Normal Equations and Analytical Solution for Linear Regression Models.ipynb

normal-equations-and-analytical-solution-for-linear-regression-models.ipynb

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        "import numpy as np\n",
        "import pandas as pd\n",
        "\n",
        "beta_zero = np.array([1,    1,    1,    1,    1,    1])\n",
        "sqr_feet = np.array([ 1000, 1500, 2000, 3000, 3800, 4500])\n",
        "bedrooms = np.array([ 1,    2,    2,    3,    4,    5])\n",
        "bathrooms = np.array([ 1,    1,    1,   2,    2,    2])\n",
        "house_age = np.array([ 20,    24,    12,   8,    13,    14])\n",
        "\n",
        "X = np.array([beta_zero, sqr_feet, bedrooms, bathrooms, house_age]).T\n",
        "y = np.array([ 100,  230,  150,  300,  390,  300]).reshape(X.shape[0],1)\n",
        "B = np.linalg.inv(X.T @ X) @ (X.T @ y)\n",
        "B = np.round(B,2)\n",
        "preds = X @ B\n",
        "preds = np.round(preds,2)"
      ]
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      "source": [
        "## Print Statements\n",
        "feats = [\"Beta Zero\",\"Sqr Feet\",\"Bedrooms\",\"Bathrooms\",\"House Age\"]\n",
        "print(pd.DataFrame(np.c_[X, y, preds], columns=[\"Beta Zero\",\"Sqr Feet\",\"Bedrooms\",\"Bathrooms\",\"House Age\",\"Target\",\"Predictions\"]))\n",
        "print(\"\\nThetas: {} \\n\".format(B.T))\n",
        "formula = \"Prediction =\" + \"\".join([\"{} x {} +\".format(\" Beta_{}\".format(str(en)), feat) for en, feat in enumerate(feats)])[:-2] \n",
        "print(\"Formula:  \" +  formula +\" \\n\" )\n",
        "print(\"\\n\".join([\"{} = \".format(pred[0]) + \"\".join([\"{} x {} + \".format(the[0], feat) for the, feat in zip(B, X[en,:])])[:-3] for en, pred in enumerate(preds)]))"
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          "text": [
            "   Beta Zero  Sqr Feet  Bedrooms  Bathrooms  House Age  Target  Predictions\n",
            "0        1.0    1000.0       1.0        1.0       20.0   100.0       139.30\n",
            "1        1.0    1500.0       2.0        1.0       24.0   230.0       197.15\n",
            "2        1.0    2000.0       2.0        1.0       12.0   150.0       128.79\n",
            "3        1.0    3000.0       3.0        2.0        8.0   300.0       302.10\n",
            "4        1.0    3800.0       4.0        2.0       13.0   390.0       310.98\n",
            "5        1.0    4500.0       5.0        2.0       14.0   300.0       339.74\n",
            "\n",
            "Thetas: [[-1.0730e+01 -1.6000e-01  1.4173e+02  1.8770e+02 -9.7000e-01]] \n",
            "\n",
            "Formula:  Prediction = Beta_0 x Beta Zero + Beta_1 x Sqr Feet + Beta_2 x Bedrooms + Beta_3 x Bathrooms + Beta_4 x House Age \n",
            "\n",
            "139.3 = -10.73 x 1 + -0.16 x 1000 + 141.73 x 1 + 187.7 x 1 + -0.97 x 20\n",
            "197.15 = -10.73 x 1 + -0.16 x 1500 + 141.73 x 2 + 187.7 x 1 + -0.97 x 24\n",
            "128.79 = -10.73 x 1 + -0.16 x 2000 + 141.73 x 2 + 187.7 x 1 + -0.97 x 12\n",
            "302.1 = -10.73 x 1 + -0.16 x 3000 + 141.73 x 3 + 187.7 x 2 + -0.97 x 8\n",
            "310.98 = -10.73 x 1 + -0.16 x 3800 + 141.73 x 4 + 187.7 x 2 + -0.97 x 13\n",
            "339.74 = -10.73 x 1 + -0.16 x 4500 + 141.73 x 5 + 187.7 x 2 + -0.97 x 14\n"
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