laabh (aankade)

saankhyiki mein aur vishesh roop seey pratigaman vishleshan mein, laabh iss baat kaa ack upaay haye kii ack avalokan key swatantra charr moolya anya tippaniyon seey kitane door hain. "uchch-ausat ank", yadi koee hoe, tou swatantra charr key sambandh mein baahari hain. yaani, uchch-ausat binduon key sootra _ 1 sthaan mein koee padosi bindu naheen hotey hain, jahan "sootra _ 2" ack pratigaman model mein swatantra charr kii sankhya haye. yeh fitt kiye gaye model koo uchch laabh avalokan key karib seey gujarane kii sambhavana banaata haye. isaliye uchch-ausat ankon mein mapdand anumaanon mein badey badalaav karane kii kshamata hoti haye jaba unhein hataa diyaa jaataa haye.ee.prabhaavshaali bindu honey key liye. halanki ack prabhaavshaali bindu mein aamtaur parr uchch laabh hoga, ack uchch laabh bindu jaruri naheen kii ack prabhaavshaali bindu hoe. leverage koo aamtaur parr topi matricks key vikarn tatvon key roop mein paribhaashit kiya jaataa haye.
paribhasha aur vyaakhyaaen.
raikhik pratigaman model sootra _ 3, sootra _ 4 parr vichaar karein. arthaat, sootra _ 5, jahan, sootra _ 6 sootra _ 7 design matricks haye jisaki panktiyaan tippaniyon key anuroop hain aur jinake collum swatantra yaa vyakhyatmak charr key anuroop hain. sootra _ 8 swatantra avalokan sootra _ 9 key liye "laabh kaa score" iss prakaar diyaa gayaa haih
iss prakaar sootra _ 8 leverage score koo sootra _ 9 key beach kii 'bhaarit' doori key roop mein dekhaa jaa sakata haye (mahalanobis doori key saath iska sambandh dekhein). ise usa degree key roop mein bhee vyakhya kii jaa sakati haye jisake dwara sootra _ 8 koo (aashrit) maan (i) maapa jaataa haye.ee.sootra _ 17 sootra _ 8 fitt (anumaanit) moolya (i.ee.sootra _ 19): ganitiya roop seey, 
isaliye, laabh key ank koo avalokan aatm-samvedansheelta yaa aatm-prabhaav key roop mein bhee jaanaa jaataa haye. iss tathya kaa upayog karate hue kii sootra _ 21 (i.ee.uparokt abhivyakti mein, bhavishyavani sootra _ 22 sootra _ 23 kaa sootra _ 6 kii seema sthaan parr ortho-projection haye, hamein sootra _ 25 milata haye. dhyaan dein kii yeh laabh sabhi tippaniyon key vyakhyatmak charr sootra _ 26 key moolyon parr nirbhar kartaa haye lekin aashrit charr sootra _ 27 key kissy bhee moolya parr naheen.
leverage kaa upayog karke aiks mein outlier kaa nirdhaaran.
badaa leverage sootra _ 40 ack sootra _ 41 seey mell khaata haye joe charam haye. ack samanya niyam sootra _ 41 kii pehchaan karna haye jiska laabh moolya sootra _ 43 ausat laabh sootra _ 44 seey 2 gunaa adhik haye (oopar sampatti 2 dekhein). yaani, yadi sootra _ 45 haye, tou sootra _ 41 koo ack baahari maanaa jaayega. kuchh saankhyikeevid sootra _ 48 key bajaay sootra _ 47 kii seema koo pasand karate hain.
mahalanobis doori kaa sambandh.
leverage kaa sambandh mahalanobis doori (pramaan) seey haye. vishesh roop seey, kuchh sootra _ 7 matricks sootra _ 6 key liye, sootra _ 41 kii vargakar mahalanobis doori (jahaan sootra _ 56 kaa sootra _ 55 kaa sootra _ 5 kaa sootra _ 5 haye) sootra _ 56 kaa sootra _ 5 kaa vector haye, sootra _ 5 haye, jahaan sootra _ 5 sootra _ 4 kaa anumaanit sahprasaran matricks haye. yeh sootra _ 6 key hait matricks key leverage sootra _ 28 seey sambandhit haye, jisamen 1 key collum vector koo jodaa gayaa haye. donon key beach sambandh haih
yeh sambandh hamein laabh koo saarthak ghatakon mein vighatit karane mein saksham banaata haye taaki uchch laabh key kuchh sroton kii vishleshanatmak roop seey jaanch kii jaa sakey.
prabhaav karyon kaa sambandh.
pratigaman sandarbh mein, humm ack ekal detta bindu koo hataane parr anumaanit gunank kiss hudd taka badal jaayega, isaki ganana karane key liye laabh uthaane aur prabhaav karyon koo jodate hain. pratigaman avashishton koo sootra _ 63 key roop mein darshaate hue, sootra kaa upayog karke anumaanit gunank sootra _ 64 kii tulanaa anumaanit gunank sootra _ 65 seey kii jaa sakati haye. 
young (2019) avashisht niyantranon key baad iss sootra key ack sanskaran kaa upayog kartaa haye. iss sootra key liye antargyaan praapt karane key liye, dhyaan dein kii sootra _ 67 pratigaman maapdandon koo prabhaavit karane key liye ack avalokan key liye kshamata koo pakadata haye, aur isaliye sootra _ 68 pratigaman maapdandon parr apane fitt moolya seey usa tippaniyon key vichalan key vaastavik prabhaav koo pakadata haye. sootra taba sootra _ 69 dwara vibhajit hotaa haye iss tathya key liye kii humm avalokan koo isake moolya koo samaayojit karane key bajaay hataa dete hain, iss tathya koo darshaata haye kii hataane seey uchch-ausat tippaniyon (i.ee. baahari sahparivartan moolyon key saath). pratigaman sandarbh mein saankhyikiya prabhaav karyon key liye samanya sootron koo lagu karate samay isi tarah key sootra utpann hotey hain.
avashisht bhinnata parr prabhaav.
yadi humm ack sadharan nyuntam varg setting mein hain jisamen nishchit sootra _ 6 aur homocedastic pratigaman trutiyon kaa sootra _ 71 sootra _ 72 haye, tou sootra _ 8 pratigaman avashisht, sootra _ 74 mein bhinnata haye.
dusare shabdon mein, ack avalokan kaa laabh score usa avalokan key model key galat anuman mein shore kii degree nirdhaarit kartaa haye, jisamen uchch laabh cumm shore kii or leey jaataa haye. yeh iss tathya seey anusaran kartaa haye kii sootra _ 76 samamit aur samamit haye aur sootra _ 77 haye, isaliye, sootra _ 78 haye.
sambandhit chhaatrakrit avashisht-isake avalokan-vishisht anumaanit avashisht bhinnata key liye samaayojit avashisht-taba hotaa haye
jahan sootra _ 80 sootra _ 81 kaa ack upayukt anuman haye.
aanshik laabh.
aanshik laabh (pee. ell.) pratyek avalokan key kull laabh mein vyaktigat swatantra charr key yogdan kaa ack upaay haye. arthaat, pl iss baat kaa ack upaay haye kii kaise "sootra _ 82" ack charr key roop mein pratigaman model mein jodaa jaataa haye. isaki ganana iss prakaar kii jaati haih
jahan sootra _ 84 swatantra charr kaa soochkaank haye, sootra _ 85 avalokan kaa soochkaank haye aur sootra _ 86 shesh swatantra charr key khilaf "sootra _ 87" koo pratigaman karane seey avashisht hain. dhyaan dein kii aanshik laabh sootra 89 charr key liye aanshik pratigaman plot mein sootra 8 bindu kaa laabh haye. ack swatantra charr key liye badey aanshik laabh key saath detta bindu swachaalit pratigaman model nirmaan prakriyaon mein usa charr key chayan parr anuchit prabhaav daal sakate hain.
software karyanvayan.
kaee karyakram aur saankhyiki package, jaise kii aar, python, aadi., laabh uthaane key karyanvayan koo shamil karein.

