ЗАДАНИЕ: Используя данные, приведённые в работе №3, требуется:
1. Оценить парные связи всех переменных на уровне значимости 5%. В случае наличия значимой связи для пары переменных построить уравнение регрессии, рассматривая переменную Х как независимую.
2. Построить график регрессионной модели.
3. Оценить значимость построенных регрессионных моделей.
4. Оценить качество построенных регрессионных моделей.
5. Проверить выполнение основных предпосылок нормальной регрессионной модели (провести анализ остатков).
6. Построить 95% и 99% доверительные интервалы для всех параметров моделей.
7. Рассчитать прогнозные значения для величин, на 15% превышающих максимальные значения независимых переменных. Построить соответствующие доверительные интервалы.
8. Составьте отчёт о проделанной работе по вашему индивидуальному варианту.
Вариант 1
Номера наблюдений | X1 | Y1 | X2 | Y2 |
3,708 | 17,79 | 8,78 | 26,61 | |
4,548 | 18,644 | 7,904 | 25,88 | |
3,896 | 18,004 | 8,122 | 25,954 | |
3,02 | 16,866 | 8,07 | 25,942 | |
4,202 | 18,276 | 7,592 | 25,638 | |
4,626 | 18,422 | 7,922 | 25,874 | |
4,192 | 18,082 | 8,566 | 26,63 | |
3,33 | 17,43 | 6,93 | 24,76 | |
3,898 | 17,778 | 8,15 | 25,97 | |
3,832 | 17,846 | 7,518 | 25,592 | |
3,374 | 17,544 | 8,27 | 26,068 | |
3,718 | 17,508 | 8,162 | 26,412 | |
3,932 | 18,032 | 8,976 | 27,078 | |
3,438 | 17,522 | 7,956 | 25,662 | |
4,678 | 18,364 | 8,308 | 26,756 | |
3,898 | 17,684 | 7,802 | 25,856 | |
3,736 | 17,798 | 7,956 | 25,926 | |
4,596 | 18,772 | 7,678 | 25,724 | |
4,394 | 18,546 | 7,732 | 25,828 | |
4,026 | 18,35 | 7,658 | 25,602 | |
4,64 | 18,924 | 8,17 | 26,28 | |
3,58 | 17,792 | 8,304 | 26,008 | |
3,742 | 17,468 | 8,48 | 26,808 | |
4,492 | 18,592 | 8,14 | 26,026 | |
3,54 | 17,236 | 8,452 | 26,396 | |
4,034 | 17,662 | 7,648 | 25,596 | |
2,95 | 16,976 | 8,618 | 26,85 | |
3,936 | 17,868 | 7,586 | 25,258 | |
4,644 | 18,764 | 7,294 | 25,264 | |
4,078 | 18,336 | 8,08 | 26,2 | |
3,572 | 17,324 | 8,036 | 26,288 | |
4,494 | 18,216 | 7,622 | 25,786 | |
4,402 | 18,626 | 7,728 | 25,922 | |
4,102 | 17,962 | 8,632 | 26,884 | |
4,318 | 18,328 | 8,04 | 26,152 | |
4,086 | 18,504 | 8,534 | 26,572 |
Вариант 2
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|
Номера наблюдений | X1 | Y1 | X2 | Y2 |
0,898 | 7,952 | 3,011 | 11,927 | |
1,046 | 7,991 | 3,233 | 12,265 | |
0,804 | 7,845 | 3,34 | 12,255 | |
0,899 | 7,839 | 3,025 | 11,935 | |
0,615 | 7,665 | 2,415 | 11,33 | |
0,967 | 7,781 | 2,774 | 11,748 | |
1,151 | 8,263 | 2,814 | 11,911 | |
0,637 | 7,722 | 3,085 | 11,984 | |
0,993 | 8,202 | 3,217 | 12,236 | |
0,46 | 7,383 | 2,985 | 11,921 | |
1,197 | 8,058 | 2,761 | 11,843 | |
0,918 | 7,884 | 2,743 | 11,579 | |
0,809 | 7,704 | 3,031 | 12,156 | |
1,109 | 8,114 | 2,97 | 12,026 | |
0,669 | 7,711 | 2,928 | 11,781 | |
1,147 | 8,223 | 2,816 | 11,864 | |
1,224 | 8,272 | 2,902 | 11,89 | |
0,963 | 8,125 | 2,779 | 11,751 | |
1,263 | 8,161 | 2,911 | 11,887 | |
1,248 | 8,336 | 2,789 | 11,812 | |
1,272 | 8,332 | 2,597 | 11,582 | |
0,74 | 7,846 | 3,102 | 11,954 | |
0,899 | 7,792 | 2,851 | 11,878 | |
0,821 | 7,684 | 3,19 | 12,354 | |
0,72 | 7,568 | 3,176 | 12,148 | |
0,916 | 7,966 | 3,438 | 12,489 | |
0,425 | 7,438 | 3,259 | 12,375 | |
0,818 | 7,849 | 2,928 | 11,913 | |
1,196 | 8,246 | 3,02 | 11,963 | |
0,989 | 8,118 | 2,99 | 12,05 | |
0,866 | 7,873 | 2,709 | 11,746 | |
0,736 | 7,612 | 2,968 | 12,094 | |
1,001 | 7,931 | 3,266 | 12,392 | |
1,051 | 8,088 | 2,746 | 11,769 | |
1,27 | 8,412 | 3,035 | 12,09 | |
1,289 | 8,132 | 3,104 | 12,328 |
Вариант 3
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|
Номера наблюдений | X1 | Y1 | X2 | Y2 |
3,6741 | 5,7324 | 4,1433 | 6,8679 | |
3,5562 | 5,6685 | 4,317 | 6,9915 | |
3,537 | 5,6688 | 4,2456 | 6,9012 | |
3,531 | 5,5854 | 4,2678 | 6,9594 | |
3,6894 | 5,8158 | 4,1517 | 6,8586 | |
3,5157 | 5,6283 | 4,1934 | 6,8493 | |
3,4995 | 5,6145 | 4,0395 | 6,714 | |
3,5061 | 5,6316 | 4,2405 | 6,9102 | |
3,5748 | 5,6769 | 4,1277 | 6,8388 | |
3,6822 | 5,7966 | 4,1856 | 6,882 | |
3,5847 | 5,6526 | 4,1703 | 6,8784 | |
3,5898 | 5,7048 | 4,3464 | 7,0617 | |
3,6966 | 5,8146 | 4,0941 | 6,7896 | |
3,6591 | 5,7819 | 4,1598 | 6,8742 | |
3,6051 | 5,6493 | 4,1472 | 6,8394 | |
3,6603 | 5,7939 | 4,1592 | 6,8883 | |
3,6303 | 5,7414 | 4,1388 | 6,8457 | |
3,5844 | 5,7006 | 4,2183 | 6,8931 | |
3,5613 | 5,6202 | 4,272 | 7,0212 | |
3,4425 | 5,5464 | 4,2927 | 7,0275 | |
3,6039 | 5,7525 | 4,1487 | 6,8403 | |
3,7017 | 5,7546 | 4,2462 | 7,0134 | |
3,5847 | 5,6667 | 4,2225 | 6,8955 | |
3,5577 | 5,6262 | 4,2243 | 6,9618 | |
3,6129 | 5,7756 | 4,2801 | 6,9858 | |
3,5604 | 5,6697 | 4,1934 | 6,8889 | |
3,6288 | 5,7123 | 4,2849 | 6,9945 | |
3,696 | 5,8386 | 4,2255 | 6,942 | |
3,5904 | 5,6802 | 4,1379 | 6,7887 | |
3,6738 | 5,7888 | 4,221 | 6,9039 | |
3,453 | 5,5299 | 4,2105 | 6,8913 | |
3,6939 | 5,7633 | 4,1883 | 6,8811 | |
3,6153 | 5,6943 | 4,2948 | 7,0326 | |
3,6477 | 5,7492 | 4,206 | 6,9228 | |
3,6117 | 5,7504 | 4,212 | 6,93 | |
3,5358 | 5,5986 | 4,2054 | 6,9432 |
Вариант 4
Номера наблюдений | X1 | Y1 | X2 | Y2 |
3,248 | 17,344 | 6,604 | 24,58 | |
2,24 | 15,936 | 7,152 | 25,096 | |
3,194 | 16,916 | 6,322 | 24,486 | |
2,442 | 16,168 | 7,18 | 25,508 | |
2,138 | 16,222 | 6,656 | 24,362 | |
2,726 | 17,05 | 6,358 | 24,302 | |
3,018 | 17,028 | 6,74 | 24,852 | |
2,902 | 16,976 | 6,292 | 24,338 | |
2,03 | 16,13 | 5,63 | 23,46 | |
3,378 | 17,064 | 7,008 | 25,456 | |
2,636 | 16,568 | 6,286 | 23,958 | |
3,102 | 17,326 | 6,428 | 24,622 | |
2,436 | 16,498 | 6,656 | 24,626 | |
3,192 | 17,292 | 6,84 | 24,726 | |
2,272 | 16,024 | 6,736 | 24,988 | |
1,65 | 15,676 | 7,318 | 25,55 | |
2,802 | 16,662 | 7,332 | 25,584 | |
2,532 | 16,546 | 6,218 | 24,292 | |
3,344 | 17,464 | 5,994 | 23,964 | |
3,326 | 17,122 | 6,622 | 24,574 | |
2,598 | 16,384 | 6,502 | 24,556 | |
1,72 | 15,566 | 6,77 | 24,642 | |
2,408 | 16,49 | 7,48 | 25,31 | |
2,632 | 16,732 | 7,676 | 25,778 | |
2,892 | 16,782 | 7,266 | 25,33 | |
3,094 | 17,246 | 6,432 | 24,528 | |
2,596 | 16,704 | 6,822 | 24,654 | |
3,34 | 17,624 | 6,87 | 24,98 | |
2,786 | 17,204 | 7,234 | 25,272 | |
2,418 | 16,208 | 6,862 | 25,112 | |
2,734 | 16,362 | 6,348 | 24,296 | |
2,074 | 16,244 | 6,97 | 24,768 | |
2,598 | 16,478 | 6,85 | 24,67 | |
2,778 | 17,036 | 6,78 | 24,9 | |
2,28 | 16,492 | 7,004 | 24,708 | |
3,296 | 17,472 | 6,378 | 24,424 |
Вариант 5
Номера наблюдений | X1 | Y1 | X2 | Y2 |
4,3372 | 17,011 | 8,902 | 24,949 | |
4,7818 | 17,448 | 7,8328 | 24,074 | |
4,5082 | 8,335 | 24,373 | ||
4,3462 | 16,757 | 8,3458 | 24,771 | |
4,6774 | 17,654 | 8,6806 | 24,915 | |
4,5082 | 16,916 | 8,0218 | 24,27 | |
4,0942 | 16,77 | 8,1604 | 24,096 | |
5,0428 | 17,733 | 8,326 | 24,423 | |
3,997 | 16,687 | 7,237 | 23,284 | |
3,718 | 16,179 | 8,263 | 24,348 | |
4,8862 | 17,495 | 8,236 | 24,537 | |
4,3678 | 16,721 | 8,632 | 25,127 | |
5,1364 | 17,895 | 7,9102 | 24,152 | |
4,5424 | 17,081 | 7,8274 | 23,732 | |
4,5064 | 17,204 | 8,3098 | 24,359 | |
5,1796 | 17,888 | 7,5646 | 23,738 | |
4,6234 | 17,515 | 7,8922 | 24,042 | |
4,186 | 16,512 | 8,6068 | 24,756 | |
4,9618 | 17,763 | 7,9552 | 24,33 | |
5,176 | 18,032 | 8,353 | 24,652 | |
4,3624 | 17,018 | 8,1604 | 24,333 | |
4,222 | 17,013 | 8,4736 | 24,407 | |
4,9546 | 17,691 | 7,9588 | 24,245 | |
3,655 | 16,278 | 8,7562 | 25,165 | |
4,7728 | 17,274 | 8,7094 | 24,967 | |
4,5388 | 17,229 | 9,0784 | 25,37 | |
4,6306 | 16,896 | 7,8832 | 24,036 | |
5,2102 | 17,528 | 8,4772 | 25,08 | |
5,0446 | 17,394 | 7,8598 | 24,207 | |
4,6918 | 17,166 | 8,7688 | 25,196 | |
4,2148 | 16,592 | 8,2324 | 24,659 | |
4,4488 | 17,061 | 7,7662 | 24,033 | |
4,6702 | 17,502 | 8,272 | 24,58 | |
5,0932 | 17,78 | 8,1136 | 24,292 | |
4,0366 | 16,79 | 8,443 | 24,461 | |
5,1634 | 17,58 | 8,1298 | 24,287 |
Вариант 6
Номера наблюдений | X1 | Y1 | X2 | Y2 |
2,6228 | 8,2628 | 4,6404 | 11,881 | |
2,5332 | 8,166 | 4,562 | 11,694 | |
2,8692 | 8,5076 | 4,2116 | 11,402 | |
2,7268 | 8,2828 | 4,4764 | 11,702 | |
2,6812 | 8,3844 | 4,282 | 11,53 | |
2,382 | 8,022 | 3,822 | 10,954 | |
2,906 | 8,6196 | 4,318 | 11,562 | |
2,3996 | 8,0676 | 4,358 | 11,477 | |
2,6244 | 8,1972 | 4,0844 | 11,153 | |
2,258 | 7,7964 | 4,278 | 11,427 | |
2,4252 | 8,0588 | 4,2324 | 11,315 | |
2,5444 | 8,1692 | 4,2324 | 11,42 | |
2,6636 | 8,1148 | 4,1092 | 11,288 | |
2,5468 | 8,0372 | 4,442 | 11,773 | |
2,6908 | 8,2348 | 4,5028 | 11,804 | |
2,8884 | 8,5588 | 4,1212 | 11,34 | |
2,6844 | 8,4516 | 4,4636 | 11,679 | |
2,482 | 8,1668 | 4,3716 | 11,453 | |
2,9076 | 8,5556 | 3,9676 | 11,156 | |
2,7308 | 8,3604 | 4,0868 | 11,305 | |
2,9004 | 8,4188 | 4,2188 | 11,4 | |
2,466 | 7,9444 | 4,4308 | 11,608 | |
2,8076 | 8,4684 | 4,1428 | 11,381 | |
2,6084 | 8,2516 | 4,2988 | 11,432 | |
2,6604 | 8,39 | 4,1132 | 11,291 | |
2,6092 | 8,1612 | 4,31 | 11,438 | |
2,4788 | 7,9796 | 4,2644 | 11,565 | |
2,8108 | 8,5004 | 4,1412 | 11,419 | |
2,23 | 7,8404 | 4,4972 | 11,79 | |
2,9212 | 8,3956 | 4,3732 | 11,752 | |
2,8476 | 8,3364 | 4,0988 | 11,364 | |
2,6092 | 8,1236 | 4,1708 | 11,392 | |
2,5372 | 8,0532 | 4,3148 | 11,615 | |
2,7772 | 8,3812 | 4,266 | 11,511 | |
2,5828 | 8,1884 | 4,0572 | 11,287 | |
2,8468 | 8,4868 | 4,306 | 11,46 |
Вариант 7
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Номера наблюдений | X1 | Y1 | X2 | Y2 |
5,047 | 25,726 | 10,903 | 37,984 | |
3,625 | 24,664 | 12,127 | 39,475 | |
4,948 | 25,969 | 10,477 | 37,588 | |
5,047 | 25,867 | 11,425 | 38,155 | |
5,329 | 26,956 | 12,001 | 39,058 | |
6,139 | 26,833 | 11,083 | 38,011 | |
4,558 | 25,186 | 11,254 | 38,632 | |
5,803 | 27,139 | 10,792 | 38,083 | |
4,57 | 25,888 | 11,656 | 38,212 | |
5,503 | 26,614 | 10,588 | 37,657 | |
4,51 | 25,054 | 11,878 | 38,794 | |
4,813 | 25,402 | 11,92 | 39,412 | |
4,357 | 25,483 | 11,134 | 37,693 | |
5,317 | 26,704 | 11,32 | 38,5 | |
6,217 | 26,746 | 11,662 | 39,334 | |
4,777 | 25,462 | 11,443 | 38,818 | |
4,762 | 25,885 | 12,37 | 39,115 | |
5,251 | 25,693 | 10,672 | 37,594 | |
3,73 | 24,499 | 11,305 | 38,113 | |
5,353 | 26,143 | 12,148 | 39,526 | |
5,791 | 27,019 | 10,798 | 37,942 | |
5,104 | 26,002 | 10,579 | 37,087 | |
6,022 | 27,166 | 11,056 | 38,02 | |
4,804 | 25,897 | 11,134 | 38,089 | |
5,098 | 26,248 | 12,664 | 39,817 | |
6,16 | 27,586 | 11,455 | 38,62 | |
5,488 | 26,323 | 12,049 | 39,145 | |
5,941 | 26,524 | 10,633 | 37,879 | |
4,195 | 25,345 | 9,595 | 36,34 | |
4,261 | 25,516 | 11,605 | 38,302 | |
5,239 | 26,725 | 10,687 | 37,603 | |
5,677 | 26,692 | 11,26 | 38,428 | |
6,166 | 27,346 | 10,141 | 37,096 | |
5,938 | 27,088 | 11,41 | 38,239 | |
6,094 | 27,358 | 10,717 | 37,786 | |
5,044 | 26,206 | 11,383 | 38,131 |
Вариант 8
Номера наблюдений | X1 | Y1 | X2 | Y2 |
2,957 | 6,4775 | 4,225 | 8,6825 | |
2,8625 | 6,3875 | 3,7625 | 8,22 | |
3,153 | 6,678 | 4,065 | 8,5365 | |
2,785 | 6,2465 | 4,0475 | 8,5155 | |
3,1865 | 6,6355 | 4,0105 | 8,4985 | |
3,1305 | 6,6865 | 3,962 | 8,5105 | |
2,9595 | 6,407 | 4,0705 | 8,633 | |
3,0805 | 6,599 | 3,928 | 8,4395 | |
2,7675 | 6,274 | 4,1845 | 8,7425 | |
3,014 | 6,497 | 3,9265 | 8,3445 | |
2,9655 | 6,397 | 4,15 | 8,732 | |
3,167 | 6,691 | 4,006 | 8,5 | |
3,1095 | 6,612 | 4,04 | 8,568 | |
3,0385 | 6,4455 | 3,942 | 8,429 | |
3,1995 | 6,621 | 4,107 | 8,719 | |
2,8735 | 6,416 | 4,0975 | 8,547 | |
3,0555 | 6,5205 | 4,188 | 8,751 | |
2,964 | 6,4795 | 4,019 | 8,5115 | |
3,191 | 6,721 | 3,8535 | 8,346 | |
3,0045 | 6,4745 | 4,0675 | 8,5225 | |
2,923 | 6,361 | 4,039 | 8,602 | |
2,925 | 6,478 | 4,106 | 8,532 | |
2,988 | 6,4915 | 3,9095 | 8,428 | |
3,19 | 6,761 | 4,0725 | 8,6 | |
3,179 | 6,723 | 3,9495 | 8,461 | |
3,0045 | 6,451 | 3,9805 | 8,494 | |
3,0515 | 6,656 | 4,1635 | 8,673 | |
3,078 | 6,5505 | 4,1715 | 8,6875 | |
2,915 | 6,339 | 4,143 | 8,629 | |
2,8895 | 6,4105 | 4,019 | 8,4455 | |
3,013 | 6,538 | 4,274 | 8,7995 | |
3,0495 | 6,614 | 4,05 | 8,58 | |
3,1535 | 6,584 | 3,9355 | 8,4765 | |
3,0365 | 6,6175 | 3,9445 | 8,4305 | |
3,1285 | 6,6665 | 3,963 | 8,487 | |
3,004 | 6,531 | 4,0605 | 8,5185 |
Вариант 9
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|
Номера наблюдений | X1 | Y1 | X2 | Y2 |
4,4096 | 11,662 | 7,0217 | 16,204 | |
4,2376 | 11,535 | 6,7591 | 15,925 | |
4,5064 | 11,772 | 6,6828 | 15,866 | |
4,0553 | 11,186 | 6,6561 | 15,86 | |
4,6589 | 11,812 | 6,9115 | 16,214 | |
4,8134 | 12,075 | 6,6921 | 15,903 | |
4,7629 | 12,051 | 6,482 | 15,801 | |
4,8896 | 12,246 | 6,7076 | 16,034 | |
4,664 | 11,912 | 6,4099 | 15,704 | |
4,5775 | 11,596 | 6,4387 | 15,682 | |
4,3437 | 11,663 | 6,7766 | 15,894 | |
4,0193 | 11,243 | 6,9383 | 16,328 | |
4,8824 | 11,987 | 6,5798 | 15,825 | |
4,424 | 11,666 | 6,5973 | 15,852 | |
4,4735 | 11,691 | 6,3718 | 15,68 | |
4,4271 | 11,496 | 6,8672 | 16,306 | |
4,5075 | 11,656 | 6,6973 | 15,875 | |
4,4148 | 11,517 | 6,7034 | 16,102 | |
4,3396 | 11,422 | 6,6385 | 16,038 | |
4,3231 | 11,377 | 6,8528 | 16,094 | |
4,8422 | 12,102 | 6,5706 | 15,828 | |
4,6125 | 11,75 | 6,9455 | 16,345 | |
4,2706 | 11,524 | 6,5973 | 15,716 | |
4,525 | 11,786 | 7,1226 | 16,445 | |
4,9092 | 11,957 | 6,7786 | 16,279 | |
4,7238 | 11,939 | 6,6406 | 15,968 | |
4,8669 | 12,168 | 6,4542 | 15,748 | |
4,5075 | 11,607 | 6,518 | 15,816 | |
4,5734 | 11,95 | 6,4439 | 15,685 | |
4,6002 | 11,943 | 6,6612 | 15,993 | |
4,8144 | 11,881 | 6,4253 | 15,78 | |
4,527 | 11,702 | 6,4068 | 15,508 | |
4,215 | 11,476 | 6,069 | 15,251 | |
4,6043 | 12,03 | 6,895 | 16,185 | |
4,767 | 12,092 | 6,4799 | 15,85 | |
4,8917 | 12,163 | 6,2564 | 15,511 |
Вариант 10
Номера наблюдений | X1 | Y1 | X2 | Y2 |
8,2518 | 20,222 | 12,563 | 27,719 | |
8,0223 | 19,994 | 11,863 | 26,913 | |
8,9658 | 20,947 | 11,818 | 27,098 | |
8,8417 | 20,932 | 11,669 | 27,134 | |
8,2603 | 19,982 | 12,038 | 27,55 | |
9,044 | 21,185 | 12,045 | 27,438 | |
8,5867 | 20,368 | 12,437 | 27,951 | |
8,2756 | 20,228 | 11,863 | 27,137 | |
9,0321 | 20,759 | 11,834 | 27,093 | |
8,3572 | 20,269 | 11,49 | 26,853 | |
8,143 | 20,223 | 12,158 | 27,207 | |
8,4133 | 20,211 | 12,028 | 27,175 | |
8,9182 | 20,903 | 12,019 | 27,222 | |
8,7703 | 20,679 | 11,934 | 27,329 | |
8,9199 | 20,584 | 11,579 | 27,018 | |
8,4133 | 20,131 | 11,732 | 27,078 | |
8,6717 | 20,635 | 11,553 | 26,892 | |
8,5731 | 20,828 | 12,354 | 27,686 | |
7,6075 | 19,53 | 12,425 | 27,923 | |
8,6632 | 20,47 | 12,381 | 27,736 | |
7,9679 | 20,012 | 12,13 | 27,258 | |
8,4422 | 20,427 | 12,73 | 28,116 | |
8,4116 | 20,403 | 12,004 | 27,161 | |
8,5221 | 20,698 | 11,609 | 26,862 | |
8,4456 | 20,288 | 11,548 | 26,569 | |
8,109 | 19,751 | 12,284 | 27,537 | |
8,8349 | 20,864 | 11,672 | 27,054 | |
9,0763 | 20,709 | 12,162 | 27,843 | |
9,0066 | 21,056 | 11,626 | 26,965 | |
7,9305 | 19,916 | 10,991 | 26,146 | |
9,0474 | 21,049 | 11,3 | 26,574 | |
8,5289 | 20,113 | 11,601 | 26,857 | |
8,2807 | 19,948 | 12,308 | 27,887 | |
8,5663 | 20,686 | 11,968 | 27,37 | |
8,1362 | 19,825 | 11,931 | 27,445 | |
7,667 | 19,436 | 11,96 | 27,151 |