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Консультация № 199564
09.11.2020, 23:48
0.00 руб.
0
2
1
Здравствуйте, уважаемые эксперты! Прошу Вашей помощи в решении следующей задачи:
Дано:
(38.4, -115.7) (52.6, -113.5) (38.8, -126.5) (12.1, -34.6) (44.9, -164.8)
(21.4, -51.1) (26.0, -85.3) (24.9, -84.7) (34.7, -91.3) (35.3, -124.1)
(17.5, -36.6) (25.0, -72,3) (15.4, -47.6) (31.6, -68.4) (35.3, -71,9)
(19.6, -63.7) (41.5, -110.4) (47.0, -108.3) (36.2, -128.4) (25.5, -92.9)
(39.9, -136.0) (33.7, -91.1) (34.8, -114.5) (29.8, -110.4) (27.9, -65.7)
(36.5, -71.4) (19.3, -37.8) (13.6, -38.6) (32.2, -117.6) (22.6, -82.4)
(33.4, -79.5) (16.0, -39.0) (23.6, -63.8) (35.8, -94.1) (33.2, -80.0)
(36.4, -101.8) (34.3, -117.3) (44.7, -170.2) (51.0, -143.3) (-0.7, 7.9)
(19.9, -41.2) (24.8, -79.7) (29.0, -75.3) (43.8, -166.4)
По данным выборки двумерной случайной величины определить:
1) вектор математического ожидания;
2) вектор дисперсии;
3) выборочный коэффициент корреляции;
4) выборочное уравнение прямой линии регрессии Y на X в виде Y = a X + b.
Спасибо!
Дано:
(38.4, -115.7) (52.6, -113.5) (38.8, -126.5) (12.1, -34.6) (44.9, -164.8)
(21.4, -51.1) (26.0, -85.3) (24.9, -84.7) (34.7, -91.3) (35.3, -124.1)
(17.5, -36.6) (25.0, -72,3) (15.4, -47.6) (31.6, -68.4) (35.3, -71,9)
(19.6, -63.7) (41.5, -110.4) (47.0, -108.3) (36.2, -128.4) (25.5, -92.9)
(39.9, -136.0) (33.7, -91.1) (34.8, -114.5) (29.8, -110.4) (27.9, -65.7)
(36.5, -71.4) (19.3, -37.8) (13.6, -38.6) (32.2, -117.6) (22.6, -82.4)
(33.4, -79.5) (16.0, -39.0) (23.6, -63.8) (35.8, -94.1) (33.2, -80.0)
(36.4, -101.8) (34.3, -117.3) (44.7, -170.2) (51.0, -143.3) (-0.7, 7.9)
(19.9, -41.2) (24.8, -79.7) (29.0, -75.3) (43.8, -166.4)
По данным выборки двумерной случайной величины определить:
1) вектор математического ожидания;
2) вектор дисперсии;
3) выборочный коэффициент корреляции;
4) выборочное уравнение прямой линии регрессии Y на X в виде Y = a X + b.
Спасибо!
Обсуждение
14.11.2020, 05:00
общий
это ответ
Здравствуйте, Svet_Vitalievna!
1) Вектор математического ожидания для выборки двумерной случайной величины определяем по стандартной формуле для выборочного среднего:
В данном случае для выборки длиной n = 44 имеем
и
2) Дисперсия также определяется по стандартным формулам:
либо
В данном случае
и
3) Выборочный коэффициент корреляции для двумерной случайной величины определяется выражением
В данном случае
и
Вычисленный коэффициент корреляции по абсолютной величине близок к единице, следовательно, степень линейной зависимости X и Y достаточно высока. Отрицательное значение коэффициента означает обратную линейную зависимость (с ростом одной из величин другая уменьшается, и наоборот).
4) Параметры линейной регрессии Y = aX + b определяются системой
В данном случае система имеет вид
и её решением будет a = -3.04212, b = 3.9251.
График случайной величины и функции линейной регрессии:
1) Вектор математического ожидания для выборки двумерной случайной величины определяем по стандартной формуле для выборочного среднего:
В данном случае для выборки длиной n = 44 имеем
и
2) Дисперсия также определяется по стандартным формулам:
либо
В данном случае
и
3) Выборочный коэффициент корреляции для двумерной случайной величины определяется выражением
В данном случае
и
Вычисленный коэффициент корреляции по абсолютной величине близок к единице, следовательно, степень линейной зависимости X и Y достаточно высока. Отрицательное значение коэффициента означает обратную линейную зависимость (с ростом одной из величин другая уменьшается, и наоборот).
4) Параметры линейной регрессии Y = aX + b определяются системой
В данном случае система имеет вид
и её решением будет a = -3.04212, b = 3.9251.
График случайной величины и функции линейной регрессии:
5
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