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b/idz4/report.tex new file mode 100644 index 0000000..8b9a53d --- /dev/null +++ b/idz4/report.tex @@ -0,0 +1,691 @@ +\documentclass[a4paper, final]{article} +%\usepackage{literat} % Нормальные шрифты +\usepackage[14pt]{extsizes} % для того чтобы задать нестандартный 14-ый размер шрифта +\usepackage{tabularx} +\usepackage[T2A]{fontenc} +\usepackage[utf8]{inputenc} +\usepackage[russian]{babel} +\usepackage{amsmath} +\usepackage{amssymb} +\usepackage[left=15mm, top=15mm, right=15mm, bottom=15mm, footskip=10mm]{geometry} +\usepackage{ragged2e} %для растягивания по ширине +\usepackage{setspace} %для межстрочно го интервала +\usepackage{moreverb} %для работы с листингами +\usepackage{indentfirst} % для абзацного отступа +\usepackage{moreverb} %для печати в листинге исходного кода программ +\usepackage{pdfpages} %для вставки других pdf файлов +\usepackage{tikz} +\usepackage{graphicx} +\usepackage{afterpage} +\usepackage{longtable} +\usepackage{float} + + + +% \usepackage[paper=A4,DIV=12]{typearea} +\usepackage{pdflscape} +% \usepackage{lscape} + +\usepackage{array} +\usepackage{multirow} + +\renewcommand\verbatimtabsize{4\relax} +\renewcommand\listingoffset{0.2em} %отступ от номеров строк в листинге +\renewcommand{\arraystretch}{1.4} % изменяю высоту строки в таблице +\usepackage[font=small, singlelinecheck=false, justification=centering, format=plain, labelsep=period]{caption} %для настройки заголовка таблицы +\usepackage{listings} %листинги +\usepackage{xcolor} % цвета +\usepackage{hyperref}% для гиперссылок +\usepackage{enumitem} %для перечислений + +\newcommand{\specialcell}[2][l]{\begin{tabular}[#1]{@{}l@{}}#2\end{tabular}} + + +\setlist[enumerate,itemize]{leftmargin=1.2cm} %отступ в перечислениях + +\hypersetup{colorlinks, + allcolors=[RGB]{010 090 200}} %красивые гиперссылки (не красные) + +% подгружаемые языки — подробнее в документации listings (это всё для листингов) +\lstloadlanguages{ SQL} +% включаем кириллицу и добавляем кое−какие опции +\lstset{tabsize=2, + breaklines, + basicstyle=\footnotesize, + columns=fullflexible, + flexiblecolumns, + numbers=left, + numberstyle={\footnotesize}, + keywordstyle=\color{blue}, + inputencoding=cp1251, + extendedchars=true +} +\lstdefinelanguage{MyC}{ + language=SQL, +% ndkeywordstyle=\color{darkgray}\bfseries, +% identifierstyle=\color{black}, +% morecomment=[n]{/**}{*/}, +% commentstyle=\color{blue}\ttfamily, +% stringstyle=\color{red}\ttfamily, +% morestring=[b]", +% showstringspaces=false, +% morecomment=[l][\color{gray}]{//}, + keepspaces=true, + escapechar=\%, + texcl=true +} + +\textheight=24cm % высота текста +\textwidth=16cm % ширина текста +\oddsidemargin=0pt % отступ от левого края +\topmargin=-1.5cm % отступ от верхнего края +\parindent=24pt % абзацный отступ +\parskip=5pt % интервал между абзацами +\tolerance=2000 % терпимость к "жидким" строкам +\flushbottom % выравнивание высоты страниц + + +% Настройка листингов +\lstset{ + language=python, + extendedchars=\true, + inputencoding=utf8, + keepspaces=true, + % captionpos=b, % подписи листингов снизу +} + +\begin{document} % начало документа + + + + % НАЧАЛО ТИТУЛЬНОГО ЛИСТА + \begin{center} + \hfill \break + \hfill \break + \normalsize{МИНИСТЕРСТВО НАУКИ И ВЫСШЕГО ОБРАЗОВАНИЯ РОССИЙСКОЙ ФЕДЕРАЦИИ\\ + федеральное государственное автономное образовательное учреждение высшего образования «Санкт-Петербургский политехнический университет Петра Великого»\\[10pt]} + \normalsize{Институт компьютерных наук и кибербезопасности}\\[10pt] + \normalsize{Высшая школа технологий искусственного интеллекта}\\[10pt] + \normalsize{Направление: 02.03.01 <<Математика и компьютерные науки>>}\\ + + \hfill \break + \hfill \break + \hfill \break + \hfill \break + \large{Индивидуальное домашнее задание №4}\\ + \large{по дисциплине}\\ + \large{<<Математическая статистика>>}\\ + \large{Вариант 27}\\ + + % \hfill \break + \hfill \break + \end{center} + + \small{ + \begin{tabular}{lrrl} + \!\!\!Студент, & \hspace{2cm} & & \\ + \!\!\!группы 5130201/20102 & \hspace{2cm} & \underline{\hspace{3cm}} &Тищенко А. А. \\\\ + \!\!\!Преподаватель & \hspace{2cm} & \underline{\hspace{3cm}} & Малов С. В. \\\\ + &&\hspace{4cm} + \end{tabular} + \begin{flushright} + <<\underline{\hspace{1cm}}>>\underline{\hspace{2.5cm}} 2025г. + \end{flushright} + } + + \hfill \break + % \hfill \break + \begin{center} \small{Санкт-Петербург, 2025} \end{center} + \thispagestyle{empty} % выключаем отображение номера для этой страницы + + % КОНЕЦ ТИТУЛЬНОГО ЛИСТА + \newpage + \section {Задание №1} + \begin{figure}[h!] + \centering + \includegraphics[width=1\linewidth]{img/task1.png} + \end{figure} + + \subsection{Пункт a} + + \begin{figure}[h!] + \centering + \includegraphics[width=0.75\linewidth]{img/task1_1.png} + \end{figure} + + + \textbf{Формулировка линейной регрессионной модели} + Линейная регрессионная модель зависимости $Y$ от $X$ имеет вид: + $$ + Y = \beta_1 + \beta_2 X + \epsilon, + $$ + где: + - $\beta_1$ — параметр сдвига, + - $\beta_2$ — параметр масштаба, + - $\epsilon$ — случайная ошибка. + + \textbf{Построение МНК-оценок параметров} + Метод наименьших квадратов (МНК) используется для нахождения оценок $\hat{\beta_1}$ и $\hat{\beta_2}$, которые минимизируют сумму квадратов остатков. + + $\beta_1 = 15.5869$ + + $\beta_2 = -0.2522$ + + $R^2$ линейной модели: 0.0144 + + \begin{figure}[h!] + \centering + \includegraphics[width=1\linewidth]{img/task1_2.png} + \end{figure} + + \textbf{Распределение точек относительно линии} + Точки разбросаны, линия не отражает тренд, что говорит о плохом соответствии. + + \textbf{Наклон линии}: Линия близка к горизонтальной, зависимость слабая. + + Таким образом, Между $X$ и $Y$ нет линейной зависимости. Линейная модель не подходит для описания данных. + + \newpage + \subsection{Пункт b} + + \textbf{Формулировка полиномиальной регрессионной модели} + Полиномиальная регрессионная модель зависимости $Y$ от $X$ имеет вид: + $$ + Y = \beta_1 + \beta_2 X + \beta_3 X^2 + \epsilon, + $$ + где: + \begin{itemize} + \item $\beta_1$ — параметр сдвига, + \item $\beta_2$ — линейный коэффициент при $X$, + \item $\beta_3$ — квадратичный коэффициент при $X^2$, + \item $\epsilon$ — случайная ошибка + \end{itemize} + + \begin{figure}[h!] + \centering + \includegraphics[width=1\linewidth]{img/task1_3.png} + \end{figure} + + Полиномиальная модель: + $\beta_1 = 16.8727$ + $\beta_2 = -1.1208$ + $\beta_3 = 0.1296$ + + $R^2$ полиномиальной модели: 0.0240 + + + \textbf{Распределение точек относительно линии}: Точки разбросаны, линия не отражает тренд, что говорит о плохом соответствии. + + \textbf{Низкий R²} означает, что квадратичная модель плохо описывает связь между $X$ и $Y$. + + \textbf{Результаты указывают на то, что квадратичная модель не подходит для описания данных.} + + \newpage + \subsection{Пункт c} + + \begin{figure}[h!] + \centering + \includegraphics[width=0.95\linewidth]{img/task1_4.png} + \end{figure} + + \begin{figure}[h!] + \centering + \includegraphics[width=0.9\linewidth]{img/task1_5.png} + \end{figure} + + \newpage + \textbf{Проверка нормальности с помощью критерия $\chi^2$} + + Этапы: + \begin{enumerate} + \item Гипотезы: + \begin{itemize} + \item $H_0$: Остатки имеют нормальное распределение. + \item $H_1$: Остатки не имеют нормального распределения. + \end{itemize} + \item Разделить данные на интервалы (бины): Используем те же интервалы, что и в гистограмме. + \item Рассчитать наблюдаемые ($O_i$) и ожидаемые ($E_i$) частоты: + \begin{itemize} + \item $E_i = N \cdot P$ (для $i$-го интервала), где $P$ — вероятность из нормального распределения $N(\mu, \sigma^2)$. + \end{itemize} + \item Вычислить статистику $\chi^2$: + $$ + \chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}. + $$ + \item Сравнить с критическим значением $\chi^2$: Если $\chi^2 > \chi^2_{\text{крит}}$, отвергаем $H_0$. + \end{enumerate} + + Хи-квадрат статистика: 2.7737 + + Критическое значение: 13.3882 + + p-value: 0.7348 + + Не отвергаем $H_0$: распределение нормальное + + \textbf{Визуально:} Остатки близки к нормальному распределению. + + \textbf{Статистически:} Критерий $\chi^2$ не выявил значимых отклонений от нормальности на уровне $\alpha=0.02$. + + Предположение о нормальности ошибок выполняется. + + \subsection{Пункт d} + + Частные интервалы строятся для каждого параметра отдельно, используя t-распределение. + + \textbf{Формула:} + $$ + \hat{\beta_j} \pm t_{1-\alpha/2, n-p} \cdot SE(\hat{\beta_j}), + $$ + где: + \begin{itemize} + \item $\hat{\beta_j}$ - оценка параметра, + \item $SE(\hat{\beta_j})$ - стандартная ошибка параметра, + \item $t_{1-\alpha/2}$ - критическое значение t-распределения, + \item $n$ - число наблюдений, + \item $p$ - число параметров модели (для квадратичной модели $p = 3$). + \end{itemize} + + Доверительные интервалы (уровень 0.98): + \begin{itemize} + \item Доверительный интервал для $\beta_2$ (98.0\%): [-4.2930, 2.0514] + \item Доверительный интервал для $\beta_3$ (98.0\%): [-0.3310, 0.5902] + \end{itemize} + + \textbf{Совместные доверительные интервалы} + Совместные интервалы учитывают корреляцию между оценками параметров. Используем метод Бонферрони или F-распределение. + + \textbf{Метод Бонферрони} + + Формула: + $$ + \hat{\beta_j} \pm t_{1-\alpha/(2k),n-p} \cdot SE(\hat{\beta_j}), + $$ + где $k=2$ (число параметров $\beta_2$ и $\beta_3$). + + + \begin{figure}[h!] + \centering + \includegraphics[width=1\linewidth]{img/task1_6.png} + \end{figure} + + Ковариационная матрица для $\beta_2$ и $\beta_3$: + + \begin{verbatim} + X X2 + X 1.734960 -0.245172 + X2 -0.245172 0.036575 + \end{verbatim} + + Совместные интервалы (Бонферрони): + \begin{itemize} + \item $\beta_2$: [-4.657, 2.415] + \item $\beta_3$: [-0.384, 0.643] + \end{itemize} + + \textbf{Метод F-распределения} + + Формула: + $$ + (\hat{\beta} - \beta)^T \cdot Cov(\hat{\beta})^{-1} \cdot (\hat{\beta} - \beta) \leq F_{1-\alpha, 2, n-p}, + $$ + где $F_{1-\alpha, 2, n-p}$ - критическое значение F-распределения. + + Полная ковариационная матрица: + \begin{verbatim} + const X X2 + const 4.7543 -2.7403 0.3629 + X -2.7403 1.7350 -0.2452 + X2 0.3629 -0.2452 0.0366 + \end{verbatim} + + Вектор оценок параметров [$\beta_2$, $\beta_3$]: + [-1.120772, 0.129577] + + \subsection{Пункт e} + \textbf{Гипотеза линейности} + \begin{itemize} + \item $H_0$: Зависимость $Y$ от $X$ линейна ($\beta_3 = 0$). + \item $H_1$: Зависимость нелинейна ($\beta_3 \neq 0$). + \end{itemize} + + \textbf{Гипотеза независимости} + \begin{itemize} + \item $H_0$: $Y$ не зависит от $X$ линейна ($\beta_2 = \beta_3 = 0$). + \item $H_1$: $Y$ зависит от $X$ линейна (хотя бы один из $\beta_2, \beta_3 \neq 0$). + \end{itemize} + + \textbf{Проверка гипотезы линейности ($H_0: \beta_3 = 0$):} + \begin{itemize} + \item t-статистика: 0.6775 + \item p-значение: 0.5014 + \item Нет оснований отвергать гипотезу о линейности (p > 0.02). + \end{itemize} + + \textbf{Проверка гипотезы независимости ($H_0: \beta_2 = 0$):} + \begin{itemize} + \item t-статистика: -0.8509 + \item p-значение: 0.3991 + \item Нет оснований отвергать гипотезу о независимости (p > 0.02). + \end{itemize} + + + \newpage + \subsection{Пункт f} + Сравнение моделей по AIC и BIC: + \begin{verbatim} + Модель AIC BIC + Линейная 232.83 236.66 + Квадратичная 234.35 240.08 + \end{verbatim} + + \textbf{AIC/BIC} линейной модели меньше, она лучше описывает данные. + + \subsection{Пункт g} + \textbf{Характер зависимости $Y$ от $X$} + \begin{itemize} + \item \textbf{Линейная модель:} + $$ + Y = 15.59 - 0.25X,\ R^2 = 0.014. + $$ + \begin{itemize} + \item Крайне низкий $R^2$ (1.4\%) указывает на отсутствие линейной зависимости. + \item Коэффициент $\beta_2 = -0.25$ статистически незначим (доверительный интервал [-4.29, 2.05] включает ноль). + \end{itemize} + + \item \textbf{Квадратичная модель:} + $$ + Y = 16.87 - 1.12X + 0.13X^2,\ R^2 = 0.024. + $$ + \begin{itemize} + \item $R^2 = 2.4\%$ показывает, что модель объясняет лишь незначительную часть вариации. + \item Коэффициенты: + \begin{itemize} + \item $\beta_2 = -1.12$ (линейный член): интервал [-4.29, 2.05] включает ноль. + \item $\beta_3 = 0.13$ (квадратичный член): интервал [-0.33, 0.59] включает ноль. + \end{itemize} + \end{itemize} + \end{itemize} + + \textbf{Проверка гипотез}\\ + Остатки близки к нормальному распределению. Критерий $\chi^2$ не выявил значимых отклонений от нормальности на уровне $\alpha=0.02$. + + \textit{Предположение о нормальности ошибок выполняется.} + + \textbf{AIC/BIC} + \begin{center} + \begin{tabular}{|l|c|c|} + \hline + Модель & AIC & BIC \\ + \hline + Линейная & 232.83 & 236.66 \\ + \hline + Квадратичная & 234.35 & 240.08 \\ + \hline + \end{tabular} + \end{center} + + \begin{itemize} + \item \textbf{Линейная модель} имеет более низкие AIC/BIC, чем квадратичная. + \end{itemize} + + \textbf{Аномалии в результатах} + \begin{itemize} + \item \textbf{Парадокс низкого $R^2$:} + \begin{itemize} + \item Обе модели объясняют менее 3\% вариации, что ставит под сомнение их практическую применимость. + \end{itemize} + \end{itemize} + + \textbf{Итоговый вывод} + \begin{itemize} + \item \textbf{Отсутствие значимой связи:} Ни линейная, ни квадратичная модели не демонстрируют статистически значимой зависимости $Y$ от $X$ на уровне $\alpha=0.02$. + \item \textbf{Рекомендации:} + \begin{itemize} + \item Проверить данные на наличие выбросов или ошибок. + \item Рассмотреть другие предикторы или преобразования. + \item Увеличить объем данных для повышения надежности тестов. + \end{itemize} + \end{itemize} + + \newpage + \section{Задание 2} + + \begin{figure}[h!] + \centering + \includegraphics[width=1\linewidth]{img/task2.png} + \end{figure} + + \subsection{Пункт a} + \textbf{1. Формулировка модели двухфакторного дисперсионного анализа} + + Модель с взаимодействием факторов: + $$ + Y_{ijk} = \mu + \alpha_i + \beta_j + (\alpha \beta)_{ij} + \epsilon_{ijk}, + $$ + где: + \begin{itemize} + \item $Y_{ijk}$ — наблюдаемое значение переменной $Y$ для $i$-го уровня фактора $A$, $j$-го уровня фактора $B$, $k$-го повторения, + \item $\mu$ — общее среднее, + \item $\alpha_i$ — эффект $i$-го уровня фактора $A$, + \item $\beta_j$ — эффект $j$-го уровня фактора $B$, + \item $(\alpha \beta)_{ij}$ — эффект взаимодействия факторов $A$ и $B$, + \item $\epsilon_{ijk} \sim N(0, \sigma^2)$ — случайная ошибка. + \end{itemize} + + \newpage + \textbf{2. Построение МНК-оценок параметров} + + Оценки параметров полной модели: + \begin{verbatim} + Intercept 11.998333 + C(A)[T.2] 2.440000 + C(B)[T.2] -2.586667 + C(B)[T.3] 4.146667 + C(B)[T.4] -0.345000 + C(A)[T.2]:C(B)[T.2] 10.131667 + C(A)[T.2]:C(B)[T.3] 1.561667 + C(A)[T.2]:C(B)[T.4] 3.795000 + \end{verbatim} + + \textbf{3. Несмещенная оценка дисперсии} + + Несмещенная оценка дисперсии ошибок: + $$ + \hat{\sigma}^2 = \frac{SS_{\text{res}}}{df_{\text{res}}} = 0.757, + $$ + где: + \begin{itemize} + \item $SS_{\text{res}}$ — сумма квадратов остатков, + \item $df_{\text{res}} = n - p$ — степени свободы ($n$ — число наблюдений, $p$ — число параметров). + \end{itemize} + + \subsection{Пункт b} + + Сводная таблица средних значений Y: + + \begin{verbatim} + B 1 2 3 4 + A + 1 11.998333 9.411667 16.145000 11.653333 + 2 14.438333 21.983333 20.146667 17.888333 + \end{verbatim} + + \begin{figure}[h!] + \centering + \includegraphics[width=1\linewidth]{img/task2_1.png} + \end{figure} + + \textbf{Визуальная проверка аддитивности:} + + \begin{itemize} + \item 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. + \item Следствия: Взаимодействие факторов может означать, что влияние одного фактора на зависимую переменную $Y$ зависит от другого фактора. + \end{itemize} + + + \newpage + \subsection{Пункт c} + + \begin{figure}[h!] + \centering + \includegraphics[width=1\linewidth]{img/task2_2.png} + \end{figure} + + \begin{figure}[h!] + \centering + \includegraphics[width=0.8\linewidth]{img/task2_3.png} + \end{figure} + + \textbf{Тест Шапиро-Уилка:} p-value = 0.949 + + \textbf{Не отвергаем $H_0$: остатки нормальны.} + + \textbf{Результаты:} + \begin{itemize} + \item Гистограмма: Распределение остатков близко к нормальному, совпадает с наложенной кривой $N(0, \sigma^2)$. + \item Q-Q график: Точки лежат вдоль линии $y=x$, что подтверждает нормальность. + \item Тест Шапиро-Уилка: гипотеза о нормальности не отвергается. + \end{itemize} + + \subsection{Пункт d} + Таблица ANOVA: + + \begin{verbatim} + df sum_sq mean_sq F PR(>F) + C(A) 1.0 478.108752 478.108752 631.694471 4.061068e-26 + C(B) 3.0 153.241356 51.080452 67.489330 1.051893e-15 + C(A):C(B) 3.0 178.558140 59.519380 78.639144 8.022881e-17 + Residual 40.0 30.274683 0.756867 NaN NaN + \end{verbatim} + + \textbf{Результаты ANOVA} + \begin{itemize} + \item Фактор A: + $$ + F = 631.69,\ p\text{-value} < 0.001 \ \rightarrow \ \text{значимо влияет на } Y. + $$ + + \item Фактор B: + $$ + F = 67.49,\ p\text{-value} < 0.001 \ \rightarrow \ \text{значимо влияет на } Y. + $$ + + \item Взаимодействие $A \times B$: + $$ + F = 78.64,\ p\text{-value} < 0.001 \ \rightarrow \ \text{значимо влияет на } Y. + $$ + + \item Вывод: + На уровне значимости $\alpha=0.02$ все факторы (A, B) и их взаимодействие \textbf{значимо} ($p < 0.02$). Это означает, что влияние фактора A на Y зависит от уровня фактора B, и наоборот. + \end{itemize} + + \subsection{Пункт e} + + Для выбора оптимальной модели используются критерии: + \begin{itemize} + \item AIC оценивает баланс между качеством подгонки модели и её сложностью, накладывая штраф за избыточное количество параметров. + \item BIC работает аналогично AIC, но применяет более строгий штраф за сложность, особенно при больших объемах данных. + \end{itemize} + + Сравниваем две модели: + \begin{enumerate} + \item Полная модель (с взаимодействием): + $$ + Y \sim A + b + A : B. + $$ + \item Аддитивная модель (без взаимодействия): + $$ + Y \sim A + B. + $$ + \end{enumerate} + + \begin{verbatim} + Модель AIC BIC + Полная 130.10 145.07 + Аддитивная 216.79 226.15 + \end{verbatim} + + \textbf{Вывод о сравнении моделей} + + \begin{itemize} + \item \textbf{Результаты AIC и BIC:} + \begin{itemize} + \item Полная модель имеет AIC = 130.10, в то время как аддитивная модель имеет AIC = 216.79. Это указывает на значительное преимущество полной модели. + \item Полная модель также имеет BIC = 145.07, а аддитивная модель — BIC = 226.15. Разница подтверждает выбор полной модели. + \end{itemize} + + \item \textbf{Заключение:} + \begin{itemize} + \item Полная модель \textbf{предпочтительнее}, так как она лучше соответствует данным, что подтверждается меньшими значениями AIC и BIC. + \item Аддитивная модель не учитывает взаимодействие факторов. + \end{itemize} + \end{itemize} + + \subsection{Пункт f} + + \textbf{1. Основные эффекты факторов A и B} + \begin{itemize} + \item \textbf{Фактор A:} + Оказал сильное статистически значимое влияние на $Y$ ($F=631.69, p<0.001$). + + + \item \textbf{Фактор B:} + Также значимо влияет на $Y$ ($F=67.49, p<0.001$). + \end{itemize} + + \textbf{2. Взаимодействие факторов $A \times B$} + \begin{itemize} + \item \textbf{Статистическая значимость:} + Взаимодействие значимо ($F=78.64, p<0.001$). + + \item \textbf{Визуальное подтверждение:} + График зависимости $Y$ от $A$ при фиксированных $B$ показывает пересечение линий (особенно для $B=4$), что указывает на неаддитивность эффектов. + \end{itemize} + + + \textbf{3. Выбор оптимальной модели} + + AIC/BIC: + + \begin{tabularx}{\textwidth}{|c|X|X|} + \hline + Модель & AIC & BIC \\ + \hline + Полная (с взаимодействием) & 130.10 & 145.07 \\ + \hline + Аддитивная & 216.79 & 226.15 \\ + \hline + \end{tabularx} + + Разница $\Delta AIC = 86.69$ и $\Delta BIC = 81.08$ явно указывает на преимущество полной модели. + + Аддитивная модель не учитывает взаимодействие, что приводит к потере информации. + + + \textbf{4. Нормальность остатков} + + \begin{itemize} + \item Тест Шапиро-Уилка: + $$p\text{-value} = 0.949 \implies \text{гипотеза о нормальности остатков не отвергается}.$$ + \item Графическая проверка: + Гистограмма остатков близка к нормальной форме. + \item Q-Q график показывает совпадение точек с линией $y = x$. + \end{itemize} + + \textbf{Рекомендации:} + Для прогнозирования $Y$ необходимо учитывать взаимодействие $A \times B$, так как его игнорирование приведет к систематической ошибке. + + + \textbf{Итоговый вывод} + \begin{enumerate} + \item Полная модель с взаимодействием предпочтительна по критериям AIC/BIC и объясняет данные лучше аддитивной. + \item Нормальность остатков подтверждена тестами и графиками. + \end{enumerate} + + \textbf{Рекомендации:} + \begin{itemize} + \item Проверить данные на наличие выбросов для уровня $B=4$. + \item Использовать полную модель для прогнозирования и анализа эффектов. + \end{itemize} +\end{document} \ No newline at end of file diff --git a/idz4/ИДЗ 4_1 Артём.ipynb b/idz4/ИДЗ 4_1 Артём.ipynb new file mode 100644 index 0000000..9a99f67 --- /dev/null +++ b/idz4/ИДЗ 4_1 Артём.ipynb @@ -0,0 +1,1265 @@ +{ + "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": [ + "
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" + ], + "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": [ + "
" + ] + }, + "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": [ + "
" + ] + }, + "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": [ + "
" + ] + }, + "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": [ + "
" + ] + }, + "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": 10, + "id": "72be1710", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "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": 9, + "id": "bd170677", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Хи-квадрат статистика: 2.7737\n", + "Критическое значение: 13.3882\n", + "p-value: 0.7348\n", + "Не отвергаем H0: распределение нормальное\n" + ] + } + ], + "source": [ + "# 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", + "\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": 17, + "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": 69, + "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": 86, + "id": "68365ffd", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "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": 90, + "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": 19, + "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": 11, + "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": 20, + "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 $X$ линейна ($\\beta_2 = \\beta_3 = 0$).\n", + "- $H_1$: $Y$ зависит от $X$ линейна (хотя бы один из $\\beta_2, \\beta_3 \\neq 0$)." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "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": 16, + "id": "405456a9", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Проверка гипотез:\n", + "Проверка гипотезы линейности (H₀: β₃ = 0):\n", + "t-статистика: 0.6775\n", + "p-значение: 0.5014\n", + "Нет оснований отвергать гипотезу о линейности\n", + "\n", + "Проверка гипотезы независимости (H₀: β₂ = 0):\n", + "t-статистика: -0.8509\n", + "p-значение: 0.3991\n", + "Нет оснований отвергать гипотезу о независимости\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\Users\\margaery\\AppData\\Local\\Temp\\ipykernel_15852\\3529389018.py:4: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`\n", + " print(f\"t-статистика: {model_poly.tvalues[2]:.4f}\")\n", + "C:\\Users\\margaery\\AppData\\Local\\Temp\\ipykernel_15852\\3529389018.py:5: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`\n", + " print(f\"p-значение: {model_poly.pvalues[2]:.4f}\")\n", + "C:\\Users\\margaery\\AppData\\Local\\Temp\\ipykernel_15852\\3529389018.py:6: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`\n", + " if model_poly.pvalues[2] < alpha:\n", + "C:\\Users\\margaery\\AppData\\Local\\Temp\\ipykernel_15852\\3529389018.py:13: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`\n", + " print(f\"t-статистика: {model_poly.tvalues[1]:.4f}\")\n", + "C:\\Users\\margaery\\AppData\\Local\\Temp\\ipykernel_15852\\3529389018.py:14: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`\n", + " print(f\"p-значение: {model_poly.pvalues[1]:.4f}\")\n", + "C:\\Users\\margaery\\AppData\\Local\\Temp\\ipykernel_15852\\3529389018.py:15: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`\n", + " if model_poly.pvalues[1] < alpha:\n" + ] + } + ], + "source": [ + "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" + ] + }, + { + "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": 19, + "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" + ] + } + ], + "source": [ + "# f) AIC и BIC\n", + "# Добавляем константную модель для сравнения\n", + "model_const = sm.OLS(df['Y'], sm.add_constant(np.ones(len(df)))).fit()\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" + ] + }, + { + "cell_type": "markdown", + "id": "d66aad56", + "metadata": {}, + "source": [ + "**AIC/BIC** линейной модели меньше, она лучше описывает данные." + ] + }, + { + "cell_type": "markdown", + "id": "a6887b63", + "metadata": {}, + "source": [ + "## Пункт g)\n", + "### Характер зависимости $Y$ от $X$\n", + "- **Линейная модель:**\n", + " $$\n", + " Y = 15.59 - 0.25X,\\ R^2 = 0.014.\n", + " $$\n", + " - Крайне низкий $R^2$ (1.4%) указывает на отсутствие линейной зависимости.\n", + " - Коэффициент $\\beta_2 = -0.25$ статистически незначим (доверительный интервал [−4.29, 2.05] включает ноль).\n", + "\n", + "- **Квадратичная модель:**\n", + " $$\n", + " Y = 16.87 - 1.12X + 0.13X^2,\\ R^2 = 0.024.\n", + " $$\n", + " - $R^2 = 2.4\\%$ показывает, что модель объясняет лишь незначительную часть вариации.\n", + " - Коэффициенты:\n", + " - $\\beta_2 = -1.12$ (линейный член): интервал [−4.29, 2.05] включает ноль.\n", + " - $\\beta_3 = 0.13$ (квадратичный член): интервал [−0.33, 0.59] включает ноль.\n", + "\n", + "### Проверка гипотез\n", + "Остатки близки к нормальному распределению. Критерий $\\chi^2$ не выявил значимых отклонений от нормальности на уровне $\\alpha=0.02$.\n", + "\n", + "*Предположение о нормальности ошибок выполняется.*\n", + "\n", + "### AIC/BIC\n", + "| Модель | AIC | BIC |\n", + "|----------------|--------|--------|\n", + "| Линейная | 232.83 | 236.66 |\n", + "| Квадратичная | 234.35 | 240.08 |\n", + "\n", + "- **Линейная модель** имеет более низкие AIC/BIC, чем квадратичная.\n", + "\n", + "### Аномалии в результатах\n", + "\n", + "**Парадокс низкого $R^2$:**\n", + " - Обе модели объясняют менее 3% вариации, что ставит под сомнение их практическую применимость.\n", + "\n", + "### Итоговый вывод\n", + "- **Отсутствие значимой связи:** Ни линейная, ни квадратичная модели не демонстрируют статистически значимой зависимости $Y$ от $X$ на уровне $\\alpha=0.02$.\n", + "- **Артефакты анализа:** Низкий $R^2$, незначимые коэффициенты и противоречивые результаты тестов указывают на то, что переменная $X$ не является релевантным предиктором для $Y$ в данном наборе данных.\n", + "- **Рекомендации:** \n", + " - Проверить данные на наличие выбросов или ошибок.\n", + " - Рассмотреть другие предикторы или преобразования.\n", + " - Увеличить объем данных для повышения надежности тестов." + ] + } + ], + "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 +} diff --git a/idz4/ИДЗ 4_2 Артём.ipynb b/idz4/ИДЗ 4_2 Артём.ipynb new file mode 100644 index 0000000..0cc9f55 --- /dev/null +++ b/idz4/ИДЗ 4_2 Артём.ipynb @@ -0,0 +1,634 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "05af2cce", + "metadata": {}, + "source": [ + "![Задача №2](2.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "a34b5583", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "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": 3, + "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": 4, + "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": 5, + "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": 6, + "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": 7, + "id": "ca70b1e2", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "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": 8, + "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": 9, + "id": "c77e2e2e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "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": 18, + "id": "78ffd74b", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "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": 11, + "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": 20, + "id": "a3830347", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Таблица ANOVA:\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" + ] + } + ], + "source": [ + "from statsmodels.stats.anova import anova_lm\n", + "\n", + "# ANOVA с взаимодействием\n", + "anova_table = anova_lm(model_full)\n", + "print(\"Таблица ANOVA:\")\n", + "print(anova_table)" + ] + }, + { + "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** ($p < 0.02$). 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 две модели:\n", + "1. **Полная модель** (с взаимодействием): \n", + " $$\n", + " Y \\sim A + b + A : B.\n", + " $$\n", + "2. **Аддитивная модель** (без взаимодействия):\n", + " $$\n", + " Y \\sim A + B.\n", + " $$" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "2db6d2ce", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Модель\t\tAIC\tBIC\n", + "Полная \t130.10\t145.07\n", + "Аддитивная \t216.79\t226.15\n" + ] + } + ], + "source": [ + "# Список моделей\n", + "models = {\n", + " \"Полная\": model_full,\n", + " \"Аддитивная\": model_additive\n", + "}\n", + "\n", + "# Вывод AIC и BIC\n", + "print(\"Модель\\t\\tAIC\\tBIC\")\n", + "for name, model in models.items():\n", + " print(f\"{name} \\t{model.aic:.2f}\\t{model.bic:.2f}\")" + ] + }, + { + "cell_type": "markdown", + "id": "2747e9f7", + "metadata": {}, + "source": [ + "### Вывод о сравнении моделей\n", + "\n", + "- **Результаты AIC и BIC:**\n", + " - **AIC:** Полная модель имеет AIC = 130.10, в то время как аддитивная модель имеет AIC = 216.79. Это указывает на значительное преимущество полной модели.\n", + " - **BIC:** Полная модель также имеет BIC = 145.07, а аддитивная модель — BIC = 226.15. Разница подтверждает выбор полной модели.\n", + "\n", + "- **Заключение:**\n", + " - Полная модель **предпочтительнее**, так как она лучше соответствует данным, что подтверждается меньшими значениями AIC и BIC.\n", + " - Аддитивная модель не учитывает взаимодействие факторов." + ] + }, + { + "cell_type": "markdown", + "id": "6dff2300", + "metadata": {}, + "source": [ + "## Пункт f)\n", + "### 1. Основные эффекты факторов A и B\n", + "- **Фактор A:** \n", + " Оказал **сильное статистически значимое влияние** на $Y$ ($F=631.69, p<0.001$). \n", + "\n", + "\n", + "- **Фактор B:** \n", + " Также **значимо влияет** на $Y$ ($F=67.49, p<0.001$). \n", + "\n", + "### 2. Взаимодействие факторов $A \\times B$\n", + "- **Статистическая значимость:** \n", + " Взаимодействие **значимо** ($F=78.64, p<0.001$).\n", + " \n", + "- **Визуальное подтверждение:** \n", + " График зависимости $Y$ от $A$ при фиксированных $B$ показывает пересечение линий (особенно для $B=4$), что указывает на **неаддитивность эффектов**.\n", + "\n", + "\n", + "### 3. Выбор оптимальной модели\n", + "- **AIC/BIC:** \n", + " | Модель | AIC | BIC |\n", + " |-----------------|--------|--------|\n", + " | Полная (с взаимодействием) | 130.10 | 145.07 |\n", + " | Аддитивная | 216.79 | 226.15 |\n", + "\n", + " - Разница $\\Delta AIC = 86.69$ и $\\Delta BIC = 81.08$ **явно указывает на преимущество полной модели**. \n", + " - Аддитивная модель не учитывает взаимодействие, что приводит к потере информации.\n", + "\n", + "\n", + "### 4. Нормальность остатков\n", + "- **Тест Шапиро-Уилка:** \n", + " $$p\\text{-value} = 0.949 \\implies \\text{гипотеза о нормальности остатков не отвергается}.$$\n", + "- **Графическая проверка:** \n", + " - Гистограмма остатков близка к нормальной форме. \n", + " - Q-Q график показывает совпадение точек с линией $y = x$.\n", + "\n", + "\n", + "- **Рекомендации:** \n", + " Для прогнозирования $Y$ **необходимо учитывать взаимодействие** $A \\times B$, так как его игнорирование приведет к систематической ошибке.\n", + "\n", + "\n", + "## Итоговый вывод\n", + "1. **Полная модель с взаимодействием** предпочтительна по критериям AIC/BIC и объясняет данные лучше аддитивной. \n", + "2. **Нормальность остатков** подтверждена тестами и графиками.\n", + "\n", + "**Рекомендации:** \n", + "- Проверить данные на наличие выбросов для уровня $B=4$. \n", + "- Использовать полную модель для прогнозирования и анализа эффектов." + ] + }, + { + "cell_type": "markdown", + "id": "2135d306", + "metadata": {}, + "source": [] + } + ], + "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 +}