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Консультация № 180823
17.11.2010, 16:37
0.00 руб.
17.11.2010, 18:05
0
4
1
Здравствуйте, УЭ!
Вопрос по теме Метод наименьших квадратов.
Доказать, что угол
наклона прямой в вещественной плоскости, проходящей через начало координат в среднем квадратичном как можно ближе к m заданным точкам 
определяется формулой:
Вопрос по теме Метод наименьших квадратов.
Доказать, что угол
наклона прямой в вещественной плоскости, проходящей через начало координат в среднем квадратичном как можно ближе к m заданным точкам определяется формулой:
Обсуждение
17.11.2010, 16:49
общий
Вопрос должен выглядеть так?
Доказать, что угол наклона прямой в вещественной плоскости, проходящей через начало координат в среднем квадратичном как можно ближе к m заданным точкам определяется формулой:
Доказать, что угол
наклона прямой в вещественной плоскости, проходящей через начало координат в среднем квадратичном как можно ближе к m заданным точкам определяется формулой:
17.11.2010, 17:28
общий
это ответ
Здравствуйте, Amfisat!
Согласно методу наименьших квадратов для прямой y=ax должно быть минимально выражение
f=[$8721$](aai-bi)2
В точке минимума производная f по переменной a должна быть равна нулю:
2[$8721$](aai-bi)ai=0
Это дает уравнение
a([$8721$]ai2)=[$8721$]aibi
Отюда находим a (коэффициент при x - угловой коэффициент прямой - и есть тангенс угла наклона прямой).
a=[$8721$]aibi/[$8721$]ai2
Согласно методу наименьших квадратов для прямой y=ax должно быть минимально выражение
f=[$8721$](aai-bi)2
В точке минимума производная f по переменной a должна быть равна нулю:
2[$8721$](aai-bi)ai=0
Это дает уравнение
a([$8721$]ai2)=[$8721$]aibi
Отюда находим a (коэффициент при x - угловой коэффициент прямой - и есть тангенс угла наклона прямой).
a=[$8721$]aibi/[$8721$]ai2
5
Спасибо! Очень помогли!
17.11.2010, 17:39
общий
Пока писал ответ в более общем виде появлилось уточнение модератора, в соотвествии с которым я внес нужные изменения в ответ.
Форма ответа
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