1942:
1769:
1565:
464:
906:
1840:
One approach is to use a linear approximation to the nonlinear model, which may be a close approximation in the vicinity of the solution, and then apply the analysis for a linear problem to find an approximate confidence region. This may be a reasonable approach if the confidence region is not very
1805:
Confidence regions can be defined for any probability distribution. The experimenter can choose the significance level and the shape of the region, and then the size of the region is determined by the probability distribution. A natural choice is to use as a boundary a set of points with constant
80:
mean, when one confidence region has been calculated, that there is a 95% probability that the "true" values lie inside the region, since we do not assume any particular probability distribution of the "true" values and we may or may not have other information about where they are likely to lie.
71:
The confidence region is calculated in such a way that if a set of measurements were repeated many times and a confidence region calculated in the same way on each set of measurements, then a certain percentage of the time (e.g. 95%) the confidence region would include the point representing the
1764:{\displaystyle (\mathbf {b} -{\boldsymbol {\hat {\beta }}})^{\prime }\mathbf {Q} ^{\prime }\mathbf {Q} (\mathbf {b} -{\boldsymbol {\hat {\beta }}})={\frac {p}{n-p}}(\mathbf {Z} ^{\prime }\mathbf {Z} -\mathbf {b} ^{\prime }\mathbf {Q} ^{\prime }\mathbf {Z} )F_{1-\alpha }(p,n-p).}
326:
990:
773:
1332:
167:
1272:
1065:. The lengths of the axes of the ellipsoid are proportional to the reciprocals of the values on the diagonals of the diagonal matrix, and the directions of these axes are given by the rows of the 3rd matrix of the decomposition.
633:
1388:
1532:
459:{\displaystyle ({\boldsymbol {\hat {\beta }}}-\mathbf {b} )^{\operatorname {T} }\mathbf {X} ^{\operatorname {T} }\mathbf {X} ({\boldsymbol {\hat {\beta }}}-\mathbf {b} )\leq ps^{2}F_{1-\alpha }(p,\nu ),}
1485:
1439:
901:{\displaystyle ({\boldsymbol {\hat {\beta }}}-\mathbf {b} )^{\operatorname {T} }\mathbf {C} _{\mathbf {\beta } }^{-1}({\boldsymbol {\hat {\beta }}}-\mathbf {b} )\leq pF_{1-\alpha }(p,\nu ),}
1059:
1019:
528:
1129:
1103:
914:
246:
1161:
1109:(in other words, the errors in the observations are not independently distributed), and/or the standard deviations of the errors are not all equal. Suppose the covariance matrix of
500:
1557:
738:
314:
220:
121:
1195:
567:
285:
1831:
684:
707:
1294:
129:
762:
1222:
575:
1347:
1492:
96:
2018:
1985:
1963:
1209:
representing the covariance of pairs of individual observations, as well as not necessarily having all the diagonal elements equal.
66:
1445:
1399:
1794:
686:
1062:
985:{\displaystyle \mathbf {C} _{\mathbf {\beta } }=s^{2}\left(\mathbf {X} ^{\operatorname {T} }\mathbf {X} \right)^{-1}}
2050:
1844:
1035:
995:
504:
1112:
1086:
229:
1078:
1956:
1950:
1834:
710:
253:
1134:
480:
1856:
1540:
716:
297:
203:
104:
1206:
1967:
1074:
90:
197:
535:
257:
60:
40:
1178:
72:"true" values of the set of variables being estimated. However, unless certain assumptions about
1918:
545:
263:
181:
1809:
2014:
1861:
657:
643:
73:
692:
51:
around a point which is an estimated solution to a problem, although other shapes can occur.
1327:{\displaystyle \mathbf {Y} =\mathbf {X} {\boldsymbol {\beta }}+{\boldsymbol {\varepsilon }}}
162:{\displaystyle \mathbf {Y} =\mathbf {X} {\boldsymbol {\beta }}+{\boldsymbol {\varepsilon }}}
1871:
1866:
1202:
1032:-dimensional Cartesian parameter space R. The centre of the ellipsoid is at the estimate
1267:{\displaystyle \mathbf {P} ^{\prime }\mathbf {P} =\mathbf {P} \mathbf {P} =\mathbf {V} }
2030:
2007:
1779:
747:
647:
2044:
628:{\displaystyle s^{2}={\frac {\varepsilon ^{\operatorname {T} }\varepsilon }{n-p}}.}
1106:
28:
1383:{\displaystyle \mathbf {Z} =\mathbf {Q} {\boldsymbol {\beta }}+\mathbf {f} ,}
1061:. According to Press et al., it is easier to plot the ellipsoid after doing
200:(which can represent a physical model) which is assumed to be known exactly,
17:
1919:
Estimating average growth trajectories in shape-space using kernel smoothing
1025:
741:
48:
36:
1527:{\displaystyle \mathbf {f} =\mathbf {P} ^{-1}{\boldsymbol {\varepsilon }}}
539:
1337:
can then be transformed by left-multiplying each term by the inverse of
1841:
large and the second derivatives of the model are also not very large.
1537:
A joint confidence region for the parameters, i.e. for the elements of
2028:
Press, W.H.; S.A. Teukolsky; W.T. Vetterling; B.P. Flannery (1992) .
1083:
Now consider the more general case where some distinct elements of
477:
is the number of parameters, i.e. number of elements of the vector
1197:
in the more specific case handled in the previous section, (where
85:
The case of independent, identically normally-distributed errors
67:
Multivariate normal distribution § Geometric interpretation
1935:
252:-dimensional column vector of errors which are assumed to be
180:-dimensional column vector containing observed values of the
1708:
1696:
1676:
1609:
1597:
1233:
1480:{\displaystyle \mathbf {Q} =\mathbf {P} ^{-1}\mathbf {X} }
1434:{\displaystyle \mathbf {Z} =\mathbf {P} ^{-1}\mathbf {Y} }
2036:(2nd ed.). Cambridge UK: Cambridge University Press.
260:
with zero mean and each having the same unknown variance
2032:
Numerical
Recipes in C: The Art of Scientific Computing
1212:
It is possible to find a nonsingular symmetric matrix
1812:
1568:
1543:
1495:
1448:
1402:
1350:
1297:
1225:
1181:
1137:
1115:
1089:
1038:
998:
917:
776:
750:
719:
695:
660:
578:
548:
507:
483:
329:
300:
266:
232:
206:
132:
107:
61:
Confidence interval § Meaning and interpretation
1917:Hutton TJ, Buxton BF, Hammond P, Potts HWW (2003).
2029:
2006:
1825:
1763:
1551:
1526:
1479:
1433:
1382:
1326:
1266:
1189:
1155:
1123:
1097:
1053:
1013:
984:
900:
756:
732:
701:
678:
627:
561:
522:
494:
458:
316:is represented by the set of values of the vector
308:
279:
240:
214:
161:
115:
1636:
1586:
1045:
1005:
992:is the least-squares scaled covariance matrix of
841:
786:
514:
389:
339:
1797:which are the parameters of this distribution.
473:represents any point in the confidence region,
294:) % confidence region for the elements of
2013:(2nd ed.). USA: John Wiley and Sons Ltd.
1559:, is then bounded by the ellipsoid given by:
1054:{\displaystyle {\boldsymbol {\hat {\beta }}}}
1014:{\displaystyle {\boldsymbol {\hat {\beta }}}}
523:{\displaystyle {\boldsymbol {\hat {\beta }}}}
8:
1124:{\displaystyle {\boldsymbol {\varepsilon }}}
1098:{\displaystyle {\boldsymbol {\varepsilon }}}
241:{\displaystyle {\boldsymbol {\varepsilon }}}
47:-dimensional space, often represented as an
530:is the vector of estimated parameters, and
1281:is a square root of the covariance matrix
226:parameters which are to be estimated, and
1986:Learn how and when to remove this message
1817:
1811:
1725:
1713:
1707:
1702:
1695:
1690:
1681:
1675:
1670:
1648:
1631:
1630:
1622:
1614:
1608:
1603:
1596:
1581:
1580:
1572:
1567:
1544:
1542:
1519:
1510:
1505:
1496:
1494:
1472:
1463:
1458:
1449:
1447:
1426:
1417:
1412:
1403:
1401:
1372:
1364:
1359:
1351:
1349:
1319:
1311:
1306:
1298:
1296:
1259:
1251:
1246:
1238:
1232:
1227:
1224:
1182:
1180:
1147:
1138:
1136:
1116:
1114:
1090:
1088:
1040:
1039:
1037:
1000:
999:
997:
973:
963:
957:
952:
939:
925:
924:
919:
916:
868:
850:
836:
835:
823:
817:
816:
811:
804:
795:
781:
780:
775:
749:
724:
718:
694:
659:
599:
592:
583:
577:
553:
547:
509:
508:
506:
484:
482:
426:
416:
398:
384:
383:
375:
369:
364:
357:
348:
334:
333:
328:
301:
299:
271:
265:
233:
231:
207:
205:
154:
146:
141:
133:
131:
123:to the following overdetermined problem:
108:
106:
1949:This article includes a list of general
320:which satisfy the following inequality:
1883:
1778:represents the percentage point of the
1633:
1583:
1545:
1520:
1365:
1320:
1312:
1205:,) but here is allowed to have nonzero
1156:{\displaystyle \mathbf {V} \sigma ^{2}}
1117:
1091:
1042:
1002:
838:
783:
511:
495:{\displaystyle {\boldsymbol {\beta }},}
485:
386:
336:
302:
234:
208:
155:
147:
109:
1552:{\displaystyle {\boldsymbol {\beta }}}
1341:, forming the new problem formulation
1175:nonsingular matrix which was equal to
1069:Weighted and generalised least squares
733:{\displaystyle X^{\operatorname {T} }}
309:{\displaystyle {\boldsymbol {\beta }}}
215:{\displaystyle {\boldsymbol {\beta }}}
116:{\displaystyle {\boldsymbol {\beta }}}
7:
1923:IEEE Transactions on Medical Imaging
767:The expression can be rewritten as:
1955:it lacks sufficient corresponding
958:
805:
725:
600:
370:
358:
222:is a column vector containing the
25:
101:Suppose we have found a solution
2005:Draper, N.R.; H. Smith (1981) .
1940:
1714:
1703:
1691:
1682:
1671:
1623:
1615:
1604:
1573:
1506:
1497:
1473:
1459:
1450:
1427:
1413:
1404:
1373:
1360:
1352:
1307:
1299:
1260:
1252:
1247:
1239:
1228:
1183:
1139:
1024:The above inequality defines an
964:
953:
920:
851:
812:
796:
399:
376:
365:
349:
290:A joint 100(1 −
142:
134:
1908:Draper and Smith (1981, p. 109)
1899:Draper and Smith (1981, p. 108)
97:Hotelling's T-squared statistic
1890:Draper and Smith (1981, p. 94)
1755:
1737:
1718:
1666:
1642:
1619:
1593:
1569:
892:
880:
855:
832:
801:
777:
450:
438:
403:
380:
354:
330:
43:. It is a set of points in an
1:
1847:approaches can also be used.
196:matrix of observed values of
1190:{\displaystyle \mathbf {I} }
1063:singular value decomposition
2009:Applied Regression Analysis
562:{\displaystyle \sigma ^{2}}
280:{\displaystyle \sigma ^{2}}
2067:
1288:The least-squares problem
1072:
94:
88:
64:
58:
1826:{\displaystyle \chi ^{2}}
1079:Generalized least squares
254:independently distributed
711:statistical significance
679:{\displaystyle \nu =n-p}
1970:more precise citations.
1857:Circular error probable
702:{\displaystyle \alpha }
1827:
1765:
1553:
1528:
1481:
1435:
1384:
1328:
1268:
1191:
1157:
1125:
1099:
1075:Weighted least squares
1055:
1015:
986:
902:
758:
734:
713:level, and the symbol
703:
680:
629:
563:
524:
496:
460:
310:
281:
242:
216:
163:
117:
91:Ordinary least squares
1828:
1766:
1554:
1529:
1482:
1436:
1385:
1329:
1269:
1207:off-diagonal elements
1192:
1158:
1126:
1100:
1073:Further information:
1056:
1016:
987:
903:
759:
735:
704:
681:
630:
564:
525:
497:
461:
311:
282:
243:
217:
198:independent variables
164:
118:
89:Further information:
65:Further information:
1810:
1566:
1541:
1493:
1446:
1400:
1348:
1295:
1223:
1179:
1135:
1113:
1087:
1036:
996:
915:
774:
748:
717:
693:
658:
576:
546:
505:
481:
327:
298:
264:
258:normal distributions
230:
204:
130:
105:
39:generalization of a
1785:and the quantities
1105:have known nonzero
831:
536:reduced chi-squared
469:where the variable
74:prior probabilities
41:confidence interval
1823:
1801:Nonlinear problems
1795:degrees of freedom
1761:
1549:
1524:
1477:
1431:
1380:
1324:
1264:
1187:
1153:
1121:
1095:
1051:
1011:
982:
898:
810:
754:
730:
699:
687:degrees of freedom
676:
625:
559:
520:
492:
456:
306:
277:
238:
212:
182:dependent variable
159:
113:
76:are made, it does
2051:Estimation theory
1996:
1995:
1988:
1862:Linear regression
1664:
1639:
1589:
1048:
1008:
844:
789:
757:{\displaystyle X}
644:quantile function
620:
540:unbiased estimate
517:
392:
342:
37:multi-dimensional
33:confidence region
16:(Redirected from
2058:
2037:
2035:
2024:
2012:
1991:
1984:
1980:
1977:
1971:
1966:this article by
1957:inline citations
1944:
1943:
1936:
1930:
1915:
1909:
1906:
1900:
1897:
1891:
1888:
1832:
1830:
1829:
1824:
1822:
1821:
1770:
1768:
1767:
1762:
1736:
1735:
1717:
1712:
1711:
1706:
1700:
1699:
1694:
1685:
1680:
1679:
1674:
1665:
1663:
1649:
1641:
1640:
1632:
1626:
1618:
1613:
1612:
1607:
1601:
1600:
1591:
1590:
1582:
1576:
1558:
1556:
1555:
1550:
1548:
1533:
1531:
1530:
1525:
1523:
1518:
1517:
1509:
1500:
1486:
1484:
1483:
1478:
1476:
1471:
1470:
1462:
1453:
1440:
1438:
1437:
1432:
1430:
1425:
1424:
1416:
1407:
1389:
1387:
1386:
1381:
1376:
1368:
1363:
1355:
1333:
1331:
1330:
1325:
1323:
1315:
1310:
1302:
1273:
1271:
1270:
1265:
1263:
1255:
1250:
1242:
1237:
1236:
1231:
1196:
1194:
1193:
1188:
1186:
1162:
1160:
1159:
1154:
1152:
1151:
1142:
1130:
1128:
1127:
1122:
1120:
1104:
1102:
1101:
1096:
1094:
1060:
1058:
1057:
1052:
1050:
1049:
1041:
1020:
1018:
1017:
1012:
1010:
1009:
1001:
991:
989:
988:
983:
981:
980:
972:
968:
967:
962:
961:
956:
944:
943:
931:
930:
929:
923:
907:
905:
904:
899:
879:
878:
854:
846:
845:
837:
830:
822:
821:
815:
809:
808:
799:
791:
790:
782:
763:
761:
760:
755:
739:
737:
736:
731:
729:
728:
708:
706:
705:
700:
685:
683:
682:
677:
634:
632:
631:
626:
621:
619:
608:
604:
603:
593:
588:
587:
568:
566:
565:
560:
558:
557:
529:
527:
526:
521:
519:
518:
510:
501:
499:
498:
493:
488:
465:
463:
462:
457:
437:
436:
421:
420:
402:
394:
393:
385:
379:
374:
373:
368:
362:
361:
352:
344:
343:
335:
315:
313:
312:
307:
305:
286:
284:
283:
278:
276:
275:
247:
245:
244:
239:
237:
221:
219:
218:
213:
211:
168:
166:
165:
160:
158:
150:
145:
137:
122:
120:
119:
114:
112:
21:
2066:
2065:
2061:
2060:
2059:
2057:
2056:
2055:
2041:
2040:
2027:
2021:
2004:
2001:
1992:
1981:
1975:
1972:
1962:Please help to
1961:
1945:
1941:
1934:
1933:
1916:
1912:
1907:
1903:
1898:
1894:
1889:
1885:
1880:
1872:Credible region
1867:Confidence band
1853:
1813:
1808:
1807:
1803:
1721:
1701:
1689:
1669:
1653:
1602:
1592:
1564:
1563:
1539:
1538:
1504:
1491:
1490:
1457:
1444:
1443:
1411:
1398:
1397:
1346:
1345:
1293:
1292:
1226:
1221:
1220:
1203:identity matrix
1177:
1176:
1143:
1133:
1132:
1111:
1110:
1085:
1084:
1081:
1071:
1034:
1033:
994:
993:
951:
950:
946:
945:
935:
918:
913:
912:
864:
800:
772:
771:
746:
745:
720:
715:
714:
691:
690:
656:
655:
609:
595:
594:
579:
574:
573:
549:
544:
543:
503:
502:
479:
478:
422:
412:
363:
353:
325:
324:
296:
295:
267:
262:
261:
228:
227:
202:
201:
128:
127:
103:
102:
99:
93:
87:
69:
63:
57:
23:
22:
15:
12:
11:
5:
2064:
2062:
2054:
2053:
2043:
2042:
2039:
2038:
2025:
2019:
2000:
1997:
1994:
1993:
1976:September 2011
1948:
1946:
1939:
1932:
1931:
1910:
1901:
1892:
1882:
1881:
1879:
1876:
1875:
1874:
1869:
1864:
1859:
1852:
1849:
1820:
1816:
1802:
1799:
1772:
1771:
1760:
1757:
1754:
1751:
1748:
1745:
1742:
1739:
1734:
1731:
1728:
1724:
1720:
1716:
1710:
1705:
1698:
1693:
1688:
1684:
1678:
1673:
1668:
1662:
1659:
1656:
1652:
1647:
1644:
1638:
1635:
1629:
1625:
1621:
1617:
1611:
1606:
1599:
1595:
1588:
1585:
1579:
1575:
1571:
1547:
1535:
1534:
1522:
1516:
1513:
1508:
1503:
1499:
1488:
1475:
1469:
1466:
1461:
1456:
1452:
1441:
1429:
1423:
1420:
1415:
1410:
1406:
1391:
1390:
1379:
1375:
1371:
1367:
1362:
1358:
1354:
1335:
1334:
1322:
1318:
1314:
1309:
1305:
1301:
1275:
1274:
1262:
1258:
1254:
1249:
1245:
1241:
1235:
1230:
1185:
1150:
1146:
1141:
1119:
1093:
1070:
1067:
1047:
1044:
1028:region in the
1007:
1004:
979:
976:
971:
966:
960:
955:
949:
942:
938:
934:
928:
922:
909:
908:
897:
894:
891:
888:
885:
882:
877:
874:
871:
867:
863:
860:
857:
853:
849:
843:
840:
834:
829:
826:
820:
814:
807:
803:
798:
794:
788:
785:
779:
753:
727:
723:
698:
675:
672:
669:
666:
663:
648:F-distribution
636:
635:
624:
618:
615:
612:
607:
602:
598:
591:
586:
582:
556:
552:
516:
513:
491:
487:
467:
466:
455:
452:
449:
446:
443:
440:
435:
432:
429:
425:
419:
415:
411:
408:
405:
401:
397:
391:
388:
382:
378:
372:
367:
360:
356:
351:
347:
341:
338:
332:
304:
274:
270:
236:
210:
170:
169:
157:
153:
149:
144:
140:
136:
111:
86:
83:
56:
55:Interpretation
53:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2063:
2052:
2049:
2048:
2046:
2034:
2033:
2026:
2022:
2020:0-471-02995-5
2016:
2011:
2010:
2003:
2002:
1998:
1990:
1987:
1979:
1969:
1965:
1959:
1958:
1952:
1947:
1938:
1937:
1928:
1924:
1920:
1914:
1911:
1905:
1902:
1896:
1893:
1887:
1884:
1877:
1873:
1870:
1868:
1865:
1863:
1860:
1858:
1855:
1854:
1850:
1848:
1846:
1845:Bootstrapping
1842:
1838:
1836:
1818:
1814:
1800:
1798:
1796:
1792:
1788:
1784:
1783:-distribution
1782:
1777:
1758:
1752:
1749:
1746:
1743:
1740:
1732:
1729:
1726:
1722:
1686:
1660:
1657:
1654:
1650:
1645:
1627:
1577:
1562:
1561:
1560:
1514:
1511:
1501:
1489:
1467:
1464:
1454:
1442:
1421:
1418:
1408:
1396:
1395:
1394:
1377:
1369:
1356:
1344:
1343:
1342:
1340:
1316:
1303:
1291:
1290:
1289:
1286:
1284:
1280:
1256:
1243:
1219:
1218:
1217:
1215:
1210:
1208:
1204:
1200:
1174:
1170:
1166:
1148:
1144:
1108:
1080:
1076:
1068:
1066:
1064:
1031:
1027:
1022:
977:
974:
969:
947:
940:
936:
932:
926:
895:
889:
886:
883:
875:
872:
869:
865:
861:
858:
847:
827:
824:
818:
792:
770:
769:
768:
765:
751:
743:
721:
712:
696:
688:
673:
670:
667:
664:
661:
653:
649:
645:
641:
622:
616:
613:
610:
605:
596:
589:
584:
580:
572:
571:
570:
554:
550:
541:
537:
533:
489:
476:
472:
453:
447:
444:
441:
433:
430:
427:
423:
417:
413:
409:
406:
395:
345:
323:
322:
321:
319:
293:
288:
272:
268:
259:
255:
251:
225:
199:
195:
191:
187:
183:
179:
175:
151:
138:
126:
125:
124:
98:
92:
84:
82:
79:
75:
68:
62:
54:
52:
50:
46:
42:
38:
34:
30:
19:
18:Error ellipse
2031:
2008:
1982:
1973:
1954:
1926:
1922:
1913:
1904:
1895:
1886:
1843:
1839:
1804:
1790:
1786:
1780:
1775:
1773:
1536:
1392:
1338:
1336:
1287:
1282:
1278:
1276:
1213:
1211:
1198:
1172:
1168:
1164:
1082:
1029:
1023:
910:
766:
651:
639:
637:
531:
474:
470:
468:
317:
291:
289:
249:
223:
193:
189:
185:
177:
173:
171:
100:
77:
70:
44:
32:
26:
1968:introducing
1835:chi-squared
1277:In effect,
1026:ellipsoidal
1999:References
1951:references
1929:(6):747-53
1837:) values.
1216:such that
1107:covariance
740:means the
95:See also:
59:See also:
29:statistics
1815:χ
1750:−
1733:α
1730:−
1709:′
1697:′
1687:−
1677:′
1658:−
1637:^
1634:β
1628:−
1610:′
1598:′
1587:^
1584:β
1578:−
1546:β
1521:ε
1512:−
1465:−
1419:−
1366:β
1321:ε
1313:β
1234:′
1145:σ
1118:ε
1092:ε
1046:^
1043:β
1006:^
1003:β
975:−
927:β
890:ν
876:α
873:−
859:≤
848:−
842:^
839:β
825:−
819:β
793:−
787:^
784:β
742:transpose
697:α
671:−
662:ν
638:Further,
614:−
606:ε
597:ε
569:equal to
551:σ
515:^
512:β
486:β
448:ν
434:α
431:−
407:≤
396:−
390:^
387:β
346:−
340:^
337:β
303:β
269:σ
235:ε
209:β
156:ε
148:β
110:β
49:ellipsoid
2045:Category
1851:See also
1793:are the
1163:, where
1964:improve
1201:is the
709:is the
650:, with
646:of the
642:is the
534:is the
2017:
1953:, but
1393:where
1167:is an
911:where
292:α
248:is an
188:is an
176:is an
172:where
1878:Notes
1774:Here
538:, an
256:with
35:is a
2015:ISBN
1789:and
1171:-by-
1077:and
654:and
192:-by-
31:, a
1791:n-p
1487:and
1131:is
744:of
542:of
78:not
27:In
2047::
1927:22
1925:,
1921:.
1285:.
1021:.
764:.
689:,
287:.
184:,
2023:.
1989:)
1983:(
1978:)
1974:(
1960:.
1833:(
1819:2
1787:p
1781:F
1776:F
1759:.
1756:)
1753:p
1747:n
1744:,
1741:p
1738:(
1727:1
1723:F
1719:)
1715:Z
1704:Q
1692:b
1683:Z
1672:Z
1667:(
1661:p
1655:n
1651:p
1646:=
1643:)
1624:b
1620:(
1616:Q
1605:Q
1594:)
1574:b
1570:(
1515:1
1507:P
1502:=
1498:f
1474:X
1468:1
1460:P
1455:=
1451:Q
1428:Y
1422:1
1414:P
1409:=
1405:Z
1378:,
1374:f
1370:+
1361:Q
1357:=
1353:Z
1339:P
1317:+
1308:X
1304:=
1300:Y
1283:V
1279:P
1261:V
1257:=
1253:P
1248:P
1244:=
1240:P
1229:P
1214:P
1199:I
1184:I
1173:n
1169:n
1165:V
1149:2
1140:V
1030:p
978:1
970:)
965:X
959:T
954:X
948:(
941:2
937:s
933:=
921:C
896:,
893:)
887:,
884:p
881:(
870:1
866:F
862:p
856:)
852:b
833:(
828:1
813:C
806:T
802:)
797:b
778:(
752:X
726:T
722:X
674:p
668:n
665:=
652:p
640:F
623:.
617:p
611:n
601:T
590:=
585:2
581:s
555:2
532:s
490:,
475:p
471:b
454:,
451:)
445:,
442:p
439:(
428:1
424:F
418:2
414:s
410:p
404:)
400:b
381:(
377:X
371:T
366:X
359:T
355:)
350:b
331:(
318:b
273:2
250:n
224:p
194:p
190:n
186:X
178:n
174:Y
152:+
143:X
139:=
135:Y
45:n
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.