From 9f9fdc4c6e75c0770ddfb232eaa6d973fe060da9 Mon Sep 17 00:00:00 2001 From: Ogarkov Ilya Date: Fri, 24 Oct 2025 11:36:12 +0300 Subject: [PATCH] =?UTF-8?q?=D0=BF=D0=BE=D1=87=D1=82=D0=B8=20=D0=B4=D0=BE?= =?UTF-8?q?=D0=B4=D0=B5=D0=BB=D0=B0=D0=BD=D0=BD=D1=8B=D0=B9=20=D0=BE=D1=82?= =?UTF-8?q?=D1=87=D1=91=D1=82=20=D0=BA=D1=80=D0=BE=D0=BC=D0=B5=208-=D0=BE?= =?UTF-8?q?=D0=B3=D0=BE=20=D0=BF=D1=83=D0=BD=D0=BA=D1=82=D0=B0,=20=D0=B8?= =?UTF-8?q?=D0=B7=D0=BC=D0=B5=D0=BD=D0=B5=D0=BD=D1=91=D0=BD=20task3=5FHW.p?= =?UTF-8?q?y?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../task3_HW.py | 255 +++++++++++++++--- ИАД/lr1/~$чёт1лр.docx | Bin 0 -> 162 bytes ...$чёт1лр_переделанный.docx | Bin 0 -> 162 bytes ...чёт1лр_переделанный.docx | Bin 0 -> 800527 bytes 4 files changed, 216 insertions(+), 39 deletions(-) create mode 100644 ИАД/lr1/~$чёт1лр.docx create mode 100644 ИАД/lr1/~$чёт1лр_переделанный.docx create mode 100644 ИАД/lr1/Отчёт1лр_переделанный.docx diff --git a/ИАД/lr1/python-files переделаные/task3_HW.py b/ИАД/lr1/python-files переделаные/task3_HW.py index 4a96fc0..b150fa8 100644 --- a/ИАД/lr1/python-files переделаные/task3_HW.py +++ b/ИАД/lr1/python-files переделаные/task3_HW.py @@ -14,53 +14,230 @@ df = pd.read_csv('SOCR_Data_MLB_HeightsWeights.txt', sep='\t', nrows=115, usecol # Кодируем категориальный признак "Position" df['Position_num'] = pd.factorize(df['Position'])[0] -# === Множественная регрессия (Weight = f(Position, Height, Age)) === -X = df[['Position_num', 'Height(inches)', 'Age']] -y = df['Weight(pounds)'] - -model = LinearRegression().fit(X, y) -y_pred = model.predict(X) - -# === Остатки === -res2 = y - y_pred - -# === Проверка нормальности остатков === -print('=== Проверка нормальности остатков ===') -shapiro_stat, shapiro_p = stats.shapiro(res2) -print(f"Статистика Шапиро–Уилка: {shapiro_stat:.4f}, p-value = {shapiro_p:.4f}") -if shapiro_p > 0.05: - print("→ Остатки распределены нормально (нет оснований отвергнуть H₀).") +print("=" * 60) +print("ПАРНАЯ РЕГРЕССИЯ: Weight = f(Height)") +print("=" * 60) + +# === ПАРНАЯ РЕГРЕССИЯ (Weight = f(Height)) === +X_simple = df[['Height(inches)']] +y_simple = df['Weight(pounds)'] + +model_simple = LinearRegression().fit(X_simple, y_simple) +y_pred_simple = model_simple.predict(X_simple) + +# Параметры модели +r_squared_simple = model_simple.score(X_simple, y_simple) +n_simple = len(y_simple) +adj_r_squared_simple = 1 - (1 - r_squared_simple) * (n_simple - 1) / (n_simple - 2) +std_error_simple = np.std(y_simple - y_pred_simple) +multiple_r_simple = np.sqrt(r_squared_simple) + +print('ПАРАМЕТРЫ ПАРНОЙ РЕГРЕССИИ:') +print(f'Коэффициент детерминации R²: {r_squared_simple:.4f}') +print(f'Скорректированный R²: {adj_r_squared_simple:.4f}') +print(f'Множественный коэффициент корреляции R: {multiple_r_simple:.4f}') +print(f'Стандартная ошибка регрессии: {std_error_simple:.4f}') +print(f'Коэффициенты модели (b0 + b1*x): {model_simple.intercept_:.4f} [{model_simple.coef_[0]:.4f}]') + +# === Остатки парной регрессии === +residuals_simple = y_simple - y_pred_simple + +# === ПРОВЕРКА НОРМАЛЬНОСТИ ОСТАТКОВ (Парная регрессия) === +print('\nПРОВЕРКА НОРМАЛЬНОСТИ ОСТАТКОВ (Парная регрессия):') + +# Тест Шапиро-Уилка +shapiro_stat_simple, shapiro_p_simple = stats.shapiro(residuals_simple) +print(f'Тест Шапиро-Уилка:') +print(f'Статистика: {shapiro_stat_simple:.4f}, p-value = {shapiro_p_simple:.4f}') +if shapiro_p_simple > 0.05: + print('→ Остатки распределены нормально (H₀ не отвергается)') +else: + print('→ Остатки не распределены нормально (H₀ отвергается)') + +# Тест Колмогорова-Смирнова +ks_stat_simple, ks_p_simple = stats.kstest(residuals_simple, 'norm', args=(np.mean(residuals_simple), np.std(residuals_simple))) +print(f'\nТест Колмогорова-Смирнова:') +print(f'Статистика: {ks_stat_simple:.4f}, p-value = {ks_p_simple:.4f}') +if ks_p_simple > 0.05: + print('→ Остатки распределены нормально (H₀ не отвергается)') +else: + print('→ Остатки не распределены нормально (H₀ отвергается)') + +# === СТАТИСТИКА ДУРБИНА-УОТСОНА (Парная регрессия) === +dw_stat_simple = durbin_watson(residuals_simple) +print(f'\nСтатистика Дурбина–Уотсона: {dw_stat_simple:.4f}') + +if dw_stat_simple < 1.5: + print('→ Наблюдается ПОЛОЖИТЕЛЬНАЯ автокорреляция остатков') +elif dw_stat_simple > 2.5: + print('→ Наблюдается ОТРИЦАТЕЛЬНАЯ автокорреляция остатков') +else: + print('→ Автокорреляция остатков ОТСУТСТВУЕТ (остатки независимы)') + +# === ГРАФИКИ ДЛЯ ПАРНОЙ РЕГРЕССИИ === +fig1, axes1 = plt.subplots(2, 2, figsize=(15, 12)) +fig1.suptitle('АНАЛИЗ ОСТАТКОВ: ПАРНАЯ РЕГРЕССИЯ (Weight = f(Height))', fontsize=16) + +# 1. Гистограмма +axes1[0, 0].hist(residuals_simple, bins=15, density=True, alpha=0.7, color='lightblue', edgecolor='black') +xmin, xmax = axes1[0, 0].get_xlim() +x = np.linspace(xmin, xmax, 100) +p = stats.norm.pdf(x, np.mean(residuals_simple), np.std(residuals_simple)) +axes1[0, 0].plot(x, p, 'k', linewidth=2, label='Нормальное распределение') +axes1[0, 0].set_title('Гистограмма остатков') +axes1[0, 0].set_xlabel('Остатки') +axes1[0, 0].set_ylabel('Плотность') +axes1[0, 0].legend() +axes1[0, 0].grid(True, alpha=0.3) + +# 2. QQ-plot +sm.qqplot(residuals_simple, line='s', ax=axes1[0, 1]) +axes1[0, 1].set_title('QQ-график остатков') +axes1[0, 1].grid(True, alpha=0.3) + +# 3. Остатки vs Предсказанные значения +axes1[1, 0].scatter(y_pred_simple, residuals_simple, alpha=0.7, color='blue') +axes1[1, 0].axhline(y=0, color='red', linestyle='--') +axes1[1, 0].set_xlabel('Предсказанные значения') +axes1[1, 0].set_ylabel('Остатки') +axes1[1, 0].set_title('Остатки vs Предсказанные значения') +axes1[1, 0].grid(True, alpha=0.3) + +# 4. Фактические vs Предсказанные значения +axes1[1, 1].scatter(y_simple, y_pred_simple, alpha=0.7, color='green') +min_val = min(y_simple.min(), y_pred_simple.min()) +max_val = max(y_simple.max(), y_pred_simple.max()) +axes1[1, 1].plot([min_val, max_val], [min_val, max_val], 'r--', label='Идеальная линия') +axes1[1, 1].set_xlabel('Фактические значения') +axes1[1, 1].set_ylabel('Предсказанные значения') +axes1[1, 1].set_title('Фактические vs Предсказанные значения') +axes1[1, 1].legend() +axes1[1, 1].grid(True, alpha=0.3) + +plt.tight_layout() +plt.show() + +print("\n" + "=" * 60) +print("МНОЖЕСТВЕННАЯ РЕГРЕССИЯ: Weight = f(Position, Height, Age)") +print("=" * 60) + +# === МНОЖЕСТВЕННАЯ РЕГРЕССИЯ (Weight = f(Position, Height, Age)) === +X_multi = df[['Position_num', 'Height(inches)', 'Age']] +y_multi = df['Weight(pounds)'] + +model_multi = LinearRegression().fit(X_multi, y_multi) +y_pred_multi = model_multi.predict(X_multi) + +# Параметры модели +r_squared_multi = model_multi.score(X_multi, y_multi) +n_multi = len(y_multi) +p_multi = X_multi.shape[1] +adj_r_squared_multi = 1 - (1 - r_squared_multi) * (n_multi - 1) / (n_multi - p_multi - 1) +std_error_multi = np.std(y_multi - y_pred_multi) +multiple_r_multi = np.sqrt(r_squared_multi) + +print('ПАРАМЕТРЫ МНОЖЕСТВЕННОЙ РЕГРЕССИИ:') +print(f'Коэффициент детерминации R²: {r_squared_multi:.4f}') +print(f'Скорректированный R²: {adj_r_squared_multi:.4f}') +print(f'Множественный коэффициент корреляции R: {multiple_r_multi:.4f}') +print(f'Стандартная ошибка регрессии: {std_error_multi:.4f}') +print(f'Коэффициенты модели: {model_multi.intercept_:.4f} {model_multi.coef_}') + +# === Остатки множественной регрессии === +residuals_multi = y_multi - y_pred_multi + +# === ПРОВЕРКА НОРМАЛЬНОСТИ ОСТАТКОВ (Множественная регрессия) === +print('\nПРОВЕРКА НОРМАЛЬНОСТИ ОСТАТКОВ (Множественная регрессия):') + +# Тест Шапиро-Уилка +shapiro_stat_multi, shapiro_p_multi = stats.shapiro(residuals_multi) +print(f'Тест Шапиро-Уилка:') +print(f'Статистика: {shapiro_stat_multi:.4f}, p-value = {shapiro_p_multi:.4f}') +if shapiro_p_multi > 0.05: + print('→ Остатки распределены нормально (H₀ не отвергается)') else: - print("→ Остатки не распределены нормально (отвергаем H₀).") + print('→ Остатки не распределены нормально (H₀ отвергается)') + +# Тест Колмогорова-Смирнова +ks_stat_multi, ks_p_multi = stats.kstest(residuals_multi, 'norm', args=(np.mean(residuals_multi), np.std(residuals_multi))) +print(f'\nТест Колмогорова-Смирнова:') +print(f'Статистика: {ks_stat_multi:.4f}, p-value = {ks_p_multi:.4f}') +if ks_p_multi > 0.05: + print('→ Остатки распределены нормально (H₀ не отвергается)') +else: + print('→ Остатки не распределены нормально (H₀ отвергается)') + +# === СТАТИСТИКА ДУРБИНА-УОТСОНА (Множественная регрессия) === +dw_stat_multi = durbin_watson(residuals_multi) +print(f'\nСтатистика Дурбина–Уотсона: {dw_stat_multi:.4f}') + +if dw_stat_multi < 1.5: + print('→ Наблюдается ПОЛОЖИТЕЛЬНАЯ автокорреляция остатков') +elif dw_stat_multi > 2.5: + print('→ Наблюдается ОТРИЦАТЕЛЬНАЯ автокорреляция остатков') +else: + print('→ Автокорреляция остатков ОТСУТСТВУЕТ (остатки независимы)') + +# === ГРАФИКИ ДЛЯ МНОЖЕСТВЕННОЙ РЕГРЕССИИ === +fig2, axes2 = plt.subplots(2, 2, figsize=(15, 12)) +fig2.suptitle('АНАЛИЗ ОСТАТКОВ: МНОЖЕСТВЕННАЯ РЕГРЕССИЯ (Weight = f(Position, Height, Age))', fontsize=16) + +# 1. Гистограмма +axes2[0, 0].hist(residuals_multi, bins=15, density=True, alpha=0.7, color='lightcoral', edgecolor='black') +xmin, xmax = axes2[0, 0].get_xlim() +x = np.linspace(xmin, xmax, 100) +p = stats.norm.pdf(x, np.mean(residuals_multi), np.std(residuals_multi)) +axes2[0, 0].plot(x, p, 'k', linewidth=2, label='Нормальное распределение') +axes2[0, 0].set_title('Гистограмма остатков') +axes2[0, 0].set_xlabel('Остатки') +axes2[0, 0].set_ylabel('Плотность') +axes2[0, 0].legend() +axes2[0, 0].grid(True, alpha=0.3) -# === Графики остатков === -plt.figure(figsize=(12, 5)) +# 2. QQ-plot +sm.qqplot(residuals_multi, line='s', ax=axes2[0, 1]) +axes2[0, 1].set_title('QQ-график остатков') +axes2[0, 1].grid(True, alpha=0.3) -# Гистограмма -plt.subplot(1, 2, 1) -sns.histplot(res2, bins=20, kde=True, color='lightblue', edgecolor='black') -plt.title('Гистограмма остатков') -plt.xlabel('Остатки') +# 3. Остатки vs Предсказанные значения +axes2[1, 0].scatter(y_pred_multi, residuals_multi, alpha=0.7, color='red') +axes2[1, 0].axhline(y=0, color='red', linestyle='--') +axes2[1, 0].set_xlabel('Предсказанные значения') +axes2[1, 0].set_ylabel('Остатки') +axes2[1, 0].set_title('Остатки vs Предсказанные значения') +axes2[1, 0].grid(True, alpha=0.3) -# QQ-график -plt.subplot(1, 2, 2) -sm.qqplot(res2, line='s', ax=plt.gca()) -plt.title('QQ-график остатков') +# 4. Фактические vs Предсказанные значения +axes2[1, 1].scatter(y_multi, y_pred_multi, alpha=0.7, color='orange') +min_val = min(y_multi.min(), y_pred_multi.min()) +max_val = max(y_multi.max(), y_pred_multi.max()) +axes2[1, 1].plot([min_val, max_val], [min_val, max_val], 'r--', label='Идеальная линия') +axes2[1, 1].set_xlabel('Фактические значения') +axes2[1, 1].set_ylabel('Предсказанные значения') +axes2[1, 1].set_title('Фактические vs Предсказанные значения') +axes2[1, 1].legend() +axes2[1, 1].grid(True, alpha=0.3) plt.tight_layout() plt.show() -# === Статистика Дурбина–Уотсона === -dw_stat = durbin_watson(res2) +# === СРАВНЕНИЕ МОДЕЛЕЙ === +print("\n" + "=" * 60) +print("СРАВНЕНИЕ МОДЕЛЕЙ") +print("=" * 60) -# Явный вывод для отчёта -print('\n=== Статистика Дурбина–Уотсона ===') -print(f"Значение статистики Дурбина–Уотсона: {dw_stat:.4f}") +print(f"{'Параметр':<30} {'Парная':<15} {'Множественная':<15}") +print(f"{'-'*60}") +print(f"{'R²':<30} {r_squared_simple:<15.4f} {r_squared_multi:<15.4f}") +print(f"{'Скорректированный R²':<30} {adj_r_squared_simple:<15.4f} {adj_r_squared_multi:<15.4f}") +print(f"{'Стандартная ошибка':<30} {std_error_simple:<15.4f} {std_error_multi:<15.4f}") +print(f"{'Shapiro-Wilk p-value':<30} {shapiro_p_simple:<15.4f} {shapiro_p_multi:<15.4f}") +print(f"{'Kolmogorov-Smirnov p-value':<30} {ks_p_simple:<15.4f} {ks_p_multi:<15.4f}") +print(f"{'Durbin-Watson':<30} {dw_stat_simple:<15.4f} {dw_stat_multi:<15.4f}") -# Интерпретация -if dw_stat < 1.5: - print("→ Наблюдается положительная автокорреляция остатков.") -elif dw_stat > 2.5: - print("→ Наблюдается отрицательная автокорреляция остатков.") +# Вывод о лучшей модели +print(f"\nВЫВОД:") +if adj_r_squared_multi > adj_r_squared_simple and std_error_multi < std_error_simple: + print("→ МНОЖЕСТВЕННАЯ РЕГРЕССИЯ показывает лучшие результаты") else: - print("→ Автокорреляция остатков отсутствует (остатки независимы).") + print("→ ПАРНАЯ РЕГРЕССИЯ показывает сравнимые или лучшие 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