sample data set.<br>\n",
        "With an error_margin of only 4.8% of the target variable range and a coefficient of determination of 0.87 out of 1.0"
      ]
    }
  ]
}