¡ÒÃÇÔà¤ÃÒÐËìÃÕà¡Ãʪѹ (Regression Analysis)

㹡ÒÃá¡é»Ñ­ËÒÍÒ¨ÁÕ 2 µÑÇá»ÃËÃ×ÍÁÒ¡¡ÇèÒà¢éÒÁÒà¡ÕèÂÇ¢éͧ´éÇ ÁÕ¤ÇÒÁ¨Óà»ç¹ËÃ×ͤÇÒÁÊӤѭ·ÕèµéͧËÒẺËØè¹áÅÐÊÓÃǨ¤ÇÒÁÊÑÁ¾Ñ¹¸ì¢Í§µÑÇá»ÃàËÅèÒ¹Ñé¹ àªè¹ 㹡Ãкǹ¡ÒÃÊѧà¤ÃÒÐËì·Ò§à¤ÁռżÅÔµ·Õèä´éÁÕ¤ÇÒÁÊÑÁ¾Ñ¹¸ì¡ÑºÍسËÀÙÁÔ·Õèãªé㹡ÒüÅÔµ¨Ö§Ê¹ã¨·Õè¨ÐÊÃéҧẺËØè¹·ÕèáÊ´§¤ÇÒÁÊÑÁ¾Ñ¹¸ìÃÐËÇèÒ§¼Å¼ÅÔµ·Õèä´é¡ÑºÍسËÀÙÁÔ·Õèãªé áÅйÓẺËØè¹¹Õéä»ãªé㹡ÒäҴ¤Ð๠(Prediction) ËÃ×Í»ÃѺ¡Ãкǹ¡ÒÃãËéàËÁÒÐÊÁ (Process optimization) ËÃ×ÍÍÒ¨ãªé㹡ÒäǺ¤ØÁ¡Ãкǹ¡ÒüÅÔµ (Process control)

â´Â·ÑèÇä» µÑÇá»ÃµÒÁáµèÅеÑÇá»ÃËÃ×ͤèҵͺʹͧ (Response; Y) ¨Ð¢Ö鹡ѺµÑÇá»ÃÍÔÊÃÐ K (Independent ËÃ×Í Regressor variables) àªè¹ X1,X2,…,Xk ¤ÇÒÁÊÑÁ¾Ñ¹¸ìÃÐËÇèÒ§µÑÇá»ÃàËÅèÒ¹Õé ÊÒÁÒö͸ԺÒÂâ´ÂẺËØè¹·Ò§¤³ÔµÈÒʵÃì·ÕèàÃÕ¡ÇèÒ “ ÊÁ¡ÒÃÃÕà¡Ãʪѹ ” ( ÊÁ¡Òö´¶Í : Regression equation) ẺËØè¹ÃÕà¡ÃʪѹÊÍ´¤Åéͧ¡Ñº¡ÅØèÁ¢éÍÁÙŢͧµÑÇÍÂèÒ§ ºÒ§¡Ã³Õ¼Ùé·´Åͧ·ÃÒº¶Ö§¿Ñ§¡ìªÑ¹¤ÇÒÁÊÑÁ¾Ñ¹¸ì·Õèá·é¨ÃÔ§ÃÐËÇèÒ§µÑÇá»Ã àªè¹ y = (x1,x2,…xk) à»ç¹µé¹ ÍÂèÒ§äáçµÒÁ â´ÂÊèǹãË­è¨ÐäÁè·ÃÒº¿Ñ§¡ìªÑ¹¤ÇÒÁÊÑÁ¾Ñ¹¸ì·Õèá·é¨ÃÔ§ÃÐËÇèÒ§µÑÇá»Ã ´Ñ§¹Õé¼Ùé·´Åͧ¨Ö§»ÃÐÁÒ³¤èҢͧ¿Ñ§¡ìªÑ¹à¾×èÍ»ÃÐÁÒ³¤èÒ â´ÂÁÑ¡ãªéẺËØ蹢ͧâ¾ÅÕâ¹àÁÕÂÅ (Polynomial)

ÇÔ¸ÕÃÕà¡Ãʪѹ ÍÒ¨ãªéÇÔà¤ÃÒÐËì¢éÍÁÙŨҡ¡Ò÷´Åͧ·ÕèäÁèä´éÇҧἹ àªè¹ ÍÒ¨¹Ó¢éÍÁÙŨҡ »ÃÒ¡®¡Òóì·ÕèäÁèÊÒÁÒö¤Çº¤ØÁä´éËÃ×Í¢éÍÁÙÅ·Ò§»ÃÐÇѵÔÈÒʵÃì ÍÂèÒ§äáçµÒÁ ¡ÒÃÇÔà¤ÃÒÐËìÃÕà¡ÃʪѹÁÕ»ÃÐ⪹ìÍÂèÒ§ÁÒ¡ÊÓËÃѺ¡Ò÷´Åͧ·ÕèÁÕ¡ÒÃÇҧἹäÇé ÍÒ¨¡ÅèÒÇä´éÇèÒ ¡ÒÃÇÔà¤ÃÒÐËì¤ÇÒÁá»Ã»Ãǹ (ANOVA) à»ç¹¡ÒÃÇҧἹ¡Ò÷´Åͧà¾×èͪèÇÂ㹡ÒèÓṡÇèһѨ¨ÑÂã´ÊӤѭ¢³Ð·ÕèÃÕà¡Ãʪѹãªéà¾×èÍÊÃéҧẺËØ蹤ÇÒÁÊÑÁ¾Ñ¹¸ìàªÔ§»ÃÔÁÒ³¢Í§»Ñ¨¨Ñ·ÕèÊӤѭµèͤèҵͺʹͧ

ÃÕà¡ÃʪѹàÊ鹵çẺ§èÒ (Simple Linear Regression)

ËÒ¡µéͧ¡ÒÃËÒ¤ÇÒÁÊÑÁ¾Ñ¹¸ìÃÐËÇèÒ§µÑÇá»ÃÍÔÊÃеÑÇá»Ãà´ÕÂÇ (x) ¡Ñº¤èҵͺʹͧ y µÑÇá»Ã x ÁÑ¡à»ç¹µÑÇá»Ãª¹Ô´µèÍà¹×èͧ ¹Ñ蹤×Í ÊÒÁÒö¤Çº¤ØÁä´éâ´Â¼Ùé·´Åͧ «Öè§ãËé¤èҵͺʹͧËÃ×ͤèÒÊѧࡵ y ·Õèä´é

ËÒ¡¤ÇÒÁÊÑÁ¾Ñ¹¸ì·Õèá·é¨ÃÔ§ÃÐËÇèÒ§ y áÅÐ x à»ç¹àÊ鹵ç áÅФèÒÊѧࡵ y ã¹áµèÅÐÃдѺ¢Í§ x à»ç¹µÑÇá»ÃÍÔÊÃРẺËØè¹·Õèä´é¨Ðà»ç¹

ËÒ¡ÁÕ¢éÍÁÙÅ n ¤Ùè àªè¹ (y 1 ,x 1 ) , (y 2 ,x 2 ),…, (y n ,x n ) ¨ÐÊÒÁö»ÃÐÁÒ³¤èҢͧ¾ÒÃÒÁÔàµÍÃì¢Í§áººËØè¹ áÅÐ â´ÂÇÔ¸Õ Least squares «Ö觨Ðä´éẺËØè¹ fitted simple linear regression ´Ñ§¹Õé

µÑÇÍÂèÒ§ 4.1 㹡ÒÃÈÖ¡ÉÒ¶Ö§¼Å¢Í§ÍѵÃҡǹµèÍ»ÃÔÁÒ³ÊÒÃÍÔ¹·ÃÕÂì·Õèä´é㹡ÒüÅÔµ¡Ã´ÍÐÁÔ⹪¹Ô´Ë¹Öè§ä´é¼Å´Ñ§¹Õé ( ´Ñ´á»Å§¨Ò¡ Montgomery ,1991)

- ¡Ò÷ӡÒÃÇÔà¤ÃÒÐËì Simple linear regression â´Â Statistix

·Ó¡Òûé͹¢éÍÁÙÅ â´ÂÊÃéÒ§µÑÇá»Ã 2 µÑÇá»Ã áÅлé͹ã¹ÅѡɳÐÃÙ»·Õè 4.1 ¨Ò¡¹Ñé¹·Ó¡ÒÃÇÔà¤ÃÒÐËìâ´ÂàÅ×Í¡àÁ¹Ù Statistic\Linear Models\Linear Regression… àÅ×Í¡µÑÇá»ÃµÒÁ¤×Í Yield áÅеÑÇá»ÃÍÔÊÃÐ ¤×Í Speed ãËéÊѧࡵÃÙ»·Õè 4.1 ãËéàÅ×Í¡ fit constant à¾×èͤӹdz¤èÒ ´éÇ ( ËҡẺËØè¹ËÃ×ÍÊÁ¡ÒõѴ¨Ø´ origin äÁèµéͧàÅ×Í¡ fit constant )

ÃÙ»·Õè 4.1 ¡Òûé͹¢éÍÁÙÅÊÓËÃѺ¡ÒÃÇÔà¤ÃÒÐËì Linear Regression â´Â SXW

ÃÙ»·Õè 4.2 ¡ÒÃàÅ×Í¡µÑÇá»Ãà¾×èÍ¡ÒÃÇÔà¤ÃÒÐËì Linear Regression

ä´é¼Å¡ÒÃÇÔà¤ÃÒÐËì´Ñ§¹Õé

ÊÁ¡Ò÷Õèä´é¨Ðà»ç¹

Yieid = -0.28928 + 0.45664 * speed

â´Â·ÕèÁÕ¤èÒ R Square (ÊÑÁ»ÃÐÊÔ·¸ì¢Í§¡ÒõѴÊԹ㨠; Coefficient of Determination) = 0.9338 ËÃ×Í 93.38 % ¤èÒ R 2 ¹Õé͸ԺÒÂä´éÇèÒ ¼Å¢Í§ Yield (y) ·Õèä´éà»ç¹¼ÅËÃ×ÍÍÔ·¸Ô¾Å¨Ò¡µÑÇá»Ã Speed(x) 93.38 % Êèǹ·ÕèàËÅ×ÍÍÕ¡ 6.62 % à»ç¹¼Å¨Ò¡µÑÇá»ÃËÃ×ͻѨ¨ÑÂÍ×è¹·ÕèäÁè·ÃÒºä´é ´Ñ§¹Ñé¹ËÒ¡ÁÕÊÒÁ¡ÒÃÁÕ¤èÒ R square ÂÔè§ÊÙ§à·èÒã´ ¤ÇÒÁáÁè¹ÂӢͧ¡ÒùÓÊÁ¡ÒÃä»ãªéà¾×èÍ·Ó¹ÒÂËÃ×ͤҴ¤Ð๼ÅÅѾ¸ìÂèÍÁÁÕÊÙ§ÁÒ¡ÂÔ觢Öé¹ â´Â·ÑèÇä» ÊÁ¡Ò÷ÕèÁÑ¡¹Óä»ãªé¤ÇÃÁÕ¤èÒ R Square ÍÂèÒ§¹éÍ 0.75 (Haaland , 1989 áÅÐ Hu , 1999) ËÒ¡ÊÙ§¡ÇèÒ 0.90 ¶×ÍÇèÒ´ÕÁÒ¡ (¤èÒ R 2 ÁÕ¤èÒµÑé§áµè 0 ¶Ö§ 1 â´Â·Õè 0 áÊ´§ÇèÒäÁèÁÕ¤ÇÒÁÊÑÁ¾Ñ¹¸ìã´ æ ÃÐËÇèÒ§µÑÇá»ÃµÒÁáÅÐÍÔÊÃÐ , 1 áÊ´§ÇèÒÁÕ¤ÇÒÁÊÑÁ¾Ñ¹¸ì¡Ñ¹ÍÂèÒ§ÊÁºÙóì) ÍÂèÒ§äáçµÒÁ¤èÒ R 2 à»ç¹¡ÒûÃÐÁÒ³ Goodness of fit ·Õèà¡Ô¹¨ÃÔ§ ¨Ö§ÁÑ¡ãªé¤èÒ adjusted R square 㹡ÒÃÇÑ´ Goodness of fit á·¹ (Hu, 1999) â´Â·ÑèÇä» adjusted R Square ¨ÐÁÕ¤èÒµèÓ¡ÇèÒܤèÒ R Square àÅ硹éÍ áÅÐ㹺ҧ¡Ã³ÕÍÒ¨¾ºà»ç¹¤èҵԴźä´é 㹡ÒÃÇÔà¤ÃÒÐËì Regression µéͧ·´ÊͺÊÁÁص԰ҹáÅÐáÊ´§¤èÒ F-ratio ËÃ×Í P äÇé´éÇÂàÊÁÍ ¤èÒF-ratio ËÃ×ͤèÒ P «Ö觨ÐáÊ´§¼Å¡ÒÃÇÔà¤ÃÒÐËìµÒÁÊÁÁص԰ҹ ´Ñ§¹Õé

¹Ñ蹤×Í ¤èÒ : ¨Ðà·èҡѺ¤èÒã´¤èÒ˹Öè§ àªè¹ 0 ËÃ×ÍäÁè ËÒ¡ÂÍÁÃѺ H o ÂèÍÁáÊ´§ÇèÒ äÁèÁÕ¤ÇÒÁÊÑÁ¾Ñ¹¸ìÃÐËÇèÒ§¤èÒ x áÅÐ y ã¹·Ò§µÃ§¢éÒÁËÒ¡»¯Ôàʸ H o ÂèÍÁáÊ´§ÇèÒÁÕ¤ÇÒÁÊÑÁ¾Ñ¹¸ì¡Ñ¹ÃÐËÇèÒ§ ¤èÒ x áÅÐ y ËÃ×Íà»ç¹¡Ò÷´ÊͺÇèÒ ¤èÒ R 2 à»ç¹ 0 ËÃ×ÍäÁèËÒ¡ P ÁÕ¤èÒÁÒ¡¡ÇèÒ 0.05 ¹Ñ蹤×Í áººËØè¹·Õè¡Ó˹´äÇéäÁèÁÕ¹ÑÂÊӤѭ·Ò§Ê¶ÔµÔ¡Ñº¢éÍÁÙŴѧ¡ÅèÒÇ ËÃ×ͤèÒ R Square à·èҡѺ 0 ¹Ñè¹àͧ ÊÓËÃѺ SXW ËÒ¡¤èÒ P ÁÒ¡¡ÇèÒ 0.05 â»Ãá¡ÃÁ¨ÐäÁèáÊ´§¤èÒµÑÇá»ÃáÅÐÊÑÁ»ÃÐÊÔ·¸Ôì ã¹ Predictor variables ÍÂèÒ§äáçµÒÁ ËÒ¡¤èÒ P ¹éÍ¡ÇèÒËÃ×Íà·èҡѺ 0.05 â»Ãá¡ÃÁ¨ÐáÊ´§¤èÒµÑÇá»ÃáÅÐÊÑÁ»ÃÐÊÔ·¸Ôìã¹ Predictor variables (ãËéÊѧࡵ¤èÒ P ËÅѧµÑÇá»Ãã¹ Predictor variables «Ö觨ÐÁÕ¤èÒÊÍ´¤Åéͧ¡Ñº¤èÒ P ã¹Êèǹ·éÒ¢ͧ¡ÒÃÇÔà¤ÃÒÐËì)

- ¡ÒÃÇÔà¤ÃÒÐËì Simple linear regression â´Â SPSS

¡Òûé͹¢éÍÁÙÅ ÁÕÅѡɳÐàªè¹à´ÕÂǡѺ SXW ¤×ÍÁÕ 2 µÑÇá»Ã ´Ñ§ÃÙ»·Õè 4.3

ÃÙ»·Õè 4.3 ¡Òûé͹¢éÍÁÙÅÊÓËÃѺ¡ÒÃÇÔà¤ÃÒÐËì Linear Regression â´Â SPSS

¨Ò¡¹Ñé¹·Ó¡ÒÃÇÔà¤ÃÒÐËìâ´Â àÅ×Í¡àÁ¹Ù Analyze\ Regression\Linear… ¨ÐáÊ´§ªèͧãËéàÅ×Í¡µÑÇá»ÃµÒÁáÅеÑÇá»ÃÍÔÊÃдѧÃÙ»·Õè 4.4

ÃÙ»·Õè 4.4 ¡ÒÃàÅ×Í¡µÑÇá»Ã㹡ÒÃÇÔà¤ÃÒÐËì Simple Linear Regression

ÃÙ»·Õè 4.5 ¡ÒáÓ˹´¡ÒÃÇÔà¤ÃÒÐËì¤èÒ¤§·Õè ¼Å¡ÒÃÇÔà¤ÃÒÐËìà»ç¹´Ñ§¹Õé

ËÒ¡µéͧ¡Òäӹdz¤èÒ¤§·Õè ãËéàÅ×Í¡·Õè Options áÅÐàÅ×Í¡ªèͧ include constant in equation ( â´Â»¡µÔ â»Ãá¡ÃÁ¡Ó˹´ãËé¤Ó¹Ç³¤èÒ¤§·ÕèäÇéàÊÁÍ ) áÅСÓ˹´ÇÔ¸Õ¡ÒÃÇÔà¤ÃÒÐËì (Method) à»ç¹áºº “ Enter” ´Ñ§ÃÙ»·Õè 4.5

¼Å¡ÒÃÇÔà¤ÃÒÐËì·Õèä´é áÊ´§ª×è͵ÑÇá»ÃáÅÐÇÔ¸Õ·Õèãªé㹡ÒÃÇÔà¤ÃÒÐËì ¾ºÇèÒ ¤ÇÒÁÊÑÁ¾Ñ¹¸ì·Õèä´éà»ç¹ÊÁ¡ÒÃàÊ鹵ç¤×Í

Yield = -0.289 + 0.457 * Speed â´Â·ÕèÁÕ¤èÒ R Square = 0.934

ÃÕà¡ÃʪѹàÊ鹵çẺËÅÒµÑÇá»Ã (Multiple Linear Regression)

㹡Ò÷´Åͧâ´Â·ÑèÇä» ÁÑ¡ÁÕµÑÇá»ÃÍÔÊÃзÕèʹã¨ÈÖ¡ÉÒÁÒ¡¡ÇèÒ 1 µÑÇá»Ã àªè¹ ¼Å¼ÅÔµ·Õèä´éÍÒ¨¢Ö鹡ѺÍسËÀÙÁÔ ÃÐÂÐàÇÅÒ㹡ÒüÅÔµ ËÃ×ͤÇÒÁ´Ñ¹ à»ç¹µé¹ ẺËØè¹·ÑèÇä»ÁÕÅѡɳдѧ¹Õé

¡Ò÷´ÊͺÊÁÁص԰ҹ â´Â¡ÒáÓ˹´ÊÁÁص԰ҹ ´Ñ§¹Õé

µÑÇÍÂèÒ§·Õè 4.2 㹡ÒÃÈÖ¡ÉÒ¶Ö§ÍسËÀÙÁÔ ¤ÇÒÁ´Ñ¹ áÅФÇÒÁà¢éÁ¢é¹¢Í§ÊÒõÑé§µé¹ µèÍ¡ÒüÅÔµÊÒê¹Ô´Ë¹Öè§ â´Â·ÕèáµèÅлѨ¨ÑÂÁÕ¡Òüѹá»Ã 2 ÃдѺ áÅÐãªé¡ÒèѴ¡Ò÷´ÅͧẺ 23 Factorial ä´é¼Å¡Ò÷´Åͧ´Ñ§¹Õé

- ¡ÒÃÇÔà¤ÃÒÐËì Multiple linear regression â´Â Statistix

·Ó¡Òûé͹¢éÍÁÙÅ â´ÂÊÃéÒ§ 4 µÑÇá»Ã áÅлé͹ã¹á¹Ç¤ÍÅÑÁ¹ì´Ñ§ÃÙ»·Õè ãËéÊѧࡵÇèÒ¨ÐãªéÃËÑÊ (code) ÊÓËÃѺÃдѺµèÒ§æ ã¹áµèÅеÑÇá»Ã

ÃÙ»·Õè 4.6 ¡Òûé͹¢éÍÁÙÅÊÓËÃѺ Multiple linear regression

ÃÙ»·Õè 4.7 ¡ÒÃàÅ×Í¡µÑÇá»Ãà¾×èÍÇÔà¤ÃÒÐËì Multiple linear regression

¼Å¡ÒÃÇÔà¤ÃÒÐËìà»ç¹´Ñ§¹Õé

¨Ò¡¼Å¡ÒÃÇÔà¤ÃÒÐËì¢éÒ§µé¹ ¡Ò÷´ÊͺÊÁÁص԰ҹ (Regession) ÁÕ¤èÒ P à·èҡѺ 0.0001 ·ÓãËé·ÃÒºÇèÒÁÕ ÍÂèÒ§¹éÍ 1 ¤èÒ·ÕèäÁèà·èҡѺ 0 àÁ×è;ԨÒóҵÑÇá»ÃÍÔÊÃÐ ¾ºÇèÒµÑÇá»Ã Pressure áÅÐ Temp ÁÕ¤èÒ P ¹éÍ¡ÇèÒ 0.05 (0.0000 áÅÐ 0.0006 µÒÁÅӴѺ ) ÊèǹµÑÇá»Ã Conc ÁÕ¤èÒ P 0.1210 «Öè§ÍÒ¨¨ÐäÁèãªéµÑÇá»Ã Conc ã¹ÊÁ¡Òáçä´é â´ÂãËé¹ÓÍÍ¡¨Ò¡µÑÇá»ÃÍÔÊÃÐã¹ÃÙ»·Õè … àËÅ×Í੾ÒеÑÇá»Ã Temp áÅÐ Pressure áÅзӡÒÃÇÔà¤ÃÒÐËìµèÍä» ¨Ðä´é¤èÒ R 2 ¨Ò¡à©¾ÒÐ 2 µÑÇá»Ã ËÒ¡äÁè¹ÓµÑÇá»Ã Conc ÍÍ¡ ¤èÒ R 2 ·Õèä´é¨Ðà»ç¹¢Í§·Ñé§ 3 µÑÇá»Ã

¨Ò¡¼Å¡ÒÃÇÔà¤ÃÒÐËìä´éÊÁ¡ÒäÇÒÁÊÑÁ¾Ñ¹¸ì´Ñ§¹Õé

Yield = 51.125 + 1.125*Conc + 10.625*Pressure + 5.625*Temp ; R Square = 0.9911

¨Ò¡ÊÑÁ»ÃÐÊÔ·¸ì¢Í§áµèÅеÑÇá»Ã ·ÓãËé·ÃÒºä´éÇèÒµÑÇá»Ãã´ÁÕÍÔ·¸Ô¾ÅÊÙ§¡ÇèÒ ¡ÅèÒǤ×Í à¹×èͧ¨Ò¡ÃдѺ·Õè¼Ñ¹á»Ãã¹µÑÇá»Ãä´éà¢éÒÃËÑÊäÇé ( ¤×Í –1 áÅÐ 1) ËÒ¡ÊÑÁ»ÃÐÊÔ·¸Ôì¢Í§µÑÇá»ÃÊÙ§¡ÇèÒµÑÇá»ÃÍ×è¹ ( äÁè¤Ô´à¤Ã×èͧËÁÒºǡËÃ×Íź à¤Ã×èͧËÁÒ´ѧ¡ÅèÒÇáÊ´§ÇèÒÁÕ¤ÇÒÁÊÑÁ¾Ñ¹¸ìẺá»ÃµÒÁ¡Ñ¹ËÃ×Íá»Ã¼¡¼Ñ¹¡Ñ¹ µÒÁÅӴѺ ) ÂèÍÁáÊ´§ÇèÒ µÑÇá»Ã¹Ñé¹ÁÕÍÔ·¸Ô¾ÅµèͤèÒ y ÊÙ§¡ÇèÒÍÕ¡µÑÇá»Ã˹Öè§ ¹Í¡¨Ò¡¹Õé ÍÒ¨Êѧࡵä´é¨Ò¡¤èÒ P ¢Í§µÑÇá»Ã â´ÂÂÔè§ÁÕ¤èÒ P ¹éÍÂà·èÒã´ ¨ÐÁÕÍÔ·¸Ô¾ÅÁÒ¡¢Öé¹à·èÒ¹Ñé¹

¨Ò¡µÑÇÍÂèÒ§ Êѧࡵä´éÇèÒ ·Ø¡µÑÇá»ÃÍÔÊÃÐÁÕÍÔ·¸Ô¾Å·Ò§ºÇ¡ ( ÁÕÊÑÁ»ÃÐÊÔ·¸ìà»ç¹ºÇ¡ ) ¡ÅèÒǤ×Í ËÒ¡à¾ÔèÁÃдѺ¢Í§µÑÇá»Ã¢Ö鹨ҡ –1 ¶Ö§ 1 ¤èÒ y ·Õèä´é¨Ðà¾ÔèÁÊÙ§¢Öé¹ ËÒõéͧ¡ÒäèÒ Yield ÊÙ§ÊØ´¨Ö§¤ÇÃãªé·ÕèÃдѺ¢Í§áµèÅеÑÇá»Ã·ÕèÃдѺÊÙ§·Ñé§ÊÔé¹

¹Í¡¨Ò¡¹ÕéËÒ¡ Yield ÊÙ§ÊØ´äÁèãªèÊÔ觷Õè¾Ô¨ÒóÒà¾Õ§ÍÂèÒ§à´ÕÂÇ ¡ÒþԨÒóÒÃдѺ¤ÇÒÁ´Ñ¹ ÍسËÀÙÁÔáÅФÇÒÁà¢éÁ¢é¹¢Í§·Õèʹã¨ËÃ×ÍÀÒÂãµé¢éͨӡѴÍ×è¹ ÍÒ¨¹Ó令ӹdzËÒ Yield ·Õè¤Ò´ÇèÒ¨Ðä´é «Öè§à»ç¹ÍÕ¡·Ò§àÅ×͡˹Öè§ã¹¡ÒùÓä»»ÃÐÂØ¡µìãªé

ÊÓËÃѺ¡ÒÃÇÔà¤ÃÒÐËì¼Åâ´Â SPSS ¹Ñé¹ ÊÒÁÒöãªéËÅѡࡳ±ì´Ñ§·Õèä´é¡ÅèÒÇ㹡è͹˹éÒ