{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Prediction Intervals with Changing Variance\n",
        "\n",
        "Module 8 notebook lab. This notebook uses original Ceteris Lab teaching data and does not report real empirical findings.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Learning goal\n",
        "Plot prediction intervals under changing variance.\n",
        "\n",
        "Dataset: MODULE8_HOUSING_VARIANCE_SYNTHETIC. Variables: house_id, price, log_price, lotsize, sqrft, bedrooms.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "import statsmodels.api as sm\n",
        "\n",
        "df = pd.read_csv(\"/data/module-8/module8_housing_variance_synthetic.csv\")\n",
        "X = sm.add_constant(df[[\"sqrft\", \"lotsize\"]])\n",
        "model = sm.OLS(df[\"price\"], X).fit(cov_type=\"HC1\")\n",
        "grid = pd.DataFrame({\"sqrft\": np.linspace(df[\"sqrft\"].min(), df[\"sqrft\"].max(), 30), \"lotsize\": df[\"lotsize\"].median()})\n",
        "pred = model.get_prediction(sm.add_constant(grid, has_constant=\"add\")).summary_frame()\n",
        "plt.plot(grid[\"sqrft\"], pred[\"mean\"], label=\"mean prediction\")\n",
        "plt.fill_between(grid[\"sqrft\"], pred[\"obs_ci_lower\"], pred[\"obs_ci_upper\"], alpha=0.2, label=\"prediction interval\")\n",
        "plt.xlabel(\"Square feet\")\n",
        "plt.ylabel(\"Price\")\n",
        "plt.legend()\n",
        "plt.title(\"Prediction intervals widen with uncertainty\")\n",
        "plt.show()\n",
        "print(pred[[\"mean\", \"obs_ci_lower\", \"obs_ci_upper\"]].head().round(2))\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Reflection\n",
        "Write two sentences: one sentence explaining what the diagnostic or robust result says, and one sentence explaining a limitation or next step.\n"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "name": "python",
      "version": "3.11"
    },
    "ceteris_lab": {
      "module": "Module 8",
      "lesson": "Prediction under Heteroskedasticity",
      "dataset": "MODULE8_HOUSING_VARIANCE_SYNTHETIC",
      "copyright": "Original Ceteris Lab notebook. No external text, tables, or figures are reproduced."
    }
  },
  "nbformat": 4,
  "nbformat_minor": 5
}