{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "05af2cce",
   "metadata": {},
   "source": [
    "![Задача №1](1.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a34b5583",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Размер X: 50\n",
      "Размер Y: 50\n"
     ]
    },
    {
     "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>X</th>\n",
       "      <th>Y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4</td>\n",
       "      <td>12.33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>16.61</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>6</td>\n",
       "      <td>12.47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2</td>\n",
       "      <td>14.36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>13.21</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   X      Y\n",
       "0  4  12.33\n",
       "1  3  16.61\n",
       "2  6  12.47\n",
       "3  2  14.36\n",
       "4  1  13.21"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Данные\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "data = {\n",
    "    'Y': [12.33, 16.61, 12.47, 14.36, 13.21, 13.76, 13.93, 13.96, 15.96, 15.99, \n",
    "          17.32, 14.10, 12.97, 13.60, 16.37, 16.11, 9.24, 15.51, 14.24, 17.23, \n",
    "          15.14, 14.73, 15.52, 10.07, 21.27, 16.86, 13.98, 11.07, 13.70, 13.91, \n",
    "          17.70, 14.08, 15.65, 13.14, 17.43, 18.79, 12.59, 15.99, 12.53, 16.03, \n",
    "          11.63, 18.01, 15.33, 11.65, 10.32, 18.06, 17.83, 14.46, 13.13, 17.11],\n",
    "    'X': [4, 3, 6, 2, 1, 3, 4, 3, 4, 2, 5, 4, 4, 4, 3, 4, 2, 2, 3, 3, \n",
    "              2, 3, 4, 4, 2, 4, 4, 4, 5, 4, 3, 4, 3, 4, 2, 4, 3, 2, 3, 5, \n",
    "              3, 4, 3, 4, 3, 1, 3, 1, 5, 6]\n",
    "}\n",
    "Y = np.array([12.33, 16.61, 12.47, 14.36, 13.21, 13.76, 13.93, 13.96, 15.96, 15.99, \n",
    "              17.32, 14.10, 12.97, 13.60, 16.37, 16.11, 9.24, 15.51, 14.24, 17.23, \n",
    "              15.14, 14.73, 15.52, 10.07, 21.27, 16.86, 13.98, 11.07, 13.70, 13.91, \n",
    "              17.70, 14.08, 15.65, 13.14, 17.43, 18.79, 12.59, 15.99, 12.53, 16.03, \n",
    "              11.63, 18.01, 15.33, 11.65, 10.32, 18.06, 17.83, 14.46, 13.13, 17.11])\n",
    "X = np.array([4, 3, 6, 2, 1, 3, 4, 3, 4, 2, 5, 4, 4, 4, 3, 4, 2, 2, 3, 3, \n",
    "              2, 3, 4, 4, 2, 4, 4, 4, 5, 4, 3, 4, 3, 4, 2, 4, 3, 2, 3, 5, \n",
    "              3, 4, 3, 4, 3, 1, 3, 1, 5, 6])\n",
    "\n",
    "# Проверка размеров массивов\n",
    "print(f\"Размер X: {len(X)}\")\n",
    "print(f\"Размер Y: {len(Y)}\")\n",
    "\n",
    "Y = list(map(float, \"12.33, 16.61, 12.47, 14.36, 13.21, 13.76, 13.93, 13.96, 15.96, 15.99, 17.32, 14.10, 12.97, 13.60, 16.37, 16.11, 9.24, 15.51, 14.24, 17.23, 15.14, 14.73, 15.52, 10.07, 21.27, 16.86, 13.98, 11.07, 13.70, 13.91, 17.70, 14.08, 15.65, 13.14, 17.43, 18.79, 12.59, 15.99, 12.53, 16.03, 11.63, 18.01, 15.33, 11.65, 10.32, 18.06, 17.83, 14.46, 13.13, 17.11\".split(\", \")))\n",
    "X = list(map(int, \"4, 3, 6, 2, 1, 3, 4, 3, 4, 2, 5, 4, 4, 4, 3, 4, 2, 2, 3, 3, 2, 3, 4, 4, 2, 4, 4, 4, 5, 4, 3, 4, 3, 4, 2, 4, 3, 2, 3, 5, 3, 4, 3, 4, 3, 1, 3, 1, 5, 6\".split(\", \")))\n",
    "\n",
    "df = pd.DataFrame({\"X\": X, \"Y\": Y})\n",
    "\n",
    "Y = df[\"Y\"]\n",
    "X = df[\"X\"]\n",
    "\n",
    "data_len = len(df)\n",
    "alpha = 0.02\n",
    "h = 1.40\n",
    "\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2bdb245",
   "metadata": {},
   "source": [
    "## Пункт а)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "76cc48d6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Строим графически результаты эксперимента\n",
    "df.plot(kind=\"scatter\", x=\"X\", y=\"Y\", grid=True, title = \"Результаты эксперимента\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ee4a1cb",
   "metadata": {},
   "source": [
    "### Формулировка линейной регрессионной модели\n",
    "Линейная регрессионная модель зависимости $Y$ от $X$ имеет вид:\n",
    "$$\n",
    "Y = \\beta_1 + \\beta_2 X + \\epsilon,\n",
    "$$\n",
    "где:\n",
    "- $\\beta_1$ — параметр сдвига,\n",
    "- $\\beta_2$ — параметр масштаба,\n",
    "- $\\epsilon$ — случайная ошибка.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24a6df07",
   "metadata": {},
   "source": [
    "### Построение МНК-оценок параметров\n",
    "Метод наименьших квадратов (МНК) используется для нахождения оценок $\\hat{\\beta_1}$ и $\\hat{\\beta_2}$, которые минимизируют сумму квадратов остатков."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "161fc934",
   "metadata": {},
   "outputs": [],
   "source": [
    "# import statsmodels.api as sm\n",
    "# # МНК оценки параметров линейной модели\n",
    "# X_with_const = sm.add_constant(X)\n",
    "# linear_model = sm.OLS(Y, X_with_const)\n",
    "# linear_results = linear_model.fit()\n",
    "\n",
    "# # Построение линии регрессии\n",
    "# # x_line = np.linspace(min(X), max(X), 100)\n",
    "# # y_line = linear_results.params[0] + linear_results.params[1] * x_line\n",
    "# # plt.plot(x_line, y_line, 'r', label=f'Y = {linear_results.params[0]:.4f} + {linear_results.params[1]:.4f}X')\n",
    "# # plt.legend()\n",
    "# # plt.show()\n",
    "\n",
    "# print(\"a) Линейная регрессионная модель:\")\n",
    "# print(f\"β₁ (сдвиг) = {linear_results.params[0]:.4f}\")\n",
    "# print(f\"β₂ (масштаб) = {linear_results.params[1]:.4f}\")\n",
    "# print(linear_results.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "cd0ce073",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "β₁ = 15.5869 β₂ = -0.2522\n",
      "\n",
      "R² линейной модели: 0.0144\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "import statsmodels.api as sm\n",
    "\n",
    "plt.figure(figsize=(10, 6))\n",
    "sns.scatterplot(x='X', y='Y', data=df, label='Данные')\n",
    "X = sm.add_constant(df['X'])\n",
    "model_lin = sm.OLS(df['Y'], X).fit()\n",
    "beta1_lin, beta2_lin = model_lin.params\n",
    "x_vals = np.linspace(df['X'].min(), df['X'].max(), 100)\n",
    "y_lin = beta1_lin + beta2_lin * x_vals\n",
    "print(f\"\\nβ₁ = {beta1_lin:.4f} β₂ = {beta2_lin:.4f}\")\n",
    "print(f\"\\nR² линейной модели: {model_lin.rsquared:.4f}\")\n",
    "\n",
    "plt.plot(x_vals, y_lin, color='red', label='Линейная регрессия')\n",
    "plt.title('Линейная регрессия Y от X')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed0c79e5",
   "metadata": {},
   "source": [
    "*Распределение точек относительно линии*: Точки разбросаны, линия не отражает тренд, что говорит о плохом соответствии.\n",
    "\n",
    "*Наклон линии*: Линия близка к горизонтальной, зависимость слабая.\n",
    "\n",
    "##### Таким образом, Между $X$ и $Y$ нет линейной зависимости. Линейная модель не подходит для описания данных."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f0ab745c",
   "metadata": {},
   "source": [
    "## Пункт b)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4523a637",
   "metadata": {},
   "source": [
    "### Формулировка полиномиальной регрессионной модели\n",
    "Полиномиальная регрессионная модель зависимости $Y$ от $X$ имеет вид:\n",
    "$$\n",
    "Y = \\beta_1 + \\beta_2 X + \\beta_3 X^2 + \\epsilon,\n",
    "$$\n",
    "где:\n",
    "- $\\beta_1$ — параметр сдвига,\n",
    "- $\\beta_2$ — линейный коэффициент при $X$,\n",
    "- $\\beta_3$ —  квадратичный коэффициент при $X^2$,\n",
    "- $\\epsilon$ — случайная ошибка"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "00f87b02",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Полиномиальная модель:\n",
      "β₁ = 16.8727\n",
      "β₂ = -1.1208\n",
      "β₃ = 0.1296\n",
      "\n",
      "R² полиномиальной модели: 0.0240\n"
     ]
    }
   ],
   "source": [
    "df['X2'] = df['X']**2\n",
    "X_poly = sm.add_constant(df[['X', 'X2']])\n",
    "model_poly = sm.OLS(df['Y'], X_poly).fit()\n",
    "beta1_poly, beta2_poly, beta3_poly = model_poly.params\n",
    "y_poly = beta1_poly + beta2_poly * x_vals + beta3_poly * x_vals**2\n",
    "\n",
    "plt.figure(figsize=(10, 6))\n",
    "sns.scatterplot(x='X', y='Y', data=df, label='Данные')\n",
    "plt.plot(x_vals, y_poly, color='green', label='Полиномиальная регрессия')\n",
    "plt.title('Полиномиальная регрессия Y от X')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "\n",
    "print(\"\\nПолиномиальная модель:\")\n",
    "print(f\"β₁ = {beta1_poly:.4f}\")\n",
    "print(f\"β₂ = {beta2_poly:.4f}\")\n",
    "print(f\"β₃ = {beta3_poly:.4f}\")\n",
    "print(f\"\\nR² полиномиальной модели: {model_poly.rsquared:.4f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "611ce9cc",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Y = np.array([12.33, 16.61, 12.47, 14.36, 13.21, 13.76, 13.93, 13.96, 15.96, 15.99, \n",
    "#               17.32, 14.10, 12.97, 13.60, 16.37, 16.11, 9.24, 15.51, 14.24, 17.23, \n",
    "#               15.14, 14.73, 15.52, 10.07, 21.27, 16.86, 13.98, 11.07, 13.70, 13.91, \n",
    "#               17.70, 14.08, 15.65, 13.14, 17.43, 18.79, 12.59, 15.99, 12.53, 16.03, \n",
    "#               11.63, 18.01, 15.33, 11.65, 10.32, 18.06, 17.83, 14.46, 13.13, 17.11])\n",
    "# X = np.array([4, 3, 6, 2, 1, 3, 4, 3, 4, 2, 5, 4, 4, 4, 3, 4, 2, 2, 3, 3, \n",
    "#               2, 3, 4, 4, 2, 4, 4, 4, 5, 4, 3, 4, 3, 4, 2, 4, 3, 2, 3, 5, \n",
    "#               3, 4, 3, 4, 3, 1, 3, 1, 5, 6])\n",
    "\n",
    "# # Проверка размеров массивов\n",
    "# print(f\"Размер X: {len(X)}\")\n",
    "# print(f\"Размер Y: {len(Y)}\")\n",
    "\n",
    "# X_squared = X**2\n",
    "# X_poly = np.column_stack((np.ones(len(X)), X, X_squared))\n",
    "# poly_model = sm.OLS(Y, X_poly)\n",
    "# poly_results = poly_model.fit()\n",
    "\n",
    "# plt.figure(figsize=(10, 6))\n",
    "# plt.scatter(X, Y)\n",
    "# plt.xlabel('X')\n",
    "# plt.ylabel('Y')\n",
    "# plt.title('Полиномиальная модель Y = β₁ + β₂X + β₃X²')\n",
    "# plt.grid(True)\n",
    "\n",
    "# # Построение полиномиальной регрессии\n",
    "# x_poly_line = np.linspace(min(X), max(X), 100)\n",
    "# y_poly_line = poly_results.params[0] + poly_results.params[1] * x_poly_line + poly_results.params[2] * x_poly_line**2\n",
    "# plt.plot(x_poly_line, y_poly_line, 'g', \n",
    "#          label=f'Y = {poly_results.params[0]:.4f} + {poly_results.params[1]:.4f}X + {poly_results.params[2]:.4f}X²')\n",
    "# plt.legend()\n",
    "# plt.show()\n",
    "\n",
    "# print(\"\\nb) Полиномиальная модель:\")\n",
    "# print(f\"β₁ = {poly_results.params[0]:.4f}\")\n",
    "# print(f\"β₂ = {poly_results.params[1]:.4f}\")\n",
    "# print(f\"β₃ = {poly_results.params[2]:.4f}\")\n",
    "# print(poly_results.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ed88a1f",
   "metadata": {},
   "source": [
    "*Распределение точек относительно линии*: Точки разбросаны, линия не отражает тренд, что говорит о плохом соответствии.  \n",
    "*Низкий R²* означает, что квадратичная модель плохо описывает связь между $X$ и $Y$.  \n",
    "##### Результаты указывают на то, что квадратичная модель не подходит для описания данных."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59500230",
   "metadata": {},
   "source": [
    "## Пункт c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a299faff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Остатки для каждого наблюдения:\n",
      " Наблюдение  Остаток (residual)\n",
      "          1             -2.1329\n",
      "          2              1.9334\n",
      "          3             -2.3429\n",
      "          4             -0.7895\n",
      "          5             -2.6715\n",
      "          6             -0.9166\n",
      "          7             -0.5329\n",
      "          8             -0.7166\n",
      "          9              1.4971\n",
      "         10              0.8405\n",
      "         11              2.8117\n",
      "         12             -0.3629\n",
      "         13             -1.4929\n",
      "         14             -0.8629\n",
      "         15              1.6934\n",
      "         16              1.6471\n",
      "         17             -5.9095\n",
      "         18              0.3605\n",
      "         19             -0.4366\n",
      "         20              2.5534\n",
      "         21             -0.0095\n",
      "         22              0.0534\n",
      "         23              1.0571\n",
      "         24             -4.3929\n",
      "         25              6.1205\n",
      "         26              2.3971\n",
      "         27             -0.4829\n",
      "         28             -3.3929\n",
      "         29             -0.8083\n",
      "         30             -0.5529\n",
      "         31              3.0234\n",
      "         32             -0.3829\n",
      "         33              0.9734\n",
      "         34             -1.3229\n",
      "         35              2.2805\n",
      "         36              4.3271\n",
      "         37             -2.0866\n",
      "         38              0.8405\n",
      "         39             -2.1466\n",
      "         40              1.5217\n",
      "         41             -3.0466\n",
      "         42              3.5471\n",
      "         43              0.6534\n",
      "         44             -2.8129\n",
      "         45             -4.3566\n",
      "         46              2.1785\n",
      "         47              3.1534\n",
      "         48             -1.4215\n",
      "         49             -1.3783\n",
      "         50              2.2971\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import chi2, norm\n",
    "from scipy.stats import chi2_contingency\n",
    "from scipy import stats\n",
    "\n",
    "\n",
    "residuals = model_poly.resid\n",
    "plt.figure(figsize=(10, 6))\n",
    "sns.histplot(residuals, kde=False, bins=8, stat='density')\n",
    "\n",
    "# Добавление теоретической кривой нормального распределения\n",
    "x = np.linspace(min(residuals), max(residuals), 100)\n",
    "plt.plot(x, stats.norm.pdf(x, np.mean(residuals), np.std(residuals)), \n",
    "         'r-', label='Нормальное распределение')\n",
    "plt.legend()\n",
    "plt.title('Гистограмма остатков полиномиальной модели')\n",
    "plt.xlabel('Остатки')\n",
    "plt.ylabel('Плотность')\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "\n",
    "# Создаем DataFrame с остатками\n",
    "residuals_df = pd.DataFrame({\n",
    "    'Наблюдение': range(1, len(residuals)+1),\n",
    "    'Остаток (residual)': residuals\n",
    "})\n",
    "\n",
    "# Форматируем вывод остатков\n",
    "residuals_df['Остаток (residual)'] = residuals_df['Остаток (residual)'].round(4)\n",
    "\n",
    "# Выводим таблицу с остатками\n",
    "print(\"Остатки для каждого наблюдения:\")\n",
    "print(residuals_df.to_string(index=False))\n",
    "\n",
    "# # Тест хи-квадрат на нормальность (пример)\n",
    "# observed, bins = np.histogram(residuals, bins=8, density=True)\n",
    "# expected = norm.pdf(bins[:-1], np.mean(residuals), np.std(residuals))\n",
    "# chi2_stat, p_value = chi2_contingency([observed, expected])[0:2]\n",
    "# print(f'Хи-квадрат тест: p-value = {p_value:.4f}')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "72be1710",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "\n",
    "sm.qqplot(residuals, line='45', fit=True)\n",
    "plt.title(\"Q-Q график остатков\")\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef5fef28",
   "metadata": {},
   "source": [
    "### Проверка нормальности с помощью критерия $\\chi^2$\n",
    "\n",
    "**Этапы:**\n",
    "1. **Гипотезы:**\n",
    "   - $H_0$: Остатки имеют нормальное распределение.\n",
    "   - $H_1$: Остатки не имеют нормального распределения.\n",
    "2. **Разделить данные на интервалы (бины):** Используем те же интервалы, что и в гистограмме.\n",
    "3. **Рассчитать наблюдаемые ($O_i$) и ожидаемые ($E_i$) частоты:**\n",
    "   - $E_i = N \\cdot P$ (для $i$-го интервала), где $P$ — вероятность из нормального распределения $N(\\mu, \\sigma^2)$.\n",
    "4. **Вычислить статистику $\\chi^2$:**\n",
    "   $$\n",
    "   \\chi^2 = \\sum \\frac{(O_i - E_i)^2}{E_i}.\n",
    "   $$\n",
    "5. **Сравнить с критическим значением $\\chi^2$:** Если $\\chi^2 > \\chi^2_{\\text{крит}}$, отвергаем $H_0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "bd170677",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Оценка μ (среднее остатков): -0.0000\n",
      "Оценка σ (стандартное отклонение отстатков): 2.3980\n",
      "[ 5  8 15  8 14] [ 5.312141    8.34056556 11.88152698 11.5684878  12.28662505]\n",
      "\n",
      "Результаты после объединения интервалов:\n",
      "Интервалы\t\tНаблюдаемо\tОжидаемо\tВклад в χ²\n",
      "[-5.9095, -2.9020]\t     5      \t5.31\t\t0.0183\n",
      "[-2.9020, -1.3982]\t     8      \t8.34\t\t0.0139\n",
      "[-1.3982, 0.1055]\t     15     \t11.88\t\t0.8185\n",
      "[0.1055, 1.6093]\t     8      \t11.57\t\t1.1008\n",
      "[1.6093, 6.1205]\t     14     \t12.29\t\t0.2389\n",
      "\n",
      "Количество интервалов после объединения: 5\n",
      "Степени свободы: 2 (5 интервалов - 1 - 2 оцененных параметра)\n",
      "Статистика χ²: 2.1904\n",
      "Критическое значение (α=0.02): 7.8240\n",
      "p-value: 0.3345\n",
      "Не отвергаем H₀: распределение нормальное\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.stats import chi2, norm\n",
    "# Вычисление параметров нормального распределения\n",
    "mu = np.mean(residuals)  # Среднее остатков\n",
    "std = np.std(residuals, ddof=1)  # Стандартное отклонение (несмещенное)\n",
    "print(f\"Оценка μ (среднее остатков): {mu:.4f}\")\n",
    "print(f\"Оценка σ (стандартное отклонение отстатков): {std:.4f}\")\n",
    "\n",
    "# Разбиение на интервалы\n",
    "observed_freq, bins = np.histogram(residuals, bins=8)\n",
    "n = len(residuals)\n",
    "n_bins = len(observed_freq)\n",
    "\n",
    "# Вычисление ожидаемых частот\n",
    "expected_freq = np.zeros(n_bins)\n",
    "for i in range(n_bins):\n",
    "    cdf_start = norm.cdf(bins[i], mu, std)\n",
    "    cdf_end = norm.cdf(bins[i+1], mu, std)\n",
    "    expected_freq[i] = n * (cdf_end - cdf_start)\n",
    "\n",
    "# Объединение интервалов с expected_freq < 5\n",
    "observed_list = observed_freq.tolist()\n",
    "expected_list = expected_freq.tolist()\n",
    "bins_list = bins.tolist()\n",
    "\n",
    "# i = 0\n",
    "# while i < len(expected_list):\n",
    "#     if expected_list[i] < 5:\n",
    "#         # Если последний интервал, объединить с предыдущим\n",
    "#         if i == len(expected_list) - 1:\n",
    "#             if i > 0:  # Если есть предыдущий интервал\n",
    "#                 expected_list[i-1] += expected_list[i]\n",
    "#                 observed_list[i-1] += observed_list[i]\n",
    "#                 del expected_list[i]\n",
    "#                 del observed_list[i]\n",
    "#                 del bins_list[i+1]\n",
    "#                 i -= 1  # Вернуться к новому интервалу\n",
    "#         else:\n",
    "#             # Объединить с следующим интервалом\n",
    "#             expected_list[i] += expected_list[i+1]\n",
    "#             observed_list[i] += observed_list[i+1]\n",
    "#             del expected_list[i+1]\n",
    "#             del observed_list[i+1]\n",
    "#             del bins_list[i+1]\n",
    "#     else:\n",
    "#         i += 1\n",
    "i = 0\n",
    "while i < len(expected_list):\n",
    "    if expected_list[i] < 5:\n",
    "        if i == len(expected_list) - 1:          # последний интервал\n",
    "            if i > 0:\n",
    "                expected_list[i-1] += expected_list[i]\n",
    "                observed_list[i-1] += observed_list[i]\n",
    "                del expected_list[i]\n",
    "                del observed_list[i]\n",
    "                del bins_list[i]                 # ← исправлено\n",
    "                i -= 1\n",
    "        else:                                    # объединяем с правым\n",
    "            expected_list[i] += expected_list[i+1]\n",
    "            observed_list[i] += observed_list[i+1]\n",
    "            del expected_list[i+1]\n",
    "            del observed_list[i+1]\n",
    "            del bins_list[i+1]                   # граница между i и i+1\n",
    "    else:\n",
    "        i += 1\n",
    "\n",
    "\n",
    "# Проверка минимального количества интервалов\n",
    "if len(expected_list) < 3:\n",
    "    # Если интервалов меньше 3, принудительно объединяем все интервалы\n",
    "    expected_list = [sum(expected_list)]\n",
    "    observed_list = [sum(observed_list)]\n",
    "    bins_list = [bins[0], bins[-1]]\n",
    "    print(\"Внимание: после объединения остался только 1 интервал!\")\n",
    "\n",
    "# Преобразование в массивы NumPy\n",
    "observed_merged = np.array(observed_list)\n",
    "expected_merged = np.array(expected_list)\n",
    "\n",
    "# Расчет статистики хи-квадрат\n",
    "chi2_stat = np.sum((observed_merged - expected_merged)**2 / expected_merged)\n",
    "\n",
    "# Степени свободы\n",
    "k = len(observed_merged)  # Количество интервалов после объединения\n",
    "dof = k - 1 - 2  # k-1 интервалов минус 2 оцененных параметра (μ и σ)\n",
    "if dof < 1:\n",
    "    dof = 1  # Минимум 1 степень свободы\n",
    "\n",
    "critical_value = chi2.ppf(1 - alpha, dof)\n",
    "p_value = 1 - chi2.cdf(chi2_stat, dof)\n",
    "print(observed_merged, expected_merged)\n",
    "# Вывод результатов\n",
    "print(\"\\nРезультаты после объединения интервалов:\")\n",
    "print(\"Интервалы\\t\\tНаблюдаемо\\tОжидаемо\\tВклад в χ²\")\n",
    "\n",
    "for i in range(len(observed_merged)):\n",
    "    lower = bins_list[i]\n",
    "    upper = bins_list[i+1]\n",
    "    contrib = (observed_merged[i] - expected_merged[i])**2 / expected_merged[i]\n",
    "    print(f\"[{lower:.4f}, {upper:.4f}]\\t{observed_merged[i]:^12}\\t{expected_merged[i]:.2f}\\t\\t{contrib:.4f}\")\n",
    "\n",
    "print(f\"\\nКоличество интервалов после объединения: {k}\")\n",
    "print(f\"Степени свободы: {dof} (5 интервалов - 1 - 2 оцененных параметра)\")\n",
    "print(f\"Статистика χ²: {chi2_stat:.4f}\")\n",
    "print(f\"Критическое значение (α={alpha}): {critical_value:.4f}\")\n",
    "print(f\"p-value: {p_value:.4f}\")\n",
    "\n",
    "# Проверка гипотезы\n",
    "if chi2_stat > critical_value:\n",
    "    print(\"Отвергаем H₀: распределение не нормальное\")\n",
    "else:\n",
    "    print(\"Не отвергаем H₀: распределение нормальное\")\n",
    "\n",
    "\n",
    "# # Разбиение на интервалы (используем 6 интервалов для примера)\n",
    "# mu = np.mean(residuals)  # Среднее остатков\n",
    "# std = np.std(residuals, ddof=1)  # Стандартное отклонение (несмещенное)\n",
    "# observed_freq, bins = np.histogram(residuals, bins=8)\n",
    "# n_bins = len(observed_freq)\n",
    "\n",
    "# # Ожидаемые частоты для нормального распределения\n",
    "# expected_freq = []\n",
    "# for i in range(n_bins):\n",
    "#     bin_start = bins[i]\n",
    "#     bin_end = bins[i+1]\n",
    "#     cdf_start = norm.cdf(bin_start, mu, std)\n",
    "#     cdf_end = norm.cdf(bin_end, mu, std)\n",
    "#     expected_freq.append(len(residuals) * (cdf_end - cdf_start))\n",
    "\n",
    "# # Критерий хи-квадрат\n",
    "# chi2_stat = sum((observed_freq - expected_freq)**2 / expected_freq)\n",
    "# dof = n_bins - 1 - 2  # 2 параметра (mu, std) оценены по данным\n",
    "# alpha = 0.02\n",
    "# critical_value = chi2.ppf(1 - alpha, dof)\n",
    "# p_value = 1 - chi2.cdf(chi2_stat, dof)\n",
    "# print(observed_freq, expected_freq);\n",
    "\n",
    "# print(f\"Хи-квадрат статистика: {chi2_stat:.4f}\")\n",
    "# print(f\"Критическое значение: {critical_value:.4f}\")\n",
    "# print(f\"p-value: {p_value:.4f}\")\n",
    "\n",
    "# # Визуальная оценка\n",
    "# if chi2_stat > critical_value:\n",
    "#     print(\"Отвергаем H0: распределение не нормальное\")\n",
    "# else:\n",
    "#     print(\"Не отвергаем H0: распределение нормальное\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "f498c322",
   "metadata": {},
   "outputs": [],
   "source": [
    "# from scipy.stats import chi2\n",
    "\n",
    "# # Разбиваем остатки на бины (используем те же, что в гистограмме)\n",
    "# counts, bin_edges = np.histogram(residuals, bins=8, density=False)\n",
    "# bin_centers = (bin_edges[:-1] + bin_edges[1:]) / 2\n",
    "\n",
    "# # Ожидаемые частоты для каждого бина\n",
    "\n",
    "# # Ожидаемые частоты для нормального распределения\n",
    "# expected = []\n",
    "# for i in range(n_bins):\n",
    "#     bin_start = bins[i]\n",
    "#     bin_end = bins[i+1]\n",
    "#     cdf_start = norm.cdf(bin_start, mu, std)\n",
    "#     cdf_end = norm.cdf(bin_end, mu, std)\n",
    "#     expected.append(len(residuals) * (cdf_end - cdf_start))\n",
    "\n",
    "# # Удалим бины с ожидаемой частотой < 5 (требование χ²)\n",
    "# observed_filtered = []\n",
    "# expected_filtered = []\n",
    "# for o, e in zip(counts, expected):\n",
    "#     if e >= 5:\n",
    "#         observed_filtered.append(o)\n",
    "#         expected_filtered.append(e)\n",
    "\n",
    "# # Статистика χ²\n",
    "# chi2_stat = sum((o - e)**2 / e for o, e in zip(observed_filtered, expected_filtered))\n",
    "\n",
    "# # Степени свободы: (число бинов - 1 - число параметров распределения)\n",
    "# df_chi2 = len(observed_filtered) - 1 - 1  # 1 параметр σ, mu известен (?)\n",
    "# p_value = 1 - chi2.cdf(chi2_stat, df_chi2)\n",
    "\n",
    "# print(f\"χ² = {chi2_stat:.3f}, p-value = {p_value:.3f}\")\n",
    "\n",
    "# # Критическое значение χ² (α = 0.01)\n",
    "# chi2_crit = chi2.ppf(1 - alpha, df_chi2)\n",
    "# print(f\"Критическое значение χ² (α=0.01): {chi2_crit:.3f}\")\n",
    "\n",
    "# # Вывод\n",
    "# if chi2_stat > chi2_crit:\n",
    "#     print(\"Отвергаем H₀: остатки не нормальны.\")\n",
    "# else:\n",
    "#     print(\"Не отвергаем H₀: остатки нормальны.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d221f57a",
   "metadata": {},
   "source": [
    "**Визуально:** Остатки близки к нормальному распределению.\n",
    "\n",
    "**Статистически:** Критерий $\\chi^2$ не выявил значимых отклонений от нормальности на уровне $\\alpha=0.02$.\n",
    "\n",
    "##### Предположение о нормальности ошибок выполняется."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc40aaba",
   "metadata": {},
   "source": [
    "## Пункт d)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff51dc4b",
   "metadata": {},
   "source": [
    "### Частные доверительные интервалы\n",
    "Частные интервалы строятся для каждого параметра отдельно, используя t-распределение.\n",
    "\n",
    "**Формула:**\n",
    "$$\n",
    "\\hat{\\beta_j} \\pm t_{1-\\alpha/2, n-p} \\cdot SE(\\hat{\\beta_j}),\n",
    "$$\n",
    "где:\n",
    "- $\\hat{\\beta_j}$ - оценка параметра,\n",
    "- $SE(\\hat{\\beta_j})$ - стандартная ошибка параметра,\n",
    "- $t_{1-\\alpha/2}$ - критическое значение t-распределения,\n",
    "- $n$ - число наблюдений,\n",
    "- $p$ - число параметров модели (для квадратичной модели $p = 3$).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "ca6842f7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Доверительные интервалы (уровень 0.98):\n",
      "           0         1\n",
      "X  -4.292994  2.051449\n",
      "X2 -0.331008  0.590162\n",
      "Доверительный интервал для β₂ (98.0%): [-4.2930, 2.0514]\n",
      "Доверительный интервал для β₃ (98.0%): [-0.3310, 0.5902]\n"
     ]
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "conf_int = model_poly.conf_int(alpha=alpha)\n",
    "print(f\"Доверительные интервалы (уровень {1-alpha}):\")\n",
    "print(conf_int.loc[['X', 'X2']])\n",
    "\n",
    "print(\"Доверительный интервал для β₂ (98.0%): [-4.2930, 2.0514]\")\n",
    "print(\"Доверительный интервал для β₃ (98.0%): [-0.3310, 0.5902]\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "657258f6",
   "metadata": {},
   "source": [
    "### Совместные доверительные интервалы\n",
    "Совместные интервалы учитывают корреляцию между оценками параметров. Используем метод **Бонферрони** или **F-распределение**.\n",
    "\n",
    "#### Метод Бонферрони\n",
    "**Формула:**\n",
    "$$\n",
    "\\hat{\\beta_j} \\pm t_{1-\\alpha/(2k),n-p} \\cdot SE(\\hat{\\beta_j}),\n",
    "$$\n",
    "где $k=2$ (число параметров $\\beta_2$ и $\\beta_3$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "68365ffd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import f\n",
    "\n",
    "# Параметры модели\n",
    "n = model_poly.nobs  # количество наблюдений\n",
    "k = 2                # количество параметров (β2, β3)\n",
    "alpha = 0.02         # уровень значимости\n",
    "\n",
    "# Ковариационная матрица оценок параметров\n",
    "cov_matrix = model_poly.cov_params().loc[['X', 'X2'], ['X', 'X2']]\n",
    "\n",
    "# Критическое значение F-распределения\n",
    "f_critical = f.ppf(1 - alpha, dfn=k, dfd=n - model_poly.df_model - 1)\n",
    "\n",
    "# Точки оценок параметров\n",
    "beta2_hat, beta3_hat = model_poly.params[['X', 'X2']]\n",
    "\n",
    "# Границы совместной доверительной области (эллипс)\n",
    "# Для простоты выведем диапазоны по осям\n",
    "eigenvalues, eigenvectors = np.linalg.eigh(cov_matrix * f_critical * k)\n",
    "angle = np.degrees(np.arctan2(*eigenvectors[:, 0][::-1]))\n",
    "\n",
    "# Визуализация\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.scatter(beta2_hat, beta3_hat, color='red', label='Оценки параметров')\n",
    "ellipse = plt.matplotlib.patches.Ellipse(\n",
    "    (beta2_hat, beta3_hat),\n",
    "    2 * np.sqrt(eigenvalues[0]),\n",
    "    2 * np.sqrt(eigenvalues[1]),\n",
    "    angle=angle,\n",
    "    edgecolor='blue',\n",
    "    facecolor='none',\n",
    "    label=f'Совместный ДИ (F-распределение)'\n",
    ")\n",
    "plt.gca().add_patch(ellipse)\n",
    "plt.xlabel('β2 (X)')\n",
    "plt.ylabel('β3 (X²)')\n",
    "plt.title('Совместный доверительный интервал для β2 и β3')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "76e0b82d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# from scipy.stats import t\n",
    "# import statsmodels.api as sm\n",
    "\n",
    "# # Число параметров k = 2 (beta2 и beta3)\n",
    "# k = 2\n",
    "\n",
    "# # Критическое значение t-распределения\n",
    "# t_crit = t.ppf(1 - alpha/(2*k), model_poly.df_resid)\n",
    "\n",
    "# # Совместные интервалы Бонферрони\n",
    "# beta2_conf_bonf = [\n",
    "#     model_poly.params.iloc[1] - t_crit * model_poly.bse.iloc[1],\n",
    "#     model_poly.params.iloc[1] + t_crit * model_poly.bse.iloc[1]\n",
    "# ]\n",
    "\n",
    "\n",
    "# beta3_conf_bonf = [\n",
    "#     model_poly.params.iloc[2] - t_crit * model_poly.bse.iloc[2],\n",
    "#     model_poly.params.iloc[2] + t_crit * model_poly.bse.iloc[2]\n",
    "# ]\n",
    "\n",
    "# print(f\"Совместный интервал (Бонферрони) для beta2: [{beta2_conf_bonf[0]:.3f}, {beta2_conf_bonf[1]:.3f}]\")\n",
    "# print(f\"Совместный интервал (Бонферрони) для beta3: [{beta3_conf_bonf[0]:.3f}, {beta3_conf_bonf[1]:.3f}]\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "f791c572",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Ковариационная матрица для β2 и β3:\n",
      "           X        X2\n",
      "X   1.734960 -0.245172\n",
      "X2 -0.245172  0.036575\n",
      "\n",
      "Совместные интервалы (Бонферрони):\n",
      "β2: [-4.657, 2.415]\n",
      "β3: [-0.384, 0.643]\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import t\n",
    "# Ковариационная матрица\n",
    "cov_matrix = model_poly.cov_params().loc[['X', 'X2'], ['X', 'X2']]\n",
    "print(\"\\nКовариационная матрица для β2 и β3:\")\n",
    "print(cov_matrix)\n",
    "\n",
    "# Совместные интервалы Бонферрони\n",
    "m = 2  # количество параметров\n",
    "alpha_bonferroni = alpha / m\n",
    "t_crit = t.ppf(1 - alpha_bonferroni/2, df=model_poly.df_resid)\n",
    "\n",
    "beta2_se = np.sqrt(cov_matrix.iloc[0, 0])\n",
    "beta3_se = np.sqrt(cov_matrix.iloc[1, 1])\n",
    "\n",
    "bonferroni_beta2 = [\n",
    "    beta2_poly - t_crit * beta2_se,\n",
    "    beta2_poly + t_crit * beta2_se\n",
    "]\n",
    "\n",
    "bonferroni_beta3 = [\n",
    "    beta3_poly - t_crit * beta3_se,\n",
    "    beta3_poly + t_crit * beta3_se\n",
    "]\n",
    "\n",
    "print(\"\\nСовместные интервалы (Бонферрони):\")\n",
    "print(f\"β2: [{bonferroni_beta2[0]:.3f}, {bonferroni_beta2[1]:.3f}]\")\n",
    "print(f\"β3: [{bonferroni_beta3[0]:.3f}, {bonferroni_beta3[1]:.3f}]\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cdc01a33",
   "metadata": {},
   "source": [
    "#### Метод F-распределения\n",
    "**Формула:**\n",
    "$$\n",
    "(\\hat{\\beta} - \\beta)^T \\cdot Cov(\\hat{\\beta})^{-1} \\cdot (\\hat{\\beta} - \\beta) \\leq F_{1-\\alpha, 2, n-p},\n",
    "$$\n",
    "где $F_{1-\\alpha, 2, n-p}$ - критическое значение F-распределения."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "9b48da35",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Полная ковариационная матрица:\n",
      "        const       X      X2\n",
      "const  4.7543 -2.7403  0.3629\n",
      "X     -2.7403  1.7350 -0.2452\n",
      "X2     0.3629 -0.2452  0.0366\n",
      "[-1.120772, 0.129577]\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import f\n",
    "full_cov_matrix = model_poly.cov_params()\n",
    "print(\"\\nПолная ковариационная матрица:\")\n",
    "print(full_cov_matrix.round(4))\n",
    "\n",
    "beta2_hat = model_poly.params['X']\n",
    "beta3_hat = model_poly.params['X2']\n",
    "\n",
    "print(f\"[{beta2_hat:3f}, {beta3_hat:3f}]\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "b34812e2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# from scipy.stats import f\n",
    "\n",
    "# # Параметры модели\n",
    "# n = model_poly.nobs  # количество наблюдений\n",
    "# k = 2                # количество параметров (β2, β3)\n",
    "# alpha = 0.02         # уровень значимости\n",
    "\n",
    "# # Ковариационная матрица оценок параметров\n",
    "# cov_matrix = model_poly.cov_params().loc[['X', 'X2'], ['X', 'X2']]\n",
    "\n",
    "# # Критическое значение F-распределения\n",
    "# f_critical = f.ppf(1 - alpha, dfn=k, dfd=n - model_poly.df_model - 1)\n",
    "\n",
    "# # Точки оценок параметров\n",
    "# beta2_hat, beta3_hat = model_poly.params[['X', 'X2']]\n",
    "\n",
    "# # Границы совместной доверительной области (эллипс)\n",
    "# # Для простоты выведем диапазоны по осям\n",
    "# eigenvalues, eigenvectors = np.linalg.eigh(cov_matrix * f_critical * k)\n",
    "# angle = np.degrees(np.arctan2(*eigenvectors[:, 0][::-1]))\n",
    "\n",
    "# # Визуализация\n",
    "# plt.figure(figsize=(10, 6))\n",
    "# plt.scatter(beta2_hat, beta3_hat, color='red', label='Оценки параметров')\n",
    "# ellipse = plt.matplotlib.patches.Ellipse(\n",
    "#     (beta2_hat, beta3_hat),\n",
    "#     2 * np.sqrt(eigenvalues[0]),\n",
    "#     2 * np.sqrt(eigenvalues[1]),\n",
    "#     angle=angle,\n",
    "#     edgecolor='blue',\n",
    "#     facecolor='none',\n",
    "#     label=f'Совместный ДИ (F-распределение)'\n",
    "# )\n",
    "# plt.gca().add_patch(ellipse)\n",
    "# plt.xlabel('β2 (X)')\n",
    "# plt.ylabel('β3 (X²)')\n",
    "# plt.title('Совместный доверительный интервал для β2 и β3')\n",
    "# plt.legend()\n",
    "# plt.grid(True)\n",
    "# plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed363cbc",
   "metadata": {},
   "source": [
    "## Пункт e)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd92108d",
   "metadata": {},
   "source": [
    "#### Гипотеза линейности\n",
    "- $H_0$: Зависимость $Y$ от $X$ линейна ($\\beta_3 = 0$).\n",
    "- $H_1$: Зависимость нелинейна ($\\beta_3 \\neq 0$).\n",
    "\n",
    "#### Гипотеза независимости\n",
    "- $H_0$: $Y$ не зависит от $X$ линейно ($\\beta_2 = \\beta_3 = 0$).\n",
    "- $H_1$: $Y$ зависит от $X$ линейно (хотя бы один из $\\beta_2, \\beta_3 \\neq 0$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "1fde6d40",
   "metadata": {},
   "outputs": [],
   "source": [
    "# import statsmodels.api as sm\n",
    "# from sklearn.preprocessing import PolynomialFeatures\n",
    "\n",
    "# # Создание моделей\n",
    "# # Константная модель (Y ~ 1)\n",
    "# X_const = sm.add_constant(np.ones(len(Y)))\n",
    "# model_const = sm.OLS(Y, X_const).fit()\n",
    "\n",
    "# # Линейная модель (Y ~ X)\n",
    "# X_linear = sm.add_constant(X)\n",
    "# model_linear = sm.OLS(Y, X_linear).fit()\n",
    "\n",
    "# # Квадратичная модель (Y ~ X + X²)\n",
    "# poly = PolynomialFeatures(degree=2, include_bias=False)\n",
    "# X_poly = poly.fit_transform(X.values.reshape(-1, 1))\n",
    "# X_poly_sm = sm.add_constant(X_poly)\n",
    "# model_poly = sm.OLS(Y, X_poly_sm).fit()\n",
    "\n",
    "# # F-тест: Линейная vs. Квадратичная\n",
    "# ftest_linear_vs_poly = model_poly.compare_f_test(model_linear)\n",
    "# print(f\"F-тест (линейная vs. квадратичная): F = {ftest_linear_vs_poly[0]:.3f}, p-value = {ftest_linear_vs_poly[1]:.3f}\")\n",
    "\n",
    "# # F-тест: Константная vs. Квадратичная\n",
    "# ftest_const_vs_poly = model_poly.compare_f_test(model_const)\n",
    "# print(f\"F-тест (константная vs. квадратичная): F = {ftest_const_vs_poly[0]:.3f}, p-value = {ftest_const_vs_poly[1]:.3f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "405456a9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Проверка гипотез:\n",
      "\n",
      "Проверка гипотезы линейности (H₀: β₃ = 0):\n",
      "F-статистика: 0.4591\n",
      "p-значение: 0.5014\n",
      "Нет оснований отвергать гипотезу о линейности (alpha=0.02)\n",
      "\n",
      "Проверка гипотезы независимости (H₀: β₂ = β₃ = 0):\n",
      "F-статистика: 0.5770\n",
      "p-значение: 0.5655\n",
      "Нет оснований отвергать гипотезу о независимости (alpha=0.02)\n"
     ]
    }
   ],
   "source": [
    "model_const = sm.OLS(df['Y'], sm.add_constant(np.ones(len(df)))).fit()\n",
    "\n",
    "# print(\"\\nПроверка гипотез:\")\n",
    "# # Тест на линейность (значимость β₃)\n",
    "# print(\"Проверка гипотезы линейности (H₀: β₃ = 0):\")\n",
    "# print(f\"t-статистика: {model_poly.tvalues[2]:.4f}\")\n",
    "# print(f\"p-значение: {model_poly.pvalues[2]:.4f}\")\n",
    "# if model_poly.pvalues[2] < alpha:\n",
    "#     print(f\"Гипотеза о линейности отвергается\")\n",
    "# else:\n",
    "#     print(f\"Нет оснований отвергать гипотезу о линейности\")\n",
    "\n",
    "# # Тест на независимость (значимость β₂)\n",
    "# print(\"\\nПроверка гипотезы независимости (H₀: β₂ = 0):\")\n",
    "# print(f\"t-статистика: {model_poly.tvalues[1]:.4f}\")\n",
    "# print(f\"p-значение: {model_poly.pvalues[1]:.4f}\")\n",
    "# if model_poly.pvalues[1] < alpha:\n",
    "#     print(f\"Гипотеза о независимости отвергается\")\n",
    "# else:\n",
    "#     print(f\"Нет оснований отвергать гипотезу о независимости\")\n",
    "\n",
    "from statsmodels.stats.anova import anova_lm\n",
    "\n",
    "print(\"\\nПроверка гипотез:\")\n",
    "\n",
    "# Сравнение моделей для проверки гипотез\n",
    "# 1. Сравнение линейной и квадратичной моделей (проверка линейности)\n",
    "anova_results_lin = anova_lm(model_lin, model_poly)\n",
    "print(\"\\nПроверка гипотезы линейности (H₀: β₃ = 0):\")\n",
    "print(f\"F-статистика: {anova_results_lin.F[1]:.4f}\")\n",
    "print(f\"p-значение: {anova_results_lin['Pr(>F)'][1]:.4f}\")\n",
    "\n",
    "if anova_results_lin['Pr(>F)'][1] < alpha:\n",
    "    print(\"Гипотеза о линейности отвергается (alpha=0.02)\")\n",
    "else:\n",
    "    print(\"Нет оснований отвергать гипотезу о линейности (alpha=0.02)\")\n",
    "\n",
    "# 2. Сравнение константной и квадратичной моделей (проверка независимости)\n",
    "anova_results_const = anova_lm(model_const, model_poly)\n",
    "print(\"\\nПроверка гипотезы независимости (H₀: β₂ = β₃ = 0):\")\n",
    "print(f\"F-статистика: {anova_results_const.F[1]:.4f}\")\n",
    "print(f\"p-значение: {anova_results_const['Pr(>F)'][1]:.4f}\")\n",
    "\n",
    "if anova_results_const['Pr(>F)'][1] < alpha:\n",
    "    print(\"Гипотеза о независимости отвергается (alpha=0.02)\")\n",
    "else:\n",
    "    print(\"Нет оснований отвергать гипотезу о независимости (alpha=0.02)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "259f90f3",
   "metadata": {},
   "source": [
    "- **Проверка гипотезы линейности (H₀: β₃ = 0):**\n",
    "  - Нет оснований отвергать гипотезу о линейности (p > 0.02).\n",
    "\n",
    "- **Проверка гипотезы независимости (H₀: β₂ = 0):**\n",
    "  - Нет оснований отвергать гипотезу о независимости (p > 0.02)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eccd4f5e",
   "metadata": {},
   "source": [
    "## Пункт f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "c00ff024",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Сравнение моделей по AIC и BIC:\n",
      "--------------------------------------\n",
      "Модель           AIC       BIC\n",
      "Линейная        232.83     236.66\n",
      "Квадратичная    234.35     240.08\n",
      "Константная     231.56     233.47\n"
     ]
    }
   ],
   "source": [
    "# f) AIC и BIC\n",
    "# Добавляем константную модель для сравнения\n",
    "\n",
    "print(\"\\nСравнение моделей по AIC и BIC:\")\n",
    "print(\"--------------------------------------\")\n",
    "print(\"Модель           AIC       BIC\")\n",
    "print(f\"Линейная        {model_lin.aic:.2f}     {model_lin.bic:.2f}\")\n",
    "print(f\"Квадратичная    {model_poly.aic:.2f}     {model_poly.bic:.2f}\")\n",
    "print(f\"Константная     {model_const.aic:.2f}     {model_const.bic:.2f}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d66aad56",
   "metadata": {},
   "source": [
    "**AIC/BIC** константной модели меньше, она лучше описывает данные.  \n",
    "Это согласуется с F-тестами: константная модель лучше описывает данные"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "venv",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}