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Консультация № 190798
27.03.2017, 12:51
0.00 руб.
30.03.2017, 14:13
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1
1
Здравствуйте уважаемые эксперты! Прошу Вас помочь в решении задачи. Заранее большое спасибо!
Экспериментальные данные о переменных
и 
приведены в таблице
В результате их выравнивания получена функция
Используя метод наименьших квадратов, аппроксимировать эти данные линейной зависимостью 
(найти параметры 
и 
). Выяснить, какая из двух линий лучше (в смысле метода наименьших квадратов) выравнивает экспериментальные данные. Сделать чертёж.
Экспериментальные данные о переменных
и приведены в таблицеВ результате их выравнивания получена функция
Используя метод наименьших квадратов, аппроксимировать эти данные линейной зависимостью (найти параметры и ). Выяснить, какая из двух линий лучше (в смысле метода наименьших квадратов) выравнивает экспериментальные данные. Сделать чертёж.Обсуждение
30.03.2017, 14:13
общий
это ответ
Здравствуйте, ms.nastasya2512!
Вычислим коэффициенты
Нормальная система для заданной аппроксимирующей функции имеет вид
Заполним, выполнив нужные вычисления, следующую таблицу
Используя данные в последней строке таблицы, перепишем систему
и решим её:
Следовательно, искомая линейная зависимость имеет вид
Составим таблицу, в которой обозначим
и выполним вычисления.
Получили, что сумма квадратов отклонений при приближении экспериментальных данных функцией
составляет приблизительно 
а при приближении функцией 
- приблизительно 
Значит, второе приближение лучше.
Рисунок к решению задачи показан ниже. На нём экспериментальные точки имеют черный цвет, линия - синий, линия - красный.
Вычислим коэффициенты
Нормальная система для заданной аппроксимирующей функции имеет видЗаполним, выполнив нужные вычисления, следующую таблицу
Используя данные в последней строке таблицы, перепишем систему
и решим её:Следовательно, искомая линейная зависимость имеет вид
Составим таблицу, в которой обозначим
и выполним вычисления.Получили, что сумма квадратов отклонений при приближении экспериментальных данных функцией
составляет приблизительно а при приближении функцией - приблизительно Значит, второе приближение лучше.Рисунок к решению задачи показан ниже. На нём экспериментальные точки имеют черный цвет, линия
- синий, линия - красный.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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