{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "05af2cce",
   "metadata": {},
   "source": [
    "![Задача №2](2.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a34b5583",
   "metadata": {},
   "outputs": [
    {
     "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>Y</th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>13.17</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>11.78</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>11.70</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>12.54</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>11.59</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Y  A  B\n",
       "0  13.17  1  1\n",
       "1  11.78  1  1\n",
       "2  11.70  1  1\n",
       "3  12.54  1  1\n",
       "4  11.59  1  1"
      ]
     },
     "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",
    "import statsmodels.api as sm\n",
    "\n",
    "Y = list(map(float, \"13.17, 11.78, 11.70, 12.54, 11.59, 11.21, 9.57, 9.07, 10.10, 10.60, 9.22, 7.91, 17.17, 14.74, 16.37, 15.34, 16.72, 16.53, 11.08, 12.01, 12.62, 11.07, 11.36, 11.78, 14.85, 14.60, 15.40, 13.23, 15.32, 13.23, 21.08, 20.70, 23.04, 21.22, 23.35, 22.51, 20.08, 18.89, 21.47, 19.55, 20.88, 20.01, 17.06, 18.76, 18.05, 17.83, 17.33, 18.30\".split(\", \")))\n",
    "A = [1]*24 + [2]*24\n",
    "B = [1]*6 + [2]*6 + [3]*6 + [4]*6 + [1]*6 + [2]*6 + [3]*6 + [4]*6\n",
    "\n",
    "df = pd.DataFrame({\"Y\": Y, \"A\": A, \"B\": B})\n",
    "\n",
    "Y = df[\"Y\"]\n",
    "A = df[\"A\"]\n",
    "B = df[\"B\"]\n",
    "alpha = 0.02\n",
    "h = 0.82\n",
    "\n",
    "df.head()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2bdb245",
   "metadata": {},
   "source": [
    "## Пункт а)\n",
    "### 1. Формулировка модели двухфакторного дисперсионного анализа\n",
    "Модель с взаимодействием факторов:\n",
    "$$\n",
    "Y_{ijk} = \\mu + \\alpha_i + \\beta_j + (\\alpha \\beta)_{ij} + \\epsilon_{ijk},\n",
    "$$\n",
    "где:\n",
    "- $Y_{ijk}$ — наблюдаемое значение переменной $Y$ для $i$-го уровня фактора $A$, $j$-го уровня фактора $B$, $k$-го повторения,\n",
    "- $\\mu$ — общее среднее,\n",
    "- $\\alpha_i$ — эффект $i$-го уровня фактора $A$,\n",
    "- $\\beta_j$ — эффект $j$-го уровня фактора $B$,\n",
    "- $(\\alpha \\beta)_{ij}$ — эффект взаимодействия факторов $A$ и $B$,\n",
    "- $\\epsilon_{ijk} \\sim N(0, \\sigma^2)$ — случайная ошибка.\n",
    "\n",
    "### 2. Построение МНК-оценок параметров"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "31f5b8b6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Оценки параметров полной модели:\n",
      "Intercept              11.998333\n",
      "C(A)[T.2]               2.440000\n",
      "C(B)[T.2]              -2.586667\n",
      "C(B)[T.3]               4.146667\n",
      "C(B)[T.4]              -0.345000\n",
      "C(A)[T.2]:C(B)[T.2]    10.131667\n",
      "C(A)[T.2]:C(B)[T.3]     1.561667\n",
      "C(A)[T.2]:C(B)[T.4]     3.795000\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "from statsmodels.formula.api import ols\n",
    "\n",
    "# Формируем модель с взаимодействием\n",
    "model_full = ols('Y ~ C(A) + C(B) + C(A):C(B)', data=df).fit()\n",
    "\n",
    "# МНК-оценки параметров\n",
    "params = model_full.params\n",
    "print(\"Оценки параметров полной модели:\")\n",
    "print(params)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f22e1f79",
   "metadata": {},
   "source": [
    "### 3. Несмещенная оценка дисперсии\n",
    "Несмещенная оценка дисперсии ошибок:\n",
    "$$\n",
    "\\hat{\\sigma}^2 = \\frac{SS_{\\text{res}}}{df_{\\text{res}}},\n",
    "$$\n",
    "где:\n",
    "- $SS_{\\text{res}}$ — сумма квадратов остатков,\n",
    "- $df_{\\text{res}} = n - p$ — степени свободы ($n$ — число наблюдений, $p$ — число параметров)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7594c82a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Несмещенная оценка дисперсии: 0.757\n"
     ]
    }
   ],
   "source": [
    "# Несмещенная оценка дисперсии\n",
    "sigma2 = model_full.mse_resid\n",
    "print(f\"Несмещенная оценка дисперсии: {sigma2:.3f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08b41deb",
   "metadata": {},
   "source": [
    "## Пункт b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "db397206",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Сводная таблица средних значений Y:\n",
      "B          1          2          3          4\n",
      "A                                            \n",
      "1  11.998333   9.411667  16.145000  11.653333\n",
      "2  14.438333  21.983333  20.146667  17.888333\n"
     ]
    }
   ],
   "source": [
    "# Группируем данные по комбинациям A и B, вычисляем средние Y\n",
    "grouped = df.groupby(['A', 'B'])['Y'].mean().reset_index()\n",
    "\n",
    "# Создаём сводную таблицу для визуализации\n",
    "pivot_table = grouped.pivot(index='A', columns='B', values='Y')\n",
    "print(\"Сводная таблица средних значений Y:\")\n",
    "print(pivot_table)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ca70b1e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "\n",
    "# Уровни фактора B\n",
    "B_levels = df['B'].unique()\n",
    "\n",
    "# Цвета для каждого уровня B\n",
    "colors = ['blue', 'green', 'red', 'purple']\n",
    "\n",
    "for b, color in zip(B_levels, colors):\n",
    "    # Фильтруем данные для текущего уровня B\n",
    "    subset = grouped[grouped['B'] == b]\n",
    "    plt.plot(subset['A'], subset['Y'], \n",
    "             marker='o', \n",
    "             linestyle='-', \n",
    "             color=color, \n",
    "             label=f'B={b}')\n",
    "\n",
    "plt.xlabel('A')\n",
    "plt.ylabel('Y')\n",
    "plt.title('Зависимость Y от A при фиксированных уровнях B')\n",
    "plt.legend(title='Уровень B')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d69862e",
   "metadata": {},
   "source": [
    "### Визуальная проверка аддитивности:\n",
    "\n",
    "- **Пересечение линий:** График зависимости $Y$ от $A$ при фиксированных $B$ показывает, что линии для разных уровней $B$ пересекаются, особенно при $B=4$. Это указывает на **наличие взаимодействия** между факторами.\n",
    "- **Следствия:** Взаимодействие факторов может означать, что влияние одного фактора на зависимую переменную $Y$ зависит от другого фактора.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2acc6fe6",
   "metadata": {},
   "source": [
    "## Пункт c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "382c3054",
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.formula.api import ols\n",
    "\n",
    "# Аддитивная модель\n",
    "model_additive = ols('Y ~ C(A) + C(B)', data=df).fit()\n",
    "\n",
    "# Остатки модели\n",
    "residuals = model_additive.resid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "c77e2e2e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Определение границ бинов\n",
    "min_res = np.floor(residuals.min() / h) * h\n",
    "max_res = np.ceil(residuals.max() / h) * h\n",
    "bin_edges = np.arange(min_res, max_res + h, h)\n",
    "\n",
    "# Гистограмма\n",
    "plt.figure(figsize=(12, 4))\n",
    "plt.hist(residuals, bins=bin_edges, density=True, color='blue', edgecolor='black')\n",
    "plt.xlabel('Остатки')\n",
    "plt.ylabel('Плотность')\n",
    "plt.title('Гистограмма остатков (h = 0.82)')\n",
    "plt.grid(True)\n",
    "\n",
    "# Наложение нормального распределения\n",
    "mu = 0  # Остатки центрированы вокруг 0\n",
    "sigma = np.std(residuals)\n",
    "x = np.linspace(mu - 3*sigma, mu + 3*sigma, 100)\n",
    "plt.plot(x, 1/(sigma * np.sqrt(2 * np.pi)) * np.exp(-(x - mu)**2 / (2 * sigma**2)), \n",
    "         color='red', linewidth=2, label='N(0, σ²)')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "78ffd74b",
   "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": "code",
   "execution_count": 10,
   "id": "87f134c2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Тест Шапиро-Уилка: p-value = 0.949\n",
      "Не отвергаем H₀: остатки нормальны.\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import shapiro\n",
    "\n",
    "stat, p_value = shapiro(residuals)\n",
    "print(f\"Тест Шапиро-Уилка: p-value = {p_value:.3f}\")\n",
    "if p_value < 0.02:\n",
    "    print(\"Отвергаем H₀: остатки не нормальны.\")\n",
    "else:\n",
    "    print(\"Не отвергаем H₀: остатки нормальны.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d4cf712",
   "metadata": {},
   "source": [
    "### Результаты\n",
    "- **Гистограмма:** Распределение остатков близко к нормальному, совпадает с наложенной кривой $N(0, \\sigma^2)$.\n",
    "- **Q-Q график:** Точки лежат вдоль линии $y=x$, что подтверждает нормальность.\n",
    "- **Тест Шапиро-Уилка:** гипотеза о нормальности не отвергается."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0ccccb4",
   "metadata": {},
   "source": [
    "## Пункт d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a3830347",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Таблица ANOVA для полной модели:\n",
      "             df      sum_sq     mean_sq           F        PR(>F)\n",
      "C(A)        1.0  478.108752  478.108752  631.694471  4.061068e-26\n",
      "C(B)        3.0  153.241356   51.080452   67.489330  1.051893e-15\n",
      "C(A):C(B)   3.0  178.558140   59.519380   78.639144  8.022881e-17\n",
      "Residual   40.0   30.274683    0.756867         NaN           NaN\n",
      "\n",
      "Отсортированная таблица дисперсионного анализа:\n",
      "             df      sum_sq     mean_sq           F        PR(>F)\n",
      "C(A)        1.0  478.108752  478.108752  631.694471  4.061068e-26\n",
      "C(A):C(B)   3.0  178.558140   59.519380   78.639144  8.022881e-17\n",
      "C(B)        3.0  153.241356   51.080452   67.489330  1.051893e-15\n",
      "Residual   40.0   30.274683    0.756867         NaN           NaN\n"
     ]
    }
   ],
   "source": [
    "from statsmodels.stats.anova import anova_lm\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "from statsmodels.formula.api import ols\n",
    "\n",
    "# Предположим, df - ваш DataFrame с колонками 'Y', 'A', 'B'\n",
    "# где A и B - категориальные факторы\n",
    "\n",
    "# 1. Построение моделей\n",
    "model_full = ols('Y ~ C(A) + C(B) + C(A):C(B)', data=df).fit()\n",
    "model_additive = ols('Y ~ C(A) + C(B)', data=df).fit()\n",
    "model_onlyA = ols('Y ~ C(A)', data=df).fit()\n",
    "model_onlyB = ols('Y ~ C(B)', data=df).fit()\n",
    "model_const = ols('Y ~ 1', data=df).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "4d18ccf9",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\margaery\\AppData\\Local\\Temp\\ipykernel_18780\\711296804.py:36: FutureWarning: The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.\n",
      "  return pd.concat([df, pd.DataFrame([row])], ignore_index=True)\n",
      "C:\\Users\\margaery\\AppData\\Local\\Temp\\ipykernel_18780\\711296804.py:57: FutureWarning: The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.\n",
      "  AOV = pd.concat([AOV, pd.DataFrame([error_row])], ignore_index=True)\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>H</th>\n",
       "      <th>RSS</th>\n",
       "      <th>Df</th>\n",
       "      <th>MRSS</th>\n",
       "      <th>F</th>\n",
       "      <th>x_alpha</th>\n",
       "      <th>Pr(&gt;F)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>H_(12)</td>\n",
       "      <td>208.832823</td>\n",
       "      <td>3.0</td>\n",
       "      <td>69.610941</td>\n",
       "      <td>78.639144</td>\n",
       "      <td>3.667421</td>\n",
       "      <td>8.022881e-17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>H_(1)</td>\n",
       "      <td>362.074179</td>\n",
       "      <td>6.0</td>\n",
       "      <td>60.345697</td>\n",
       "      <td>73.064237</td>\n",
       "      <td>2.876587</td>\n",
       "      <td>5.459874e-20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>H_(2)</td>\n",
       "      <td>686.941575</td>\n",
       "      <td>4.0</td>\n",
       "      <td>171.735394</td>\n",
       "      <td>216.902976</td>\n",
       "      <td>3.295372</td>\n",
       "      <td>1.537422e-26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>H_(0)</td>\n",
       "      <td>840.182931</td>\n",
       "      <td>7.0</td>\n",
       "      <td>120.026133</td>\n",
       "      <td>152.868556</td>\n",
       "      <td>2.744837</td>\n",
       "      <td>8.275092e-27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Err</td>\n",
       "      <td>30.274683</td>\n",
       "      <td>40.0</td>\n",
       "      <td>0.756867</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        H         RSS    Df        MRSS           F   x_alpha        Pr(>F)\n",
       "0  H_(12)  208.832823   3.0   69.610941   78.639144  3.667421  8.022881e-17\n",
       "1   H_(1)  362.074179   6.0   60.345697   73.064237  2.876587  5.459874e-20\n",
       "2   H_(2)  686.941575   4.0  171.735394  216.902976  3.295372  1.537422e-26\n",
       "3   H_(0)  840.182931   7.0  120.026133  152.868556  2.744837  8.275092e-27\n",
       "4     Err   30.274683  40.0    0.756867         NaN       NaN          None"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "from scipy.stats import f\n",
    "\n",
    "# Функция для сравнения моделей и извлечения нужных данных\n",
    "def compare_models(reduced_model, full_model):\n",
    "    anova_result = sm.stats.anova_lm(reduced_model, full_model)\n",
    "    return {\n",
    "        'df_diff': anova_result['df_diff'].iloc[1],  # Разница степеней свободы\n",
    "        'ss_diff': anova_result['ss_diff'].iloc[1],  # Разница в RSS\n",
    "        'rss_reduced': reduced_model.ssr,  # RSS редуцированной модели\n",
    "        'rss_full': full_model.ssr,       # RSS полной модели\n",
    "        'F': anova_result['F'].iloc[1],   # F-статистика\n",
    "        'p_value': anova_result['Pr(>F)'].iloc[1]  # P-значение\n",
    "    }\n",
    "\n",
    "# Сравнение моделей\n",
    "anova_additive = compare_models(model_additive, model_full)\n",
    "anova_A = compare_models(model_onlyA, model_full)\n",
    "anova_B = compare_models(model_onlyB, model_full)\n",
    "anova_null = compare_models(model_const, model_full)\n",
    "\n",
    "# Создание DataFrame для результатов\n",
    "columns = ['H', 'RSS', 'Df', 'Sum of Sq', 'F', 'x_alpha', 'Pr(>F)']\n",
    "AOV = pd.DataFrame(columns=columns)\n",
    "\n",
    "# Функция для добавления строк в AOV\n",
    "def add_aov_row(df, name, anova_result, rdf, alpha):\n",
    "    row = {\n",
    "        'H': name,\n",
    "        'RSS': anova_result['rss_reduced'],  # Теперь берём RSS редуцированной модели\n",
    "        'Df': anova_result['df_diff'],\n",
    "        'Sum of Sq': anova_result['ss_diff'],\n",
    "        'F': anova_result['F'],\n",
    "        'x_alpha': f.ppf(1 - alpha, anova_result['df_diff'], rdf),\n",
    "        'Pr(>F)': f\"{anova_result['p_value']:.7g}\", \n",
    "    }\n",
    "    return pd.concat([df, pd.DataFrame([row])], ignore_index=True)\n",
    "\n",
    "# Получение residual degrees of freedom из полной модели\n",
    "rdf = model_full.df_resid\n",
    "\n",
    "# Добавление строк в AOV\n",
    "AOV = add_aov_row(AOV, 'H_(12)', anova_additive, rdf, alpha)\n",
    "AOV = add_aov_row(AOV, 'H_(1)', anova_A, rdf, alpha)\n",
    "AOV = add_aov_row(AOV, 'H_(2)', anova_B, rdf, alpha)\n",
    "AOV = add_aov_row(AOV, 'H_(0)', anova_null, rdf, alpha)\n",
    "\n",
    "# Добавление строки ошибок (RSS полной модели)\n",
    "error_row = {\n",
    "    'H': 'Err',\n",
    "    'RSS': model_full.ssr,\n",
    "    'Df': rdf,\n",
    "    'Sum of Sq': None,\n",
    "    'F': None,\n",
    "    'x_alpha': None,\n",
    "    'Pr(>F)': None\n",
    "}\n",
    "AOV = pd.concat([AOV, pd.DataFrame([error_row])], ignore_index=True)\n",
    "\n",
    "# Вычисление MRSS (Mean Residual Sum of Squares)\n",
    "AOV['MRSS'] = AOV['RSS'] / AOV['Df']\n",
    "\n",
    "# Финальная обработка AOV (перестановка столбцов)\n",
    "AOV1 = AOV[['H', 'RSS', 'Df', 'MRSS', 'F', 'x_alpha', 'Pr(>F)']]\n",
    "\n",
    "# Вывод результатов\n",
    "AOV1\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9a05af7",
   "metadata": {},
   "source": [
    "### Результаты ANOVA\n",
    "Из таблицы ANOVA:\n",
    "- **Фактор A:**\n",
    "  $$\n",
    "  F = 631.69,\\ p\\text{-value} < 0.001 \\ \\rightarrow \\ \\text{значимо влияет на } Y.\n",
    "  $$\n",
    "  \n",
    "- **Фактор B:**\n",
    "  $$\n",
    "  F = 67.49,\\ p\\text{-value} < 0.001 \\ \\rightarrow \\ \\text{значимо влияет на } Y.\n",
    "  $$\n",
    "  \n",
    "- **Взаимодействие $A \\times B$:**\n",
    "  $$\n",
    "  F = 78.64,\\ p\\text{-value} < 0.001 \\ \\rightarrow \\ \\text{значимо влияет на } Y.\n",
    "  $$\n",
    "\n",
    "- **Вывод:**\n",
    "  На уровне значимости $\\alpha=0.02$ все факторы (A, B) и их взаимодействие **значимо**. Это означает, что влияние фактора A на Y зависит от уровня фактора B, и наоборот."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0121b2ed",
   "metadata": {},
   "source": [
    "## Пункт e)\n",
    "Для выбора оптимальной модели используются критерии:\n",
    "- AIC оценивает баланс между качеством подгонки модели и её сложностью, накладывая штраф за избыточное количество параметров.\n",
    "- BIC работает аналогично AIC, но применяет более строгий штраф за сложность, особенно при больших объемах данных.\n",
    "\n",
    "Сравниваем модели:\n",
    "1. **Полная модель** (с взаимодействием): \n",
    "   $$\n",
    "   Y \\sim A + B + AB.\n",
    "   $$\n",
    "2. **Аддитивная модель** (без взаимодействия):\n",
    "   $$\n",
    "   Y \\sim A + B.\n",
    "   $$\n",
    "3. **Только А**:\n",
    "   $$\n",
    "   Y \\sim A\n",
    "   $$\n",
    "4. **Только В**:\n",
    "   $$\n",
    "   Y \\sim B\n",
    "   $$\n",
    "5. **Константная**:\n",
    "   $$\n",
    "   Y \\sim 1\n",
    "   $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "2db6d2ce",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Сравнение моделей по AIC и BIC:\n",
      "        Модель         AIC         BIC\n",
      "0       Полная  130.095418  145.065027\n",
      "1   Аддитивная  216.794085  226.150090\n",
      "2     Только A  237.209208  240.951610\n",
      "3     Только B  271.948414  279.433218\n",
      "4  Константная  275.614194  277.485395\n"
     ]
    }
   ],
   "source": [
    "\n",
    "# 3. Таблица AIC/BIC для всех моделей (как во втором изображении)\n",
    "models = {\n",
    "    'Полная': model_full,\n",
    "    'Аддитивная': model_additive,\n",
    "    'Только A': model_onlyA,\n",
    "    'Только B': model_onlyB,\n",
    "    'Константная': model_const\n",
    "}\n",
    "\n",
    "results = []\n",
    "for name, model in models.items():\n",
    "    results.append({\n",
    "        'Модель': name,\n",
    "        'AIC': model.aic,\n",
    "        'BIC': model.bic\n",
    "    })\n",
    "\n",
    "aic_bic_table = pd.DataFrame(results)\n",
    "print(\"\\nСравнение моделей по AIC и BIC:\")\n",
    "print(aic_bic_table)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2747e9f7",
   "metadata": {},
   "source": [
    "### Вывод о сравнении моделей\n",
    "\n",
    "- **Результаты AIC и BIC:**\n",
    "  - **AIC:** Минимален у полной модели (не меньше чем на 86.7 меньше, чем у остальных).\n",
    "  - **BIC:** Минимален у полной модели (не меньше чем на 81.08 меньше, чем у остальных).\n",
    "\n",
    "- **Заключение:**\n",
    "  - Полная модель **предпочтительнее**, так как она лучше соответствует данным, что подтверждается меньшими значениями AIC и BIC."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2135d306",
   "metadata": {},
   "source": []
  }
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