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Консультация № 185128
09.01.2012, 12:01
51.74 руб.
0
1
1
Уважаемые эксперты! Пожалуйста, помогите решить задачу:
Экспериментально получены пять значений искомой функции y=f(x) при пяти значениях аргумента, которые записаны в таблице. Методом наименьших квадратов найти функции y=f(x) в виде y=ax+b.
Спасибо.
Экспериментально получены пять значений искомой функции y=f(x) при пяти значениях аргумента, которые записаны в таблице. Методом наименьших квадратов найти функции y=f(x) в виде y=ax+b.
Код:
x 1 2 3 4 5
========================
y 5.2 6.2 4.7 2.7 3.2
Спасибо.
Обсуждение
09.01.2012, 14:10
общий
это ответ
Здравствуйте, lamed!
Заполним следующую таблицу:
Составляем систему нормальных уравнений:
55a + 15b = 58,5,
15a + 5b = 22.
Решая эту систему, находим a = -0,75, b = 6,65.
Значит, зависимость между x и y представляется формулой
y = -0,75x + 6,65.
С уважением.
Заполним следующую таблицу:
Код:
i x_i y_i (x_i)^2 (x_i)(y_i)
=============================
1 1 5,2 1 5,2
2 2 6,2 4 12,4
3 3 4,7 9 14,1
4 4 2,7 16 10,8
5 5 3,2 25 16
-----------------------------
[$8721$] 15 22 55 58,5
Составляем систему нормальных уравнений:
55a + 15b = 58,5,
15a + 5b = 22.
Решая эту систему, находим a = -0,75, b = 6,65.
Значит, зависимость между x и y представляется формулой
y = -0,75x + 6,65.
С уважением.
5
Спасибо, Андрей Владимирович! С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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