鍜ㄨ宸ョ▼甯従(xi脿n)浠ｅ伐绋嬪挩瑭㈡柟娉曟杩颁覆璎�6
鐎忚
鏀惰棌
銆€銆€绗簩绡€(ji茅) 鍥犳灉鍒嗘瀽娉�-1
銆€銆€鍥犳灉鍒嗘瀽娉曚富瑕佸寘鎷�:
銆€銆€鍥炴鍒嗘瀽娉�.
銆€銆€褰堟€х郴鏁�(sh霉)鍒嗘瀽娉�.
銆€銆€娑堣不绯绘暩(sh霉)娉曠瓑鏂规硶銆�
銆€銆€鍥炴鍒嗘瀽娉曟槸鍒嗘瀽鐩搁棞(gu膩n)鍥犵礌鐩镐簰闂�(gu膩n)绯荤殑涓€绋暩(sh霉)鐞嗙当(t菕ng)瑷堟柟娉�锛岄€氶亷寤虹珛涓€鍊嬫垨涓€绲勮嚜璁婇噺鑸囩浉闂�(gu膩n)闅ㄦ(j墨)璁婇噺鐨勫洖姝稿垎鏋愭ā鍨�锛屼締闋�(y霉)娓浉闂�(gu膩n)闅ㄦ(j墨)璁婇噺鐨勬湭渚嗗€�?锛涜钵w鍒嗘瀽娉曟寜鍒嗘瀽涓嚜璁婇噺鐨勫€嬫暩(sh霉)鍒嗙偤涓€鍏冨洖姝歌垏澶氬厓鍥炴;鎸夎嚜璁婇噺鑸囧洜璁婇噺鐨勯棞(gu膩n)绯诲垎鐐虹窔鎬у洖姝歌垏闈炵窔鎬у洖姝搞€備笉璜栨槸涓€鍏冨洖姝告ā鍨嬮倓鏄鍏冨洖姝告ā鍨�锛岄爯(y霉)娓ā鍨嬬殑寤虹珛瑕佺稉(j墨ng)閬庡毚(y谩n)鏍肩殑绲�(t菕ng)瑷堟椹楋紝鍚﹀墖妯″瀷涓嶈兘鎴愮珛銆�
銆€銆€褰堟€х郴鏁�(sh霉)娉曟槸鈥曠ó鐩稿皪绨″柈鏄撹鐨勫畾閲忛爯(y霉)娓柟娉�锛岄€氶亷瑷堢畻鏌愬叐鍊嬭畩閲忕浉灏嶈畩鍖栧綀鎬ч棞(gu膩n)绯伙紝褰堟€ф槸鈥曞€嬬浉灏嶉噺锛屽畠琛￠噺鏌愨€曡畩閲忕殑鏀硅畩鎵€寮曡捣鐨勫彟鈥曡畩閲忕殑鐩稿皪璁婂寲銆�
銆€銆€娑堣不绯绘暩(sh霉)娉曟槸鎸夎妤�(y猫)銆侀儴闁€銆佸湴鍗€(q奴)銆佷汉鍙�銆佺兢楂旂瓑灏嶆煇鐢�(ch菐n)鍝佺殑娑堣不鑰呴€�(j矛n)琛屽垎鏋愶紝瑾�(r猫n)璀樺拰鎺屾彙娑堣不鑰呰垏鐢�(ch菐n)鍝佺殑鏁�(sh霉)閲忛棞(gu膩n)绯�锛屽緸鑰岄爯(y霉)娓敘(ch菐n)鍝侀渶姹傞噺銆�
銆€銆€涓€銆佷竴鍏冪窔鎬у洖姝�
銆€銆€(涓€)鍩烘湰鍏紡
銆€銆€濡傛灉闋�(y霉)娓皪璞¤垏涓昏褰遍熆鍥犵礌涔嬮枔瀛樺湪绶氭€ч棞(gu膩n)绯�锛屽皣闋�(y霉)娓皪璞′綔鐐哄洜璁婇噺y锛屽皣涓昏褰遍熆鍥犵礌浣滅偤鑷畩閲弜锛屽嵆寮曡捣鍥犺畩閲弝璁婂寲鐨勮畩閲�锛屽墖瀹冨€戜箣闁撶殑闂�(gu膩n)绯诲彲浠ョ敤涓€鍏冨洖姝告ā鍨嬭〃绀虹偤濡備笅褰㈠紡锛�
銆€銆€y=a+bx+e
銆€銆€鍏朵腑锛歛鍜宐鏄彮绀簒鍜寉涔嬮枔闂�(gu膩n)绯荤殑绯绘暩(sh霉)锛宎鐐哄洖姝稿父鏁�(sh霉)锛宐鐐哄洖姝哥郴鏁�(sh霉)
銆€銆€e鏄宸爡鎴栫ū鍥炴浣欓爡銆�
銆€銆€灏嶄簬姣忕祫鍙互瑙€瀵熷埌鐨勮畩閲弜锛寉鐨勬暩(sh霉)鍊紉i锛寉i锛屾豢瓒充笅闈㈢殑闂�(gu膩n)绯伙細
銆€銆€yi =a+bxi+ei
銆€銆€鍏朵腑ei鏄宸爡锛屾槸鐢╝+bxi鍘讳及瑷堝洜璁婇噺yi鐨勫€艰€岀敘(ch菐n)鐢熺殑瑾ゅ樊銆�
銆€銆€鍦ㄥ闅涢爯(y霉)娓腑锛宔i鏄劇娉曢爯(y霉)娓殑锛屽洖姝搁爯(y霉)娓槸鍊熷姪a+bxi寰楀埌闋�(y霉)娓皪璞＄殑浼拌▓鍊紋i銆傜偤浜嗙⒑瀹歛鍜宐锛屽緸鑰屾彮绀鸿畩閲弝鑸噚涔嬮枔鐨勯棞(gu膩n)绯�锛屽叕寮忓彲浠ヨ〃绀虹偤锛�
銆€銆€y=a+bX
銆€銆€鍏紡y(t菕ng)=a+bX鏄紡y(t菕ng)=a+bx+e鐨勬摤鍚堟洸绶�?锛熸ⅱ宀愁巰闂疯儉銊楅挌銆婎懞鏈斻剶顒�?OLS)姹傚嚭鍥炴绯绘暩(sh霉)銆傛渶灏忎簩涔樻硶鍩烘湰鍘熷墖鏄皪浜庣⒑瀹氱殑鏂圭▼锛屼娇瑙€瀵熷€煎皪浼扮畻鍊煎亸宸殑骞虫柟鍜屾渶灏�銆傜敱姝ゆ眰寰楃殑鍥炴绯绘暩(sh霉)鐐猴細
銆€銆€b=[鈭憍iYi鈥晉鈭憏i]/鈭憍i2鈥晉鈭憍i
銆€銆€a=y鈥�-bx鈥�
銆€銆€寮忎腑锛歺i銆亂i鍒嗗垾鏄嚜璁婇噺x鍜屽洜璁婇噺y鐨勮瀵熷€�锛寈-銆亂-鍒嗗垾鐐簒鍜寉鐨勫钩鍧囧€�.
銆€銆€x-=鈭憍i/ n
銆€銆€y-= 鈭憏i/ n
銆€銆€灏嶄簬姣忎竴鍊嬭嚜璁婇噺鐨勬暩(sh霉)鍊�锛岄兘鏈夋摤鍚堝€硷細
銆€銆€yi鈥�=a+bxi
銆€銆€yi鈥欒垏瀵﹂殯瑙€瀵熷€肩殑宸�锛屼究鏄畼宸爡
銆€銆€ei=yi涓€yi鈥�
銆€銆€(浜�)鍥炴妾㈤
銆€銆€鍦ㄥ埄鐢ㄥ洖姝告ā鍨嬮€�(j矛n)琛岄爯(y霉)娓檪锛岄渶瑕佸皪鍥炴绯绘暩(sh霉)銆佸洖姝告柟绋嬮€�(j矛n)琛屾椹楋紝浠ュ垽瀹氶爯(y霉)娓ā鍨嬬殑鍚堢悊鎬у拰閬╃敤鎬�銆傛椹楁柟娉曟湁鏂瑰樊鍒嗘瀽銆佺浉闂�(gu膩n)妾㈤銆乼妾㈤銆丗妾㈤銆� 灏嶄簬涓€鍏冨洖姝�锛岀浉闂�(gu膩n)妾㈤鑸噒妾㈤銆丗妾㈤鐨勬晥鏋滄槸绛夊悓鐨�锛屽洜姝�锛屽湪涓€鑸儏娉佷笅锛岄€氶亷鍏朵腑涓€闋呮椹楀氨鍙互浜�銆傚皪浜庡鍏冨洖姝稿垎鏋�锛宼妾㈤鑸嘑妾㈤鐨勪綔鐢ㄥ嵒鏈夊緢澶х殑宸暟銆�
銆€銆€1.鏂瑰樊鍒嗘瀽
銆€銆€閫氶亷鎺ㄥ皫(d菐o)锛屽彲浠ュ緱鍑猴細
銆€銆€鈭�(yi鈥晊-)2= 鈭�(yi鈥晊i鈥�)2+鈭�(yi鈥晊-)2
銆€銆€鍏朵腑锛�
銆€銆€鈭�(yi鈥欌€晊-)2=TSS锛岀ū鐐哄亸宸钩鏂瑰拰锛�
銆€銆€鍙嶆槧浜唍鍊媦鍊肩殑鍒嗘暎绋嬪害锛屽張绋辩附璁婂樊銆�
銆€銆€鈭�(yi鈥晊i鈥�)2=RSS,绋辩偤鍥炴骞虫柟鍜�锛�
銆€銆€鍙嶆槧浜唜灏峺绶氭€у奖闊跨殑澶у皬锛屽張绋卞彲瑙ｉ噵璁婂樊銆�
銆€銆€鈭�(yi鈥晊i鈥�)2=ESS锛岀ū鐐烘畼宸钩鏂瑰拰锛�
銆€銆€鏍规摎(j霉)鍥炴妯″瀷鐨勫亣瑷�(sh猫)姊濅欢锛孍SS鏄敱娈樺樊闋卐閫犳垚鐨�锛屽畠鍙嶆槧浜嗛櫎x灏峺鐨勭窔鎬у奖闊夸箣澶栫殑涓€鍒囦娇y璁婂寲鐨勫洜绱狅紝鍏朵腑鍖呮嫭x灏峺鐨勯潪绶氭€у奖闊垮強瑙€瀵熻宸�銆傚洜鐐哄畠鐒℃硶鐢▁渚嗚В閲嬶紝鏁呭張绋辨湭瑙ｉ噵璁婂樊銆�
銆€銆€鎵€浠�锛孴SS=RSS+ESS
銆€銆€鍏跺闅涙剰缇╂槸绺借畩宸瓑浜庡彲瑙ｉ噵璁婂樊鑸囨湭瑙ｉ噵璁婂樊涔嬪拰銆�
銆€銆€鍦ㄩ€�(j矛n)琛屾椹楁檪锛岄€氬父鍏堥€�(j矛n)琛屾柟宸垎鏋�锛屼竴鏂归潰鍙互妾㈤鍦ㄨ▓绠椾笂鏈夌劇閷;鍙︿竴鏂归潰锛屼篃鍙互鎻愪緵鍏朵粬妾㈤鎵€闇€瑕佺殑鍩烘湰鏁�(sh霉)鎿�(j霉)銆�
銆€銆€瀹氱京鍙焙绯绘暩(sh霉)R2锛�
銆€銆€R2 =RSS/TSS
銆€銆€R2 鐨勫ぇ灏忚〃鏄庝簡y鐨勮畩鍖栦腑鍙互鐢▁渚嗚В閲嬬殑鐧惧垎姣旓紝鍥犳锛孯2 鏄⿻鍍瑰叐鍊嬭畩閲忎箣闁撶窔鎬ч棞(gu膩n)绯诲挤(qi谩ng)寮辩殑涓€鍊嬫寚妯�(bi膩o)?锛熸ⅱ瑭�?d菐o)鍑�锛�
銆€銆€R2 = RSS/TSS=鈭�(yi鈥晊i鈥�)2 /鈭�(yi鈥晊-)2
銆€銆€=1- ESS/ TSS=1-鈭�(yi鈥晊-)2 /鈭�(yi鈥晊-)2
