lab3/lab3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "fb3598c2-a7fc-455e-b273-70513f53b3e0",
   "metadata": {},
   "source": [
    "# Лабораторная 3. Линейная регрессия"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46a11c9e-60fb-4604-9d42-8d10fe604d77",
   "metadata": {},
   "source": [
    "## Датасет\n",
    "\n",
    "#### Используемый датасет представляет собой синтетический набор данных об успеваемости учащихся. Каждая запись состоит из различных предикторов и индексов успеваемости."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "99c5a8f9-c472-4c57-9032-2f06c5083731",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "       Hours Studied  Previous Scores   Sleep Hours  \\\n",
      "count   10000.000000     10000.000000  10000.000000   \n",
      "mean        4.992900        69.445700      6.530600   \n",
      "std         2.589309        17.343152      1.695863   \n",
      "min         1.000000        40.000000      4.000000   \n",
      "25%         3.000000        54.000000      5.000000   \n",
      "50%         5.000000        69.000000      7.000000   \n",
      "75%         7.000000        85.000000      8.000000   \n",
      "max         9.000000        99.000000      9.000000   \n",
      "\n",
      "       Sample Question Papers Practiced  Performance Index  \n",
      "count                      10000.000000       10000.000000  \n",
      "mean                           4.583300          55.224800  \n",
      "std                            2.867348          19.212558  \n",
      "min                            0.000000          10.000000  \n",
      "25%                            2.000000          40.000000  \n",
      "50%                            5.000000          55.000000  \n",
      "75%                            7.000000          71.000000  \n",
      "max                            9.000000         100.000000  \n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "df = pd.read_csv('Student_Performance.csv')\n",
    "\n",
    "pd.set_option('display.max_columns', None)\n",
    "print(df.describe())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c864f8f-d732-4644-9216-6575e74ec9c5",
   "metadata": {},
   "source": [
    "#### Итак,\n",
    "\n",
    "- **Количество**: count = `10_000` элементов в датасете\n",
    "- **Среднее значение**:\n",
    "$$\n",
    "\\text{mean} = \\frac{1}{n} \\sum_{i=1}^{n} x_i\n",
    "$$\n",
    "\n",
    " mean =\n",
    "  - `4.993` часов в среднем студенты провели за учёбой (лодыри жесть)\n",
    "  - `69.446` - такую оценку в среднем студенты получили на тестах\n",
    "  - `6.53` часов в среднем студенты спали (оптимистично)\n",
    "  - `4.58` - работ студенты нарешали для практики\n",
    "  - `55.225` - средний перформанс студента на курсе (выше 50%, уже хорошо)\n",
    "\n",
    "- **Стандартное отклонение**:\n",
    "$$\n",
    "\\text{std} = \\sqrt{\\frac{1}{n} \\sum_{i=1}^{n} (x_i - \\bar{x})^2}\n",
    "$$\n",
    " std (standart deviation) =\n",
    "  - `2.589` часов - отклонение по времени, потраченному на учёбу.\n",
    "  - `17.34` - отклонение по результатам тестов. (жесть разброс, рандомычи)\n",
    "  - `1.696` часов - отклонение по количеству сна.\n",
    "  - `2.867` - отклонение по количеству решённых работ для практики.\n",
    "  - `19.213` - отклонение по перформансу студентов. (опять огромный разброс, значит у всех сильно разный перформанс, что очевидно, в целом)\n",
    "\n",
    "- **Минимум**:\n",
    "    - `1.0` часов - минимальное количество часов, которое студенты провели за учёбой. (он выбрал быть счастливым)\n",
    "    - `40.0` - минимальная оценка, которую получили студенты на тестах. (да ну, никто 0 не получал?)\n",
    "    - `4.0` часов - минимальное количество часов сна. (слабые, никто даже 0-1.5 диапазон не потестил)\n",
    "    - `0.0` - минимальное количество решённых работ для практики. (силён, надежда умирает последней)\n",
    "    - `10.0` - минимальный перформанс студента (сплоховал конечно).\n",
    "\n",
    "- **Максимум**:\n",
    "    - `9.0` часов - максимальное количество часов, которое студенты провели за учёбой.\n",
    "    - `99.0` - максимальная оценка, которую получили студенты на тестах.\n",
    "    - `9.0` часов - максимальное количество часов сна.\n",
    "    - `9.0` - максимальное количество решённых работ для практики.\n",
    "    - `100.0` - максимальный перформанс студента (отличный результат).\n",
    "\n",
    "- **25% квартиль (Q1)**:\n",
    "    - `3.0` часов - 25% студентов учились меньше или ровно 3 часа.\n",
    "    - `54.0` - 25% студентов получили оценку ниже или равную 54 на тестах.\n",
    "    - `5.0` часов - 25% студентов спали меньше или ровно 5 часов.\n",
    "    - `2.0` - 25% студентов решили меньше или ровно 2 работы.\n",
    "    - `40.0` - перформанс 25% студентов был ниже 40.\n",
    "\n",
    "- **50% квартиль (Медиана)**:\n",
    "    - `5.0` часов - 50% студентов учились меньше или ровно 5 часов.\n",
    "    - `69.0` - 50% студентов получили оценку ниже или равную 69.\n",
    "    - `7.0` часов - 50% студентов спали меньше или ровно 7 часов.\n",
    "    - `5.0` - 50% студентов решили меньше или ровно 5 работ.\n",
    "    - `55.0` - медианный перформанс студентов (середина группы).\n",
    "\n",
    "- **75% квартиль (Q3)**:\n",
    "    - `7.0` часов - 75% студентов учились меньше или ровно 7 часов.\n",
    "    - `85.0` - 75% студентов получили оценку ниже или равную 85.\n",
    "    - `8.0` часов - 75% студентов спали меньше или ровно 8 часов.\n",
    "    - `7.0` - 75% студентов решили меньше или ровно 7 работ.\n",
    "    - `71.0` - перформанс 75% студентов был ниже 71.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c388971-5013-498d-8d7b-295ebb575ae2",
   "metadata": {},
   "source": [
    "### Визуализация датасета"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "07ac4b6e-3a8c-4a24-9b55-0107dafe6e6f",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1000x800 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "df.hist(figsize=(10,8))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb9cc17b-9fe3-447b-bef1-5414685cb4ad",
   "metadata": {},
   "source": [
    "## Предварительная обработка данных\n",
    "### Обработка отсутствующих значений"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "afab8afd-2c9c-4e11-aa13-73e4553da415",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hours Studied                       0\n",
      "Previous Scores                     0\n",
      "Extracurricular Activities          0\n",
      "Sleep Hours                         0\n",
      "Sample Question Papers Practiced    0\n",
      "Performance Index                   0\n",
      "dtype: int64\n"
     ]
    }
   ],
   "source": [
    "# Проверка датасета на наличие пропусков\n",
    "print(df.isnull().sum())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62bb7e02-c44c-4d26-a5f5-14036d886515",
   "metadata": {},
   "source": [
    "Получается, что датасет `полностью заполнен`, не нужно никак заполнять пропуски, ибо их просто нет.  \n",
    "\n",
    "(А как можно было бы? Imputation ->   \n",
    "средним значением, медианой(для числ. данных),   \n",
    "часто встречающимся значением (для кат. данных))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6226fd08-fb5c-40a0-99e8-c27078ca01e4",
   "metadata": {},
   "source": [
    "### Кодирование категориальных признаков\n",
    "\n",
    "Что за **категориальные** признаки? Это такие признаки, представляющие *группы* или *категории*, а не количественные измерения чего-то. Их нельзя количественно сравнить, как например количество сна, чей-то рост и т.д.\n",
    "\n",
    "В моём датасете категориальный признак один, и им является `Extracurricular Activities`. Он делит всех студентов **на две категории** - Yes/No, т.е. учавствует ли студент во внеклассных активностях, или нет. Это не числовая характеристика, и её нужно как-то **закодировать** в числа, чтобы с ней могла работать модель МО.\n",
    "\n",
    "Я закодирую простым способом - `Label Encoding`. То бишь, просто заменю Yes на 1, и No на 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9df20229-89e1-4e57-9e2e-a2239da2dde7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Hours Studied  Previous Scores  Extracurricular Activities  Sleep Hours  \\\n",
      "0              7               99                           1            9   \n",
      "1              4               82                           0            4   \n",
      "2              8               51                           1            7   \n",
      "3              5               52                           1            5   \n",
      "4              7               75                           0            8   \n",
      "\n",
      "   Sample Question Papers Practiced  Performance Index  \n",
      "0                                 1               91.0  \n",
      "1                                 2               65.0  \n",
      "2                                 2               45.0  \n",
      "3                                 2               36.0  \n",
      "4                                 5               66.0  \n"
     ]
    }
   ],
   "source": [
    "df['Extracurricular Activities'] = df['Extracurricular Activities'].map({'Yes': 1, 'No': 0})\n",
    "print(df.head())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e32aca93-f582-450e-bdfc-7ee0fe6a603e",
   "metadata": {},
   "source": [
    "### Нормализация данных\n",
    "\n",
    "Это преобразование числ. данных к *единому масштабу*. Основной вопрос - зачем? Потому что некоторые алгоритмы МО чувствительны к масштабу признаков. Например, используемая в этой исследовательской работе - **линейная регрессия**.\n",
    "\n",
    "Простыми словами - если признак имеет значения в диапазоне 0-1000, а другой какой-то признак - в диапазоне 0-10, то модель может отдать непропорционально большие коэффициенты признаку с большим масштабом, игнорируя мелкие, но на самом деле возможно даже более влиятельные признаки."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc713eea-9d5e-4f7e-9e9e-db915c7a6e97",
   "metadata": {},
   "source": [
    "Теперь вопрос, а как нормализовать?\n",
    "\n",
    "Самый простой способ - **mix-max нормализация**: приводим все значения к диапазону от 0 до 1:\n",
    "$$\n",
    "x_{norm} = \\frac{x-x_{min}}{x_{max}-x_{min}}\n",
    "$$\n",
    "\n",
    "$x$ — исходное значение признака.  \n",
    "$x_{min}$ и $x_{max}$ — минимальные и максимальные значения признака соответственно."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b6938b3b-3558-4b94-999f-b3652a666b83",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Hours Studied  Previous Scores  Extracurricular Activities  Sleep Hours  \\\n",
      "0          0.750         1.000000                           1          1.0   \n",
      "1          0.375         0.711864                           0          0.0   \n",
      "2          0.875         0.186441                           1          0.6   \n",
      "3          0.500         0.203390                           1          0.2   \n",
      "4          0.750         0.593220                           0          0.8   \n",
      "\n",
      "   Sample Question Papers Practiced  Performance Index  \n",
      "0                          0.111111               91.0  \n",
      "1                          0.222222               65.0  \n",
      "2                          0.222222               45.0  \n",
      "3                          0.222222               36.0  \n",
      "4                          0.555556               66.0  \n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "def min_max_normalize(column):\n",
    "    return (column - np.min(column)) / (np.max(column) - np.min(column))\n",
    "\n",
    "columns_to_scale = ['Hours Studied', 'Previous Scores', 'Sleep Hours', 'Sample Question Papers Practiced']\n",
    "\n",
    "for col in columns_to_scale:\n",
    "    df[col] = min_max_normalize(df[col])\n",
    "\n",
    "print(df.head())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a23bca8d-bd11-44f6-a6d2-f69018acee45",
   "metadata": {},
   "source": [
    "## Разделение данных на обучающий и тестовый наборы"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "7d85be1b-694c-4b9e-b897-14d0685bfacd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Размер обучающей выборки: (8000, 5)\n",
      "Размер тестовой выборки: (2000, 5)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "# Разделим данные на признаки (X) и целевую переменную (y)\n",
    "X = df.drop('Performance Index', axis=1).values\n",
    "y = df['Performance Index'].values\n",
    "\n",
    "# Определим размер обучающей выборки (80% от общего количества данных)\n",
    "train_size = int(0.8 * len(X))\n",
    "\n",
    "# Перемешаем индексы для случайного разделения\n",
    "indices = np.random.permutation(len(X))\n",
    "\n",
    "# Разделим данные на обучающую и тестовую выборки\n",
    "train_indices = indices[:train_size]\n",
    "test_indices = indices[train_size:]\n",
    "\n",
    "X_train, X_test = X[train_indices], X[test_indices]\n",
    "y_train, y_test = y[train_indices], y[test_indices]\n",
    "\n",
    "# Проверим размеры полученных наборов\n",
    "print(f'Размер обучающей выборки: {X_train.shape}')\n",
    "print(f'Размер тестовой выборки: {X_test.shape}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f0455da7-d5f9-4dc3-9406-a8782f037dd8",
   "metadata": {},
   "source": [
    "### Небольшое пояснение\n",
    "\n",
    "Чё ваще мы делаем?  \n",
    "|> мы хотим предсказать по признакам X, какая будет целевая переменная Y  \n",
    "|> поэтому, мы делим столбцы на X и Y  \n",
    "\n",
    "Зачем делить выборку на *тестовую* и *обучающую*?  \n",
    "|> так работает МО:  \n",
    "|> обучающая выборка - данные, на которых обучается модель (анализ зависимостей между признаками (input) и целевой переменной (output), настройка своих коэффициентов)  \n",
    "|> тестовая выборка - данные, которые **не использовались** при обучении. Нужны чтоб проверить как модель будет предсказывать значения на новых данных.  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a153a5c-238a-4d8e-b8fc-b2d34b810994",
   "metadata": {},
   "source": [
    "## Реализация линейной регрессии с использованием метода наименьших квадратов\n",
    "\n",
    "### 1. Постановка задачи\n",
    "Цель — реализовать *линейную регрессию* для предсказания целевой переменной (в данном случае `Performance Index`) на основе других признаков. Буду находить оптимальные коэффициенты линейной модели с использованием **метода наименьших квадратов**.\n",
    "\n",
    "### 2. Линейная модель\n",
    "Регрессионная модель представляется в матричном виде следующим образом:\n",
    "\n",
    "$$\n",
    "y = X \\beta\n",
    "$$\n",
    "\n",
    "Где:\n",
    "- $y$ — целевая переменная (вектор).\n",
    "- $X$ — матрица признаков (с добавленным столбцом единиц для учета смещения).\n",
    "- $\\beta$ — вектор коэффициентов, который мы ищем.\n",
    "\n",
    "### 3. Метод наименьших квадратов\n",
    "Чтобы найти коэффициенты $\\beta$, мы минимизируем сумму квадратов разностей между фактическими значениями $y$ и предсказанными значениями $\\hat{y} = X \\beta$. Оптимальные коэффициенты $\\beta$ находятся по следующей формуле:\n",
    "\n",
    "$$\n",
    "\\beta = (X^T X)^{-1} X^T y\n",
    "$$\n",
    "\n",
    "Где:\n",
    "- $X^T$ — транспонированная матрица признаков.\n",
    "- $(X^T X)^{-1}$ — обратная матрица для произведения $X^T X$.\n",
    "- $y$ — вектор целевых значений.\n",
    "\n",
    "### 4. Шаги реализации\n",
    "1. Добавляем столбец единиц к признакам $X$, чтобы учесть смещение (intercept).\n",
    "2. Вычисляем оптимальные коэффициенты $\\beta$ с использованием метода наименьших квадратов.\n",
    "3. Предсказываем значения целевой переменной $y$ на основе найденных коэффициентов.\n",
    "4. Вычисляем и проверяем предсказания как для обучающих данных, так и для тестовых.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f32f9131-ac78-44b4-8022-5554151c9239",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Коэффициенты модели: [11.42608264 22.85065775 60.09127101  0.61927923  2.42993221  1.70869218]\n",
      "Пример предсказанных значений: [62.14152637 15.65775349 86.2932466  46.38294789 18.02304579]\n",
      "Пример предсказанных значений для теста: [37.12269914 57.91044131 62.77176486 56.87260507 82.4658461 ]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "# Добавляем столбец единиц к X для учёта коэффициента смещения (intercept)\n",
    "# c_ - concatenate, просто матрицы складываем\n",
    "# ones - просто массив единичек\n",
    "X_train_with_bias = np.c_[np.ones(X_train.shape[0]), X_train]\n",
    "\n",
    "# 1. Вычисляем коэффициенты бета с использованием метода наименьших квадратов\n",
    "# beta = (X^T X)^{-1} X^T y\n",
    "# .T - транспонирование матрицы\n",
    "# @ - матричное умножение\n",
    "beta = np.linalg.inv(X_train_with_bias.T @ X_train_with_bias) @ X_train_with_bias.T @ y_train\n",
    "\n",
    "# 2. Предсказание для тренировочного набора\n",
    "y_train_pred = X_train_with_bias @ beta\n",
    "\n",
    "# Проверим коэффициенты и предсказания\n",
    "print(\"Коэффициенты модели:\", beta)\n",
    "print(\"Пример предсказанных значений:\", y_train_pred[:5])\n",
    "\n",
    "# Теперь сделаем предсказания на тестовых данных\n",
    "X_test_with_bias = np.c_[np.ones(X_test.shape[0]), X_test]\n",
    "y_test_pred = X_test_with_bias @ beta\n",
    "\n",
    "# Проверим пример предсказаний на тестовых данных\n",
    "print(\"Пример предсказанных значений для теста:\", y_test_pred[:5])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ea53bad-9a51-42e8-958e-d427e9e2414b",
   "metadata": {},
   "source": [
    "Итак, мы нашли **коэффициенты регрессии**. Теперь у нас есть линейная функция, которая \"наилучшим\" образом описывает зависимость между предикторами x_i и зависимой переменной y."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cdcb81b9-4eb2-457e-866a-e427d4fdc28b",
   "metadata": {},
   "source": [
    "## Построение 3х моделей с различными наборами признаков"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c75ac77f-69ac-4f58-9792-f23865049025",
   "metadata": {},
   "source": [
    "Модель 2: Используем только один или два признака, например, Hours Studied и Sample Question Papers Practiced.    \n",
    "Модель 3: Используем только ключевые признаки, такие как Hours Studied, Previous Scores и Sleep Hours.   \n",
    "Модель 4: Используем все признаки для предсказания целевой переменной.   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "4052516e-8222-438d-a08c-3a1068380dcb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Коэффициенты для модели 4 (все признаки): [11.42608264 22.85065775 60.09127101  0.61927923  2.42993221  1.70869218]\n",
      "Коэффициенты для модели 3 (Hours Studied, Previous Scores, Sleep Hours): [12.58123885 22.87880535 60.13324606  2.39943048]\n",
      "Коэффициенты для модели 2 (Hours Studied, Sample Question Papers Practiced): [42.9323012  22.0423514   2.57312769]\n"
     ]
    }
   ],
   "source": [
    "def build_and_evaluate_model(X, y):\n",
    "    # смещение\n",
    "    X_with_bias = np.c_[np.ones(X.shape[0]), X]\n",
    "    \n",
    "    # коэф-ты\n",
    "    beta = np.linalg.inv(X_with_bias.T @ X_with_bias) @ X_with_bias.T @ y\n",
    "    \n",
    "    # предсказываем зависимую переменную\n",
    "    y_pred = X_with_bias @ beta\n",
    "    \n",
    "    # возвращаем коэф-ты и предсказания\n",
    "    return beta, y_pred\n",
    "\n",
    "# м4\n",
    "X_model_1 = X_train\n",
    "beta_1, y_train_pred_1 = build_and_evaluate_model(X_model_1, y_train)\n",
    "print(\"Коэффициенты для модели 4 (все признаки):\", beta_1)\n",
    "\n",
    "# м3\n",
    "X_model_2 = X_train[:, [0, 1, 3]]\n",
    "beta_2, y_train_pred_2 = build_and_evaluate_model(X_model_2, y_train)\n",
    "print(\"Коэффициенты для модели 3 (Hours Studied, Previous Scores, Sleep Hours):\", beta_2)\n",
    "\n",
    "# м2\n",
    "X_model_3 = X_train[:, [0, 4]]\n",
    "beta_3, y_train_pred_3 = build_and_evaluate_model(X_model_3, y_train)\n",
    "print(\"Коэффициенты для модели 2 (Hours Studied, Sample Question Papers Practiced):\", beta_3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85a20e6e-6a56-4ddb-8457-9a073d9bb974",
   "metadata": {},
   "source": [
    "## Оценка производительности"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89ed0596-1e37-4ecb-8f1c-c6d010d91deb",
   "metadata": {},
   "source": [
    "## Коэффициент детерминации \\( R^2 \\)\n",
    "\n",
    "Формула для расчета коэффициента детерминации:\n",
    "\n",
    "$$\n",
    "R^2 = 1 - \\frac{\\sum (y_{\\text{true}} - y_{\\text{pred}})^2}{\\sum (y_{\\text{true}} - \\bar{y})^2}\n",
    "$$\n",
    "\n",
    "Где:\n",
    "- $ y_{\\text{true}} $ — истинные значения целевой переменной.\n",
    "- $ y_{\\text{pred}} $ — предсказанные значения.\n",
    "- $ \\bar{y} $ — среднее значение целевой переменной.\n",
    "- $ \\sum (y_{\\text{true}} - y_{\\text{pred}})^2 $ — сумма квадратов остатков (SSR).\n",
    "- $ \\sum (y_{\\text{true}} - \\bar{y})^2 $ — общая сумма квадратов (SST)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "0148ceef-d3d7-461b-bb89-bd161811e50a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R^2 для модели 4 (все признаки): 0.9887812699685805\n",
      "R^2 для модели 3 (Hours Studied, Previous Scores, Sleep Hours): 0.9876978860537021\n",
      "R^2 для модели 2 (Hours Studied, Sample Question Papers Practiced): 0.14133014072632766\n"
     ]
    }
   ],
   "source": [
    "def r_squared(y_true, y_pred):\n",
    "    ss_res = np.sum((y_true - y_pred) ** 2)\n",
    "    ss_tot = np.sum((y_true - np.mean(y_true)) ** 2)\n",
    "    return 1 - (ss_res / ss_tot)\n",
    "\n",
    "# Модель 4\n",
    "X_model_4 = X_train\n",
    "beta_4, y_train_pred_4 = build_and_evaluate_model(X_model_4, y_train)\n",
    "r2_model_4 = r_squared(y_train, y_train_pred_4)\n",
    "print(\"R^2 для модели 4 (все признаки):\", r2_model_4)\n",
    "\n",
    "# Модель 3\n",
    "X_model_3 = X_train[:, [0, 1, 3]]  # Hours Studied, Previous Scores, Sleep Hours\n",
    "beta_3, y_train_pred_3 = build_and_evaluate_model(X_model_3, y_train)\n",
    "r2_model_3 = r_squared(y_train, y_train_pred_3)\n",
    "print(\"R^2 для модели 3 (Hours Studied, Previous Scores, Sleep Hours):\", r2_model_3)\n",
    "\n",
    "# Модель 2\n",
    "X_model_2 = X_train[:, [0, 4]]  # Hours Studied, Sample Question Papers Practiced\n",
    "beta_2, y_train_pred_2 = build_and_evaluate_model(X_model_2, y_train)\n",
    "r2_model_2 = r_squared(y_train, y_train_pred_2)\n",
    "print(\"R^2 для модели 2 (Hours Studied, Sample Question Papers Practiced):\", r2_model_2)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa20c1b1-3e19-40f5-92c4-067277d198ba",
   "metadata": {},
   "source": [
    "Производительность моделей, в порядке убывания, указана по аналогиями с автомобилями БМВ серии M:\n",
    "  - чем больше M, тем тяжелее и сложнее модель (тяжелее, дороже, сложнее машина)\n",
    "  - чем больше M, тем более точна модель (больше функций, мощнее двигатель, лучше тормоза и трансмиссия у автомобиля)\n",
    "  - идеальный баланс, как обычно - золотая середина (m3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6173bb9-1651-4412-acbc-67fece73962b",
   "metadata": {},
   "source": [
    "|m2|m3|m4|\n",
    "|-|-|-|\n",
    "|![m2](https://i.pinimg.com/736x/fb/bf/42/fbbf426c5427cfe7d46b9e8359bc40ba.jpg)|![m3cs](https://i.pinimg.com/564x/da/26/39/da263925cc98828ad390477779d4aabf.jpg)|![m4cs](https://i.pinimg.com/564x/61/ca/c0/61cac0b2e1e9d1aeb87c2d2c3fb217c2.jpg)|"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ec60e2a-030a-4501-b628-f4b33e8f5477",
   "metadata": {},
   "source": [
    "### Итоговый вывод и сравнение моделей\n",
    "\n",
    "#### Модель 4 (все признаки)\n",
    "- **\\( R^2 = 0.9887\\)** — наилучший результат, почти идеальная точность.\n",
    "- Важные признаки: Previous Scores (60.08), Hours Studied (22.81).\n",
    "- **Вывод**: Подходит для максимальной точности, если доступны все данные.\n",
    "\n",
    "#### Модель 3 (Hours Studied, Previous Scores, Sleep Hours)\n",
    "- **\\( R^2 = 0.9875\\)** — практически такая же точность, как у модели 4.\n",
    "- Важные признаки: Previous Scores (60.09), Hours Studied (22.83).\n",
    "- **Вывод**: Более экономная модель с высокой точностью. Использовать, если нужно меньше признаков.\n",
    "\n",
    "#### Модель 2 (Hours Studied, Sample Question Papers Practiced)\n",
    "- **\\( R^2 = 0.1412\\)** — очень низкая точность.\n",
    "- Важные признаки: Hours Studied (22.11), Sample Question Papers Practiced (1.83).\n",
    "- **Вывод**: Не рекомендуется, так как двух признаков недостаточно для точных предсказаний.\n",
    "\n",
    "### Рекомендации:\n",
    "- **Модель 4** — для максимальной точности.\n",
    "- **Модель 3** — для более простой модели с высокой точностью.\n",
    "- **Модель 2** — слишком упрощенная, с низкой точностью.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3594d684-f18f-4e58-b44c-14bf507114df",
   "metadata": {},
   "source": [
    "# Бонус: крутите барабан"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b49ed8c-a404-4ded-aa8d-8f6c562c4a3f",
   "metadata": {},
   "source": [
    "### Шаги для введения синтетического признака:\n",
    "Скрафтим синтетический признак, который отражает баланс между тем, насколько **мало** студент занимался и насколько **много** он спал. Назовём этот признак **\"Chose to Be Happy Index\"**.\n",
    "\n",
    "Примерная формула:\n",
    "\n",
    "$$\n",
    "\\text{CTBH} = \\frac{\\text{Sleep Hours}}{(\\text{Hours Studied} + 1) \\cdot (\\text{Sample Question Papers Practiced} + 1)}\n",
    "$$\n",
    "\n",
    "Этот индекс будет выше для студентов, которые уже поняли смысл жизни и преисполнились в своём сознании, больше времени проводят со своими родными, девушками/жёнами, трогают траву и т.д.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b8c37105-a485-4db0-a2ea-758519fd3b53",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9887814514612749"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['CTBH'] = df['Sleep Hours'] / ((df['Hours Studied'] + 1) * (df['Sample Question Papers Practiced'] + 1))\n",
    "\n",
    "# Обновим тренировочные данные с учетом нового признака\n",
    "X_train_with_happiness = np.c_[X_train, df['CTBH'].iloc[:X_train.shape[0]]]\n",
    "\n",
    "# Строим модель и оцениваем её с использованием нового синтетического признака\n",
    "beta_happiness, y_train_pred_happiness = build_and_evaluate_model(X_train_with_happiness, y_train)\n",
    "\n",
    "# Рассчитаем коэффициент детерминации R^2\n",
    "r2_happiness = r_squared(y_train, y_train_pred_happiness)\n",
    "r2_happiness"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9da097c7-9611-4276-9273-8fb6d6854a61",
   "metadata": {},
   "source": [
    "Что сказать, ну коэф. детерминации теперь лучше всех моделей m2-4.\n",
    "Получили следующий аппарат получается:\n",
    "\n",
    "|m5|\n",
    "|-|\n",
    "|![m5](https://i.pinimg.com/736x/8c/f2/fb/8cf2fb2bcdd4ffacfea727751f2a360f.jpg)|"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "789ba6f8-5f42-4dcb-bb53-353322fa3c22",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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