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                "text": [
                  "=== Variance Inflation Factor (VIF) ===\n"
                ]
              },
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                  "text/plain": "  Variable         VIF\n0       X1  115.393690\n1       X2  110.553122\n2       X3    3.104472",
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                "text": [
                  "\n",
                  "💡 Aplicación financiera:\n",
                  "- Evaluar correlación entre variables independientes como activos financieros o indicadores macroeconómicos.\n",
                  "- VIF > 5-10 indica multicolinealidad problemática, que puede distorsionar coeficientes de regresión.\n",
                  "- Permite decidir si se eliminan variables, combinan o aplican técnicas de regularización.\n"
                ]
              }
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              "<div style=\"max-width:800px; border: 1px solid var(--colab-border-color);\"><style>\n",
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              "         var(--colab-secondary-surface-color); padding: 8px 12px;\n",
              "         border-bottom: 1px solid var(--colab-border-color);\"><b>simulador_vif</b><br/>def simulador_vif(n=50, corr=0.8, ruido=5)</pre><pre class=\"function-repr-contents function-repr-contents-collapsed\" style=\"\"><a class=\"filepath\" style=\"display:none\" href=\"#\">/tmp/ipykernel_2056/1747280716.py</a>Simula variables independientes correlacionadas y calcula VIF.\n",
              "\n",
              "Parámetros:\n",
              "- n: número de observaciones\n",
              "- corr: correlación entre X1 y X2\n",
              "- ruido: desviación estándar del ruido aleatorio</pre></div>"
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          },
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        }
      ],
      "source": [
        "# 📦 Librerías necesarias\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "from sklearn.linear_model import LinearRegression\n",
        "from statsmodels.stats.outliers_influence import variance_inflation_factor\n",
        "from ipywidgets import interact, IntSlider, FloatSlider\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# 🔹 Función simuladora de multicolinealidad\n",
        "def simulador_vif(n=50, corr=0.8, ruido=5):\n",
        "    \"\"\"\n",
        "    Simula variables independientes correlacionadas y calcula VIF.\n",
        "\n",
        "    Parámetros:\n",
        "    - n: número de observaciones\n",
        "    - corr: correlación entre X1 y X2\n",
        "    - ruido: desviación estándar del ruido aleatorio\n",
        "    \"\"\"\n",
        "\n",
        "    # 🔹 Generar variable X1\n",
        "    X1 = np.linspace(0, 100, n)\n",
        "\n",
        "    # 🔹 Generar X2 correlacionada con X1\n",
        "    X2 = corr*X1 + np.random.normal(0, ruido, n)\n",
        "\n",
        "    # 🔹 Generar una tercera variable independiente sin correlación\n",
        "    X3 = np.random.normal(50, 20, n)\n",
        "\n",
        "    # 🔹 Crear DataFrame\n",
        "    df = pd.DataFrame({'X1': X1, 'X2': X2, 'X3': X3})\n",
        "\n",
        "    # 🔹 Calcular VIF para cada variable\n",
        "    vif_data = pd.DataFrame()\n",
        "    vif_data[\"Variable\"] = df.columns\n",
        "    vif_data[\"VIF\"] = [variance_inflation_factor(df.values, i) for i in range(df.shape[1])]\n",
        "\n",
        "    print(\"=== Variance Inflation Factor (VIF) ===\")\n",
        "    display(vif_data)\n",
        "\n",
        "    # 🔹 Gráfica de correlación\n",
        "    plt.figure(figsize=(8,6))\n",
        "    plt.scatter(X1, X2, color='blue', alpha=0.6, label='X1 vs X2')\n",
        "    plt.xlabel('X1')\n",
        "    plt.ylabel('X2')\n",
        "    plt.title('Visualización de Colinealidad entre X1 y X2')\n",
        "    plt.legend()\n",
        "    plt.show()\n",
        "\n",
        "    print(\"\\n💡 Aplicación financiera:\")\n",
        "    print(\"- Evaluar correlación entre variables independientes como activos financieros o indicadores macroeconómicos.\")\n",
        "    print(\"- VIF > 5-10 indica multicolinealidad problemática, que puede distorsionar coeficientes de regresión.\")\n",
        "    print(\"- Permite decidir si se eliminan variables, combinan o aplican técnicas de regularización.\")\n",
        "\n",
        "# 🔹 Interactividad\n",
        "interact(\n",
        "    simulador_vif,\n",
        "    n=IntSlider(value=50, min=10, max=200, step=5, description='N° Observaciones'),\n",
        "    corr=FloatSlider(value=0.8, min=-1, max=1, step=0.05, description='Correlación X1-X2'),\n",
        "    ruido=FloatSlider(value=5, min=0, max=50, step=1, description='Ruido')\n",
        ")"
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