2 кореляція регрессия
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Для того, щоб обчислити X , X 2 будуємо таку таблицю, що є аналогом таблиці розподілу одновимірної дискретної випадкової величини :
xi |
1,0226 |
1,2918 |
1,561 |
1,8302 |
2,0994 |
2,3686 |
2,6378 |
2,907 |
3,1762 |
3,4454 |
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ni |
2 |
6 |
20 |
26 |
23 |
9 |
8 |
4 |
1 |
1 |
100 |
xi ni |
2,0452 |
7,7508 |
31,22 |
47,5852 |
48,2862 |
21,3174 |
21,1024 |
11,628 |
3,1762 |
3,4454 |
197,5568 |
xi2 |
1,0457 |
1,6687 |
2,4367 |
3,34964 |
4,4075 |
5,6103 |
6,9580 |
8,4506 |
10,0882 |
11,8708 |
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xi2 ni |
2,0914 |
10,0122 |
48,734 |
87,09064 |
101,3725 |
50,4927 |
55,664 |
33,8024 |
10,0882 |
11,8708 |
411,219 |
Тут першій рядок – вибіркові значення, а другій – частоти, з якими ці значення зустрічаються в вибірки. В останньому стовпчику записуємо суму
всіх елементів по рядочку. Тоді X , X 2 , s( X ) обчислюємо за формулами
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xi ni , |
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X 2 |
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xi2 ni , |
D( X ) X 2 (X |
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N i 1 |
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1,9756 , |
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X 2 |
4,1122 |
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)2 3,9030 , |
D(X ) 0,2092 , s(X ) 0,4574 |
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Аналогічно, для того, щоб обчислити |
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Y 2 |
будуємо таку таблицю, |
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y j |
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0,5475 |
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0,6825 |
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0,8175 |
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0,9525 |
1,0875 |
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1,2225 |
1,3575 |
1,4925 |
1,6275 |
1,7625 |
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25 |
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100 |
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yj |
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mj |
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0,5475 |
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3,4125 |
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20,4375 |
21,9075 |
26,1 |
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15,8925 |
6,7875 |
1,4925 |
3,255 |
1,7625 |
101,595 |
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y2j |
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0,2998 |
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0,46588 |
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0,66838 |
0,9073 |
1,1827 |
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1,4945 |
1,8428 |
2,2276 |
2,6488 |
3,106 |
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0,2998 |
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2,3290 |
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16,7077 |
20,8669 |
28,3837 |
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19,4286 |
9,21405 |
2,2276 |
5,2975 |
3,1064 |
107,8612 |
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Y 1 yj mj , |
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Y 2 1 y2j mj , |
D(Y ) Y 2 (Y )2 , s(Y ) D(Y ) |
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)2 1,0321, D(Y ) 0,0465 , s(Y ) 0,2156 |
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1,0159 , |
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Y 2 |
1,0786 , |
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(Y |
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21
Порівняння обчислених наближених значень, яки отримані за допомогою згрупованих даних , з тими що обчислені безпосередньо з вибіркових значень, показує, що вони співпадають з достатньою точністю :
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Y |
D(X ) D(Y ) |
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Вибіркові дані |
1,9800 |
0,9932 |
0,2096 |
0,0474 |
Згруповані дані |
1,9756 |
1,0159 |
0,2092 |
0,0465 |
Для обчислення XY будуємо таблицю, яку отримуємо з Таблиці 1, в кожну не порожню клітинку якій записуємо добуток xi y j nij ,
Y \ X |
1,0226 |
1,2918 |
1,561 |
1,8302 |
2,0994 |
2,3686 |
2,6378 |
2,907 |
3,1762 |
3,4454 |
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1,7625 |
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6,072 |
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1,6275 |
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4,731 |
5,169 |
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1,4925 |
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4,339 |
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1,3575 |
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5,700 |
3,215 |
3,581 |
3,946 |
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1,2225 |
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4,475 |
7,699 |
14,478 |
9,674 |
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1,0875 |
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6,790 |
11,942 |
20,548 |
5,152 |
8,606 |
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0,9525 |
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7,434 |
15,689 |
13,998 |
2,256 |
2,512 |
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0,8175 |
0,836 |
2,112 |
12,761 |
13,466 |
3,432 |
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2,376 |
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0,6825 |
0,698 |
2,645 |
1,065 |
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0,5475 |
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0,707 |
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1,534 |
5,464 |
28,051 |
45,572 |
51,377 |
25,101 |
24,373 |
15,392 |
5,169 |
6,072 |
208,108 |
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В останньому рядку обчислюємо суму по стовпчику, а потім знаходимо суму чисел з останнього рядка.
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X Y |
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xi y jnij 2,0811 |
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Зараз є все необхідне для обчислення коефіцієнта кореляції і рівнянь регресії.
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2,0811 1,9756 1,0159 |
0,7515 |
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0,4574 0,2156 |
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X 2 |
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Y 2 |
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22
ВИСНОВОК : Виходячи з обчисленого вибіркового коефіцієнта кореляції
можна припускати наявність сильної додатної лінійної залежності між випадковими величинами, вибірка з яких досліджується.
Для порівняння наведемо значення вибіркового коефіцієнта кореляції, який був обчислений безпосередньо з вибіркових даних без розбиття на групи:
0,7676 - як видно, точність достатня для більшості практичних досліджень.
Рівняння регресії Y по X буде таким :
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(x |
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y 1,0159 2,0811 1,9756 1,0159 (x 1,9756) |
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XY |
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s( X )2 |
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0,2092 |
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y 1,0159 0,3542(x 1,9756) |
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y 0,3542x 0,3161 |
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Відповідно, рівняння регресії X по Y буде таким : |
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2,0811 1,9756 1,0159 ( y 1,0159) |
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XY |
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s(Y )2 |
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x 1,9756 1,5935 ( y 1,0159) ; |
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y 0,6275x 0,2238 |
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Для порівняння наведемо рівняння регресії, яки були обчислені безпосередньо з вибіркових даних без розбиття на групи:
y 0,3651x 0,2703 ; y 0,6196x 0,2338
За результатами обчислень будуємо графіки прямих регресії на тому самому малюнку, де зображено поле кореляції ( якщо ви маєте такий малюнок ).
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Якщо малюнку, на якому зображені всі вибіркові дані, немає , то графіки прямих регресії будуємо на малюнку, на якому зображений прямокутник з клітинками, в яких вказані частоти.
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4. ВАРИАНТИ ЗАВДАНЬ ДЛЯ САМОСТІЙНОГО ВИКОНАННЯ
Вариант 1
[[5.984, -5.944], [10.46, -49.63], [3.637, -13.49], [13.45, -25.91], [13.32, -6.398], [3.816, -15.08], [3.938, -11.60], [.8208e-1, -2.236],[1.897, -5.060], [2.787, -6.410], [11.14, -33.89], [12.81, -21.06], [8.471, -24.25], [7.360, -17.14], [2.206, -4.280], [8.039, -22.00], [9.542, -12.31], [.1515, -2.383], [.3613, -3.402], [13.83, -19.63], [4.871, -14.42], [13.34, -17.80], [13.48, -32.01], [.9388, -2.022], [9.233, -15.18], [4.509, -14.68], [13.80, -35.99], [12.40, -43.13], [11.56, -28.65], [4.918, -10.94], [7.826, -5.096], [10.32, -31.65],[7.458, -27.03], [.4535, -1.892], [5.100, -10.60], [8.690, -22.45],[3.487, -.8170], [10.44, -28.84],[2.622, -4.933],[3.648, -.9178], [4.792, -13.60], [12.20, -1.235], [11.67, -23.11], [2.768, -3.098],[5.509, -18.69], [9.569, -15.40], [12.13, -30.03], [4.371, -7.239],[.4987, -.5080], [8.336, -15.58], [13.29, -44.62], [13.66, -21.66],[7.220, -22.29], [4.945, -8.516], [.3931, -1.209], [11.93, -13.26], [3.480, -9.988], [7.084, -4.939], [10.37, -7.554], [9.383, -33.95], [5.180, -19.97], [11.22, -11.73], [1.964, -3.585], [11.62, -29.34],[3.665, -7.838], [7.512, -7.884], [4.591, -4.235], [1.673, -6.036],[6.649, -21.96], [1.628, -4.906], [.5754e-1, -1.538], [4.351, -2.907], [6.068, -8.690], [.4140e-1, -1.045],
[4.099, -8.444], [13.93, 3.231],[2.827, -4.645], [10.35, -37.20], [6.663, -11.59], [1.070, -4.278],[12.71, -13.18], [4.770, -12.50], [5.477, -12.80],[7.591, -24.77] , [.9094, -3.084], [6.497, -22.78], [11.14, -19.10], [3.206, -11.21],[10.51, -21.49], [.3444, -2.629], [8.018, -9.829], [8.306, -4.032],[3.395, -7.178], [7.861, -20.91], [7.305, -11.78], [3.310, -7.637],[7.202, -15.28], [2.393, -8.905], [8.886, -13.37], [6.804, -19.74]]
Вариант 2
[[3.787, -8.116], [13.66, -25.39], [3.122, -6.376], [6.490, -16.06], [9.282, -27.65], [.5268, -2.738], [6.514, -21.26], [5.179, -21.17], [.6895, -2.837], [5.334, -17.41], [9.180, -26.04], [2.698, -5.884], [9.213, -12.84], [11.90, -14.42], [8.998, -18.66], [1.044, -3.689], [9.050, -16.01], [6.308, -23.29], [4.110, -9.828], [7.486, -12.58], [11.67, -38.60], [4.012, -7.454], [8.127, -5.906], [2.659, -3.644], [6.174, -9.911], [13.53, -21.27], [12.04, -14.71], [9.958, -25.22], [7.192, -19.55], [2.757, -7.183], [10.26, -17.74], [12.07, -28.69], [10.90, -22.96], [13.38, -41.89], [5.173, -12.80], [11.14, -21.50], [6.902, -24.12], [10.05, -14.16], [4.704, -24.52], [10.59, -23.48], [3.697, -7.948], [6.539, -21.03], [11.04, -16.97], [10.39, -15.98], [2.885, -4.389], [12.28, -17.29], [12.07, -31.73], [6.300, -22.20], [7.643, -17.35], [8.823, -11.13], [.2334, -.9206], [11.80, -27.66], [13.28, -15.93], [13.98, -18.50], [12.97, -26.43], [13.50, -42.02], [5.977, -5.689], [13.45, -29.00], [13.29, 1.220], [4.365, -20.39], [3.944, -10.59], [7.822, -19.58], [12.43, -30.68], [6.723, -23.55], [13.73, -57.82], [10.55, -24.10], [11.53, -21.08], [2.598, -6.232], [.6920, -3.085], [2.540, -3.534], [12.35, -30.00], [3.170, -5.615], [4.312, -9.124], [10.09, -17.63], [2.897, -10.72], [8.397, -31.42], [3.256, -6.120], [7.924, -21.45], [12.35, -30.55], [10.70, -26.58], [1.395, -4.391], [3.661, -8.173], [12.36, -33.40], [1.474, -4.783], [10.45, -6.997], [5.565, -10.37], [12.00, -29.39], [12.09, -29.29], [10.40, -23.38], [.6488, -2.494], [4.789, -8.954], [2.702, -2.327], [2.772, -6.939], [.3972, -2.559], [2.240, -3.381], [2.026, -8.115], [9.689, -17.23], [7.986, -10.29], [10.71, -29.80], [10.94, -25.49]]
25
Вариант 3
[[5.914, -12.91], [11.01, -13.84], [12.02, -45.48], [.7620, -1.422], [12.15, 4.542], [8.392, -18.29], [8.284, -14.21], [1.429, -5.545], [11.40, -31.03], [1.602, -1.575], [10.44, 14.63], [1.900, -7.591], [9.845, -22.77], [14.00, -20.57], [7.071, -13.29], [.9559, -3.604], [3.602, -7.104], [7.158, -14.97], [8.918, -21.73], [4.011, -12.73], [5.757, -10.42], [13.54, -34.31], [.1011, -.4389], [10.37, -27.13], [10.86, -33.23], [4.197, -14.55], [11.94, -44.85], [5.026, -10.08], [2.523, -4.587], [5.445, -11.26], [10.18, -29.03], [10.06, -19.63], [7.767, -8.860], [8.296, -19.47], [12.63, -12.01], [2.066, -5.081], [10.06, -22.63], [4.658, -5.817], [1.469, -2.781], [.2905, -1.397], [4.346, -9.421], [12.45, -25.29], [5.757, -5.343], [9.397, -19.34], [6.808, -2.062], [4.159, -11.30], [.6934, -.8287], [3.605, -13.92], [7.721, -13.62], [3.874, -5.834], [7.133, -9.145], [5.229, -8.209], [13.01, -24.46], [6.518, -25.90], [13.40, -37.06], [12.91, -45.27], [8.201, -35.86], [10.45, -38.61], [4.200, -7.312], [1.232, -3.499], [4.612, -14.40], [11.44, -25.58], [13.70, -21.46], [11.10, -32.45], [.8463, -2.498], [2.050, -2.610], [3.241, -9.068], [7.052, -15.72], [10.20, -22.92], [6.479, -14.93], [10.52, -30.09], [.9013, -1.338], [5.037, -6.896], [11.20, -38.84], [6.696, -14.46], [1.802, -3.459], [2.369, -9.200], [2.864, -7.947], [11.32, -8.689], [2.076, -8.978], [1.502, -1.118], [13.38, -28.67], [1.991, -2.042], [9.625, -19.69], [7.259, -14.87], [9.652, -24.92], [9.517, -28.46], [1.968, -5.738], [5.398, -10.89], [2.730, -10.29], [3.872, -9.642], [13.35, -20.22], [10.38, -25.72], [8.366, -16.09], [5.680, -10.76], [2.234, -6.523], [.8396, -3.025], [6.516, -20.35], [3.982, 1.093], [11.69, -41.79]]
Вариант 4
[[8.270, -10.23], [1.569, -1.580], [.9722, -2.977], [1.053, -2.590], [4.955, -1.339], [5.712, -14.75], [7.694, -15.32], [7.435, -10.46], [3.707, -4.357], [4.252, -9.555], [9.836, -26.69], [13.42, -6.459], [5.306, -16.53], [12.96, -37.42], [8.719, -12.26], [7.998, -15.50], [2.929, -5.825], [8.505, -18.63], [8.966, -24.35], [2.275, -7.699], [6.325, -.9731], [9.486, -31.39], [5.097, -9.931], [7.549, -16.61], [11.84, -22.35], [7.496, -22.13], [13.94, -22.94], [5.067, -13.68], [3.606, -10.59], [13.41, -32.28], [6.257, -7.602], [3.783, -12.54], [2.031, -4.984], [9.996, -17.39], [6.618, -15.21], [6.521, -15.93], [10.55, -27.50], [1.704, -3.610], [7.700, -26.99], [3.987, -3.063], [9.857, -23.38], [2.267, .1793], [4.565, -5.875], [11.46, -26.75], [8.911, -22.36], [9.400, -19.48], [10.39, -18.32], [2.951, -4.943], [7.304, -5.519], [4.773, -12.48], [6.803, -13.69], [5.293, -10.15], [9.276, -22.78], [6.783, -24.91], [9.132, -29.21], [13.76, -22.03], [9.024, -16.87], [3.877, -8.734], [13.92, -12.20], [9.390, -25.32], [5.113, -8.553], [8.813, -23.85], [12.95, -15.22], [13.41, -26.14], [.9605e-1, -.9828], [3.388, -14.09], [2.712, -3.734], [10.66, -23.03], [.3494, -1.299], [2.002, -5.403], [.6822e-1, -.6879], [10.49, -29.00], [4.533, -10.42], [.5428, -1.917], [6.987, -22.38], [6.555, -12.51], [10.50, -11.65], [7.689, -9.059], [6.579, -5.380], [7.629, -24.20], [2.453, -3.655], [6.780, -16.80], [.2006, -.6639], [2.715, -7.970], [11.02, -23.47], [6.346, -12.22], [11.01, -3.771], [11.45, -2.676], [8.471, -34.93], [2.293, -6.114], [.9388, -1.633], [2.943, -8.784], [4.075, -5.502], [6.973, -9.229], [13.69, -46.44], [.1516, -.6305], [11.34, -20.66], [7.410, -27.44], [13.50, -10.29], [13.21, -4.442]]
26
Вариант 5
[[.3424, -1.044], [11.70, -31.19], [7.749, -17.94], [1.442, -2.698], [8.627, -10.23], [10.75, -13.77], [6.023, -11.34], [11.46, 4.274], [12.52, -35.83], [5.582, -5.765], [12.32, 3.924], [10.83, -30.57], [5.124, -4.654], [13.75, -26.05], [12.21, -24.22], [6.139, -17.86], [12.99, -34.42], [13.27, -21.38], [8.817, -17.71], [10.79, -23.51], [13.86, -42.17], [3.389, -13.75], [5.628, -25.00], [2.234, -6.264], [8.480, -12.03], [5.872, -15.29], [10.34, -32.48], [9.052, -31.08], [.6455, -.3677], [2.635, -8.658], [12.16, -26.47], [13.24, -35.07], [7.270, -10.28], [.8817, -3.497], [9.394, -31.89], [12.43, -35.88], [5.216, -7.345], [10.62, -14.75], [.5488, -.6132], [8.575, -14.06], [9.933, -8.551], [12.63, -21.01], [12.76, -1.560], [12.05, -26.88], [6.632, -10.09], [.6912, -1.972], [3.948, -2.067], [13.00, -12.96], [12.48, -20.28], [4.869, -19.48], [8.098, -15.18], [.9526, -3.167], [1.481, -.3637], [6.748, -4.254], [7.778, -5.512], [10.30, -32.43], [12.35, -14.43], [4.855, -7.906], [13.56, -55.08], [5.984, -7.675], [2.433, -8.235], [5.300, -17.20], [11.01, -22.40], [8.246, -18.32], [1.155, -1.178], [.8329, -2.378], [8.690, -25.24], [5.678, -16.26], [.3830, -.5389], [5.912, -20.70], [7.830, 8.280], [10.09, -12.49], [9.625, -24.91], [13.36, -1.485], [9.034, -24.61], [8.862, -27.15], [7.216, -2.083], [9.901, -12.55], [5.883, -16.67], [5.229, -6.447], [13.12, -32.05], [13.62, -18.56], [7.704, 1.307], [.8889, -.8836], [12.30, 5.450], [3.095, -5.567], [5.972, -20.57], [3.730, -11.60], [5.306, -8.808], [2.754, -4.873], [13.66, -30.85], [13.59, -1.486], [5.610, -15.27], [13.32, -26.95], [12.06, -1.263], [9.023, -18.13], [12.98, -18.81], [5.684, -10.25], [6.229, -.3319], [7.584, -14.11]]
Вариант 6
[[5.677, -11.76], [12.50, -52.84], [9.297, -27.90], [2.719, -5.940], [11.85, -29.31], [11.45, -20.69], [3.690, -3.554], [12.59, -5.724], [9.572, -1.506], [8.040, -21.74], [8.709, -13.51], [3.991, -3.221], [8.532, -3.553], [2.703, -3.665], [3.868, 3.426], [8.469, -30.85], [12.81, -31.53], [.7473, -2.847], [2.115, -4.621], [8.424, -22.49], [13.03, -47.79], [6.086, -14.80], [8.844, -28.46], [3.259, -1.839], [1.614, -4.742], [9.125, -14.07], [4.799, -13.89], [11.76, -18.50], [6.322, -11.31], [1.314, -2.609], [9.489, -35.48], [6.202, -15.21], [11.56, -28.48], [10.23, -17.59], [9.412, -16.45], [7.311, -19.28], [9.148, -15.85], [11.92, -12.32], [3.769, -8.570], [6.161, -8.694], [8.649, -26.59], [3.842, -4.791], [8.530, -19.14], [6.233, -7.277], [7.839, -10.25], [11.13, -26.23], [6.047, -18.33], [3.689, -13.37], [11.74, -43.22], [13.89, -36.91], [13.48, -28.97], [13.59, -31.76], [9.978, -6.487], [2.636, -6.582], [1.428, -.7755], [.2614e-1, .3322], [.7375, -1.168], [11.23, -26.38], [2.678, -3.505], [7.221, 2.893], [6.588, -16.35], [.7536e-1, -.2886], [11.27, -20.27], [5.715, -14.53], [7.986, -23.56], [.1681, -.901e-1], [.2058e-1, -.2281e-1], [2.848, -4.912], [3.401, -13.77],
[6.649, -34.92], [7.435, -18.33], [6.464, -6.887], [12.98, -44.64], [9.449, -15.19], [10.23, -24.47], [11.72, -24.08], [.1847, -.6558], [10.16, -21.60], [8.519, -23.37], [2.696, -8.081], [1.245, -.4395], [9.807, -3.381], [1.443, -4.719], [11.05, -25.28], [9.320, -20.36], [6.434, -20.29], [4.645, -7.943], [11.61, -30.89], [10.12, -28.31], [11.14, -18.08], [7.106, -12.58], [2.670, -3.600], [1.681, -4.471], [5.970, -9.802], [5.442, -4.379], [11.08, -12.21], [2.187, -3.764], [3.242, -7.832], [3.044, 3.099], [9.591, -9.151]]
27
Вариант 7
[[3.119, -5.191], [12.08, -14.82], [5.751, -5.247], [11.08, -15.50], [9.864, -18.51], [13.46, -37.96], [8.924, -20.48], [7.259, -20.33], [3.287, -6.367], [10.82, -38.48], [12.85, -34.80], [10.83, -4.922], [7.053, -19.64], [11.55, -31.10], [10.51, -3.583], [9.335, -23.46], [6.391, -17.53], [9.446, -24.87], [10.20, -15.96], [9.915, -30.28], [12.62, -27.69], [10.22, -29.08], [7.365, .1731], [12.67, -24.37], [10.68, -20.68], [9.482, -17.06], [12.34, -38.34], [13.05, -11.01], [3.046, -8.513], [7.977, -20.74], [5.716, -15.12], [10.41, -26.32], [9.418, -14.61], [2.645, -10.37], [1.498, -1.730], [5.739, -9.691], [9.003, -11.16], [10.10, -35.86], [13.70, -56.97], [5.811, -13.13], [3.563, -8.028], [7.470, -11.58], [9.612, -34.84], [2.240, -2.061], [2.311, -6.671], [9.523, -8.532], [11.33, -25.50], [11.49, -35.58], [8.117, -5.918], [5.580, -8.340], [.2397e-1, .9221], [.9152, -2.694], [13.65, -34.25], [8.371, -17.96], [13.92, -28.04], [12.08, -26.46], [.1483e-1, .7842], [12.57, -18.76], [7.335, -10.99], [9.409, -12.71], [2.013, -5.011], [9.659, -13.90], [2.853, -8.240], [11.07, -29.83], [5.802, -22.84], [7.966, -3.957], [11.07, -6.704], [13.89, -29.64], [11.07, -19.17], [12.65, -21.71], [9.771, -31.82], [10.90, -18.67], [10.06, -19.14], [8.828, -27.30], [4.753, -6.930], [5.229, -2.198], [10.09, -18.33], [9.192, 5.322], [13.05, -2.868], [9.232, -9.553], [6.997, .68e-2], [6.516, -7.657], [11.02, -28.48], [10.91, -10.56], [2.022, -4.922], [7.011, -19.73], [4.606, -7.973], [7.634, -17.48], [5.579, -7.427], [5.229, -14.39], [3.403, -10.85], [6.360, -11.27], [2.626, -8.123], [12.01, -25.27], [3.216, -9.187], [2.730, -2.213], [2.857, -1.866], [.2920, -.487e-1], [4.360, -6.259], [7.784, -5.073]]
Вариант 8
[[4.490, -16.58], [1.589, -2.927], [2.465, -12.36], [11.64, 9.626], [9.264, -18.81], [11.87, -45.31], [3.961, -10.66], [4.493, -10.21], [7.507, -7.584], [5.600, -3.619], [11.74, -12.28], [12.04, -27.79], [4.402, -6.633], [3.654, -9.538], [9.442, -6.706], [12.40, -28.07], [2.332, -3.625], [6.621, -14.95], [4.396, -.9722], [12.25, -28.47], [4.067, -8.425], [9.635, -35.22], [3.170, .2775], [1.730, -3.888], [13.67, -54.83], [5.208, -6.757], [8.238, -8.674], [4.420, -9.513], [13.35, -17.25], [10.08, -14.11], [7.626, -12.96], [6.759, -.9700], [8.196, -12.11], [.2192, .1806], [7.393, -11.76], [12.02, -11.90], [13.26, -33.45], [9.594, -20.94], [6.392, -16.86], [12.20, -42.10], [11.59, -2.190], [7.045, -16.25], [4.085, -4.564], [1.919, -6.468], [7.323, -21.58], [7.673, -24.19], [13.86, -33.03], [6.206, -23.49], [3.122, -3.567], [1.103, .2812], [9.667, -34.71], [4.291, -.6480], [12.36, -38.32], [6.397, -6.875], [2.080, .2662], [9.486, -22.10], [11.76, -28.88], [13.36, -27.64], [13.46, -40.85], [.1646, .3517], [6.451, -.5065], [8.021, .8057], [12.87, -16.82], [9.229, -1.993], [9.373, -11.37], [10.96, -34.07], [8.599, -28.55], [4.913, -10.85], [4.857, .9574], [5.957, -13.21], [13.40, -31.84], [10.76, -8.509], [9.860, 5.561], [3.016, -4.471], [8.966, -18.54], [.4603, -.4743], [11.03, -26.52], [11.96, -41.55], [6.497, .382e-1], [11.65, -11.29], [8.603, -32.11], [8.469, .7559], [8.408, 2.345], [8.301, -1.550], [12.41, -41.63], [8.259, -13.13], [8.509, -16.05], [9.936, -25.25], [12.30, -25.92], [12.67, -5.470], [7.615, -12.16], [13.25, -26.92], [8.002, -15.53], [9.957, -15.57], [1.513, -2.173], [11.23, -19.96], [12.35, -17.04], [4.267, -11.18], [.5516, -1.099], [10.90, -34.24]]
28
Вариант 9
[[1.544, -.1610], [9.341, -38.52], [7.116, -23.14], [.9524, 1.001], [2.215, -6.732], [8.477, -18.30], [8.288, -6.395], [13.71, -41.41], [1.257, -.498], [13.27, -38.29], [2.736, -4.901], [8.938, -6.967], [8.002, -12.57], [13.54, -12.15], [11.11, -36.41], [4.876, -17.83], [6.124, -17.44], [.7109, .256], [.9237, -1.925], [.1520, .9495], [11.81, -27.27], [3.528, -2.810], [13.51, -33.46], [3.872, .108], [9.913, 3.455], [3.273, -6.741], [12.43, -30.52], [11.77, -5.531], [12.81, -13.24], [8.638, -23.69], [13.90, -43.49], [10.26, -13.88], [12.18, -22.54], [4.010, -6.033], [.5551, .7668], [10.31, -19.88], [13.43, -33.13], [8.820, -23.23], [9.864, -32.39], [4.739, -9.480], [8.074, -26.87], [4.747, -.975], [12.95, -17.38], [8.617, -17.56], [7.777, -3.451], [5.978, -17.04], [6.549, -11.41], [13.19, -27.19], [1.173, -2.144], [.8456, -.624], [13.31, -14.38], [7.804, -21.69], [11.03, -11.90], [11.65, -27.38], [3.674, -12.86], [9.213, -1.228], [9.351, -3.171], [9.950, -10.05], [.9856, -1.184], [13.28, -17.44], [13.80, -20.73], [5.683, -5.819], [3.343, -3.094], [9.762, -13.36], [6.562, -17.03], [11.15, -19.14], [2.954, -7.112], [.2258, .7062], [7.339, -6.410], [2.127, -2.309], [3.293, -5.432], [3.150, .9598], [5.516, -9.203], [3.630, -3.420], [.3710, 1.053], [12.59, -27.76], [5.362, -13.56], [10.56, -20.46], [13.35, -24.78], [8.414, -17.63], [2.446, -2.173], [7.545, 9.505], [5.932, -9.759], [7.896, -13.15], [7.778, -22.89], [.5376e-1, 1.015], [5.838, -18.14], [7.710, -16.44], [5.827, -10.29], [8.873, -14.44], [.2925, .8296], [1.462, -.500], [3.938, -1.805], [5.104, -8.312], [9.267, -21.30], [5.474, -15.05], [4.932, -4.269], [11.00, -16.32], [13.72, -11.02], [5.886, -7.906]]
Вариант 10
[[8.358, -14.07], [12.95, -37.85], [1.824, -1.610], [6.730, -32.39], [3.765, -2.543], [2.409, -7.381], [13.39, -16.04], [.2855, 1.175], [12.94, -36.73], [8.866, -22.18], [12.47, -19.41], [1.943, -.497], [11.91, -16.42], [5.421, -13.18], [10.21, -26.31], [13.81, -15.24], [.1418, .7775], [4.458, -5.718], [9.845, -14.88], [6.633, -8.081], [6.733, -21.90], [10.95, -36.98], [7.868, -18.32], [1.568, -1.689], [2.773, -3.616], [11.08, -15.23], [7.832, -22.35], [1.557, -5.144], [4.017, -13.41], [9.306, -23.47], [9.653, -19.85], [7.431, -11.59], [13.92, -36.01], [4.567, -12.28], [.6707e-2, 1.019], [13.16, -39.82], [1.066, -2.212], [3.633, -3.270], [2.986, -3.930], [13.58, -19.88], [5.600, -8.470], [12.56, -46.79], [7.836, -23.41], [1.338, 1.316], [7.458, -11.61], [9.073, -29.07], [8.443, -5.498], [11.60, -36.94], [6.915, -14.50], [10.57, -27.81], [5.995, -15.03], [9.076, -26.27], [4.143, -10.98], [3.051, -7.495], [7.612, -.314], [5.705, -14.73], [.8240, -.833], [2.590, -1.084], [.9692, -.894e-1], [5.968, -13.47], [10.56, -33.19], [10.37, -6.204], [2.141, -.922], [3.864, -6.533], [12.56, -28.64], [10.23, -32.52], [4.351, -8.753], [7.868, -16.41], [10.41, -32.09], [11.02, -17.32], [4.834, .281e-1], [4.644, -11.50], [3.916, -4.826], [1.368, -2.985], [6.555, -21.22], [5.754, -2.944], [10.58, -22.20], [7.811, -21.17], [7.066, -15.10], [12.23, -17.98], [12.13, -16.53], [3.237, -3.547], [.1338, .5888], [13.30, -17.19], [5.138, -6.023], [10.63, -18.98], [9.022, -18.91], [8.988, -3.383], [3.927, 1.747], [.5513, -.5655], [1.036, -3.079], [10.11, -23.30], [7.781, -5.269], [5.505, -14.36], [13.74, -43.60], [3.654, -12.21], [4.327, -.8837], [12.99, -31.25], [8.341, -13.15], [11.67, -40.45]]
29
Вариант 11
[[6.514, -10.66], [3.452, -6.196], [2.933, -2.584], [13.39, -14.00], [7.263, -4.692], [4.673, -6.931], [12.36, .659], [9.360, -13.60], [10.59, -5.781], [5.286, -3.167], [10.47, -10.83], [12.97, -12.92], [3.567, -5.845], [13.36, -14.79], [5.055, -3.923], [12.00, -21.26], [2.689, -4.612], [.6891, -2.182], [.2684, -2.321], [1.910, -2.882], [11.58, -16.81], [9.764, -5.577], [2.631, -5.446], [8.641, -9.116], [12.83, -26.99], [5.508, -3.680], [3.475, .2014], [2.698, -4.570], [.9198, -2.212], [10.78, -13.06], [3.893, 1.190], [10.61, -8.531], [12.39, -14.71], [1.183, -1.748], [1.311, -2.199], [6.236, -6.129], [1.456, -2.698], [10.61, -17.26], [3.892, -3.279], [10.31, -12.59], [.1053, -1.600], [4.381, -7.197], [5.852, -7.373], [10.35, -14.60], [10.41, -17.86], [1.464, -3.094], [1.694, -2.216], [2.447, -2.800], [5.271, -4.924], [10.51, -13.91], [12.53, -11.52], [2.986, -4.128], [7.430, -9.525], [10.93, -13.82], [11.92, -20.94], [.1005, -1.652], [6.287, -4.389], [.8313, -2.710], [3.017, -6.895], [5.621, -9.095], [11.48, -13.44], [10.91, -24.16], [10.59, -9.508], [1.996, -2.448], [3.199, -4.548], [.3189, -1.767], [7.715, -9.972], [9.667, -7.885], [2.611, -4.363], [8.088, -11.79], [5.859, -1.430], [11.39, -11.67], [1.463, -2.743], [11.78, -17.04], [1.292, -4.139], [8.145, -10.26], [1.814, -4.024], [5.747, -5.341], [9.923, -9.143], [6.831, -9.030], [.1079, -1.682], [7.197, -6.552], [4.014, -5.180], [5.047, -9.100], [5.480, -4.103], [9.807, -10.62], [.7486e-1, -1.163], [11.70, -8.286], [11.73, -13.95], [5.170, -8.719], [13.59, -16.65], [4.708, -3.691], [11.19, -12.27], [9.856, -9.657], [7.412, -13.79], [13.79, -23.75], [1.623, -3.365], [1.293, -3.245], [3.672, -7.325], [4.455, -5.414]]
Вариант 12
[[13.37, -9.428], [8.029, -9.086], [10.05, -3.567], [13.65, -19.01], [8.579, -16.33], [11.55, -13.41], [10.11, -16.90], [7.904, -8.254], [13.48, -15.09], [10.59, -21.39], [9.297, -12.90], [13.15, -.8200], [2.999, -5.855], [.3269, -.7809], [5.660, -9.900], [3.482, -3.497], [5.130, -5.746], [12.90, -7.293], [4.217, -4.030], [2.388, -1.507], [8.354, -8.712], [12.39, .853], [12.37, -1.865], [12.70, -24.03], [1.383, -3.608], [11.39, -19.45], [7.084, -13.42], [5.165, -3.526], [7.755, -3.594], [3.948, -3.409], [1.606, -4.464], [3.360, -5.393], [.1963, -.9934], [5.190, -4.377], [2.374, -5.318], [4.922, -1.547], [1.101, -1.978], [.9358, -1.679], [2.677, -4.695], [13.90, -11.16], [9.054, -5.913], [13.66, -13.66], [7.314, -6.455], [10.57, -9.417], [8.921, -9.649], [7.760, -8.635], [1.604, -3.236], [6.874, -9.356], [3.378, -4.245], [7.900, -6.457], [2.491, -2.950], [11.35, -2.982], [4.129, -4.157], [11.07, -11.50], [4.518, -7.504], [1.758, -4.091], [12.67, -11.51], [4.547, -4.737], [2.719, -2.256], [13.97, -8.412], [2.111, -3.587], [10.24, -8.323], [12.46, -20.89], [2.573, -4.673], [11.09, -16.69], [.9527, -2.430], [3.755, -9.353], [7.662, -11.14], [1.709, -4.158], [10.87, -11.35], [4.837, -4.379], [2.628, -3.503], [6.742, -4.170], [9.019, -6.509], [4.339, -4.432], [2.817, -.3823], [11.24, -12.52], [12.03, -19.88], [8.831, -14.35], [9.751, -6.471], [.3262, -1.266], [.6266, -1.571], [11.12, -9.994], [2.202, -2.103], [12.93, -11.89], [5.212, -5.298], [.8133, -1.977], [3.132, -6.235], [11.06, -16.06], [7.676, -3.798], [12.79, -4.978], [5.419, -3.618], [7.860, -5.996], [4.364, -8.507], [4.263, -2.314], [8.823, -7.349], [8.023, -7.435], [1.422, -1.338], [2.639, -4.772], [9.222, -13.01]]
30