Ordinary_Least_Square_using_statsmodel.ipynb

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        "id": "view-in-github",
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      "source": [
        "<a href=\"https://colab.research.google.com/github/sfansaria/Machine-Learning/blob/main/Ordinary_Least_Square_using_statsmodel.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/drive')"
      ],
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          "base_uri": "https://localhost:8080/"
        },
        "id": "QVEJYfiLtirZ",
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      },
      "execution_count": 61,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Drive already mounted at /content/drive; to attempt to forcibly remount, call drive.mount(\"/content/drive\", force_remount=True).\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 62,
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        "outputId": "0163987a-90be-41ea-b3ee-70d759bca37d"
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      "outputs": [
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          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Requirement already satisfied: statsmodels in /usr/local/lib/python3.10/dist-packages (0.14.0)\n",
            "Requirement already satisfied: numpy>=1.18 in /usr/local/lib/python3.10/dist-packages (from statsmodels) (1.23.5)\n",
            "Requirement already satisfied: scipy!=1.9.2,>=1.4 in /usr/local/lib/python3.10/dist-packages (from statsmodels) (1.10.1)\n",
            "Requirement already satisfied: pandas>=1.0 in /usr/local/lib/python3.10/dist-packages (from statsmodels) (1.5.3)\n",
            "Requirement already satisfied: patsy>=0.5.2 in /usr/local/lib/python3.10/dist-packages (from statsmodels) (0.5.3)\n",
            "Requirement already satisfied: packaging>=21.3 in /usr/local/lib/python3.10/dist-packages (from statsmodels) (23.1)\n",
            "Requirement already satisfied: python-dateutil>=2.8.1 in /usr/local/lib/python3.10/dist-packages (from pandas>=1.0->statsmodels) (2.8.2)\n",
            "Requirement already satisfied: pytz>=2020.1 in /usr/local/lib/python3.10/dist-packages (from pandas>=1.0->statsmodels) (2023.3.post1)\n",
            "Requirement already satisfied: six in /usr/local/lib/python3.10/dist-packages (from patsy>=0.5.2->statsmodels) (1.16.0)\n"
          ]
        }
      ],
      "source": [
        "pip install statsmodels"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Import libraries\n",
        "import statsmodels.api as sm\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "#read the data\n",
        "\n",
        "data = pd.read_csv('/content/drive/My Drive/ml_datasets/train_ols.csv')\n",
        "\n",
        "data.head()\n"
      ],
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      "execution_count": 63,
      "outputs": [
        {
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              "    x          y\n",
              "0  77  79.775152\n",
              "1  21  23.177279\n",
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    {
      "cell_type": "code",
      "source": [
        "#define the variables\n",
        "\n",
        "x = data['x'].tolist()\n",
        "print(x)\n",
        "y = data['y'].tolist()\n",
        "print(y)"
      ],
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        "colab": {
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        "id": "uN8Po9IJt76z",
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            "[77, 21, 22, 20, 36, 15, 62, 95, 20, 5, 4, 19, 96, 62, 36, 15, 65, 14, 87, 69, 89, 51, 89, 27, 97, 58, 79, 21, 93, 27, 99, 31, 33, 80, 28, 47, 53, 69, 28, 33, 91, 71, 50, 76, 4, 37, 70, 68, 40, 35, 94, 88, 52, 31, 59, 0, 39, 64, 69, 57, 13, 72, 76, 61, 82, 18, 41, 50, 55, 13, 46, 13, 79, 53, 15, 28, 81, 69, 52, 84, 68, 27, 56, 48, 40, 39, 82, 100, 59, 43, 67, 38, 63, 91, 60, 14, 21, 87, 73, 32, 2, 82, 19, 74, 42, 12, 1, 90, 89, 0, 41, 16, 94, 97, 66, 24, 17, 90, 13, 0, 64, 96, 98, 12, 41, 47, 78, 20, 89, 29, 64, 75, 12, 25, 28, 30, 65, 59, 64, 53, 71, 97, 73, 9, 12, 63, 99, 60, 35, 2, 60, 32, 94, 84, 63, 22, 81, 93, 33, 7, 42, 46, 54, 16, 49, 43, 95, 66, 21, 35, 80, 37, 54, 56, 1, 32, 58, 32, 46, 72, 17, 97, 93, 91, 37, 4, 54, 51, 27, 46, 92, 73, 77, 91, 61, 99, 4, 72, 19, 57, 78, 26, 74, 90, 66, 13, 40, 77, 67, 75, 23, 45, 59, 44, 23, 55, 55, 95, 12, 4, 7, 100, 48, 42, 96, 39, 100, 87, 14, 14, 37, 5, 88, 91, 65, 74, 56, 16, 5, 28, 92, 46, 54, 39, 44, 31, 68, 86, 90, 38, 21, 95, 56, 60, 65, 78, 89, 6, 67, 36, 16, 100, 45, 73, 57, 20, 76, 34, 55, 72, 55, 8, 56, 72, 58, 6, 96, 23, 58, 23, 19, 25, 64, 21, 59, 19, 16, 42, 43, 61, 92, 11, 41, 1, 8, 71, 46, 55, 62, 47]\n",
            "[79.77515201, 23.17727887, 25.60926156, 17.85738813, 41.84986439, 9.805234876, 58.87465933, 97.61793701, 18.39512747, 8.746747654, 2.811415826, 17.09537241, 95.14907176, 61.38800663, 40.24701716, 14.82248589, 66.95806869, 16.63507984, 90.65513736, 77.22982636, 92.11906278, 46.91387709, 89.82634442, 21.71380347, 97.41206981, 57.01631363, 78.31056542, 19.1315097, 93.03483388, 26.59112396, 97.55155344, 31.43524822, 35.12724777, 78.61042432, 33.07112825, 51.69967172, 53.62235225, 69.46306072, 27.42497237, 36.34644189, 95.06140858, 68.16724757, 50.96155532, 78.04237454, 5.607664865, 36.11334779, 67.2352155, 65.01324035, 38.14753871, 34.31141446, 95.28503937, 87.84749912, 54.08170635, 31.93063515, 59.61247085, -1.040114209, 47.49374765, 62.60089773, 70.9146434, 56.14834113, 14.05572877, 68.11367147, 75.59701346, 59.225745, 85.45504157, 17.76197116, 38.68888682, 50.96343637, 51.83503872, 17.0761107, 46.56141773, 10.34754461, 77.91032969, 50.17008622, 13.25690647, 31.32274932, 73.9308764, 74.45114379, 52.01932286, 83.68820499, 70.3698748, 23.44479161, 49.83051801, 49.88226593, 41.04525583, 33.37834391, 81.29750133, 105.5918375, 56.82457013, 48.67252645, 67.02150613, 38.43076389, 58.61466887, 89.12377509, 60.9105427, 13.83959878, 16.89085185, 84.06676818, 70.34969772, 33.38474138, -1.63296825, 88.54475895, 17.44047622, 75.69298554, 41.97607107, 12.59244741, 0.275307261, 98.13258005, 87.45721555, -2.344738542, 39.3294153, 16.68715211, 96.58888601, 97.70342201, 67.01715955, 25.63476257, 13.41310757, 95.15647284, 9.744164258, -3.467883789, 62.82816355, 97.27405461, 95.58017185, 7.468501839, 45.44599591, 46.69013968, 74.4993599, 21.63500655, 91.59548851, 26.49487961, 67.38654703, 74.25362837, 12.07991648, 21.32273728, 29.31770045, 26.48713683, 68.94699774, 59.10598995, 64.37521087, 60.20758349, 70.34329706, 97.1082562, 75.7584178, 10.80462727, 12.11219941, 63.28312382, 98.03017721, 63.19354354, 34.8534823, -2.819913974, 59.8313966, 29.38505024, 97.00148372, 85.18657275, 61.74063192, 18.84798163, 78.79008525, 95.12400481, 30.48881287, 10.41468095, 38.98317436, 46.11021062, 52.45103628, 21.16523945, 52.28620611, 44.18863945, 97.13832018, 67.22008001, 18.98322306, 24.3884599, 79.44769523, 40.03504862, 53.32005764, 54.55446979, -2.761182595, 37.80182795, 57.48741435, 36.06292994, 49.83538167, 74.68953276, 14.86159401, 101.0697879, 99.43577876, 91.69240746, 34.12473248, 6.079390073, 59.07247174, 56.43046022, 30.49412933, 48.35172635, 89.73153611, 72.86282528, 80.97144285, 91.36566374, 60.07137496, 99.87382707, 8.655714172, 69.39858505, 19.38780134, 53.11628433, 78.39683006, 25.75612514, 75.07484683, 92.88772282, 69.45498498, 13.12109842, 48.09843134, 79.3142548, 68.48820749, 73.2300846, 24.68362712, 41.90368917, 62.22635684, 45.96396877, 23.52647153, 51.80035866, 51.10774273, 95.79747345, 9.241138977, 7.646529763, 9.281699753, 103.5266162, 47.41006725, 42.03835773, 96.11982476, 38.05766408, 105.4503788, 88.80306911, 15.49301141, 12.42624606, 40.00709598, 5.634030902, 87.36938931, 89.73951993, 66.61499643, 72.9138853, 57.19103506, 11.21710477, 0.676076749, 28.15668543, 95.3958003, 52.05490703, 59.70864577, 36.79224762, 37.08457698, 24.18437976, 67.28725332, 82.870594, 89.899991, 36.94173178, 19.87562242, 90.71481654, 61.09367762, 60.11134958, 64.83296316, 81.40381769, 92.40217686, 2.576625376, 63.80768172, 38.67780759, 16.82839701, 99.78687252, 44.68913433, 71.00377824, 51.57326718, 19.87846479, 79.50341495, 34.58876491, 55.7383467, 68.19721905, 55.81628509, 9.391416798, 56.01448111, 77.9969477, 55.37049953, 11.89457829, 94.79081712, 25.69041546, 53.52042319, 18.31396758, 21.42637785, 30.41303282, 67.68142149, 17.0854783, 60.91792707, 14.99514319, 16.74923937, 41.46923883, 42.84526108, 59.12912974, 91.30863673, 8.673336357, 39.31485292, 5.313686205, 5.405220518, 68.5458879, 47.33487629, 54.09063686, 63.29717058, 52.45946688]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#adding the constant term\n",
        "x = sm.add_constant(x)\n",
        "print(x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kDqpFKVYucxJ",
        "outputId": "1a9dc733-8889-4f03-936a-81c58d3f574a"
      },
      "execution_count": 65,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[  1.  77.]\n",
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            " [  1.  89.]\n",
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            " [  1.  90.]\n",
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            " [  1.  71.]\n",
            " [  1.  97.]\n",
            " [  1.  73.]\n",
            " [  1.   9.]\n",
            " [  1.  12.]\n",
            " [  1.  63.]\n",
            " [  1.  99.]\n",
            " [  1.  60.]\n",
            " [  1.  35.]\n",
            " [  1.   2.]\n",
            " [  1.  60.]\n",
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            " [  1.  94.]\n",
            " [  1.  84.]\n",
            " [  1.  63.]\n",
            " [  1.  22.]\n",
            " [  1.  81.]\n",
            " [  1.  93.]\n",
            " [  1.  33.]\n",
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            " [  1.  21.]\n",
            " [  1.  35.]\n",
            " [  1.  80.]\n",
            " [  1.  37.]\n",
            " [  1.  54.]\n",
            " [  1.  56.]\n",
            " [  1.   1.]\n",
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            " [  1.  46.]\n",
            " [  1.  72.]\n",
            " [  1.  17.]\n",
            " [  1.  97.]\n",
            " [  1.  93.]\n",
            " [  1.  91.]\n",
            " [  1.  37.]\n",
            " [  1.   4.]\n",
            " [  1.  54.]\n",
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            " [  1.  46.]\n",
            " [  1.  92.]\n",
            " [  1.  73.]\n",
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            " [  1.  91.]\n",
            " [  1.  61.]\n",
            " [  1.  99.]\n",
            " [  1.   4.]\n",
            " [  1.  72.]\n",
            " [  1.  19.]\n",
            " [  1.  57.]\n",
            " [  1.  78.]\n",
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            " [  1.  66.]\n",
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            " [  1.  55.]\n",
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            " [  1.  12.]\n",
            " [  1.   4.]\n",
            " [  1.   7.]\n",
            " [  1. 100.]\n",
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            " [  1.  96.]\n",
            " [  1.  39.]\n",
            " [  1. 100.]\n",
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            " [  1.  14.]\n",
            " [  1.  14.]\n",
            " [  1.  37.]\n",
            " [  1.   5.]\n",
            " [  1.  88.]\n",
            " [  1.  91.]\n",
            " [  1.  65.]\n",
            " [  1.  74.]\n",
            " [  1.  56.]\n",
            " [  1.  16.]\n",
            " [  1.   5.]\n",
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            " [  1.  54.]\n",
            " [  1.  39.]\n",
            " [  1.  44.]\n",
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            " [  1.  86.]\n",
            " [  1.  90.]\n",
            " [  1.  38.]\n",
            " [  1.  21.]\n",
            " [  1.  95.]\n",
            " [  1.  56.]\n",
            " [  1.  60.]\n",
            " [  1.  65.]\n",
            " [  1.  78.]\n",
            " [  1.  89.]\n",
            " [  1.   6.]\n",
            " [  1.  67.]\n",
            " [  1.  36.]\n",
            " [  1.  16.]\n",
            " [  1. 100.]\n",
            " [  1.  45.]\n",
            " [  1.  73.]\n",
            " [  1.  57.]\n",
            " [  1.  20.]\n",
            " [  1.  76.]\n",
            " [  1.  34.]\n",
            " [  1.  55.]\n",
            " [  1.  72.]\n",
            " [  1.  55.]\n",
            " [  1.   8.]\n",
            " [  1.  56.]\n",
            " [  1.  72.]\n",
            " [  1.  58.]\n",
            " [  1.   6.]\n",
            " [  1.  96.]\n",
            " [  1.  23.]\n",
            " [  1.  58.]\n",
            " [  1.  23.]\n",
            " [  1.  19.]\n",
            " [  1.  25.]\n",
            " [  1.  64.]\n",
            " [  1.  21.]\n",
            " [  1.  59.]\n",
            " [  1.  19.]\n",
            " [  1.  16.]\n",
            " [  1.  42.]\n",
            " [  1.  43.]\n",
            " [  1.  61.]\n",
            " [  1.  92.]\n",
            " [  1.  11.]\n",
            " [  1.  41.]\n",
            " [  1.   1.]\n",
            " [  1.   8.]\n",
            " [  1.  71.]\n",
            " [  1.  46.]\n",
            " [  1.  55.]\n",
            " [  1.  62.]\n",
            " [  1.  47.]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Perform the regression and fitting the model\n",
        "\n",
        "result = sm.OLS(y, x).fit()\n",
        "\n",
        "\n",
        "#print the summary table\n",
        "print(result.summary())\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "r-O452MSurxO",
        "outputId": "0b515bb8-2e08-4fa9-86c3-2399537cd9c5"
      },
      "execution_count": 66,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "                            OLS Regression Results                            \n",
            "==============================================================================\n",
            "Dep. Variable:                      y   R-squared:                       0.989\n",
            "Model:                            OLS   Adj. R-squared:                  0.989\n",
            "Method:                 Least Squares   F-statistic:                 2.709e+04\n",
            "Date:                Mon, 11 Sep 2023   Prob (F-statistic):          1.33e-294\n",
            "Time:                        15:11:57   Log-Likelihood:                -757.98\n",
            "No. Observations:                 300   AIC:                             1520.\n",
            "Df Residuals:                     298   BIC:                             1527.\n",
            "Df Model:                           1                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "const         -0.4618      0.360     -1.284      0.200      -1.169       0.246\n",
            "x1             1.0143      0.006    164.598      0.000       1.002       1.026\n",
            "==============================================================================\n",
            "Omnibus:                        1.034   Durbin-Watson:                   2.006\n",
            "Prob(Omnibus):                  0.596   Jarque-Bera (JB):                0.825\n",
            "Skew:                           0.117   Prob(JB):                        0.662\n",
            "Kurtosis:                       3.104   Cond. No.                         120.\n",
            "==============================================================================\n",
            "\n",
            "Notes:\n",
            "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Prediction of the model\n",
        "'''\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "# reading data from the csv\n",
        "data = pd.read_csv('/content/drive/My Drive/ml_datasets/train_ols.csv')\n",
        "#data = pd.read_csv('train.csv')\n",
        "\n",
        "# plotting the original values\n",
        "x = data['x'].tolist()\n",
        "y = data['y'].tolist()\n",
        "plt.scatter(x, y)\n",
        "\n",
        "# finding the maximum and minimum\n",
        "# values of x, to get the\n",
        "# range of data\n",
        "max_x = data['x'].max()\n",
        "min_x = data['x'].min()\n",
        "\n",
        "# range of values for plotting\n",
        "# the regression line\n",
        "x = np.arange(min_x, max_x, 1)\n",
        "\n",
        "# the substituted equation\n",
        "y = 1.0143 * x - 0.4618\n",
        "\n",
        "# plotting the regression line\n",
        "plt.plot(y, 'r')\n",
        "plt.show()\n",
        "'''"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 87
        },
        "id": "b84iZdopySgS",
        "outputId": "1aabeb65-1256-441d-e364-f63e8fc991dc"
      },
      "execution_count": 67,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "\"\\nimport pandas as pd\\nimport matplotlib.pyplot as plt\\nimport numpy as np\\n \\n# reading data from the csv\\ndata = pd.read_csv('/content/drive/My Drive/ml_datasets/train_ols.csv')\\n#data = pd.read_csv('train.csv')\\n \\n# plotting the original values\\nx = data['x'].tolist()\\ny = data['y'].tolist()\\nplt.scatter(x, y)\\n \\n# finding the maximum and minimum\\n# values of x, to get the\\n# range of data\\nmax_x = data['x'].max()\\nmin_x = data['x'].min()\\n \\n# range of values for plotting\\n# the regression line\\nx = np.arange(min_x, max_x, 1)\\n \\n# the substituted equation\\ny = 1.0143 * x - 0.4618\\n \\n# plotting the regression line\\nplt.plot(y, 'r')\\nplt.show()\\n\""
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {},
          "execution_count": 67
        }
      ]
    }
  ]
}