From 295c3ccb09421587b19f9795ba94a870006c86e7 Mon Sep 17 00:00:00 2001 From: Artem Date: Thu, 23 Oct 2025 18:48:44 +0300 Subject: [PATCH] =?UTF-8?q?23:10=20=D0=B4=D0=BE=D0=B1=D0=B0=D0=B2=D0=BB?= =?UTF-8?q?=D0=B5=D0=BD=D0=B0=20=D1=87=D0=B0=D1=81=D1=82=D1=8C=20=D0=9B?= =?UTF-8?q?=D0=A01?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- ИАД/lr1/task1_Fisher.py | 65 +++++++++++ ИАД/lr1/task1_HW.py | 73 ++++++++++++ ИАД/lr1/task2_Fisher.py | 102 +++++++++++++++++ ИАД/lr1/task2_HW.py | 95 ++++++++++++++++ ИАД/lr1/task3_Fisher.py | 105 ++++++++++++++++++ ИАД/lr1/task5_Fisher.py | 45 ++++++++ ...ит_знач_ДурбинВатсон.jpg | Bin 0 -> 198606 bytes 7 files changed, 485 insertions(+) create mode 100644 ИАД/lr1/task1_Fisher.py create mode 100644 ИАД/lr1/task1_HW.py create mode 100644 ИАД/lr1/task2_Fisher.py create mode 100644 ИАД/lr1/task2_HW.py create mode 100644 ИАД/lr1/task3_Fisher.py create mode 100644 ИАД/lr1/task5_Fisher.py create mode 100644 ИАД/lr1/Крит_знач_ДурбинВатсон.jpg diff --git a/ИАД/lr1/task1_Fisher.py b/ИАД/lr1/task1_Fisher.py new file mode 100644 index 0000000..317462b --- /dev/null +++ b/ИАД/lr1/task1_Fisher.py @@ -0,0 +1,65 @@ +import numpy as np +from sklearn.datasets import load_iris +import pandas as pd +import matplotlib.pyplot as plt +import seaborn as sb +import pingouin as pg +from scipy import stats + +# Датасет Ирисы Фишера +iris = load_iris() +#iris_pd=pd.DataFrame(data=np.c_[iris['data'], iris['target']], columns=iris['feature_names'] + ['target']) +iris_pd=pd.DataFrame(data=np.c_[iris['data']], columns=iris['feature_names']) + +# Формирование выборок по признакам +x1 = np.array(iris_pd['sepal length (cm)']) # первый признак - длина чашелистика +x2 = np.array(iris_pd['sepal width (cm)']) # второй признак - ширина чашелистика +x3 = np.array(iris_pd['petal length (cm)']) # третий признак - длина лепестка +x4 = np.array(iris_pd['petal width (cm)']) # четвертый признак - ширина лепестка + +# Проверка на нормальность по критерию К-С +print('Тест Колмогорова-Смирнова. Уровень значимости a = 0.05') + +for col in iris['feature_names']: + x = iris_pd[col] + x_mean, std = np.mean(x), np.std(x, ddof = 1) + x_std = (x - x_mean)/std + pvalue = stats.kstest(x_std, "norm", alternative='less').pvalue + if pvalue > 0.05: result = 'H0 не должна быть отвергнута' + else: result = 'H0 должна быть отвергнута' + print('Для {}: p-value: {}, так что {}'.format(col, pvalue, result)) + +# Построение диаграммы Тьюки +fig1, axes = plt.subplots(1, 3, figsize=(20, 4)) +axes[0].boxplot([x1,x2,x3,x4], tick_labels = ['Sepal Length', 'Sepal Width', 'Petal Length', 'Petal Width']) +axes[0].set_title('Диаграмма Тьюки') + + +# Построение тепловой карты парных коэффициентов корреляции +corrMatrix = iris_pd.corr() +axes[1].set_title('Тепловая карта парных коэфф. корреляции') +sb.heatmap(corrMatrix, annot=True, linewidths=0.5, xticklabels = False, yticklabels = False, ax = axes[1]) + + +# Построение тепловой карты частных коэффициентов корреляции +pCorrMatrix = iris_pd.pcorr() +axes[2].set_title('Тепловая карта частных коэфф. корреляции') +sb.heatmap(pCorrMatrix, annot=True, linewidths=0.5, xticklabels = False, yticklabels = False, ax = axes[2]) + + +# Построение гистограмм по выборкам +fig2, axes = plt.subplots(2, 2, figsize=(10, 7)) + +axes[0,0].hist(x1) +axes[0,0].set_title('Гисотграмма по значениям X1') + +axes[0,1].hist(x2) +axes[0,1].set_title('Гисотграмма по значениям X2') + +axes[1,0].hist(x3) +axes[1,0].set_title('Гисотграмма по значениям X3') + +axes[1,1].hist(x4) +axes[1,1].set_title('Гисотграмма по значениям X4') + +plt.show() \ No newline at end of file diff --git a/ИАД/lr1/task1_HW.py b/ИАД/lr1/task1_HW.py new file mode 100644 index 0000000..cd61f38 --- /dev/null +++ b/ИАД/lr1/task1_HW.py @@ -0,0 +1,73 @@ +import numpy as np +import pandas as pd +import matplotlib.pyplot as plt +import seaborn as sb +import pingouin as pg +from scipy import stats + +# Датасет "Рост-Вес-Возраст-Позиция" +columns = ['Position', 'Height(inches)', 'Weight(pounds)', 'Age'] + +df = pd.read_csv('SOCR_Data_MLB_HeightsWeights.txt', sep='\t', nrows = 115, usecols = columns) + +#replace_dict = {'Catcher':1, 'First_Baseman':2, 'Second_Baseman':3, 'Shortstop':4, 'Third_Baseman':5, +# 'Outfielder':6, 'Designated_Hitter':7, 'Starting_Pitcher':8, 'Relief_Pitcher':9} + +#pd.set_option('future.no_silent_downcasting', True) +#df['Position'] = df['Position'].replace(replace_dict) +#Index(['Name', 'Team', 'Position', 'Height(inches)', 'Weight(pounds)', 'Age'], dtype='object') + + + +# Построение диаграммы Тьюки +fig1, axes = plt.subplots(2, 2, zfigsize=(10, 10)) +fig1.suptitle('Диаграммы Тюки по признакам') + +axes[0,0].boxplot(df['Position'], tick_labels = ['Position']) +axes[0,1].boxplot(df['Height(inches)'], tick_labels = ['Height(inches)']) +axes[1,0].boxplot(df['Weight(pounds)'], tick_labels = ['Weight(pounds)']) +axes[1,1].boxplot(df['Age'], tick_labels = ['Age']) + +fig2, axes = plt.subplots(1, 2, figsize=(12, 5)) +fig2.suptitle('Тепловые карты') + +# Построение тепловой карты парных коэффициентов корреляции +corrMatrix = df.corr() +axes[0].set_title('Тепловая карта парных коэфф. корреляции') +sb.heatmap(corrMatrix, annot=True, linewidths=0.5, xticklabels = False, yticklabels = False, ax = axes[0]) + + +# Построение тепловой карты частных коэффициентов корреляции +pCorrMatrix = df.pcorr() +axes[1].set_title('Тепловая карта частных коэфф. корреляции') +sb.heatmap(pCorrMatrix, annot=True, linewidths=0.5, xticklabels = False, yticklabels = False, ax = axes[1]) + + + +print('Тест Колмогорова-Смирнова. Уровень значимости a = 0.05') + +for col in columns: + x = df[col] + x_mean, std = np.mean(x), np.std(x, ddof = 1) + x_std = (x - x_mean)/std + pvalue = stats.kstest(x_std, "norm", alternative='less').pvalue + if pvalue > 0.05: result = 'H0 не должна быть отвергнута' + else: result = 'H0 должна быть отвергнута' + print('Для {}: p-value: {}, так что {}'.format(col, pvalue, result)) + +# Построение гистограмм по выборкам +fig2, axes = plt.subplots(2, 2, figsize=(10, 7)) + +axes[0,0].hist(df['Position']) +axes[0,0].set_title('Гисотграмма по значениям Position') + +axes[0,1].hist(df['Height(inches)']) +axes[0,1].set_title('Гисотграмма по значениям Height(inches)') + +axes[1,0].hist(df['Weight(pounds)']) +axes[1,0].set_title('Гисотграмма по значениям Weight(pounds)') + +axes[1,1].hist(df['Age']) +axes[1,1].set_title('Гисотграмма по значениям Age') + +plt.show() \ No newline at end of file diff --git a/ИАД/lr1/task2_Fisher.py b/ИАД/lr1/task2_Fisher.py new file mode 100644 index 0000000..8b5770b --- /dev/null +++ b/ИАД/lr1/task2_Fisher.py @@ -0,0 +1,102 @@ +import numpy as np +from sklearn.datasets import load_iris +from sklearn.linear_model import LinearRegression +from sklearn.metrics import r2_score +import pandas as pd +import matplotlib.pyplot as plt +import seaborn as sb +import pingouin as pg +from scipy import stats + +# Датасет Ирисы Фишера +iris = load_iris() +iris_pd=pd.DataFrame(data=np.c_[iris['data'], iris['target']], columns=iris['feature_names'] + ['target']) + +# Формирование выборок по признакам +x1 = np.array(iris_pd['sepal length (cm)']) # первый признак - длина чашелистика +x2 = np.array(iris_pd['sepal width (cm)']) # второй признак - ширина чашелистика +x3 = np.array(iris_pd['petal length (cm)']) # третий признак - длина лепестка +x4 = np.array(iris_pd['petal width (cm)']) # четвертый признак - ширина лепестка + +# Пусть X4 - выходные переменные, а X3 - входные переменные, так как они коррелируют сильнее остальных комбинаций +fig, axes = plt.subplots(2, 2, figsize=(10, 10)) + +axes[0,0].scatter(x3, x4) +axes[0,0].set_title('Зависимость X4 от X3') + +axes[0,1].scatter(x3, x4) +axes[0,1].set_title('Предсказанные значения') + + + +# Парная регрессия +N = 150 +K = 2 +lr = LinearRegression().fit(x3.reshape(-1,1), x4) + +#line_x3 = np.linspace(min(x3), max(x3),150) +line_y1 = lr.predict(x3.reshape(-1,1)) +axes[0,0].plot(x3, line_y1, color='red', linewidth=2) + +line_x3_pred = np.linspace(min(x3), 2*max(x3), 150) +line_y1_pred = lr.predict(line_x3_pred.reshape(-1,1)) +axes[0,1].plot(line_x3_pred, line_y1_pred, color='red', linewidth=2) + +meanY = np.mean(x4) +Qreg = np.sum((line_y1 - meanY)**2) +Qtotal = np.sum((x4 - meanY)**2) +Qint = np.sum((x4 - line_y1)**2) +Sreg = (1/(K-1))*Qreg +Stotal = (1/(N-1))*Qtotal +Sint = (1/(N-K))*Qint + +print(np.dot(x4 - line_y1, line_y1)) + +print('Парная регрессия. Коэффициент детерминации: ', r2_score(x4,line_y1)) +print('Скорр. коэффициент детерминации: ', 1 - (1 - r2_score(x4,line_y1)*(149/147))) +print('Множ. коэффициент корреляции: ', np.sqrt(r2_score(x4,line_y1))) +print('Стандартная ошибка регрессии: ', np.sqrt(Qint/147)) + +# Множественная регрессия +N = 150 +K = 4 +X = np.vstack((x1, x2, x3)).T +mr = LinearRegression().fit(X, x4) + +line_x1 = np.linspace(min(x1), max(x1), 150) +line_x2 = np.linspace(min(x2), max(x2), 150) +line_x3 = np.linspace(min(x3), max(x3), 150) + +line_y2 = mr.coef_[0] * line_x1 + mr.coef_[1] * line_x2 + mr.coef_[2] * line_x3 + mr.intercept_ +axes[0,0].plot(line_x3, line_y2, color='green', linewidth=2) + +line_x1_pred = np.linspace(min(x1), 2*max(x1), 150) +line_x2_pred = np.linspace(min(x2), 2*max(x2), 150) +line_x3_pred = np.linspace(min(x3), 2*max(x3), 150) +line_y2_pred = mr.coef_[0] * line_x1_pred + mr.coef_[1] * line_x2_pred + mr.coef_[2] * line_x3_pred + mr.intercept_ +axes[0,1].plot(line_x3_pred, line_y2_pred, color='green', linewidth=2) + +Qreg = np.sum((line_y2 - meanY)**2) +Qint = np.sum((x4 - line_y2)**2) +Sreg = (1/(K-1))*Qreg +Stotal = (1/(N-1))*Qtotal +Sint = (1/(N-K))*Qint + +print('Множ. регресиия. Коэффициент детерминации: ', r2_score(x4,line_y2)) +print('Скорр. коэффициент детерминации: ', 1 - (1 - r2_score(x4,line_y2)*(149/147))) +print('Множ. коэффициент корреляции: ', np.sqrt(r2_score(x4,line_y2))) +print('Стандартная ошибка регрессии: ', np.sqrt(Qint/147)) + +# График остатков +residuals1 = x4 - line_y1 +residuals2 = x4 - line_y2 + +axes[1,0].scatter([i for i in range(1,151)], residuals1) +axes[1,0].set_title('Парная регрессия. График остатков') + +axes[1,1].scatter([i for i in range(1,151)], residuals2) +axes[1,1].set_title('Множ. регрессия. График остатков') + + +plt.show() + diff --git a/ИАД/lr1/task2_HW.py b/ИАД/lr1/task2_HW.py new file mode 100644 index 0000000..b211083 --- /dev/null +++ b/ИАД/lr1/task2_HW.py @@ -0,0 +1,95 @@ +import numpy as np +from sklearn.linear_model import LinearRegression +from sklearn.metrics import r2_score +import pandas as pd +import matplotlib.pyplot as plt +from scipy import stats +from mpl_toolkits.mplot3d import Axes3D + +# Датасет "Рост-Вес-Возраст-Позиция" +columns = ['Position', 'Height(inches)', 'Weight(pounds)', 'Age'] + +df = pd.read_csv('SOCR_Data_MLB_HeightsWeights.txt', sep='\t', nrows = 115, usecols = columns) + +# Пусть Weight(pounds) - выходные переменные, а Height(inches) - входные переменные, так как они коррелируют сильнее остальных комбинаций +fig1, axes = plt.subplots(1, 3, figsize=(15, 5)) +fig1.suptitle('Парная регрессия') + +axes[0].scatter(df['Height(inches)'], df['Weight(pounds)']) +axes[0].set_xlabel('Height(inches)') +axes[0].set_ylabel('Weight(pounds)') +axes[0].set_title('График регрессии') + + + + +# Парная регрессия +N = 115 +lr = LinearRegression().fit(df['Height(inches)'].values.reshape(-1, 1), df['Weight(pounds)']) + +#line_height = np.linspace(min(df['Height(inches)']), max(df['Height(inches)']),115) +line_weight1 = lr.predict(df['Height(inches)'].values.reshape(-1, 1)) +axes[0].plot(df['Height(inches)'], line_weight1, color='red', linewidth=2) + +Qreg = np.sum((line_weight1 - df['Weight(pounds)'].mean())**2) +Qres = np.sum((df['Weight(pounds)'] - line_weight1)**2) +Qtotal = np.sum((df['Weight(pounds)'] - df['Weight(pounds)'].mean())**2) + +res = df['Weight(pounds)'] - line_weight1 + +axes[1].scatter(line_weight1, res) +axes[1].axhline(y=0, color='red', linestyle='--') +axes[1].set_xlabel('Предсказанные значения') +axes[1].set_ylabel('Остаточные ошибки') +axes[1].set_title('Анализ остатков') + +axes[2].hist(res) +axes[2].set_xlabel('Остаточные ошибки') +axes[2].set_ylabel('Количество точек') +axes[2].set_title('Гистограмма остатков') + +#print(np.dot(df['Weight(pounds)'] - line_weight1,line_weight1)) + +#print(Qtotal, Qreg, Qres) +#print(Qreg/Qtotal, 1 - Qres/Qtotal) + +print('Парная регрессия. Коэффициент детерминации: ', r2_score(df['Weight(pounds)'],line_weight1)) +print('Скорр. коэффициент детерминации: ', 1 - (1 - r2_score(df['Weight(pounds)'],line_weight1)*(115/113))) +print('Множ. коэффициент корреляции: ', np.sqrt(r2_score(df['Weight(pounds)'],line_weight1))) +print('Стандартная ошибка регрессии: ', np.sqrt(Qres/113)) + +# Множественная регрессия +K = 4 +X = np.vstack((df['Position'], df['Height(inches)'], df['Age'])).T +mr = LinearRegression().fit(X, df['Weight(pounds)']) +line_weight2 = mr.predict(X) + +fig2, axes = plt.subplots(1, 2, figsize=(10, 5)) +fig2.suptitle('Множественная регрессия') +#print(line_weight2) +#axes[0].scatter(df['Height(inches)'], line_weight2, color='red', linewidth=2) + +Qreg = np.sum((line_weight2 - df['Weight(pounds)'].mean())**2) +Qres = np.sum((df['Weight(pounds)'] - line_weight2)**2) + +res = df['Weight(pounds)'] - line_weight2 + +axes[0].scatter(line_weight2, res) +axes[0].axhline(y=0, color='red', linestyle='--') +axes[0].set_xlabel('Предсказанные значения') +axes[0].set_ylabel('Остаточные ошибки') +axes[0].set_title('Анализ остатков') + +axes[1].hist(res) +axes[1].set_xlabel('Остаточные ошибки') +axes[1].set_ylabel('Количество точек') +axes[1].set_title('Гистограмма остатков') + +print('Парная регрессия. Коэффициент детерминации: ', r2_score(df['Weight(pounds)'],line_weight2)) +print('Скорр. коэффициент детерминации: ', 1 - (1 - r2_score(df['Weight(pounds)'],line_weight2)*(115/113))) +print('Множ. коэффициент корреляции: ', np.sqrt(r2_score(df['Weight(pounds)'],line_weight2))) +print('Стандартная ошибка регрессии: ', np.sqrt(Qres/113)) + +plt.show() + + diff --git a/ИАД/lr1/task3_Fisher.py b/ИАД/lr1/task3_Fisher.py new file mode 100644 index 0000000..ae6266d --- /dev/null +++ b/ИАД/lr1/task3_Fisher.py @@ -0,0 +1,105 @@ +import numpy as np +from sklearn.datasets import load_iris +from sklearn.linear_model import LinearRegression +from sklearn.metrics import r2_score +import pandas as pd +import matplotlib.pyplot as plt +import seaborn as sb +import pingouin as pg +from scipy import stats + +# Датасет Ирисы Фишера +iris = load_iris() +iris_pd=pd.DataFrame(data=np.c_[iris['data'], iris['target']], columns=iris['feature_names'] + ['target']) + +# Формирование выборок по признакам +x1 = np.array(iris_pd['sepal length (cm)']) # первый признак - длина чашелистика +x2 = np.array(iris_pd['sepal width (cm)']) # второй признак - ширина чашелистика +x3 = np.array(iris_pd['petal length (cm)']) # третий признак - длина лепестка +x4 = np.array(iris_pd['petal width (cm)']) # четвертый признак - ширина лепестка + +# Пусть X4 - выходные переменные, а X3 - входные переменные, так как они коррелируют сильнее остальных комбинаций +fig, axes = plt.subplots(2, 2, figsize=(10, 10)) + + +# Парная регрессия +N = 150 +K = 2 +lr = LinearRegression().fit(x3.reshape(-1,1), x4) + +line_x3 = np.linspace(min(x3), max(x3),150) +line_y1 = lr.predict(line_x3.reshape(-1,1)) + +line_x3_pred = np.linspace(min(x3), 2*max(x3), 150) +line_y1_pred = lr.predict(line_x3_pred.reshape(-1,1)) + +meanY = np.mean(x4) +Qreg = np.sum((line_y1 - meanY)**2) +Qtotal = np.sum((x4 - meanY)**2) +Qint = np.sum((x4 - line_y1)**2) +Sreg = (1/(K-1))*Qreg +Stotal = (1/(N-1))*Qtotal +Sint = (1/(N-K))*Qint + + +# Множественная регрессия +N = 150 +K = 4 +X = np.vstack((x1, x2, x3)).T +mr = LinearRegression().fit(X, x4) + +line_x1 = np.linspace(min(x1), max(x1), 150) +line_x2 = np.linspace(min(x2), max(x2), 150) +line_x3 = np.linspace(min(x3), max(x3), 150) + +line_y2 = mr.coef_[0] * line_x1 + mr.coef_[1] * line_x2 + mr.coef_[2] * line_x3 + mr.intercept_ + +line_x1_pred = np.linspace(min(x1), 2*max(x1), 150) +line_x2_pred = np.linspace(min(x2), 2*max(x2), 150) +line_x3_pred = np.linspace(min(x3), 2*max(x3), 150) +line_y2_pred = mr.coef_[0] * line_x1_pred + mr.coef_[1] * line_x2_pred + mr.coef_[2] * line_x3_pred + mr.intercept_ + +Qreg = np.sum((line_y2 - meanY)**2) +Qint = np.sum((x4 - line_y2)**2) +Sreg = (1/(K-1))*Qreg +Stotal = (1/(N-1))*Qtotal +Sint = (1/(N-K))*Qint + + +# График остатков +residuals1 = x4 - line_y1 +residuals2 = x4 - line_y2 + +axes[0,0].hist(residuals1) +axes[0,1].hist(residuals2) + + +plt.show() + +# Проверка остатков на нормальность по критерию К-С +print('Тест Колмогорова-Смирнова. Уровень значимости a = 0.05') + +for x in [residuals1,residuals2]: + x_mean, std = np.mean(x), np.std(x, ddof = 1) + x_std = (x - x_mean)/std + pvalue = stats.kstest(x_std, "norm", alternative='less').pvalue + if pvalue > 0.05: result = 'H0 не должна быть отвергнута' + else: result = 'H0 должна быть отвергнута' + print('p-value: {}, так что {}'.format(pvalue, result)) + +# Статистика Дурбина-Уотсона +# для парной регрессии +a1 = 0 +gl = 1.706 +gu = 1.760 +for i in range(N-1): a1 += (residuals1[i] - residuals1[i+1])**2 +gamma = a1/sum(residuals1**2) +print(gamma, gl, gu) + +# для множ. регрессии +a2 = 0 +gl = 1.679 +gu = 1.788 +for i in range(N-1): a2 += (residuals2[i] - residuals2[i+1])**2 +gamma = a2/sum(residuals2**2) +print(gamma, gl, gu) \ No newline at end of file diff --git a/ИАД/lr1/task5_Fisher.py b/ИАД/lr1/task5_Fisher.py new file mode 100644 index 0000000..bcafb61 --- /dev/null +++ b/ИАД/lr1/task5_Fisher.py @@ -0,0 +1,45 @@ +import numpy as np +from sklearn.datasets import load_iris +from sklearn.linear_model import LinearRegression +from sklearn.metrics import mean_squared_error, r2_score +from sklearn.model_selection import train_test_split +import pandas as pd +import matplotlib.pyplot as plt + +# Датасет Ирисы Фишера +iris = load_iris() +iris_pd=pd.DataFrame(data=np.c_[iris['data'], iris['target']], columns=iris['feature_names'] + ['target']) + +# Формирование выборок по признакам +x1 = np.array(iris_pd['sepal length (cm)']) # первый признак - длина чашелистика +x2 = np.array(iris_pd['sepal width (cm)']) # второй признак - ширина чашелистика +x3 = np.array(iris_pd['petal length (cm)']) # третий признак - длина лепестка +x4 = np.array(iris_pd['petal width (cm)']) # четвертый признак - ширина лепестка + +X = np.column_stack((x1, x2, x3)) + +# Разделение на обучающую и тестовую выборки +X_train, X_test, y_train, y_test = train_test_split(X, x4, test_size=0.25, random_state=42) + + + +model = LinearRegression() +model.fit(X_train, y_train) + +y_pred = 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