Задача 1. Не решаем.

Задача 2. Используя метод наименьших квадратов, найти параметры зависимости y = f(ax + b) во всех шести случаях, вычислить величины квадратических отклонений, для случая с наименьшим отклонением сделать рисунок.

Задача 3. Не решаем.

Задача 4. Не решаем.

Задача 5. 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 = aX + b. Сделать рисунок.

Вариант №1

Задача 1.

2.0 4.8 5.2 3.8 3.5 3.2 3.2 3.9 4.9 2.8 3.7 1.8 3.4 2.3 3.2 4.5 0.5 3.3 2.8 2.5 1.4 3.2 3.5 2.2 2.3 3.5 3.5 4.1 4.4 2.3 1.9 2.2 3.8 3.4 2.2 3.1 2.1 2.1 3.2 2.5 2.1 2.9 2.8 3.1 4.3 2.8 4.0 2.3 2.7 2.4 2.4 2.3 2.4 2.9 2.2 3.6 2.1 3.2 2.3 2.9 2.0 4.7 3.5 2.8 3.0 -0.2 3.6 3.1 3.3 1.4 2.6 2.6 1.8 4.3 1.8 0.7 4.6 3.0 1.9 3.7 3.2 2.6 2.6 4.2 2.9 2.3 5.4 3.3 3.1 2.8 2.7 2.7 1.8 2.8 4.6 2.7 1.4 3.9 3.7 2.5

Задача 2.

X 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0

Y 16.9 19.5 24.5 31.0 35.2 41.3 48.2 57.0 64.6 72.3

Задача 3.

γ = 0.95

18.3 15.5 24.5 24.7 18.0 13.3 15.4 10.1 23.1 19.3 5.7 11.6 14.3 -4.5 20.3 32.3

Задача 4.

 = 9, γ = 0.99

38.3 26.1 10.5 26.9 25.4 12.1 12.3 15.1 14.0 21.6 23.5 13.0 21.4 24.1 26.6 25.8 12.7 15.2 32.9 22.1 25.7 13.6 27.8 22.8 10.1 27.8 23.8 19.8 24.7 29.2 24.4 5.6 19.4 30.1 15.3 8.4 14.2 22.8 30.8 36.2 22.0 20.5 14.1 18.6 14.7 24.1 26.9 26.2 8.8 22.5 26.3 37.0 37.3 25.1 17.4 37.1 29.6 27.9 30.1 6.2 20.8 27.0 19.2 20.9 28.0 22.2 12.7 15.5 19.6 24.5 24.2 35.4 34.7 25.1 14.1 19.6 40.8 18.4 30.1 26.1 43.0 40.3 27.4 20.1 29.2 25.0 31.5 34.7 5.1 24.6 8.1 33.7 32.2 10.3 29.0 12.6 26.0 28.4 11.1 33.4

Задача 5.

(41.2, 116.5) (48.1, 124.6) (53.2, 153.9) (39.1, 99.0) (50.2, 191.6) (39.0, 94.9) (39.4, 100.2) (50.2, 178.6) ( 48.3, 118.7) (39.6, 117.0) (41.3, 81.7) (35.2, 88.0) (47.9, 159.4) (34.6, 124.4) (33.2, 103.4) (35.7, 94.9) (36.8, 90.8) (50.8, 180.5) (44.5, 152.0) (46.3, 167.6) (34.8, 84.6) (39.2, 124.5) (36.8, 131.7) (46.0, 99.8) (40.4, 144.8) (41.5, 120.6) (44.5, 109.7) (38.9, 93.5) (49.8, 136.8) (45.6, 107.6) (33.0, 102.9) (47.6, 102.9) (32.5, 116.7) (42.0, 134.0) (54.1, 157.9) (35.4, 109.1) (37.9, 92.4) (38.6, 120.7) (35.6, 96.1) (33.6, 73.2) (27.7, 61.5) (47.1, 95.0) (29.9, 82.8) (50.1, 110.5)

Вариант №2

Задача 1.

34.0 36.1 34.3 34.4 34.1 35.6 35.9 34.4 35.2 34.2 35.8 35.2 34.3 34.8 35.1 34.5 34.6 34.2 34.4 34.2 34.8 35.0 34.8 37.7 34.3 36.0 36.0 35.1 34.2 34.2 34.4 34.3 34.0 34.0 36.4 34.1 35.1 34.7 34.1 34.1 34.2 34.2 34.6 35.0 36.5 34.1 34.4 34.2 34.6 35.0 34.1 35.0 34.6 34.3 34.3 34.3 34.1 36.5 34.2 34.8 34.5 34.8 34.1 36.2 34.0 34.2 34.7 35.8 35.1 35.3 34.4 35.2 35.9 35.7 34.7 34.9 35.0 35.8 35.1 35.5 34.8 34.8 36.4 34.9 34.5 34.5 34.6 34.4 35.0 34.1 35.2 34.6 34.3 34.9 34.1 34.2 35.1 37.5 35.1 34.0

Задача 2.

X 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0

Y 1.1 0.7 3.1 6.9 19.8 55.2 147.4 404.2 1096.8 2981.5

Задача 3.

γ = 0.999

8.0 -1.1 13.5 10.0 2.4 4.1 20.0 12.4 13.4 4.8 7.8 0.0 10.9 13.7 6.6

Задача 4.

 = 7, γ = 0.99

13.4 8.6 22.1 2.3 14.6 13.0 11.1 29.4 23.3 1.7 13.6 2.1 21.6 6.1 8.6 6.6 16.0 11.6 16.6 1.6 15.8 18.9 10.6 11.9 0.1 10.7 3.8 -3.6 15.4 7.9 4.5 17.7 10.8 19.6 18.5 15.5 9.3 21.7 6.6 10.5 10.4 8.2 16.0 22.6 20.5 11.6 23.2 23.0 9.5 11.3 14.9 19.9 13.4 13.9 19.5 19.8 21.0 3.2 14.0 19.1 17.9 8.6 11.2 16.2 13.9 16.2 17.1 7.7 12.5 2.7 16.5 20.2 15.5 14.5 5.6 16.5 12.3 9.9 11.9 17.6 6.6 20.3 9.7 13.2 17.4 5.1 13.0 23.3 6.8 9.8 15.5 16.2 18.4 9.2 5.7 10.9 8.8 7.4 16.2 9.9

Задача 5.

(50.0, -92.8) (27.4, -49.5) (47.7,-105.8) (35.1, -67.0) (30.5, -55.7) (39.5, -67.3)

(54.8, -89.1) (57.3,-134.2) (43.0,-109.1) (43.7, -68.7) (34.6, -74.6) (47.2,-105.6)

(42.4,-106.2) (57.6,-164.1) (38.8, -59.7) (37.3, -81.7) (35.5, -67.2) (41.9,-119.3)

(23.0, -64.2) (45.3, -96.5) (51.5,-148.9) (50.9,-118.5) (58.6,-151.8) (33.6, -65.7)

(31.2, -83.0) (35.3, -68.9) (49.8, -87.0) (38.5, -58.9) (32.9, -71.8) (54.4,-103.4)

(39.3, -58.7) (46.0,-107.7) (25.0, -43.4) (31.6, -70.0) (29.0, -76.4) (27.4, -56.9)

(46.4,-111.0) (35.0, -71.5) (39.5,-104.4) (27.1, -47.6)