Контрольная работа: Эконометрика
3041
42931
624261
>> format long
>> a\b
ans =
70.030968707669246
-8.789656532559803
1.130190950098223
Таким образом, a=70.030968707669246
b= -8.789656532559803
c=1.130190950098223
Уравнение аппроксимирующей параболы 
| X | Y |  |  |  |  | |
| 1 | 12 | 130 | 127.30 | 0.02 | 7.28 | 903.16 |
| 2 | 13 | 170 | 146.77 | 0.14 | 539.74 | 98.95 |
| 3 | 12 | 110 | 127.30 | 0.16 | 299.38 | 2505.27 |
| 4 | 11 | 121 | 110.10 | 0.09 | 118.86 | 1525.11 |
| 5 | 15 | 130 | 192.48 | 0.48 | 3903.64 | 903.16 |
| 6 | 12 | 120 | 127.30 | 0.06 | 53.33 | 1604.21 |
| 7 | 11 | 110 | 110.10 | 0.00 | 0.01 | 2505.27 |
| 8 | 8 | 70 | 72.05 | 0.03 | 4.19 | 8109.48 |
| 9 | 12 | 140 | 127.30 | 0.09 | 161.22 | 402.11 |
| 10 | 12 | 120 | 127.30 | 0.06 | 53.33 | 1604.21 |
| 11 | 13 | 150 | 146.77 | 0.02 | 10.45 | 101.06 |
| 12 | 12 | 120 | 127.30 | 0.06 | 53.33 | 1604.21 |
| 13 | 14 | 200 | 168.49 | 0.16 | 992.68 | 1595.79 |
| 14 | 13 | 130 | 146.77 | 0.13 | 281.16 | 903.16 |
| 15 | 15 | 240 | 192.48 | 0.20 | 2258.24 | 6391.58 |
| 16 | 16 | 200 | 218.73 | 0.09 | 350.64 | 1595.79 |
| 17 | 17 | 290 | 247.23 | 0.15 | 1829.10 | 16886.32 |
| 18 | 18 | 290 | 278.00 | 0.04 | 144.02 | 16886.32 |
| 19 | 17 | 200 | 247.23 | 0.24 | 2230.86 | 1595.79 |
| 253 | 3041 | 2.21 | 13291.44 | 67720.95 |
r 
= 0.88
r > 0, следовательно, связь прямая.
|r|>0.65 – связь тесная
= 11.65%
= 0.90
Поскольку 
>r, то кривая лучше аппроксимирует зависимость
3. Логарифмическая зависимость
y = a + b lnx
После замены lnx=z получим линейную зависимость, формулы для вычисления коэффициентов которой известны. После обратной замены получим:
| lnX | Y | lnXY | (lnX)^2 | Y^2 | ||
| 1 | 12 | 2.48 | 130 | 323.04 | 6.17 | 16900 |
| 2 | 13 | 2.56 | 170 | 436.04 | 6.58 | 28900 |
| 3 | 12 | 2.48 | 110 | 273.34 | 6.17 | 12100 |
| 4 | 11 | 2.40 | 121 | 290.15 | 5.75 | 14641 |
| 5 | 15 | 2.71 | 130 | 352.05 | 7.33 | 16900 |
| 6 | 12 | 2.48 | 120 | 298.19 | 6.17 | 14400 |
| 7 | 11 | 2.40 | 110 | 263.77 | 5.75 | 12100 |
| 8 | 8 | 2.08 | 70 | 145.56 | 4.32 | 4900 |
| 9 | 12 | 2.48 | 140 | 347.89 | 6.17 | 19600 |
| 10 | 12 | 2.48 | 120 | 298.19 | 6.17 | 14400 |
| 11 | 13 | 2.56 | 150 | 384.74 | 6.58 | 22500 |
| 12 | 12 | 2.48 | 120 | 298.19 | 6.17 | 14400 |
| 13 | 14 | 2.64 | 200 | 527.81 | 6.96 | 40000 |
| 14 | 13 | 2.56 | 130 | 333.44 | 6.58 | 16900 |
| 15 | 15 | 2.71 | 240 | 649.93 | 7.33 | 57600 |
| 16 | 16 | 2.77 | 200 | 554.52 | 7.69 | 40000 |
| 17 | 17 | 2.83 | 290 | 821.63 | 8.03 | 84100 |
| 18 | 18 | 2.89 | 290 | 838.21 | 8.35 | 84100 |
| 19 | 17 | 2.83 | 200 | 566.64 | 8.03 | 40000 |
| å | 48.86 | 3041 | 8003.32 | 126.34 | 554441 |
a= -542.07
b=273.01
Уравнение аппроксимирующей логарифмической зависимости
| X | lnX | Y | | | | | |
| 1 | 12 | 2.48 | 130 | 136.33 | 0.05 | 40.09 | 903.16 |
| 2 | 13 | 2.56 | 170 | 158.18 | 0.07 | 139.61 | 98.95 |
| 3 | 12 | 2.48 | 110 | 136.33 | 0.24 | 693.36 | 2505.27 |
| 4 | 11 | 2.40 | 121 | 112.58 | 0.07 | 70.95 | 1525.11 |
| 5 | 15 | 2.71 | 130 | 197.25 | 0.52 | 4522.87 | 903.16 |
| 6 | 12 | 2.48 | 120 | 136.33 | 0.14 | 266.73 | 1604.21 |
| 7 | 11 | 2.40 | 110 | 112.58 | 0.02 | 6.64 | 2505.27 |
| 8 | 8 | 2.08 | 70 | 25.64 | 0.63 | 1968.20 | 8109.48 |
| 9 | 12 | 2.48 | 140 | 136.33 | 0.03 | 13.46 | 402.11 |
| 10 | 12 | 2.48 | 120 | 136.33 | 0.14 | 266.73 | 1604.21 |
| 11 | 13 | 2.56 | 150 | 158.18 | 0.05 | 66.98 | 101.06 |
| 12 | 12 | 2.48 | 120 | 136.33 | 0.14 | 266.73 | 1604.21 |
| 13 | 14 | 2.64 | 200 | 178.42 | 0.11 | 465.85 | 1595.79 |
| 14 | 13 | 2.56 | 130 | 158.18 | 0.22 | 794.35 | 903.16 |
| 15 | 15 | 2.71 | 240 | 197.25 | 0.18 | 1827.37 | 6391.58 |
| 16 | 16 | 2.77 | 200 | 214.87 | 0.07 | 221.18 | 1595.79 |
| 17 | 17 | 2.83 | 290 | 231.42 | 0.20 | 3431.25 | 16886.32 |
| 18 | 18 | 2.89 | 290 | 247.03 | 0.15 | 1846.60 | 16886.32 |
| 19 | 17 | 2.83 | 200 | 231.42 | 0.16 | 987.41 | 1595.79 |
| å | 48.86 | 3041 | 3.18 | 17896.35 | 67720.95 |