ارزيابي بيزي نشانگرهاي زيستي وابسته به متغير هاي زماني...

8

Transcript of ارزيابي بيزي نشانگرهاي زيستي وابسته به متغير هاي زماني...

ù¢�¨ üΡ ö��¨Â𤠥� ù¢�Ôµ¨� �� ýÀ���ª�¡2ü�ùø�î ¥øÂú� Âµî¢ - 1ý¥¤¢�ð ¢�¥Âúªö�Âú� ù�ÚÈ÷�¢ ¤�õ� §��ª¤�î 1¤�Èî ©¥�õ� ǹ�¨ ö�õ¥�¨ ¤�õ� ¤�þ¢�µ¨� 2ý� û©ø¤ ¥� ��À û� È õ ýÀ � �� ª� ¡ ý� � ¤� õ� Ý Ü ä ¤¢ �f � Þ ã õ :ùÀ � Ø �ù¢�Ôµ¨� ... ø üܬ� ý�û�Ôó�õ ,ÂÈ�ê ý�û��Þõ ,ý��ª�¡ Û�ܽ� À�÷�õ ýÀ���Ö±ÏÂÑ÷ ¤¢ �ú÷� ö�Þµ¡�¨ �þ ø �ûùøÂð ¢�Àã� ¢¤�õ ¤¢ ü®Âê º�û �û©ø¤ ßþ� ¤¢ .¢�ªüõö��¨Âð¤ ý�ûñÀõ ¥� ù¢�Ôµ¨� �� �î ´¨� ßþ� Â� ü㨠®�� ÇûøÄ� ¤¢ .¢�ªüÞ÷ �µêÂðö���ä�� ,ß��ã � °þ® ý�±¨�½õ ´þ�ú ÷ ¤¢ ø ü÷��¨Âð¤ Í¡ ©¥� � ,ù¢�¨ üΡ��Àû�Èõ üØþ¢�÷ �Àä �þ üØþ¢�÷ ¢¤�õ ¤¢ ,ü÷��¨Âð¤ ñÀõ ¢�±ú� ǹ�¨ ý�Â� ý¤��ãõ�û�ܬ�ê ÅþÂ��õ ýø¤ Â� �ûÛ�ܽ� ,ÀþÀ� ©ø¤ ßþ� ¤¢ .Ýþ¥�¢Â³� �ûù¢�¢ ýÀ���ª�¡ ��ÂÑ÷ ¤¢ ü¨À�Üì� ý�ܬ�ê �¤ ��Àû�Èõ ß�� Û¬��ê ý�±¨�½õ ý��±õ .¢Â�ðüõ ��¹÷�.¢Â�ðüõ ¤�Âì ù¢�Ôµ¨� ¢¤�õ ,üΡ ö��¨Âð¤ ø ýÀ���ª�¡ ¶½±õ ø¢ Âû ¤¢ �î Ýþ��µêÂð�þ ¢¤�¢ ¢��ø ,ýÀ���ª�¡ ý�Â� ýÂ�ßÿÞÎõ ø µú� ©ø¤ �þ� �î ñ��¨ ßþ� �� ¾¨�� ý�Â�,ü÷��¨Âð¤ ñÀõ �� �ûù¢�¢ °¨��õ Çû�î ø Çþ��ê� �� �î üþ�÷��� ßþ� �� ý¤��ê��Â÷ Â�¡ßþ� ¥� ×þ Âû .´¨� ùÀª ý¥�¨ù¢��� ø ü��ÂÏ Õ�Ö½� Ý�� ͨ�� À���� �¤ ���ú� ý�ûñÀõ�� ¤��ê��Â÷ ¥� Û¬�� ¸þ�µ÷ ý�Æþ�Öõ �� �úµ÷� ¤¢ .´¨� �ª�¡ ×þ ÂÚ÷��� ,���ú� ý�ûñÀõ.Ýþ��µ¡�¢Â� (SPSS) ý¤�õ� ¸þ�¤ ¤��ê� �Â÷ ¸þ�µ÷ý� û� Ü ¬� ê ,ù¢� ¨ ü Î ¡ ö� � ¨Â ð¤ ,ýÀ � �� ª� ¡ :ýÀ � Ü î ý� ûù��ø.ü¨À�Üì��õÀÖõ 1? ´Æ�� ýÀ���ª�¡´¡��ª ,¢�Âê� ü��þ¥ ¤� ý�Â� �¤ é¤�ãµõ Â�è Ý�û�Ôõ ö���üõ ,�ûù¢�¢ ö¢Âî ýÀ���µ¨¢ ��.¢¤ø� Ýû�Âê ,Í��ø ¤ ¢¤�õ ¤¢ °ó�� ý�û­Âê ö¢Âî ¢�ú�È�� ø ù¢�µê�¤ø¢ ��Àû�Èõý�Â� ÂÈ�ê ý�û��Þõ ¥� ù¢�Ôµ¨� ö�»Þû ýÀ���Ö±Ï ý�û©ø¤ �� ö¢Âî ý��ª�¡ý�û�Ôó�õ ý�Ü�¨ø �� �÷�Þ÷ ��Â��ç� ö¢Âî �¬�¡ ,�ãõ�� ø¢ ýÀ��ù¢¤ ø ý¥�¨�À�¢�ªüõ ¯��Âõ ��Üãõ ý�û�µ¨¢ ¥� ý¢�Àã� �� ö¢Âî ýÀ���Ö±Ï .¢¤�¢ �ø�Ô� ... ø üܬ�Û� ܽ� .´¨�û�µ¨¢ ßþ� ¥� üØþ � � À þÀ� ��Àû�ÈõÉ�Ê¿� ö� üÜÞä éÀû ø�þ ø �ûùøÂð ¢�Àã� ¢¤�õ ¤¢ ü®Âê º�û ö� ¤¢ �î ´¨� üÞþÀì ©ø¤ ×þ ý�û�ª�¡.¢�ªüÞ÷ �µêÂð ÂÑ÷ ¤¢ �ú÷� ö�Þµ¡�¨§�¨� Â� �î ´¨� �ûÂ�çµõ �þ ��Àû�Èõ ýÀ���µ¨¢ ý�û©ø¤ ¥� üØþ ýÀ���ª�¡

2�� ¥��÷ �f¤�±�� ßþ�Â���� .À�îüõ ýÀ���Ö±Ï �¤ �ûù¢�¢ ,�û´ú��Èõ �Àä �þ ø �û´ú��Èõ×þ ��¿µ÷� ¢¤�õ ¤¢ ý¤��Æ� ý�û´��û£ .Ýþ¤�¢ ´ú��Èõ �� "üØþ¢�÷' ýù¥�À÷� ×þ"�µ¨���' ,"�µÆÆð' ý�ûÂ�çµõ ´�±Ï Ýúõ ý�ûü¨¤Â� �î ¢¤�¢ ¢��ø ´ú��Èõ ýù¥�À÷�"üµ±Æ÷' �þ ø "ý��ܬ�ê' ,"ü±��Â�' ,"üÞ¨�' ýÂ�ðù¥�À÷� ý�û§��Öõ �þ "üþ��ø¢' �þ ø.¢�ªüõ Ûõ�ª �¤ üä�®�õ Ç÷�¢ ø:�î ý��÷�ð �� ´¨� �ª�¡ k ß�� ,¢Âê �þ á�®�õ n ýÀ��Ý�ÆÖ� ,éÀû.¢�ª °Æµ�õ �ª�¡ ×þ �� �ú�� ø �ú�� ¢Âê Âû �.Àª�� ¢�Âê� Ûî Ûõ�ª �û�ª�¡ �ä�Þ¹õ �.À�ª�� (ßÚÞû) Ýû ��±ª ßØÞõ À� �� ,�ª�¡Ýû ¢�Âê� �.À�ª�� (ßÚÞû Â�è) ��±ª�÷ ,�ª�¡Ýû Â�è ¢�Âê� �n� p ýù¢�¢ ÅþÂ��õ ×þ ,üÜî ´ó�� ¤¢ ý��ª�¡ Û�ܽ� ý�Â� ü¨�¨� ý�ûù¢�¢.À÷�ªüõ Ý�ÆÖ� ùøÂð k �� X ÅþÂ��õ ÂΨ n �î ´¨�.À÷�ªüÞ÷ ¥�è� (Xn�p) ��¡ ý�ûù¢�¢ ÅþÂ��õ �� ,ý��ª�¡ Û�ܽ� ý�û©ø¤ µÈ�����È� �Àä �þ ���È� ÂÚ÷�È÷ �î ´¨� ýÂþ¢�Öõ Ûõ�ª �î À÷¤�¢ ¤�î ø ¨ üÆþÂ��õ �� �ØÜ�ø¢ ¥� ×þ Âû ý�Â� �� ÷ ´��Âì �ÞÜî �Ï��Âõ ����¢� ¤¢ .´¨� ¬��ä ýø¢ �� ø¢ ß���î ¢¤�¢ ¢��ø ´��Âì ǹ�¨ ý�Â� üÔܵ¿õ ý�ûù�¤ .¢�ªüõ ù¢Â� ¤�î �� ë�ê �¤�±ä.À÷¤�¢ üÚµÆ� �ûÂ�çµõ á�÷ �� �f�ÀÞä�� ,��j ¢Âê ø Xi = (xi1; xi2; : : : ; xip) ��ä�Ï� �� ,��i ¢Âê ß�� ý¤�õ� ý�ܬ�ê:´¨� Âþ¥ Ûت �� Xj = (xj1; xj2; : : : ; xjp) ��ä�Ï�d(x; y) =p(x � y)0A(x� y)¢��ø ßþ� �� .´¨�ûù¢�¢ Å÷�þ¤��î-Å÷�þ¤�ø ÅþÂ��õ S �î A = S�1 :Ýþ¤�¢ �f �Þãõö���üÞ÷ �¤ �û´�Þî ßþ� � þ�Þµõ ý�û�µ¨¢ ,ß�È�� ��ä�Ï� ßµª�¢ ¤��µ¡� ¤¢ öøÀ�¼��Â� �ûù¢�¢ ýÀ���ª�¡ ý�Â� ü¨À�Üì� �ܬ�ê �î ´¨� Û�ó¢ ß�Þû �� .¢Âî �±¨�½õ.¢�ªüõ ù¢�¢ö� �ø¢ ö��� ø ´¨� ýÀã�p ý�Ìê ¤¢ �ÎÖ÷ ø¢ ß�� üØþ��ê �ܬ�ê ü¨À�Üì� �ܬ�ê:Àþ�üõ ´¨¢ �� Âþ¥ �Î��¤ ¥�d2ij = pXk=1(xik � xjk)2 = (xi � xj)0(xi � xj) = jjxi � xj jj2Àª��üõ AB Í¡ù¤�� ñ�Ï ,ýÀã� 2 ý�Ìê ¤¢ �ܬ�ê ßþ� Çþ�Þ÷ ,p = 2 �î üõ�Ú�û��i ¢Âê ÂÚ÷��� (xA1; xA2) ��ʵ¿õ �� A �ÎÖ÷ .´¨� ùÀª ù¢�¢ Çþ�Þ÷ Âþ¥ Ûت ¤¢ �î.Àª��üõ ýÀã� 2 ý�Ìê ßþ� ¤¢ ,��j ¢Âê ÂÚ÷��� (xB1; xB2) ��ʵ¿õ �� B �ÎÖ÷ ø

3ýÀã�2 ý�Ìê ¤¢ �ÎÖ÷ ø¢ �ܬ�ê :1 Ûت���� �¤�¬�� �î ´¨� ��úÔõ ö� �� ,À�ª�� Â�×þ¢�÷ ÂÚþÀØþ �� �ÎÖ÷ ø¢ ßþ� �� Âûü�ãþ ,�ø�Ô� ø¢ ßþ� Âð� �î ý¤�Ï�� .À÷¤�À÷ ü÷�À�� �ø�Ô� ,xB2 �� xA2 ø xB1 �� xA1À�û��¡ Õ±Î�õ Ýû Â� B ø A �ÎÖ÷ ø¢ À�ª�� ÂÔ¬ ø¢ Âû ,xB2 � xA2 ø xB1 � xA1¯�Ö÷ �ܬ�ê Àª�� �µª�¢ ÂÔ¬ �� ý¢�þ¥ �ø�Ô� ,ø¢ ßþ� ¥� üØþ Ûì�À� Âð� ÅØäÂ� .¢��.¢�� Àû��¡ ï¤�� ¤��Æ� ,(dAB) ,B ø A�� ù��ª ßþ� ¢� þ¥ üÚµÆ��ø ,ü¨À�Üì� �ܬ�ê ©ø¤ ¥� ù¢�Ôµ¨� ý�ûÉÖ÷ ¥� üØþµÈ�� ,�û¢Â�¤�î ¥� ý¤��Æ� ¤¢ .´¨� �ú÷� Å÷�þ¤�ø ��÷ ø �ûÂ�çµõ ýÂ�ðù¥�À÷� §��Öõý� � íµÈõ §��Öõ ×þ ý�¤�¢ ,À ÷�ª ù¢Â � ¤� î � � Û� ܽ� ¤¢ À þ� � �î üþ�û � ç µ õ�� �ûÂ�çµõ ´ã�±Ï �þ À��ø�Ôµõ ,��Ô¬ ýÂ�ðù¥�À÷� ý�û§��Öõ ù�ðÂû .À�µÆ�÷ ýÂ�ðù¥�À÷�,Û¬��ê �±¨�½õ ¥� Ç�� �î ´¨� ßþ� Â� ��¬�� ,À÷¤�À÷ íµÈõ §��Öõ �î ´¨� ý��÷�ð¢¤�À÷�µ¨� ý�ûù¢�¢ ¥� ù¢�Ôµ¨� �� ų¨ .À÷�ª ¢¤�À÷�µ¨� ý¤�õ� ��úÔõ �� ��¡ ý�ûù¢�¢.¢�ª �±¨�½õ �ú÷� ß�� ü¨À�Üì� �ܬ�ê ,ùÀª¢�Àã� �� Â��Â� ö� ý�ûö�µ¨ ø �ûÂΨ ¢�Àã� �î ´¨� üã�Âõ üÆþÂ��õ ,�ܬ�ê ÅþÂ��õ��j ¢Âê ø ��i ¢Âê �ܬ�ê ö���õ ÂÚ÷��� ,��j ö�µ¨ ø ��i ÂΨ �� ¯��Âõ ÂÊ�ä .´¨� ¢�Âê�.À�µÆû ÂÔ¬ ,ÅþÂ��õ ßþ� üܬ� ÂÎì ýø¤ ¬��ä �î ´¨� üúþÀ� .Àª��üõýÀ � �� ª� ¡ ×� � Ø � ¥� ù¢� Ô µ ¨� ý� � À þ� � ,Û¬�� ê Å þ �� õ � ± ¨� ½ õ ¥� Å ��î ;´¨� ü±��Âõ �ÜÆܨ ©ø¤ ,�û×��Ø� ßþÂ�ñ�Þãõ ßþ� ¥� üØþ .¢�ª ýÂ�ðÝ�ÞÊ�Ý�ÆÖ� ùøÂð ø¢ �� ¢�¡ ,×��Ø� ßþ� .¢�ªüõ �û�ª�¡ �Ü�Âõ �� �Ü�Âõ Û�ØÈ� Ûõ�ª:¢�ªüõ1Ýî�µõ :12ùÀª ýÀ��Ý�ÆÖ� :2¢� ê� ¢�À ã � � � ü � ã þ .´¨� �ª�¡ ×þ ü þ� ú � � � � ¢�¡ ¢Â ê  û �À µ �� ,ñø� ©ø¤ ¤¢ø ùÀª ��è¢� Ýû ¤¢ �û�ª�¡ ßþ� �Àì �� �Àì ýÀã� Û��Âõ ¤¢ ų¨ .¢¤�¢ ¢��ø �ª�¡Agglomerative 1Divisive 2

4×þ ¤¢ ¢�Âê� �Þû ¡� �Ü�Âõ ¤¢ �î ý¤�Ï�� .À�û¢üõ Û�ØÈ� �¤ µð¤�� ý�û�ª�¡.À÷Â�ðüõ ¤�Âì �ª�¡�� �Ü�Âõ ų¨ ø À÷�ªüõ ¤�Ñ�õ �ª�¡ ×þ ¤¢ ¢�Âê� �Þû �Àµ�� ,�ø¢ ýÀ��ùøÂ𠤢.À÷�ªüõ ¢�¹þ� ÀþÀ� ý�û�ª�¡ �Ü�ÂõùÄ þø � � ø Ýî� µõ ü± ��Âõ �ÜÆܨ ý�û©ø¤ ¥� ù¢�Ô µ¨� ,ÇûøÄ� ßþ� ¤¢ �õ �îÂÞ �.´¨� 3ýÀ÷��� ý�û©ø¤:4üØ� À÷���ß� � ý�û´ú ��È õ � þ Û¬�� ê À ÷�� �üõ ,üØ � À ÷� � � Ý µ þ¤�Ú ó� ×þ ý�ûý¢ø¤ø�û�þ�ÆÞû ßþÂ�×þ¢�÷ ö¢Âî °�îÂ� �� üØ� ý�û´�û�õ ¥� �û�µ¨¢ .Àª�� ��ª� ý�û�ø¥ßþµÈ�� �þ �ܬ�ê ßþµÞî Â� ´ó�¢ �þ�ÆÞû ßþÂ�×þ¢�÷ ��ά� �î À÷�ªüõ Û�ØÈ�.¢¤�¢ ´ú��Èõø ù¢Âî �À�� �¤ (À�µÆû �ûdij ö� ý�Ìä� �î) D ÅþÂ��õ ¤¢ �ܬ�ê ßþµÞî Àþ�� �Àµ��.Ý��î °�îÂ� UV ý�ª�¡ ö¢¤ø� ´¨¢ �� ý�Â� �¤ V ø U À�÷�õ ÂÒ��µõ ý��ª�:´¨� Âþ¥ Ûت �� D ÅþÂ��õ ¤�µ¡�¨D = fdijg = 123...n 266664 0d21 0d31 d32 0... ... ... . . .dn1 dn2 dn3 dn�1;n�1 0377775� � �¤ W À � ÷� õ Â Ú þ¢ ý� ª� ¡  û ø UV ß � � Û ¬�� ê À ã � ý� Ü � õ ¤¢dUW ø dVW ý�û´�Þî �� ßþ� ¤¢ .Ý��îüõ �±¨�½õ d(UV )W = minfdUW ; dVW gW ø V ý�û�ª�¡ ø W ø U ý�û�ª�¡ üÚþ�ÆÞû ßþÂ�×þ¢�÷ ß�� Û¬��ê °��Â� ��.´¨�¤�¢�Þ÷ ×þ Ûت �� ý¤�¢�Þ÷ �¤�¬�� ö���üõ �¤ üØ� À÷��� ýÀ���ª�¡ ¸þ�µ÷üþ�ûùÂ𠤢 �û�¡�ª .À�µÆû �û�ª�¡ ÂÚ÷�È÷ ,´¡¤¢ ý�û�¡�ª �î ¢�¢ Çþ�Þ÷ 5üµ¡¤¢�¤ ü½Î¨ ,(´ú��Èõ �þ) �ܬ�ê ¤�½õ ×þ ¢�Àµõ� ¤¢ ö�ȵ�ã®ø �î À÷�ªüõ °�îÂ�.¢À÷���üõ á�ìø �� �ûüÚµ¨��� ö� ¤¢ �î Àû¢ ö�È÷?´Æ�� 6ö��¨Â𤤢 �¤ ö��¨Âð¤ ��ά� 1885 ñ�¨ ¤¢ 7"ö�µó�ð Å�Æ÷�Âê¨' ¤�� ß�µÆ¿÷ ý�Â�Linkage Methods 3Single Linkage 4Dendrogram 5Regression 6Sir Fran is Galton 7

5Í��ø¤ .´ê�þ ´�ó�±Öõ ´ä¨ �� ø Â�â�¨ø ¢�ã�� ¤¢ ö� ¥� Å� ø ¢Â� ¤�î �� ¢�¡ �ó�Öõ:¢Âî ýÀ��Ý�ÆÖ� �µ¨¢ �¨ �� ö���üõ �¤ Â�çµõ ø¢ ö��õ ¢���õÛ��ì Ûõ�î ¤�Ï�� ,ü®�þ¤ Ý�û�Ôõ ���¤�� ¤¢ �fõ�Þä Í��ø ¤ á�÷ ßþ� :ý±� Í��ø ¤ �.À�µÆû ö���Ûõ�î ¤�Ï�� ,üØþ��ê Ý�û�Ôõ ���¤�� ¤¢ �fõ�Þä Í��ø ¤ á�÷ ßþ� :ý±� �Þ�÷ Í��ø ¤ �.À�µÆû ö��� Û��ìý¢Àä ��ä�Ï� ¤�µ¡�¨ ø ��¹� §�¨� Â� �f õ�Þä Í��ø ¤ á�÷ ßþ� :ü�¹� Í��ø ¤ �.¢�ªüõ ý¤�Áð�þ�� ùÀª ù¢�¢.Ýþ¤�¢ ¤�î ø¨ ü�¹� Í��ø ¤ ü�ãþ ,��¨ á�÷ �� ,ý¥�¨ñÀõ ø ¤�õ� ¤¢ �f �Þãõö� ¤¢ �î y ø x Â�çµõ ø¢ ¢���õ Âþ¢�Öõ ß�� �Î��¤ ß��ã� ¥� ´¨� �¤�±ä üþ�ú÷ éÀû.´¨� x �� �µÆ��ø Â�çµõ y �î üó�� ¤¢ ,À�îüõ ÛÞä ÛÖµÆõ Â�çµõ ×þ �¤�¬�� xüê¢�Ê� �÷�Þ÷ ý�û�µê�þ �� ü���µ¨¢ ¥� Å� ,Â�çµõ ø¢ ß�� �Î��¤ �ãó�Îõ ø ü¨¤Â� ´ú�.´¨� Ç�î�Â� ¤�¢�Þ÷ ݨ¤ ,üÖÎ�õ ��ð ß�óø� ,À�µÆû ùÀû�Èõ ´Ô� �¤�¬�� �î üþ��nüê¢�Ê� �÷�Þ÷ ý�û�µê�þ §�¨�Â� Â�çµõ ø¢ ß�� ßØÞõ �Î��¤ ÂÚ÷��� ø ÂÚ÷�þ�Þ÷ ¤�¢�Þ÷ ßþ�¤¢ ýÂÑ÷ �þ üܱì á�Ï� º�û ´¨� ßØÞõ �ãó�Îõ ¢¤�õ ¢¤��õ ¥� ý¤��Æ� ¤¢ .¢�� Àû��¡°¨��õ À÷ø ¤ ×þ ���¤� ´ú� Ç�î�Â� ¤�¢�Þ÷ ßþ�Â���� .Àª�� �µª�À÷ ¢��ø y ø x ß�� À÷ø ¤.´¨� ¤�¢¤�¡Â� ý�ûÄþø ´�Þû� ¥� ý¤�õ� ñÀõ ý�Â�ù¢�¨ üΡ ü÷��¨Âð¤ ñÀõ�Ü�¨ø �� y ø x ý�ûÂ�çµõ ù�Ú÷� ,Àª�� Ý�ÖµÆõ Í¡ ×þ �fÖ�ì¢ y ø x ö��õ �Î��¤ Âð�°�ª �1 ø �À±õ ¥� ­Âä �0 �î ý¤�Ï�� .À÷�ªüõ ¯��Âõ Ýû �� y = �0 + �1x ñ�õÂêø À�µÆû ��Üãõ�÷ �ûµõ�¤�� ßþ� .Ý�õ�÷üõ ý¤�õ� ñÀõ ý�ûµõ�¤�� �¤ �1 ø �0 .´¨� Í¡.À��îüõ ß��ã� �¤ ´¨�¤ Í¡ ö�ØõÂþ¥ �Î��¤ ¥� ù¢�Ôµ¨� �� ö���üõ �¤ �1 ñ�ú¹õ µõ�¤�� ,��ã�Âõ Ûì�À� ©ø¤ §�¨�Â�:¢Âî ¢¤ø�Â��̂1 = SxySxx = Pni=1(xi � �x)(yi � �y)Pni=1(xi � �x)2.´¨� �±¨�½õ Û��ì (R2) ß��ã� °þ® ×þ ,ù¢�¨ üΡ ü÷��¨Âð¤ ñÀõ Âû ý�Â�:¢�ªüõ �±¨�½õ Âþ¥ �¤�¬�� ñÀõ ß��ã� °þ®R2 = SSRSST.SSR = �̂1Sxy ø SST =Pni=1(yi � �y)2 ö� ¤¢ �î

6�� ¤�ÀÖõ ßþ� ¤ÀÖ� Âû �î �¤�¬ ßþ� �� .Àª��üõ [0;1℄ ýù¥�� �� ÕÜãµõ R2 ¤�ÀÖõ.´¨� µú� ùÀª ù¢�¢ ©¥�Â� ö��¨Âð¤ Í¡ ,Àª�� Â�×þ¢�÷ ×þ�� ,ù¢�¨ üΡ ö��¨Âð¤ ý�ûñÀõ ¥� ù¢�Ôµ¨� ø ©ø¤ ø¢ ßþ� °�îÂ� �� Ýþ¤�¢ üã¨ý�ûñÀõ ��¿µ÷� ¶ä�� ü÷��¨Âð¤ ý�û©ø¤ ýÂ�ð¤�î �� .Ýþ¥�¢Â³� ��Àû�Èõ ýÀ���µ¨¢.Àª À�û��¡ ¢�¹þ� �û�ª�¡ ,�ûñÀõ ßþ� §�¨� Â� �î ¢�ªüõ ���ú�ý�Â� ùÄþø ¤��ê� �Â÷ ×þ ý¥�¨ ù¢��� ø ü��ÂÏ �� ��Àì� Õ�Ö½� ùøÂð ,�µ¨�¤ ßþ� ¤¢,Û�ÊÔ� �� �î ´¨� ù¢�Þ÷ ù¢�¨ üΡ ü÷��¨Â𤠩ø¤ ¥� ù¢�Ôµ¨� �� ýÀ�� �ª�¡ ��¹÷�¤��Æ� ��±¨�½õ ��¹÷� ¥� Å� ¤��ê��Â÷ ßþ� .´¡�¢Â� Ý�û��¡ ö� ¢ÂØÜÞä ýù�½÷ �����¤� �¤ ��Àû�Èõ ý�Â� ýÀ���ª�¡ ßþµú� ,ý¤�ÂØ� ý�û©ø¤ ¥� ù¢�Ôµ¨� �� ø ü÷��Ï.¢�¢ Àû��¡ý¢�ú�È�� ©ø¤ ݵþ¤�Úó��� �¤ ö¢Âî ý��ª�¡ .Ý��îüõ �±¨�½õ �¤ (�û�ܬ�ê ÅþÂ��õ) D ÅþÂ��õ ¥�è� ¤¢:Ý��îüõ ¥�è� ùÀû�Èõ ø¢ ßþÂ�×þ¢�÷ ö¢Âî ùøÂðÝû´¨� ý�ù¢�¢ ø¢ ÂÚ÷��� �þ�¤¢ ßþ� .Ý��îüõ �À�� �¤ D ÅþÂ��õ �þ�¤¢ ßþµØ��î :1 ��ð.Ýþ¢Âî ¢�¹þ� �¤ ñø� ý�ª�¡ Å� .À÷¤�¢ Ýû �� �¤ �ܬ�ê ßþµÞî �î�� .À÷¤�¢ ��óø� ýù¢�¢ ø¢ �� �¤ �ܬ�ê ßþµÞî �î Ýþ¢Âðüõ ù¢�¢ ø¢ ñ�±÷¢ �� :2 ��ð.À÷�ªüõ �Ìä 4 ,ñø� ý�ª�¡ ýùÀ�û¢Û�ØÈ� ý�Ìä� ,ÀþÀ� ýù¢�¢ ø¢ ßþ� ßµê�þñÀõ ß� óø� ø Ý �û¢üõ ©¥� � ,ù¢�¢ ¤�ú� ßþ� � � �¤ ü ÷� �¨Â ð¤ Í¡ ñ�� :3 �� ð� ±¨�½õ �¤ R2 ù¤� õ� ¤�ÀÖ õ ñÀõ ßþ� ý� � .Ý þ¤ø�üõ ´¨¢ � � �¤ (M1) ü÷� �¨Âð¤.Ý��îüõý�ª�¡ ýùÀ�û¢ Û�ØÈ� ýù¢�¢ 4 ßµª�¢ �� ,¤�� ßþ� .Ýþ¢Âðüõ¥�� 2 ��ð �� :4 ��ð�µª�¢ �¤ �ܬ�ê ßþµÞî ,�ª�¡ ßþ� ý�Ìä� �� �î Ýþ¢Âðüõ ÂÚþ¢ ýù¢�¢ 4 ñ�±÷¢ �� ,ñø�.À�ª���¤ (M2) ü÷��¨Âð¤ ñÀõ ß�õø¢ ø Ýþ¤�¢ ù¢�¢ 8 ¤�� ßþ� .Ýþ¢Âðüõ¥�� 3 ��ð �� :5 ��ð.Ý��îüõ �±¨�½õ ��÷ �¤M2 ñÀõ R2 ø Ýþ¤ø�üõ ´¨¢ �� ù¢�¢ 8 ßþ� ý�Â��� R2k �î ´¨� ßþ� ��k �Ü�Âõ ¤¢ ý¤�� �ª�¡ ¥� ÀþÀ� �Ìä �ø¡ ø Óì�� ¯ÂªÕÖ½õ ÂÑ÷ �� üÚµÆ� Çþ��ê� ßþ� ö���õ) Àª�� �µª�À÷ ü¨�ƽõ Çþ��ê� ,R2k�1 ´±Æ÷� � Ý þ¢Âðüõ¥� � ñø� �� ð � � ,�ø¡ ¯Âª öÀª ¤� ì � � � .(0=0011 ñ�·õ ý� � .¢¤�¢.Ýþ¥�Æ� �¤ ýÀã� ý�ª�¡:´¨� ý¤ø® Âþ¥ ¢¤��õ �� ���� ,©ø¤ ßþ� µú� í¤¢ ý�Â�ø¢ ßþ� ý�ܬ�ê �� ÂÒ��µõ ý�þ¤�¢ ,¢�ªüõ ü¨¤Â� ù¢�¢ ø¢ ý�ܬ�ê �î ��ð Âû ¤¢ �1ý�û��𠤢 .¢�ªüõ ö� ßþ�Úþ�� "ÂÔ¬' ø ¢ø¤üõ ß�� ¥� ,D ÅþÂ��õ ¤¢ ,ù¢�¢.À�ª�� ÂÔ¬ Â�è �î À÷�ªüõ ü¨¤Â� üþ�û�þ�¤¢ ÍÖê ýÀã�

7,ÂÔ¬ Â�è ý�þ�¤¢ �î À��þüõ �õ�¢� ü÷�õ¥ �� ýÀ���ª�¡ ,ùÀª Âî£ ¢¤�õ �� ���� �� �2.Àª�� �µª�¢ ¢��ø ,D ÅþÂ��õ ¤¢ü¨¤Â� ¢¤�õ ý�ª�¡ �� Àþ�� �î ÀþÀ� ý�ûù¢�¢ ¢¤�¢ ö�Øõ� ,¢¤��õ ¥� ý¤��Æ� ¤¢ �3¢¤�õ ý�ª�¡ �� ý¤�ÂØ� ýù¢�¢ ¢ø¤ø ¥� ,âì��õ ßþ� ¤¢ !À�ª�� ý¤�ÂØ� ,À÷�ª ¢¤�ø.Àõ� Àû��¡ ÛÞä �� ýÂ�ð�Ü� ,ÂÑ÷ü¨¤Â� Àþ�� ùÀû�Èõ n ýÀ���ª�¡ ý�Â� ´ó�� n2 ,ùÀª Ó�¬�� ݵþ¤�Úó� §�¨� Â� �4�� ,üܬ� ÂÎì ý�û�þ�¤¢ ö¢�� ÂÔ¬ ø ,D ÅþÂ��õ ö¤�Ö� �� ���� �� ¤�ÀÖõ ßþ� .¢�ª.À��þüõ Çû�î ,´ó�� (n2 � n)=2ýù¢�¢ ,�÷�ð�À� ý�ª�¡ À�� �þ ø¢ ¤¢ �î ´¨� üã�±Ï �f õ�î ,4 À�� �� ���� �� �5:¢�ªüõ ÛÞä Âþ¥ �¤�¬�� ,¢¤��õ �÷�ð ßþ� ¤¢ .Àª�� ¢���õ ý¤�ÂØ�¥� �ûù¢�¢ ý��Üî ý�ܬ�ê �� À��þüõ �õ�¢� ,ùÀª Âî£ ñ�ø ¤ Õ±Ï üܬ� ݵþ¤�Úó� �1� 5.¢�ª ü¨¤Â� ,ÂÚþÀØþ.À÷�ªüõ É¿Èõ ,À÷¤�¢ ý¤�ÂØ� ý�ûù¢�¢ �î üþ�û�ª�¡ �2� 5.À÷�ªüõ éÁ� �û�ª�¡ ý��Üî ¥� ý¤�ÂØ� ý�ûù¢�¢ �3� 5.¢�ªüõ �µêÂð ÂÑ÷ ¤¢ (data1) ý¤�ÂØ� ýù¢�¢ ß�óø� �4� 5ß��ã� °þ® ,´¨� ùÀª éÁ� ù¢�¢ �ú÷� ¥� data1 �î üþ�û�ª�¡ ý��Üî ý�Â� �5� 5.¢�ªüõ �±¨�½õ ,(R21) ñø�.¢�ªüõ �ê�®� ,¢�� ùÀª éÁ� �ú÷� ¥� �î üþ�û�ª�¡ ý�Þû �� ù¤��ø¢ data1 �6� 5� ±¨�½õ data1 ¤�Ì� � � � û�ª�¡ ý�� Ü î ý� � ,(R22) �ø¢ ß� � ã � °þ® �7� 5.¢�ªüõý��Üî ý�Â� ,((R22�R21) ü�ãþ) �ø¢ ß��ã� °þ® ø ñø� ß��ã� °þ® �ø�Ô� �8� 5.¢�ªüõ �±¨�½õ ,ü¨¤Â� ¢¤�õ ý�û�ª�¡¤¢ ýµÈ�� Çþ��ê� ,ö� ¤�Ì� �î ´¨� ý��ª�¡ �� ÕÜãµõ ý¤�ÂØ� ýù¢�¢ �9� 5¢��ø �¤�¬ ¤¢) .À � îüõ ¢�¹ þ� �ª�¡ ö� ü÷� �¨Â ð¤ ñÀõ ß� � ã � °þ®Ý�ÞÊ� �� ÂÑ÷ ¢¤�õ ù¢�¢ É�Ê¿� ,�ûñÀõ ß��ã� °þ® ¤¢ Â��Â� Çþ��ê�.(¢�ªüõ ¤�Áð�ø ÕÖ½õö�õ¥ ø ´ì¢ �� ��ð Âû ��±¨�½õ ø ´¨� Â�ð´ìø ¤��Æ� ݵþ¤�Úó� ßþ� ¤�ÂØ� �î �¹÷� ¥��î ´¨� ùÀª ü��ÂÏ ý¤��ê��Â÷ ,�ûÂ���³õ�î ¢��ø ÓÎó �� ø ,´¨� À�õ¥��÷ ý¢�þ¥ ¤��Æ�.Àª��üõ ÂÑ÷ ¢¤�õ ݵþ¤�Úó� ý�Â�� �� ¤¢�ìü÷��¨Âð¤ ý�ûÍ¡ ©¥�Â� ø ��±¨�½õ ý�Þ÷ À÷ø ¤ :2 Ûت:Àª��üõ Âþ¥ �¤�¬�� Õ�Ö½� ßþ� ¤¢ ùÀõ� ´¨À� üþ�ú÷ ý�û�ª�¡

8

ø ßþ �¤ø¢ ,ßþ �×þ¢� ÷ ý�û©ø¤ �� �î SPSS ¤�� ê�� ÷ ¤¢ ýÀ� ��ª�¡ ¸þ� µ ÷ � � �î:Àª��üõ �Æþ�Öõ Û��ì Âþ¥ �¤�¬�� �ܬ�ê ß�Ú÷��õâ��Âõ,ö�úÔ¬� üµã�¬ ù�ÚÈ÷�¢ ÂÈ÷ �îÂõ ,¤�õ� ø ñ�Þµ�� ü÷�±õ ,(1384) .� ,ö��¨¤� �.ö�úÔ¬�,ö�Âú � ù�ÚÈ÷�¢ ,üÏ�±� µ¨� ¤�õ� ø ñ�Þµ�� ,(1382) .ö ,¤� µ¨ø¢¢� þ� ,.� ,ת��.ö�Âú�Douglas, ., Montgomery, et al, (2004), Introdu tion to Linear RegressionAnalysis, New York.Alvin, C. Ren her (1988), Methods of Multivariate Analysis, United Statesof Ameri a.Douglas, C., Montgomery, et al, (2000), Applied Multivariate Statisti alAnalysis, New York.Galton, F. (1885), Regression TowardsMedio rity in Heredity Stature. Jour-nal of Anthropologi al Institute, 15, 246-263. [Histori prespe tive on re-gression℄.Greve, K.W. et al, (2002), Wis onsin Card Sorting Test in Chroni SevereTraumati Brain Injury: F tor Stru ture and Performan e Subgroups,Brain Injury, 16, 29-40.