 

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺎﺻﻴﺔ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‬ ‫ﺍﳌﺘﻌﺪﺩ‪.‬‬ ‫ﺍﻟﺮﻳﺎﺽ‪ .‬ﺟﺎﻣﻌﺔ ﺍﳌﻠﻚ ﺳﻌﻮﺩ‪ .‬ﻗﺴﻢ ﺍﻹﺣﺼﺎﺀ ﻭﲝﻮﺙ ﺍﻟﻌﻤﻠﻴﺎﺕ ‪1431‬ﻫـ ‪ 2010‬ﻡ‪.‬‬

‫ﺑﺄﺷﺮﺍﻑ ﺃ‪.‬ﺩ‪ /‬ﻋﺒﺪﺍﷲ ﺑﻦ ﻋﺒﺪﺍﻟﻜﺮﱘ ﺍﻟﺸﻴﺤﺔ‪.‬‬ ‫ﺇﻋﺪﺍﺩ‪ /‬ﻋﺒﺪﺍﻟﻌﺰﻳﺰ ﺑﻦ ﻣﻨﺎﺣﻲ ﺍﳌﻄﲑﻱ‪.‬‬

‫ﺷﻜﺮﹰﺍ ﻟﻜﻢ‪.‬‬ ‫ﺍﺷﻜﺮ ﺃﻋﻀﺎﺀ ﻫﻴﺌﺔ ﺍﻟﺘﺪﺭﻳﺲ ﰲ ﻗﺴﻢ ﺍﻹﺣﺼﺎﺀ ﻭﲝﻮﺙ ﺍﻟﻌﻤﻠﻴﺎﺕ ﻭﲨﻴﻊ ﻣﻦ ‪‬ﻠﺖ ﻣﻦ ﲝﺮ‬ ‫ﻋﻠﻤﻬﻢ ﻭﺑﺎﻷﺧﺺ ﺍﻷﺳﺘﺎﺫ ﺍﻟﺪﻛﺘﻮﺭ‪ /‬ﻋﺒﺪﺍﷲ ﺑﻦ ﻋﺒﺪﺍﻟﻜﺮﱘ ﺍﻟﺸﻴﺤﺔ‪.‬‬

‫ﺍﻟﻔﻬﺮﺱ‪.‬‬ ‫ﺍﳌﻮﺍﺿﻴﻊ‬ ‫ﺍﳌﻘﺪﻣﺔ ﻭﺃﻫﺪﺍﻑ ﺍﻟﺒﺤﺚ‪..............................................................‬‬ ‫‪ 1‬ﲢﺪﻳﺪ ﻣﺸﺎﻫﺪﺍﺕ ﻗﺎﺻﻴﺔ ﰲ ‪) X‬ﺍﳌﺘﻐﲑ ﺍﳌﺴﺘﻘﻞ( – ﻣﺼﻔﻮﻓﺔ ﺍﻟﻘﺒﻌﺔ ﻭﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ‪............‬‬ ‫ﺣﺎﻻﺕ ﻗﺎﺻﻴﺔ‪.......................................................................‬‬ ‫ﺍﺳﺘﺨﺪﺍﻡ ﻣﺼﻔﻮﻓﺔ ﺍﻟﻘﺒﻌﺔ "‪ "H‬ﻭﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ‪........................................ hii‬‬ ‫ﻃﺮﻳﻘﺔ ﻛﺸﻒ ﺍﻟﻘﻴﻢ ﺍﻟﻘﺎﺻﻴﺔ ﰲ ﺍﳌﺘﻐﲑﺍﺕ ﺍﳌﺴﺘﻘﻠﺔ ﺑﺎﺳﺘﺨﺪﺍﻡ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ‪............... hii‬‬ ‫‪ 2‬ﲢﺪﻳﺪ ﻣﺸﺎﻫﺪﺍﺕ ﻗﺎﺻﻴﺔ ﰲ ‪) Y‬ﺍﳌﺘﻐﲑ ﺍﻟﺘﺎﺑﻊ( – ﺑﻮﺍﻗﻲ ﺍﳊﺬﻑ ﺍﳌﻌﲑﺓ‪.....................‬‬ ‫ﺣﺴﺎﺏ )ﺑﻮﺍﻗﻲ ﺍﳊﺬﻑ(‪..............................................................‬‬ ‫ﺑﻮﺍﻗﻲ ﺍﳊﺬﻑ ﺍﳌﻌﲑﺓ )ﺑﻮﺍﻗﻲ ﺳﺘﻮﺩﻧﺖ ﺍﶈﺬﻭﻓﺔ(‪.........................................‬‬ ‫ﻃﺮﻳﻘﺔ ﻛﺸﻒ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺎﺻﻴﺔ ﰲ ﺍﳌﺘﻐﲑ ﺍﻟﺘﺎﺑﻊ ‪....................................Y‬‬ ‫‪ 3‬ﲢﺪﻳﺪ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ – ﺗﺪﺍﺑﲑ ) ‪Cook’s Distance, DFBETAS,‬‬ ‫‪.................................................(DFFITS, COVRATIO‬‬ ‫‪ 3-1‬ﺍﻟﺘﺄﺛﲑ ﻋﻠﻰ ﻗﻴﻢ ﺍﻟﺘﻮﻓﻴﻘﻴﺔ – ﻣﻘﻴﺎﺱ )‪......................................(DFFITS‬‬ ‫ﻃﺮﻳﻘﺔ ﻛﺸﻒ ﺍﻟﺘﺄﺛﲑ ﻟﻘﻴﻤﺔ ‪ DFFITS‬ﻋﻠﻰ ﺍﻟﻨﻤﻮﺫﺝ‪..................................‬‬ ‫‪ 3-2‬ﺍﻟﺘﺄﺛﲑ ﻋﻠﻰ ﻣﻌﺎﻣﻼﺕ ﺍﻻﳓﺪﺍﺭ – ﻣﻘﻴﺎﺱ )‪.............................(DFBETAS‬‬ ‫ﻃﺮﻳﻘﺔ ﻛﺸﻒ ﺍﻟﺘﺄﺛﲑ ﻟﻘﻴﻤﺔ ‪ DFBETAS‬ﻋﻠﻰ ﺍﻟﻨﻤﻮﺫﺝ‪..............................‬‬ ‫‪ 3-3‬ﻗﻴﺎﺱ ﺍﻷﺛﺮ ﻋﻠﻰ ﻛﻞ ﻣﻌﺎﻣﻼﺕ ﺍﻻﳓﺪﺍﺭ – ﻣﻘﻴﺎﺱ ﻣﺴﺎﻓﺔ ﻛﻮﻙ ‪.......................Di‬‬ ‫ﻃﺮﻳﻘﺔ ﻛﺸﻒ ﺍﻟﺘﺄﺛﲑ ﻟﻘﻴﻤﺔ ﻣﺴﺎﻓﺔ ﻛﻮﻙ ‪...........................................Di‬‬ ‫‪ 3-4‬ﻗﻴﺎﺱ ﺍﻷﺛﺮ ﻋﻠﻰ ﺍﻷﺧﻄﺎﺀ ﺍﳌﻌﻴﺎﺭﻳﺔ – ﻣﻘﻴﺎﺱ ‪........................COVRATIO‬‬ ‫ﻃﺮﻳﻘﺔ ﻛﺸﻒ ﺍﻟﺘﺄﺛﲑ ﻟﻘﻴﻤﺔ ‪ COVRATIO‬ﻋﻠﻰ ﺍﻷﺧﻄﺎﺀ ﺍﳌﻌﻴﺎﺭﻳﺔ‪..................‬‬ ‫‪ 4‬ﺗﺸﺨﻴﺼﺎﺕ ﺍﻹﺭﺗﺒﺎﻃﻴﺔ ﺍﳋﻄﻴﺔ ﺍﳌﺘﻌﺪﺩﺓ ‪ -‬ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ‪..................................‬‬ ‫ﻋﺎﻣﻞ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ )‪.........................................................(VIF‬‬ ‫ﻃﺮﻳﻘﺔ ﺍﻟﻜﺸﻒ ﻋﻦ ﻭﺟﻮﺩ ﺍﺭﺗﺒﺎﻁ ﺧﻄﻲ ﻣﺘﻌﺪﺩ‪.........................................‬‬ ‫ﻣﺘﻮﺳﻂ ﻗﻴﻢ ﻋﻮﺍﻣﻞ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ ﳌﻌﺎﻣﻼﺕ ﺍﻻﳓﺪﺍﺭ‪....................................‬‬ ‫‪5‬‬

‫ﺩﺭﺍﺳﺔ ﲡﺮﻳﺒﻴﺔ )ﳏﺎﻛﺎﺓ( ﳌﻘﺎﺭﻧﺔ ﺣﺴﻦ ﺃﺩﺍﺀ ﻣﻘﺎﻳﻴﺲ ﺍﻛﺘﺸﺎﻑ ﺍﳊﺎﻻﺕ ﺍﳌﺆﺛﺮﺓ ﻟﻨﻤﻮﺫﺝ ﺍﳓﺪﺍﺭ‬ ‫ﺧﻄﻲ ﺑﺴﻴﻂ‪........................................................................‬‬ ‫ﺍﳌﺮﺍﺟﻊ‪.............................................................................‬‬

‫ﺍﻟﺼﻔﺤﺔ‬ ‫‪I,II‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪23‬‬ ‫‪23‬‬ ‫‪24‬‬ ‫‪25‬‬ ‫‪32‬‬ ‫‪32‬‬ ‫‪33‬‬ ‫‪34‬‬ ‫‪35‬‬ ‫‪35‬‬ ‫‪36‬‬ ‫‪36‬‬ ‫‪37‬‬ ‫‪53‬‬ ‫‪55‬‬ ‫‪55‬‬ ‫‪56‬‬ ‫‪60‬‬ ‫‪86‬‬

‫‪I‬‬

‫ﺍﳌﻘﺪﻣﺔ‪-:‬‬ ‫ﲢﻠﻴﻞ ﺍﻻﳓﺪﺍﺭ‪ .‬ﻫﻮ ﺃﺩﺍﺓ ﺇﺣﺼﺎﺋﻴﺔ ﺗﺴﺘﻔﻴﺪ ﻣﻦ ﺍﻟﻌﻼﻗﺔ ﺑﲔ ﻣﺘﻐﲑﺍﺕ ﻛﻤﻴﺔ ﺃﻭ ﻭﺻﻔﻴﺔ‪ ،‬ﻭﺫﻟﻚ‬ ‫ﻼ‬ ‫ﻟﻠﻮﺻﻒ ﺃﻭ ﺍﻟﺴﻴﻄﺮﺓ ﺃﻭ ﺍﻟﺘﻨﺒﺆ ﺑﺄﺣﺪ ﺍﳌﺘﻐﲑﺍﺕ ﺍﺳﺘﻨﺎﺩﹰﺍ ﺇﱃ ﻗﻴﻢ ﺍﳌﺘﻐﲑ ﺃﻭ ﺍﳌﺘﻐﲑﺍﺕ ﺍﻷﺧﺮﻯ‪ ،‬ﻓﻤـﺜ ﹰ‬ ‫ﳝﻜﻦ ﺍﻻﺳﺘﻔﺎﺩﺓ ﻣﻦ " ﲢﻠﻴﻞ ﺍﻻﳓﺪﺍﺭ " ﻋﻨﺪ ﺩﺭﺍﺳﺔ ﺍﻟﻌﻼﻗﺔ ﺑﲔ "ﺍﻟﺪﻭﺍﺀ ﻭﺍﺳﺘﺠﺎﺑﺔ ﺍﳌﺮﺿﻰ" ﰲ ﺍﻟﺘﻨﺒـﺆ‬ ‫ﺑﺎﻻﺳﺘﺠﺎﺑﺔ ﺣﺎﳌﺎ ﺗﺘﻮﻓﺮ ﻟﻨﺎ ﻣﻘﺎﺩﻳﺮ ﺗﺮﻛﻴﺰ ﺍﻟﺪﻭﺍﺀ ﻭﺗﺄﺛﲑﻩ ﻋﻠﻰ ﺍﳌﺮﻳﺾ‪.‬‬ ‫ﻟﻜﻦ ﺍﻟﺘﺤﻠﻴﻞ ﺍﻹﺣﺼﺎﺋﻲ ﻗﺪ ﻳﺘﺄﺛﺮ ﺑﺒﻌﺾ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺎﺻﻴﺔ )ﺍﻟﺸﺎﺫﺓ( ﺃﻭ ﺍﳋﺎﺭﺟﺔ ﻭﺍﳌﺘﻄﺮﻓﺔ‬ ‫– ‪ -Outlying & extreme observation‬ﺍﻟﱵ ﺭﲟﺎ ﻣﻦ ﺷﺄ‪‬ﺎ ﻳﻜﻮﻥ ﳍﺎ ﺗﺄﺛﲑ ﻭﺍﺿـﺢ‬ ‫ﻋﻠﻰ ﺍﻟﻨﺘﺎﺋﺞ ﻭﺍﻟﺘﺤﻠﻴﻞ‪ .‬ﻳﺮﺟﻊ ﺑﺮﻭﺯ ﺍﻟﺒﻴﺎﻧﺎﺕ ﺍﻟﻘﺎﺻﻴﺔ ﺇﱃ ﺃﺧﻄﺎﺀ ﺇﻣﺎ ﰲ ﻣﺮﺣﻠﺔ ﲨﻊ ﺍﻟﺒﻴﺎﻧـﺎﺕ ﺃﻭ ﰲ‬ ‫ﻣﺮﺣﻠﺔ ﺍﳌﻌﺎﳉﺔ ﻛﺈﺩﺧﺎﻝ ﺍﻟﺒﻴﺎﻧﺎﺕ ﰲ ﺍﳊﺎﺳﺐ ﻭﻗﺪ ﺗﻜﻮﻥ ﺍﻟﺒﻴﺎﻧﺎﺕ ﺣﻘﻴﻘﺔ ﻧﺎﲡﺔ ﻋﻦ ﻇـﺮﻭﻑ ﻏـﲑ‬ ‫ﻼ ﺣﺪﻭﺙ ﻛﻮﺍﺭﺙ ﻃﺒﻴﻌﻴﺔ ﻛﺎﻟﺰﻻﺯﻝ‪ ،‬ﺍﻷﻋﺎﺻﲑ‪ ،‬ﺍﻷﻣﻄﺎﺭ ﺍﻟﻐﺰﻳﺮﺓ ﻳﺆﺛﺮ ﻋﻠﻰ ﻣـﺴﺘﻮﻳﺎﺕ‬ ‫ﻋﺎﺩﻳﺔ‪ ،‬ﻓﻤﺜ ﹰ‬ ‫ﺍﻹﻧﺘﺎﺝ ﺍﻟﺰﺍﺭﻋﻲ ﻭﺍﳊﻴﻮﺍﱐ ﻭﺍﻟﺼﻨﺎﻋﻲ‪ ،‬ﺇﺿﺮﺍﺏ ﻋﻤﺎﻝ ﰲ ﻣﻨﺸﺄﺓ ﻣﺎ ﻳﺆﺛﺮ ﻋﻠﻰ ﺇﻧﺘﺎﺟﻬﺎ‪ ،‬ﺍﳊﺮﻭﺏ ﺑـﲔ‬ ‫ﺍﻟﺪﻭﻝ ﺗﺆﺛﺮ ﻋﻠﻰ ﺍﻗﺘﺼﺎﺩﻳﺎﺕ ﻫﺬﻩ ﺍﻟﺪﻭﻝ‪ .‬ﻓﻔﻲ ﻫﺬﺍ ﺍﻟﺒﺤﺚ ﺳﻮﻑ ﻧﺘﻄﺮﻕ ﺇﱃ ﺍﻟﺘﺸﺨﻴﺼﺎﺕ ﺍﶈـﺴﻨﺔ‬ ‫ﻟﻠﺘﺤﻘﻖ ﻣﻦ ﺻﻼﺣﻴﺔ ﳕﻮﺫﺝ ﺍﻻﳓﺪﺍﺭ‪ ،‬ﻭﺗﺘﻀﻤﻦ ﻃﺮﻕ ﻟﻜﺸﻒ ﻣﺸﺎﻫﺪﺍﺕ ﻗﺎﺻـﻴﺔ ‪ ،‬ﻭﺍﳌـﺸﺎﻫﺪﺍﺕ‬ ‫ﺍﳌﺆﺛﺮﺓ ‪ ،‬ﻭﺍﳋﻄﻴﺔ ﺍﳌﺘﻌﺪﺩﺓ ‪ ،‬ﻭﺃﻳﻀﹰﺎ ﺳﻮﻑ ﻧﺪﺭﺱ ﻛﻴﻒ ﺳﺘﺘﻢ ﺍﻟﺘﺪﺍﺑﲑ ﺍﻟﻌﻼﺟﻴﺔ ﳍﺎ ﺑﺈﺫﻥ ﺍﷲ‪ .‬ﻭﺫﻟﻚ‬ ‫ﺇﳝﺎﻧﺎ ﻣﻨﺎ ﺑﺪﻭﺭﻩ ﻛﺄﺩﺍﺓ ﻣﻬﻤﺔ ﰲ ﺍﻟﺘﻨﺒﺆ ﻭﲢﻠﻴﻞ ﺍﻟﺒﻴﺎﻧﺎﺕ ﺍﻹﺣﺼﺎﺋﻴﺔ‪.‬‬ ‫ﺃﻫﺪﺍﻑ ﺍﻟﺒﺤﺚ‪-:‬‬ ‫‬ ‫‬ ‫‬ ‫‬

‫ﲢﺴﻴﻨﺎﺕ ﻟﺼﻼﺣﻴﺔ ﳕﻮﺫﺝ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬ ‫ﻃﺮﻕ ﻛﺸﻒ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺎﺻﻴﺔ )ﺍﻟﺸﺎﺫﺓ(‪.‬‬ ‫ﻃﺮﻕ ﻛﺸﻒ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﳕﻮﺫﺝ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬ ‫ﺗﺸﺨﻴﺼﺎﺕ ﺍﻹﺭﺗﺒﺎﻃﻴﻪ ﺍﳋﻄﻴﺔ ﺍﳌﺘﻌﺪﺩﺓ‪.‬‬

‫ﺍﻟﱪﺍﻣﺞ ﺍﳌﺴﺘﺨﺪﻣﺔ‪-:‬‬ ‫‬ ‫‬ ‫‬

‫‪Microsoft Office Excel‬‬ ‫‪SPSS 17‬‬ ‫‪MINITAB 14‬‬ ‫‪II‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫)‪ (1‬ﲢﺪﻳﺪ ﻣﺸﺎﻫﺪﺍﺕ ﻗﺎﺻﻴﺔ ﰲ ‪) X‬ﺍﳌﺘﻐﲑ ﺍﳌﺴﺘﻘﻞ ( – ﻣﺼﻔﻮﻓﺔ ﺍﻟﻘﺒﻌﺔ ﻭﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ‪-:‬‬ ‫ ﺣﺎﻻﺕ ﻗﺎﺻﻴﺔ‪:‬‬‫ﻛﺜﲑﹰﺍ ﻣﺎ ﲢﺘﻮﻱ ﳎﻤﻮﻋﺔ ﻣﻦ ﺍﻟﺒﻴﺎﻧﺎﺕ ﰲ ﺗﻄﺒﻴﻖ ﲢﻠﻴﻞ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ ﻋﻠﻰ ﺑﻌﺾ ﺍﳊـﺎﻻﺕ‬ ‫ﺍﻟﻘﺎﺻﻴﺔ ﺃﻭ ﺍﳌﺘﻄﺮﻓﺔ ﺃﻱ ﺃﻥ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳋﺎﺻﺔ ‪‬ﺬﻩ ﺍﳊﺎﻻﺕ ﺗﻜﻮﻥ ﻣﻨﻔﺼﻠﺔ ﺑﻮﺿـﻮﺡ ﻋـﻦ ﺑﻘﻴـﺔ‬ ‫ﺍﳌﺸﺎﻫﺪﺍﺕ‪ .‬ﻭﻗﺪ ﺗﺄﺛﺮ ﻋﻠﻰ ﺩﺍﻟﺔ ﺍﻻﳓﺪﺍﺭ ﺍﻟﺘﻮﻓﻴﻘﻴﺔ ﻭﻣﻦ ﺍﳌﻬﻢ ﺩﺭﺍﺳﺔ ﺍﳊﺎﻻﺕ ﺍﻟﻘﺎﺻﻴﺔ ﺑﻌﻨﺎﻳﺔ ﻭﺗﻘﺮﻳﺮ ﻣﺎ‬ ‫ﺇﺫﺍ ﻛﺎﻥ ﻳﻨﺒﻐﻲ ﺍﻻﺣﺘﻔﺎﻅ ‪‬ﺎ ﺃﻭ ﺇﻟﻐﺎﺅﻫﺎ ﺃﻭ ﺗﻘﻠﻴﻞ ﺃﺛﺮﻫﺎ‪.‬‬ ‫ﻭﰲ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ ﲟﺘﻐﲑ ﻣﺴﺘﻘﻞ ﻭﺍﺣﺪ ﺃﻭ ﻣﺘﻐﲑﻳﻦ ﻳﻜﻮﻥ ﻣﻦ ﺍﻟﺴﻬﻞ ﻧﺴﺒﻴﹰﺎ ﺍﻟﺘﻌﺮﻑ ﻋﻠﻰ‬ ‫ﻣﺸﺎﻫﺪﺍﺕ ﻗﺎﺻﻴﺔ ﰲ ﻗﻴﻢ ‪) X‬ﺍﳌﺘﻐﲑ ﺍﳌﺴﺘﻘﻞ( ﺃﻭ ﰲ ‪) Y‬ﺍﳌﺘﻐﲑ ﺍﻟﺘﺎﺑﻊ( ﺑﻮﺳﺎﺋﻞ ﻣﺜﻞ ﺍﻟﺮﺳﻢ ﺍﻟﺼﻨﺪﻭﻗﻲ‬ ‫"‪ ،"Box plot‬ﺭﺳﻮﻡ ﺍﳉﺬﻉ ﻭﺍﻟﻮﺭﻗﺔ "‪ ،"Stem-and-leaf Plot‬ﺭﺳﻮﻡ ﺍﻻﻧﺘﺸﺎﺭ‬ ‫"‪ ،"Scatter Plot‬ﻭﺭﺳﻮﻡ ﺍﻟﺒﻮﺍﻗﻲ "‪."Residuals Plot‬‬ ‫ﺇﻻ ﺍﻧﻪ ﻋﻨﺪﻣﺎ ﻳﺸﻤﻞ ﳕﻮﺫﺝ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ ﻋﻠﻰ ﺃﻛﺜﺮ ﻣﻦ ﻣﺘﻐﲑﻳﻦ ﻣﺴﺘﻘﻠﲔ‪ ،‬ﻳﺼﺒﺢ ﺍﻟﺘﻌﺮﻑ‬ ‫ﻋﻠﻰ ﻣﺸﺎﻫﺪﺍﺕ ﻗﺎﺻﻴﺔ ﺑﺎﻟﻮﺳﺎﺋﻞ ﺍﻟﺴﺎﺑﻘﺔ ﺃﻣﺮﹰﺍ ﺻﻌﺒﹰﺎ ﻭﻗﺪ ﻻ ﻧﺘﻤﻜﻦ ﻣﻦ ﺍﻛﺘﺸﺎﻑ ﻗﺎﺻﻴﺎﺕ ﻟﺬﻟﻚ‬ ‫ﻧﺘﻌﺮﻑ ﺍﻵﻥ ﻋﻠﻰ ﺍﺳﺘﺨﺪﺍﻡ ﻣﺼﻔﻮﻓﺔ ﺍﻟﻘﺒﻌﺔ "‪ "Hat Matrix‬ﺍﻟﱵ ﻗﺪ ﺗﺴﺎﻋﺪ ﰲ ﺍﻛﺘﺸﺎﻑ ﺍﳊﺎﻻﺕ‬ ‫ﺍﻟﻘﺎﺻﻴﺔ ﰲ ﳕﻮﺫﺝ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ ﺑﺄﻛﺜﺮ ﻣﻦ ﻣﺘﻐﲑ ﻣﺴﺘﻘﻞ‪.‬‬

‫ ﺍﺳﺘﺨﺪﺍﻡ ﻣﺼﻔﻮﻓﺔ ﺍﻟﻘﺒﻌﺔ "‪ "H‬ﻟﻠﺘﻌﺮﻑ ﻋﻠﻰ ﻣﺸﺎﻫﺪﺍﺕ ﻗﺎﺻﻴﺔ ﰲ ﺍﳌﺘﻐﲑ ﺍﳌﺴﺘﻘﻞ ‪.X‬‬‫ﺗﻌﺮﻑ ﻣﺼﻔﻮﻓﺔ ﺍﻟﻘﺒﻌﺔ ‪ H‬ﺑﺎﻟﻌﻼﻗﺔ ﺍﻟﺘﺎﻟﻴﺔ‪:‬‬ ‫'‪X‬‬

‫ﻭﺣﻴﺚ ﺃﻥ‬

‫‪hii‬‬

‫‪( X ' X ) −1‬‬

‫‪X‬‬

‫=‪H‬‬

‫ﻫﻮ ﺍﻟﻌﻨﺼﺮ ﺍﻟﻘﻄﺮﻱ ﳌﺼﻔﻮﻓﺔ ﺍﻟﻘﺒﻌﺔ ‪ H‬ﻭﻳﻌﺮﻑ ﺑﺎﻟﻌﻼﻗﺔ ﺍﻟﺘﺎﻟﻴﺔ‪:‬‬ ‫‪Xi‬‬

‫‪( X ' X ) −1‬‬

‫''‪X i‬‬

‫= ‪hii‬‬

‫‪1‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫ﻭﺣﻴﺚ ﺃﻥ‬

‫‪Xi‬‬

‫ﲣﺺ ﻓﻘﻂ ﺍﳌﺸﺎﻫﺪﺓ ‪: i‬‬ ‫‪ 1 ‬‬ ‫‪ X ‬‬ ‫‪ i ,1 ‬‬ ‫‪Xi = . ‬‬ ‫‪‬‬ ‫‪‬‬ ‫‪ . ‬‬ ‫‪ X i , p −1 ‬‬ ‫‪‬‬ ‫‪‬‬

‫ﻛﺬﻟﻚ ﻣﻦ ﺧﻮﺍﺹ ﺍﻟﻌﻨﺼﺮ ﺍﻟﻘﻄﺮﻱ ﺃﻥ ﻗﻴﻤﺘﻬﺎ ﺗﻘﻊ ﺑﲔ ﺍﻟﺼﻔﺮ ﻭﺍﻟﻮﺍﺣﺪ ﻭﺍﻥ ﳎﻤﻮﻋﻬﺎ ﻳﺴﺎﻭﻱ ‪:p‬‬ ‫‪=p‬‬

‫‪n‬‬

‫‪∑h‬‬

‫‪0 ≤ hii ≤ 1 ,‬‬

‫‪ii‬‬

‫‪i =1‬‬

‫ﺣﻴﺚ ‪ p‬ﺗﺴﺎﻭﻱ ﻋﺪﺩ ﻣﻌﺎﱂ ﰲ ﳕﻮﺫﺝ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬ ‫ ﻃﺮﻳﻘﺔ ﻛﺸﻒ ﺍﻟﻘﻴﻢ ﺍﻟﻘﺎﺻﻴﺔ ﰲ ﺍﳌﺘﻐﲑﺍﺕ ﺍﳌﺴﺘﻘﻠﺔ ﺑﺎﺳﺘﺨﺪﺍﻡ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ‪: hii‬‬‫ﺗﻌﺘﱪ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ‬ ‫ﻭﻓﻘﹰﺎ ﻟﻠﻌﻼﻗﺔ‪.‬‬

‫‪hii‬‬

‫ﻛﺒﲑﺓ ﺇﺫﺍ ﲡﺎﻭﺯﺕ ﺿﻌﻒ ﻣﺘﻮﺳﻂ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ﻭﻧﺮﻣﺰ ﳍﺎ ﺑـ‬

‫_‬

‫‪h‬‬

‫ﻭﻫﻲ ﺗـﺴﺎﻭﻱ‬ ‫‪n‬‬

‫‪p‬‬ ‫‪n‬‬

‫ﺑﺎﻟﺘﺎﱄ ﻓﺄﻥ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ﺍﻷﻛﱪ ﻣﻦ ﺿﻌﻒ ﻣﺘﻮﺳﻂ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ‬

‫‪2p‬‬ ‫‪n‬‬

‫‪∑h‬‬

‫‪ii‬‬

‫=‬

‫‪i =1‬‬

‫‪n‬‬

‫_‬

‫=‪h‬‬

‫ﺗﻌﺘﱪ ﻗﻴﻢ ﻗﺎﺻﻴﺔ ﻭﻓﻘﹰﺎ ﳍﺬﻩ‬

‫ﺍﻟﻘﺎﻋﺪﺓ‪ ،‬ﻭﻫﻲ ﻣﺆﺷﺮ ﺟﻴﺪ ﻟﻮﺟﻮﺩ ﻣﺸﺎﻫﺪﺍﺕ ﻗﺎﺻﻴﺔ‪ .‬ﺃﻱ ﺇﺫﺍ ﻛﺎﻥ‪:‬‬ ‫‪2p‬‬ ‫‪n‬‬

‫> ‪hii‬‬

‫ ﺗﻄﺒﻴﻖ )‪:(1-1‬‬‫ﰲ ﺑﻴﺎﻧﺎﺕ ﻃﺒﻴﺔ ﺳﺤﺒﺖ ﻣﻦ ﻣﺴﺘﺸﻔﻰ ﺃ‪‬ﺎ ﻟﻠﻨﺴﺎﺀ ﻭﺍﻟﻮﻻﺩﺓ ﻟﻘﻴﺎﺱ ﺍﻟﻌﻼﻗﺔ ﺑﲔ ﻭﺯﻥ ﺍﻟﻄﻔﻞ‬ ‫)ﺑﺎﻟﻜﻴﻠﻮ ﺟﺮﺍﻡ( ﻭﺗﺄﺛﺮﻩ ﺑﺰﻳﺎﺩﺓ ﺍﻟﻌﻤﺮ)ﺳﻨﺔ( ﻭﺍﻟﻄﻮﻝ)ﺳﻢ( ﻟﻌﻴﻨﺔ ﻣﻦ ‪ 50‬ﻃﻔﻞ ﻛﺎﻧﺖ ﺍﻟﺒﻴﺎﻧﺎﺕ ﻛﺎﻟﺘﺎﱄ‪:‬‬ ‫الطول = ‪X2‬‬

‫العمر = ‪X1‬‬

‫الوزن = ‪Y‬‬

‫المشاھدات‬

‫الطول = ‪X2‬‬

‫العمر = ‪X1‬‬

‫الوزن = ‪Y‬‬

‫المشاھدات‬

‫‪57‬‬ ‫‪63‬‬ ‫‪92‬‬ ‫‪53‬‬ ‫‪98‬‬ ‫‪102‬‬

‫‪0.33‬‬ ‫‪0.75‬‬ ‫‪3.83‬‬ ‫‪0.25‬‬ ‫‪4.75‬‬ ‫‪4.67‬‬

‫‪5.3‬‬ ‫‪6.5‬‬ ‫‪13.5‬‬ ‫‪4.5‬‬ ‫‪15.5‬‬ ‫‪16.5‬‬

‫‪26‬‬ ‫‪27‬‬ ‫‪28‬‬ ‫‪29‬‬ ‫‪30‬‬ ‫‪31‬‬

‫‪84‬‬ ‫‪95‬‬ ‫‪65‬‬ ‫‪100‬‬ ‫‪70‬‬ ‫‪70‬‬

‫‪3‬‬ ‫‪5‬‬ ‫‪0.5‬‬ ‫‪4‬‬ ‫‪1.33‬‬ ‫‪1‬‬

‫‪11.5‬‬ ‫‪16‬‬ ‫‪6.5‬‬ ‫‪17‬‬ ‫‪8.5‬‬ ‫‪8.8‬‬

‫‪1‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪5‬‬ ‫‪6‬‬

‫‪2‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬ ‫الطول = ‪X2‬‬

‫العمر = ‪X1‬‬

‫الوزن = ‪Y‬‬

‫المشاھدات‬

‫الطول = ‪X2‬‬

‫العمر = ‪X1‬‬

‫الوزن = ‪Y‬‬

‫المشاھدات‬

‫‪80‬‬ ‫‪96‬‬ ‫‪103‬‬ ‫‪83‬‬ ‫‪52‬‬ ‫‪50‬‬ ‫‪70‬‬ ‫‪72‬‬ ‫‪95‬‬ ‫‪31‬‬ ‫‪46‬‬ ‫‪46‬‬ ‫‪51‬‬ ‫‪46‬‬ ‫‪36‬‬ ‫‪46‬‬ ‫‪35‬‬ ‫‪49‬‬ ‫‪40‬‬

‫‪1.75‬‬ ‫‪5.25‬‬ ‫‪4.83‬‬ ‫‪2‬‬ ‫‪0.17‬‬ ‫‪0.08‬‬ ‫‪1‬‬ ‫‪1.33‬‬ ‫‪3.75‬‬ ‫‪0.17‬‬ ‫‪0.08‬‬ ‫‪0.33‬‬ ‫‪0.08‬‬ ‫‪0.01‬‬ ‫‪0.58‬‬ ‫‪0.08‬‬ ‫‪0.2‬‬ ‫‪0‬‬ ‫‪0.08‬‬

‫‪11‬‬ ‫‪17.5‬‬ ‫‪14.55‬‬ ‫‪10‬‬ ‫‪4‬‬ ‫‪3.5‬‬ ‫‪8‬‬ ‫‪8‬‬ ‫‪14‬‬ ‫‪1.75‬‬ ‫‪3.2‬‬ ‫‪5.55‬‬ ‫‪2.75‬‬ ‫‪1.35‬‬ ‫‪5.5‬‬ ‫‪4.5‬‬ ‫‪3.25‬‬ ‫‪3.3‬‬ ‫‪1.4‬‬

‫‪32‬‬ ‫‪33‬‬ ‫‪34‬‬ ‫‪35‬‬ ‫‪36‬‬ ‫‪37‬‬ ‫‪38‬‬ ‫‪39‬‬ ‫‪40‬‬ ‫‪41‬‬ ‫‪42‬‬ ‫‪43‬‬ ‫‪44‬‬ ‫‪45‬‬ ‫‪46‬‬ ‫‪47‬‬ ‫‪48‬‬ ‫‪49‬‬ ‫‪50‬‬

‫‪118‬‬ ‫‪95‬‬ ‫‪94‬‬ ‫‪97‬‬ ‫‪76‬‬ ‫‪96‬‬ ‫‪73‬‬ ‫‪100‬‬ ‫‪115‬‬ ‫‪76‬‬ ‫‪98‬‬ ‫‪80‬‬ ‫‪63‬‬ ‫‪105‬‬ ‫‪94‬‬ ‫‪118‬‬ ‫‪90‬‬ ‫‪100‬‬ ‫‪56‬‬

‫‪6.17‬‬ ‫‪3.42‬‬ ‫‪3.67‬‬ ‫‪5.42‬‬ ‫‪1.17‬‬ ‫‪4.42‬‬ ‫‪1.17‬‬ ‫‪2.75‬‬ ‫‪6.25‬‬ ‫‪1.5‬‬ ‫‪4.25‬‬ ‫‪2‬‬ ‫‪0.42‬‬ ‫‪5.58‬‬ ‫‪3.42‬‬ ‫‪6.17‬‬ ‫‪3‬‬ ‫‪5.25‬‬ ‫‪0.33‬‬

‫‪22‬‬ ‫‪13‬‬ ‫‪12.5‬‬ ‫‪15.5‬‬ ‫‪9.5‬‬ ‫‪15.5‬‬ ‫‪9.5‬‬ ‫‪14.5‬‬ ‫‪19‬‬ ‫‪9‬‬ ‫‪14‬‬ ‫‪10.5‬‬ ‫‪6‬‬ ‫‪15‬‬ ‫‪13‬‬ ‫‪21‬‬ ‫‪12‬‬ ‫‪17.5‬‬ ‫‪5.5‬‬

‫‪7‬‬ ‫‪8‬‬ ‫‪9‬‬ ‫‪10‬‬ ‫‪11‬‬ ‫‪12‬‬ ‫‪13‬‬ ‫‪14‬‬ ‫‪15‬‬ ‫‪16‬‬ ‫‪17‬‬ ‫‪18‬‬ ‫‪19‬‬ ‫‪20‬‬ ‫‪21‬‬ ‫‪22‬‬ ‫‪23‬‬ ‫‪24‬‬ ‫‪25‬‬

‫ﺍﳌﺼﺪﺭ‪ :‬ﻣﺴﺘﺸﻔﻰ ﺃ‪‬ﺎ ﻟﻠﻨﺴﺎﺀ ﻭﺍﻟﻮﻻﺩﺓ ﻭﺍﳌﺮﺍﻛﺰ ﺍﻟﺼﺤﻴﺔ‪ ،‬ﻭﺯﺍﺭﺓ ﺍﻟﺼﺤﺔ‪ ،‬ﺍﳌﻤﻠﻜﺔ ﺍﻟﻌﺮﺑﻴﺔ ﺍﻟﺴﻌﻮﺩﻳﺔ‪.‬‬

‫ ﺍﻟﺘﺤﻠﻴﻞ ﺍﻹﺣﺼﺎﺋﻲ‪:‬‬‫ﺑﺎﺳﺘﺨﺪﺍﻡ ﺑﺮﻧﺎﻣﺞ ﺍﳊﺰﻡ ﺍﻹﺣﺼﺎﺋﻴﺔ ‪ Minitab‬ﺳﻮﻑ ﻧﻘﻮﻡ ﺑﺎﺳﺘﺨﺮﺍﺝ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ﳌﺼﻔﻮﻓﺔ‬ ‫ﺍﻟﻘﺒﻌﺔ ﻭﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺎﺻﻴﺔ ﰲ ﺍﻟﻌﻤﺮ)ﺳﻨﺔ( ﻭﺍﻟﻄﻮﻝ)ﺳﻢ(‪.‬‬ ‫‪H 0 : β i = 0 Vs H 1 : β i ≠ 0 , i = 0,1,2‬‬ ‫‪MTB > copy c2-c4 m2‬‬ ‫‪MTB > trans m2 m1‬‬ ‫‪MTB > print m1‬‬

‫‪Data Display‬‬ ‫‪Matrix M1‬‬ ‫‪1.00‬‬ ‫‪1.17‬‬ ‫‪73.00‬‬

‫‪1.00‬‬ ‫‪4.42‬‬ ‫‪96.00‬‬

‫‪1.00‬‬ ‫‪5.25‬‬ ‫‪100.00‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪83‬‬ ‫‪1.00‬‬ ‫‪0.08‬‬ ‫‪46.00‬‬

‫‪1.00‬‬ ‫‪1.17‬‬ ‫‪76.00‬‬ ‫‪1‬‬ ‫‪3‬‬ ‫‪90‬‬

‫‪1.00‬‬ ‫‪4.83‬‬ ‫‪103.00‬‬ ‫‪1.00‬‬ ‫‪0.58‬‬ ‫‪36.00‬‬

‫‪1.00‬‬ ‫‪5.42‬‬ ‫‪97.00‬‬

‫‪1.00‬‬ ‫‪6.17‬‬ ‫‪118.00‬‬ ‫‪1.00‬‬ ‫‪5.25‬‬ ‫‪96.00‬‬

‫‪1.00‬‬ ‫‪0.01‬‬ ‫‪46.00‬‬

‫‪1.00‬‬ ‫‪3.67‬‬ ‫‪94.00‬‬

‫‪1.00‬‬ ‫‪3.42‬‬ ‫‪94.00‬‬ ‫‪1.00‬‬ ‫‪1.75‬‬ ‫‪80.00‬‬

‫‪1.00‬‬ ‫‪0.08‬‬ ‫‪51.00‬‬

‫‪1.00‬‬ ‫‪3.42‬‬ ‫‪95.00‬‬

‫‪1.00‬‬ ‫‪5.58‬‬ ‫‪105.00‬‬

‫‪1.00‬‬ ‫‪4.67‬‬ ‫‪102.00‬‬

‫‪1.00‬‬ ‫‪0.33‬‬ ‫‪46.00‬‬

‫‪1.00‬‬ ‫‪6.17‬‬ ‫‪118.00‬‬

‫‪1.00‬‬ ‫‪0.42‬‬ ‫‪63.00‬‬ ‫‪1.00‬‬ ‫‪4.75‬‬ ‫‪98.00‬‬

‫‪1.00‬‬ ‫‪0.08‬‬ ‫‪46.00‬‬

‫‪1‬‬ ‫‪1‬‬ ‫‪70‬‬

‫‪1‬‬ ‫‪2‬‬ ‫‪80‬‬

‫‪1.00‬‬ ‫‪0.25‬‬ ‫‪53.00‬‬

‫‪1.00‬‬ ‫‪0.17‬‬ ‫‪31.00‬‬

‫‪1.00‬‬ ‫‪1.33‬‬ ‫‪70.00‬‬

‫‪1.00‬‬ ‫‪4.25‬‬ ‫‪98.00‬‬ ‫‪1.00‬‬ ‫‪3.83‬‬ ‫‪92.00‬‬

‫‪1.00‬‬ ‫‪3.75‬‬ ‫‪95.00‬‬

‫‪1‬‬ ‫‪4‬‬ ‫‪100‬‬

‫‪1.0‬‬ ‫‪1.5‬‬ ‫‪76.0‬‬

‫‪1.0‬‬ ‫‪0.5‬‬ ‫‪65.0‬‬ ‫‪1.00‬‬ ‫‪6.25‬‬ ‫‪115.00‬‬

‫‪1‬‬ ‫‪5‬‬ ‫‪95‬‬

‫‪1‬‬ ‫‪3‬‬ ‫‪84‬‬

‫‪1.00‬‬ ‫‪2.75‬‬ ‫‪100.00‬‬

‫‪1.00‬‬ ‫‪0.75‬‬ ‫‪63.00‬‬

‫‪1.00‬‬ ‫‪0.33‬‬ ‫‪57.00‬‬

‫‪1.00‬‬ ‫‪0.33‬‬ ‫‪56.00‬‬

‫‪1‬‬ ‫‪1‬‬ ‫‪70‬‬

‫‪1.00‬‬ ‫‪0.08‬‬ ‫‪50.00‬‬

‫‪1.00‬‬ ‫‪0.17‬‬ ‫‪52.00‬‬

‫‪1.00‬‬ ‫‪1.33‬‬ ‫‪72.00‬‬

‫‪3‬‬

.‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‬ 1.0 0.2 35.0 MTB MTB MTB MTB MTB MTB

1 0 49 > > > > > >

1.00 0.08 40.00

mult m1 m2 m3 inve m3 m4 mult m2 m4 m5 mult m5 m1 m6 diag m6 c7 print c7

Data Display c7 0.022076 0.039554 0.093248 0.087871 0.040729 0.042400 0.060389 0.084663

0.078866 0.031462 0.044360 0.034254 0.051293 0.045179 0.044283

0.055454 0.105199 0.037205 0.074242 0.045145 0.046438 0.053426

0.042491 0.067968 0.035570 0.039365 0.049567 0.036624 0.162376

0.030500 0.041652 0.051890 0.040315 0.095124 0.032757 0.054312

MTB > Name c4 "e(Y|X1,X2)" c5 "hii" MTB > Regress 'Y' 2 'X1' 'X2'; SUBC> Residuals 'e(Y|X1,X2)'; SUBC> Hi 'hii'; SUBC> Constant; SUBC> Brief 2.

Regression Analysis: Y versus X1; X2 The regression equation is Y = - 2.22 + 1.20 X1 + 0.125 X2

Predictor Constant X1 X2

Coef -2.2212 1.1980 0.12512

S = 1.09433

SE Coef 0.9633 0.2087 0.01823

R-Sq = 96.2%

T -2.31 5.74 6.86

P 0.026 0.000 0.000

Analysis of Variance Source Regression Residual Error Total

Source X1 X2

DF 1 1

DF 2 47 49

SS 1441.91 56.29 1498.20

MS 720.96 1.20

F 602.02

P 0.000

Seq SS 1385.50 56.41

Unusual Observations Obs

4

X1

Y

Fit

SE Fit

Residual

St Resid

0.046438 0.050106 0.078185 0.035737 0.048535 0.177329 0.135402

0.087871 0.124435 0.035855 0.030171 0.050308 0.054312 0.047070

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬ ‫‪-2.48R‬‬ ‫‪-2.06R‬‬ ‫‪2.52R‬‬

‫‪-2.601‬‬ ‫‪-2.196‬‬ ‫‪2.522‬‬

‫‪0.306‬‬ ‫‪0.253‬‬ ‫‪0.441‬‬

‫‪17.601‬‬ ‫‪3.546‬‬ ‫‪2.978‬‬

‫‪15.000‬‬ ‫‪1.350‬‬ ‫‪5.500‬‬

‫‪5.58‬‬ ‫‪0.01‬‬ ‫‪0.58‬‬

‫‪20‬‬ ‫‪45‬‬ ‫‪46‬‬

‫‪R denotes an observation with a large standardized residual.‬‬

‫ﺣﻴﺚ ﺃﻥ ﻗﻴﻤﺔ ﺍﳌﺘﻮﺳﻂ‬

‫_‬

‫‪h‬‬

‫ﻟﻘﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ﺗﺴﺎﻭﻱ‪:‬‬ ‫‪3‬‬ ‫‪= 0.06‬‬ ‫‪50‬‬

‫_‬

‫=‪h‬‬

‫ﻭﻗﻴﻤﺔ ﺿﻌﻒ ﻣﺘﻮﺳﻂ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ﺗﺴﺎﻭﻱ‪:‬‬ ‫‪2*3‬‬ ‫‪= 0.12‬‬ ‫‪50‬‬

‫>=‬

‫ ﺟﺪﻭﻝ )‪ (1-1‬ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ﻭﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺼﻴﺔ ﰲ ﺍﳌﺘﻐﲑﺍﺕ ﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ )ﻭﺯﻥ ﺍﻟﻄﻔﻞ(‪.‬‬‫)‪Big (hii‬‬

‫‪0.124435‬‬

‫‪hii‬‬

‫)‪e(Y|X1,X2‬‬

‫‪X2‬‬

‫‪X1‬‬

‫‪Y‬‬

‫‪i‬‬

‫‪0.022076‬‬ ‫‪0.078866‬‬ ‫‪0.055454‬‬ ‫‪0.042491‬‬ ‫‪0.0305‬‬ ‫‪0.046438‬‬ ‫‪0.087871‬‬ ‫‪0.039554‬‬ ‫‪0.031462‬‬ ‫‪0.105199‬‬ ‫‪0.067968‬‬ ‫‪0.041652‬‬ ‫‪0.050106‬‬ ‫‪0.124435‬‬ ‫‪0.093248‬‬ ‫‪0.04436‬‬ ‫‪0.037205‬‬ ‫‪0.03557‬‬ ‫‪0.05189‬‬ ‫‪0.078185‬‬ ‫‪0.035855‬‬ ‫‪0.087871‬‬ ‫‪0.034254‬‬ ‫‪0.074242‬‬ ‫‪0.039365‬‬ ‫‪0.040315‬‬ ‫‪0.035737‬‬ ‫‪0.030171‬‬ ‫‪0.040729‬‬ ‫‪0.051293‬‬ ‫‪0.045145‬‬ ‫‪0.049567‬‬ ‫‪0.095124‬‬

‫‪-0.38264‬‬ ‫‪0.34503‬‬ ‫‪-0.01037‬‬ ‫‪1.91748‬‬ ‫‪0.36969‬‬ ‫‪1.06503‬‬ ‫‪2.06567‬‬ ‫‪-0.76209‬‬ ‫‪-1.43648‬‬ ‫‪-0.90837‬‬ ‫‪0.81067‬‬ ‫‪0.41477‬‬ ‫‪1.18602‬‬ ‫‪0.91501‬‬ ‫‪-0.65482‬‬ ‫‪-0.08468‬‬ ‫‪-1.1318‬‬ ‫‪0.31585‬‬ ‫‪-0.1643‬‬ ‫‪-2.60098‬‬ ‫‪-0.63697‬‬ ‫‪1.06567‬‬ ‫‪-0.63334‬‬ ‫‪0.91995‬‬ ‫‪0.31934‬‬ ‫‪-0.00578‬‬ ‫‪-0.05965‬‬ ‫‪-0.37793‬‬ ‫‪-0.20947‬‬ ‫‪-0.23081‬‬ ‫‪0.36457‬‬ ‫‪1.11535‬‬ ‫‪1.42041‬‬

‫‪84‬‬ ‫‪95‬‬ ‫‪65‬‬ ‫‪100‬‬ ‫‪70‬‬ ‫‪70‬‬ ‫‪118‬‬ ‫‪95‬‬ ‫‪94‬‬ ‫‪97‬‬ ‫‪76‬‬ ‫‪96‬‬ ‫‪73‬‬ ‫‪100‬‬ ‫‪115‬‬ ‫‪76‬‬ ‫‪98‬‬ ‫‪80‬‬ ‫‪63‬‬ ‫‪105‬‬ ‫‪94‬‬ ‫‪118‬‬ ‫‪90‬‬ ‫‪100‬‬ ‫‪56‬‬ ‫‪57‬‬ ‫‪63‬‬ ‫‪92‬‬ ‫‪53‬‬ ‫‪98‬‬ ‫‪102‬‬ ‫‪80‬‬ ‫‪96‬‬

‫‪3‬‬ ‫‪5‬‬ ‫‪0.5‬‬ ‫‪4‬‬ ‫‪1.33‬‬ ‫‪1‬‬ ‫‪6.17‬‬ ‫‪3.42‬‬ ‫‪3.67‬‬ ‫‪5.42‬‬ ‫‪1.17‬‬ ‫‪4.42‬‬ ‫‪1.17‬‬ ‫‪2.75‬‬ ‫‪6.25‬‬ ‫‪1.5‬‬ ‫‪4.25‬‬ ‫‪2‬‬ ‫‪0.42‬‬ ‫‪5.58‬‬ ‫‪3.42‬‬ ‫‪6.17‬‬ ‫‪3‬‬ ‫‪5.25‬‬ ‫‪0.33‬‬ ‫‪0.33‬‬ ‫‪0.75‬‬ ‫‪3.83‬‬ ‫‪0.25‬‬ ‫‪4.75‬‬ ‫‪4.67‬‬ ‫‪1.75‬‬ ‫‪5.25‬‬

‫‪11.5‬‬ ‫‪16‬‬ ‫‪6.5‬‬ ‫‪17‬‬ ‫‪8.5‬‬ ‫‪8.8‬‬ ‫‪22‬‬ ‫‪13‬‬ ‫‪12.5‬‬ ‫‪15.5‬‬ ‫‪9.5‬‬ ‫‪15.5‬‬ ‫‪9.5‬‬ ‫‪14.5‬‬ ‫‪19‬‬ ‫‪9‬‬ ‫‪14‬‬ ‫‪10.5‬‬ ‫‪6‬‬ ‫‪15‬‬ ‫‪13‬‬ ‫‪21‬‬ ‫‪12‬‬ ‫‪17.5‬‬ ‫‪5.5‬‬ ‫‪5.3‬‬ ‫‪6.5‬‬ ‫‪13.5‬‬ ‫‪4.5‬‬ ‫‪15.5‬‬ ‫‪16.5‬‬ ‫‪11‬‬ ‫‪17.5‬‬

‫‪1‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪5‬‬ ‫‪6‬‬ ‫‪7‬‬ ‫‪8‬‬ ‫‪9‬‬ ‫‪10‬‬ ‫‪11‬‬ ‫‪12‬‬ ‫‪13‬‬ ‫‪14‬‬ ‫‪15‬‬ ‫‪16‬‬ ‫‪17‬‬ ‫‪18‬‬ ‫‪19‬‬ ‫‪20‬‬ ‫‪21‬‬ ‫‪22‬‬ ‫‪23‬‬ ‫‪24‬‬ ‫‪25‬‬ ‫‪26‬‬ ‫‪27‬‬ ‫‪28‬‬ ‫‪29‬‬ ‫‪30‬‬ ‫‪31‬‬ ‫‪32‬‬ ‫‪33‬‬

‫‪5‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬ ‫)‪Big (hii‬‬

‫‪0.177329‬‬

‫‪0.162376‬‬ ‫‪0.135402‬‬

‫‪hii‬‬ ‫‪0.048535‬‬ ‫‪0.050308‬‬ ‫‪0.0424‬‬ ‫‪0.045179‬‬ ‫‪0.046438‬‬ ‫‪0.036624‬‬ ‫‪0.032757‬‬ ‫‪0.177329‬‬ ‫‪0.054312‬‬ ‫‪0.060389‬‬ ‫‪0.044283‬‬ ‫‪0.053426‬‬ ‫‪0.162376‬‬ ‫‪0.054312‬‬ ‫‪0.135402‬‬ ‫‪0.04707‬‬ ‫‪0.084663‬‬

‫)‪e(Y|X1,X2‬‬ ‫‪-1.90223‬‬ ‫‪-0.5595‬‬ ‫‪-0.48851‬‬ ‫‪-0.63046‬‬ ‫‪0.26503‬‬ ‫‪-0.38055‬‬ ‫‪-0.15744‬‬ ‫‪-0.11107‬‬ ‫‪-0.42999‬‬ ‫‪1.6205‬‬ ‫‪-1.50558‬‬ ‫‪-2.19613‬‬ ‫‪2.52216‬‬ ‫‪0.87001‬‬ ‫‪0.85252‬‬ ‫‪-0.6095‬‬ ‫‪-1.4793‬‬

‫‪X2‬‬ ‫‪103‬‬ ‫‪83‬‬ ‫‪52‬‬ ‫‪50‬‬ ‫‪70‬‬ ‫‪72‬‬ ‫‪95‬‬ ‫‪31‬‬ ‫‪46‬‬ ‫‪46‬‬ ‫‪51‬‬ ‫‪46‬‬ ‫‪36‬‬ ‫‪46‬‬ ‫‪35‬‬ ‫‪49‬‬ ‫‪40‬‬

‫‪X1‬‬ ‫‪4.83‬‬ ‫‪2‬‬ ‫‪0.17‬‬ ‫‪0.08‬‬ ‫‪1‬‬ ‫‪1.33‬‬ ‫‪3.75‬‬ ‫‪0.17‬‬ ‫‪0.08‬‬ ‫‪0.33‬‬ ‫‪0.08‬‬ ‫‪0.01‬‬ ‫‪0.58‬‬ ‫‪0.08‬‬ ‫‪0.2‬‬ ‫‪0‬‬ ‫‪0.08‬‬

‫‪Y‬‬ ‫‪14.55‬‬ ‫‪10‬‬ ‫‪4‬‬ ‫‪3.5‬‬ ‫‪8‬‬ ‫‪8‬‬ ‫‪14‬‬ ‫‪1.75‬‬ ‫‪3.2‬‬ ‫‪5.55‬‬ ‫‪2.75‬‬ ‫‪1.35‬‬ ‫‪5.5‬‬ ‫‪4.5‬‬ ‫‪3.25‬‬ ‫‪3.3‬‬ ‫‪1.4‬‬

‫‪i‬‬ ‫‪34‬‬ ‫‪35‬‬ ‫‪36‬‬ ‫‪37‬‬ ‫‪38‬‬ ‫‪39‬‬ ‫‪40‬‬ ‫‪41‬‬ ‫‪42‬‬ ‫‪43‬‬ ‫‪44‬‬ ‫‪45‬‬ ‫‪46‬‬ ‫‪47‬‬ ‫‪48‬‬ ‫‪49‬‬ ‫‪50‬‬

‫ ﺍﻻﺳﺘﻨﺘﺎﺝ‪:‬‬‫ﻧﻼﺣﻆ ﻣﻦ ﺍﳉﺪﻭﻝ)‪ ،(1-1‬ﺃﻥ ﻫﻨﺎﻙ ﺃﺭﺑﻊ ﻗﻴﻢ ﺷﺎﺫﺓ ﺃﻱ ﺃﻥ ﳍﺎ ﻗﻴﻢ ﺍﻛﱪ ﻣﻦ ﺿﻌﻒ ﻣﺘﻮﺳﻂ‬ ‫ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ﺣﻴﺚ ﺗﺸﲑ ﺇﱃ ﺃ‪‬ﺎ ﻣﺸﺎﻫﺪﺍﺕ ﺷﺎﺫﺓ ﰲ ﺑﻴﺎﻧﺎﺕ ﺍﻟﻌﻤﺮ)ﺳﻨﺔ( ﻭﺍﻟﻄﻮﻝ)ﺳﻢ( ﻗﺪ ﺗﺆﺩﻱ ﺇﱃ‬ ‫ﺗﺄﺛﲑ ﰲ ﲢﻠﻴﻞ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ ﻭﺍﻟﺘﻨﺒﺆ ﻟﻘﻴﻤﺔ ﺍﻟﻮﺯﻥ)ﻛﺠﻢ( ﻭﻫﻲ ﺍﳌﺸﺎﻫﺪﺍﺕ ‪ 14,41,46,48‬ﺣﻴﺚ‬ ‫ﺃﻥ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ﳍﺎ ﺗﺴﺎﻭﻱ‪:‬‬ ‫‪h14,14 = 0.124435 h41, 41 = 0.177329 h46, 46 = 0.162376 h48, 48 = 0.135402‬‬

‫ﻭﻗﺪ ﻗﻤﻨﺎ ﺑﺮﺳﻢ ﺷﻜﻞ)‪ (1-1‬ﻻﻧﺘﺸﺎﺭ ﺍﳌﺘﻐﲑﺍﺕ ﻋﻠﻰ ﺑﻌﻀﻬﺎ ﻭﲢﺪﻳﺪ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺎﺻﻴﺔ ﰲ ﺩﻭﺍﺋﺮ‬ ‫ﻣﻔﺮﻏﺔ ﺑﺎﻟﻠﻮﻥ ﺍﻷﲪﺮ ﺃﻣﺎ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻷﺧﺮﻯ ﺑﺪﻭﺍﺋﺮ ﻣﻌﺒﺌﺔ ﺑﺎﻟﻠﻮﻥ ﺍﻷﺳﻮﺩ ﻭﻧﻼﺣﻆ ﺃﻥ ﺍﳌﺸﺎﻫﺪﺍﺕ ﰲ‬ ‫ﺍﻟﺪﻭﺍﺋﺮ ﺍﳌﻔﺮﻏﺔ ﺑﺎﻟﻠﻮﻥ ﺍﻷﲪﺮ ﻏﲑ ﻣﻨﺴﺠﻤﺔ ﻣﻊ ﺑﻘﻴﺔ ﺍﻟﻨﻘﺎﻁ ﺍﻷﺧﺮﻯ ﺧﺎﺻﺔ ﺍﳊﺎﻟﺘﲔ ‪.41,46‬ﰲ‬ ‫ﺍﻟﺸﻜﻞ)‪ (1-1‬ﻣﻊ ﻣﻼﺣﻈﺔ ﺃﻥ ﻗﻴﻤﺔ ﺍﻟﺮﺍﻓﻌﺔ ‪ h41,41 = 0.177329‬ﺗﺴﺎﻭﻱ ﺛﻼﺙ ﺃﺿﻌﺎﻑ ﻣﺘﻮﺳﻂ ﻗﻴﻢ‬ ‫ﺍﻟﺮﺍﻓﻌﺔ ‪. 0.06‬‬

‫‪6‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫ ﺷﻜﻞ )‪ :(1-1‬ﺍﻧﺘﺸﺎﺭ ﺍﻟﻄﻮﻝ)ﺳﻢ( ‪ x2‬ﻋﻠﻰ ﺍﻟﻌﻤﺮ)ﺳﻨﺔ(‪. x1‬‬‫‪120‬‬

‫‪100‬‬

‫‪80‬‬ ‫‪X2‬‬ ‫‪60‬‬

‫‪40‬‬

‫‪20‬‬ ‫‪7‬‬

‫‪6‬‬

‫‪5‬‬

‫‪3‬‬

‫‪4‬‬

‫‪2‬‬

‫‪1‬‬

‫‪0‬‬

‫‪X1‬‬

‫ ﺷﻜﻞ )‪ :(1-2‬ﺍﻧﺘﺸﺎﺭ ﺍﻟﻮﺯﻥ)ﻛﺠﻢ( ‪ y‬ﻋﻠﻰ ﺍﻟﻌﻤﺮ)ﺳﻨﺔ(‪. x1‬‬‫‪Fitted Line Plot‬‬ ‫‪25‬‬

‫‪20‬‬

‫‪15‬‬ ‫‪Y‬‬ ‫‪10‬‬

‫‪5‬‬

‫‪0‬‬ ‫‪7‬‬

‫‪6‬‬

‫‪5‬‬

‫‪3‬‬

‫‪4‬‬

‫‪2‬‬

‫‪1‬‬

‫‪0‬‬

‫‪X1‬‬

‫‪7‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫ ﺷﻜﻞ )‪ :(1-3‬ﺍﻧﺘﺸﺎﺭ ﺍﻟﻮﺯﻥ)ﻛﺠﻢ( ‪ y‬ﻋﻠﻰ ﺍﻟﻄﻮﻝ)ﺳﻢ(‪.x2‬‬‫‪Fitted Line Plot‬‬ ‫‪25‬‬

‫‪20‬‬

‫‪15‬‬ ‫‪Y‬‬ ‫‪10‬‬

‫‪5‬‬

‫‪0‬‬ ‫‪120‬‬

‫‪100‬‬

‫‪60‬‬

‫‪80‬‬

‫‪40‬‬

‫‪20‬‬

‫‪X2‬‬

‫ﻧﻼﺣﻆ ﻣﻦ ﺭﺳﻮﻣﺎﺕ ﺍﻻﻧﺘﺸﺎﺭ ﺍﻟﺴﺎﺑﻘﺔ ﻟﻠﻤﺘﻐﲑﺍﺕ ﺃﻧﻨﺎ ﻻ ﻧﺴﺘﻄﻴﻊ ﺍﻛﺘﺸﺎﻑ ﲨﻴﻊ ﺍﳌﺘﻐﲑﺍﺕ‬ ‫ﺍﻟﻘﺎﺻﻴﺔ ﰲ ﺍﻟﻨﻤﻮﺫﺝ ﻭﻳﺮﺟﻊ ﺫﻟﻚ ﻻﻥ ﺍﻟﻨﻤﻮﺫﺝ ﻳﻌﺘﻤﺪ ﻋﻠﻰ ﺃﻛﺜﺮ ﻣﻦ ﻣﺘﻐﲑ‪ .‬ﻟﺬﻟﻚ ﻓﺈﻥ ﻃﺮﻳﻘﺔ‬ ‫ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺎﺻﻴﺔ ﺑﻮﺍﺳﻄﺔ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ﻭﺍﻟﻄﺮﻕ ﺍﻷﺧﺮﻯ ﺃﻓﻀﻞ ﻣﻦ ﻃﺮﻳﻘﺔ ﻣﺸﺎﻫﺪﺓ ﺍﻟﻘﻴﻢ‬ ‫ﻣﻦ ﺧﻼﻝ ﺍﻟﺮﺳﻢ‪.‬‬

‫‪8‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫ ﺷﻜﻞ )‪ :(1-4‬ﺍﻧﺘﺸﺎﺭ )ﺍﻟﺘﺮﺗﻴﺐ ﺍﻟﺘﺼﺎﻋﺪﻱ ﻟﻘﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ( )‪ h(i‬ﻋﻠﻰ ﻋﺪﺩ ﺍﳌﺸﺎﻫﺪﺍﺕ ‪.i‬‬‫‪Scatterplot of h(i) vs i‬‬ ‫‪0.20‬‬

‫‪0.15‬‬

‫)‪h(i‬‬

‫‪0.10‬‬

‫‪0.05‬‬

‫‪0.00‬‬ ‫‪50‬‬

‫‪40‬‬

‫‪20‬‬

‫‪30‬‬

‫‪10‬‬

‫‪0‬‬

‫‪i‬‬

‫ﻧﻼﺣﻆ ﻗﻴﻤﺔ ﺍﻟﺮﺍﻓﻌﺔ ﻟﻠﻤﺸﺎﻫﺪﺓ ﺭﻗﻢ ‪ 14‬ﺗﺴﺎﻭﻱ ‪ h14,14 = 0.124435‬ﻭﺗﻔﺼﻠﻬﺎ ﻓﺠﻮﺓ ﺗﺴﺎﻭﻱ‬ ‫‪ 0.064435‬ﻋﻦ ﻣﺘﻮﺳﻂ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ‪ .‬ﻭﺃﻳﻀﹰﺎ ﺍﳌﺸﺎﻫﺪﺓ ﺭﻗﻢ ‪ 48‬ﻭﻗﻴﻤﺔ ﺍﻟﺮﺍﻓﻌﺔ ﳍﺎ ﺗﺴﺎﻭﻱ‬ ‫‪ h48,48 = 0.135402‬ﻭﺗﻔﺼﻠﻬﺎ ﻓﺠﻮﺓ ﺗﺴﺎﻭﻱ ‪ 0.075402‬ﻋﻦ ﻣﺘﻮﺳﻂ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ‪ .‬ﰒ ﺍﳌﺸﺎﻫﺪﺓ‬ ‫ﺭﻗﻢ ‪ 46‬ﻭﻗﻴﻤﺔ ﺍﻟﺮﺍﻓﻌﺔ ﳍﺎ ﺗﺴﺎﻭﻱ ‪ h46,46 = 0.162376‬ﻭﺗﻔﺼﻠﻬﺎ ﻓﺠﻮﺓ ﺗﺴﺎﻭﻱ ‪ 0.102376‬ﻋﻦ‬ ‫ﻣﺘﻮﺳﻂ ﺍﻟﺮﺍﻓﻌﺔ‪ .‬ﻭﺃﺧﲑﹰﺍ ﻗﻴﻤﺔ ﺍﻟﺮﺍﻓﻌﺔ ﻟﻠﻤﺸﺎﻫﺪﺓ ﺭﻗﻢ ‪ 41‬ﻭﺗﺴﺎﻭﻱ ‪ h41,41 = 0.177329‬ﻭﺗﻔﺼﻠﻬﺎ‬ ‫ﻓﺠﻮﺓ ﺗﺴﺎﻭﻱ ‪ 0.117329‬ﻋﻦ ﻣﺘﻮﺳﻂ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ‪.‬‬

‫ ﺗﻄﺒﻴﻖ)‪:(1-2‬‬‫ﰲ ﺑﻴﺎﻧﺎﺕ ﺍﺟﺘﻤﺎﻋﻴﺔ ﺳﺤﺒﺖ ﻋﻴﻨﺔ ﻣﻦ ‪ 30‬ﺃﺳﺮﻩ ﻟﻘﻴﺎﺱ ﺍﻓﺘﺮﺍﺿﻴﺔ ﺍﳌﺼﺮﻭﻓﺎﺕ ﺍﳌﻌﻴﺸﻴﺔ ﻟﻸﺳﺮ‬ ‫)ﺑﺂﻻﻑ ﺍﻟﺮﻳﺎﻻﺕ(‪ ،‬ﻭﺑﻌﺾ ﺍﳌﺘﻐﲑﺍﺕ ﺍﳌﺆﺛﺮﺓ ﻋﻠﻴﻬﺎ ﻣﺜﻞ ﻣﺴﺘﻮﻯ ﺗﻌﻠﻴﻢ ﺭﺏ ﺍﻷﺳﺮﺓ )ﺑﺎﻟﺴﻨﺔ( ‪، x1‬‬ ‫ﻋﺪﺩ ﺍﻷﻃﻔﺎﻝ ‪ ، x2‬ﺩﺧﻞ ﺍﻷﺳﺮﺓ )ﺑﺂﻻﻑ ﺍﻟﺮﻳﺎﻻﺕ( ‪ ،x3‬ﻋﺪﺩ ﺃﻓﺮﺍﺩ ﺍﻷﺳﺮﺓ ‪.x4‬‬ ‫‪9‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫ﻛﻤﺎ ﰲ ﺍﳉﺪﻭﻝ ﺍﻟﺘﺎﱄ‪:‬‬ ‫عدد أفراد األسرة=‪X4‬‬ ‫‪5‬‬ ‫‪6‬‬ ‫‪8‬‬ ‫‪8‬‬ ‫‪9‬‬ ‫‪5‬‬ ‫‪7‬‬ ‫‪7‬‬ ‫‪6‬‬ ‫‪7‬‬ ‫‪5‬‬ ‫‪11‬‬ ‫‪9‬‬ ‫‪8‬‬ ‫‪9‬‬ ‫‪7‬‬ ‫‪8‬‬ ‫‪6‬‬ ‫‪5‬‬ ‫‪11‬‬ ‫‪10‬‬ ‫‪6‬‬ ‫‪5‬‬ ‫‪8‬‬ ‫‪5‬‬ ‫‪5‬‬ ‫‪7‬‬ ‫‪7‬‬ ‫‪7‬‬ ‫‪5‬‬

‫دخل األسرة=‪X3‬‬

‫عدد أطفال األسرة =‪X2‬‬

‫مستوى تعليم رب األسرة بالسنة =‪X1‬‬

‫‪Y‬‬

‫‪i‬‬

‫‪7‬‬ ‫‪13‬‬ ‫‪19‬‬ ‫‪13‬‬ ‫‪9.6‬‬ ‫‪8‬‬ ‫‪15‬‬ ‫‪5‬‬ ‫‪12‬‬ ‫‪14‬‬ ‫‪7‬‬ ‫‪19‬‬ ‫‪16‬‬ ‫‪11‬‬ ‫‪6‬‬ ‫‪7.6‬‬ ‫‪25‬‬ ‫‪10‬‬ ‫‪6.5‬‬ ‫‪15.1‬‬ ‫‪18‬‬ ‫‪11‬‬ ‫‪5.6‬‬ ‫‪8.5‬‬ ‫‪6.3‬‬ ‫‪14‬‬ ‫‪4.6‬‬ ‫‪7.5‬‬ ‫‪11.2‬‬ ‫‪9.5‬‬

‫‪2‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪4‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪4‬‬ ‫‪3‬‬ ‫‪6‬‬ ‫‪6‬‬ ‫‪4‬‬ ‫‪4‬‬ ‫‪3‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪6‬‬ ‫‪6‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪3‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪0‬‬

‫‪6‬‬ ‫‪16‬‬ ‫‪15‬‬ ‫‪14‬‬ ‫‪10‬‬ ‫‪10‬‬ ‫‪9‬‬ ‫‪6‬‬ ‫‪7‬‬ ‫‪12‬‬ ‫‪4‬‬ ‫‪0‬‬ ‫‪14‬‬ ‫‪5‬‬ ‫‪2‬‬ ‫‪4‬‬ ‫‪16‬‬ ‫‪4‬‬ ‫‪5‬‬ ‫‪15‬‬ ‫‪15‬‬ ‫‪2‬‬ ‫‪4‬‬ ‫‪3‬‬ ‫‪2‬‬ ‫‪5‬‬ ‫‪5‬‬ ‫‪3‬‬ ‫‪8‬‬ ‫‪7‬‬

‫‪6.2‬‬ ‫‪11.2‬‬ ‫‪11.2‬‬ ‫‪10.5‬‬ ‫‪9.3‬‬ ‫‪7.2‬‬ ‫‪13.4‬‬ ‫‪5‬‬ ‫‪11.6‬‬ ‫‪11.2‬‬ ‫‪6.2‬‬ ‫‪12‬‬ ‫‪11.3‬‬ ‫‪9.2‬‬ ‫‪5.5‬‬ ‫‪6‬‬ ‫‪12.5‬‬ ‫‪9.8‬‬ ‫‪6.1‬‬ ‫‪14.3‬‬ ‫‪15.5‬‬ ‫‪10.8‬‬ ‫‪4.5‬‬ ‫‪6.7‬‬ ‫‪4.5‬‬ ‫‪9.8‬‬ ‫‪4‬‬ ‫‪5.5‬‬ ‫‪10‬‬ ‫‪8.5‬‬

‫‪1‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪5‬‬ ‫‪6‬‬ ‫‪7‬‬ ‫‪8‬‬ ‫‪9‬‬ ‫‪10‬‬ ‫‪11‬‬ ‫‪12‬‬ ‫‪13‬‬ ‫‪14‬‬ ‫‪15‬‬ ‫‪16‬‬ ‫‪17‬‬ ‫‪18‬‬ ‫‪19‬‬ ‫‪20‬‬ ‫‪21‬‬ ‫‪22‬‬ ‫‪23‬‬ ‫‪24‬‬ ‫‪25‬‬ ‫‪26‬‬ ‫‪27‬‬ ‫‪28‬‬ ‫‪29‬‬ ‫‪30‬‬

‫ ﺍﻟﺘﺤﻠﻴﻞ ﺍﻹﺣﺼﺎﺋﻲ‪:‬‬‫ﺑﺎﺳﺘﺨﺪﺍﻡ ﺑﺮﻧﺎﻣﺞ ﺍﳊﺰﻡ ﺍﻹﺣﺼﺎﺋﻴﺔ ‪ Minitab‬ﺳﻮﻑ ﻧﻘﻮﻡ ﺑﺎﺳﺘﺨﺮﺍﺝ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ﳌﺼﻔﻮﻓﺔ‬ ‫ﺍﻟﻘﺒﻌﺔ ﻭﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﰲ ﺍﳌﺘﻐﲑﺍﺕ )ﻋﺪﺩ ﺳﻨﻮﺍﺕ ﺗﻌﻠﻴﻢ ﺭﺏ ﺍﻷﺳﺮﺓ‪ ،‬ﻋﺪﺩ ﺃﻃﻔﺎﻝ‬ ‫ﺍﻷﺳﺮﺓ‪ ،‬ﺩﺧﻞ ﺍﻷﺳﺮﺓ‪ ،‬ﻋﺪﺩ ﺃﻓﺮﺍﺩ ﺍﻷﺳﺮﺓ(‪.‬‬ ‫‪H 1 : β i ≠ 0 , i = 0,1,2,3 ,4‬‬

‫‪H 0 : β i = 0 Vs‬‬

‫"‪MTB > Name c6 " e(Y|X1,X2,X3,X4)" c7 " hii‬‬ ‫;'‪MTB > Regress 'Y' 4 'X1' 'X2' 'X3' 'X4‬‬ ‫>‪SUBC‬‬ ‫;')‪Residuals ' e(Y|X1,X2,X3,X4‬‬ ‫>‪SUBC‬‬ ‫;'‪Hi ' hii‬‬ ‫>‪SUBC‬‬ ‫;‪Constant‬‬ ‫>‪SUBC‬‬ ‫‪Brief 2.‬‬

‫‪10‬‬

.‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‬ Regression Analysis: Y versus X1; X2; X3; X4 The regression equation is Y = 2.44 + 0.0857 X1 + 0.449 X2 + 0.445 X3 - 0.058 X4

Predictor Constant X1 X2 X3 X4

Coef 2.441 0.08568 0.4488 0.44486 -0.0576

S = 1.52419

SE Coef 1.197 0.07439 0.2308 0.08162 0.2210

R-Sq = 80.2%

T 2.04 1.15 1.94 5.45 -0.26

P 0.052 0.260 0.063 0.000 0.796

Analysis of Variance Source Regression Residual Error Total

Source X1 X2 X3 X4

DF 1 1 1 1

DF 4 25 29

SS 235.203 58.079 293.282

MS 58.801 2.323

F 25.31

P 0.000

Seq SS 119.287 41.048 74.710 0.158

Unusual Observations Obs 12 17 22

X1 0.0 16.0 2.0

Y 12.000 12.500 10.800

Fit 12.951 14.920 7.608

SE Fit 1.171 1.166 0.590

Residual -0.951 -2.420 3.192

St Resid -0.98 X -2.47RX 2.27R

R denotes an observation with a large standardized residual. X denotes an observation whose X value gives it large influence.

‫ﻧﻼﺣﻆ ﺃﻥ ﺍﳌﺘﻐﲑﺍﺕ ﺍﳌﺴﺘﻘﻠﺔ ﲨﻴﻌﻬﺎ ﻏﲑ ﻣﻌﻨﻮﻳﺔ ﺃﻭ ﻻ ﺗﺼﻠﺢ ﻟﻠﻨﻤﻮﺫﺝ ﻭﳝﻜﻦ ﺣﺬﻓﻬﺎ ﻣﺎ ﻋﺪﻯ ﻣﺘﻐﲑ‬ ‫ ﻭﺑﻌﺪ ﺣﺬﻓﻬﺎ ﻭﺗﻘﺪﻳﺮ ﻣﻌﺎﺩﻟﺔ ﺍﳓﺪﺍﺭ ﻣﻦ ﺍﻟﺪﺭﺟﺔ ﺍﻟﺜﺎﻧﻴﺔ ﺑﻮﺍﺳﻄﺔ ﺍﳌﺼﺮﻭﻓﺎﺕ ﺍﳌﻌﻴﺸﻴﺔ‬.‫ﺩﺧﻞ ﺍﻷﺳﺮﺓ‬ .‫ﻭﻣﺘﻐﲑﻳﻦ ﺩﺧﻞ ﺍﻷﺳﺮﺓ ﻭﺗﺮﺑﻴﻊ ﺩﺧﻞ ﺍﻷﺳﺮﺓ ﺣﺼﻠﻨﺎ ﻋﻠﻰ ﺍﻷﰐ‬ Regression Analysis: Y versus X3; X3^2 The regression equation is Y = - 3.05 + 1.60 X3 - 0.0397 X3^2

Predictor Constant X3 X3^2

11

Coef -3.050 1.6043 -0.039674

SE Coef 1.112 0.1834 0.006768

T -2.74 8.75 -5.86

P 0.011 0.000 0.000

.‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‬ S = 1.09759

R-Sq = 88.9%

Analysis of Variance Source Regression Residual Error Total

Source X3 X3^2

DF 1 1

DF 2 27 29

SS 260.75 32.53 293.28

MS 130.38 1.20

F 108.22

P 0.000

Seq SS 219.36 41.39

Unusual Observations Obs 17 20 21

X3 25.0 15.1 18.0

Y 12.500 14.300 15.500

Fit 12.262 12.129 12.974

SE Fit 0.968 0.305 0.347

Residual 0.238 2.171 2.526

St Resid 0.46 X 2.06R 2.43R

R denotes an observation with a large standardized residual. X denotes an observation whose X value gives it large influence. MTB > copy c2-c4 m2 MTB > trans m2 m1 MTB > print m1

Data Display Matrix M1 1 7 49

1 13 169

1 25 625

1 10 100

1.00 11.20 125.44 MTB MTB MTB MTB MTB MTB

1 19 361

> > > > > >

1 13 169

1.00 6.50 42.25

1.00 9.60 92.16 1.00 15.10 228.01

1 8 64

1 15 225

1 5 25

1 12 144

1 18 324

1 11 121

1.00 5.60 31.36

1 14 196 1.00 8.50 72.25

1 7 49

1 19 361

1.00 6.30 39.69

1 16 256 1 14 196

1 11 121 1.00 4.60 21.16

1 6 36

1.00 7.60 57.76

1.00 7.50 56.25

1.00 9.50 90.25 mult m1 m2 m3 inve m3 m4 mult m2 m4 m5 mult m5 m1 m6 diag m6 c12 print c12

Data Display c12 0.062275 0.146532 0.093236 0.053234 0.054681

12

0.067151 0.060517 0.051840 0.111501 0.044728

0.121516 0.072497 0.777795 0.044594

0.067151 0.062275 0.046849 0.081898

0.045068 0.121516 0.075367 0.072497

0.047539 0.081343 0.077247 0.175648

0.076831 0.053234 0.100215 0.053226

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫ﺣﻴﺚ ﺃﻥ ﻗﻴﻤﺔ ﺍﳌﺘﻮﺳﻂ‬

‫_‬

‫‪h‬‬

‫ﻟﻘﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ﺗﺴﺎﻭﻱ‪:‬‬ ‫‪3‬‬ ‫‪= 0.1‬‬ ‫‪30‬‬

‫_‬

‫=‪h‬‬

‫ﻭﻗﻴﻤﺔ ﺿﻌﻒ ﻣﺘﻮﺳﻂ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ﺗﺴﺎﻭﻱ‪:‬‬ ‫‪2*3‬‬ ‫‪= 0.2‬‬ ‫‪30‬‬

‫>=‬

‫ ﺟﺪﻭﻝ )‪ (1-2‬ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ﻭﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺼﻴﺔ ﰲ ﺍﳌﺘﻐﲑﺍﺕ ﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ )ﺍﳌﺼﺮﻭﻓﺎﺕ‬‫ﺍﳌﻌﻴﺸﻴﺔ ﻟﻸﺳﺮ(‪.‬‬ ‫)‪Big(hii‬‬

‫‪0.777795‬‬

‫‪hii‬‬

‫)‪e(Y|X3,X3^2‬‬

‫‪X3^2‬‬

‫‪X3‬‬

‫‪Y‬‬

‫‪i‬‬

‫‪0.062275‬‬ ‫‪0.067151‬‬ ‫‪0.121516‬‬ ‫‪0.067151‬‬ ‫‪0.045068‬‬ ‫‪0.047539‬‬ ‫‪0.076831‬‬ ‫‪0.146532‬‬ ‫‪0.060517‬‬ ‫‪0.072497‬‬ ‫‪0.062275‬‬ ‫‪0.121516‬‬ ‫‪0.081343‬‬ ‫‪0.053234‬‬ ‫‪0.093236‬‬ ‫‪0.05184‬‬ ‫‪0.777795‬‬ ‫‪0.046849‬‬ ‫‪0.075367‬‬ ‫‪0.077247‬‬ ‫‪0.100215‬‬ ‫‪0.053234‬‬ ‫‪0.111501‬‬ ‫‪0.044594‬‬ ‫‪0.081898‬‬ ‫‪0.072497‬‬ ‫‪0.175648‬‬ ‫‪0.053226‬‬ ‫‪0.054681‬‬ ‫‪0.044728‬‬

‫‪-0.03634‬‬ ‫‪0.0985‬‬ ‫‪-1.9101‬‬ ‫‪-0.6015‬‬ ‫‪0.6047‬‬ ‫‪-0.04557‬‬ ‫‪1.31157‬‬ ‫‪1.02016‬‬ ‫‪1.11099‬‬ ‫‪-0.43464‬‬ ‫‪-0.03634‬‬ ‫‪-1.1101‬‬ ‫‪-1.16287‬‬ ‫‪-0.59717‬‬ ‫‪0.35224‬‬ ‫‪-0.8514‬‬ ‫‪0.23785‬‬ ‫‪0.77401‬‬ ‫‪0.39803‬‬ ‫‪2.17056‬‬ ‫‪2.5263‬‬ ‫‪1.00283‬‬ ‫‪-0.19011‬‬ ‫‪-1.02043‬‬ ‫‪-0.98267‬‬ ‫‪-1.83464‬‬ ‫‪0.50955‬‬ ‫‪-1.25088‬‬ ‫‪0.05811‬‬ ‫‪-0.11064‬‬

‫‪49‬‬ ‫‪169‬‬ ‫‪361‬‬ ‫‪169‬‬ ‫‪92.16‬‬ ‫‪64‬‬ ‫‪225‬‬ ‫‪25‬‬ ‫‪144‬‬ ‫‪196‬‬ ‫‪49‬‬ ‫‪361‬‬ ‫‪256‬‬ ‫‪121‬‬ ‫‪36‬‬ ‫‪57.76‬‬ ‫‪625‬‬ ‫‪100‬‬ ‫‪42.25‬‬ ‫‪228.01‬‬ ‫‪324‬‬ ‫‪121‬‬ ‫‪31.36‬‬ ‫‪72.25‬‬ ‫‪39.69‬‬ ‫‪196‬‬ ‫‪21.16‬‬ ‫‪56.25‬‬ ‫‪125.44‬‬ ‫‪90.25‬‬

‫‪7‬‬ ‫‪13‬‬ ‫‪19‬‬ ‫‪13‬‬ ‫‪9.6‬‬ ‫‪8‬‬ ‫‪15‬‬ ‫‪5‬‬ ‫‪12‬‬ ‫‪14‬‬ ‫‪7‬‬ ‫‪19‬‬ ‫‪16‬‬ ‫‪11‬‬ ‫‪6‬‬ ‫‪7.6‬‬ ‫‪25‬‬ ‫‪10‬‬ ‫‪6.5‬‬ ‫‪15.1‬‬ ‫‪18‬‬ ‫‪11‬‬ ‫‪5.6‬‬ ‫‪8.5‬‬ ‫‪6.3‬‬ ‫‪14‬‬ ‫‪4.6‬‬ ‫‪7.5‬‬ ‫‪11.2‬‬ ‫‪9.5‬‬

‫‪6.2‬‬ ‫‪11.2‬‬ ‫‪11.2‬‬ ‫‪10.5‬‬ ‫‪9.3‬‬ ‫‪7.2‬‬ ‫‪13.4‬‬ ‫‪5‬‬ ‫‪11.6‬‬ ‫‪11.2‬‬ ‫‪6.2‬‬ ‫‪12‬‬ ‫‪11.3‬‬ ‫‪9.2‬‬ ‫‪5.5‬‬ ‫‪6‬‬ ‫‪12.5‬‬ ‫‪9.8‬‬ ‫‪6.1‬‬ ‫‪14.3‬‬ ‫‪15.5‬‬ ‫‪10.8‬‬ ‫‪4.5‬‬ ‫‪6.7‬‬ ‫‪4.5‬‬ ‫‪9.8‬‬ ‫‪4‬‬ ‫‪5.5‬‬ ‫‪10‬‬ ‫‪8.5‬‬

‫‪1‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪5‬‬ ‫‪6‬‬ ‫‪7‬‬ ‫‪8‬‬ ‫‪9‬‬ ‫‪10‬‬ ‫‪11‬‬ ‫‪12‬‬ ‫‪13‬‬ ‫‪14‬‬ ‫‪15‬‬ ‫‪16‬‬ ‫‪17‬‬ ‫‪18‬‬ ‫‪19‬‬ ‫‪20‬‬ ‫‪21‬‬ ‫‪22‬‬ ‫‪23‬‬ ‫‪24‬‬ ‫‪25‬‬ ‫‪26‬‬ ‫‪27‬‬ ‫‪28‬‬ ‫‪29‬‬ ‫‪30‬‬

‫‪13‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫ ﺍﻻﺳﺘﻨﺘﺎﺝ‪:‬‬‫ﻧﻼﺣﻆ ﻛﻤﺎ ﰲ ﺍﳉﺪﻭﻝ)‪ ،(1-2‬ﺃﻥ ﻫﻨﺎﻙ ﻗﻴﻤﺔ ﻭﺍﺣﺪﺓ ﻓﻘﻂ ﻋﺰﻣﻬﺎ ﺍﻛﱪ ﻣﻦ ﺿﻌﻒ ﻣﺘﻮﺳﻂ‬ ‫ﺍﻟﺮﺍﻓﻌﺔ‪ ،‬ﺣﻴﺚ ﺗﺸﲑ ﺇﱃ ﺃ‪‬ﺎ ﻣﺸﺎﻫﺪﺓ ﻗﺎﺻﻴﺔ ﰲ ﺑﻴﺎﻧﺎﺕ )ﺩﺧﻞ ﺍﻷﺳﺮﺓ( ﻗﺪ ﺗﺆﺩﻱ ﺇﱃ ﺗﺄﺛﲑ ﰲ ﲢﻠﻴﻞ‬ ‫ﺍﻻﳓﺪﺍﺭ ﻭﺍﻟﺘﻨﺒﺆ ﳌﻘﺪﺍﺭ ﺍﳌﺼﺮﻭﻓﺎﺕ ﺍﳌﻌﻴﺸﻴﺔ ﻟﻸﺳﺮ ﻭﻫﻲ ﺍﳌﺸﺎﻫﺪﺓ ‪ 17‬ﺣﻴﺚ ﺃﻥ ﻗﻴﻤﺔ ﻋﺰﻡ ﻫﺬﻩ‬ ‫ﺍﳌﺸﺎﻫﺪﺓ ﺗﺴﺎﻭﻱ‪:‬‬ ‫‪h17,17 = 0.777795‬‬

‫ﻣﻊ ﻣﻼﺣﻈﺔ ﺃﻥ ﻗﻴﻤﺔ ﻋﺰﻡ ﺍﳌﺸﺎﻫﺪﺓ ‪ 17‬ﺗﺴﺎﻭﻱ ‪ 7‬ﺃﻭ ‪ 8‬ﺃﺿﻌﺎﻑ ﻣﺘﻮﺳﻂ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ‪0.1‬‬ ‫ﻭﺗﻔﺼﻠﻬﻤﺎ ﺛﻐﺮﺓ ﻛﺒﲑﺓ ﺟﺪﹰﺍ ﻋﻦ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ﺍﻷﺧﺮﻯ‪ .‬ﻟﺬﻟﻚ ﻳﻨﺒﻐﻲ ﺩﺭﺍﺳﺘﻬﺎ ﻭﻗﻴﺎﺱ ﺃﺛﺮﻫﺎ ﻋﻠﻰ‬ ‫ﺍﻟﻨﻤﻮﺫﺝ‪.‬‬ ‫ ﺷﻜﻞ )‪ :(1-5‬ﺍﻧﺘﺸﺎﺭ ﺍﳌﺼﺮﻭﻓﺎﺕ ﺍﳌﻌﻴﺸﻴﺔ‪ y‬ﻋﻠﻰ ﺩﺧﻞ ﺍﻷﺳﺮﺓ ‪.x3‬‬‫‪17.5‬‬

‫‪15.0‬‬

‫‪12.5‬‬

‫‪Y‬‬

‫‪10.0‬‬

‫‪7.5‬‬

‫‪5.0‬‬

‫‪25‬‬

‫‪20‬‬

‫‪15‬‬ ‫‪X3‬‬

‫‪10‬‬

‫‪5‬‬

‫ﻧﻼﺣﻆ ﻣﻦ ﺭﺳﻮﻣﺎﺕ ﺍﻻﻧﺘﺸﺎﺭ ﺍﻟﺴﺎﺑﻘﺔ ﻟﻠﻤﺘﻐﲑﺍﺕ ﺃﻧﻨﺎ ﻧﺴﺘﻄﻴﻊ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺘﻐﲑﺍﺕ ﺍﻟﻘﺎﺻﻴﺔ‬ ‫ﰲ ﺍﻟﻨﻤﻮﺫﺝ ﻭﻳﺮﺟﻊ ﺫﻟﻚ ﻻﻥ ﺍﻟﻨﻤﻮﺫﺝ ﻳﻌﺘﻤﺪ ﻋﻠﻰ ﻣﺘﻐﲑ ﻭﺣﻴﺪ ﻓﻘﻂ‪ .‬ﻟﺬﻟﻚ ﻓﺈﻥ ﻃﺮﻳﻘﺔ ﺍﻛﺘـﺸﺎﻑ‬ ‫‪14‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺎﺻﻴﺔ ﺑﻮﺍﺳﻄﺔ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ﻭﺍﻟﻄﺮﻕ ﺍﻷﺧﺮﻯ ﺃﻓﻀﻞ ﻣﻦ ﻃﺮﻳﻘﺔ ﻣﺸﺎﻫﺪﺓ ﺍﻟﻘﻴﻢ ﻣﻦ ﺧﻼﻝ‬ ‫ﺍﻟﺮﺳﻢ‪ .‬ﰲ ﺣﺎﻟﺔ ﺍﻋﺘﻤﺎﺩ ﺍﻟﻨﻤﻮﺫﺝ ﻋﻠﻰ ﺃﻛﺜﺮ ﻣﻦ ﻣﺘﻐﲑ‪.‬‬ ‫ ﺷﻜﻞ )‪ :(1-6‬ﺍﻧﺘﺸﺎﺭ )ﺍﻟﺘﺮﺗﻴﺐ ﺍﻟﺘﺼﺎﻋﺪﻱ ﻟﻘﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ( )‪ h(i‬ﻋﻠﻰ ﻋﺪﺩ ﺍﳌﺸﺎﻫﺪﺍﺕ ‪.i‬‬‫‪Scatterplot of h(i) vs i‬‬ ‫‪0.8‬‬ ‫‪0.7‬‬ ‫‪0.6‬‬ ‫‪0.5‬‬ ‫)‪h(i‬‬

‫‪0.4‬‬ ‫‪0.3‬‬ ‫‪0.2‬‬ ‫‪0.1‬‬ ‫‪0.0‬‬ ‫‪30‬‬

‫‪25‬‬

‫‪15‬‬ ‫‪i‬‬

‫‪20‬‬

‫‪10‬‬

‫‪0‬‬

‫‪5‬‬

‫ﻧﻼﺣﻆ ﺃﻥ ﻗﻴﻤﺔ ﺍﻟﺮﺍﻓﻌﺔ ﻟﻠﻤﺸﺎﻫﺪﺓ ﺭﻗﻢ ‪ 17‬ﺗﺴﺎﻭﻱ ‪ h17,17 = 0.777795‬ﻭﺗﻔﺼﻠﻬﺎ ﻓﺠﻮﺓ ﻋﻦ‬ ‫ﻣﺘﻮﺳﻂ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ﻣﻘﺪﺍﺭﻫﺎ ‪ 0.677795‬ﲝﺚ ﺗﻌﺘﱪ ﺍﻛﱪ ﺑـ ‪ 7‬ﺃﻭ ‪ 8‬ﺃﺿﻌﺎﻑ ﻣﺘﻮﺳـﻂ ﻗـﻴﻢ‬ ‫ﺍﻟﺮﺍﻓﻌﺔ ﻭﺗﻌﺘﱪ ﻫﺬﻩ ﺍﻟﻔﺠﻮﺓ ﻛﺒﲑﺓ ﺟﺪﹰﺍ ﻟﺬﻟﻚ ﻳﻨﺒﻐﻲ ﺩﺭﺍﺳﺘﻬﺎ ﻭﲢﺪﻳﺪ ﺃﺛﺮﻫﺎ ﻋﻠﻰ ﺍﻟﻨﻤﻮﺫﺝ‪.‬‬ ‫ ﺗﻄﺒﻴﻖ)‪:(1-3‬‬‫ﰲ ﺑﻴﺎﻧﺎﺕ ﺍﻓﺘﺮﺍﺿﻴﺔ ﻋﻦ ﺍﻷﺩﺍﺀ ﺍﻟﻮﻇﻴﻔﻲ ﻣﻦ ) ‪ 100‬ﺩﺭﺟﺔ ( ﻭﺑﻌﺾ ﺍﳌﺘﻐﲑﺍﺕ ﺍﳌﺆﺛﺮﺓ ﻋﻠﻴﻬﺎ‬ ‫ﻟﻌﻴﻨﺔ ﻋﺸﻮﺍﺋﻴﺔ ﻣﻦ ‪ 33‬ﻣﻮﻇﻒ ﻣﻦ ﻣﻨﺴﻮﰊ ﺷﺮﻛﺔ ﻣﺎ ﻛﺎﻧﺖ ﺍﻟﺒﻴﺎﻧﺎﺕ ﻛﺎﻟﺘﺎﱄ‪.‬‬ ‫مرتبة الموظف‬ ‫‪X3‬‬

‫خبرة الموظف ) سنة (‬ ‫‪X2‬‬

‫عدد سنوات التعليم‬ ‫‪X1‬‬

‫األداء الوظيفي‬ ‫‪Y‬‬

‫المشاھدات‬ ‫‪i‬‬

‫‪14‬‬ ‫‪7‬‬

‫‪19‬‬ ‫‪12‬‬

‫‪19‬‬ ‫‪12‬‬

‫‪95‬‬ ‫‪75‬‬

‫‪1‬‬ ‫‪2‬‬

‫‪15‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬ ‫مرتبة الموظف‬ ‫‪X3‬‬

‫خبرة الموظف ) سنة (‬ ‫‪X2‬‬

‫عدد سنوات التعليم‬ ‫‪X1‬‬

‫األداء الوظيفي‬ ‫‪Y‬‬

‫المشاھدات‬ ‫‪i‬‬

‫‪9‬‬ ‫‪4‬‬ ‫‪5‬‬ ‫‪4‬‬ ‫‪10‬‬ ‫‪4‬‬ ‫‪6‬‬ ‫‪5‬‬ ‫‪6‬‬ ‫‪6‬‬ ‫‪7‬‬ ‫‪10‬‬ ‫‪11‬‬ ‫‪9‬‬ ‫‪11‬‬ ‫‪11‬‬ ‫‪10‬‬ ‫‪5‬‬ ‫‪8‬‬ ‫‪6‬‬ ‫‪8‬‬ ‫‪7‬‬ ‫‪8‬‬ ‫‪12‬‬ ‫‪11‬‬ ‫‪10‬‬ ‫‪13‬‬ ‫‪14‬‬ ‫‪12‬‬ ‫‪4‬‬ ‫‪4‬‬

‫‪15‬‬ ‫‪4‬‬ ‫‪6‬‬ ‫‪6‬‬ ‫‪15‬‬ ‫‪7‬‬ ‫‪9‬‬ ‫‪7‬‬ ‫‪10‬‬ ‫‪8‬‬ ‫‪11‬‬ ‫‪17‬‬ ‫‪16‬‬ ‫‪18‬‬ ‫‪14‬‬ ‫‪17‬‬ ‫‪15‬‬ ‫‪5‬‬ ‫‪15‬‬ ‫‪10‬‬ ‫‪10‬‬ ‫‪12‬‬ ‫‪13‬‬ ‫‪14‬‬ ‫‪14‬‬ ‫‪16‬‬ ‫‪20‬‬ ‫‪21‬‬ ‫‪17‬‬ ‫‪4‬‬ ‫‪6‬‬

‫‪14‬‬ ‫‪5‬‬ ‫‪9‬‬ ‫‪8‬‬ ‫‪11‬‬ ‫‪8‬‬ ‫‪10‬‬ ‫‪9‬‬ ‫‪10‬‬ ‫‪9‬‬ ‫‪11‬‬ ‫‪12‬‬ ‫‪17‬‬ ‫‪15‬‬ ‫‪13‬‬ ‫‪16‬‬ ‫‪16‬‬ ‫‪7‬‬ ‫‪13‬‬ ‫‪10‬‬ ‫‪10‬‬ ‫‪12‬‬ ‫‪12‬‬ ‫‪12‬‬ ‫‪16‬‬ ‫‪14‬‬ ‫‪17‬‬ ‫‪18‬‬ ‫‪16‬‬ ‫‪6‬‬ ‫‪7‬‬

‫‪86‬‬ ‫‪45‬‬ ‫‪65‬‬ ‫‪56‬‬ ‫‪78‬‬ ‫‪56‬‬ ‫‪67‬‬ ‫‪66‬‬ ‫‪68‬‬ ‫‪66‬‬ ‫‪72‬‬ ‫‪87‬‬ ‫‪90‬‬ ‫‪88‬‬ ‫‪78‬‬ ‫‪88‬‬ ‫‪89‬‬ ‫‪64‬‬ ‫‪84‬‬ ‫‪67‬‬ ‫‪69‬‬ ‫‪72‬‬ ‫‪75‬‬ ‫‪75‬‬ ‫‪90‬‬ ‫‪86‬‬ ‫‪93‬‬ ‫‪94‬‬ ‫‪91‬‬ ‫‪51‬‬ ‫‪52‬‬

‫‪3‬‬ ‫‪4‬‬ ‫‪5‬‬ ‫‪6‬‬ ‫‪7‬‬ ‫‪8‬‬ ‫‪9‬‬ ‫‪10‬‬ ‫‪11‬‬ ‫‪12‬‬ ‫‪13‬‬ ‫‪14‬‬ ‫‪15‬‬ ‫‪16‬‬ ‫‪17‬‬ ‫‪18‬‬ ‫‪19‬‬ ‫‪20‬‬ ‫‪21‬‬ ‫‪22‬‬ ‫‪23‬‬ ‫‪24‬‬ ‫‪25‬‬ ‫‪26‬‬ ‫‪27‬‬ ‫‪28‬‬ ‫‪29‬‬ ‫‪30‬‬ ‫‪31‬‬ ‫‪32‬‬ ‫‪33‬‬

‫ ﺍﻟﺘﺤﻠﻴﻞ ﺍﻹﺣﺼﺎﺋﻲ‪:‬‬‫ﺑﺎﺳﺘﺨﺪﺍﻡ ﺑﺮﻧﺎﻣﺞ ﺍﳊﺰﻡ ﺍﻹﺣﺼﺎﺋﻴﺔ ‪ Minitab‬ﺳﻮﻑ ﻧﻘﻮﻡ ﺑﺎﺳﺘﺨﺮﺍﺝ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ﳌﺼﻔﻮﻓﺔ‬ ‫ﺍﻟﻘﺒﻌﺔ ﻭﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺎﺻﻴﺔ ﰲ ﺍﳌﺘﻐﲑﺍﺕ )ﻋﺪﺩ ﺳﻨﻮﺍﺕ ﺍﻟﺘﻌﻠﻴﻢ‪ ،‬ﺧﱪﺓ ﺍﳌﻮﻇﻒ)ﺳﻨﺔ(‪ ،‬ﻣﺮﺗﺒﺔ‬ ‫ﺍﳌﻮﻇﻒ(‪.‬‬ ‫‪H 1 : β i ≠ 0 , i = 0,1,2,3‬‬

‫‪H 0 : β i = 0 Vs‬‬ ‫"‪MTB > Name c5 "RESI1" c6 " hii‬‬ ‫;'‪MTB > Regress 'Y' 3 'X1' 'X2' 'X3‬‬ ‫>‪SUBC‬‬ ‫;')‪Residuals ' e(Y|X1,X2,X3‬‬ ‫>‪SUBC‬‬ ‫;'‪Hi ' hii‬‬ ‫>‪SUBC‬‬ ‫;‪Constant‬‬ ‫>‪SUBC‬‬ ‫‪Brief 2.‬‬

‫‪16‬‬

.‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‬ Regression Analysis: Y versus X1; X2; X3 The regression equation is Y = 34.7 + 2.20 X1 + 1.21 X2 - 0.081 X3

Predictor Constant X1 X2 X3

Coef 34.749 2.1965 1.2104 -0.0810

S = 3.37104

SE Coef 2.227 0.4912 0.4116 0.5592

T 15.61 4.47 2.94 -0.14

R-Sq = 94.6%

P 0.000 0.000 0.006 0.886

Analysis of Variance Source Regression Residual Error Total

Source X1 X2 X3

DF 1 1 1

DF 3 29 32

SS 5821.2 329.6 6150.7

MS 1940.4 11.4

F 170.75

P 0.000

Seq SS 5691.5 129.4 0.2

Unusual Observations Obs 14 20

X1 12.0 7.0

Y 87.000 64.000

Fit 80.874 55.772

SE Fit 1.749 1.207

Residual 6.126 8.228

St Resid 2.13R 2.61R

R denotes an observation with a large standardized residual.

‫ﻧﻼﺣﻆ ﺃﻥ ﺍﳌﺘﻐﲑﺍﺕ ﺍﳌﺴﺘﻘﻠﺔ ﲨﻴﻌﻬﺎ ﻣﻌﻨﻮﻳﺔ ﻣﺎ ﻋﺪﻯ ﻣﺘﻐﲑ ﻣﺮﺗﺒﺔ ﺍﳌﻮﻇﻒ ﻟﺬﻟﻚ ﺳﻮﻑ ﻧﻘﻮﻡ ﲝﺬﻓﻪ‬ ‫ ﻭﺑﻌﺪ ﺣﺬﻑ ﻫﺬﺍ ﺍﳌﺘﻐﲑ ﻧﻘﻮﻡ ﺑﺘﻮﻓﻴﻖ ﺩﺍﻟﺔ ﺍﳓﺪﺍﺭ ﺑﺎﳌﺘﻐﲑﺍﺕ‬،‫ﻭﺗﻮﻓﻴﻖ ﺍﻟﻨﻤﻮﺫﺝ ﺑﺪﻭﻥ ﻫﺬﺍ ﺍﳌﺘﻐﲑ‬ .‫ ﻓﺤﺼﻠﻨﺎ ﻋﻠﻰ ﺍﻷﰐ‬،‫ﺍﳌﻌﻨﻮﻳﺔ‬ Regression Analysis: Y versus X1; X2 The regression equation is Y = 34.7 + 2.17 X1 + 1.18 X2

Predictor Constant X1 X2

S = 3.31558

Coef 34.749 2.1731 1.1789

SE Coef 2.190 0.4561 0.3436

R-Sq = 94.6%

Analysis of Variance

17

T 15.87 4.76 3.43

P 0.000 0.000 0.002

.‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‬ Source Regression Residual Error Total

Source X1 X2

DF 1 1

DF 2 30 32

SS 5820.9 329.8 6150.7

MS 2910.5 11.0

F 264.75

P 0.000

Seq SS 5691.5 129.4

Unusual Observations Obs 14 20

X1 12.0 7.0

Y 87.000 64.000

Fit 80.867 55.855

SE Fit 1.719 1.045

Residual 6.133 8.145

St Resid 2.16R 2.59R

R denotes an observation with a large standardized residual. MTB > copy c12 c2 c3 m2 MTB > trans m2 m1 MTB > print m1

Data Display Matrix M1 1 19 19

1 12 12

1 14 15

1 5 4

1 10 10

1 12 12

1 12 13

1 12 14

MTB MTB MTB MTB MTB MTB

> > > > > >

1 9 6

1 8 6 1 16 14

1 11 15 1 14 16

1 8 7

1 10 9

1 9 7

1 17 20

1 18 21

1 16 17

1 10 10

1 9 8

1 6 4

1 7 6

1 11 11

1 12 17

1 17 16

1 15 18

1 13 14

1 16 17

1 16 15

1 7 5

1 13 15

1 10 10

mult m1 m2 m3 inve m3 m4 mult m2 m4 m5 mult m5 m1 m6 diag m6 c13 print c13

Data Display C13 0.188791 0.067467 0.157180 0.039478 0.113928

0.031199 0.045944 0.094319 0.039478 0.132617

0.040730 0.076465 0.035285 0.031199 0.069387

0.144172 0.039478 0.069387 0.035764 0.119732

0.120663 0.053744 0.123521 0.061806 0.087113

0.084964 0.032377 0.099387 0.182805

:‫ﻟﻘﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ﺗﺴﺎﻭﻱ‬ _

h=

_

h

0.200395 0.268799 0.056104 0.056325

‫ﺣﻴﺚ ﺃﻥ ﻗﻴﻤﺔ ﺍﳌﺘﻮﺳﻂ‬

3 = 0.0909 33

:‫ﻭﻗﻴﻤﺔ ﺿﻌﻒ ﻣﺘﻮﺳﻂ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ﺗﺴﺎﻭﻱ‬ =>

18

2*3 = 0.1818 33

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫ﻭﺗﻈﻬﺮ ﻟﻨﺎ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ﻭﺍﻟﻘﻴﻢ ﺍﻟﻘﺎﺻﻴﺔ ﻣﻨﻬﺎ ﰲ ﺍﳉﺪﻭﻝ ﺍﻟﺘﺎﱄ‪:‬‬ ‫ ﺟﺪﻭﻝ )‪ (1-3‬ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ﻭﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺼﻴﺔ ﰲ ﺍﳌﺘﻐﲑﺍﺕ ﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ )ﺍﻷﺩﺍﺀ ﺍﻟﻮﻇﻴﻔﻲ(‪.‬‬‫)‪Big (hii‬‬

‫‪hii‬‬

‫)‪e(Y1|X1,X2‬‬

‫‪X3‬‬

‫‪X2‬‬

‫‪X1‬‬

‫‪Y‬‬

‫‪i‬‬

‫‪0.188791‬‬

‫‪0.188791‬‬ ‫‪0.031199‬‬ ‫‪0.04073‬‬ ‫‪0.144172‬‬ ‫‪0.120663‬‬ ‫‪0.084964‬‬ ‫‪0.200395‬‬ ‫‪0.067467‬‬ ‫‪0.045944‬‬ ‫‪0.076465‬‬ ‫‪0.039478‬‬ ‫‪0.053744‬‬ ‫‪0.032377‬‬ ‫‪0.268799‬‬ ‫‪0.15718‬‬ ‫‪0.094319‬‬ ‫‪0.035285‬‬ ‫‪0.069387‬‬ ‫‪0.123521‬‬ ‫‪0.099387‬‬ ‫‪0.056104‬‬ ‫‪0.039478‬‬ ‫‪0.039478‬‬ ‫‪0.031199‬‬ ‫‪0.035764‬‬ ‫‪0.061806‬‬ ‫‪0.182805‬‬ ‫‪0.056325‬‬ ‫‪0.113928‬‬ ‫‪0.132617‬‬ ‫‪0.069387‬‬ ‫‪0.119732‬‬ ‫‪0.087113‬‬

‫‪-3.43627‬‬ ‫‪0.02745‬‬ ‫‪3.14466‬‬ ‫‪-5.32996‬‬ ‫‪3.61994‬‬ ‫‪-3.20697‬‬ ‫‪1.66393‬‬ ‫‪-4.38584‬‬ ‫‪-0.08976‬‬ ‫‪3.44107‬‬ ‫‪-0.26863‬‬ ‫‪2.2622‬‬ ‫‪0.37941‬‬ ‫‪6.1331‬‬ ‫‪-0.55348‬‬ ‫‪-0.56504‬‬ ‫‪-1.50338‬‬ ‫‪-1.55926‬‬ ‫‪1.79848‬‬ ‫‪8.14499‬‬ ‫‪3.31775‬‬ ‫‪-1.26863‬‬ ‫‪0.73137‬‬ ‫‪-2.97255‬‬ ‫‪-1.15142‬‬ ‫‪-2.33029‬‬ ‫‪3.97735‬‬ ‫‪1.96579‬‬ ‫‪-2.26896‬‬ ‫‪-4.62092‬‬ ‫‪1.44074‬‬ ‫‪-1.50305‬‬ ‫‪-5.03388‬‬

‫‪14‬‬ ‫‪7‬‬ ‫‪9‬‬ ‫‪4‬‬ ‫‪5‬‬ ‫‪4‬‬ ‫‪10‬‬ ‫‪4‬‬ ‫‪6‬‬ ‫‪5‬‬ ‫‪6‬‬ ‫‪6‬‬ ‫‪7‬‬ ‫‪10‬‬ ‫‪11‬‬ ‫‪9‬‬ ‫‪11‬‬ ‫‪11‬‬ ‫‪10‬‬ ‫‪5‬‬ ‫‪8‬‬ ‫‪6‬‬ ‫‪8‬‬ ‫‪7‬‬ ‫‪8‬‬ ‫‪12‬‬ ‫‪11‬‬ ‫‪10‬‬ ‫‪13‬‬ ‫‪14‬‬ ‫‪12‬‬ ‫‪4‬‬ ‫‪4‬‬

‫‪19‬‬ ‫‪12‬‬ ‫‪15‬‬ ‫‪4‬‬ ‫‪6‬‬ ‫‪6‬‬ ‫‪15‬‬ ‫‪7‬‬ ‫‪9‬‬ ‫‪7‬‬ ‫‪10‬‬ ‫‪8‬‬ ‫‪11‬‬ ‫‪17‬‬ ‫‪16‬‬ ‫‪18‬‬ ‫‪14‬‬ ‫‪17‬‬ ‫‪15‬‬ ‫‪5‬‬ ‫‪15‬‬ ‫‪10‬‬ ‫‪10‬‬ ‫‪12‬‬ ‫‪13‬‬ ‫‪14‬‬ ‫‪14‬‬ ‫‪16‬‬ ‫‪20‬‬ ‫‪21‬‬ ‫‪17‬‬ ‫‪4‬‬ ‫‪6‬‬

‫‪19‬‬ ‫‪12‬‬ ‫‪14‬‬ ‫‪5‬‬ ‫‪9‬‬ ‫‪8‬‬ ‫‪11‬‬ ‫‪8‬‬ ‫‪10‬‬ ‫‪9‬‬ ‫‪10‬‬ ‫‪9‬‬ ‫‪11‬‬ ‫‪12‬‬ ‫‪17‬‬ ‫‪15‬‬ ‫‪13‬‬ ‫‪16‬‬ ‫‪16‬‬ ‫‪7‬‬ ‫‪13‬‬ ‫‪10‬‬ ‫‪10‬‬ ‫‪12‬‬ ‫‪12‬‬ ‫‪12‬‬ ‫‪16‬‬ ‫‪14‬‬ ‫‪17‬‬ ‫‪18‬‬ ‫‪16‬‬ ‫‪6‬‬ ‫‪7‬‬

‫‪95‬‬ ‫‪75‬‬ ‫‪86‬‬ ‫‪45‬‬ ‫‪65‬‬ ‫‪56‬‬ ‫‪78‬‬ ‫‪56‬‬ ‫‪67‬‬ ‫‪66‬‬ ‫‪68‬‬ ‫‪66‬‬ ‫‪72‬‬ ‫‪87‬‬ ‫‪90‬‬ ‫‪88‬‬ ‫‪78‬‬ ‫‪88‬‬ ‫‪89‬‬ ‫‪64‬‬ ‫‪84‬‬ ‫‪67‬‬ ‫‪69‬‬ ‫‪72‬‬ ‫‪75‬‬ ‫‪75‬‬ ‫‪90‬‬ ‫‪86‬‬ ‫‪93‬‬ ‫‪94‬‬ ‫‪91‬‬ ‫‪51‬‬ ‫‪52‬‬

‫‪1‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪5‬‬ ‫‪6‬‬ ‫‪7‬‬ ‫‪8‬‬ ‫‪9‬‬ ‫‪10‬‬ ‫‪11‬‬ ‫‪12‬‬ ‫‪13‬‬ ‫‪14‬‬ ‫‪15‬‬ ‫‪16‬‬ ‫‪17‬‬ ‫‪18‬‬ ‫‪19‬‬ ‫‪20‬‬ ‫‪21‬‬ ‫‪22‬‬ ‫‪23‬‬ ‫‪24‬‬ ‫‪25‬‬ ‫‪26‬‬ ‫‪27‬‬ ‫‪28‬‬ ‫‪29‬‬ ‫‪30‬‬ ‫‪31‬‬ ‫‪32‬‬ ‫‪33‬‬

‫‪0.200395‬‬

‫‪0.268799‬‬

‫‪0.182805‬‬

‫ ﺍﻻﺳﺘﻨﺘﺎﺝ‪:‬‬‫ﻧﻼﺣﻆ ﻛﻤﺎ ﰲ ﺍﳉﺪﻭﻝ)‪ ،(1-3‬ﻭﺟﻮﺩ ﺃﺭﺑﻊ ﻗﻴﻢ ﻗﺎﺻﻴﺔ ﺗﻔﻮﻕ ﺿﻌﻒ ﻣﺘﻮﺳﻂ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ‪،‬‬ ‫ﻭﻳﺪﻝ ﺫﻟﻚ ﻋﻠﻰ ﻭﺟﻮﺩ ﻗﺎﺻﻴﺎﺕ ﰲ ﺑﻴﺎﻧﺎﺕ ﻋﺪﺩ ﺳﻨﻮﺍﺕ ﺍﻟﺘﻌﻠﻴﻢ ﻭﺧﱪﺓ ﺍﳌﻮﻇﻒ ﻭﻗﺪ ﺗﺄﺛﺮ ﻫﺬﻩ ﺍﻟﻘﻴﻢ‬ ‫ﺍﻟﻘﺎﺻﻴﺔ ﻋﻠﻰ ﲢﻠﻴﻞ ﺑﻴﺎﻧﺎﺕ ﻣﻘﺪﺍﺭ ﺍﻷﺩﺍﺀ ﺍﻟﻮﻇﻴﻔﻲ ﻟﻠﻤﻮﻇﻔﲔ‪ ،‬ﻭﻫﻲ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺜﻼﺙ‬

‫‪19‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫‪ 1,7,14,27‬ﺣﻴﺚ ﺃﻥ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ﳍﺎ ﺗﺴﺎﻭﻱ‪:‬‬ ‫‪h1,1 = 0.188791 h7 ,7 = 0.200395 h14,14 = 0.268799 h27, 27 = 0.182805‬‬

‫ﻣﻊ ﻣﻼﺣﻈﺔ ﻗﻴﻤﺔ ﺍﳌﺸﺎﻫﺪﺓ ‪ 14‬ﺑﻠﻮﻏﻬﺎ ﺛﻼﺙ ﺃﺿﻌﺎﻑ ﻣﺘﻮﺳﻂ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ‪ ،0.1818‬ﻭﺫﻟﻚ ﻳﺪﻝ‬ ‫ﻋﻠﻰ ﺃ‪‬ﺎ ﻗﺎﺻﻴﺔ ﺑﺸﻜﻞ ﻛﺒﲑ ﻭﺗﻔﺼﻠﻬﺎ ﺛﻐﺮﺓ ﻛﺒﲑﺓ ﻋﻦ ﺍﻟﺒﻴﺎﻧﺎﺕ ﻭﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻷﺧﺮﻯ‪ .‬ﻟﺬﻟﻚ ﻳﻨﺒﻐﻲ‬ ‫ﻗﻴﺎﺱ ﺃﺛﺮﻫﺎ ﻋﻠﻰ ﺍﻟﻨﻤﻮﺫﺝ‪.‬‬ ‫ ﺷﻜﻞ )‪ :(1-7‬ﺍﻧﺘﺸﺎﺭ ﻋﺪﺩ ﺳﻨﻮﺍﺕ ﺍﻟﺘﻌﻠﻴﻢ‪ x1‬ﻋﻠﻰ ﺧﱪﺓ ﺍﳌﻮﻇﻒ‪.x2‬‬‫‪20.0‬‬

‫‪17.5‬‬

‫‪15.0‬‬

‫‪X1‬‬

‫‪12.5‬‬

‫‪10.0‬‬

‫‪7.5‬‬

‫‪5.0‬‬ ‫‪22.5‬‬

‫‪20.0‬‬

‫‪17.5‬‬

‫‪15.0‬‬

‫‪12.5‬‬ ‫‪X2‬‬

‫‪10.0‬‬

‫‪7.5‬‬

‫‪5.0‬‬

‫‪20‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫ ﺷﻜﻞ )‪ :(1-8‬ﺍﻧﺘﺸﺎﺭ ﺍﻷﺩﺍﺀ ﺍﻟﻮﻇﻴﻔﻲ‪ y‬ﻋﻠﻰ ﻋﺪﺩ ﺳﻨﻮﺍﺕ ﺍﻟﺘﻌﻠﻴﻢ‪.x1‬‬‫‪100‬‬

‫‪90‬‬

‫‪80‬‬ ‫‪Y‬‬

‫‪70‬‬

‫‪60‬‬

‫‪50‬‬

‫‪40‬‬ ‫‪20.0‬‬

‫‪17.5‬‬

‫‪12.5‬‬ ‫‪X1‬‬

‫‪15.0‬‬

‫‪10.0‬‬

‫‪5.0‬‬

‫‪7.5‬‬

‫ ﺷﻜﻞ )‪ :(1-9‬ﺍﻧﺘﺸﺎﺭ ﺍﻷﺩﺍﺀ ﺍﻟﻮﻇﻴﻔﻲ‪ y‬ﻋﻠﻰ ﺧﱪﺓ ﺍﳌﻮﻇﻒ‪.x2‬‬‫‪100‬‬

‫‪90‬‬

‫‪80‬‬

‫‪Y‬‬

‫‪70‬‬

‫‪60‬‬

‫‪50‬‬

‫‪40‬‬ ‫‪22.5‬‬

‫‪20.0‬‬

‫‪17.5‬‬

‫‪15.0‬‬

‫‪12.5‬‬ ‫‪X2‬‬

‫‪10.0‬‬

‫‪7.5‬‬

‫‪5.0‬‬

‫‪21‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫ﻧﻼﺣﻆ ﻣﻦ ﺭﺳﻮﻣﺎﺕ ﺍﻻﻧﺘﺸﺎﺭ ﺍﻟﺴﺎﺑﻘﺔ ﻟﻠﻤﺘﻐﲑﺍﺕ ﺃﻧﻨﺎ ﻻ ﻧﺴﺘﻄﻴﻊ ﺍﻛﺘـﺸﺎﻑ ﺍﳌـﺸﺎﻫﺪﺍﺕ‬ ‫ﺍﻟﻘﺎﺻﻴﺔ ﺇﻻ ﺑﺼﻌﻮﺑﺔ ﺑﺎﻟﻐﺔ ﻭﻗﺪ ﻻ ﻧﺴﺘﻄﻴﻊ ﺍﻛﺘﺸﺎﻑ ﲨﻴﻊ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺎﺻﻴﺔ‪ .‬ﻭﻳﺮﺟﻊ ﺫﻟـﻚ ﻻﻥ‬ ‫ﺍﻟﻨﻤﻮﺫﺝ ﻳﻌﺘﻤﺪ ﻋﻠﻰ ﺃﻛﺜﺮ ﻣﻦ ﻣﺘﻐﲑ‪ .‬ﻟﺬﻟﻚ ﻓﺈﻥ ﻃﺮﻳﻘﺔ ﺍﻛﺘﺸﺎﻑ ﺍﻟﻘﻴﻢ ﺍﻟﻘﺎﺻﻴﺔ ﺑﻮﺍﺳﻄﺔ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ‬ ‫ﻭﺍﻟﻄﺮﻕ ﺍﻷﺧﺮﻯ ﺃﻓﻀﻞ ﻣﻦ ﻃﺮﻳﻘﺔ ﺭﺳﻢ ﺍﻻﻧﺘﺸﺎﺭ‪.‬‬ ‫ ﺷﻜﻞ )‪ :(1-10‬ﺍﻧﺘﺸﺎﺭ )ﺍﻟﺘﺮﺗﻴﺐ ﺍﻟﺘﺼﺎﻋﺪﻱ ﻟﻘﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ( )‪ h(i‬ﻋﻠﻰ ﻋﺪﺩ ﺍﳌﺸﺎﻫﺪﺍﺕ ‪.i‬‬‫‪Scatterplot of h(i) vs i‬‬ ‫‪0.30‬‬

‫‪0.25‬‬

‫‪0.20‬‬ ‫)‪h(i‬‬

‫‪0.15‬‬

‫‪0.10‬‬

‫‪0.05‬‬

‫‪0.00‬‬ ‫‪35‬‬

‫‪30‬‬

‫‪25‬‬

‫‪15‬‬

‫‪20‬‬

‫‪10‬‬

‫‪5‬‬

‫‪0‬‬

‫‪i‬‬

‫ﻧﻼﺣﻆ ﺃﻥ ﻗﻴﻤﺔ ﺍﻟﺮﺍﻓﻌﺔ ﻟﻠﻤﺸﺎﻫﺪﺓ ﺭﻗﻢ ‪ 27‬ﺗﺴﺎﻭﻱ ‪ h27, 27 = 0.182805‬ﻭﺗﻔﺼﻠﻬﺎ ﻓﺠﻮﺓ‬ ‫ﺗﺴﺎﻭﻱ ‪ 0.091905‬ﻋﻦ ﻗﻴﻤﺔ ﻣﺘﻮﺳﻂ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ‪ .‬ﻭﺃﻳﻀﹰﺎ ﻗﻴﻤﺔ ﺍﻟﺮﺍﻓﻌﺔ ﻟﻠﻤﺸﺎﻫﺪﺓ ﺭﻗﻢ ‪ 1‬ﻭﺗﺴﺎﻭﻱ‬ ‫‪ h1,1 = 0.188791‬ﻭﺗﻔﺼﻠﻬﺎ ﻓﺠﻮﺓ ﺗﺴﺎﻭﻱ ‪ 0.097891‬ﻋﻦ ﻗﻴﻤﺔ ﻣﺘﻮﺳﻂ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ‪ .‬ﰒ ﻗﻴﻤﺔ‬ ‫ﺍﻟﺮﺍﻓﻌﺔ ﻟﻠﻤﺸﺎﻫﺪﺓ ﺭﻗﻢ ‪ 7‬ﻭﺗﺴﺎﻭﻱ ‪ h7,7 = 0.200395‬ﻭﺗﻔﺼﻠﻬﺎ ﻓﺠﻮﺓ ﺗﺴﺎﻭﻱ ‪ 0.109495‬ﻋﻦ‬ ‫ﻗﻴﻤﺔ ﻣﺘﻮﺳﻂ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ‪ .‬ﻭﺃﻳﻀﹰﺎ ﺍﳌﺸﺎﻫﺪﺓ ﺭﻗﻢ ‪ 14‬ﻭﻗﻴﻤﺔ ﺍﻟﺮﺍﻓﻌﺔ ﳍﺎ ﻫﻲ ‪h14,14 = 0.268799‬‬ ‫ﻭﺗﻔﺼﻠﻬﺎ ﻓﺠﻮﺓ ﺗﺴﺎﻭﻱ ‪ 0.177899‬ﻋﻦ ﻗﻴﻤﺔ ﻣﺘﻮﺳﻂ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ‪.‬‬

‫‪22‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫)‪ (2‬ﲢﺪﻳﺪ ﻣﺸﺎﻫﺪﺍﺕ ﻗﺎﺻﻴﺔ ﰲ ‪) Y‬ﺍﳌﺘﻐﲑ ﺍﻟﺘﺎﺑﻊ ( – ﺑﻮﺍﻗﻲ ﺍﳊﺬﻑ ﺍﳌﻌﲑﺓ‪-:‬‬ ‫ﻟﻠﻜﺸﻒ ﻋﻦ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺎﺻﻴﺔ ﰲ ﺍﳌﺘﻐﲑ ﺍﻟﺘﺎﺑﻊ ‪ Y‬ﻳﺴﺘﺨﺪﻡ ﻋﺎﺩﺓ ﺑﻮﺍﻗﻲ ﺍﳊﺬﻑ ﺍﳌﻌﲑﺓ‬ ‫)ﺑﻮﺍﻗﻲ ﺳﺘﻮﺩﻧﺖ ﺍﶈﺬﻭﻓﺔ( )‪ (Studentized Deleted Residual‬ﻭﺍﻟﱵ ﻳﺘﻢ ﺍﳊﺼﻮﻝ‬ ‫ﻋﻠﻴﻬﺎ ﺑﺈﳚﺎﺩ ﺍﻟﻘﻴﻤﺔ ﺍﳌﻌﻴﺎﺭﻳﺔ ﻟﻠﺒﻮﺍﻗﻲ ﺍﶈﺬﻭﻓﺔ )‪ ،(Deleted Residual‬ﻭﺍﻟﺒﻮﺍﻗﻲ ﺍﶈﺬﻭﻓﺔ‬ ‫ﻟﻠﻤﺸﺎﻫﺪﺓ ﺭﻗﻢ )‪ (i‬ﻳﺴﺎﻭﻱ ﺍﻟﻔﺮﻕ ﺑﲔ ﻗﻴﻢ ) ‪ ( Yi‬ﺍﻟﻔﻌﻠﻴﺔ ﻭﺍﻟﻘﻴﻢ ﺍﳌﻘﺪﺭﺓ ﳍﺎ ) ) ‪ ( Yi (i‬ﺑﺎﺳﺘﺨﺪﺍﻡ ﳕﻮﺫﺝ‬ ‫ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ ﺍﻟﺬﻱ ﻳﺘﻢ ﺗﻘﺪﻳﺮﻩ ﺑﻌﺪ ﺍﺳﺘﺒﻌﺎﺩ ﺍﳌﺸﺎﻫﺪﺓ ﺭﻗﻢ )‪.(i‬‬ ‫ﻭﻳﺆﺩﻱ ﺫﻟﻚ ﺇﱃ ﲢﺴﲔ ﳚﻌﻞ ﲢﻠﻴﻞ ﺍﻟﺒﻮﺍﻗﻲ ﺃﻛﺜﺮ ﻓﻌﺎﻟﻴﺔ ﰲ ﺍﻟﻜﺸﻒ ﻋﻦ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺎﺻﻴﺔ‬ ‫ﰲ ﺍﳌﺘﻐﲑ ﺍﻟﺘﺎﺑﻊ ‪ .Y‬ﻭﳊﺴﺎﺏ )ﺑﻮﺍﻗﻲ ﺍﳊﺬﻑ(‪ .‬ﻧﺴﺘﺨﺪﻡ ﺍﻟﻄﺮﻳﻘﺔ ﺍﻟﺘﺎﻟﻴﺔ‪:‬‬ ‫ ﺣﺴﺎﺏ )ﺑﻮﺍﻗﻲ ﺍﳊﺬﻑ(‪-:‬‬‫ ﳓﺬﻑ ﺍﳌﺸﺎﻫﺪﺓ )‪.(i‬‬ ‫ ﺗﻮﻓﻴﻖ ﺩﺍﻟﺔ ﺍﳓﺪﺍﺭ ﻟﻠﻤﺸﺎﻫﺪﺍﺕ ﺍﻟﺒﺎﻗﻴﺔ ﻭﻫﻲ )‪.(n-1‬‬ ‫^‬

‫ ﺗﻘﺪﻳﺮ ﺍﻟﻘﻴﻤﺔ ﺍﳌﺘﻮﻗﻌﺔ ﻟﻠﻤﺘﻐﲑ ﺍﻟﺘﺎﺑﻊ ﺭﻗﻢ )‪ (i‬ﺑـ ) ‪ ، Y i (i‬ﻭﺫﻟﻚ ﺑﺘﻌﻮﻳﺾ ﻗﻴﻢ ﺍﳌﺘﻐﲑﺍﺕ ﺍﳌﺴﺘﻘﻠﺔ‬ ‫ﺍﳌﻨﺎﻇﺮﺓ ﻟﻠﺤﺎﻟﺔ)‪.(i‬‬ ‫ﻭﻳﺘﻢ ﺣﺴﺎﺏ ﺍﻟﺒﺎﻗﻲ ﺍﶈﺬﻭﻑ ﻛﻤﺎ ﻳﻠﻲ‪:‬‬ ‫^‬

‫) ‪d i = Yi − Y i ( i‬‬

‫ﺣﻴﺚ ﺃﻥ‪-:‬‬ ‫‪ : di‬ﺍﻟﺒﺎﻗﻲ ﺍﶈﺬﻭﻑ ﺭﻗﻢ )‪.(i‬‬ ‫‪ : Yi‬ﺍﻟﻘﻴﻤﺔ ﺍﻟﻔﻌﻠﻴﺔ ﻟﻠﻤﺘﻐﲑ ﺍﻟﺘﺎﺑﻊ ﺭﻗﻢ )‪.(i‬‬ ‫^‬

‫) ‪ : Y i (i‬ﺍﻟﻘﻴﻤﺔ ﺍﳌﻘﺪﺭﺓ ﻟﻠﻤﺘﻐﲑ ﺍﻟﺘﺎﺑﻊ ﺭﻗﻢ )‪ .(i‬ﺑﻌﺪ ﺣﺬﻑ ﺍﳌﺸﺎﻫﺪﺓ ﺭﻗﻢ )‪.(i‬‬ ‫ﻭﻣﻦ ﺍﻟﻌﻼﻗﺔ ﺍﻟﺴﺎﺑﻘﺔ ﻳﺘﻀﺢ ﺃﻧﻨﺎ ﳓﺘﺎﺝ ﺇﱃ ﻋﺪﺩ ﻛﺒﲑ ﻣﻦ ﳕﺎﺫﺝ ﺍﳓﺪﺍﺭ ﳊﺎﺳﺐ ﺍﻟﺒﻮﺍﻗﻲ ﺍﶈﺬﻭﻓﺔ ﻟﻜﻞ‬ ‫ﻣﺸﺎﻫﺪﺓ‪ .‬ﻭﻟﻜﻦ ﺗﻮﺟﺪ ﻣﻌﺎﺩﻟﺔ ﺟﱪﻳﺔ ﲤﻜﻨﻨﺎ ﻣﻦ ﺣﺴﺎﺏ ﺍﻟﺒﻮﺍﻗﻲ ﺍﶈﺬﻭﻓﺔ ‪ di‬ﻭﻫﻲ‪:‬‬ ‫‪ei‬‬ ‫‪1 − hii‬‬

‫= ‪di‬‬

‫ﺣﻴﺚ ﺃﻥ‪-:‬‬ ‫‪ : ei‬ﺍﻟﺒﻮﺍﻗﻲ ﻟﺪﺍﻟﺔ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬ ‫‪23‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫‪ : hii‬ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ﻭﻳﺘﻢ ﺍﺳﺘﺨﺮﺍﺟﻬﺎ ﻛﻤﺎ ﺳﺒﻖ ﻣﻦ ﺍﻟﻌﻨﺼﺮ ﺍﻟﻘﻄﺮﻱ ﰲ ﻣﺼﻔﻮﻓﺔ ﺍﻟﻘﺒﻌﺔ‪.‬‬ ‫ﻭﻫﻜﺬﺍ ﻓﺈﻥ ﺑﻮﺍﻗﻲ ﺍﳊﺬﻑ ﺳﺘﺤﺪﺩ ﺃﺣﻴﺎﻧﹰﺎ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺎﺻﻴﺔ ﰲ ﻗﻴﻢ ﺍﳌﺘﻐﲑ ﺍﻟﺘﺎﺑﻊ ‪ Y‬ﺣﻴﺚ ﺗﻔﺸﻞ‬ ‫ﺍﻟﺒﻮﺍﻗﻲ ﺍﻟﻌﺎﺩﻳﺔ ﰲ ﺍﻟﻘﻴﺎﻡ ﺑﺬﻟﻚ‪ ،‬ﻭﰲ ﺃﺣﻴﺎﻥ ﺃﺧﺮﻯ ﺗﻘﻮﺩ ﺑﻮﺍﻗﻲ ﺍﳊﺬﻑ ﺇﱃ ﺍﻟﺘﺤﺪﻳﺪﺍﺕ ﻧﻔﺴﻬﺎ ﺍﻟﱵ‬ ‫ﺗﻘﻮﺩ ﺇﻟﻴﻬﺎ ﺍﻟﺒﻮﺍﻗﻲ ﺍﻟﻌﺎﺩﻳﺔ‪ .‬ﻟﺬﻟﻚ ﻧﺴﺘﺨﺪﻡ ﺑﻮﺍﻗﻲ ﺍﳊﺬﻑ ﺍﳌﻌﲑﺓ )ﺑﻮﺍﻗﻲ ﺳﺘﻮﺩﻧﺖ(‪.‬‬ ‫ ﺑﻮﺍﻗﻲ ﺍﳊﺬﻑ ﺍﳌﻌﲑﺓ )ﺑﻮﺍﻗﻲ ﺳﺘﻮﺩﻧﺖ ﺍﶈﺬﻭﻓﺔ(‪:‬‬‫ﻳﻼﺣﻆ ﻣﻦ ﻋﻼﻗﺔ ﺑﻮﺍﻗﻲ ﺍﶈﺬﻭﻓﺔ ﺃﻧﻪ ﻛﻠﻤﺎ ﻛﺎﻧﺖ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ‪ hii‬ﻛﺒﲑﺓ ﻛﺎﻧﺖ ﻗﻴﻤﺔ ﺍﻟﺒﺎﻗﻲ‬ ‫ﺍﶈﺬﻭﻑ ﻛﺒﲑﺓ ﺃﻳﻀﹰﺎ‪ ،‬ﻭﻳﺘﻢ ﺣﺴﺎﺏ ﺑﻮﺍﻗﻲ ﺍﳊﺬﻑ ﺍﳌﻌﲑﺓ ﺑﻘﺴﻤﺘﻬﺎ ﻋﻠﻰ ﺍﻻﳓﺮﺍﻑ ﺍﳌﻌﻴﺎﺭﻱ ) ‪s.e(d i‬‬ ‫ﻭﻫﻜﺬﺍ ﻳﻜﻮﻥ ﺑﺎﻗﻲ ﺍﳊﺬﻑ ﺍﳌﻌﲑ ﻋﻠﻰ ﺷﻜﻞ ﺍﻟﻌﻼﻗﺘﲔ ﺍﳌﺘﻜﺎﻓﺌﺘﲔ ﺍﻟﺘﺎﻟﻴﺘﲔ‪.‬‬ ‫) ‪MSE( i‬‬ ‫‪1 − hii‬‬

‫= ) ‪s.e(d i‬‬

‫‪,‬‬

‫‪di‬‬ ‫) ‪s.e(d i‬‬

‫= ‪d *i‬‬

‫ﺣﻴﺚ ﺃﻥ‪-:‬‬ ‫* ‪ : d‬ﺑﺎﻗﻲ ﺍﳊﺬﻑ ﺍﳌﻌﲑ )ﺑﺎﻗﻲ ﺳﺘﻮﺩﻧﺖ( ﺍﶈﺬﻭﻑ ﺭﻗﻢ )‪.(i‬‬ ‫‪ : d i‬ﺍﻟﺒﺎﻗﻲ ﺍﶈﺬﻭﻑ ﺭﻗﻢ )‪.(i‬‬ ‫) ‪ : s.e(d i‬ﺍﻻﳓﺮﺍﻑ ﺍﳌﻌﻴﺎﺭﻱ ﻟﻠﺒﺎﻗﻲ ﺍﶈﺬﻭﻑ ﺭﻗﻢ )‪.(i‬‬ ‫‪ : MSE‬ﻣﺘﻮﺳﻂ ﳎﻤﻮﻉ ﻣﺮﺑﻌﺎﺕ ﺍﳋﻄﺎﺀ ﻟﻨﻤﻮﺫﺝ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ ﺍﳌﻘﺪﺭ ﺑﺎﺳﺘﺨﺪﺍﻡ ﺑﻌﺪ ﺣﺬﻑ‬ ‫ﺍﳌﺸﺎﻫﺪﺓ ﺭﻗﻢ )‪.(i‬‬ ‫‪ : hii‬ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ﺍﻟﺬﻱ ﻳﺘﻢ ﺍﺳﺘﺨﺮﺍﺟﻬﺎ ﻣﻦ ﺍﻟﻌﻨﺼﺮ ﺍﻟﻘﻄﺮﻱ ﰲ ﻣﺼﻔﻮﻓﺔ ﺍﻟﻘﺒﻌﺔ‪.‬‬ ‫ﻭﻟﺒﻮﺍﻗﻲ ﺍﳊﺬﻑ ﺍﳌﻌﲑﺓ )ﺑﻮﺍﻗﻲ ﺳﺘﻮﺩﻧﺖ ﺍﶈﺬﻭﻓﺔ( ﺗﻮﺯﻳﻊ ‪ t‬ﺑﺪﺭﺟﺔ ﺣﺮﻳﺔ )‪ (n-p-1‬ﻭﻟﺬﻟﻚ ﺟﺎﺀﺕ‬ ‫ﺍﻟﺘﺴﻤﻴﺔ )ﺑﻮﺍﻗﻲ ﺳﺘﻮﺩﻧﺖ ﺍﶈﺬﻭﻓﺔ(‪.‬‬ ‫‪i‬‬

‫‪1‬‬

‫)‪~ t ( n − p −1‬‬

‫ﺣﻴﺚ ﺃﻥ‪-:‬‬ ‫‪ : ei‬ﺍﻟﺒﻮﺍﻗﻲ ﺍﻟﻌﺎﺩﻳﺔ‪.‬‬ ‫‪ : n‬ﻋﺪﺩ ﺍﳌﺸﺎﻫﺪﺍﺕ‪.‬‬ ‫‪ : p‬ﻋﺪﺩ ﻣﻌﺎﱂ ﺍﻟﻨﻤﻮﺫﺝ‬

‫‪‬‬ ‫‪2‬‬ ‫‪n − p −1‬‬ ‫‪d i = ei ‬‬ ‫‪2 ‬‬ ‫‪ SSE (1 − hii ) − ei ‬‬ ‫*‬

‫‪. β 0 , β1 ,..., β p−1‬‬ ‫‪24‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫‪ : SSE‬ﳎﻤﻮﻉ ﻣﺮﺑﻌﺎﺕ ﺍﳋﻄﺎﺀ ﻟﻨﻤﻮﺫﺝ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ ﺍﳌﻘﺪﺭ ﺑﺎﺳﺘﺨﺪﺍﻡ ﻛﻞ ﺍﳌﺸﺎﻫﺪﺍﺕ )‪.(n‬‬ ‫‪ : hii‬ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ﺍﻟﺬﻱ ﻳﺘﻢ ﺍﺳﺘﺨﺮﺍﺟﻬﺎ ﻣﻦ ﺍﻟﻌﻨﺼﺮ ﺍﻟﻘﻄﺮﻱ ﰲ ﻣﺼﻔﻮﻓﺔ ﺍﻟﻘﺒﻌﺔ‪.‬‬ ‫ ﻃﺮﻳﻘﺔ ﻛﺸﻒ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺎﺻﻴﺔ ﰲ ﺍﳌﺘﻐﲑ ﺍﻟﺘﺎﺑﻊ ‪:Y‬‬‫ﻧﻘﻮﻡ ﺑﻮﺿﻊ ﻣﺘﺮﺍﺟﺤﺔ ﻭﻫﻲ ﻋﺒﺎﺭﺓ ﻋﻦ ﺍﻟﻘﻴﻤﺔ ﺍﳌﻄﻠﻘﺔ ﻟﺒﻮﺍﻗﻲ ﺍﳊﺬﻑ ﺍﳌﻌﲑﺓ )ﺑﻮﺍﻗﻲ ﺳﺘﻮﺩﻧﺖ‬ ‫ﺍﶈﺬﻭﻓﺔ( ﻣﻘﺎﺭﻧﺘﹰﺎ ﺑﺎﻟﻘﻴﻤﺔ ‪ t‬ﻋﻨﺪ ﺩﺭﺟﺔ ﺣﺮﻳﺔ )‪ (n-p-1‬ﻭﻣﺴﺘﻮﻯ ﻣﻌﻨﻮﻳﺔ ) ‪ ( α 0 2‬ﻓﺈﺫﺍ ﻛﺎﻥ‪.‬‬ ‫‪2 , n − p −1‬‬

‫‪d i* > tα 0‬‬

‫ﺗﻌﺘﱪ ﺍﳌﺸﺎﻫﺪﺓ )‪ (i‬ﻗﺎﺻﻴﺔ ﰲ ﺑﻴﺎﻧﺎﺕ ﺍﳌﺘﻐﲑ ﺍﻟﺘﺎﺑﻊ ‪ Y‬ﻭﺗﺴﺘﺪﻋﻲ ﺩﺭﺍﺳﺘﻬﺎ ﻭﲢﺪﻳﺪ ﻣﺪﻯ ﺗﺄﺛﲑﻫﺎ ﻋﻠﻰ‬ ‫ﺍﻟﻨﻤﻮﺫﺝ‪.‬‬ ‫ﺗﻄﺒﻴﻖ)‪-:(2-1‬‬ ‫ﺑﺎﻟﻌﻮﺩﺓ ﺇﱃ ﺗﻄﺒﻴﻖ)‪ (1-1‬ﰲ ﺑﻴﺎﻧﺎﺕ ﻣﺴﺘﺸﻔﻰ ﺃ‪‬ﺎ ﻟﻠﻨﺴﺎﺀ ﻭﺍﻟﻮﻻﺩﺓ‪ ،‬ﻧﺴﺘﺨﺮﺝ ﰲ ﻫﺬﺍ‬ ‫ﺍﻟﺘﻄﺒﻴﻖ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺎﺻﻴﺔ)ﺍﻟﺸﺎﺫﺓ( ﰲ ﻭﺯﻥ ﺍﻟﻄﻔﻞ )ﺑﺎﻟﻜﻴﻠﻮ ﺟﺮﺍﻡ( ‪ Y‬ﻭﺫﻟﻚ ﺑﺎﺳﺘﺨﺪﺍﻡ ﺑﻮﺍﻗﻲ‬ ‫ﺳﺘﻮﺩﻧﺖ ﺍﶈﺬﻭﻓﺔ‪.‬‬ ‫ﺍﻟﺘﺤﻠﻴﻞ ﺍﻹﺣﺼﺎﺋﻲ‪-:‬‬ ‫ﺑﺎﺳﺘﺨﺪﺍﻡ ﺑﺮﻧﺎﻣﺞ ﺍﳊﺰﻡ ﺍﻹﺣﺼﺎﺋﻴﺔ ‪ Minitab‬ﺳﻮﻑ ﻧﻘﻮﻡ ﺑﺎﺳﺘﺨﺮﺍﺝ ﺑﻮﺍﻗﻲ ﺳﺘﻮﺩﻧﺖ‬ ‫ﺍﶈﺬﻭﻓﺔ ﻭﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺎﺻﻴﺔ ﰲ ﻭﺯﻥ ﺍﻟﻄﻔﻞ)ﺑﺎﻟﻜﻴﻠﻮ ﺟﺮﺍﻡ(‪.‬‬ ‫‪Inverse Cumulative Distribution Function‬‬ ‫‪Student's t distribution with 46 DF‬‬ ‫‪x‬‬ ‫‪2.01290‬‬

‫) ‪P( X <= x‬‬ ‫‪0.975‬‬

‫"*‪MTB > Name c6 "di‬‬ ‫;'‪MTB > Regress 'Y' 2 'X1' 'X2‬‬ ‫>‪SUBC‬‬ ‫;'*‪SResiduals 'di‬‬ ‫>‪SUBC‬‬ ‫;‪Constant‬‬ ‫>‪SUBC‬‬ ‫‪Brief 2.‬‬

‫‪Regression Analysis: Y versus X1; X2‬‬ ‫‪The regression equation is‬‬ ‫‪Y = - 2.22 + 1.20 X1 + 0.125 X2‬‬

‫‪P‬‬

‫‪T‬‬

‫‪SE Coef‬‬

‫‪Coef‬‬

‫‪Predictor‬‬

‫‪25‬‬

.‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‬ Constant X1 X2

-2.2212 1.1980 0.12512

S = 1.09433

0.9633 0.2087 0.01823

-2.31 5.74 6.86

R-Sq = 96.2%

0.026 0.000 0.000

Analysis of Variance Source Regression Residual Error Total

Source X1 X2

DF 1 1

DF 2 47 49

SS 1441.91 56.29 1498.20

MS 720.96 1.20

F 602.02

P 0.000

Seq SS 1385.50 56.41

Unusual Observations Obs 20 45 46

X1 5.58 0.01 0.58

Y 15.000 1.350 5.500

Fit 17.601 3.546 2.978

SE Fit 0.306 0.253 0.441

Residual -2.601 -2.196 2.522

St Resid -2.48R -2.06R 2.52R

R denotes an observation with a large standardized residual.

.‫ﻛﻤﺎ ﰲ ﺍﳉﺪﻭﻝ ﺍﻟﺘﺎﱄ‬

d i*

‫ ﻭﺑﻮﺍﻗﻲ ﺳﺘﻮﺩﻧﺖ ﺑﺎﻟﺮﻣﺰ‬،( t 0.05,46 = 2.01290 ) ‫ ﻗﻴﻤﺔ‬-

.(‫( ﺑﻮﺍﻗﻲ ﺳﺘﻮﺩﻧﺖ ﻭ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺼﻴﺔ ﰲ ﺍﳌﺘﻐﲑ ﺍﻟﺘﺎﺑﻊ )ﻭﺯﻥ ﺍﻟﻄﻔﻞ‬2-1) ‫ ﺟﺪﻭﻝ‬i

Y

X1

X2

e(Y|X1,X2)

hii

di*

| di* | > t

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

11.5 16 6.5 17 8.5 8.8 22 13 12.5 15.5 9.5 15.5 9.5 14.5 19 9 14 10.5 6 15

3 5 0.5 4 1.33 1 6.17 3.42 3.67 5.42 1.17 4.42 1.17 2.75 6.25 1.5 4.25 2 0.42 5.58

84 95 65 100 70 70 118 95 94 97 76 96 73 100 115 76 98 80 63 105

-0.38264 0.34503 -0.01037 1.91748 0.36969 1.06503 2.06567 -0.76209 -1.43648 -0.90837 0.81067 0.41477 1.18602 0.91501 -0.65482 -0.08468 -1.1318 0.31585 -0.1643 -2.60098

0.022076 0.078866 0.055454 0.042491 0.0305 0.046438 0.087871 0.039554 0.031462 0.105199 0.067968 0.041652 0.050106 0.124435 0.093248 0.04436 0.037205 0.03557 0.05189 0.078185

-0.35358 0.32851 -0.00975 1.79064 0.34309 0.99664 1.97644 -0.71059 -1.3338 -0.8775 0.76733 0.38717 1.112 0.89357 -0.62839 -0.07915 -1.05403 0.2939 -0.15419 -2.47551

-2.47551

26

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬ ‫‪| di* | > t‬‬

‫‪-2.06268‬‬ ‫‪2.51824‬‬

‫*‪di‬‬

‫‪hii‬‬

‫)‪e(Y|X1,X2‬‬

‫‪X2‬‬

‫‪X1‬‬

‫‪Y‬‬

‫‪i‬‬

‫‪-0.59279‬‬ ‫‪1.01964‬‬ ‫‪-0.58892‬‬ ‫‪0.8737‬‬ ‫‪0.29773‬‬ ‫‪-0.00539‬‬ ‫‪-0.05551‬‬ ‫‪-0.35068‬‬ ‫‪-0.19544‬‬ ‫‪-0.21654‬‬ ‫‪0.34093‬‬ ‫‪1.04545‬‬ ‫‪1.36449‬‬ ‫‪-1.78204‬‬ ‫‪-0.52464‬‬ ‫‪-0.45618‬‬ ‫‪-0.58958‬‬ ‫‪0.24801‬‬ ‫‪-0.35429‬‬ ‫‪-0.14628‬‬ ‫‪-0.1119‬‬ ‫‪-0.40405‬‬ ‫‪1.52765‬‬ ‫‪-1.4073‬‬ ‫‪-2.06268‬‬ ‫‪2.51824‬‬ ‫‪0.81752‬‬ ‫‪0.83782‬‬ ‫‪-0.57055‬‬ ‫‪-1.41291‬‬

‫‪0.035855‬‬ ‫‪0.087871‬‬ ‫‪0.034254‬‬ ‫‪0.074242‬‬ ‫‪0.039365‬‬ ‫‪0.040315‬‬ ‫‪0.035737‬‬ ‫‪0.030171‬‬ ‫‪0.040729‬‬ ‫‪0.051293‬‬ ‫‪0.045145‬‬ ‫‪0.049567‬‬ ‫‪0.095124‬‬ ‫‪0.048535‬‬ ‫‪0.050308‬‬ ‫‪0.0424‬‬ ‫‪0.045179‬‬ ‫‪0.046438‬‬ ‫‪0.036624‬‬ ‫‪0.032757‬‬ ‫‪0.177329‬‬ ‫‪0.054312‬‬ ‫‪0.060389‬‬ ‫‪0.044283‬‬ ‫‪0.053426‬‬ ‫‪0.162376‬‬ ‫‪0.054312‬‬ ‫‪0.135402‬‬ ‫‪0.04707‬‬ ‫‪0.084663‬‬

‫‪-0.63697‬‬ ‫‪1.06567‬‬ ‫‪-0.63334‬‬ ‫‪0.91995‬‬ ‫‪0.31934‬‬ ‫‪-0.00578‬‬ ‫‪-0.05965‬‬ ‫‪-0.37793‬‬ ‫‪-0.20947‬‬ ‫‪-0.23081‬‬ ‫‪0.36457‬‬ ‫‪1.11535‬‬ ‫‪1.42041‬‬ ‫‪-1.90223‬‬ ‫‪-0.5595‬‬ ‫‪-0.48851‬‬ ‫‪-0.63046‬‬ ‫‪0.26503‬‬ ‫‪-0.38055‬‬ ‫‪-0.15744‬‬ ‫‪-0.11107‬‬ ‫‪-0.42999‬‬ ‫‪1.6205‬‬ ‫‪-1.50558‬‬ ‫‪-2.19613‬‬ ‫‪2.52216‬‬ ‫‪0.87001‬‬ ‫‪0.85252‬‬ ‫‪-0.6095‬‬ ‫‪-1.4793‬‬

‫‪94‬‬ ‫‪118‬‬ ‫‪90‬‬ ‫‪100‬‬ ‫‪56‬‬ ‫‪57‬‬ ‫‪63‬‬ ‫‪92‬‬ ‫‪53‬‬ ‫‪98‬‬ ‫‪102‬‬ ‫‪80‬‬ ‫‪96‬‬ ‫‪103‬‬ ‫‪83‬‬ ‫‪52‬‬ ‫‪50‬‬ ‫‪70‬‬ ‫‪72‬‬ ‫‪95‬‬ ‫‪31‬‬ ‫‪46‬‬ ‫‪46‬‬ ‫‪51‬‬ ‫‪46‬‬ ‫‪36‬‬ ‫‪46‬‬ ‫‪35‬‬ ‫‪49‬‬ ‫‪40‬‬

‫‪3.42‬‬ ‫‪6.17‬‬ ‫‪3‬‬ ‫‪5.25‬‬ ‫‪0.33‬‬ ‫‪0.33‬‬ ‫‪0.75‬‬ ‫‪3.83‬‬ ‫‪0.25‬‬ ‫‪4.75‬‬ ‫‪4.67‬‬ ‫‪1.75‬‬ ‫‪5.25‬‬ ‫‪4.83‬‬ ‫‪2‬‬ ‫‪0.17‬‬ ‫‪0.08‬‬ ‫‪1‬‬ ‫‪1.33‬‬ ‫‪3.75‬‬ ‫‪0.17‬‬ ‫‪0.08‬‬ ‫‪0.33‬‬ ‫‪0.08‬‬ ‫‪0.01‬‬ ‫‪0.58‬‬ ‫‪0.08‬‬ ‫‪0.2‬‬ ‫‪0‬‬ ‫‪0.08‬‬

‫‪13‬‬ ‫‪21‬‬ ‫‪12‬‬ ‫‪17.5‬‬ ‫‪5.5‬‬ ‫‪5.3‬‬ ‫‪6.5‬‬ ‫‪13.5‬‬ ‫‪4.5‬‬ ‫‪15.5‬‬ ‫‪16.5‬‬ ‫‪11‬‬ ‫‪17.5‬‬ ‫‪14.55‬‬ ‫‪10‬‬ ‫‪4‬‬ ‫‪3.5‬‬ ‫‪8‬‬ ‫‪8‬‬ ‫‪14‬‬ ‫‪1.75‬‬ ‫‪3.2‬‬ ‫‪5.55‬‬ ‫‪2.75‬‬ ‫‪1.35‬‬ ‫‪5.5‬‬ ‫‪4.5‬‬ ‫‪3.25‬‬ ‫‪3.3‬‬ ‫‪1.4‬‬

‫‪21‬‬ ‫‪22‬‬ ‫‪23‬‬ ‫‪24‬‬ ‫‪25‬‬ ‫‪26‬‬ ‫‪27‬‬ ‫‪28‬‬ ‫‪29‬‬ ‫‪30‬‬ ‫‪31‬‬ ‫‪32‬‬ ‫‪33‬‬ ‫‪34‬‬ ‫‪35‬‬ ‫‪36‬‬ ‫‪37‬‬ ‫‪38‬‬ ‫‪39‬‬ ‫‪40‬‬ ‫‪41‬‬ ‫‪42‬‬ ‫‪43‬‬ ‫‪44‬‬ ‫‪45‬‬ ‫‪46‬‬ ‫‪47‬‬ ‫‪48‬‬ ‫‪49‬‬ ‫‪50‬‬

‫ ﺍﻻﺳﺘﻨﺘﺎﺝ‪:‬‬‫ﻧﻼﺣﻆ ﻛﻤﺎ ﰲ ﺍﳉﺪﻭﻝ ﺍﻟﺴﺎﺑﻖ)‪ (2-1‬ﻭﺟﻮﺩ ﺛﻼﺙ ﻗﻴﻢ ﻗﺎﺻﻴﺔ ﰲ ﻭﺯﻥ ﺍﻟﻄﻔﻞ)ﺑﺎﻟﻜﻴﻠﻮ‬ ‫ﺟﺮﺍﻡ(‪ .‬ﻭﻫﻲ ﺍﳌﺸﺎﻫﺪﺍﺕ ‪ 20,45,46‬ﺣﻴﺚ ﺃﻥ ﺍﻟﻘﻴﻤﺔ ﺍﳌﻄﻠﻘﺔ ﻟﺒﻮﺍﻗﻲ ﺳﺘﻮﺩﻧﺖ ﺍﻛﱪ ﻣﻦ‬ ‫‪ t 0.05,46 = 2.01290‬ﻭﻫﺬﺍ ﻣﺆﺷﺮ ﺟﻴﺪ ﻻﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺎﺻﻴﺔ ﰲ ﻭﺯﻥ ﺍﻟﻄﻔﻞ ﺣﻴﺚ ﺃﻥ ﻗﻴﻢ‬ ‫ﺑﻮﺍﻗﻲ ﺳﺘﻮﺩﻧﺖ ﻟﻠﻤﺸﺎﻫﺪﺍﺕ ﺍﻟﺴﺎﺑﻘﺔ ﻫﻲ‪:‬‬ ‫*‬ ‫*‬ ‫*‬ ‫‪d 20‬‬ ‫‪= -2.47551 d 45‬‬ ‫‪= -2.06268 d 46‬‬ ‫‪= 2.51824‬‬

‫ﻭﺗﺴﺘﺪﻋﻲ ﻫﺬﻩ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺎﺻﻴﺔ ﺩﺭﺍﺳﺘﻬﺎ ﻭﻗﻴﺎﺱ ﺃﺛﺮﻫﺎ ﻋﻠﻰ ﺍﻟﻨﻤﻮﺫﺝ ﺍﻻﳓﺪﺍﺭﻱ‪ ،‬ﻣﻊ ﻣﻼﺣﻈﺔ ﺃﻥ‬ ‫ﻗﻴﻤﺔ ﺍﳌﺸﺎﻫﺪﺓ ‪ 46‬ﻗﺎﺻﻴﺔ ﰲ ﻛﻞ ﻣﻦ ﻭﺯﻥ ﺍﻟﻄﻔﻞ ﻭﻃﻮﻟﻪ ﻭﻋﻤﺮﺓ‪.‬‬

‫‪27‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫ﺗﻄﺒﻴﻖ)‪-:(2-2‬‬ ‫ﺑﺎﻟﻌﻮﺩﺓ ﺇﱃ ﺑﻴﺎﻧﺎﺕ ﺗﻄﺒﻴﻖ)‪ ،(1-2‬ﻭﻗﻴﺎﺱ ﺍﺛﺮ ﻋﺪﺩ ﺍﻷﻃﻔﺎﻝ ﰲ ﺍﻷﺳﺮﺓ ﻭﺩﺧﻞ ﺍﻷﺳﺮﺓ ﻋﻠﻰ‬ ‫ﻣﺴﺘﻮﻯ ﺍﳌﺼﺮﻭﻓﺎﺕ ﺍﳌﻌﻴﺸﻴﺔ ﻟﻸﺳﺮﺓ ﺍﻟﻮﺍﺣﺪﺓ‪ .‬ﺳﻮﻑ ﻧﺴﺘﺨﺮﺝ ﻫﻨﺎ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺎﺻﻴﺔ ﰲ ﺍﳌﺘﻐﲑ‬ ‫ﺍﻟﺘﺎﺑﻊ )ﺍﳌﺼﺮﻭﻓﺎﺕ ﺍﳌﻌﻴﺸﻴﺔ ﻟﻸﺳﺮﺓ ﺍﻟﻮﺍﺣﺪﺓ(‪.‬‬ ‫ ﺍﻟﺘﺤﻠﻴﻞ ﺍﻹﺣﺼﺎﺋﻲ‪-:‬‬‫ﺑﺎﺳﺘﺨﺪﺍﻡ ﺑﺮﻧﺎﻣﺞ ﺍﳊﺰﻡ ﺍﻹﺣﺼﺎﺋﻴﺔ ‪ Minitab‬ﺳﻮﻑ ﻧﻘﻮﻡ ﺑﺎﺳﺘﺨﺮﺍﺝ ﺑﻮﺍﻗﻲ ﺳﺘﻮﺩﻧﺖ‬ ‫ﺍﶈﺬﻭﻓﺔ ﻭﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺎﺻﻴﺔ ﰲ ﺍﳌﺘﻐﲑ ﺍﻟﺘﺎﺑﻊ )ﺍﳌﺼﺮﻭﻓﺎﺕ ﺍﳌﻌﻴﺸﻴﺔ ﻟﻸﺳﺮﺓ ﺍﻟﻮﺍﺣﺪﺓ(‪.‬‬ ‫‪Inverse Cumulative Distribution Function‬‬ ‫‪Student's t distribution with 26 DF‬‬ ‫‪x‬‬ ‫‪2.05553‬‬

‫) ‪P( X <= x‬‬ ‫‪0.975‬‬

‫‪Regression Analysis: Y versus X3; X3^2‬‬ ‫‪The regression equation is‬‬ ‫‪Y = - 3.05 + 1.60 X3 - 0.0397 X3^2‬‬

‫‪P‬‬ ‫‪0.011‬‬ ‫‪0.000‬‬ ‫‪0.000‬‬

‫‪T‬‬ ‫‪-2.74‬‬ ‫‪8.75‬‬ ‫‪-5.86‬‬

‫‪SE Coef‬‬ ‫‪1.112‬‬ ‫‪0.1834‬‬ ‫‪0.006768‬‬

‫‪Coef‬‬ ‫‪-3.050‬‬ ‫‪1.6043‬‬ ‫‪-0.039674‬‬

‫‪R-Sq = 88.9%‬‬

‫‪Predictor‬‬ ‫‪Constant‬‬ ‫‪X3‬‬ ‫‪X3^2‬‬

‫‪S = 1.09759‬‬

‫‪Analysis of Variance‬‬ ‫‪P‬‬ ‫‪0.000‬‬

‫‪F‬‬ ‫‪108.22‬‬

‫‪MS‬‬ ‫‪130.38‬‬ ‫‪1.20‬‬

‫‪DF‬‬ ‫‪2‬‬ ‫‪27‬‬ ‫‪29‬‬

‫‪SS‬‬ ‫‪260.75‬‬ ‫‪32.53‬‬ ‫‪293.28‬‬

‫‪Source‬‬ ‫‪Regression‬‬ ‫‪Residual Error‬‬ ‫‪Total‬‬

‫‪Seq SS‬‬ ‫‪219.36‬‬ ‫‪41.39‬‬

‫‪DF‬‬ ‫‪1‬‬ ‫‪1‬‬

‫‪Source‬‬ ‫‪X3‬‬ ‫‪X3^2‬‬

‫‪Unusual Observations‬‬ ‫‪St Resid‬‬ ‫‪0.46 X‬‬ ‫‪2.06R‬‬ ‫‪2.43R‬‬

‫‪Residual‬‬ ‫‪0.238‬‬ ‫‪2.171‬‬ ‫‪2.526‬‬

‫‪SE Fit‬‬ ‫‪0.968‬‬ ‫‪0.305‬‬ ‫‪0.347‬‬

‫‪Fit‬‬ ‫‪12.262‬‬ ‫‪12.129‬‬ ‫‪12.974‬‬

‫‪Y‬‬ ‫‪12.500‬‬ ‫‪14.300‬‬ ‫‪15.500‬‬

‫‪X3‬‬ ‫‪25.0‬‬ ‫‪15.1‬‬ ‫‪18.0‬‬

‫‪Obs‬‬ ‫‪17‬‬ ‫‪20‬‬ ‫‪21‬‬

‫‪28‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬ ‫‪R denotes an observation with a large standardized residual.‬‬ ‫‪X denotes an observation whose X value gives it large influence.‬‬

‫‪ -‬ﻗﻴﻤﺔ ) ‪ ،( t 0.05,26 = 2.05553‬ﻭﺑﻮﺍﻗﻲ ﺳﺘﻮﺩﻧﺖ ﺑﺎﻟﺮﻣﺰ‬

‫*‪d i‬‬

‫ﻛﻤﺎ ﰲ ﺍﳉﺪﻭﻝ ﺍﻟﺘﺎﱄ‪.‬‬

‫ ﺟﺪﻭﻝ )‪ (2-2‬ﺑﻮﺍﻗﻲ ﺳﺘﻮﺩﻧﺖ ﻭ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺼﻴﺔ ﰲ ﺍﳌﺘﻐﲑ ﺍﻟﺘﺎﺑﻊ )ﺍﳌﺼﺮﻭﻓﺎﺕ ﺍﳌﻌﻴﺸﻴﺔ‬‫ﻟﻸﺳﺮﺓ ﺍﻟﻮﺍﺣﺪﺓ(‪.‬‬ ‫‪| di* | > t‬‬

‫‪2.05868‬‬ ‫‪2.42648‬‬

‫*‪di‬‬

‫)‪e(Y|X3,X3^2‬‬

‫‪X3^2‬‬

‫‪X3‬‬

‫‪Y‬‬

‫‪i‬‬

‫‪-0.03419‬‬ ‫‪0.09292‬‬ ‫‪-1.85673‬‬ ‫‪-0.5674‬‬ ‫‪0.56379‬‬ ‫‪-0.04255‬‬ ‫‪1.24369‬‬ ‫‪1.00609‬‬ ‫‪1.0443‬‬ ‫‪-0.41118‬‬ ‫‪-0.03419‬‬ ‫‪-1.07908‬‬ ‫‪-1.10539‬‬ ‫‪-0.55917‬‬ ‫‪0.33701‬‬ ‫‪-0.79663‬‬ ‫‪0.45972‬‬ ‫‪0.72232‬‬ ‫‪0.37713‬‬ ‫‪2.05868‬‬ ‫‪2.42648‬‬ ‫‪0.939‬‬ ‫‪-0.18376‬‬ ‫‪-0.95116‬‬ ‫‪-0.93438‬‬ ‫‪-1.73561‬‬ ‫‪0.51132‬‬ ‫‪-1.17126‬‬ ‫‪0.05445‬‬ ‫‪-0.10314‬‬

‫‪-0.03634‬‬ ‫‪0.0985‬‬ ‫‪-1.9101‬‬ ‫‪-0.6015‬‬ ‫‪0.6047‬‬ ‫‪-0.04557‬‬ ‫‪1.31157‬‬ ‫‪1.02016‬‬ ‫‪1.11099‬‬ ‫‪-0.43464‬‬ ‫‪-0.03634‬‬ ‫‪-1.1101‬‬ ‫‪-1.16287‬‬ ‫‪-0.59717‬‬ ‫‪0.35224‬‬ ‫‪-0.8514‬‬ ‫‪0.23785‬‬ ‫‪0.77401‬‬ ‫‪0.39803‬‬ ‫‪2.17056‬‬ ‫‪2.5263‬‬ ‫‪1.00283‬‬ ‫‪-0.19011‬‬ ‫‪-1.02043‬‬ ‫‪-0.98267‬‬ ‫‪-1.83464‬‬ ‫‪0.50955‬‬ ‫‪-1.25088‬‬ ‫‪0.05811‬‬ ‫‪-0.11064‬‬

‫‪49‬‬ ‫‪169‬‬ ‫‪361‬‬ ‫‪169‬‬ ‫‪92.16‬‬ ‫‪64‬‬ ‫‪225‬‬ ‫‪25‬‬ ‫‪144‬‬ ‫‪196‬‬ ‫‪49‬‬ ‫‪361‬‬ ‫‪256‬‬ ‫‪121‬‬ ‫‪36‬‬ ‫‪57.76‬‬ ‫‪625‬‬ ‫‪100‬‬ ‫‪42.25‬‬ ‫‪228.01‬‬ ‫‪324‬‬ ‫‪121‬‬ ‫‪31.36‬‬ ‫‪72.25‬‬ ‫‪39.69‬‬ ‫‪196‬‬ ‫‪21.16‬‬ ‫‪56.25‬‬ ‫‪125.44‬‬ ‫‪90.25‬‬

‫‪7‬‬ ‫‪13‬‬ ‫‪19‬‬ ‫‪13‬‬ ‫‪9.6‬‬ ‫‪8‬‬ ‫‪15‬‬ ‫‪5‬‬ ‫‪12‬‬ ‫‪14‬‬ ‫‪7‬‬ ‫‪19‬‬ ‫‪16‬‬ ‫‪11‬‬ ‫‪6‬‬ ‫‪7.6‬‬ ‫‪25‬‬ ‫‪10‬‬ ‫‪6.5‬‬ ‫‪15.1‬‬ ‫‪18‬‬ ‫‪11‬‬ ‫‪5.6‬‬ ‫‪8.5‬‬ ‫‪6.3‬‬ ‫‪14‬‬ ‫‪4.6‬‬ ‫‪7.5‬‬ ‫‪11.2‬‬ ‫‪9.5‬‬

‫‪6.2‬‬ ‫‪11.2‬‬ ‫‪11.2‬‬ ‫‪10.5‬‬ ‫‪9.3‬‬ ‫‪7.2‬‬ ‫‪13.4‬‬ ‫‪5‬‬ ‫‪11.6‬‬ ‫‪11.2‬‬ ‫‪6.2‬‬ ‫‪12‬‬ ‫‪11.3‬‬ ‫‪9.2‬‬ ‫‪5.5‬‬ ‫‪6‬‬ ‫‪12.5‬‬ ‫‪9.8‬‬ ‫‪6.1‬‬ ‫‪14.3‬‬ ‫‪15.5‬‬ ‫‪10.8‬‬ ‫‪4.5‬‬ ‫‪6.7‬‬ ‫‪4.5‬‬ ‫‪9.8‬‬ ‫‪4‬‬ ‫‪5.5‬‬ ‫‪10‬‬ ‫‪8.5‬‬

‫‪1‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪5‬‬ ‫‪6‬‬ ‫‪7‬‬ ‫‪8‬‬ ‫‪9‬‬ ‫‪10‬‬ ‫‪11‬‬ ‫‪12‬‬ ‫‪13‬‬ ‫‪14‬‬ ‫‪15‬‬ ‫‪16‬‬ ‫‪17‬‬ ‫‪18‬‬ ‫‪19‬‬ ‫‪20‬‬ ‫‪21‬‬ ‫‪22‬‬ ‫‪23‬‬ ‫‪24‬‬ ‫‪25‬‬ ‫‪26‬‬ ‫‪27‬‬ ‫‪28‬‬ ‫‪29‬‬ ‫‪30‬‬

‫ ﺍﻻﺳﺘﻨﺘﺎﺝ‪:‬‬‫ﻧﻼﺣﻆ ﻛﻤﺎ ﰲ ﺍﳉﺪﻭﻝ ﺍﻟﺴﺎﺑﻖ)‪ .(2-2‬ﻭﺟﻮﺩ ﻗﻴﻤﺘﲔ ﻗﺎﺻﻴﺘﲔ ﰲ ﻣﺘﻐﲑ ﺍﳌﺼﺮﻭﻓﺎﺕ‬ ‫ﺍﳌﻌﻴﺸﻴﺔ ﻟﻸﺳﺮﺓ ﻭﻫﻲ ﺍﳌﺸﺎﻫﺪﺗﲔ ﺭﻗﻢ ‪ .20,21‬ﺫﻟﻚ ﻻﻥ ﻗﻴﻤﺔ ﺑﻮﺍﻗﻲ ﺍﳊﺬﻑ ﺍﳌﻌﲑﺓ ﺍﳌﻄﻠﻘﺔ ﺍﻛﱪ‬ ‫‪29‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫ﻣﻦ ﻗﻴﻤﺔ‬ ‫ﺍﻟﺘﺎﺑﻊ‪ .‬ﺣﻴﺚ ﺃ‪‬ﺎ ﺗﺴﺎﻭﻱ‪.‬‬

‫‪t 0.05, 46 = 2.05553‬‬

‫‪ .‬ﻭﻳﻌﺘﱪ ﺫﻟﻚ ﻣﺆﺷﺮ ﺟﻴﺪ ﻻﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺎﺻﻴﺔ ﰲ ﺍﳌﺘﻐﲑ‬ ‫*‬ ‫*‬ ‫‪d 20‬‬ ‫‪= 2.05868 d 21‬‬ ‫‪= 2.42648‬‬

‫ﻭﺳﺘﺪﻋﻲ ﻫﺎﺗﺎﻥ ﺍﳌﺸﺎﻫﺪﺗﺎﻥ ﺍﻟﻘﺎﺻﻴﺘﺎﻥ ﺩﺭﺍﺳﺘﻬﺎ ﻭﻗﻴﺎﺱ ﺃﺛﺮﻫﺎ ﻋﻠﻰ ﺍﻟﻨﻤﻮﺫﺝ‪.‬‬ ‫ﺗﻄﺒﻴﻖ)‪-:(2-3‬‬ ‫ﺑﺎﻟﻌﻮﺩﺓ ﺇﱃ ﺑﻴﺎﻧﺎﺕ ﺗﻄﺒﻴﻖ)‪ ،(1-3‬ﺍﳌﺘﻐﲑﺍﺕ ﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻷﺩﺍﺀ ﺍﻟﻮﻇﻴﻔﻲ)‪ 100‬ﺩﺭﺟﺔ(‬ ‫ﺳﻮﻑ ﻧﺴﺘﺨﺮﺝ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺼﻴﺔ ﰲ ﻣﺘﻐﲑ ﺍﻷﺩﺍﺀ ﺍﻟﻮﻇﻴﻔﻲ ‪.Y‬‬ ‫ ﺍﻟﺘﺤﻠﻴﻞ ﺍﻹﺣﺼﺎﺋﻲ‪-:‬‬‫ﺑﺎﺳﺘﺨﺪﺍﻡ ﺑﺮﻧﺎﻣﺞ ﺍﳊﺰﻡ ﺍﻹﺣﺼﺎﺋﻴﺔ ‪ Minitab‬ﺳﻮﻑ ﻧﻘﻮﻡ ﺑﺎﺳﺘﺨﺮﺍﺝ ﺑﻮﺍﻗﻲ ﺳﺘﻮﺩﻧﺖ‬ ‫ﺍﶈﺬﻭﻓﺔ ﻭﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺎﺻﻴﺔ ﰲ ﻣﺘﻐﲑ ﺍﻷﺩﺍﺀ ﺍﻟﻮﻇﻴﻔﻲ)‪ 100‬ﺩﺭﺟﺔ(‪.‬‬ ‫‪Inverse Cumulative Distribution Function‬‬ ‫‪Student's t distribution with 29 DF‬‬ ‫‪x‬‬ ‫‪2.04523‬‬

‫) ‪P( X <= x‬‬ ‫‪0.975‬‬

‫‪Regression Analysis: Y versus X1; X2‬‬ ‫‪The regression equation is‬‬ ‫‪Y = 34.7 + 2.17 X1 + 1.18 X2‬‬

‫‪P‬‬ ‫‪0.000‬‬ ‫‪0.000‬‬ ‫‪0.002‬‬

‫‪T‬‬ ‫‪15.87‬‬ ‫‪4.76‬‬ ‫‪3.43‬‬

‫‪SE Coef‬‬ ‫‪2.190‬‬ ‫‪0.4561‬‬ ‫‪0.3436‬‬

‫‪Coef‬‬ ‫‪34.749‬‬ ‫‪2.1731‬‬ ‫‪1.1789‬‬

‫‪R-Sq = 94.6%‬‬

‫‪Predictor‬‬ ‫‪Constant‬‬ ‫‪X1‬‬ ‫‪X2‬‬

‫‪S = 3.31558‬‬

‫‪Analysis of Variance‬‬ ‫‪P‬‬ ‫‪0.000‬‬

‫‪F‬‬ ‫‪264.75‬‬

‫‪MS‬‬ ‫‪2910.5‬‬ ‫‪11.0‬‬

‫‪SS‬‬ ‫‪5820.9‬‬ ‫‪329.8‬‬ ‫‪6150.7‬‬

‫‪DF‬‬ ‫‪2‬‬ ‫‪30‬‬ ‫‪32‬‬

‫‪Source‬‬ ‫‪Regression‬‬ ‫‪Residual Error‬‬ ‫‪Total‬‬

‫‪Seq SS‬‬

‫‪DF‬‬

‫‪Source‬‬

‫‪30‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬ ‫‪5691.5‬‬ ‫‪129.4‬‬

‫‪X1‬‬ ‫‪X2‬‬

‫‪1‬‬ ‫‪1‬‬

‫‪Unusual Observations‬‬ ‫‪St Resid‬‬ ‫‪2.16R‬‬ ‫‪2.59R‬‬

‫‪Residual‬‬ ‫‪6.133‬‬ ‫‪8.145‬‬

‫‪SE Fit‬‬ ‫‪1.719‬‬ ‫‪1.045‬‬

‫‪Fit‬‬ ‫‪80.867‬‬ ‫‪55.855‬‬

‫‪X1‬‬ ‫‪12.0‬‬ ‫‪7.0‬‬

‫‪Y‬‬ ‫‪87.000‬‬ ‫‪64.000‬‬

‫‪Obs‬‬ ‫‪14‬‬ ‫‪20‬‬

‫‪R denotes an observation with a large standardized residual.‬‬

‫‪ -‬ﻗﻴﻤﺔ ) ‪ ،( t 0.05,29 = 2.04523‬ﻭﺑﻮﺍﻗﻲ ﺳﺘﻮﺩﻧﺖ ﺑﺎﻟﺮﻣﺰ‬

‫*‪d i‬‬

‫ﻛﻤﺎ ﰲ ﺍﳉﺪﻭﻝ ﺍﻟﺘﺎﱄ‪.‬‬

‫ ﺟﺪﻭﻝ )‪ (2-3‬ﻗﻴﻢ ﺳﺘﻮﺩﻧﺖ ﺍﶈﺬﻭﻓﺔ )ﺍﻟﻘﻴﻢ ﺍﻟﻘﺎﺻﻴﺔ ﰲ ﻣﺘﻐﲑ ﺍﻷﺩﺍﺀ ﺍﻟﻮﻇﻴﻔﻲ(‪.‬‬‫‪| di* | > t‬‬

‫‪2.16323‬‬

‫‪2.58858‬‬

‫*‪di‬‬

‫)‪e(Y1|X1,X2‬‬

‫‪X3‬‬

‫‪X2‬‬

‫‪X1‬‬

‫‪Y‬‬

‫‪i‬‬

‫‪-1.1507‬‬ ‫‪0.00841‬‬ ‫‪0.96838‬‬ ‫‪-1.73769‬‬ ‫‪1.1643‬‬ ‫‪-1.01115‬‬ ‫‪0.56123‬‬ ‫‪-1.36981‬‬ ‫‪-0.02772‬‬ ‫‪1.07996‬‬ ‫‪-0.08267‬‬ ‫‪0.7014‬‬ ‫‪0.11633‬‬ ‫‪2.16323‬‬ ‫‪-0.18183‬‬ ‫‪-0.17907‬‬ ‫‪-0.46165‬‬ ‫‪-0.4875‬‬ ‫‪0.5794‬‬ ‫‪2.58858‬‬ ‫‪1.02996‬‬ ‫‪-0.39041‬‬ ‫‪0.22507‬‬ ‫‪-0.91086‬‬ ‫‪-0.35366‬‬ ‫‪-0.72561‬‬ ‫‪1.327‬‬ ‫‪0.61033‬‬ ‫‪-0.727‬‬ ‫‪-1.49645‬‬ ‫‪0.45045‬‬ ‫‪-0.48318‬‬

‫‪-3.43627‬‬ ‫‪0.02745‬‬ ‫‪3.14466‬‬ ‫‪-5.32996‬‬ ‫‪3.61994‬‬ ‫‪-3.20697‬‬ ‫‪1.66393‬‬ ‫‪-4.38584‬‬ ‫‪-0.08976‬‬ ‫‪3.44107‬‬ ‫‪-0.26863‬‬ ‫‪2.2622‬‬ ‫‪0.37941‬‬ ‫‪6.1331‬‬ ‫‪-0.55348‬‬ ‫‪-0.56504‬‬ ‫‪-1.50338‬‬ ‫‪-1.55926‬‬ ‫‪1.79848‬‬ ‫‪8.14499‬‬ ‫‪3.31775‬‬ ‫‪-1.26863‬‬ ‫‪0.73137‬‬ ‫‪-2.97255‬‬ ‫‪-1.15142‬‬ ‫‪-2.33029‬‬ ‫‪3.97735‬‬ ‫‪1.96579‬‬ ‫‪-2.26896‬‬ ‫‪-4.62092‬‬ ‫‪1.44074‬‬ ‫‪-1.50305‬‬

‫‪14‬‬ ‫‪7‬‬ ‫‪9‬‬ ‫‪4‬‬ ‫‪5‬‬ ‫‪4‬‬ ‫‪10‬‬ ‫‪4‬‬ ‫‪6‬‬ ‫‪5‬‬ ‫‪6‬‬ ‫‪6‬‬ ‫‪7‬‬ ‫‪10‬‬ ‫‪11‬‬ ‫‪9‬‬ ‫‪11‬‬ ‫‪11‬‬ ‫‪10‬‬ ‫‪5‬‬ ‫‪8‬‬ ‫‪6‬‬ ‫‪8‬‬ ‫‪7‬‬ ‫‪8‬‬ ‫‪12‬‬ ‫‪11‬‬ ‫‪10‬‬ ‫‪13‬‬ ‫‪14‬‬ ‫‪12‬‬ ‫‪4‬‬

‫‪19‬‬ ‫‪12‬‬ ‫‪15‬‬ ‫‪4‬‬ ‫‪6‬‬ ‫‪6‬‬ ‫‪15‬‬ ‫‪7‬‬ ‫‪9‬‬ ‫‪7‬‬ ‫‪10‬‬ ‫‪8‬‬ ‫‪11‬‬ ‫‪17‬‬ ‫‪16‬‬ ‫‪18‬‬ ‫‪14‬‬ ‫‪17‬‬ ‫‪15‬‬ ‫‪5‬‬ ‫‪15‬‬ ‫‪10‬‬ ‫‪10‬‬ ‫‪12‬‬ ‫‪13‬‬ ‫‪14‬‬ ‫‪14‬‬ ‫‪16‬‬ ‫‪20‬‬ ‫‪21‬‬ ‫‪17‬‬ ‫‪4‬‬

‫‪19‬‬ ‫‪12‬‬ ‫‪14‬‬ ‫‪5‬‬ ‫‪9‬‬ ‫‪8‬‬ ‫‪11‬‬ ‫‪8‬‬ ‫‪10‬‬ ‫‪9‬‬ ‫‪10‬‬ ‫‪9‬‬ ‫‪11‬‬ ‫‪12‬‬ ‫‪17‬‬ ‫‪15‬‬ ‫‪13‬‬ ‫‪16‬‬ ‫‪16‬‬ ‫‪7‬‬ ‫‪13‬‬ ‫‪10‬‬ ‫‪10‬‬ ‫‪12‬‬ ‫‪12‬‬ ‫‪12‬‬ ‫‪16‬‬ ‫‪14‬‬ ‫‪17‬‬ ‫‪18‬‬ ‫‪16‬‬ ‫‪6‬‬

‫‪95‬‬ ‫‪75‬‬ ‫‪86‬‬ ‫‪45‬‬ ‫‪65‬‬ ‫‪56‬‬ ‫‪78‬‬ ‫‪56‬‬ ‫‪67‬‬ ‫‪66‬‬ ‫‪68‬‬ ‫‪66‬‬ ‫‪72‬‬ ‫‪87‬‬ ‫‪90‬‬ ‫‪88‬‬ ‫‪78‬‬ ‫‪88‬‬ ‫‪89‬‬ ‫‪64‬‬ ‫‪84‬‬ ‫‪67‬‬ ‫‪69‬‬ ‫‪72‬‬ ‫‪75‬‬ ‫‪75‬‬ ‫‪90‬‬ ‫‪86‬‬ ‫‪93‬‬ ‫‪94‬‬ ‫‪91‬‬ ‫‪51‬‬

‫‪1‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪5‬‬ ‫‪6‬‬ ‫‪7‬‬ ‫‪8‬‬ ‫‪9‬‬ ‫‪10‬‬ ‫‪11‬‬ ‫‪12‬‬ ‫‪13‬‬ ‫‪14‬‬ ‫‪15‬‬ ‫‪16‬‬ ‫‪17‬‬ ‫‪18‬‬ ‫‪19‬‬ ‫‪20‬‬ ‫‪21‬‬ ‫‪22‬‬ ‫‪23‬‬ ‫‪24‬‬ ‫‪25‬‬ ‫‪26‬‬ ‫‪27‬‬ ‫‪28‬‬ ‫‪29‬‬ ‫‪30‬‬ ‫‪31‬‬ ‫‪32‬‬

‫‪31‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬ ‫‪| di* | > t‬‬

‫*‪di‬‬

‫)‪e(Y1|X1,X2‬‬

‫‪X3‬‬

‫‪X2‬‬

‫‪X1‬‬

‫‪Y‬‬

‫‪i‬‬

‫‪-1.58904‬‬

‫‪-5.03388‬‬

‫‪4‬‬

‫‪6‬‬

‫‪7‬‬

‫‪52‬‬

‫‪33‬‬

‫ﺍﻻﺳﺘﻨﺘﺎﺝ‪-:‬‬ ‫ﻧﻼﺣﻆ ﻣﺎ ﻛﻤﺎ ﺟﺎﺀ ﰲ ﺟﺪﻭﻝ)‪ ،(2-3‬ﺃﻥ ﻫﻨﺎﻙ ﻣﺸﺎﻫﺪﺗﺎﻥ ﻗﺎﺻﻴﺘﺎﻥ ﰲ ﻗﻴﻢ ﺍﻷﺩﺍﺀ‬ ‫ﺍﻟﻮﻇﻴﻔﻲ‪ .‬ﻭﻫﻲ ﺍﳌﺸﺎﻫﺪﺗﺎﻥ ‪ 14,20‬ﺫﻟﻚ ﻻﻥ ﻗﻴﻤﺔ ﺳﺘﻮﺩﻧﺖ ﻋﻨﺪ ﻫﺎﺗﺎﻥ ﺍﳌﺸﺎﻫﺪﺗﺎﻥ ﺍﻛﱪ ﻣﻦ ﻗﻴﻤﺔ‬ ‫) ‪.( t 0.05,29 = 2.04523‬‬ ‫*‬ ‫‪d14* = 2.16323 d 20‬‬ ‫‪= 2.58858‬‬

‫ﻟﺬﻟﻚ ﻧﻌﺘﱪﻫﺎ ﻗﺎﺻﻴﺔ‪ .‬ﻭﺗﺴﺘﺪﻋﻲ ﻫﺎﺗﺎﻥ ﺍﳊﺎﻟﺘﺎﻥ ﺩﺭﺍﺳﺘﻬﻤﺎ ﻭﻗﻴﺎﺱ ﺗﺄﺛﲑﻫﺎ ﻋﻠﻰ ﺍﻟﻨﻤﻮﺫﺝ ﻭﺍﻟﺘﺤﻠﻴﻞ‬ ‫ﺍﻹﺣﺼﺎﺋﻲ‪ .‬ﻣﻊ ﻣﻼﺣﻈﺔ ﺃﻥ ﺍﳌﺸﺎﻫﺪﺓ ‪ 14‬ﻗﺎﺻﻴﺔ ﰲ ﻣﺘﻐﲑﺍﺕ ﺍﻷﺩﺍﺀ ﻭﺍﻟﻮﻇﻴﻔﻲ ﻭﻋﺪﺩ ﺳﻨﻮﺍﺕ ﺍﳋﱪﺓ‬ ‫ﻭﻋﺪﺩ ﺳﻨﻮﺍﺕ ﺍﻟﺘﻌﻠﻴﻢ ﺃﻳﻀﺎ‪.‬‬ ‫)‪ (3‬ﲢﺪﻳﺪ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ – ﺗﺪﺍﺑﲑ ) ‪Cook’s Distance, DFBETAS,‬‬ ‫‪.(DFFITS, COVRATIO‬‬ ‫ﻼ ﻣﻦ ﺍﳌﺘﻐﲑﺍﺕ ﺍﳌﺴﺘﻘﻠﺔ ‪،x‬‬ ‫ﺳﺒﻖ ﻭﺃﻥ ﻋﺮﻓﻨﺎ ﻃﺮﻳﻘﺔ ﻛﺸﻒ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺎﺻﻴﺔ ﰲ ﻛ ﹰ‬ ‫ﻭﺍﳌﺘﻐﲑﺍﺕ ﺍﻟﺘﺎﺑﻌﺔ ‪ ،y‬ﻭﻟﻜﻦ ﺍﻟﻜﺸﻒ ﺍﳊﻘﻴﻘﻲ ﻳﻜﻤﻦ ﻓﻴﻤﺎ ﺇﺫﺍ ﻛﺎﻧﺖ ﻫﺬﻩ ﺍﳌﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ ﺃﻡ ﻻ‪.‬‬ ‫ﺣﻴﺚ ﺗﻌﺘﱪ ﺍﳌﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﺇﺫﺍ ﻛﺎﻥ ﺍﺳﺘﺒﻌﺎﺩﻫﺎ ﳛﺪﺙ ﺗﻐﲑﹰﺍ ﻣﻠﺤﻮﻇﹰﺎ ﰲ ﻗﻴﻢ ﻣﻌﺎﻣﻼﺕ ﳕﻮﺫﺝ ﺍﻻﳓﺪﺍﺭ‬ ‫ﺍﳋﻄﻲ ﻭﺍﻹﺣﺼﺎﺀﺍﺕ ﺍﳌﺮﺗﺒﻄﺔ ‪‬ﺎ‪ .‬ﻣﻊ ﺍﻟﻌﻠﻢ ﺃﻧﻪ ﻟﻴﺲ ﺑﺎﻟﻀﺮﻭﺭﺓ ﺃﻥ ﺗﻜﻮﻥ ﲨﻴﻊ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺎﺻﻴﺔ‬ ‫ﻣﺆﺛﺮﺓ‪ .‬ﻭﻳﺘﻢ ﻗﻴﺎﺱ ﻓﻴﻤﺎ ﺇﺫﺍ ﻛﺎﻧﺖ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺎﺻﻴﺔ ﻣﺆﺛﺮﺓ ﺃﻡ ﻻ‪ ،‬ﺑﺄﺭﺑﻌﺔ ﻣﻘﺎﻳﻴﺲ ﻭﻫﻲ ‪.‬‬ ‫)‪.(Cook’s Distance, DFBETAS, DFFITS, COVRATIO‬‬ ‫)‪ (3-1‬ﺍﻟﺘﺄﺛﲑ ﻋﻠﻰ ﻗﻴﻢ ﺍﻟﺘﻮﻓﻴﻘﻴﺔ – ﻣﻘﻴﺎﺱ )‪.(DFFITS‬‬‫^‬

‫ﻳﺴﺘﺨﺪﻡ ﻣﻘﻴﺎﺱ ‪ DFFITS‬ﻟﻘﻴﺎﺱ ﺃﺛﺮ ﺍﳌﺸﺎﻫﺪﺓ ﺭﻗﻢ )‪ (i‬ﻋﻠﻰ ﺍﻟﻘﻴﻤﺔ ﺍﳌﻮﻓﻘﺔ ) ‪.( Yi‬‬ ‫ﻭﺣﻴﺚ ﻳﻌﻮﺩ ﺍﳊﺮﻓﺎﻥ )‪ (DF‬ﺇﱃ ﺍﺧﺘﺼﺎﺭ ﻛﻠﻤﺔ ﺍﺧﺘﻼﻑ ﺃﻭ ﻓﺮﻕ ﻭ )‪ (FITS‬ﺇﱃ ﺍﻟﻘﻴﻢ ﺍﳌﻮﻓﻘﺔ‬ ‫^‬

‫ﻟﺬﻟﻚ ﲤﺖ ﺍﻟﺘﺴﻤﻴﺔ‪ .‬ﻭﻟﻘﺪ ﻃﻮﺭﺕ ﻣﻌﺎﺩﻟﺔ ﺟﱪﻳﺔ ﻟﻘﻴﺎﺱ ﺃﺛﺮ ﺍﳌﺸﺎﻫﺪﺓ ﺭﻗﻢ )‪ (i‬ﻋﻠﻰ ﺍﻟﻘﻴﻢ ﺍﳌﻮﻓﻘﺔ ) ‪( Yi‬‬ ‫ﻭﻫﻲ‪:‬‬ ‫‪32‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬ ‫^‬

‫^‬

‫) ‪Y i − Y i (i‬‬ ‫‪MSE (i ) hii‬‬

‫= ‪( DFFITS ) i‬‬

‫‪1‬‬

‫‪ h 2‬‬ ‫‪( DFFITS ) i = d i*  ii ‬‬ ‫‪1 − hii ‬‬

‫ﺣﻴﺚ ﺃﻥ‪-:‬‬ ‫*‪ : d i‬ﺑﻮﺍﻗﻲ ﺍﳊﺬﻑ ﺍﳌﻌﲑﺓ )ﺑﻮﺍﻗﻲ ﺳﺘﻮﺩﻧﺖ ﺍﶈﺬﻭﻓﺔ(‪.‬‬ ‫‪ : hii‬ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ﺍﻟﺬﻱ ﻳﺘﻢ ﺍﺳﺘﺨﺮﺍﺟﻬﺎ ﻣﻦ ﺍﻟﻌﻨﺼﺮ ﺍﻟﻘﻄﺮﻱ ﰲ ﻣﺼﻔﻮﻓﺔ ﺍﻟﻘﺒﻌﺔ‪.‬‬ ‫^‬

‫‪ : Y i‬ﺍﻟﻘﻴﻤﺔ ﺍﻟﺘﻮﻓﻴﻘﻴﺔ ﻟﻠﻤﺘﻐﲑ ﺍﻟﺘﺎﺑﻊ ﻟﻠﻤﺸﺎﻫﺪﺓ ﺭﻗﻢ ‪ i‬ﻋﻨﺪ ﺍﺳﺘﺨﺪﺍﻡ ﲨﻴﻊ ﺍﳌﺸﺎﻫﺪﺍﺕ ‪.n‬‬ ‫^‬

‫) ‪ : Y i (i‬ﻗﻴﻤﺔ ﺍﻟﺘﻮﻓﻴﻖ ﻟﻠﺘﻨﺒﺆ ﺑﺎﳌﺘﻐﲑ ﺍﻟﺘﺎﺑﻊ ﻋﻨﺪ ﺣﺬﻑ ﺍﳌﺸﺎﻫﺪﺓ ﺭﻗﻢ )‪.(i‬‬ ‫) ‪ : MSE(i‬ﻣﺘﻮﺳﻂ ﻣﺮﺑﻌﺎﺕ ﺍﳋﻄﺄ ﻋﻨﺪ ﺣﺬﻑ ﺍﳌﺸﺎﻫﺪﺓ ﺭﻗﻢ )‪.(i‬‬ ‫ﻭﻧﻼﺣﻆ ﻣﻦ ﺍﻟﻌﻼﻗﺔ ﺍﻟﺜﺎﻧﻴﺔ ﺍﻋﺘﻤﺎﺩﻫﺎ ﻋﻠﻰ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ) ﻟﻘﻴﺎﺱ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺎﺻﻴﺔ ﰲ ﺍﳌﺘﻐﲑ‬ ‫ﺍﳌﺴﺘﻘﻞ (‪ ،‬ﻭﺑﻮﺍﻗﻲ ﺍﳊﺬﻑ ﺍﳌﻌﲑﺓ ) ﻟﻘﻴﺎﺱ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺎﺻﻴﺔ ﰲ ﺍﳌﺘﻐﲑ ﺍﻟﺘﺎﺑﻊ ( ﺃﻱ ﺍﻧﻪ ﺇﺫﺍ ﻛﺎﻧﺖ‬ ‫ﺍﳌﺸﺎﻫﺪﺓ ﺭﻗﻢ )‪ (i‬ﻗﺎﺻﻴﺔ ﰲ ) ﺍﳌﺘﻐﲑ ﺍﳌﺴﺘﻘﻞ ‪ ( x‬ﻭﳍﺎ ﻗﻴﻤﺔ ﺍﻟﺮﺍﻓﻌﺔ ﳍﺎ ﻛﺒﲑﺓ ﻭﺃﻳﻀﹰﺎ ﺇﺫﺍ ﻛﺎﻧﺖ‬ ‫ﺍﳌﺸﺎﻫﺪﺓ )‪ (i‬ﻗﺎﺻﻴﺔ ﰲ ) ﺍﳌﺘﻐﲑ ﺍﻟﺘﺎﺑﻊ ‪ ( y‬ﻭﳍﺎ ﻗﻴﻤﺔ ﺑﺎﻗﻲ ﺳﺘﻮﺩﻧﺖ ﻛﺒﲑ ﺃﻳﻀﹰﺎ ﻓﺈﻥ ﺍﻟﻘﻴﻤﺔ ﺍﳌﻄﻠﻘﺔ ﳍﺬﺍ‬ ‫ﺍﻟﻌﺎﻣﻞ ﺳﻮﻑ ﺗﺼﺒﺢ ﻛﺒﲑﺓ ﺃﻳﻀﹰﺎ‪ ،‬ﻭﻣﻨﻬﺎ ﺗﻜﻮﻥ ﻫﺬﻩ ﺍﻟﻘﻴﻤﺔ ﺍﻟﻜﺒﲑﺓ ﻛﺪﻟﻴﻞ ﻧﺴﺘﺪﻝ ﻣﻨﻪ ﻓﻴﻤﺎ ﺇﺫﺍ ﻛﺎﻧﺖ‬ ‫ﻣﺆﺛﺮﺓ ﺃﻡ ﻻ‪.‬‬ ‫ ﻃﺮﻳﻘﺔ ﻛﺸﻒ ﺍﻟﺘﺄﺛﲑ ﻟﻘﻴﻤﺔ ‪ DFFITS‬ﻋﻠﻰ ﺍﻟﻨﻤﻮﺫﺝ‪.‬‬‫ﺗﻌﺘﱪ ﺍﳌﺸﺎﻫﺪﺓ )‪ (i‬ﻣﺆﺛﺮﺓ ﺇﺫﺍ ﻛﺎﻧﺖ ﺍﻟﻘﻴﻤﺔ ﺍﳌﻄﻠﻘﺔ ﻟﻘﻴﻤﺔ ‪ DFFITS‬ﺍﻛﱪ ﻣﻦ‬ ‫ﺇﺫﺍ ﻛﺎﻥ‪:‬‬ ‫‪p‬‬ ‫‪n‬‬

‫‪p‬‬ ‫‪n‬‬

‫‪ . 2‬ﺃﻱ‬

‫‪| DFFITS i |> 2‬‬

‫ﺣﻴﺚ ﺃﻥ‪-:‬‬ ‫‪ : n‬ﻋﺪﺩ ﺍﳌﺸﺎﻫﺪﺍﺕ‪.‬‬ ‫‪ : p‬ﻋﺪﺩ ﻣﻌﺎﱂ ﺍﻟﻨﻤﻮﺫﺝ ‪. β 0 , β1 ,..., β p−1‬‬ ‫ﻭﺫﻟﻚ ﰲ ﺣﺎﻟﺔ ﺍﻟﻌﻴﻨﺔ ﺍﻟﻜﺒﲑﺓ ﻓﻘﻂ ‪.‬‬ ‫‪33‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫ﺃﻣﺎ ﰲ ﺣﺎﻟﺔ ﺍﻟﻌﻴﻨﺔ ﺍﻟﺼﻐﲑﺓ ﻭﺍﳌﺘﻮﺳﻄﺔ ﻓﻴﻘﺘﺮﺡ ﺃﻥ ﺗﻌﺘﱪ ﺍﳊﺎﻟﺔ ﻣﺆﺛﺮﺓ ﺇﺫﺍ ﻛﺎﻧﺖ ﺍﻟﻘﻴﻤﺔ ﺍﳌﻄﻠﻘﺔ‬ ‫‪ DFFITS‬ﺍﻛﱪ ﻣﻦ ﺍﻟﻮﺍﺣﺪ ﺍﻟﺼﺤﻴﺢ‪ .‬ﻭﻣﻨﻪ ﻓﺈﻥ‪:‬‬ ‫‪| DFFITS i |> 1‬‬

‫ﻭﻳﻘﺘﺮﺡ ﺁﺧﺮﻭﻥ ﻣﺜﻞ ﺷﺎﺗﺮﺟﻲ ﻭﻫﺎﺩﻱ ))‪ (Chatterje and Hadi (1988‬ﲟﻘﺎﺭﻧﺔ ﺍﻟﻘﻴﻤﺔ‬ ‫ﻼ ﻣﻦ ﺍﳌﻘﺎﺭﻧﺔ ﰲ ﺣﺎﻟﺔ ﺍﻟﻌﻴﻨﺔ ﺍﻟﻜﺒﲑﺓ ﻭﻫﻲ‪.‬‬ ‫ﺍﳌﻄﻠﻘﺔ ‪ DFFITS‬ﺑﻌﺪﺩ ﺍﻛﱪ ﻗﻠﻴ ﹰ‬ ‫‪p‬‬ ‫‪n− p −2‬‬

‫‪| DFFITS i |> 2‬‬

‫)‪ (3-2‬ﺍﻟﺘﺄﺛﲑ ﻋﻠﻰ ﻣﻌﺎﻣﻼﺕ ﺍﻻﳓﺪﺍﺭ – ﻣﻘﻴﺎﺱ )‪.(DFBETAS‬‬‫ﻳﺴﺘﺨﺪﻡ ﻣﻘﻴﺎﺱ ‪ DFBETAS‬ﻟﻘﻴﺎﺱ ﺍﻟﻔﺮﻕ ﺑﲔ ﻣﻌﺎﻣﻼﺕ ﺍﻻﳓﺪﺍﺭ ﺍﳌﻘﺪﺭﺓ ﺑﺎﺳﺘﺨﺪﺍﻡ‬ ‫ﻛﻞ ﺍﳌﺸﺎﻫﺪﺍﺕ ﻭﻗﻴﻢ ﻣﻌﺎﻣﻼﺕ ﺍﻻﳓﺪﺍﺭ ﺍﳌﻘﺪﺭﺓ ﺑﻌﺪ ﺣﺬﻑ ﺍﳌﺸﺎﻫﺪﺓ ﺭﻗﻢ )‪ (i‬ﰲ ﻛﻞ ﻣﺮﺓ‪ .‬ﺣﻴﺚ‬ ‫ﻳﻌﻮﺩ ﺍﳊﺮﻓﺎﻥ )‪ (DF‬ﺇﱃ ﺍﺧﺘﺼﺎﺭ ﻛﻠﻤﺔ ﺍﺧﺘﻼﻑ ﺃﻭ ﻓﺮﻕ ﻭ )‪ (BETAS‬ﺇﱃ ﻣﻌﺎﻣﻼﺕ ﳕﻮﺫﺝ‬ ‫ﺍﻻﳓﺪﺍﺭ ﺍﳌﻘﺪﺭﺓ ﻟﺬﻟﻚ ﲤﺖ ﺍﻟﺘﺴﻤﻴﺔ‪ .‬ﻭﺗﻮﺟﺪ ﻣﻌﺎﺩﻟﺔ ﳚﺐ ﺣﺴﺎ‪‬ﺎ ﰲ ﻛﻞ ﻣﺮﺓ ﻳﺘﻢ ﻓﻴﻬﺎ ﺗﻮﻓﻴﻖ‬ ‫ﺍﻟﻨﻤﻮﺫﺝ ﺑﻌﺪ ﺣﺬﻑ ﻣﺸﺎﻫﺪﺓ ﺭﻗﻢ )‪ (i‬ﻭﻫﻲ ﻋﻠﻰ ﺍﻟﺸﻜﻞ ﺍﻟﺘﺎﱄ‪:‬‬ ‫‪for k = 0,1,2,..., p − 1‬‬

‫) ‪bk − bk (i‬‬ ‫‪S i ( X ' X ) −kk1‬‬

‫ﺣﻴﺚ ﺃﻥ‪-:‬‬ ‫‪ : bk‬ﻣﻌﺎﻣﻞ ﺍﻻﳓﺪﺍﺭ ﺭﻗﻢ ‪ k‬ﺍﳌﻘﺪﺭ ﺑﺎﺳﺘﺨﺪﺍﻡ ﻛﻞ ﺍﳌﺸﺎﻫﺪﺍﺕ )‪.(n‬‬ ‫) ‪ : bk (i‬ﻣﻌﺎﻣﻞ ﺍﻻﳓﺪﺍﺭ ﺭﻗﻢ ‪ k‬ﺍﳌﻘﺪﺭ ﺑﻌﺪ ﺣﺬﻑ ﺍﳌﺸﺎﻫﺪﺓ ﺭﻗﻢ )‪ (i‬ﰲ ﻛﻞ ﻣﺮﺓ‪.‬‬ ‫‪ : S i‬ﺍﳋﻄﺄ ﺍﳌﻌﻴﺎﺭﻱ ﻟﻠﺘﻘﺪﻳﺮ ﻟﻨﻤﻮﺫﺝ ﺍﻻﳓﺪﺍﺭ ﺍﻟﻘﺪﺭ ﺑﻌﺪ ﺣﺬﻑ ﺍﳌﺸﺎﻫﺪﺓ ﺭﻗﻢ )‪ (i‬ﰲ ﻛﻞ ﻣﺮﺓ‪.‬‬ ‫‪ : ( X ' X ) −kk1‬ﺍﻟﻌﻨﺼﺮ ﺍﻟﻘﻄﺮﻱ ﺭﻗﻢ ‪ k‬ﻣﻦ ﺍﳌﺼﻔﻮﻓﺔ ‪. ( X ' X ) −1‬‬

‫‪34‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫ ﻃﺮﻳﻘﺔ ﻛﺸﻒ ﺍﻟﺘﺄﺛﲑ ﻟﻘﻴﻤﺔ ‪ DFBETAS‬ﻋﻠﻰ ﺍﻟﻨﻤﻮﺫﺝ‪.‬‬‫ﺗﻌﺘﱪ ﺍﳌﺸﺎﻫﺪﺓ ﺭﻗﻢ )‪ (i‬ﻣﺆﺛﺮﺓ ﻋﻠﻰ ﻣﻌﺎﻣﻞ ﳕﻮﺫﺝ ﺍﻻﳓﺪﺍﺭ ﺭﻗﻢ )‪ (k‬ﺇﺫﺍ ﻛﺎﻧﺖ ﺍﻟﻘﻴﻤﺔ ﺍﳌﻄﻠﻘﺔ‬ ‫ﻟﻠﻔﺮﻕ ﻛﺒﲑﺓ‪ .‬ﺃﻱ ﺃﻧﻪ ﰲ ﺣﺎﻟﺔ ﺍﻟﻌﻴﻨﺔ ﺍﻟﻜﺒﲑﺓ ﺗﻜﻮﻥ ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﺇﺫﺍ ﻛﺎﻧﺖ ﺍﻟﻘﻴﻤﺔ ﺍﳌﻄﻠﻘﺔ ﳌﻘﻴﺎﺱ‬ ‫‪ DFBETAS‬ﺍﻛﱪ ﻣﻦ ‪ . 2‬ﺃﻱ ﺇﺫﺍ ﻛﺎﻥ‪:‬‬ ‫‪n‬‬

‫‪n‬‬

‫ﺃﻣﺎ ﰲ ﺣﺎﻟﺔ ﺍﻟﻌﻴﻨﺔ ﺍﻟﺼﻐﲑﺓ ﻭﺍﳌﺘﻮﺳﻄﺔ ﻓﻴﻘﺘﺮﺡ ﺃﻥ ﺗﻌﺘﱪ ﺍﳊﺎﻟﺔ ﻣﺆﺛﺮﺓ ﺇﺫﺍ ﻛﺎﻧﺖ ﺍﻟﻘﻴﻤﺔ ﺍﳌﻄﻠﻘﺔ ﳌﻘﻴﺎﺱ‬ ‫‪ DFBETAS‬ﺃﻛﱪ ﻣﻦ ﺍﻟﻮﺍﺣﺪ ﺍﻟﺼﺤﻴﺢ‪ .‬ﺃﻱ ﺇﺫﺍ ﻛﺎﻥ‪:‬‬ ‫‪| DFBETASk(i) |> 1‬‬

‫)‪ (3-3‬ﻗﻴﺎﺱ ﺍﻷﺛﺮ ﻋﻠﻰ ﻛﻞ ﻣﻌﺎﻣﻼﺕ ﺍﻻﳓﺪﺍﺭ – ﻣﻘﻴﺎﺱ ﻣﺴﺎﻓﺔ ﻛﻮﻙ‪.‬‬‫ﻳﺴﺘﺨﺪﻡ ﻣﻘﻴﺎﺱ ﻣﺴﺎﻓﺔ ﻛﻮﻙ ﻟﻘﻴﺎﺱ ﺃﺛﺮ ﺍﳌﺸﺎﻫﺪﺓ )‪ (i‬ﻋﻠﻰ ﻛﻞ ﻣﻌﺎﻣﻼﺕ ﳕﻮﺫﺝ ﺍﻻﳓﺪﺍﺭ‬ ‫ﺍﳌﻘﺪﺭﺓ‪ .‬ﻭﳜﺘﻠﻒ ﻣﻘﻴﺎﺱ ﻛﻮﻙ ﻋﻦ ﻣﻘﻴﺎﺱ ‪ ،DFBETAS‬ﺃﻥ ﻣﻘﻴﺎﺱ ﻣﺴﺎﻓﺔ ﻛﻮﻙ ﻳﻘﻴﺲ ﺃﺛﺮ‬ ‫ﺣﺬﻑ ﺍﳌﺸﺎﻫﺪﺓ ﺭﻗﻢ )‪ (i‬ﻋﻠﻰ ﻛﻞ ﻗﻴﻢ ﻣﻌﺎﻣﻼﺕ ﳕﻮﺫﺝ ﺍﻻﳓﺪﺍﺭ‪ ،‬ﻭﻣﻘﻴﺎﺱ ‪ DFBETAS‬ﻳﻘﻴﺲ‬ ‫ﺃﺛﺮ ﺣﺬﻑ ﺍﳌﺸﺎﻫﺪﺓ ﺭﻗﻢ )‪ (i‬ﻋﻠﻰ ﻛﻞ ﻣﻌﺎﻣﻞ ﻣﻦ ﻣﻌﺎﻣﻼﺕ ﺍﻟﻨﻤﻮﺫﺝ ﻋﻠﻰ ﺣﺪﻩ‪ .‬ﻭﺃﻳﻀﹰﺎ ﳝﻜﻦ‬ ‫ﺣﺴﺎﺏ ﻣﺴﺎﻓﺔ ﻛﻮﻙ ﲟﻌﺎﺩﻟﺔ ﺗﻌﺘﻤﺪ ﻋﻠﻰ ﻗﻴﻤﺔ ﺍﻟﺒﻮﺍﻗﻲ ﻭﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ﺩﻭﻥ ﺍﳊﺎﺟﺔ ﺇﱃ ﺗﻮﻓﻴﻖ ﻣﻌﺎﺩﻟﺔ‬ ‫ﺍﳓﺪﺍﺭ ﻭﺣﺬﻑ ﻣﺸﺎﻫﺪﺓ ﻭﺍﺣﺪﺓ ﰲ ﻛﻞ ﻣﺮﺓ ﻛﻤﺎ ﰲ ﻣﻘﻴﺎﺱ ‪ ،DFBETAS‬ﻭﻳﺄﺧﺬ ﻣﻘﻴﺎﺱ‬ ‫ﻣﺴﺎﻓﺔ ﻛﻮﻙ ﺍﻟﻌﻼﻗﺔ ﺍﻟﺘﺎﻟﻴﺔ‪:‬‬

‫) ) (‪(b − b( ) ) X X (b − b‬‬ ‫'‬

‫‪i‬‬

‫'‬

‫‪i‬‬

‫= ‪Di‬‬

‫‪P * MSE‬‬ ‫‪2‬‬ ‫‪e  hii ‬‬ ‫‪Di = 2i ‬‬ ‫‪‬‬ ‫‪S p  (1 − hii )2 ‬‬

‫ﺣﻴﺚ ﺃﻥ‪-:‬‬ ‫‪ : ei‬ﻗﻴﻤﺔ ﺍﻟﺒﻮﺍﻗﻲ ﺍﻟﻌﺎﺩﻳﺔ ﻟﻨﻤﻮﺫﺝ ﺍﻻﳓﺪﺍﺭ ﻋﻨﺪ ﺍﳌﺸﺎﻫﺪﺓ ﺭﻗﻢ )‪.(i‬‬ ‫‪ : hii‬ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ﺍﻟﺬﻱ ﻳﺘﻢ ﺍﺳﺘﺨﺮﺍﺟﻬﺎ ﻣﻦ ﺍﻟﻌﻨﺼﺮ ﺍﻟﻘﻄﺮﻱ ﰲ ﻣﺼﻔﻮﻓﺔ ﺍﻟﻘﺒﻌﺔ‪.‬‬

‫‪35‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫‪ : b‬ﻣﺘﺠﻪ ﻣﻌﺎﻣﻼﺕ ﺍﻻﳓﺪﺍﺭ ﺍﳌﻘﺪﺭﺓ ﺍﻟﱵ ﳓﺼﻞ ﻋﻠﻴﻬﺎ ﻟﻜﻞ ﺍﳌﺸﺎﻫﺪﺍﺕ ‪.n‬‬ ‫) ‪ : b(i‬ﻣﺘﺠﻪ ﻣﻌﺎﻣﻼﺕ ﺍﻻﳓﺪﺍﺭ ﺍﳌﻘﺪﺭﺓ ﺍﻟﱵ ﳓﺼﻠﻪ ﻋﻠﻴﻪ ﻋﻨﺪ ﺣﺬﻑ ﺍﳌﺸﺎﻫﺪﺓ ﺭﻗﻢ )‪ (i‬ﰲ ﻛﻞ ﻣﺮﺓ‪.‬‬ ‫‪ : p‬ﻋﺪﺩ ﻣﻌﺎﱂ ﺍﻟﻨﻤﻮﺫﺝ ‪. β 0 , β1 ,..., β p−1‬‬ ‫‪ : MSE‬ﻣﺘﻮﺳﻂ ﻣﺮﺑﻌﺎﺕ ﺍﳋﻄﺄ‪.‬‬ ‫ﻭﻧﻼﺣﻆ ﺍﻋﺘﻤﺎﺩ ﻣﻘﻴﺎﺱ ﻣﺴﺎﻓﺔ ﻛﻮﻙ ﻋﻠﻰ ﻫﺎﺗﺎﻥ ﺍﻟﻘﻴﻤﺘﺎﻥ‪ .‬ﺃﻱ ﺍﻧﻪ ﻋﻨﺪﻣﺎ ﺗﻜﻮﻥ ﺃﺣﺪ ﻫﺎﺗﺎﻥ ﺍﻟﻘﻴﻤﺘﺎﻥ‬ ‫ﻛﺒﲑﺓ ﺃﻭ ﻛﻼﳘﺎ ﻛﺒﲑﺗﺎﻥ ﻓﺈﻥ ﻗﻴﻤﺔ ﻣﺴﺎﻓﺔ ﻛﻮﻙ ‪ Di‬ﺳﺘﺼﺒﺢ ﻛﺒﲑﺓ ﺃﻳﻀﹰﺎ‪.‬‬ ‫ ﻃﺮﻳﻘﺔ ﻛﺸﻒ ﺍﻟﺘﺄﺛﲑ ﻟﻘﻴﻤﺔ ﻣﺴﺎﻓﺔ ﻛﻮﻙ ‪.Di‬‬‫ﺗﺘﻢ ﻣﻘﺎﺭﻧﺔ ﻣﺴﺎﻓﺔ ﻛﻮﻙ ‪ Di‬ﺑﺎﻟﻘﻴﻤﺔ ﺍﻻﺣﺘﻤﺎﻟﻴﺔ ﻟﺘﻮﺯﻳﻊ ‪ F‬ﺑﺎﻟﺸﻜﻞ ﺍﻟﺘﺎﱄ ‪ Fα , p,1− p‬ﻓﺈﺫﺍ‬ ‫ﻛﺎﻧﺖ ﻗﻴﻤﺔ ﻣﺴﺎﻓﺔ ﻛﻮﻙ ﺍﻛﱪ ﻣﻦ ﻫﺬﻩ ﺍﻟﻘﻴﻤﺔ ﻧﻌﺘﱪ ﺍﳌﺸﺎﻫﺪﺓ ﺭﻗﻢ )‪ (i‬ﻣﺆﺛﺮﺓ ﻋﻠﻰ ﻗﻴﻢ ﻣﻌﺎﻣﻼﺕ‬ ‫ﳕﻮﺫﺝ ﺍﻻﳓﺪﺍﺭ‪ .‬ﺃﻱ ﻧﻌﺘﱪ ﺍﳌﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﺇﺫﺍ ﻛﺎﻥ‪:‬‬ ‫ ﻃﺮﻳﻘﺔ ﻧﻴﺘﺮ ﻭﺁﺧﺮﻭﻥ ) ﺹ‪.((3rd ed. 1990). 404‬‬ ‫‪fot α = 0.5‬‬ ‫‬

‫‪Di > Fα , p ,n − p‬‬

‫ﻃﺮﻳﻘﺔ ﻓﻮﻛﺲ ) ﺹ‪.((1997). 281‬‬ ‫‪4‬‬ ‫‪n− p‬‬

‫ﺣﻴﺚ ﺃﻥ‪-:‬‬ ‫‪ : p‬ﻋﺪﺩ ﻣﻌﺎﱂ ﺍﻟﻨﻤﻮﺫﺝ‬ ‫‪ : n‬ﻋﺪﺩ ﺍﳌﺸﺎﻫﺪﺍﺕ‪.‬‬ ‫‪ : α‬ﺍﳌﺌﲔ ‪.%50‬‬

‫> ‪Di‬‬

‫‪. β 0 , β1 ,..., β p−1‬‬

‫)‪ (3-4‬ﻗﻴﺎﺱ ﺍﻷﺛﺮ ﻋﻠﻰ ﺍﻷﺧﻄﺎﺀ ﺍﳌﻌﻴﺎﺭﻳﺔ – ﻣﻘﻴﺎﺱ ‪.COVRATIO‬‬‫ﻧﺴﺘﺨﺪﻡ ﻣﻘﻴﺎﺱ ﺍﻷﺛﺮ ﻋﻠﻰ ﺍﻷﺧﻄﺎﺀ ﺍﳌﻌﻴﺎﺭﻳﺔ ﻟﻘﻴﺎﺱ ﺃﺛﺮ ﺃﻱ ﺣﺎﻟﺔ ﻋﻠﻰ ﻣﺼﻔﻮﻓﺔ ﺗﺒﺎﻳﻦ ﺃﻭ ﺗﻐﺎﻳﺮ‬ ‫ﻣﻌﺎﻣﻼﺕ ﺍﻻﳓﺪﺍﺭ ﺍﳌﻘﺪﺭﺓ‪ .‬ﻭﻫﻲ ﻋﺒﺎﺭﺓ ﻋﻦ ﻧﺴﺒﺔ ﳏﺪﺩﺓ ﻣﺼﻔﻮﻓﺔ ﺗﺒﺎﻳﻦ ﺃﻭ ﺗﻐﺎﻳﺮ ﻣﻌﺎﻣﻼﺕ ﺍﻻﳓﺪﺍﺭ‬ ‫ﺍﳌﻘﺪﺭﺓ ) ﻟﺬﻟﻚ ﲤﺖ ﺍﻟﺘﺴﻤﻴﺔ ( ﺑﻌﺪ ﺣﺬﻑ ﺍﳌﺸﺎﻫﺪﺓ ﺭﻗﻢ )‪ (i‬ﶈﺪﺩﺓ ﻣﺼﻔﻮﻓﺔ ﺗﺒﺎﻳﻦ ﺃﻭ ﺗﻐﺎﻳﺮ‬ ‫‪36‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫ﻣﻌﺎﻣﻼﺕ ﺍﻻﳓﺪﺍﺭ ﺍﳌﻘﺪﺭ ﺑﺎﺳﺘﺨﺪﺍﻡ ﲨﻴﻊ ﺍﳊﺎﻻﺕ )‪ .(n‬ﻭﻗﺪ ﰎ ﺗﻄﻮﻳﺮ ﻣﻌﺎﺩﻟﺔ ﺣﺴﺎﺑﻴﺔ ﺗﻌﺘﻤﺪ ﻋﻠﻰ‬ ‫ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ﻭﻗﻴﻢ ﺑﻮﺍﻗﻲ ﺳﺘﻮﺩﻧﺖ ﺍﶈﺬﻭﻓﺔ ﻭﻫﻲ ﺇﱃ ﺍﻟﺸﻜﻞ ﺍﻟﺘﺎﱄ‪:‬‬ ‫‪1‬‬ ‫‪p‬‬

‫‪‬‬ ‫‪‬‬ ‫‪‬‬ ‫‪‬‬

‫‪*2‬‬ ‫‪‬‬ ‫‪(1 − hii ) n − p − 1 + d i‬‬ ‫‪n− p‬‬ ‫‪‬‬

‫= ‪COVRATIOi‬‬

‫ﺣﻴﺚ ﺃﻥ‪-:‬‬ ‫‪ : p‬ﻋﺪﺩ ﻣﻌﺎﱂ ﺍﻟﻨﻤﻮﺫﺝ ‪. β 0 , β1 ,..., β p−1‬‬ ‫‪ : n‬ﻋﺪﺩ ﺍﳌﺸﺎﻫﺪﺍﺕ‪.‬‬ ‫‪ : hii‬ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ﺍﻟﺬﻱ ﻳﺘﻢ ﺍﺳﺘﺨﺮﺍﺟﻬﺎ ﻣﻦ ﺍﻟﻌﻨﺼﺮ ﺍﻟﻘﻄﺮﻱ ﰲ ﻣﺼﻔﻮﻓﺔ ﺍﻟﻘﺒﻌﺔ‪.‬‬ ‫*‪ : d i‬ﺑﻮﺍﻗﻲ ﺍﳊﺬﻑ ﺍﳌﻌﲑﺓ )ﺑﻮﺍﻗﻲ ﺳﺘﻮﺩﻧﺖ ﺍﶈﺬﻭﻓﺔ(‪.‬‬ ‫ﻭﻧﻼﺣﻆ ﻣﻦ ﻫﺬﻩ ﺍﳌﻌﺎﺩﻟﺔ ﻋﺪﻡ ﺍﳊﺎﺟﺔ ﺇﱃ ﺗﻮﻓﻴﻖ ‪ n‬ﻣﻦ ﻣﻌﺎﺩﻻﺕ ﺍﻻﳓﺪﺍﺭ ﻭﺫﻟﻚ ﳌﺎ ﺫﻛﺮﻧﺎ‬ ‫ﻻﻋﺘﻤﺎﺩﻫﺎ ﺍﻟﻮﺍﺿﺢ ﻋﻠﻰ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ﻭﺑﻮﺍﻗﻲ ﺳﺘﻮﺩﻧﺖ ﺍﶈﺬﻭﻓﺔ‪ .‬ﺣﻴﺚ ﺗﺰﻳﺪ ﻗﻴﻤﺔ‬ ‫‪ COVRATIO‬ﺑﺰﻳﺎﺩﺓ ﻗﻴﻢ ﺍﻟﺮﺍﻓﻌﺔ ﻭﺍﳔﻔﺎﺽ ﺑﻮﺍﻗﻲ ﺳﺘﻮﺩﻧﺖ ﺍﶈﺬﻭﻓﺔ‪ ،‬ﻭﻳﻜﻮﻥ ﺫﻟﻚ ﻣﺆﺷﺮ‬ ‫ﺟﻴﺪ ﻻﻛﺘﺸﺎﻑ ﺗﺄﺛﲑ ﻗﻴﻢ ‪ COVRATIO‬ﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻷﺧﻄﺎﺀ ﺍﳌﻌﻴﺎﺭﻳﺔ‪.‬‬ ‫ ﻃﺮﻳﻘﺔ ﻛﺸﻒ ﺍﻟﺘﺄﺛﲑ ﻟﻘﻴﻤﺔ ‪ COVRATIO‬ﻋﻠﻰ ﺍﻷﺧﻄﺎﺀ ﺍﳌﻌﻴﺎﺭﻳﺔ‪.‬‬‫ﺗﺘﻢ ﻣﻘﺎﺭﻧﺔ ﻗﻴﻤﺔ ‪ COVRATIOi‬ﺑﺎﻟﻘﻴﻤﺔ ‪ 1 ± 3 p‬ﻃﺒﻘﹰﺎ ﻟﻠﻔﺘﺮﺓ ﺍﻟﺘﺎﻟﻴﺔ‪:‬‬ ‫‪n‬‬

‫‪3p‬‬ ‫‪3p‬‬ ‫‪< COVRATIOi < 1 +‬‬ ‫‪n‬‬ ‫‪n‬‬

‫‪1−‬‬

‫ﺃﻱ ﺇﺫﺍ ﻛﺎﻧﺖ ﻗﻴﻤﺔ ‪ COVRATIOi‬ﺧﺎﺭﺝ ﻫﺬﻩ ﺍﻟﻔﺘﺮﺓ ﻓﺈﻥ ﺍﳌﺸﺎﻫﺪﺓ ﺭﻗﻢ )‪ (i‬ﺗﻌﺘﱪ ﻣﺆﺛﺮﺓ‬ ‫ﻋﻠﻰ ﻗﻴﻢ ﺍﻷﺧﻄﺎﺀ ﺍﳌﻌﻴﺎﺭﻳﺔ ﳌﻌﺎﻣﻼﺕ ﳕﻮﺫﺝ ﺍﻻﳓﺪﺍﺭ‪.‬‬

‫‪37‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫ ﺗﻄﺒﻴﻖ )‪-:(3-1‬‬‫ﺑﺎﻟﻌﻮﺩﺓ ﺇﱃ ﺑﻴﺎﻧﺎﺕ ﻭﻣﺸﺎﻫﺪﺍﺕ ﺗﻄﺒﻴﻖ )‪ (1-1‬ﻭﺗﻄﺒﻴﻖ )‪ .(2-1‬ﺳﻮﻑ ﻧﻘﻴﺲ ﰲ ﻫﺬﺍ‬ ‫ﺍﻟﺘﻄﺒﻴﻖ ﺃﺛﺮ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺎﺻﻴﺔ ﻋﻠﻰ ﺍﳌﺘﻐﲑﺍﺕ ﺃﻭﺯﺍﻥ ﺍﻷﻃﻔﺎﻝ )ﻛﻴﻠﻮ ﺟﺮﺍﻡ( ﻭﺃﻃﻮﺍﻝ ﺍﻷﻃﻔﺎﻝ )ﺳﻢ(‬ ‫ﻭﺃﻋﻤﺎﺭ ﺍﻷﻃﻔﺎﻝ )ﺳﻨﻪ( ﻭﺍﻷﺧﻄﺎﺀ ﺍﳌﻌﻴﺎﺭﻳﺔ ﰲ ﳕﻮﺫﺝ ﺍﻻﳓﺪﺍﺭ‪.‬‬ ‫ ﺍﻟﺘﺤﻠﻴﻞ ﺍﻹﺣﺼﺎﺋﻲ‪-:‬‬‫ﺑﺎﺳﺘﺨﺪﺍﻡ ﺑﺮﺍﻣﺞ ﺍﳊﺰﻡ ﺍﻹﺣﺼﺎﺋﻴﺔ ‪ Minitab‬ﻭ ‪ SPSS‬ﺳﻮﻑ ﻧﻘﻮﻡ ﺑﺎﺳﺘﺨﺮﺍﺝ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ‬ ‫ﻋﻠﻰ ﻛﻞ ﻣﻦ ﺍﳌﺘﻐﲑﺍﺕ ﺍﻷﻭﺯﺍﻥ ﻭﺍﻷﻋﻤﺎﺭ ﻭﺍﻷﻃﻮﺍﻝ ﻭﺍﻷﺧﻄﺎﺀ ﺍﳌﻌﻴﺎﺭﻳﺔ ﻟﻨﻤﻮﺫﺝ ﺍﻻﳓﺪﺍﺭ‪.‬‬ ‫‪Regression‬‬

‫]‪[DataSet1‬‬

‫‪Variables Entered/Removed‬‬ ‫‪Variables‬‬ ‫‪Method‬‬

‫‪Variables Entered‬‬

‫‪Removed‬‬

‫‪a‬‬

‫‪. Enter‬‬

‫‪X2, X1‬‬

‫‪Model‬‬ ‫‪1‬‬

‫‪a. All requested variables entered.‬‬

‫‪b‬‬

‫‪Model Summary‬‬

‫‪Std. Error of the‬‬ ‫‪Estimate‬‬ ‫‪1.0943‬‬

‫‪R Square‬‬ ‫‪.962‬‬

‫‪R‬‬ ‫‪a‬‬

‫‪.981‬‬

‫‪Model‬‬ ‫‪1‬‬

‫‪a. Predictors: (Constant), X2, X1‬‬ ‫‪b. Dependent Variable: Y‬‬

‫‪b‬‬

‫‪ANOVA‬‬

‫‪38‬‬

.‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‬ Model 1

Sum of Squares Regression Residual Total

df

Mean Square

F

1441.914

2

720.957

56.286

47

1.198

1498.199

49

Sig.

602.018

.000

a

a. Predictors: (Constant), X2, X1 b. Dependent Variable: Y

Coefficients

a

Standardized Unstandardized Coefficients Model 1

B (Constant)

Coefficients

Std. Error

t

Beta

-2.221-

.963

X1

1.198

.209

X2

.125

.018

Sig.

-2.306-

.026

.454

5.739

.000

.543

6.863

.000

a. Dependent Variable: Y

a

Residuals Statistics Minimum Predicted Value

Maximum

Mean

Std. Deviation

N

1.861

19.934

10.154

5.4246

50

-1.529-

1.803

.000

1.000

50

.163

.461

.260

.065

50

1.885

19.832

10.141

5.4317

50

-2.6010-

2.5222

.0000

1.0718

50

Std. Residual

-2.377-

2.305

.000

.979

50

Stud. Residual

-2.476-

2.518

.006

1.019

50

-2.8216-

3.0111

.0127

1.1617

50

-2.626-

2.679

.006

1.045

50

Mahal. Distance

.102

7.709

1.960

1.635

50

Cook's Distance

.000

.410

.029

.064

50

Std. Predicted Value Standard Error of Predicted Value Adjusted Predicted Value Residual

Deleted Residual Stud. Deleted Residual

39

.‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‬ Centered Leverage Value

.002

.157

.040

a. Dependent Variable: Y

Cumulative Distribution Function F distribution with 3 DF in numerator and 47 DF in denominator x 0.5

MTB MTB MTB MTB MTB

P( X <= x ) 0.315903

> > > > >

Let K1 = Let K2 = Let K3 = Let K4 = PRINT K1

2 * SQRT(3/50) 2/SQRT(50) 1+((3*3) / 50) 1-((3*3) / 50) K2 K3 K4

Data Display K1 K2 K3 K4

0.489898 0.282843 1.18000 0.820000

Regression Analysis: Y versus X1; X2 The regression equation is Y = - 2.22 + 1.20 X1 + 0.125 X2

Predictor Constant X1 X2

Coef -2.2212 1.1980 0.12512

S = 1.09433

SE Coef 0.9633 0.2087 0.01823

R-Sq = 96.2%

T -2.31 5.74 6.86

P 0.026 0.000 0.000

Analysis of Variance Source Regression Residual Error Total

Source X1 X2

DF 1 1

DF 2 47 49

SS 1441.91 56.29 1498.20

MS 720.96 1.20

F 602.02

P 0.000

Seq SS 1385.50 56.41

Unusual Observations Obs 20 45 46

40

X1 5.58 0.01 0.58

Y 15.000 1.350 5.500

Fit 17.601 3.546 2.978

SE Fit 0.306 0.253 0.441

Residual -2.601 -2.196 2.522

St Resid -2.48R -2.06R 2.52R

.033

50

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬ ‫‪R denotes an observation with a large standardized residual.‬‬

‫ ﺟﺪﻭﻝ )‪ (3-1‬ﻗﻴﻢ ﺍﻻﺧﺘﻼﻑ ﰲ ﺍﳌﺘﻐﲑ ﺍﻟﺘﺎﺑﻊ ﺍﳌﻮﻓﻖ ﻭﻣﻌﺎﻣﻼﺕ ﺍﻻﳓﺪﺍﺭ ﻭ ﻣﺴﺎﻓﺔ ﻛﻮﻙ‬‫ﻭﻣﻘﻴﺎﺱ ﻧﺴﺒﺔ ‪.COV‬‬ ‫‪Big‬‬ ‫‪COVR‬‬

‫‪Big DF‬‬

‫‪0.6338‬‬

‫‪0.7610‬‬

‫‪-0.7648‬‬

‫‪Di>F‬‬

‫‪COVR‬‬

‫‪DFFITS‬‬

‫‪Di‬‬

‫‪DF B2‬‬

‫‪DF B1‬‬

‫‪DF B0‬‬

‫‪i‬‬

‫‪1.0820‬‬ ‫‪1.1500‬‬ ‫‪1.1293‬‬ ‫‪0.9012‬‬ ‫‪1.0920‬‬ ‫‪1.0492‬‬ ‫‪0.9014‬‬ ‫‪1.0752‬‬ ‫‪0.9809‬‬ ‫‪1.1344‬‬ ‫‪1.1020‬‬ ‫‪1.1024‬‬ ‫‪1.0366‬‬ ‫‪1.1572‬‬ ‫‪1.1469‬‬ ‫‪1.1157‬‬ ‫‪1.0311‬‬ ‫‪1.0999‬‬ ‫‪1.1233‬‬ ‫‪0.7610‬‬ ‫‪1.0817‬‬ ‫‪1.0935‬‬ ‫‪1.0802‬‬ ‫‪1.0970‬‬ ‫‪1.1041‬‬ ‫‪1.1115‬‬ ‫‪1.1060‬‬ ‫‪1.0912‬‬ ‫‪1.1092‬‬ ‫‪1.1210‬‬ ‫‪1.1088‬‬ ‫‪1.0458‬‬ ‫‪1.0442‬‬ ‫‪0.9088‬‬ ‫‪1.1035‬‬ ‫‪1.0991‬‬ ‫‪1.0925‬‬ ‫‪1.1142‬‬ ‫‪1.0984‬‬ ‫‪1.1013‬‬

‫‪-0.0526‬‬ ‫‪0.0952‬‬ ‫‪-0.0023‬‬ ‫‪0.3866‬‬ ‫‪0.0603‬‬ ‫‪0.2199‬‬ ‫‪0.6338‬‬ ‫‪-0.1434‬‬ ‫‪-0.2425‬‬ ‫‪-0.3001‬‬ ‫‪0.2063‬‬ ‫‪0.0800‬‬ ‫‪0.2561‬‬ ‫‪0.3361‬‬ ‫‪-0.2002‬‬ ‫‪-0.0169‬‬ ‫‪-0.2075‬‬ ‫‪0.0559‬‬ ‫‪-0.0357‬‬ ‫‪-0.7648‬‬ ‫‪-0.1135‬‬ ‫‪0.3166‬‬ ‫‪-0.1101‬‬ ‫‪0.2468‬‬ ‫‪0.0597‬‬ ‫‪-0.0011‬‬ ‫‪-0.0106‬‬ ‫‪-0.0613‬‬ ‫‪-0.0399‬‬ ‫‪-0.0498‬‬ ‫‪0.0734‬‬ ‫‪0.2390‬‬ ‫‪0.4466‬‬ ‫‪-0.4124‬‬ ‫‪-0.1198‬‬ ‫‪-0.0952‬‬ ‫‪-0.1274‬‬ ‫‪0.0542‬‬ ‫‪-0.0684‬‬ ‫‪-0.0266‬‬

‫‪0.0009‬‬ ‫‪0.0031‬‬ ‫‪0.0000‬‬ ‫‪0.0474‬‬ ‫‪0.0012‬‬ ‫‪0.0161‬‬ ‫‪0.1254‬‬ ‫‪0.0069‬‬ ‫‪0.0193‬‬ ‫‪0.0302‬‬ ‫‪0.0143‬‬ ‫‪0.0022‬‬ ‫‪0.0217‬‬ ‫‪0.0378‬‬ ‫‪0.0135‬‬ ‫‪0.0001‬‬ ‫‪0.0143‬‬ ‫‪0.0011‬‬ ‫‪0.0004‬‬ ‫‪0.1733‬‬ ‫‪0.0044‬‬ ‫‪0.0334‬‬ ‫‪0.0041‬‬ ‫‪0.0204‬‬ ‫‪0.0012‬‬ ‫‪0.0000‬‬ ‫‪0.0000‬‬ ‫‪0.0013‬‬ ‫‪0.0005‬‬ ‫‪0.0008‬‬ ‫‪0.0018‬‬ ‫‪0.0190‬‬ ‫‪0.0652‬‬ ‫‪0.0540‬‬ ‫‪0.0049‬‬ ‫‪0.0031‬‬ ‫‪0.0055‬‬ ‫‪0.0010‬‬ ‫‪0.0016‬‬ ‫‪0.0002‬‬

‫‪-0.0039‬‬ ‫‪-0.0550‬‬ ‫‪-0.0014‬‬ ‫‪0.1863‬‬ ‫‪0.0260‬‬ ‫‪0.1368‬‬ ‫‪0.0269‬‬ ‫‪-0.0861‬‬ ‫‪-0.0795‬‬ ‫‪0.1884‬‬ ‫‪0.1612‬‬ ‫‪-0.0165‬‬ ‫‪0.1759‬‬ ‫‪0.3068‬‬ ‫‪0.0339‬‬ ‫‪-0.0116‬‬ ‫‪-0.0231‬‬ ‫‪0.0363‬‬ ‫‪-0.0189‬‬ ‫‪0.2705‬‬ ‫‪-0.0616‬‬ ‫‪0.0134‬‬ ‫‪-0.0660‬‬ ‫‪-0.1118‬‬ ‫‪0.0061‬‬ ‫‪-0.0002‬‬ ‫‪-0.0035‬‬ ‫‪0.0013‬‬ ‫‪0.0031‬‬ ‫‪0.0149‬‬ ‫‪0.0046‬‬ ‫‪0.1793‬‬ ‫‪-0.2751‬‬ ‫‪-0.0027‬‬ ‫‪-0.0921‬‬ ‫‪0.0083‬‬ ‫‪0.0211‬‬ ‫‪0.0337‬‬ ‫‪-0.0388‬‬ ‫‪-0.0089‬‬

‫‪-0.0020‬‬ ‫‪0.0732‬‬ ‫‪0.0017‬‬ ‫‪-0.0987‬‬ ‫‪-0.0328‬‬ ‫‪-0.1613‬‬ ‫‪0.1736‬‬ ‫‪0.0616‬‬ ‫‪0.0304‬‬ ‫‪-0.2451‬‬ ‫‪-0.1733‬‬ ‫‪0.0352‬‬ ‫‪-0.1971‬‬ ‫‪-0.2773‬‬ ‫‪-0.0939‬‬ ‫‪0.0125‬‬ ‫‪-0.0282‬‬ ‫‪-0.0364‬‬ ‫‪0.0250‬‬ ‫‪-0.4676‬‬ ‫‪0.0419‬‬ ‫‪0.0867‬‬ ‫‪0.0522‬‬ ‫‪0.1683‬‬ ‫‪-0.0205‬‬ ‫‪0.0005‬‬ ‫‪0.0054‬‬ ‫‪-0.0139‬‬ ‫‪0.0072‬‬ ‫‪-0.0268‬‬ ‫‪0.0152‬‬ ‫‪-0.1831‬‬ ‫‪0.3592‬‬ ‫‪-0.1105‬‬ ‫‪0.0906‬‬ ‫‪0.0168‬‬ ‫‪0.0134‬‬ ‫‪-0.0397‬‬ ‫‪0.0451‬‬ ‫‪0.0033‬‬

‫‪-0.0014‬‬ ‫‪0.0499‬‬ ‫‪0.0009‬‬ ‫‪-0.1764‬‬ ‫‪-0.0130‬‬ ‫‪-0.0924‬‬ ‫‪-0.0787‬‬ ‫‪0.0767‬‬ ‫‪0.0684‬‬ ‫‪-0.1686‬‬ ‫‪-0.1268‬‬ ‫‪0.0149‬‬ ‫‪-0.1279‬‬ ‫‪-0.2807‬‬ ‫‪-0.0161‬‬ ‫‪0.0086‬‬ ‫‪0.0233‬‬ ‫‪-0.0272‬‬ ‫‪0.0111‬‬ ‫‪-0.2150‬‬ ‫‪0.0541‬‬ ‫‪-0.0393‬‬ ‫‪0.0553‬‬ ‫‪0.0964‬‬ ‫‪0.0085‬‬ ‫‪-0.0001‬‬ ‫‪0.0010‬‬ ‫‪-0.0028‬‬ ‫‪-0.0126‬‬ ‫‪-0.0129‬‬ ‫‪-0.0065‬‬ ‫‪-0.1415‬‬ ‫‪0.2478‬‬ ‫‪0.0176‬‬ ‫‪0.0749‬‬ ‫‪-0.0310‬‬ ‫‪-0.0510‬‬ ‫‪-0.0228‬‬ ‫‪0.0250‬‬ ‫‪0.0079‬‬

‫‪1‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪5‬‬ ‫‪6‬‬ ‫‪7‬‬ ‫‪8‬‬ ‫‪9‬‬ ‫‪10‬‬ ‫‪11‬‬ ‫‪12‬‬ ‫‪13‬‬ ‫‪14‬‬ ‫‪15‬‬ ‫‪16‬‬ ‫‪17‬‬ ‫‪18‬‬ ‫‪19‬‬ ‫‪20‬‬ ‫‪21‬‬ ‫‪22‬‬ ‫‪23‬‬ ‫‪24‬‬ ‫‪25‬‬ ‫‪26‬‬ ‫‪27‬‬ ‫‪28‬‬ ‫‪29‬‬ ‫‪30‬‬ ‫‪31‬‬ ‫‪32‬‬ ‫‪33‬‬ ‫‪34‬‬ ‫‪35‬‬ ‫‪36‬‬ ‫‪37‬‬ ‫‪38‬‬ ‫‪39‬‬ ‫‪40‬‬

‫‪41‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬ ‫‪Big‬‬ ‫‪COVR‬‬

‫‪Big DF‬‬

‫‪Di>F‬‬

‫‪1.2955‬‬

‫‪-0.5084‬‬ ‫‪1.1793‬‬

‫‪0.4098‬‬

‫‪COVR‬‬

‫‪DFFITS‬‬

‫‪Di‬‬

‫‪DF B2‬‬

‫‪DF B1‬‬

‫‪DF B0‬‬

‫‪i‬‬

‫‪1.2955‬‬ ‫‪1.1162‬‬ ‫‪0.9744‬‬ ‫‪0.9808‬‬ ‫‪0.8477‬‬ ‫‪0.8244‬‬ ‫‪1.0805‬‬ ‫‪1.1792‬‬ ‫‪1.0962‬‬ ‫‪1.0230‬‬

‫‪-0.0514‬‬ ‫‪-0.0960‬‬ ‫‪0.3930‬‬ ‫‪-0.3062‬‬ ‫‪-0.5084‬‬ ‫‪1.1793‬‬ ‫‪0.1952‬‬ ‫‪0.3305‬‬ ‫‪-0.1259‬‬ ‫‪-0.4344‬‬

‫‪0.0009‬‬ ‫‪0.0031‬‬ ‫‪0.0500‬‬ ‫‪0.0306‬‬ ‫‪0.0800‬‬ ‫‪0.4098‬‬ ‫‪0.0128‬‬ ‫‪0.0366‬‬ ‫‪0.0054‬‬ ‫‪0.0615‬‬

‫‪0.0449‬‬ ‫‪0.0419‬‬ ‫‪-0.2341‬‬ ‫‪0.0270‬‬ ‫‪0.1966‬‬ ‫‪-1.0463‬‬ ‫‪-0.0853‬‬ ‫‪-0.2753‬‬ ‫‪0.0218‬‬ ‫‪0.3013‬‬

‫‪-0.0355‬‬ ‫‪-0.0164‬‬ ‫‪0.1400‬‬ ‫‪0.0552‬‬ ‫‪-0.0583‬‬ ‫‪0.8512‬‬ ‫‪0.0334‬‬ ‫‪0.2101‬‬ ‫‪0.0128‬‬ ‫‪-0.1989‬‬

‫‪-0.0496‬‬ ‫‪-0.0616‬‬ ‫‪0.3035‬‬ ‫‪-0.1002‬‬ ‫‪-0.3045‬‬ ‫‪1.1458‬‬ ‫‪0.1254‬‬ ‫‪0.3114‬‬ ‫‪-0.0513‬‬ ‫‪-0.3683‬‬

‫‪41‬‬ ‫‪42‬‬ ‫‪43‬‬ ‫‪44‬‬ ‫‪45‬‬ ‫‪46‬‬ ‫‪47‬‬ ‫‪48‬‬ ‫‪49‬‬ ‫‪50‬‬

‫ﺍﻻﺳﺘﻨﺘﺎﺝ‪-:‬‬ ‫‪ -1‬ﻣﻘﻴﺎﺱ ‪:DFFITS‬‬ ‫ﻭﺍﺿﺢ ﻣﻦ ﺟﺪﻭﻝ )‪ .(3-1‬ﺃﻥ ﻫﻨﺎﻙ ﺃﺭﺑﻊ ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ ﻋﻠﻰ ﻗﻴﻢ ﻭﺯﻥ ﺍﻟﻄﻔﻞ ﺍﳌﻮﻓﻘﺔ‬ ‫ﻭﺍﻟﻘﻴﻤﺔ ﺍﳌﻄﻠﻘﺔ ﳌﻘﻴﺎﺱ ‪ DFFITS‬ﺍﻛﱪ ﻣﻦ ‪ 0.489898‬ﻭﻫﻲ ﺍﳌﺸﺎﻫﺪﺍﺕ ‪7,20,45,46‬‬ ‫ﺣﻴﺚ ﺃﻥ ﻗﻴﻢ ﺍﺧﺘﻼﻑ ﺍﻟﺘﻘﺪﻳﺮ ﳍﺎ ﺗﺴﺎﻭﻱ‪.‬‬ ‫‪DFFITS7 = 0.6338 , DFFITS20 = -0.76484 , DFFITS45 = -0.50835 , DFFITS46 = 1.17933‬‬

‫ﻭﻻ ﻧﻨﺴﻰ ﺃﻳﻀﺎ ﺇﻥ ﺍﳌﺸﺎﻫﺪﺍﺕ ‪ 20,45,46‬ﻛﺎﻧﺖ ﻣﺸﺎﻫﺪﺍﺕ ﻗﺎﺻﻴﺔ ﺑﺎﻟﻨﺴﺒﺔ ﻟﻮﺯﻥ ﺍﻟﻄﻔﻞ ﰲ‬ ‫ﺍﳌﻮﺿﻮﻉ ﺍﻟﺴﺎﺑﻖ‪.‬‬ ‫‪ -2‬ﻣﻘﻴﺎﺱ ‪:DFBETAS‬‬ ‫ﻧﻼﺣﻆ ﻣﻦ ﺍﳉﺪﻭﻝ )‪ .(3-1‬ﺃﻥ ﻫﻨﺎﻙ ‪ 11‬ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﻋﻠﻰ ﻣﻌﺎﻣﻼﺕ ﳕﻮﺫﺝ ﺍﻻﳓﺪﺍﺭ‬ ‫ﺍﻟﺒﻌﺾ ﻣﻨﻬﺎ ﻣﺆﺛﺮ ﻋﻠﻰ ﻣﻌﺎﻣﻞ ﻭﺍﺣﺪ ﻭﻛﺬﻟﻚ ﻋﻠﻰ ﻣﻌﺎﻣﻼﻥ ﻭﺃﻳﻀﹰﺎ ﻫﻨﺎﻙ ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ ﻋﻠﻰ ﲨﻴﻊ‬ ‫ﺍﳌﻌﺎﻣﻼﺕ‪ .‬ﺣﻴﺚ ﺃﻥ ﺍﳌﺸﺎﻫﺪﺓ ﺭﻗﻢ ‪ 14‬ﻣﺆﺛﺮﺓ ﻋﻠﻰ ﺍﳌﻌﺎﻣﻞ ﺍﻟﺜﺎﻟﺚ ‪ β 2‬ﰲ ﺍﻟﻨﻤﻮﺫﺝ ﻭﻛﺬﻟﻚ‬ ‫ﺍﳌﺸﺎﻫﺪﺗﺎﻥ ‪ 20,33‬ﻣﺆﺛﺮﺗﺎﻥ ﻋﻠﻰ ﺍﳌﻌﺎﻣﻞ ﺍﻟﺜﺎﱐ ‪ β1‬ﰲ ﺍﻟﻨﻤﻮﺫﺝ ﻭﺍﳌﺸﺎﻫﺪﺍﺕ ‪ 43,45,48‬ﻣﺆﺛﺮﺓ‬ ‫ﻋﻠﻰ ﺍﳌﻌﺎﻣﻞ ﺍﻷﻭﻝ ‪ β 0‬ﰲ ﺍﻟﻨﻤﻮﺫﺝ‪ .‬ﺃﻣﺎ ﺍﳌﺸﺎﻫﺪﺓ ‪ 50‬ﻓﻬﻲ ﻣﺆﺛﺮﺓ ﻓﻘﻂ ﻋﻠﻰ ﻣﻌﺎﻣﻼﻥ ﻭﻫﻲ ﺍﳌﻌﺎﻣﻞ‬ ‫ﺍﻷﻭﻝ ﻭﺍﳌﻌﺎﻣﻞ ﺍﻟﺜﺎﻟﺚ) ‪ .( β 0 and β 2‬ﺑﺎﻟﻨﺴﺒﺔ ﻟﻠﻤﺸﺎﻫﺪﺓ ﺭﻗﻢ ‪ 46‬ﻓﻬﻲ ﻣﺆﺛﺮﺓ ﻋﻠﻰ ﲨﻴﻊ ﻣﻌﺎﻣﻼﺕ‬ ‫ﺍﻟﻨﻤﻮﺫﺝ ) ‪ .( β 0 β1 β 2‬ﻭﻣﻊ ﻣﻼﺣﻈﺔ ﺃﻥ ﺍﳌﺸﺎﻫﺪﺍﺕ ‪ 14, 46,48‬ﻛﺎﻧﺖ ﻣﺸﺎﻫﺪﺍﺕ ﻗﺎﺻﻴﺔ ﰲ‬ ‫ﺍﳌﺘﻐﲑﺍﻥ ) ﻋﻤﺮ ﻭﻃﻮﻝ ﺍﻟﻄﻔﻞ (‪.‬‬ ‫‪42‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫‪ -3‬ﻣﻘﻴﺎﺱ ﻣﺴﺎﻓﺔ ﻛﻮﻙ ‪:Di‬‬ ‫ﻧﻼﺣﻆ ﻣﻦ ﺍﳉﺪﻭﻝ )‪ .(3-1‬ﻭﺟﻮﺩ ﻣﺸﺎﻫﺪﺓ ﻭﺍﺣﺪﺓ ﻣﺆﺛﺮﺓ ﻋﻠﻰ ﻣﻌﺎﻣﻼﺕ ﺍﻻﳓﺪﺍﺭ ﻭﻫﻲ‬ ‫ﺍﳌﺸﺎﻫﺪﺓ ﺭﻗﻢ ‪ . 46‬ﺣﻴﺚ ﺃﻥ ﺍﻟﻘﻴﻤﺔ ﺍﳌﺆﺛﺮﺓ ﲟﻘﻴﺎﺱ ﻛﻮﻙ ‪ Di‬ﺗﺴﺎﻭﻱ‪.‬‬ ‫‪D46 = 0.4098‬‬

‫ﻣﻊ ﻣﻼﺣﻈﺔ ﺃﻥ ﺍﳌﺸﺎﻫﺪﺓ ‪ 46‬ﻛﺎﻧﺖ ﻣﺸﺎﻫﺪﺓ ﻗﺎﺻﻴﺔ ﰲ ﻃﻮﻝ ﻭﻋﻤﺮ ﺍﻟﻄﻔﻞ ﻭﻛﺬﻟﻚ ﻗﺎﺻﻴﺔ‬ ‫ﰲ ﻭﺯﻥ ﺍﻟﻄﻔﻞ‪.‬‬ ‫‪ -4‬ﻣﻘﻴﺎﺱ ‪:COVRATIO‬‬ ‫ﻧﻼﺣﻆ ﺃﻥ ﻫﻨﺎﻙ ﻣﺸﺎﻫﺪﺗﲔ ﻣﺆﺛﺮﺓ ﻓﻘﻂ ﻋﻠﻰ ﺍﻷﺧﻄﺎﺀ ﺍﳌﻌﻴﺎﺭﻳﺔ ﻭﻫﻲ ﺍﳌﺸﺎﻫﺪﺓ ﺭﻗﻢ ‪41,20‬‬ ‫ﻭﺗﺴﺎﻭﻱ‪.‬‬ ‫‪COVRATIO 20 = 0.661 COVRATIO 41 = 1.296‬‬

‫ﻭﻧﺘﺬﻛﺮ ﺃﻥ ﻫﺎﺗﺎﻥ ﺍﳌﺸﺎﻫﺪﺗﺎﻥ ﻛﺎﻧﺘﺎ ﺷﺎﺫﺗﺎﻥ‪ .‬ﻓﺎﳌﺸﺎﻫﺪﺓ ﺭﻗﻢ ‪ 20‬ﻛﺎﻧﺖ ﺷﺎﺫﺓ ﰲ ﻣﺘﻐﲑ ﻭﺯﻥ ﺍﻟﻄﻔﻞ‬ ‫ﺃﻣﺎ ﺍﳌﺸﺎﻫﺪﺓ ‪ 41‬ﻛﺎﻧﺖ ﺷﺎﺫﺓ ﰲ ﻣﺘﻐﲑﺍﺕ ﺍﻟﻄﻮﻝ ﻭﺍﻟﻌﻤﺮ‪.‬‬ ‫ ﺗﻄﺒﻴﻖ )‪-:(3-2‬‬‫ﺑﺎﻟﻌﻮﺩﺓ ﺇﱃ ﺑﻴﺎﻧﺎﺕ ﻭﻣﺸﺎﻫﺪﺍﺕ ﺗﻄﺒﻴﻖ )‪ (1-2‬ﻭﺗﻄﺒﻴﻖ )‪ .(2-2‬ﺳﻮﻑ ﻧﻘﻴﺲ ﰲ ﻫﺬﺍ‬ ‫ﺍﻟﺘﻄﺒﻴﻖ ﺃﺛﺮ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺎﺻﻴﺔ ﻋﻠﻰ ﺍﳌﺘﻐﲑ ﺩﺧﻞ ﺍﻷﺳﺮﺓ ﻭﺍﻟﺪﺧﻞ ﺍﳌﺮﺑﻊ ‪ .‬ﻭﺃﻳﻀﹰﺎ ﺍﻟﻘﻴﻢ ﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ‬ ‫ﺍﻹﻧﻔﺎﻕ ﺍﻟﺸﻬﺮﻱ ﺍﳌﻘﺪﺭ ﻭﻛﺬﻟﻚ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﻣﻌﺎﻣﻼﺕ ﺍﻟﻨﻤﻮﺫﺝ ﻭﺍﻷﺧﻄﺎﺀ ﺍﳌﻌﻴﺎﺭﻳﺔ‪.‬‬ ‫ ﺍﻟﺘﺤﻠﻴﻞ ﺍﻹﺣﺼﺎﺋﻲ‪-:‬‬‫ﺑﺎﺳﺘﺨﺪﺍﻡ ﺑﺮﺍﻣﺞ ﺍﳊﺰﻡ ﺍﻹﺣﺼﺎﺋﻴﺔ ‪ Minitab‬ﻭ ‪ SPSS‬ﺳﻮﻑ ﻧﻘﻮﻡ ﺑﺎﺳﺘﺨﺮﺍﺝ‬ ‫ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﻛﻞ ﻣﻦ ﻣﺘﻐﲑ ﺍﻟﺪﺧﻞ ﺍﻷﺳﺮﻱ ﻭﺍﻟﺪﺧﻞ ﺍﻷﺳﺮﻱ ﺍﳌﺮﺑﻊ ﻭﻛﺬﻟﻚ ﺍﳌﺸﺎﻫﺪﺍﺕ‬ ‫ﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﳌﺼﺮﻭﻓﺎﺕ ﺍﳌﻌﻴﺸﻴﺔ ﻭﺍﻷﺧﻄﺎﺀ ﺍﳌﻌﻴﺎﺭﻳﺔ ﺃﻳﻀﹰﺎ‪.‬‬ ‫‪Regression‬‬

‫‪43‬‬

.‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‬

[DataSet1]

Variables Entered/Removed

Model 1

Variables

Variables

Entered

Removed

X3^2, X3

Method

a

. Enter

a. All requested variables entered.

b

Model Summary

Model

R

1

.943

R Square a

Std. Error of the

Square

Estimate

.889

.881

1.0976

a. Predictors: (Constant), X3^2, X3 b. Dependent Variable: Y

b

ANOVA Model 1

Sum of Squares Regression

Mean Square

260.755

2

130.377

32.527

27

1.205

293.282

29

Residual Total

df

F

Sig.

108.224

.000

a. Predictors: (Constant), X3^2, X3 b. Dependent Variable: Y

Coefficients

a

Standardized Unstandardized Coefficients Model

44

B

Std. Error

Coefficients Beta

t

Sig.

a

.‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‬ 1

(Constant)

-3.050-

1.112

X3

1.604

.183

X3^2

-.040-

.007

-2.744-

.011

2.491

8.749

.000

-1.669-

-5.862-

.000

a. Dependent Variable: Y

a

Residuals Statistics Minimum Predicted Value

Maximum

Mean

Std. Deviation

N

3.490

13.110

8.983

2.9986

30

-1.832-

1.376

.000

1.000

30

.232

.968

.321

.135

30

3.382

13.374

8.953

2.9895

30

-1.9101-

2.5263

.0000

1.0591

30

Std. Residual

-1.740-

2.302

.000

.965

30

Stud. Residual

-1.857-

2.426

.009

1.012

30

-2.1743-

2.8077

.0300

1.1755

30

-1.951-

2.693

.017

1.055

30

Mahal. Distance

.327

21.589

1.933

3.825

30

Cook's Distance

.000

.247

.040

.064

30

Centered Leverage Value

.011

.744

.067

.132

30

Std. Predicted Value Standard Error of Predicted Value Adjusted Predicted Value Residual

Deleted Residual Stud. Deleted Residual

a. Dependent Variable: Y

MTB MTB MTB MTB MTB MTB

> > > > > >

let k1 = let k2 = let k3 = let k4 = let k5 = print k1

Data Display K1 K2 K3 K4 K5

45

0.632456 0.365148 0.148148 1.30000 0.70000

2 * SQRT(3/30) 2 / SQRT(30) 4/(30-3) 1+((3*3)/30) 1-((3*3)/30) k2 k3 k4 k5

.‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‬ Regression Analysis: Y versus X3; X3^2 The regression equation is Y = - 3.05 + 1.60 X3 - 0.0397 X3^2

Predictor Constant X3 X3^2

Coef -3.050 1.6043 -0.039674

S = 1.09759

SE Coef 1.112 0.1834 0.006768

R-Sq = 88.9%

T -2.74 8.75 -5.86

P 0.011 0.000 0.000

Analysis of Variance Source Regression Residual Error Total

Source X3 X3^2

DF 1 1

DF 2 27 29

SS 260.75 32.53 293.28

MS 130.38 1.20

F 108.22

P 0.000

Seq SS 219.36 41.39

Unusual Observations Obs 17 20 21

X3 25.0 15.1 18.0

Y 12.500 14.300 15.500

Fit 12.262 12.129 12.974

SE Fit 0.968 0.305 0.347

Residual 0.238 2.171 2.526

St Resid 0.46 X 2.06R 2.43R

R denotes an observation with a large standardized residual. X denotes an observation whose X value gives it large influence.

.COV ‫( ﻗﻴﻢ ﺍﻻﺧﺘﻼﻑ ﰲ ﺍﳌﺘﻐﲑ ﺍﻟﺘﺎﺑﻊ ﺍﳌﻮﻓﻖ ﻭ ﻣﺴﺎﻓﺔ ﻛﻮﻙ ﻭﻣﻘﻴﺎﺱ ﻧﺴﺒﺔ‬3-2) ‫ ﺟﺪﻭﻝ‬i

B0

B1

B2

cook

DFITS

COV

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

-0.005 -0.014 0.117 0.086 -0.014 -0.003 -0.211 0.377 -0.134 0.067 -0.005 0.065 0.176 0.051 0.086

0.003 0.017 -0.063 -0.105 0.043 0.001 0.235 -0.316 0.178 -0.078 0.003 -0.035 -0.185 -0.077 -0.066

-0.002 -0.016 -0.077 0.099 -0.052 0.000 -0.197 0.265 -0.175 0.070 -0.002 -0.043 0.142 0.080 0.052

0.000 0.000 0.159 0.008 0.005 0.000 0.043 0.058 0.023 0.004 0.000 0.054 0.036 0.006 0.004

-0.009 0.024 -0.726 -0.150 0.121 -0.009 0.363 0.417 0.266 -0.113 -0.009 -0.403 -0.330 -0.131 0.106

1.194 1.199 0.846 1.158 1.132 1.176 1.016 1.170 1.053 1.185 1.194 1.117 1.061 1.142 1.220

46

big(Di)

big(dfits)

0.159

-0.726

big(cov)

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬ ‫)‪big(cov‬‬

‫)‪big(dfits‬‬

‫)‪big(Di‬‬

‫‪4.922‬‬

‫‪0.847‬‬

‫‪0.247‬‬

‫‪0.595‬‬

‫‪0.637‬‬ ‫‪0.899‬‬

‫‪0.219‬‬

‫‪1.319‬‬

‫‪COV‬‬

‫‪DFITS‬‬

‫‪cook‬‬

‫‪B2‬‬

‫‪B1‬‬

‫‪B0‬‬

‫‪i‬‬

‫‪1.100‬‬ ‫‪4.922‬‬ ‫‪1.108‬‬ ‫‪1.192‬‬ ‫‪0.727‬‬ ‫‪0.595‬‬ ‫‪1.071‬‬ ‫‪1.256‬‬ ‫‪1.058‬‬ ‫‪1.105‬‬ ‫‪0.847‬‬ ‫‪1.319‬‬ ‫‪1.012‬‬ ‫‪1.184‬‬ ‫‪1.171‬‬

‫‪-0.185‬‬ ‫‪0.847‬‬ ‫‪0.159‬‬ ‫‪0.106‬‬ ‫‪0.637‬‬ ‫‪0.899‬‬ ‫‪0.222‬‬ ‫‪-0.064‬‬ ‫‪-0.205‬‬ ‫‪-0.278‬‬ ‫‪-0.505‬‬ ‫‪0.233‬‬ ‫‪-0.280‬‬ ‫‪0.013‬‬ ‫‪-0.022‬‬

‫‪0.012‬‬ ‫‪0.247‬‬ ‫‪0.009‬‬ ‫‪0.004‬‬ ‫‪0.118‬‬ ‫‪0.219‬‬ ‫‪0.017‬‬ ‫‪0.001‬‬ ‫‪0.014‬‬ ‫‪0.026‬‬ ‫‪0.078‬‬ ‫‪0.019‬‬ ‫‪0.026‬‬ ‫‪0.000‬‬ ‫‪0.000‬‬

‫‪-0.018‬‬ ‫‪0.661‬‬ ‫‪-0.079‬‬ ‫‪0.041‬‬ ‫‪-0.340‬‬ ‫‪-0.081‬‬ ‫‪-0.136‬‬ ‫‪-0.035‬‬ ‫‪0.034‬‬ ‫‪-0.119‬‬ ‫‪0.313‬‬ ‫‪0.158‬‬ ‫‪-0.036‬‬ ‫‪-0.008‬‬ ‫‪0.009‬‬

‫‪0.042‬‬ ‫‪-0.532‬‬ ‫‪0.070‬‬ ‫‪-0.055‬‬ ‫‪0.407‬‬ ‫‪0.243‬‬ ‫‪0.131‬‬ ‫‪0.044‬‬ ‫‪-0.011‬‬ ‫‪0.156‬‬ ‫‪-0.350‬‬ ‫‪-0.185‬‬ ‫‪0.072‬‬ ‫‪0.008‬‬ ‫‪-0.007‬‬

‫‪-0.088‬‬ ‫‪0.414‬‬ ‫‪-0.033‬‬ ‫‪0.077‬‬ ‫‪-0.368‬‬ ‫‪-0.281‬‬ ‫‪-0.087‬‬ ‫‪-0.055‬‬ ‫‪-0.042‬‬ ‫‪-0.212‬‬ ‫‪0.300‬‬ ‫‪0.216‬‬ ‫‪-0.141‬‬ ‫‪-0.005‬‬ ‫‪0.002‬‬

‫‪16‬‬ ‫‪17‬‬ ‫‪18‬‬ ‫‪19‬‬ ‫‪20‬‬ ‫‪21‬‬ ‫‪22‬‬ ‫‪23‬‬ ‫‪24‬‬ ‫‪25‬‬ ‫‪26‬‬ ‫‪27‬‬ ‫‪28‬‬ ‫‪29‬‬ ‫‪30‬‬

‫ﺍﻻﺳﺘﻨﺘﺎﺝ‪-:‬‬ ‫‪ -1‬ﻣﻘﻴﺎﺱ ‪:DFFITS‬‬ ‫ﻧﻼﺣﻆ ﻣﻦ ﺍﳉﺪﻭﻝ )‪ (3-2‬ﻭﺟﻮﺩ ﺃﺭﺑﻊ ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ ﻋﻠﻰ ﻣﺘﻐﲑ ﺍﳌﺼﺮﻭﻓﺎﺕ ﺍﳌﻌﻴﺸﻴﺔ‬ ‫ﺍﳌﻘﺪﺭ‪ .‬ﻭﻳﺮﺟﻊ ﺗﺄﺛﲑﻫﺎ ﻛﻤﺎ ﺫﻛﺮﻧﺎ ﺑﺄﻥ ﺍﻟﻘﻴﻤﺔ ﺍﳌﻄﻠﻘﺔ ﳍﺬﺍ ﺍﳌﻘﻴﺎﺱ ﺍﻛﱪ ﻣﻦ‪ 0.632456‬ﻟﺬﻟﻚ‬ ‫ﻧﻌﺘﱪﻫﺎ ﻣﺆﺛﺮﺓ ﻋﻠﻰ ﻣﺘﻐﲑ ﺍﳌﺼﺮﻭﻓﺎﺕ ﺍﳌﻌﻴﺸﻴﺔ ﺍﳌﻘﺪﺭ‪ ،‬ﺣﻴﺚ ﺃﻥ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﻫﻲ‬ ‫ﻼ ﻣﻨﻬﺎ‪.‬‬ ‫‪ 3,17,20,21‬ﻭﺗﺴﺎﻭﻱ ﻛ ﹰ‬ ‫‪DFFITS3 = -0.726 , DFFITS17 = 0.847 , DFFITS20 = 0.637 , DFFITS21 = 0.899‬‬

‫ﻛﻤﺎ ﻧﻼﺣﻆ ﺃﻥ ﺍﳌﺸﺎﻫﺪﺍﺕ ‪ 20‬ﻭ ‪ 21‬ﻛﺎﻧﺖ ﻗﻴﻢ ﻗﺎﺻﻴﺔ ﺑﺎﻟﻨﺴﺒﺔ ﳌﺘﻐﲑ ﺍﳌﺼﺮﻭﻓﺎﺕ ﺍﳌﻌﻴﺸﻴﺔ‪.‬‬ ‫‪ -2‬ﻣﻘﻴﺎﺱ ‪:DFBETAS‬‬ ‫ﻣﻦ ﺍﳉﺪﻭﻝ )‪ (3-2‬ﻳﺘﺒﲔ ﻟﻨﺎ ﺃﻥ ﲬﺲ ﻗﻴﻢ ﺗﺄﺛﺮ ﻋﻠﻰ ﻣﻌﺎﻣﻼﺕ ﳕﻮﺫﺝ ﺍﻻﳓﺪﺍﺭ ﻭﺍﳌﺘﻐﲑﺍﺕ‬ ‫ﺍﳌﺴﺘﻘﻠﺔ ﻣﻊ ﻣﻼﺣﻈﺔ ﺃﻥ ﺑﻌﺾ ﻫﺬﻩ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﻻ ﺗﺄﺛﺮ ﻋﻠﻰ ﲨﻴﻊ ﺍﳌﻌﺎﻣﻼﺕ ﺑﻞ ﺇﻥ ﺑﻌﺾ ﻣﻨﻬﺎ‬ ‫ﻼ ﻣﻊ ﺍﻟﺘﺬﻛﲑ ﺃﻥ ﳕﻮﺫﺝ ﺍﻻﳓﺪﺍﺭ ﰲ ﻫﺬﺍ‬ ‫ﻻ ﻳﺆﺛﺮ ﺳﻮﻯ ﻋﻠﻰ ﻋﺎﻣﻞ ﻭﺍﻟﺒﻌﺾ ﺍﻷﺧﺮ ﻳﺆﺛﺮ ﻋﻠﻰ ﻋﺎﻣ ﹰ‬ ‫ﺍﻟﺘﻄﺒﻴﻖ ﳛﺘﻮﻱ ﻋﻠﻰ ﺛﻼﺙ ﻣﻌﺎﱂ‪ .‬ﻓﺎﳌﺸﺎﻫﺪﺓ ‪ 8‬ﺗﺄﺛﺮ ﻋﻠﻰ ﺍﳌﻌﺎﻣﻞ ﺍﻷﻭﻝ ‪ β 0‬ﻓﻘﻂ‪ ،‬ﻭﺍﳌﺸﺎﻫﺪﺓ ‪ 20‬ﺗﺄﺛﺮ‬

‫‪47‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫ﻋﻠﻰ ﺍﳌﻌﺎﻣﻠﲔ ﺍﻷﻭﻝ ‪ β 0‬ﻭﺍﻟﺜﺎﱐ ‪ ، β1‬ﺃﻣﺎ ﺑﺎﻟﻨﺴﺒﺔ ﻟﻠﻤﺸﺎﻫﺪﺓ ‪ 17‬ﻓﻬﻲ ﻣﺆﺛﺮﺓ ﻋﻠﻰ ﲨﻴﻊ ﻋﻮﺍﻣﻞ ﺩﺍﻟﺔ‬ ‫ﺍﻻﳓﺪﺍﺭ ﰲ ﻫﺬﺍ ﺍﻟﺘﻄﺒﻴﻖ ) ‪.( β 0 β1 β 2‬‬ ‫‪ -3‬ﻣﻘﻴﺎﺱ ﻣﺴﺎﻓﺔ ﻛﻮﻙ ‪:Di‬‬ ‫ﺑﺎﻟﻨﺴﺒﺔ ﳌﻘﻴﺎﺱ ﻛﻮﻙ ﻓﺄﻥ ﺍﳉﺪﻭﻝ )‪ .(3-2‬ﳛﺘﻮﻱ ﻋﻠﻰ ﺛﻼﺙ ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ ﻋﻠﻰ ﲨﻴﻊ‬ ‫ﻣﺘﻐﲑﺍﺕ ﳕﻮﺫﺝ ﺍﻻﳓﺪﺍﺭ ﻭﻫﻲ ﺍﳌﺸﺎﻫﺪﺍﺕ ‪ 3,17,21‬ﺣﻴﺚ ﺃﻥ ﻗﻴﻤﻬﺎ ﺗﺴﺎﻭﻱ‪.‬‬ ‫‪ D3 = 0.159 , D17 = 0.247 , D21 = 0.219‬ﻣﻊ ﻣﻼﺣﻈﺔ ﺍﻥ ﺍﳌﺸﺎﻫﺪﺓ ‪ 17‬ﻛﺎﻧﺖ ﻣﺸﺎﻫﺪﺓ‬ ‫ﻗﺎﺻﻴﺔ ﰲ ﻣﺘﻐﲑ ﺍﻟﺪﺧﻞ ﺍﻷﺳﺮﻱ‪ ،‬ﺃﻣﺎ ‪ 21‬ﻓﺄ‪‬ﺎ ﻗﺎﺻﻴﺔ ﻓﻘﻂ ﰲ ﺍﳌﺼﺮﻭﻓﺎﺕ ﺍﳌﻌﻴﺸﻴﺔ‪ .‬ﺑﺎﻟﻨﺴﺒﺔ ﳌﺸﺎﻫﺪﺓ‬ ‫‪ 3‬ﻛﺎﻧﺖ ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﻋﻠﻰ ﻗﻴﻢ ﺍﳌﺼﺮﻭﻓﺎﺕ ﺍﳌﻌﻴﺸﻴﺔ ﺍﳌﻮﻓﻘﺔ‪.‬‬ ‫‪ -4‬ﻣﻘﻴﺎﺱ ‪:COVRATIO‬‬ ‫ﻣﻦ ﺟﺪﻭﻝ )‪ (3-2‬ﻫﻨﺎﻙ ﺛﻼﺙ ﻣﺸﺎﻫﺪﺍﺕ ﺗﺄﺛﺮ ﻋﻠﻰ ﻗﻴﻢ ﺍﻷﺧﻄﺎﺀ ﺍﳌﻌﻴﺎﺭﻳﺔ‪ .‬ﻭﻫﻲ‬ ‫ﺍﳌﺸﺎﻫﺪﺍﺕ ‪ 17,21,27‬ﺣﻴﺚ ﺃﻥ ﻗﻴﻤﻬﺎ ﺗﺴﺎﻭﻱ‪.‬‬ ‫‪COVRATIO17 = 4.922 COVRATIO 21 = 0.595 COVRATIO 27 = 1.319‬‬

‫ﻣﻊ ﻣﻼﺣﻈﺔ ﺗﻜﺮﺍﺭ ﺍﳌﺸﺎﻫﺪﺓ ‪ 17‬ﻋﻠﻰ ﰲ ﻛﻞ ﺍﳌﻘﺎﻳﻴﺲ ﺣﻴﺚ ﺃﻥ ﺗﻔﺼﻠﻬﺎ ﺛﻐﺮﺓ ﻛﺒﲑﺓ ﻋﻦ ﺍﳌﺸﺎﻫﺪﺍﺕ‬ ‫ﺍﳌﺴﺠﻠﺔ ﰲ ﺍﻟﺘﻄﺒﻴﻖ‪ .‬ﻭﺃﻳﻀﹰﺎ ﻣﻼﺣﻈﺔ ﺗﻜﺮﺍﺭ ﺗﺄﺛﲑ ﺍﳌﺸﺎﻫﺪﺓ ‪ 21‬ﻋﻠﻰ ﺑﻌﺾ ﺍﳌﻘﺎﻳﻴﺲ ﺍﻟﺴﺎﺑﻘﺔ‪.‬‬

‫ ﺗﻄﺒﻴﻖ )‪-:(3-3‬‬‫ﺑﺎﻟﻌﻮﺩﺓ ﺇﱃ ﺑﻴﺎﻧﺎﺕ ﻭﻣﺸﺎﻫﺪﺍﺕ ﺗﻄﺒﻴﻖ )‪ (1-3‬ﻭﺗﻄﺒﻴﻖ )‪ .(2-3‬ﺳﻮﻑ ﻧﻘﻴﺲ ﰲ ﻫﺬﺍ‬ ‫ﺍﻟﺘﻄﺒﻴﻖ ﺃﺛﺮ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﻘﺎﺻﻴﺔ ﻋﻠﻰ ﺍﳌﺘﻐﲑ ﺍﻷﺩﺍﺀ ﺍﻟﻮﻇﻴﻔﻲ ﻭﺧﱪﺓ ﺍﳌﻮﻇﻒ ﻭﻋﺪﺩ ﺳﻨﻮﺍﺕ ﺍﻟﺪﺭﺍﺳﺔ‪.‬‬ ‫ﻭﻛﺬﻟﻚ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻷﺧﻄﺎﺀ ﺍﳌﻌﻴﺎﺭﻳﺔ ﰲ ﳕﻮﺫﺝ ﺍﻻﳓﺪﺍﺭ‪.‬‬ ‫ ﺍﻟﺘﺤﻠﻴﻞ ﺍﻹﺣﺼﺎﺋﻲ‪-:‬‬‫ﺑﺎﺳﺘﺨﺪﺍﻡ ﺑﺮﺍﻣﺞ ﺍﳊﺰﻡ ﺍﻹﺣﺼﺎﺋﻴﺔ ‪ Minitab‬ﻭ ‪ SPSS‬ﺳﻮﻑ ﻧﻘﻮﻡ ﺑﺎﺳﺘﺨﺮﺍﺝ‬ ‫ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﺑﺸﻜﻞ ﻋﺎﻡ ﻋﻠﻰ ﺍﻟﻨﻤﻮﺫﺝ‪.‬‬

‫‪48‬‬

.‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‬ Regression

[DataSet1]

Variables Entered/Removed Variables Model 1

Removed

Variables Entered X2, X1

Method

a

. Enter

a. All requested variables entered.

b

Model Summary

Std. Error of the Model

R

1

R Square .973

a

.946

Estimate

.943

3.316

a. Predictors: (Constant), X2, X1 b. Dependent Variable: Y

b

ANOVA Model 1

Sum of Squares Regression Residual Total

df

Mean Square

5820.935

2

2910.467

329.792

30

10.993

6150.727

32

F

Sig.

264.754

.000

a. Predictors: (Constant), X2, X1 b. Dependent Variable: Y

Coefficients

a

Standardized Model

49

Unstandardized Coefficients

Coefficients

t

Sig.

a

.‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‬ B 1

(Constant)

Std. Error

Beta

34.749

2.190

X1

2.173

.456

X2

1.179

.344

15.868

.000

.574

4.765

.000

.414

3.431

.002

a. Dependent Variable: Y

a

Residuals Statistics Minimum Predicted Value

Maximum

Mean

Std. Deviation

N

50.33

98.62

75.09

13.487

33

-1.836-

1.745

.000

1.000

33

.586

1.719

.954

.302

33

51.23

99.33

75.04

13.496

33

Residual

-5.330-

8.145

.000

3.210

33

Std. Residual

-1.608-

2.457

.000

.968

33

Stud. Residual

-1.738-

2.589

.006

1.036

33

Deleted Residual

-6.228-

9.044

.046

3.690

33

Stud. Deleted Residual

-1.802-

2.888

.016

1.078

33

Mahal. Distance

.029

7.632

1.939

1.872

33

Cook's Distance

.000

.573

.053

.109

33

Centered Leverage Value

.001

.238

.061

.059

33

Std. Predicted Value Standard Error of Predicted Value Adjusted Predicted Value

a. Dependent Variable: Y

Cumulative Distribution Function F distribution with 3 DF in numerator and 30 DF in denominator x 0.5 MTB MTB MTB MTB MTB

P( X <= x ) 0.314880 > > > > >

Let K1 = Let K2 = Let K3 = Let K4 = print k1

Data Display K1

50

0.603023

2*SQRT(3/33) 2 / SQRT(33) 1+ ((3*3) /33) 1- ((3*3) /33) k2 k3 k4

.‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‬ K2 K3 K4

0.348155 1.27273 0.727273

Regression Analysis: Y versus X1; X2 The regression equation is Y = 34.7 + 2.17 X1 + 1.18 X2

Predictor Constant X1 X2

Coef 34.749 2.1731 1.1789

S = 3.31558

SE Coef 2.190 0.4561 0.3436

T 15.87 4.76 3.43

R-Sq = 94.6%

P 0.000 0.000 0.002

Analysis of Variance Source Regression Residual Error Total

Source X1 X2

DF 1 1

DF 2 30 32

SS 5820.9 329.8 6150.7

MS 2910.5 11.0

F 264.75

P 0.000

Seq SS 5691.5 129.4

Unusual Observations Obs 14 20

X1 12.0 7.0

Y 87.000 64.000

Fit 80.867 55.855

SE Fit 1.719 1.045

Residual 6.133 8.145

St Resid 2.16R 2.59R

R denotes an observation with a large standardized residual.

‫( ﻗﻴﻢ ﺍﻻﺧﺘﻼﻑ ﰲ ﺍﳌﺘﻐﲑ ﺍﻟﺘﺎﺑﻊ ﺍﳌﻮﻓﻖ ﻭﻣﻌﺎﻣﻼﺕ ﺍﻻﳓﺪﺍﺭ ﻭ ﻣﺴﺎﻓﺔ ﻛﻮﻙ‬3-3) ‫ ﺟﺪﻭﻝ‬.COV ‫ﻭﻣﻘﻴﺎﺱ ﻧﺴﺒﺔ‬ i

DF B0

DF B1

DF B2

Di

DFITS

COVR

1 2 3 4 5 6 7 8 9 10 11

0.432 0.000 -0.031 -0.692 0.075 -0.164 0.158 -0.285 -0.003 0.116 -0.011

-0.402 0.000 0.013 0.307 0.248 -0.064 -0.248 0.052 -0.001 0.114 0.004

0.265 0.000 0.023 -0.084 -0.331 0.144 0.254 0.047 0.002 -0.182 -0.002

0.103 0.000 0.013 0.170 0.062 0.032 0.026 0.045 0.000 0.032 0.000

-0.558 0.001 0.199 -0.739 0.434 -0.308 0.278 -0.374 -0.006 0.312 -0.016

1.192 1.143 1.049 0.941 1.096 1.090 1.341 0.978 1.160 1.064 1.152

51

Di>F

Big DF

Big COVR

-0.739

1.341

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬ ‫‪Big COVR‬‬

‫‪Big DF‬‬

‫‪Di>F‬‬

‫‪1.404‬‬

‫‪0.573‬‬

‫‪1.309‬‬

‫‪0.576‬‬

‫‪0.959‬‬

‫‪0.636‬‬

‫‪COVR‬‬

‫‪DFITS‬‬

‫‪Di‬‬

‫‪DF B2‬‬

‫‪DF B1‬‬

‫‪DF B0‬‬

‫‪i‬‬

‫‪1.113‬‬ ‫‪1.143‬‬ ‫‪0.910‬‬ ‫‪1.309‬‬ ‫‪1.218‬‬ ‫‪1.123‬‬ ‫‪1.162‬‬ ‫‪1.221‬‬ ‫‪0.576‬‬ ‫‪1.053‬‬ ‫‪1.135‬‬ ‫‪1.147‬‬ ‫‪1.050‬‬ ‫‪1.134‬‬ ‫‪1.119‬‬ ‫‪1.130‬‬ ‫‪1.130‬‬ ‫‪1.185‬‬ ‫‪1.011‬‬ ‫‪1.166‬‬ ‫‪1.229‬‬ ‫‪0.932‬‬

‫‪0.166‬‬ ‫‪0.021‬‬ ‫‪1.404‬‬ ‫‪-0.077‬‬ ‫‪-0.057‬‬ ‫‪-0.087‬‬ ‫‪-0.131‬‬ ‫‪0.215‬‬ ‫‪0.959‬‬ ‫‪0.251‬‬ ‫‪-0.078‬‬ ‫‪0.045‬‬ ‫‪-0.163‬‬ ‫‪-0.067‬‬ ‫‪-0.185‬‬ ‫‪0.636‬‬ ‫‪0.148‬‬ ‫‪-0.259‬‬ ‫‪-0.598‬‬ ‫‪0.121‬‬ ‫‪-0.176‬‬ ‫‪-0.504‬‬

‫‪0.009‬‬ ‫‪0.000‬‬ ‫‪0.573‬‬ ‫‪0.002‬‬ ‫‪0.001‬‬ ‫‪0.003‬‬ ‫‪0.006‬‬ ‫‪0.016‬‬ ‫‪0.246‬‬ ‫‪0.021‬‬ ‫‪0.002‬‬ ‫‪0.001‬‬ ‫‪0.009‬‬ ‫‪0.002‬‬ ‫‪0.012‬‬ ‫‪0.131‬‬ ‫‪0.007‬‬ ‫‪0.023‬‬ ‫‪0.114‬‬ ‫‪0.005‬‬ ‫‪0.011‬‬ ‫‪0.080‬‬

‫‪-0.041‬‬ ‫‪-0.001‬‬ ‫‪1.322‬‬ ‫‪0.051‬‬ ‫‪-0.038‬‬ ‫‪-0.023‬‬ ‫‪0.013‬‬ ‫‪-0.143‬‬ ‫‪-0.338‬‬ ‫‪0.162‬‬ ‫‪-0.008‬‬ ‫‪0.005‬‬ ‫‪0.027‬‬ ‫‪-0.026‬‬ ‫‪-0.132‬‬ ‫‪-0.503‬‬ ‫‪0.079‬‬ ‫‪-0.119‬‬ ‫‪-0.213‬‬ ‫‪-0.012‬‬ ‫‪0.044‬‬ ‫‪0.013‬‬

‫‪0.003‬‬ ‫‪-0.001‬‬ ‫‪-1.235‬‬ ‫‪-0.064‬‬ ‫‪0.026‬‬ ‫‪0.013‬‬ ‫‪-0.047‬‬ ‫‪0.176‬‬ ‫‪0.062‬‬ ‫‪-0.132‬‬ ‫‪0.020‬‬ ‫‪-0.012‬‬ ‫‪-0.027‬‬ ‫‪0.024‬‬ ‫‪0.123‬‬ ‫‪0.573‬‬ ‫‪-0.052‬‬ ‫‪0.046‬‬ ‫‪0.031‬‬ ‫‪0.043‬‬ ‫‪0.010‬‬ ‫‪0.131‬‬

‫‪0.104‬‬ ‫‪0.010‬‬ ‫‪0.663‬‬ ‫‪0.053‬‬ ‫‪0.000‬‬ ‫‪-0.010‬‬ ‫‪0.068‬‬ ‫‪-0.136‬‬ ‫‪0.632‬‬ ‫‪0.068‬‬ ‫‪-0.053‬‬ ‫‪0.031‬‬ ‫‪-0.029‬‬ ‫‪-0.026‬‬ ‫‪-0.087‬‬ ‫‪-0.393‬‬ ‫‪0.007‬‬ ‫‪0.079‬‬ ‫‪0.255‬‬ ‫‪-0.063‬‬ ‫‪-0.132‬‬ ‫‪-0.428‬‬

‫‪12‬‬ ‫‪13‬‬ ‫‪14‬‬ ‫‪15‬‬ ‫‪16‬‬ ‫‪17‬‬ ‫‪18‬‬ ‫‪19‬‬ ‫‪20‬‬ ‫‪21‬‬ ‫‪22‬‬ ‫‪23‬‬ ‫‪24‬‬ ‫‪25‬‬ ‫‪26‬‬ ‫‪27‬‬ ‫‪28‬‬ ‫‪29‬‬ ‫‪30‬‬ ‫‪31‬‬ ‫‪32‬‬ ‫‪33‬‬

‫ﺍﻻﺳﺘﻨﺘﺎﺝ‪-:‬‬ ‫‪ -1‬ﻣﻘﻴﺎﺱ ‪:DFFITS‬‬ ‫ﻭﺍﺿﺢ ﻣﻦ ﺟﺪﻭﻝ )‪ (3-3‬ﺃﻥ ﻫﻨﺎﻙ ﺃﺭﺑﻊ ﻗﻴﻢ ﻣﺆﺛﺮﺓ ﻋﻠﻰ ﻗﻴﻢ ﺍﻷﺩﺍﺀ ﺍﻟﻮﻇﻴﻔﻲ ﺍﳌﻮﻓﻘﺔ ‪.‬‬ ‫ﻭﺫﻟﻚ ﺣﺴﺐ ﻣﻘﻴﺎﺱ ﻧﻴﺘﺮ ﻭﺁﺧﺮﻭﻥ ﺍﻟﺬﻱ ﻳﻨﺺ ﻋﻠﻰ ﺃﻥ ﺍﻟﻘﻴﻤﺔ ﺍﳌﻄﻠﻘﺔ ﻟﻘﻴﻤﺔ ‪ DFFITS‬ﺍﻛﱪ ﻣﻦ‬ ‫‪ 0.603023‬ﻟﺬﻟﻚ ﻧﻌﺘﱪ ﻫﺬﻩ ﺍﳌﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ‪ .‬ﺣﻴﺚ ﺃﻥ ﻫﺬﻩ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﻫﻲ‬ ‫‪ 4,14,20,27‬ﻭﻗﻴﻢ ‪ DFFITS‬ﳍﺎ ﺗﺴﺎﻭﻱ ‪.‬‬ ‫‪DFFITS4 = -0.739 , DFFITS14 = 1.404 , DFFITS20 = 0.959 , DFFITS27 = 0.636‬‬

‫ﻣﻊ ﻣﻼﺣﻈﺔ ﺃﻥ ﺍﳌﺸﺎﻫﺪﺍﺕ‪ 14,20 .‬ﻛﺎﻧﺖ ﻗﺎﺻﻴﺔ ﰲ ﻣﺘﻐﲑ ﺍﻷﺩﺍﺀ ﺍﻟﻮﻇﻴﻔﻲ‪ .‬ﻭﻛﺬﻟﻚ ﻣﻊ ﻣﻼﺣﻈﺔ‬ ‫ﺃﻥ ﺍﻟﻘﻴﻢ ﻟﻠﻤﺸﺎﻫﺪﺍﺕ ‪ 4,27‬ﻟﻴﺴﺖ ﺑﻌﻴﺪﺓ ﻋﻦ ﺍﻟﻘﻴﻤﺔ ‪ 0.603023‬ﺃﻱ ﺍﻧﻪ ﻟﻮ ﺍﺳﺘﺨﺪﻣﻨﺎ ﻣﻘﻴﺎﺱ‬ ‫ﺷﺎﺗﺮﺟﻲ ﻭﻫﺎﺩﻱ ﻣﻦ ﺍﳌﻤﻜﻦ ﺃﻥ ﺗﻜﻮﻥ ﻫﺬﻩ ﺍﳌﺸﺎﻫﺪﺍﺕ ﻏﲑ ﻣﺆﺛﺮﺓ ﻋﻠﻰ ﳕﻮﺫﺝ ﺍﻻﳓﺪﺍﺭ‪.‬‬

‫‪52‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫‪ -2‬ﻣﻘﻴﺎﺱ ‪:DFBETAS‬‬ ‫ﻧﻼﺣﻆ ﺃﻥ ﻫﻨﺎﻙ ‪ 11‬ﻗﻴﻤﺔ ﰲ ﻣﺸﺎﻫﺪﺍﺕ ﻣﺘﻜﺮﺭﺓ ﺗﺆﺛﺮ ﻋﻠﻰ ﻣﻌﺎﻣﻼﺕ ﳕﻮﺫﺝ ﺍﻻﳓﺪﺍﺭ‬ ‫ﻭﻣﺘﻐﲑﺍﺕ ﻋﺪﺩ ﺳﻨﻮﺍﺕ ﺍﻟﺘﻌﻠﻴﻢ ﻭﺧﱪﺓ ﺍﳌﻮﻇﻒ ﻣﻊ ﺍﳌﻼﺣﻈﺔ ﺃﻥ ﺑﻌﻀﻬﺎ ﻳﺆﺛﺮ ﻋﻠﻰ ﻣﻌﺎﻣﻞ ﻭﺍﺣﺪ‬ ‫ﻭﺍﻟﺒﻌﺾ ﻣﻌﺎﻣﻼﻥ ﻭﺍﻵﺧﺮ ﻋﻠﻰ ﲨﻴﻊ ﺍﳌﻌﺎﻣﻼﺕ‪ .‬ﻣﺜﻞ ﺍﳌﺸﺎﻫﺪﺓ ﺭﻗﻢ ‪ 1‬ﻓﺈ‪‬ﺎ ﺗﺆﺛﺮ ﻋﻠﻰ ﺍﳌﻌﺎﻣﻞ ﺍﻷﻭﻝ‬ ‫‪ β 0‬ﻭﻛﺬﻟﻚ ﺍﳌﻌﺎﻣﻞ ﺍﻟﺜﺎﱐ ‪ . β1‬ﺃﻣﺎ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺭﻗﻢ ‪ 4,20,33‬ﻓﺈ‪‬ﺎ ﺗﺆﺛﺮ ﻓﻘﻂ ﻋﻠﻰ ﺍﳌﻌﺎﻣﻞ ﺍﻷﻭﻝ‬ ‫‪ β 0‬ﻟﻠﻨﻤﻮﺫﺝ‪ .‬ﻭﺍﳌﺸﺎﻫﺪﺗﺎﻥ ‪ 14,27‬ﺗﺆﺛﺮ ﻋﻠﻰ ﲨﻴﻊ ﻣﻌﺎﻣﻼﺕ ﳕﻮﺫﺝ ﺍﻻﳓﺪﺍﺭ ) ‪ .( β 0 β1 β 2‬ﻣﻊ‬ ‫ﻣﻼﺣﻈﺔ ﺍﻥ ﺍﳌﺸﺎﻫﺪﺍﺕ ‪ 1,14,27‬ﻛﺎﻧﺖ ﻗﺎﺻﻴﺔ ﰲ ﻣﺘﻐﲑﺍﺕ ﺧﱪﺓ ﺍﳌﻮﻇﻒ ﻭﻋﺪﺩ ﺳﻨﻮﺍﺕ ﺍﻟﺘﻌﻠﻴﻢ‪.‬‬ ‫‪ -3‬ﻣﻘﻴﺎﺱ ﻣﺴﺎﻓﺔ ﻛﻮﻙ ‪:Di‬‬ ‫ﻣﻦ ﻋﻤﻮﺩ ‪ Di‬ﻧﻼﺣﻆ ﻭﺟﻮﺩ ﻣﺸﺎﻫﺪﺓ ﻭﺍﺣﺪﺓ ﻣﺆﺛﺮﺓ ﻋﻠﻰ ﲨﻴﻊ ﻣﺘﻐﲑﺍﺕ ﺍﻟﻨﻤﻮﺫﺝ‪ .‬ﻭﻫﻲ‬ ‫ﺍﳌﺸﺎﻫﺪﺍﺕ ‪ 14‬ﺣﻴﺚ ﺃﻥ ﻗﻴﻤﺔ ﻫﺬﻩ ﺍﳌﺸﺎﻫﺪﺓ ﺗﺴﺎﻭﻱ‪ D14 = 0.573 .‬ﻣﻊ ﻣﻼﺣﻈﺔ ﺃﻥ ﺍﳌﺸﺎﻫﺪﺍﺕ‬ ‫‪ 14‬ﻛﺎﻧﺖ ﻣﺸﺎﻫﺪﺍﺕ ﻗﺎﺻﻴﺔ ﻭﻣﺆﺛﺮﺓ ﻋﻠﻰ ﻣﺘﻐﲑ ﺍﻷﺩﺍﺀ ﺍﻟﻮﻇﻴﻔﻲ‪ .‬ﻭ ﻗﺎﺻﻴﺔ ﻭﻣﺆﺛﺮﺓ ﺑﺎﻟﻨﺴﺒﺔ ﳌﺘﻐﲑﺍﺕ‬ ‫ﺧﱪﺓ ﺍﳌﻮﻇﻒ ﻭﻋﺪﺩ ﺳﻨﻮﺍﺕ ﺍﻟﺘﻌﻠﻴﻢ ﺃﻳﻀﹰﺎ‪.‬‬ ‫‪ -4‬ﻣﻘﻴﺎﺱ ‪:COVRATIO‬‬ ‫ﻣﻘﻴﺎﺱ ﻧﺴﺒﺔ ﺍﻟﺘﻐﺎﻳﺮ ﺃﻭ ﺍﻟﺘﺒﺎﻳﻦ ﻳﻮﺿﺢ ﺃﻥ ﻫﻨﺎﻙ ‪ 3‬ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻷﺧﻄﺎﺀ ﺍﳌﻌﻴﺎﺭﻳﺔ‬ ‫ﻭﻫﻲ ﺍﳌﺸﺎﻫﺪﺍﺕ ‪ . 7,15,20‬ﺫﻟﻚ ﻷ‪‬ﺎ ﺗﻔﻮﻕ ﺍﻟﻘﻴﻤﺔ ﺍﻟﱵ ﺍﻗﺘﺮﺍﺣﻬﺎ ﺑﻴﻠﺴﻲ ﻭﺁﺧﺮﻭﻥ ﺣﻴﺚ ﺃﻥ ﻗﻴﻢ‬ ‫ﻫﺬﻩ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺗﺴﺎﻭﻱ‪.‬‬ ‫‪COVRATIO 7 = 1.341 COVRATIO15 = 1.309 COVRATIO 20 = 0.576‬‬

‫ﻭﻻ ﻧﻨﺴﻰ ﺃﻳﻀﹰﺎ ﺃﻥ ﺍﳌﺸﺎﻫﺪﺓ ‪ 7‬ﻛﺎﻧﺖ ﻣﺸﺎﻫﺪﺓ ﻗﺎﺻﻴﺔ ﰲ ﺍﳌﺘﻐﲑﺍﺕ ﻋﺪﺩ ﺳﻨﻮﺍﺕ ﺍﻟﺘﻌﻠﻴﻢ ﻭﺧﱪﺓ‬ ‫ﺍﳌﻮﻇﻒ ﻟﻨﻤﻮﺫﺝ ﺍﻻﳓﺪﺍﺭ ﻭﻛﺬﻟﻚ ﺍﳌﺸﺎﻫﺪﺓ ‪ 20‬ﻛﺎﻧﺖ ﻗﺎﺻﻴﺔ ﰲ ﻣﺘﻐﲑ ﺍﻷﺩﺍﺀ ﺍﻟﻮﻇﻴﻔﻲ‪.‬‬ ‫)‪ (4‬ﺗﺸﺨﻴﺼﺎﺕ ﺍﻹﺭﺗﺒﺎﻃﻴﺔ ﺍﳋﻄﻴﺔ ﺍﳌﺘﻌﺪﺩﺓ ‪ -‬ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ‪.‬‬ ‫ﻫﻨﺎﻙ ﻃﺮﻕ ﻛﺜﲑﺓ ﳌﻌﺮﻓﺔ ﻣﺎ ﺇﺫﺍ ﻛﺎﻥ ﻫﻨﺎﻙ ﺍﺭﺗﺒﺎﻁ ﺧﻄﻲ ﻣﺘﻌﺪﺩ ﺑﲔ ﺍﳌﺘﻐﲑﺍﺕ ﺍﳌﺴﺘﻘﻠﺔ ﰲ‬ ‫ﳕﻮﺫﺝ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪ .‬ﻓﻤﻦ ﻫﺬﻩ ﺍﻟﻄﺮﻕ‪.‬‬ ‫‪53‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫‪ -1‬ﻋﻨﺪ ﻭﺟﻮﺩ ﺍﺭﺗﺒﺎﻁ ﺧﻄﻲ ﻣﺘﻌﺪﺩ ﻓﺈﻥ ﺃﻱ ﺗﻐﻴﲑ ﻃﻔﻴﻒ ﰲ ﺍﻟﻌﻴﻨﺔ ﻛﺤﺬﻑ ﺃﻭ ﺇﺿﺎﻓﺔ ﻣﺸﺎﻫﺪﺓ‬ ‫ﺃﻭ ﳎﻤﻮﻋﺔ ﺇﺿﺎﻓﻴﺔ ﻣﻦ ﺍﳌﺸﺎﻫﺪﺍﺕ ﻗﺪ ﻳﺘﺴﺒﺐ ﰲ ﺗﻐﻴﲑ ﻣﻌﺎﻣﻼﺕ ﺍﻟﻨﻤﻮﺫﺝ‪.‬‬ ‫‪ -2‬ﺗﺼﺒﺢ ﺍﻻﳓﺮﺍﻓﺎﺕ ﺍﳌﻌﻴﺎﺭﻳﺔ ﺍﳌﻘﺪﺭﺓ ﳌﻌﺎﻣﻼﺕ ﺍﻻﳓﺪﺍﺭ ﻛﺒﲑﺓ ﻋﻨﺪﻣﺎ ﺗﻜﻮﻥ ﺍﳌﺘﻐﲑﺍﺕ ﺍﳌﺴﺘﻘﻠﺔ‬ ‫ﰲ ﳕﻮﺫﺝ ﺍﻻﳓﺪﺍﺭ ﻣﺮﺗﺒﻄﺔ ﻓﻴﻤﺎ ﺑﻴﻨﻬﺎ ﺍﺭﺗﺒﺎﻃﺎ ﻋﺎﻟﻴﹰﺎ‪.‬‬ ‫‪ -3‬ﻓﺤﺺ ﻣﺼﻔﻮﻓﺔ ﻣﻌﺎﻣﻼﺕ ﺍﻻﺭﺗﺒﺎﻁ ﺍﳋﻄﻲ ﺍﻟﺒﺴﻴﻂ ﺑﲔ ﺃﺯﻭﺍﺝ ﺍﳌﺘﻐﲑﺍﺕ ﺍﳌﺴﺘﻘﻠﺔ ) ‪( Rxx‬‬ ‫ﺣﻴﺚ ﺃﻥ‪.‬‬ ‫‪, h, k = 1,2,..., p − 1‬‬

‫) ‪∑ ( X − X )( X − X‬‬ ‫) ‪∑ (X − X ) ∑ ( X − X‬‬ ‫‪hi‬‬

‫‪k1‬‬

‫‪2‬‬

‫‪k1‬‬

‫‪hi‬‬

‫‪.... rx1xp −1 ‬‬ ‫‪....‬‬ ‫‪: ‬‬ ‫= ‪, rxh, x1‬‬ ‫‪....‬‬ ‫‪: ‬‬ ‫‪‬‬ ‫‪1 ‬‬

‫‪1 rx1x 2‬‬ ‫‪‬‬ ‫‪.‬‬ ‫‪=‬‬ ‫‪‬‬ ‫‪‬‬ ‫‪‬‬

‫‪R XX‬‬

‫ﻭﲟﻼﺣﻈﺔ ﻗﻴﻢ ﻣﻌﺎﻣﻼﺕ ﺍﻻﺭﺗﺒﺎﻁ ﺇﺫﺍ ﻭﺟﺪ ﺃﻥ ﻫﻨﺎﻙ ﺍﺭﺗﺒﺎﻃﹰﺎ ﻗﻮﻳﹰﺎ ﺑﲔ ﻣﺘﻐﲑﻳﻦ ﻣﺴﺘﻘﻠﲔ ﺩﻝ ﺫﻟﻚ ﻋﻠﻰ‬ ‫ﺍﺣﺘﻤﺎﻝ ﻭﺟﻮﺩ ﺍﺭﺗﺒﺎﻁ ﺧﻄﻲ ﻣﺘﻌﺪﺩ‪.‬‬ ‫‪ -4‬ﺗﻮﻓﻴﻖ ﻋﺪﺩ ) ‪ ( p-1‬ﻣﻦ ﳕﺎﺫﺝ ﺍﻻﳓﺪﺍﺭ ﻟﻜﻞ ﻣﺘﻐﲑ ﻣﺴﺘﻘﻞ ﻋﻠﻰ ﺑﻘﻴﺔ ﺍﳌﺘﻐﲑﺍﺕ ﺍﳌﺴﺘﻘﻠﺔ‬ ‫ﺑﺎﻟﻄﺮﻳﻘﺔ ﺍﻟﺘﺎﻟﻴﺔ‪.‬‬ ‫‪X 1 = b0 + b2 X 2 + ... + b p −1 X p −1 + ε i‬‬ ‫‪X 2 = b0 + b1 X 1 + ... + b p −1 X p −1 + ε i‬‬ ‫‪.‬‬ ‫‪.‬‬ ‫‪X p −1 = b0 + b2 X 2 + ... + b p −2 X p −2 + ε i‬‬

‫ﻓﺈﺫﺍ ﻛﺎﻧﺖ ﻗﻴﻤﺔ ﺃﺣﺪ ﻣﻌﺎﻣﻼﺕ ﺍﻟﺘﺤﺪﻳﺪ ) ‪ ( R 2‬ﳍﺬﻩ ﺍﻟﻨﻤﺎﺫﺝ ﺗﻘﺘﺮﺏ ﻣﻦ ﺍﻟﻮﺍﺣﺪ ﺍﻟﺼﺤﻴﺢ ﺩﻝ‬ ‫ﺫﻟﻚ ﻋﻠﻰ ﻭﺟﻮﺩ ﺍﺭﺗﺒﺎﻁ ﺧﻄﻲ ﻣﺘﻌﺪﺩ‪.‬‬ ‫ﺑﻌﺪ ﺃﻥ ﺫﻛﺮﻧﺎ ﺑﻌﺾ ﺍﳌﺆﺷﺮﺍﺕ ﻟﻜﺸﻒ ﻭﺟﻮﺩ ﺍﻻﺭﺗﺒﺎﻃﻴﺔ ﺍﳋﻄﻴﺔ ﺍﳌﺘﻌﺪﺩﺓ ﻧﻼﺣﻆ ﺃﻥ ﺑﻌﺾ‬ ‫ﻫﺬﻩ ﺍﻟﻄﺮﻕ ﺟﻴﺪ ﻭﺍﻟﺒﻌﺾ ﺍﻵﺧﺮ ﺃﻗﻞ ﺟﻮﺩﺓ ﻭﺍﻟﺒﻌﺾ ﻳﺴﺘﻬﻠﻚ ﺍﳉﻬﺪ ﻭﺍﻟﺒﻌﺾ ﺍﻵﺧﺮ ﺑﺴﻴﻂ ﻭﻟﻜﻦ‬ ‫ﻳﺴﺘﻬﻠﻚ ﺍﻟﻮﻗﺖ ﻟﺬﻟﻚ ﻧﻠﺠﺄ ﻟﻠﻄﺮﻳﻘﺔ ﺍﻷﺳﺎﺳﻴﺔ ﻭﺍﻟﻮﺍﺳﻌﺔ ﺍﻻﺳﺘﺨﺪﺍﻡ ﻣﺜﻞ ﻋﺎﻣﻞ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ‬ ‫)‪.(VIF‬‬ ‫‪54‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫ ﻋﺎﻣﻞ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ )‪.(VIF‬‬‫ﺗﻌﺘﱪ ﻃﺮﻳﻘﺔ ﻋﺎﻣﻞ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ ﻣﻦ ﺍﻟﻄﺮﻕ ﺍﻟﺮﲰﻴﺔ ﻭﺍﻷﺳﺎﺳﻴﺔ ﺍﻻﺳﺘﺨﺪﺍﻡ ﻟﻠﻜﺸﻒ ﻋﻦ‬ ‫ﻭﺟﻮﺩ ﺍﻹﺭﺗﺒﺎﻃﺔ ﺍﳋﻄﻴﺔ ﺍﳌﺘﻌﺪﺩﺓ ﻭﺗﻘﻴﺲ ﻋﻮﺍﻣﻞ ﺍﻟﺘﻀﺨﻢ ﻣﺪﻯ ﺗﻀﺨﻢ ﺗﺒﺎﻳﻨﺎﺕ ﻣﻌﺎﻣﻼﺕ ﺍﻻﳓﺪﺍﺭ‬ ‫ﺍﳌﻘﺪﺭ ﰲ ﻭﺟﻮﺩ ﺍﻻﺭﺗﺒﺎﻃﺔ ﺍﳋﻄﻴﺔ ﺍﳌﺘﻌﺪﺩﺓ‪ .‬ﻭﻳﺘﻢ ﺣﺴﺎﺏ ﻋﺎﻣﻞ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ ﺑﺎﻟﻌﻼﻗﺔ ﺍﻟﺘﺎﻟﻴﺔ‪:‬‬ ‫‪, k = 1,2,...., p − 1 , 1 ≤ VIFk ≤ ∞ , 0 ≤ Rk2 ≤ 1‬‬

‫‪VIFk = (1 − Rk2 ) −1‬‬

‫ﺣﻴﺚ ﺃﻥ‪-:‬‬ ‫‪ : VIFk‬ﻋﺎﻣﻞ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ ﻟﻠﻤﺘﻐﲑ ﺍﳌﺴﺘﻘﻞ ﺭﻗﻢ )‪.(k‬‬ ‫‪ : Rk2‬ﻣﻌﺎﻣﻞ ﺍﻟﺘﺤﺪﻳﺪ ﻟﻨﻤﻮﺫﺝ ﺍﳓﺪﺍﺭ ﺍﳌﺘﻐﲑ ﺍﳌﺴﺘﻘﻞ ﺭﻗﻢ )‪ (k‬ﻋﻠﻰ ﺑﻘﻴﺔ ﺍﳌﺘﻐﲑﺍﺕ ﺍﳌﺴﺘﻘﻠﺔ ) ‪.( p − 2‬‬ ‫ﻓﺈﺫﺍ ﻛﺎﻥ ﻋﺎﻣﻞ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ ) ‪ ( VIFk‬ﻛﺒﲑﹰﺍ ﻛﺎﻧﺖ ﻫﺬﻩ ﺩﻻﻟﻪ ﻭﺍﺿﺤﺔ ﻋﻠﻰ ﻭﺟﻮﺩ ﺍﺭﺗﺒﺎﻁ ﺧﻄﻲ‬ ‫ﻣﺘﻌﺪﺩ‪.‬‬ ‫ ﻃﺮﻳﻘﺔ ﺍﻟﻜﺸﻒ ﻋﻦ ﻭﺟﻮﺩ ﺍﺭﺗﺒﺎﻁ ﺧﻄﻲ ﻣﺘﻌﺪﺩ‪.‬‬‫ﻋﻨﺪ ﺍﺳﺘﺨﺮﺍﺝ ﻋﺎﻣﻞ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ ) ‪ ( VIFk‬ﻭﻣﻘﺎﺭﻧﺘﻪ ﻣﻊ ﺍﻟﻘﻴﻤﺔ )‪ .(10‬ﺇﺫﺍ ﻛﺎﻥ ﻋﺎﻣﻞ‬ ‫ﺍﻟﺘﻀﺨﻢ ﺍﻛﱪ ﻣﻦ ﻫﺬﻩ ﺍﻟﻘﻴﻤﺔ ﻳﻜﻮﻥ ﺫﻟﻚ ﺩﻟﻴﻞ ﻋﻠﻰ ﻭﺟﻮﺩ ﺍﺭﺗﺒﺎﻁ ﺧﻄﻲ ﻣﺘﻌﺪﺩ ﻣﺮﺗﻔﻊ‪ .‬ﺃﻱ ﺇﺫﺍ‬ ‫ﻛﺎﻥ‪:‬‬ ‫‪VIFk > 10 , k = 1,2,..., p − 1‬‬

‫ﻭﺑﺎﳌﺜﻞ ﻓﺈﺫﺍ ﻛﺎﻧﺖ ﻗﻴﻤﺔ ﻣﻌﺎﻣﻞ ﺍﻟﺘﺤﺪﻳﺪ ) ‪ ( Rk2‬ﻟﻨﻤﻮﺫﺝ ﺍﳓﺪﺍﺭ ﺍﳌﺘﻐﲑ ﺍﳌﺴﺘﻘﻞ ﺭﻗﻢ )‪ (k‬ﻋﻠﻰ ﺑﻘﻴﺔ‬ ‫ﺍﳌﺘﻐﲑﺍﺕ ﺍﳌﺴﺘﻘﻠﺔ ) ‪ ( p − 2‬ﻣﺴﺎﻭﻳﺔ ﻟـ ) ‪ ( Rk2 = 0.90‬ﻳﻼﺣﻆ ﻋﺪﺓ ﻣﻼﺣﻈﺎﺕ‪.‬‬ ‫ ﻳﺄﺧﺬ ﻋﺎﻣﻞ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ ﻗﻴﻢ ﺃﻛﱪ ﺃﻭ ﺗﺴﺎﻭﻱ ﺍﻟﻮﺍﺣﺪ ﺃﻱ ﺃﻥ ‪. VIFk ≥ 1‬‬ ‫ ﰲ ﺣﺎﻟﺔ ﻭﺟﻮﺩ ﺍﺭﺗﺒﺎﻁ ﺧﻄﻲ ﺗﺎﻡ ﺑﲔ ﺍﳌﺘﻐﲑ ﺍﳌﺴﺘﻘﻞ ﺭﻗﻢ )‪ (k‬ﻭﺑﻘﻴﺔ ﺍﳌﺘﻐﲑﺍﺕ ﺍﳌﺴﺘﻘﻠﺔ‬ ‫) ‪ ( p − 2‬ﻓﺈﻥ ﻋﺎﻣﻞ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ ﻳﺬﻫﺐ ﺇﱃ ﺍﳌﺎﻻ‪‬ﺎﻳﻪ‪ .‬ﻭﰲ ﺣﺎﻟﺔ ﻋﺪﻡ ﻭﺟﻮﺩ ﺍﺭﺗﺒﺎﻁ ﺧﻄﻲ‬ ‫ﺑﲔ ﺍﳌﺘﻐﲑ ﺍﳌﺴﺘﻘﻞ ﺭﻗﻢ )‪ (k‬ﻭﺑﻘﻴﺔ ﺍﳌﺘﻐﲑﺍﺕ ﺍﳌﺴﺘﻘﻠﺔ ) ‪ ( p − 2‬ﻓﺄﻥ ﻗﻴﻤﺔ ﻋﺎﻣﻞ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ‬ ‫ﺗﻜﻮﻥ ﻣﺴﺎﻭﻱ ﻟﻠﻮﺍﺣﺪ ﺍﻟﺼﺤﻴﺢ‪.‬‬

‫‪55‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫ ﻣﺘﻮﺳﻂ ﻗﻴﻢ ﻋﻮﺍﻣﻞ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ ﳌﻌﺎﻣﻼﺕ ﺍﻻﳓﺪﺍﺭ‪.‬‬‫ﺗﺴﺘﺨﺪﻡ ﻋﻮﺍﻣﻞ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ ) ‪ ( VIF ' s‬ﻟﻘﻴﺎﺱ ﻣﺪﻯ ﺑﻌﺪ ﻣﻘﺪﺭﺍﺕ ﺍﳌﺮﺑﻌﺎﺕ ﺍﻟﺼﻐﺮﻯ ﻋﻦ‬ ‫ﻗﻴﻤﻬﺎ ﺍﳊﻘﻴﻘﻴﺔ‪ .‬ﺣﻴﺚ ﺗﺄﺧﺬ ﺍﻟﻘﻴﻢ ﺍﳌﺘﻮﻗﻌﺔ ‪‬ﻤﻮﻉ ﻣﺮﺑﻌﺎﺕ ﺍﻟﻔﺮﻭﻕ ﺑﲔ ﻣﻌﺎﻣﻼﺕ ﺍﻻﳓﺪﺍﺭ ﺍﳌﻘﺪﺭﺓ‬ ‫ﻭﻗﻴﻤﻬﺎ ﺍﳊﻘﻴﻘﺔ‪ ،‬ﻭﺗﻜﻮﻥ ﻋﻠﻰ ﺍﻟﺸﻜﻞ ﺍﻟﺘﺎﱄ‪.‬‬ ‫‪p −1‬‬ ‫‪ P −1‬‬ ‫‪‬‬ ‫‪E ∑ (bk' − β k' ) 2  = (σ ' ) 2 ∑ VIFk‬‬ ‫‪k =1‬‬ ‫‪K =1‬‬ ‫‪‬‬

‫)*(‬

‫ﻭﰲ ﺣﺎﻟﺔ ﻋﺪﻡ ﻭﺟﻮﺩ ﺇﺭﺗﺒﺎﻃﻴﺔ ﺧﻄﻴﺔ ﺑﲔ ﺍﳌﺘﻐﲑﺍﺕ ﺍﳌﺴﺘﻘﻠﺔ‪ ،‬ﺗﻜﻮﻥ ﻗﻴﻢ ﻋﻮﺍﻣﻞ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ ﲨﻴﻌﻬﺎ‬ ‫ﻣﺴﺎﻭﻳﺔ ﻟﻠﻮﺍﺣﺪ ﺍﻟﺼﺤﻴﺢ‪ .‬ﺣﻴﺚ ﺗﺼﺒﺢ ﺍﻟﻘﻴﻢ ﺍﳌﺘﻮﻗﻌﺔ ‪‬ﻤﻮﻉ ﻣﺮﺑﻌﺎﺕ ﺍﻟﻔﺮﻭﻕ ﺍﻟﺴﺎﺑﻘﺔ ﺑﺎﻟﻘﻴﻤﺔ ﺍﻟﺘﺎﻟﻴﺔ‪:‬‬ ‫‪ P −1‬‬ ‫‪‬‬ ‫)‪E ∑ (bk' − β k' ) 2  = (σ ' ) 2 ( p − 1‬‬ ‫‪ K =1‬‬ ‫‪‬‬

‫)* *(‬

‫ﻣﻦ ﰒ ﳝﻜﻦ ﺣﺴﺎﺏ ﻧﺴﺒﺔ ﺍﻟﻨﺎﲡﲔ ﺍﻟﺴﺎﺑﻘﲔ )**()*( ﺑﺎﻟﻄﺮﻳﻘﺔ ﺍﻟﺘﺎﻟﻴﺔ‪:‬‬ ‫‪p −1‬‬

‫‪p −1‬‬

‫‪∑VIF‬‬

‫‪k‬‬

‫‪k =1‬‬

‫=‬

‫)‪( p − 1‬‬

‫‪σ 2 ∑VIFk‬‬ ‫‪k =1‬‬

‫)‪σ 2 ( p − 1‬‬

‫ﺣﻴﺚ ﺗﻌﻄﻲ ﻫﺬﻩ ﺍﻟﻨﺴﺒﺔ ﻣﻌﻠﻮﻣﺎﺕ ﻣﻔﻴﺪﺓ ﻋﻦ ﺗﺄﺛﲑ ﺍﳋﻄﻴﺔ ﺍﳌﺘﻌﺪﺩﺓ ﻋﻠﻰ ﳎﻤﻮﻉ ﻣﺮﺑﻌﺎﺕ ﺍﳋﻄﺄ‪.‬‬ ‫ﻭﻧﻼﺣﻆ ﺃﻳﻀﹰﺎ ﺃﻥ ﻫﺬﻩ ﺍﻟﻨﺴﺒﺔ ﻫﻲ ﻣﺘﻮﺳﻂ ﻗﻴﻢ ‪ VIF ' s‬ﻭﺳﻨﺮﻣﺰ ﳍﺎ ﺑﺎﻟﺮﻣﺰ ) ‪.( VIF‬‬ ‫‪p −1‬‬

‫‪∑VIF‬‬

‫‪k‬‬

‫‪k =1‬‬

‫)‪( p − 1‬‬

‫= ‪VIF‬‬

‫ﻓﺈﺫﺍ ﻛﺎﻧﺖ ﺍﳌﺘﻐﲑﺍﺕ ﺍﳌﺴﺘﻘﻠﺔ ﻣﺘﻌﺎﻣﺪﺓ ﺃﻱ ﻻ ﻳﻮﺟﺪ ﺍﺭﺗﺒﺎﻁ ﺧﻄﻲ‪ ،‬ﻓﺈﻥ ﺍﳌﺘﻮﺳﻂ ﻳﺴﺎﻭﻱ ﻭﺍﺣﺪ‬ ‫ﺻﺤﻴﺢ‪ .‬ﻟﺬﻟﻚ ﳒﺪ ﺃﻧﻪ ﻛﻠﻤﺎ ﺯﺍﺩﺕ ﻗﻴﻤﺔ ﻣﺘﻮﺳﻂ ﻋﻮﺍﻣﻞ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ ﻋﻦ ﺍﻟﻮﺍﺣﺪ ﺩﻝ ﺫﻟﻚ ﻋﻠﻰ‬ ‫ﻭﺟﻮﺩ ﻣﺸﻜﻠﺔ ﺍﻹﺭﺗﺒﺎﻃﻴﺔ ﺍﳋﻄﻴﺔ ﺍﳌﺘﻌﺪﺩﺓ ﺑﲔ ﺍﳌﺘﻐﲑﺍﺕ ﺍﳌﺴﺘﻘﻠﺔ‪.‬‬ ‫ ﺗﻄﺒﻴﻖ )‪:(4-1‬‬‫ﺑﺎﻟﺮﺟﻮﻉ ﺇﱃ ﺗﻄﺒﻴﻖ )‪ (1-1‬ﻭﺑﻴﺎﻧﺎﺕ ﻟﻘﻴﺎﺱ ﺍﻟﻌﻼﻗﺔ ﺑﲔ ﻭﺯﻥ ﺍﻟﻄﻔﻞ )ﺑﺎﻟﻜﻴﻠﻮ ﺟﺮﺍﻡ( ﻭﺗﺄﺛﺮﻩ‬ ‫ﺑﺰﻳﺎﺩﺓ ﺍﻟﻌﻤﺮ)ﺳﻨﺔ( ﻭﺍﻟﻄﻮﻝ)ﺳﻢ( ﻟﻌﻴﻨﺔ ﻣﻦ ‪ 50‬ﻃﻔﻞ‪ .‬ﺳﻨﻘﻴﺲ ﻋﻮﺍﻣﻞ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ‪.‬‬

‫‪56‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫ ﺍﻟﺘﺤﻠﻴﻞ ﺍﻹﺣﺼﺎﺋﻲ‪-:‬‬‫ﳊﺴﺎﺏ ﻋﺎﻣﻞ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ ﻳﻜﻔﻲ ﺑﻨﺎﺀ ﳕﻮﺫﺝ ﺍﳓﺪﺍﺭ ﺍﻟﻌﻤﺮ ﻋﻠﻰ ﺍﻟﻄﻮﻝ ﺃﻭ ﺍﻟﻌﻜﺲ ﻭﲟﺎ ﺃﻥ‬ ‫ﻣﻌﺎﻣﻞ ﺍﻟﺘﺤﺪﻳﺪ ﳍﺬﺍ ﺍﻟﻨﻤﻮﺫﺝ ﻳﺴﺎﻭﻱ ‪ Rx21 = 0.872 ≈ 0.90‬ﻓﺈﻥ ﻋﺎﻣﻞ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ ﻭﺍﳌﺘﻮﺳﻂ‬ ‫ﻳﻜﻮﻥ ﻛﺎﻟﺘﺎﱄ‪:‬‬ ‫ﻣﺘﻐﲑ‬

‫‪(VIF) k >10‬‬

‫‪Rk2‬‬

‫‪(VIF)k‬‬

‫‪X1‬‬

‫‪No‬‬

‫‪0.872‬‬

‫‪7.8125‬‬

‫‪(VIF) k = 7.8125‬‬

‫‪(VIF) k = 7.8125‬‬

‫ﻭﲟﺎ ﺃﻥ ﻗﻴﻤﺔ ﻋﺎﻣﻞ ﺍﻟﺘﻀﺨﻢ ﳌﻌﺎﻣﻠﻲ ﺍﻻﳓﺪﺍﺭ ﻫﻲ ‪ 7.8125‬ﻓﺈﻥ ﻗﻴﻤﺔ ﻣﺘﻮﺳﻂ ﻋﺎﻣﻠﻲ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ‬ ‫ﺃﻳﻀﹰﺎ ‪7.8125‬‬ ‫ﺍﻻﺳﺘﻨﺘﺎﺝ ‪-:‬‬ ‫ﻳﻼﺣﻆ ﺃﻥ ﻗﻴﻤﺔ ﻋﺎﻣﻞ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ ﺍﻗﻞ ﻣﻦ ‪ 10‬ﻭﻟﻜﻦ ﻣﺘﻮﺳﻂ ﻋﻮﺍﻣﻞ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ‬ ‫ﺗﻔﻮﻕ ﻗﻴﻤﺔ ‪ 1‬ﺃﻱ ‪ VIFk > 1‬ﺫﻟﻚ ﻧﻘﻮﻝ ﺃﻥ ﻫﻨﺎﻙ ﻣﺸﻜﻠﺔ ﺍﻹﺭﺗﺒﺎﻃﻴﺔ ﺍﳋﻄﻴﺔ ﺍﳌﺘﻌﺪﺩﺓ ﰲ ﻫﺬﺍ ﺍﻟﺘﻄﺒﻴﻖ‬ ‫ﺃﻱ ﻳﻜﻔﻲ ﺍﻻﺳﺘﻐﻨﺎﺀ ﻋﻦ ﺍﺣﺪ ﺍﳌﺘﻐﲑﺍﺕ ﺍﳌﺴﺘﻘﻠﺔ ﻭﻳﺘﻢ ﺍﺧﺘﻴﺎﺭ ﺃﻓﻀﻠﻬﻤﺎ ﻛﻠﻤﺎ ﺯﺍﺩ ﻣﻌﺎﻣﻞ ﺍﻟﺘﺤﺪﻳﺪ ﻋﻦ‬ ‫ﺍﻵﺧﺮ ﺃﻱ ﳔﺘﺎﺭ ﺍﳌﺘﻐﲑ ﺍﳌﺴﺘﻘﻞ ﺍﻟﺜﺎﱐ ﻋﻨﺪ ﻣﺎ ﻳﻜﻮﻥ ‪ . R y2, x 2 > R y2, x1‬ﰲ ﻫﺬﻩ ﺍﳊﺎﻟﺔ ﺳﻨﺨﺘﺎﺭ ‪ y‬ﻭﺯﻥ‬ ‫ﺍﻟﻄﻔﻞ ﻣﻊ ‪ x2‬ﻃﻮﻝ ﺍﻟﻄﻔﻞ‪.‬‬ ‫ ﺗﻄﺒﻴﻖ )‪:(4-2‬‬‫ﺑﺎﻟﺮﺟﻮﻉ ﺇﱃ ﺗﻄﺒﻴﻖ )‪ (1-2‬ﻭﺍﻟﻌﻴﻨﺔ ﺍﻟﱵ ﺳﺤﺒﺖ ﻣﻦ ‪ 30‬ﺃﺳﺮﻩ ﻟﻘﻴﺎﺱ ﺍﻓﺘﺮﺍﺿﻴﺔ ﺍﳌﺼﺮﻭﻓﺎﺕ‬ ‫ﺍﳌﻌﻴﺸﻴﺔ ﻟﻸﺳﺮ )ﺑﺂﻻﻑ ﺍﻟﺮﻳﺎﻻﺕ(‪ ،‬ﻭﺑﻌﺾ ﺍﳌﺘﻐﲑﺍﺕ ﺍﳌﺆﺛﺮﺓ ﻋﻠﻴﻬﺎ ﻣﺜﻞ ﻣﺴﺘﻮﻯ ﺗﻌﻠﻴﻢ ﺭﺏ ﺍﻷﺳﺮﺓ‬ ‫)ﺑﺎﻟﺴﻨﺔ( ‪ ، x1‬ﻋﺪﺩ ﺍﻷﻃﻔﺎﻝ ‪ ، x2‬ﺩﺧﻞ ﺍﻷﺳﺮﺓ )ﺑﺂﻻﻑ ﺍﻟﺮﻳﺎﻻﺕ( ‪ ،x3‬ﻋﺪﺩ ﺃﻓﺮﺍﺩ ﺍﻷﺳﺮﺓ ‪،x4‬‬ ‫ﺳﻨﻘﻴﺲ ﻋﻮﺍﻣﻞ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ‪.‬‬

‫‪57‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫ ﺍﻟﺘﺤﻠﻴﻞ ﺍﻹﺣﺼﺎﺋﻲ‪-:‬‬‫ﳊﺴﺎﺏ ﻋﺎﻣﻞ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ ﻧﻘﻮﻡ ﺑﺒﻨﺎﺀ ﳕﻮﺫﺝ ﺍﳓﺪﺍﺭ ﻛﻞ ﻣﺘﻐﲑ ﻣﻦ ﺍﳌﺘﻐﲑﺍﺕ ﺍﳌﺴﺘﻘﻠﺔ ﻋﻠﻰ‬ ‫ﺍﻵﺧﺮ ﻭﳓﺴﺐ ﻣﻌﺎﻣﻞ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ ﻓﻨﺤﺼﻞ ﻋﻠﻰ ﺍﻟﻨﺘﺎﺋﺞ ﺍﻟﺘﺎﻟﻴﺔ‪:‬‬ ‫ﻣﺘﻐﲑ‬

‫‪(VIF)k >10‬‬

‫‪Rk2‬‬

‫‪(VIF)k‬‬

‫‪x1‬‬ ‫‪x2‬‬ ‫‪x3‬‬ ‫‪x4‬‬

‫‪No‬‬ ‫‪No‬‬ ‫‪No‬‬ ‫‪No‬‬

‫‪0.4‬‬ ‫‪0.461‬‬ ‫‪0.507‬‬ ‫‪0.493‬‬

‫‪1.666666667‬‬ ‫‪1.85528757‬‬ ‫‪2.028397566‬‬ ‫‪1.972386588‬‬

‫‪(VIF) k = 1.881‬‬

‫‪(VIF) k = 2.0284‬‬

‫ﺍﻻﺳﺘﻨﺘﺎﺝ ‪-:‬‬ ‫ﻧﻼﺣﻆ ﺃﻥ ﲨﻴﻊ ﻗﻴﻢ ﻋﻮﺍﻣﻞ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ ﺃﻗﻞ ﻣﻦ ﺍﻟﻘﻴﻤﺔ ‪ 10‬ﻟﺬﻟﻚ ﻻ ﻳﻮﺟﺪ ﻣﺸﻜﻠﺔ‬ ‫ﺍﻹﺭﺗﺒﺎﻃﻴﺔ ﺍﳋﻄﻴﺔ ﺍﳌﺘﻌﺪﺩﺓ ﺑﲔ ﻣﺘﻐﲑﺍﺕ ﻣﺴﺘﻮﻯ ﺗﻌﻠﻴﻢ ﺭﺏ ﺍﻵﺳﺮﺓ ﻭﻋﺪﺩ ﺍﻷﻃﻔﺎﻝ ﻭﺩﺧﻞ ﺍﻵﺳﺮﺓ‬ ‫ﻭﻋﺪﺩ ﺃﻓﺮﺍﺩ ﺍﻵﺳﺮﺓ‪.‬‬ ‫ ﺗﻄﺒﻴﻖ )‪:(4-3‬‬‫ﺑﺎﻟﺮﺟﻮﻉ ﺇﱃ ﺗﻄﺒﻴﻖ )‪ (1-3‬ﰲ ﺍﻷﺩﺍﺀ ﺍﻟﻮﻇﻴﻔﻲ ﻣﻦ ) ‪ 100‬ﺩﺭﺟﺔ ( ﻭﺑﻌﺾ ﺍﳌﺘﻐﲑﺍﺕ ﺍﳌﺆﺛﺮﺓ‬ ‫ﻋﻠﻴﻬﺎ ﻟﻌﻴﻨﺔ ﻋﺸﻮﺍﺋﻴﺔ ﻣﻦ ‪ 33‬ﻣﻮﻇﻒ ﻣﻦ ﻣﻨﺴﻮﰊ ﺷﺮﻛﺔ ﻣﺎ‪ .‬ﺳﻨﻘﻴﺲ ﻋﻮﺍﻣﻞ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ‪.‬‬ ‫ ﺍﻟﺘﺤﻠﻴﻞ ﺍﻹﺣﺼﺎﺋﻲ‪-:‬‬‫ﳊﺴﺎﺏ ﻋﺎﻣﻞ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ ﻧﻘﻮﻡ ﺑﺒﻨﺎﺀ ﳕﻮﺫﺝ ﺍﳓﺪﺍﺭ ﻛﻞ ﻣﺘﻐﲑ ﻣﻦ ﺍﳌﺘﻐﲑﺍﺕ ﺍﳌﺴﺘﻘﻠﺔ ﻋﻠﻰ‬ ‫ﺍﻵﺧﺮ ﻭﳓﺴﺐ ﻣﻌﺎﻣﻞ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ ﻓﻨﺤﺼﻞ ﻋﻠﻰ ﺍﻟﻨﺘﺎﺋﺞ ﺍﻟﺘﺎﻟﻴﺔ‪:‬‬ ‫ﻣﺘﻐﲑ‬

‫‪(VIF) k >10‬‬

‫‪Rk2‬‬

‫‪(VIF)k‬‬

‫‪x1‬‬ ‫‪x2‬‬ ‫‪x3‬‬

‫‪No‬‬ ‫‪Yes‬‬ ‫‪No‬‬

‫‪0.89‬‬ ‫‪0.911‬‬ ‫‪0.882‬‬

‫‪9.090909091‬‬ ‫‪11.23595506‬‬ ‫‪8.474576271‬‬

‫‪(VIF) k = 11.23596‬‬

‫‪(VIF) k = 9.6005‬‬

‫‪58‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫ﺍﻻﺳﺘﻨﺘﺎﺝ ‪-:‬‬ ‫ﻭﺍﺿﺢ ﰲ ﺍﳉﺪﻭﻝ ﺍﻟﺴﺎﺑﻖ ﺃﻥ ﲨﻴﻊ ﻋﻮﺍﻣﻞ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ ﺍﻗﻞ ﻣﻦ ﺍﻟﻘﻴﻤﺔ ‪ 10‬ﻣﺎ ﻋﺪﻯ ﻋﺎﻣﻞ‬ ‫ﺗﻀﺨﻢ ﺧﱪﺓ ﺍﳌﻮﻇﻒ ﺣﻴﺚ ﺃﻥ ﻗﻴﻤﺖ ﻋﺎﻣﻞ ﺍﻟﺘﻀﺨﻢ ﺗﺴﺎﻭﻱ ‪ (VIF) x2 = 11.236‬ﻭﺗﻌﲏ ﻭﺟﻮﺩ‬ ‫ﻣﺸﻜﻠﺔ ﺍﻹﺭﺗﺒﺎﻃﻴﺔ ﺍﳋﻄﻴﺔ ﺍﳌﺘﻌﺪﺩﺓ ﰲ ﻭﺟﻮﺩ ﺍﳌﺘﻐﲑ ‪ x2‬ﺧﱪﺓ ﺍﳌﻮﻇﻒ‪ .‬ﻛﺬﻟﻚ ﻧﻼﺣﻆ ﺃﻥ ﻣﺘﻮﺳﻂ‬ ‫ﻋﻮﺍﻣﻞ ﺍﻟﺘﻀﺨﻢ ﻳﺴﺎﻭﻱ ‪ (VIF) k = 9.6005‬ﻭﻫﺬﺍ ﺍﻳﻀﹰﺎ ﻓﻴﻪ ﺩﻻﻟﺔ ﻋﻠﻰ ﻭﺟﻮﺩ ﺍﳌﺸﻜﻠﺔ ﻟﺬﻟﻚ ﻻ ﺑﺪ‬ ‫ﻣﻦ ﺣﻞ ﻣﺸﻜﻠﺔ ﺍﻹﺭﺗﺒﺎﻃﻴﺔ ﺍﳋﻄﻴﺔ ﺍﳌﺘﻌﺪﺩﺓ ﻭﻫﻨﺎﻙ ﻋﺪﺓ ﻃﺮﻕ ﻟﻠﺘﻐﻠﺐ ﻋﻠﻰ ﻫﺬﻩ ﺍﳌﺸﻜﻠﺔ‪ .‬ﻓﻌﻠﻰ ﺳﺒﻴﻞ‬ ‫ﺍﳌﺜﺎﻝ ﻗﺪ ﻳﻜﻮﻥ ﻣﻦ ﺍﳌﻨﺎﺳﺐ ﺇﻟﻐﺎﺀ ﺍﳌﺘﻐﲑ ﺍﳌﺴﺘﻘﻞ ) ‪ . (R22 = 0.911 , x2‬ﻭﺍﻻﻛﺘﻔﺎﺀ ﺑﺎﳌﺘﻐﲑﺍﺕ‬ ‫ﺍﳌﺴﺘﻘﻠﺔ ‪ x1 x3‬ﻭﺇﻋﺎﺩﺓ ﻛﺘﺎﺑﺔ ﺍﻟﻨﻤﻮﺫﺝ ﺍﻻﳓﺪﺍﺭﻱ ﺑﺎﻟﺸﻜﻞ ﺍﻟﺘﺎﱄ‪. y = β 0 + β1 x1 + β 3 x3 :‬‬ ‫ ﺍﻟﺘﺤﻠﻴﻞ ﺍﻹﺣﺼﺎﺋﻲ ‪-: 2‬‬‫ﳊﺴﺎﺏ ﻋﺎﻣﻞ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ ﻳﻜﻔﻲ ﺑﻨﺎﺀ ﳕﻮﺫﺝ ﺍﳓﺪﺍﺭ ﻋﺪﺩ ﺳﻨﻮﺍﺕ ﺍﻟﺘﻌﻠﻴﻢ ﻋﻠﻰ ﻣﺮﺗﺒﺔ‬ ‫ﺍﳌﻮﻇﻒ ﺃﻭ ﺍﻟﻌﻜﺲ ﻭﲟﺎ ﺃﻥ ﻣﻌﺎﻣﻞ ﺍﻟﺘﺤﺪﻳﺪ ﳍﺬﺍ ﺍﻟﻨﻤﻮﺫﺝ ﻳﺴﺎﻭﻱ ‪ Rx21 = 0.836‬ﻓﺈﻥ ﻋﺎﻣﻞ ﺗﻀﺨﻢ‬ ‫ﺍﻟﺘﺒﺎﻳﻦ ﻭﺍﳌﺘﻮﺳﻂ ﻳﻜﻮﻥ ﻛﺎﻟﺘﺎﱄ‪:‬‬ ‫ﻣﺘﻐﲑ‬

‫‪(VIF) k >10‬‬

‫‪Rk2‬‬

‫‪(VIF) k‬‬

‫‪x1‬‬

‫‪No‬‬

‫‪0.836‬‬

‫‪6.097560976‬‬

‫‪(VIF) k = 6.09756‬‬

‫‪(VIF) k = 6.09756‬‬

‫ﺍﻻﺳﺘﻨﺘﺎﺝ ‪-: 2‬‬ ‫ﻳﻼﺣﻆ ﺃﻥ ﻗﻴﻤﺔ ﻋﺎﻣﻞ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ ﺍﻗﻞ ﻣﻦ ‪ 10‬ﻭﻟﻜﻦ ﻣﺘﻮﺳﻂ ﻋﻮﺍﻣﻞ ﺗﻀﺨﻢ ﺍﻟﺘﺒﺎﻳﻦ‬ ‫ﺗﻔﻮﻕ ﻗﻴﻤﺔ ‪ 1‬ﺃﻱ ‪ VIFk > 1‬ﺫﻟﻚ ﻧﻘﻮﻝ ﺃﻥ ﻫﻨﺎﻙ ﻣﺸﻜﻠﺔ ﺍﻹﺭﺗﺒﺎﻃﻴﺔ ﺍﳋﻄﻴﺔ ﺍﳌﺘﻌﺪﺩﺓ ﰲ ﻫﺬﺍ ﺍﻟﺘﻄﺒﻴﻖ‬ ‫ﺃﻱ ﻳﻜﻔﻲ ﺍﻻﺳﺘﻐﻨﺎﺀ ﻋﻦ ﺍﺣﺪ ﺍﳌﺘﻐﲑﺍﺕ ﺍﳌﺴﺘﻘﻠﺔ ﻭﻳﺘﻢ ﺍﺧﺘﻴﺎﺭ ﺃﻓﻀﻠﻬﻤﺎ ﻛﻠﻤﺎ ﺯﺍﺩ ﻣﻌﺎﻣﻞ ﺍﻟﺘﺤﺪﻳﺪ ﻋﻦ‬ ‫ﺍﻵﺧﺮ ﺃﻱ ﳔﺘﺎﺭ ﺍﳌﺘﻐﲑ ﺍﳌﺴﺘﻘﻞ ﺍﻷﻭﻝ ﻋﻨﺪ ﻣﺎ ﻳﻜﻮﻥ ‪ . R y2, x1 > R y2, x3‬ﰲ ﻫﺬﻩ ﺍﳊﺎﻟﺔ ﺳﻨﺨﺘﺎﺭ ‪ y‬ﺍﻷﺩﺍﺀ‬ ‫ﺍﻟﻮﻇﻴﻔﻲ ﻣﻊ ‪ x1‬ﻋﺪﺩ ﺳﻨﻮﺍﺕ ﺍﻟﺘﻌﻠﻴﻢ‪.‬‬

‫‪59‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫)‪ (5‬ﺩﺭﺍﺳﺔ ﲡﺮﻳﺒﻴﺔ )ﳏﺎﻛﺎﺓ( ﳌﻘﺎﺭﻧﺔ ﺣﺴﻦ ﺃﺩﺍﺀ ﻣﻘﺎﻳﻴﺲ ﺍﻛﺘﺸﺎﻑ ﺍﳊﺎﻻﺕ ﺍﳌﺆﺛﺮﺓ ﻟﻨﻤﻮﺫﺝ ﺍﳓﺪﺍﺭ‬ ‫ﺧﻄﻲ ﺑﺴﻴﻂ‪-:‬‬ ‫ﺍﻟﻄﺮﻳﻘﺔ ﺍﻓﺘﺮﺿﻨﺎﻫﺎ ﲟﺤﺎﻛﺎﺓ ﻟﻌﻴﻨﺔ ﻣﻦ ‪ 10‬ﻣﺸﺎﻫﺪﺍﺕ ﻟﻨﻤﺎﺫﺝ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ ﺍﻟﺒﺴﻴﻂ‪ ،‬ﻋﺪﺩ‬ ‫‪ 200‬ﻣﺮﺓ ﺣﻴﺚ ﺃﻥ ‪ 100‬ﻣﺮﺓ ﻣﻦ ﻫﺬﻩ ﺍﶈﺎﻛﺎﺓ ﺗﻜﻮﻥ ﺑﺸﻜﻠﻬﺎ ﺍﻻﻓﺘﺮﺍﺿﻲ ﻭ ‪ 100‬ﻣﺮﺓ ﺳﻨﻀﻴﻒ‬ ‫ﺇﻟﻴﻬﺎ ﺍﳌﺸﺎﻫﺪﺓ ﺭﻗﻢ ‪ 11‬ﻭﻫﻲ ﻋﺒﺎﺭﺓ ﻋﻦ ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﻋﻠﻰ ﳕﻮﺫﺝ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ ﺍﻟﺒﺴﻴﻂ‬ ‫ﻭﻟﻨﻔﺘﺮﺽ ﺃ‪‬ﺎ ﻧﺎﲡﺔ ﻋﻦ ﻇﺮﻭﻑ ﻏﲑ ﻃﺒﻴﻌﻴﺔ‪ ،‬ﻭﺗﺄﺧﺬ ﺍﻟﻘﻴﻤﺔ ﺍﻟﺘﺎﻟﻴﺔ ) ‪ .( x11 = 20, y11 = 0‬ﻟﻨﻔﺲ‬ ‫ﺍﻟﺒﻴﺎﻧﺎﺕ ﺍﻟﺴﺎﺑﻘﺔ‪.‬‬ ‫ﺣﻴﺚ ﺗﺘﻢ ﺍﶈﺎﻛﺎﺓ ﻟﻠﻌﻴﻨﺔ ﲢﺖ ﺍﻟﺸﺮﻭﻁ ﺍﻟﺘﺎﻟﻴﺔ‪) :‬ﺩ‪ .‬ﻋﺼﺎﻡ ﻭﺁﺧﺮﻭﻥ )‪.((2008‬‬ ‫) ‪y = β 0 + β1 x1 + ε i , yi ~ ! ( β 0 + β1 x1 , σ 2 ) , ε i ~ ! (0, σ 2‬‬ ‫) ‪βˆ0 ~ ! ( β 0 , σ 2 ( 1 n + X −2 ) / S xx ) , βˆ1 ~ ! ( β 1 , σ 2 / S xx‬‬

‫ﻭﻟﻘﺪ ﻗﻤﻨﺎ ﺑﺎﻻﺳﺘﻌﺎﻧﺔ ﺑﺎﻟﻨﻤﻮﺫﺟﲔ ﺍﻟﺘﺎﻟﻴﲔ ﻟﻠﻤﺤﺎﻛﺎﺓ‪:‬‬ ‫‪1) Y / X ~ ! (5 + 2 X ,2) , β 0 = 5 , β1 = 2 , σ 2 = 2‬‬ ‫‪2) Y / X ~ ! (5 + 2 X ,1) , β 0 = 5 , β1 = 2 , σ 2 = 1‬‬

‫ﺣﻴﺚ ﺃﻥ ﻗﻴﻢ ﺍﳌﺘﻐﲑ ﺍﳌﺴﺘﻘﻞ ‪ Xi‬ﺗﻜﻮﻥ ﳏﺪﺩﺓ ﻭﳝﻜﻦ ﺍﻟﺘﺤﻜﻢ ‪‬ﺎ ﻭﺗﻮﻟﻴﺪﻫﺎ ﺑﺸﻜﻞ ﻋﺸﻮﺍﺋﻲ ﺣﺴﺐ‬ ‫ﻣﺎ ﻧﺮﻏﺐ ﻭﻟﻘﺪ ﻗﻤﻨﺎ ﺑﺎﺧﺘﻴﺎﺭﻫﺎ ﺑﺸﻜﻞ ﻋﺸﻮﺍﺋﻲ ﲝﻴﺚ ﺗﻨﺘﻤﻲ ﻟﻔﺘﺮﺓ ﺍﻷﻋﺪﺍﺩ ﺍﻟﺼﺤﻴﺤﺔ ﻣﻦ ‪ 1‬ﺇﱃ‬ ‫‪ ،10‬ﺃﻣﺎ ﻗﻴﻢ ﺍﳌﺘﻐﲑ ﺍﻟﺘﺎﺑﻊ ﻓﻘﺪ ﰎ ﺗﻮﻟﻴﺪﻫﺎ ﺑﺎﻻﻋﺘﻤﺎﺩ ﻋﻠﻰ ﺍﻟﺘﻮﺯﻳﻊ ﺍﻟﺸﺮﻃﻲ )‪ ، Y / X ~ ! (5 + 2 x,2‬ﻭ‬ ‫ﺍﻟﺘﻮﺯﻳﻊ ﺍﻟﺸﺮﻃﻲ )‪ Y / X ~ ! (5 + 2 x,1‬ﻭﻣﻦ ﺍﳌﻔﻴﺪ ﺭﺳﻢ ﺑﻌﺾ ﺍﻟﺮﺳﻮﻣﺎﺕ ﳌﻌﺎﻳﻨﺔ ﻃﺒﻴﻌﻴﺔ ﺍﻟﺒﻴﺎﻧﺎﺕ‬ ‫ﺍﶈﺎﻛﺎﺓ ﻟﻨﻤﻮﺫﺝ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ ﻛﻤﺎ ﰲ ﺷﻜﻞ )‪.(5-1‬‬

‫‪60‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫ﺷﻜﻞ )‪ :(5-1‬ﺑﻌﺾ ﺍﻟﺮﺳﻮﻣﺎﺕ ﻟﻄﺒﻴﻌﻴﺔ ﺍﻟﺒﻴﺎﻧﺎﺕ ﺍﶈﺎﻛﺎﺓ‪.‬‬

‫ﻭﺑﻌﺪ ﺗﻜﺮﺍﺭ ﺍﻟﺘﺠﺮﺑﺔ ﻭﺍﶈﺎﻛﺎﺓ ﻟﻌﺪﺓ ﻣﺮﺍﺕ ﻓﺈﻧﻨﺎ ﺳﻮﻑ ﳓﺼﻞ ﻋﻠﻰ ﻗﻴﻢ ﳐﺘﻠﻔﺔ ﻟﻠﻤﺘﻐﲑ ﺍﻟﺘﺎﺑﻊ ﻣﻊ‬ ‫ﻣﻼﺣﻈﺔ ﺍﺳﺘﺨﺪﺍﻣﻨﺎ ﻟﻨﻔﺲ ﻣﻘﺪﺭﺍﺕ ﺍﻟﻨﻤﻮﺫﺝ ﺣﻴﺚ ﺃﻥ ﻣﻌﺎﱂ ﺍﻟﻨﻤﻮﺫﺝ ﻭﺍﻟﺘﺒﺎﻳﻦ ﻟﻸﺧﻄﺎﺀ ﺍﻟﻌﺸﻮﺍﺋﻴﺔ‬ ‫ﺗﻈﻬﺮ ﺑﺎﻟﺼﻮﺭﺓ ﺍﻟﺘﺎﻟﻴﺔ ﶈﺎﻛﺎﺓ ‪ 10‬ﳕﺎﺫﺝ ﻟﻼﳓﺪﺍﺭ ﺍﳋﻄﻲ ﺍﻟﺒﺴﻴﻂ ﻣﻊ ﺍﻟﺘﻮﺯﻳﻊ ﺍﻟﺸﺮﻃﻲ‬ ‫)‪. Y / X ~ ! (5 + 2 x,1‬‬ ‫ﺟﺪﻭﻝ )‪:(5-1‬‬ ‫‪Averages‬‬

‫‪10‬‬

‫‪9‬‬

‫‪8‬‬

‫‪7‬‬

‫‪6‬‬

‫‪5‬‬

‫‪4‬‬

‫‪3‬‬

‫‪2‬‬

‫‪1‬‬

‫‪i‬‬

‫‪5‬‬

‫‪4.7‬‬

‫‪5.41‬‬

‫‪5.01‬‬

‫‪6.88‬‬

‫‪2.9‬‬

‫‪3.6‬‬

‫‪6.1‬‬

‫‪6.29‬‬

‫‪6.33‬‬

‫‪4.13‬‬

‫‪β0‬‬

‫‪2‬‬

‫‪1.4‬‬

‫‪3.91‬‬

‫‪2.22‬‬

‫‪1.91‬‬

‫‪0.1‬‬

‫‪2.32‬‬

‫‪2.1‬‬

‫‪2.45‬‬

‫‪4.21‬‬

‫‪2.37‬‬

‫‪1‬‬

‫‪1.3‬‬

‫‪-1.5‬‬

‫‪1.04‬‬

‫‪1.96‬‬

‫‪2.8‬‬

‫‪1.72‬‬

‫‪1.3‬‬

‫‪0.68‬‬

‫‪1.67‬‬

‫‪0.88‬‬

‫‪β1‬‬ ‫‪σˆ ei2‬‬

‫)‬

‫)‬

‫ﺗﻄﺒﻴﻖ )‪-:(5-1‬‬ ‫ﺩﺍﻟﺔ ﺍﶈﺎﻛﺎﺓ ﺍﳌﺴﺘﺨﺪﻣﺔ ﺑﻮﺍﺳﻄﺔ ‪:SPSS‬‬ ‫‪COMPUTE Y=RV.NORMAL(5+2 * x+ RV.NORMAL(0,1),1).‬‬ ‫‪EXECUTE.‬‬

‫‪61‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫ﺃﻭ ﹰﻻ‪ :‬ﺍﶈﺎﻛﺎﺓ ﻟـ ‪ 100‬ﳕﻮﺫﺝ ﺍﻷﻭﱃ ﻋﻨﺪ ﻋﺪﻡ ﺇﺿﺎﻓﺔ ﺍﳌﺸﺎﻫﺪﺓ ﺍﳌﺆﺛﺮﺓ )ﻣﺸﺎﻫﺪﺓ ﺭﻗﻢ ‪ (11‬ﺣﻴﺚ‬ ‫ﺗﻜﻮﻥ ﺍﳌﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﺣﺴﺐ ﺍﳌﻘﺎﻳﻴﺲ ﺍﻟﺘﺎﻟﻴﺔ‪:‬‬ ‫‪DFFITS i > 0.894427‬‬ ‫‪DFBETAS i > 0.632455‬‬ ‫‪Di > 0.5‬‬ ‫‪0.8 < COVRATIOi < 1.6‬‬

‫ﺟﺪﻭﻝ)‪ :(5-2‬ﻋﺪﺩ ﺍﳊﺎﻻﺕ ﺍﳌﻜﺘﺸﻔﺔ ﻛﺤﺎﻻﺕ ﻣﺆﺛﺮﺓ ﰲ ﻇﻞ ﻋﺪﻡ ﻭﺟﻮﺩ ﺣﺎﻻﺕ ﻣﺆﺛﺮﺓ‪.‬‬ ‫‪DFB1‬‬

‫‪DFBo‬‬

‫‪DFFITS‬‬

‫‪COVR‬‬

‫‪Di‬‬

‫ﺍﻟﺘﺠﺮﺑﺔ‬

‫‪2‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪2‬‬

‫‪2‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬

‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬

‫‪4‬‬ ‫‪3‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪5‬‬ ‫‪5‬‬ ‫‪5‬‬ ‫‪3‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪3‬‬ ‫‪1‬‬ ‫‪5‬‬ ‫‪1‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪3‬‬ ‫‪3‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪5‬‬ ‫‪3‬‬ ‫‪5‬‬ ‫‪4‬‬ ‫‪3‬‬ ‫‪5‬‬ ‫‪1‬‬ ‫‪3‬‬

‫‪1‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪1‬‬

‫‪1‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪5‬‬ ‫‪6‬‬ ‫‪7‬‬ ‫‪8‬‬ ‫‪9‬‬ ‫‪10‬‬ ‫‪11‬‬ ‫‪12‬‬ ‫‪13‬‬ ‫‪14‬‬ ‫‪15‬‬ ‫‪16‬‬ ‫‪17‬‬ ‫‪18‬‬ ‫‪19‬‬ ‫‪20‬‬ ‫‪21‬‬ ‫‪22‬‬ ‫‪23‬‬ ‫‪24‬‬ ‫‪25‬‬ ‫‪26‬‬ ‫‪27‬‬ ‫‪28‬‬ ‫‪29‬‬ ‫‪30‬‬ ‫‪31‬‬ ‫‪32‬‬ ‫‪33‬‬ ‫‪34‬‬ ‫‪35‬‬ ‫‪36‬‬

‫‪62‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬ ‫‪DFB1‬‬

‫‪DFBo‬‬

‫‪DFFITS‬‬

‫‪COVR‬‬

‫‪Di‬‬

‫ﺍﻟﺘﺠﺮﺑﺔ‬

‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪3‬‬ ‫‪1‬‬ ‫‪3‬‬

‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬

‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪3‬‬ ‫‪1‬‬ ‫‪1‬‬

‫‪4‬‬ ‫‪5‬‬ ‫‪1‬‬ ‫‪4‬‬ ‫‪6‬‬ ‫‪3‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪6‬‬ ‫‪4‬‬ ‫‪3‬‬ ‫‪3‬‬ ‫‪3‬‬ ‫‪5‬‬ ‫‪3‬‬ ‫‪3‬‬ ‫‪3‬‬ ‫‪3‬‬ ‫‪3‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪5‬‬ ‫‪3‬‬ ‫‪3‬‬ ‫‪3‬‬ ‫‪3‬‬ ‫‪3‬‬ ‫‪3‬‬ ‫‪3‬‬ ‫‪1‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪4‬‬ ‫‪5‬‬ ‫‪5‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪2‬‬

‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪0‬‬

‫‪37‬‬ ‫‪38‬‬ ‫‪39‬‬ ‫‪40‬‬ ‫‪41‬‬ ‫‪42‬‬ ‫‪43‬‬ ‫‪44‬‬ ‫‪45‬‬ ‫‪46‬‬ ‫‪47‬‬ ‫‪48‬‬ ‫‪49‬‬ ‫‪50‬‬ ‫‪51‬‬ ‫‪52‬‬ ‫‪53‬‬ ‫‪54‬‬ ‫‪55‬‬ ‫‪56‬‬ ‫‪57‬‬ ‫‪58‬‬ ‫‪59‬‬ ‫‪60‬‬ ‫‪61‬‬ ‫‪62‬‬ ‫‪63‬‬ ‫‪64‬‬ ‫‪65‬‬ ‫‪66‬‬ ‫‪67‬‬ ‫‪68‬‬ ‫‪69‬‬ ‫‪70‬‬ ‫‪71‬‬ ‫‪72‬‬ ‫‪73‬‬ ‫‪74‬‬ ‫‪75‬‬ ‫‪76‬‬ ‫‪77‬‬ ‫‪78‬‬ ‫‪79‬‬ ‫‪80‬‬ ‫‪81‬‬ ‫‪82‬‬ ‫‪83‬‬ ‫‪84‬‬

‫‪63‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬ ‫‪DFB1‬‬

‫‪DFBo‬‬

‫‪DFFITS‬‬

‫‪COVR‬‬

‫‪Di‬‬

‫ﺍﻟﺘﺠﺮﺑﺔ‬

‫‪2‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪3‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪134‬‬ ‫‪13.4%‬‬

‫‪1‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪110‬‬ ‫‪11%‬‬

‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪3‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪133‬‬ ‫‪13.3%‬‬

‫‪3‬‬ ‫‪4‬‬ ‫‪4‬‬ ‫‪1‬‬ ‫‪3‬‬ ‫‪5‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪3‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪3‬‬ ‫‪5‬‬ ‫‪3‬‬ ‫‪3‬‬ ‫‪2‬‬ ‫‪320‬‬ ‫‪32%‬‬

‫‪1‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪70‬‬ ‫‪7%‬‬

‫‪85‬‬ ‫‪86‬‬ ‫‪87‬‬ ‫‪88‬‬ ‫‪89‬‬ ‫‪90‬‬ ‫‪91‬‬ ‫‪92‬‬ ‫‪93‬‬ ‫‪94‬‬ ‫‪95‬‬ ‫‪96‬‬ ‫‪97‬‬ ‫‪98‬‬ ‫‪99‬‬ ‫‪100‬‬ ‫=‪Total‬‬ ‫=‪Percent‬‬

‫ﺟﺪﻭﻝ )‪ :(5-3‬ﻣﻠﺨﺺ ﻋﺪﺩ ﺍﳊﺎﻻﺕ ﺍﳌﻜﺘﺸﻔﺔ ﻛﺤﺎﻻﺕ ﻣﺆﺛﺮﺓ )ﰲ ﻇﻞ ﻋﺪﻡ ﻭﺟﻮﺩ ﺣﺎﻻﺕ‬ ‫ﻣﺆﺛﺮﺓ(‪:‬‬ ‫‪Total‬‬

‫‪6‬‬

‫‪5‬‬

‫‪4‬‬

‫‪3‬‬

‫‪2‬‬

‫‪1‬‬

‫*‪0‬‬

‫ﺍﳌﻘﻴﺎﺱ‬

‫‪100‬‬

‫‪0‬‬

‫‪0‬‬

‫‪0‬‬

‫‪0‬‬

‫‪11‬‬

‫‪48‬‬

‫‪41‬‬

‫‪Di‬‬

‫‪100‬‬

‫‪2‬‬

‫‪14‬‬

‫‪16‬‬

‫‪44‬‬

‫‪18‬‬

‫‪6‬‬

‫‪0‬‬

‫‪100‬‬

‫‪0‬‬

‫‪0‬‬

‫‪0‬‬

‫‪2‬‬

‫‪35‬‬

‫‪57‬‬

‫‪6‬‬

‫‪100‬‬

‫‪0‬‬

‫‪0‬‬

‫‪0‬‬

‫‪0‬‬

‫‪31‬‬

‫‪48‬‬

‫‪21‬‬

‫‪100‬‬

‫‪0‬‬

‫‪0‬‬

‫‪0‬‬

‫‪4‬‬

‫‪38‬‬

‫‪46‬‬

‫‪12‬‬

‫‪COVR‬‬ ‫‪DFFITS‬‬ ‫‪DFBo‬‬ ‫‪DFB1‬‬

‫‪64‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫ﺭﺳﻮﻣﺎﺕ ﺗﻮﺿﻴﺤﻴﺔ ﻟﻌﺪﺩ ﺍﳊﺎﻻﺕ ﺍﳌﻜﺘﺸﻔﺔ ﻛﺤﺎﻻﺕ ﻣﺆﺛﺮﺓ )ﰲ ﻇﻞ ﻋﺪﻡ ﻭﺟﻮﺩ ﺣﺎﻻﺕ ﻣﺆﺛﺮﺓ(‪:‬‬ ‫ﺷﻜﻞ )‪ :(5-2‬ﺭﺳﻢ ﳌﻘﻴﺎﺱ ﻣﺴﺎﻓﺔ ﻛﻮﻙ ﻭ ﻣﻘﻴﺎﺱ ‪:COVR‬‬

‫ﺷﻜﻞ )‪ :(5-3‬ﺭﺳﻢ ﳌﻘﻴﺎﺱ ‪ DFFITS‬ﻭ ‪:DFBo‬‬

‫ﺷﻜﻞ )‪ :(5-4‬ﺭﺳﻢ ﳌﻘﻴﺎﺱ ‪:DFB1‬‬

‫ﺍﻟﻨﺘﺎﺋﺞ )ﺑﺪﻭﻥ ﺇﺿﺎﻓﺔ ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ(‪:‬‬ ‫ ﻋﺪﺩ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﺍﻟﱵ ﺍﻛﺘﺸﻔﺘﻬﺎ ﺍﳌﻘﺎﻳﻴﺲ ﲨﻴﻌﻬﺎ ﻋﻨﺪ ﻋﺪﻡ ﺇﺿﺎﻓﺔ ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ‬ ‫)ﻣﺸﺎﻫﺪﺓ ﺭﻗﻢ ‪ (11‬ﻟﻨﻔﺲ ﺍﳌﻘﺪﺭﺍﺕ ﲞﻄﺄ ﻋﺸﻮﺍﺋﻲ ﻳﺘﺒﻊ ﺍﻟﺘﻮﺯﻳﻊ ﺍﻟﻄﺒﻴﻌﻲ ﲟﺘﻮﺳﻂ ﺻﻔﺮ‬ ‫‪65‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫‬

‫‬

‫‬

‫ﻭﺗﺒﺎﻳﻦ ‪ . ε i ~ ! (0,2) 2‬ﺗﺴﺎﻭﻱ ‪ 767‬ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﻣﻦ ‪ 1000‬ﻣﺸﺎﻫﺪﺓ ﻣﻮﺯﻋﺔ ﻋﻠﻰ‬ ‫ﲨﻴﻊ ﺍﳌﻘﺎﻳﻴﺲ‪ ،‬ﻣﻦ ﳏﺎﻛﺎﺓ ‪ 100‬ﳕﻮﺫﺝ ﺍﳓﺪﺍﺭ ﺧﻄﻲ ﺑﺴﻴﻂ‪ .‬ﺑﻨﺴﺒﺔ ‪ %76.7‬ﻣﻦ ﳎﻤﻮﻉ‬ ‫ﺍﳌﺸﺎﻫﺪﺍﺕ‪ .‬ﲝﻴﺚ ﻳﻌﺘﱪ ﺍﻛﺘﺸﺎﻑ ﻫﺬﻩ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﻫﻨﺎ ﺑﺎﳋﻄﺄ ﻭﺗﺘﺒﺎﻳﻦ ﻫﺬﻩ ﺍﳌﻘﺎﻳﻴﺲ‬ ‫ﰲ ﲢﺪﻳﺪﻫﺎ ﺍﳋﺎﻃﺊ ﻋﻠﻰ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﻏﲑ ﺍﳌﺆﺛﺮﺓ ﻛﻤﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ‪ ،‬ﺣﻴﺚ‬ ‫ﺗﻔﻮﻗﺖ ﺑﻌﺾ ﺍﳌﻘﺎﻳﻴﺲ ﻋﻠﻰ ﺍﻷﺧﺮﻯ ﰲ ﻗﻠﺔ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﺑﺎﳋﻄﺄ‪ ،‬ﻭﰲ ﻣﺎ ﻳﻠﻲ‬ ‫ﺗﻔﺼﻴﻞ ﳍﺬﺍ ﺍﻻﺧﺘﻼﻑ‪.‬‬ ‫ﻣﻘﻴﺎﺱ ‪ :Di‬ﻳﻌﺘﱪ ﻣﻘﻴﺎﺱ ﻣﺴﺎﻓﺔ ﻛﻮﻙ ﻫﻮ ﺍﻷﻓﻀﻞ‪ .‬ﻷﻧﻪ ﺍﳌﻘﻴﺎﺱ ﺍﻟﺬﻱ ﺍﻛﺘﺸﻒ ﺍﻗﻞ‬ ‫ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﺑﺎﳋﻄﺄ‪ .‬ﲝﻴﺚ ﺃﻥ ﳎﻤﻮﻉ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﱵ ﺍﻛﺘﺸﻔﻬﺎ ﻫﺬﺍ ﺍﳌﻘﻴﺎﺱ ﺗﺴﺎﻭﻱ‬ ‫‪ 70‬ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﺑﺎﳋﻄﺄ‪ .‬ﻣﻦ ‪ 1000‬ﻣﺸﺎﻫﺪﺓ ﺑﻨﺴﺒﺔ ‪ %7‬ﻣﻦ ﳎﻤﻮﻉ ﺍﳌﺸﺎﻫﺪﺍﺕ‪.‬‬ ‫ﻭﺗﺘﻮﺯﻉ ﳎﻤﻮﻉ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺇﱃ ﺩﺭﺟﺎﺕ ﻓﻔﻲ ﺑﻌﺾ ﺍﻟﺘﺠﺎﺭﺏ ﺍﻛﺘﺸﻒ ﻣﻘﻴﺎﺱ ﻣﺴﺎﻓﺔ ﻛﻮﻙ‬ ‫ﰲ ‪ 48‬ﲡﺮﺑﺔ ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﻭﺍﺣﺪﺓ ﺑﺎﳋﻄﺄ ﺃﻱ ﺑﻨﺴﺒﺔ ‪ %48‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ ﺍﻛﺘﺸﻒ ‪‬ﺎ‬ ‫ﻣﺸﺎﻫﺪﺓ ﻭﺍﺣﺪﺓ ﻣﺆﺛﺮﺓ ﻭ ﰲ ‪ 11‬ﲡﺮﺑﺔ ﺍﻛﺘﺸﻒ ﻣﺸﺎﻫﺪﺗﲔ ﻣﺆﺛﺮﺓ ﻓﻘﻂ ﺑﻨﺴﺒﺔ ‪ %11‬ﺑﻴﻨﻤﺎ‬ ‫ﰲ ‪ 41‬ﲡﺮﺑﺔ ﱂ ﻳﻜﺘﺸﻒ ﺃﻱ ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ ﺃﻱ ﺑﻨﺴﺒﺔ ‪ %41‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ ﱂ ﻳﻜﺘﺸﻒ‬ ‫ﺃﻱ ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ‪ .‬ﻟﺬﻟﻚ ﺍﻋﺘﱪﻧﺎﻩ ﺃﻓﻀﻞ ﺍﳌﻘﺎﻳﻴﺲ ﺣﱴ ﺍﻵﻥ‪.‬‬ ‫ﻣﻘﻴﺎﺱ ‪ :COVR‬ﻳﻌﺘﱪ ﻫﺬﺍ ﺍﳌﻘﻴﺎﺱ ﻫﻮ ﺍﻷﺳﻮﺀ ﺑﲔ ﺍﳌﻘﺎﻳﻴﺲ ﻭﺫﻟﻚ ﻻﻛﺘﺸﺎﻓﻪ ﻣﺸﺎﻫﺪﺍﺕ‬ ‫ﻛﺜﲑﺓ ﻣﺆﺛﺮﺓ ﺑﺎﳋﻄﺄ‪ .‬ﲝﻴﺚ ﺍﻛﺘﺸﻒ ‪ 320‬ﻣﺸﺎﻫﺪﺓ ﻣﻦ ‪ 1000‬ﻣﺸﺎﻫﺪﺓ ﻭﺫﻟﻚ ﻣﻦ ﳏﺎﻛﺎﺓ‬ ‫‪ 100‬ﳕﻮﺫﺝ‪ .‬ﺑﻨﺴﺒﺔ ‪ %32.0‬ﻣﻦ ﳎﻤﻮﻉ ﺍﳌﺸﺎﻫﺪﺍﺕ‪ .‬ﻭﻗﺪ ﺗﻮﺯﻋﺖ ﻫﺬﻩ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺇﱃ‬ ‫ﺩﺭﺟﺎﺕ ﲝﻴﺚ ﺍﻛﺘﺸﻒ ﰲ ‪ 6‬ﲡﺎﺭﺏ ﻣﺸﺎﻫﺪﺓ ﻭﺍﺣﺪﺓ ﻓﻘﻂ ﻭﺫﻟﻚ ﺑﻨﺴﺒﺔ ‪ .%6‬ﻭ ‪18‬‬ ‫ﲡﺮﺑﺔ ﺍﻛﺘﺸﻒ ﻣﺸﺎﻫﺪﺗﲔ ﻣﺆﺛﺮﺓ ﺑﻨﺴﺒﺔ ‪ .%18‬ﻭ ‪ 44‬ﲡﺮﺑﺔ ﺍﻛﺘﺸﻒ ﻓﻴﻬﺎ ‪ 3‬ﻣﺸﺎﻫﺪﺍﺕ‬ ‫ﻣﺆﺛﺮﺓ ﺑﻨﺴﺒﺔ ‪ .%44‬ﻭ ‪ 16‬ﲡﺮﺑﺔ ﺍﻛﺘﺸﻒ ‪ 4‬ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ ﺑﻨﺴﺒﺔ ‪ .%16‬ﻭﺃﻳﻀﹰﺎ ‪14‬‬ ‫ﲡﺮﺑﺔ ﺍﻛﺘﺸﻒ ﻓﻴﻬﺎ ‪ 5‬ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ ﺑﻨﺴﺒﺔ ‪ .%14‬ﻭﲡﺮﺑﺘﲔ ﺍﻛﺘﺸﻒ ‪ 6‬ﻣﺸﺎﻫﺪﺍﺕ‬ ‫ﻣﺆﺛﺮﺓ ﺑﻨﺴﺒﺔ ‪ .%2‬ﻭﻧﻼﺣﻆ ﺃﻳﻀﹰﺎ ﺍﻧﻪ ﱂ ﺗﺴﻠﻢ ﺃﻱ ﲡﺮﺑﺔ ﱂ ﻳﻜﺘﺸﻒ ‪‬ﺎ ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ‬ ‫ﺑﺎﳋﻄﺄ ﲝﻴﺚ ﺍﻧﻪ ﰲ ‪ 100‬ﳕﻮﺫﺝ ﰲ ﻛﻞ ﻣﺮﺓ ﻳﻜﺘﺸﻒ ﻋﺪﺩ ﻣﻦ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﺑﺎﳋﻄﺄ‪.‬‬ ‫ﻟﺬﻟﻚ ﻳﻌﺘﱪ ﻣﻘﻴﺎﺱ ﺳﻲﺀ ﻟﻠﻐﺎﻳﺔ‪.‬‬ ‫ﻣﻘﻴﺎﺱ ‪ :DFFITS‬ﺍﻛﺘﺸﻒ ﻫﺬﺍ ﺍﳌﻘﻴﺎﺱ ‪ 133‬ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﻣﻦ ‪ 1000‬ﻣﺸﺎﻫﺪﺓ‬

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‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

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‫ﺑﻨﺴﺒﺔ ‪ %13.3‬ﻭﺗﻌﺘﱪ ﻫﺬﻩ ﺍﻟﻨﺴﺒﺔ ﻗﺮﻳﺒﺔ ﳌﻘﻴﺎﺱ ﻣﺴﺎﻓﺔ ﻛﻮﻙ‪ .‬ﻭﺗﺘﻮﺯﻉ ﻫﺬﻩ ﺍﳌﺸﺎﻫﺪﺍﺕ‬ ‫ﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻟﺸﻜﻞ ﺍﻟﺘﺎﱄ‪ 57 :‬ﲡﺮﺑﺔ ﺍﻛﺘﺸﻒ ‪‬ﺎ ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﻭﺍﺣﺪﺓ ﺃﻱ ﺑﻨﺴﺒﺔ ‪.%57‬‬ ‫ﻭ‪ 35‬ﲡﺮﺑﺔ ﺍﻛﺘﺸﻒ ‪‬ﺎ ﻣﺸﺎﻫﺪﻳﻦ ﻣﺆﺛﺮﺓ ﺑﻨﺴﺒﺔ ‪ %35‬ﻭ ﲡﺮﺑﺘﲔ ﻓﻘﻂ ﺍﻛﺘﺸﻒ ‪‬ﺎ ﺛﻼﺙ‬ ‫ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ ﺍﻱ ﺑﻨﺴﺒﺔ ‪ %2‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ ﺍﻛﺘﺸﻒ ‪‬ﺎ ﺛﻼﺙ ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ‪.‬‬ ‫ﻭﻧﻼﺣﻆ ﺃﻳﻀﹰﺎ ﺃﻥ ‪ 6‬ﲡﺎﺭﺏ ﱂ ﻳﻜﺘﺸﻒ ‪‬ﺎ ﺃﻱ ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ ﺃﻱ ﺍﻥ ‪ %6‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ‬ ‫ﱂ ﻳﻜﺘﺸﻒ ‪‬ﺎ ﺃﻱ ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ‪.‬‬ ‫ﻣﻘﻴﺎﺱ ‪ :DFBo‬ﳛﺘﻞ ﻫﺬﺍ ﺍﳌﻘﻴﺎﺱ ﺍﳌﺮﺗﺒﺔ ﺍﻟﺜﺎﻧﻴﺔ ﺑﻌﺪ ﻣﻘﻴﺎﺱ ﻣﺴﺎﻓﺔ ﻛﻮﻙ ﲝﻴﺚ ﺍﻧﻪ ﺍﻛﺘﺸﻒ‬ ‫‪ 110‬ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﻏﲑ ﻓﻌﻠﻴﺔ ﻣﻦ ‪ 1000‬ﻣﺸﺎﻫﺪﺓ‪ .‬ﺑﻨﺴﺒﺔ ‪ %11‬ﻭﺗﻌﺘﱪ ﻫﺬﻩ ﺍﻟﻨﺴﺒﺔ‬ ‫ﺍﻷﻗﺮﺏ ﺣﱴ ﺍﻵﻥ ﻟﻨﺴﺒﺔ ﻣﻘﻴﺎﺱ ﻣﺴﺎﻓﺔ ﻛﻮﻙ‪ .‬ﻭﺃﻳﻀﹰﺎ ﻳﻌﺘﱪ ﺍﻷﻗﻞ ﺍﻛﺘﺸﺎﻑ ﻟﻠﻤﺸﺎﻫﺪﺍﺕ‬ ‫ﺍﳌﺆﺛﺮﺓ ﺑﺎﳋﻄﺄ ﺑﻌﺪ ﻣﻘﻴﺎﺱ ﻣﺴﺎﻓﺔ ﻛﻮﻙ‪ .‬ﺣﻴﺚ ﺗﺘﻮﺯﻉ ﻋﺪﺩ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﻜﺘﺸﻔﺔ‬ ‫ﻛﻤﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ ﻛﺎﻟﺘﺎﱄ‪ 48 :‬ﲡﺮﺑﺔ ﺍﻛﺘﺸﻒ ‪‬ﺎ ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﻭﺍﺣﺪﺓ ﺃﻱ ﺃﻥ ﰲ ‪%48‬‬ ‫ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ ﺍﻛﺘﺸﻒ ‪‬ﺎ ﻣﺸﺎﻫﺪﺓ ﻭﺍﺣﺪﺓ ﻣﺆﺛﺮﺓ ﻓﻘﻂ‪ .‬ﻭ‪ 31‬ﲡﺮﺑﺔ ﺍﻛﺘﺸﻒ ‪‬ﺎ ﻣﺸﺎﻫﺪﺗﲔ‬ ‫ﻣﺆﺛﺮﺓ ﺑﻨﺴﺒﺔ ‪ %31‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ‪ .‬ﻣﻊ ﻣﻼﺣﻈﺔ ﺍﻧﻪ ﰲ ‪ 21‬ﲡﺮﺑﺔ ﺃﻭ ﺑﻨﺴﺒﺔ ‪ %21‬ﱂ‬ ‫ﻳﻜﺘﺸﻒ ﺃﻱ ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ ﻋﻠﻰ ﻫﺬﻩ ﺍﻟﻨﻤﺎﺫﺝ‪.‬‬ ‫ﻣﻘﻴﺎﺱ ‪ :DFB1‬ﻫﺬﺍ ﺍﳌﻘﻴﺎﺱ ﺍﻛﺘﺸﻒ ‪ 134‬ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﺑﺎﳋﻄﺄ ﻣﻦ ‪ 1000‬ﻣﺸﺎﻫﺪﺓ‬ ‫ﺑﻨﺴﺒﺔ ‪ .%13.4‬ﻭﻳﻌﺘﱪ ﻫﺬﺍ ﺍﳌﻘﻴﺎﺱ ﺃﺳﻮﺀ ﻣﻦ ﻣﻘﻴﺎﺱ ‪ DFBo‬ﺑﺪﺭﺟﺔ ﺑﺴﻴﻄﺔ‪ .‬ﺣﻴﺚ‬ ‫ﺗﻘﺴﻤﺖ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻟﺘﺠﺎﺭﺏ ﻛﺎﻟﺘﺎﱄ‪ 46 :‬ﲡﺮﺑﺔ ﺍﻛﺘﺸﻒ ‪‬ﺎ ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ‬ ‫ﻭﺍﺣﺪﺓ ﺑﻨﺴﺒﺔ ‪ %46‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ‪ .‬ﻭ‪ 38‬ﲡﺮﺑﺔ ﺃﻭ ﺑﻨﺴﺒﺔ ‪ %38‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ ﺍﻛﺘﺸﻒ ‪‬ﺎ‬ ‫ﻣﺸﺎﻫﺪﺗﲔ ﻣﺆﺛﺮﺓ ﻭ ‪ 4‬ﲡﺎﺭﺏ ﺃﻭ ‪ %4‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ ﺍﻛﺘﺸﻒ ‪‬ﺎ ‪ 3‬ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ ‪.‬‬ ‫ﻭﺃﻳﻀﹰﺎ ﻫﻨﺎﻙ ‪ 12‬ﲡﺮﺑﺔ ﱂ ﻳﻜﺘﺸﻒ ‪‬ﺎ ﺃﻱ ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ ﺃﻱ ﺃﻥ ﻧﺴﺒﺔ ﺍﻟﺘﺠﺎﺭﺏ ﺍﻟﱵ ﱂ‬ ‫ﻳﻜﺘﺸﻒ ‪‬ﺎ ﺃﻱ ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ ﻫﻲ ‪.%12‬‬

‫ﺛﺎﻧﻴﹰﺎ‪ :‬ﺍﶈﺎﻛﺎﺓ ﻟـ ‪ 100‬ﳕﻮﺫﺝ ﻋﻨﺪ ﺇﺿﺎﻓﺔ ﺍﳌﺸﺎﻫﺪﺓ ﺍﳌﺆﺛﺮﺓ )ﻣﺸﺎﻫﺪﺓ ﺭﻗﻢ ‪ (11‬ﻟﻨﻔﺲ ﺍﻟﺒﻴﺎﻧﺎﺕ‬ ‫ﺍﻟﺴﺎﺑﻘﺔ ﺣﻴﺚ ﺗﻜﻮﻥ ﺍﳌﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﺣﺴﺐ ﺍﳌﻘﺎﻳﻴﺲ ﺍﻟﺘﺎﻟﻴﺔ‪:‬‬

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‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬ ‫‪DFFITS i > 0.852802‬‬ ‫‪DFBETAS i > 0.603022‬‬ ‫‪Di > 0.44444‬‬ ‫‪0.4545 < COVRATIOi < 1.5454‬‬

‫ﺟﺪﻭﻝ)‪ :(5-4‬ﻋﺪﺩ ﺍﳊﺎﻻﺕ ﺍﳌﻜﺘﺸﻔﺔ ﻛﺤﺎﻻﺕ ﻣﺆﺛﺮﺓ ﰲ ﻇﻞ ﻭﺟﻮﺩ ﺣﺎﻟﺔ ﻣﺆﺛﺮﺓ ﻭﺍﺣﺪﺓ‪.‬‬ ‫‪DFB1‬‬

‫‪DFBo‬‬

‫‪DFFITS‬‬

‫‪COVR‬‬

‫‪Di‬‬

‫ﺍﻟﺘﺠﺮﺑﺔ‬

‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪3‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬

‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬

‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬

‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬

‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬

‫‪1‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪5‬‬ ‫‪6‬‬ ‫‪7‬‬ ‫‪8‬‬ ‫‪9‬‬ ‫‪10‬‬ ‫‪11‬‬ ‫‪12‬‬ ‫‪13‬‬ ‫‪14‬‬ ‫‪15‬‬ ‫‪16‬‬ ‫‪17‬‬ ‫‪18‬‬ ‫‪19‬‬ ‫‪20‬‬ ‫‪21‬‬ ‫‪22‬‬ ‫‪23‬‬ ‫‪24‬‬ ‫‪25‬‬ ‫‪26‬‬ ‫‪27‬‬ ‫‪28‬‬ ‫‪29‬‬ ‫‪30‬‬ ‫‪31‬‬ ‫‪32‬‬ ‫‪33‬‬ ‫‪34‬‬ ‫‪35‬‬ ‫‪36‬‬ ‫‪37‬‬ ‫‪38‬‬ ‫‪39‬‬ ‫‪40‬‬

‫‪68‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬ ‫‪DFB1‬‬

‫‪DFBo‬‬

‫‪DFFITS‬‬

‫‪COVR‬‬

‫‪Di‬‬

‫ﺍﻟﺘﺠﺮﺑﺔ‬

‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪3‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬

‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪3‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬

‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪3‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬

‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬

‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬

‫‪41‬‬ ‫‪42‬‬ ‫‪43‬‬ ‫‪44‬‬ ‫‪45‬‬ ‫‪46‬‬ ‫‪47‬‬ ‫‪48‬‬ ‫‪49‬‬ ‫‪50‬‬ ‫‪51‬‬ ‫‪52‬‬ ‫‪53‬‬ ‫‪54‬‬ ‫‪55‬‬ ‫‪56‬‬ ‫‪57‬‬ ‫‪58‬‬ ‫‪59‬‬ ‫‪60‬‬ ‫‪61‬‬ ‫‪62‬‬ ‫‪63‬‬ ‫‪64‬‬ ‫‪65‬‬ ‫‪66‬‬ ‫‪67‬‬ ‫‪68‬‬ ‫‪69‬‬ ‫‪70‬‬ ‫‪71‬‬ ‫‪72‬‬ ‫‪73‬‬ ‫‪74‬‬ ‫‪75‬‬ ‫‪76‬‬ ‫‪77‬‬ ‫‪78‬‬ ‫‪79‬‬ ‫‪80‬‬ ‫‪81‬‬ ‫‪82‬‬ ‫‪83‬‬ ‫‪84‬‬ ‫‪85‬‬ ‫‪86‬‬ ‫‪87‬‬ ‫‪88‬‬

‫‪69‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬ ‫‪DFB1‬‬

‫‪DFBo‬‬

‫‪DFFITS‬‬

‫‪COVR‬‬

‫‪Di‬‬

‫ﺍﻟﺘﺠﺮﺑﺔ‬

‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪129‬‬ ‫‪12.9%‬‬

‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪148‬‬ ‫‪14.8%‬‬

‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪137‬‬ ‫‪13.7%‬‬

‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪112‬‬ ‫‪11.2%‬‬

‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪112‬‬ ‫‪11.2%‬‬

‫‪89‬‬ ‫‪90‬‬ ‫‪91‬‬ ‫‪92‬‬ ‫‪93‬‬ ‫‪94‬‬ ‫‪95‬‬ ‫‪96‬‬ ‫‪97‬‬ ‫‪98‬‬ ‫‪99‬‬ ‫‪100‬‬ ‫=‪Total‬‬ ‫=‪Percent‬‬

‫ﺟﺪﻭﻝ)‪ :(5-5‬ﻣﻠﺨﺺ ﻋﺪﺩ ﺍﳊﺎﻻﺕ ﺍﳌﻜﺘﺸﻔﺔ ﻛﺤﺎﻻﺕ ﻣﺆﺛﺮﺓ )ﰲ ﻇﻞ ﻭﺟﻮﺩ ﺣﺎﻟﺔ ﻣﺆﺛﺮﺓ‬ ‫ﻭﺍﺣﺪﺓ(‪.‬‬ ‫‪Total‬‬

‫‪6‬‬

‫‪5‬‬

‫‪4‬‬

‫‪3‬‬

‫‪2‬‬

‫*‪1‬‬

‫‪0‬‬

‫ﺍﳌﻘﻴﺎﺱ‬

‫‪100‬‬

‫‪0‬‬

‫‪0‬‬

‫‪0‬‬

‫‪0‬‬

‫‪12‬‬

‫‪88‬‬

‫‪0‬‬

‫‪100‬‬

‫‪0‬‬

‫‪0‬‬

‫‪0‬‬

‫‪0‬‬

‫‪12‬‬

‫‪88‬‬

‫‪0‬‬

‫‪Di‬‬ ‫‪COVR‬‬

‫‪100‬‬

‫‪0‬‬

‫‪0‬‬

‫‪0‬‬

‫‪1‬‬

‫‪35‬‬

‫‪64‬‬

‫‪0‬‬

‫‪100‬‬

‫‪0‬‬

‫‪0‬‬

‫‪0‬‬

‫‪4‬‬

‫‪40‬‬

‫‪56‬‬

‫‪0‬‬

‫‪100‬‬

‫‪0‬‬

‫‪0‬‬

‫‪0‬‬

‫‪2‬‬

‫‪25‬‬

‫‪73‬‬

‫‪0‬‬

‫‪DFFITS‬‬ ‫‪DFBo‬‬ ‫‪DFB1‬‬

‫ﺭﺳﻮﻣﺎﺕ ﺗﻮﺿﻴﺤﻴﺔ ﻟﻌﺪﺩ ﺍﳊﺎﻻﺕ ﺍﳌﻜﺘﺸﻔﺔ ﻛﺤﺎﻻﺕ ﻣﺆﺛﺮﺓ )ﰲ ﻇﻞ ﻭﺟﻮﺩ ﺣﺎﻟﺔ ﻣﺆﺛﺮﺓ ﻭﺍﺣﺪﺓ(‪.‬‬ ‫ﺷﻜﻞ )‪ :(5-5‬ﺭﺳﻢ ﳌﻘﻴﺎﺱ ﻣﺴﺎﻓﺔ ﻛﻮﻙ ﻭ ﻣﻘﻴﺎﺱ ‪:COVR‬‬

‫‪70‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫ﺷﻜﻞ )‪ :(5-6‬ﺭﺳﻢ ﳌﻘﻴﺎﺱ ‪ DFFITS‬ﻭ ‪:DFBo‬‬

‫ﺷﻜﻞ )‪ :(5-7‬ﺭﺳﻢ ﳌﻘﻴﺎﺱ ‪:DFB1‬‬

‫ﺍﻟﻨﺘﺎﺋﺞ )ﻣﻊ ﺇﺿﺎﻓﺔ ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ(‪:‬‬ ‫ﻳﻼﺣﻆ ﻋﺪﺓ ﻣﻼﺣﻈﺎﺕ‪:‬‬ ‫ ﻋﺪﺩ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﺍﻟﱵ ﺍﻛﺘﺸﻔﺘﻬﺎ ﺍﳌﻘﺎﻳﻴﺲ ﲨﻴﻌﻬﺎ ﻋﻨﺪ ﺇﺿﺎﻓﺔ ﺍﳌﺸﺎﻫﺪﺓ ﺍﳌﺆﺛﺮﺓ ﻣﺸﺎﻫﺪﺓ‬ ‫ﺭﻗﻢ ‪ 11‬ﺗﺴﺎﻭﻱ ‪ 638‬ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﻣﻦ ‪ 1000‬ﻣﺸﺎﻫﺪﺓ ﻣﻮﺯﻋﺔ ﻋﻠﻰ ﲨﻴﻊ ﺍﳌﻘﺎﻳﻴﺲ‪.‬‬ ‫ﺑﻨﺴﺒﺔ ‪ %63.8‬ﻣﻦ ﲨﻴﻊ ﺍﳌﺸﺎﻫﺪﺍﺕ‪ .‬ﻛﻤﺎ ﻳﻼﺣﻆ ﻣﻦ ﺍﻟﺮﺳﻮﻣﺎﺕ ﺍﻟﺘﻮﺿﻴﺤﻴﺔ ﺗﻄﺎﺑﻖ ﺃﻭ‬ ‫ﺗﺸﺎﺑﻪ ﺑﻌﺾ ﺍﳌﻘﺎﻳﻴﺲ ﰲ ﻋﺪﺩ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ‪ .‬ﲝﻴﺚ ﺗﺸﺎﺑﻪ ﻣﻘﻴﺎﺱ ﻣﺴﺎﻓﺔ ﻛﻮﻙ‬ ‫‪ Di‬ﻣﻊ ﻣﻘﻴﺎﺱ ‪ COVR‬ﻭﻣﻘﻴﺎﺱ ‪ DFFITS‬ﻣﻊ ﻣﻘﻴﺎﺱ ‪ .DFBETAS‬ﻭﺫﻟﻚ‬ ‫ﺣﺴﺐ ﻧﻈﺮﺓ ﺃﻭﻟﻴﺔ ﻟﻠﺮﺳﻮﻣﺎﺕ ﺍﻟﺘﻮﺿﻴﺤﻴﺔ‪.‬‬ ‫ ﻣﻘﻴﺎﺱ ‪ :Di‬ﻣﺎ ﺯﺍﻝ ﻣﻘﻴﺎﺱ ﻣﺴﺎﻓﺔ ﻛﻮﻙ ﻫﻮ ﺍﻷﻓﻀﻞ ﲝﻴﺚ ﺍﻧﻪ ﺍﻛﺘﺸﻒ ‪ 112‬ﻣﺸﺎﻫﺪﺓ‬ ‫ﻣﺆﺛﺮﺓ ﻣﻦ ‪ 1000‬ﻣﺸﺎﻫﺪﺓ‪ .‬ﻣﻨﻬﺎ ‪ 12‬ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﺑﺎﳋﻄﺄ ﺃﻱ ﺍﻧﻪ ﺍﻛﺘﺸﻒ ﻣﺸﺎﻫﺪﺍﺕ‬ ‫ﻣﺆﺛﺮﺓ ﺑﺎﳋﻄﺄ ﺑﻨﺴﺒﺔ ‪ %1.2‬ﻣﻦ ﳎﻤﻮﻉ ﺍﳌﺸﺎﻫﺪﺍﺕ ﻭ ‪ 100‬ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﺣﻘﻴﻘﺔ ﻭﻫﻲ‬ ‫‪71‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

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‫ﺍﳌﺸﺎﻫﺪﺓ ﺭﻗﻢ ‪ 11‬ﺍﻟﱵ ﻗﻤﻨﺎ ﺑﺈﺿﺎﻓﺘﻬﺎ ﶈﺎﻛﺎﺓ ‪ 100‬ﳕﻮﺫﺝ ﺍﳓﺪﺍﺭ‪ .‬ﻭﺫﻟﻚ ﺑﻨﺴﺒﺔ ‪%11.2‬‬ ‫ﻣﻦ ﳎﻤﻮﻉ ﺍﳌﺸﺎﻫﺪﺍﺕ‪ .‬ﲝﻴﺚ ﺗﻮﺯﻋﺖ ﻫﺬﻩ ﺍﳌﺸﺎﻫﺪﺍﺕ ﻛﺎﻟﺘﺎﱄ‪ 88 :‬ﲡﺮﺑﻪ ﺍﻭ ‪ %88‬ﻣﻦ‬ ‫ﺍﻟﺘﺠﺎﺭﺏ ﺍﻛﺘﺸﻒ ‪‬ﺎ ﺍﳌﻘﻴﺎﺱ ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﻭﺍﺣﺪﺓ ﻭﻫﻲ ﺍﳌﺸﺎﻫﺪﺓ ﺍﻟﱵ ﻗﻤﻨﺎ ﺑﺈﺿﺎﻓﺘﻬﺎ‪.‬‬ ‫ﻭ‪ 12‬ﲡﺮﺑﺔ ﺃﻭ ‪ %12‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ ﺍﻛﺘﺸﻒ ‪‬ﺎ ﻣﺸﺎﻫﺪﺗﲔ ﻣﺆﺛﺮﺓ ﺍﺣﺪﻫﺎ ﺍﳌﺸﺎﻫﺪﺓ ﺍﻟﱵ ﻗﻤﻨﺎ‬ ‫ﺑﺈﺿﺎﻓﺘﻬﺎ ﻭﺍﻷﺧﺮﻯ ﺗﻌﺘﱪ ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﻣﻜﺘﺸﻔﺔ ﺑﺎﳋﻄﺄ‪.‬‬ ‫ﻣﻘﻴﺎﺱ ‪ :COVR‬ﻳﻼﺣﻆ ﻫﻨﺎ ﺃﻥ ﻫﺬﺍ ﺍﳌﻘﻴﺎﺱ ﺗﻄﺎﺑﻖ ﲤﺎﻣﹰﺎ ﻣﻊ ﻣﻘﻴﺎﺱ ﻣﺴﺎﻓﺔ ﻛﻮﻙ ﰲ‬ ‫ﻋﺪﺩ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﺍﳌﻜﺘﺸﻔﺔ ﻭﺃﻳﻀﹰﺎ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﺑﺎﳋﻄﺄ‪ .‬ﲝﻴﺚ ﺗﻮﺯﻋﺖ ﻫﺬﻩ‬ ‫ﺍﳌﺸﺎﻫﺪﺍﺕ ﻋﻠﻰ ﺍﻟﺸﻜﻞ ﺍﻟﺘﺎﱄ‪ 88 :‬ﲡﺮﺑﺔ ﺃﻭ ‪ %88‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ ﺍﻛﺘﺸﻒ ‪‬ﺎ ﺍﳌﻘﻴﺎﺱ‬ ‫ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﻭﺍﺣﺪﺓ ﻭﻫﻲ ﺍﳌﺸﺎﻫﺪﺓ ﺍﻟﱵ ﻗﻤﻨﺎ ﺑﺈﺿﺎﻓﺘﻬﺎ‪ .‬ﻭ‪ 12‬ﲡﺮﺑﺔ ﺃﻭ ‪ %12‬ﻣﻦ‬ ‫ﺍﻟﺘﺠﺎﺭﺏ ﺍﻛﺘﺸﻒ ‪‬ﺎ ﻣﺸﺎﻫﺪﺗﲔ ﻣﺆﺛﺮﺓ ﺍﺣﺪﻫﺎ ﺍﳌﺸﺎﻫﺪﺓ ﺍﻟﱵ ﻗﻤﻨﺎ ﺑﺈﺿﺎﻓﺘﻬﺎ ﻭﺍﻷﺧﺮﻯ ﺗﻌﺘﱪ‬ ‫ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﻣﻜﺘﺸﻔﺔ ﺑﺎﳋﻄﺄ‪.‬‬ ‫ﻣﻘﻴﺎﺱ ‪ :DFFITS‬ﺍﻛﺘﺸﻒ ﻫﺬﺍ ﺍﳌﻘﻴﺎﺱ ﺑﻌﺪ ﺇﺿﺎﻓﺔ ﺍﳌﺸﺎﻫﺪﺓ ﺍﳌﺆﺛﺮﺓ ‪ 137‬ﻣﺸﺎﻫﺪﺓ‬ ‫ﻣﺆﺛﺮﺓ ﻣﻦ ‪ 1000‬ﻣﺸﺎﻫﺪﺓ‪ .‬ﺑﻨﺴﺒﺔ ‪ %13.7‬ﻣﻦ ﳎﻤﻮﻉ ﺍﳌﺸﺎﻫﺪﺍﺕ ﲝﻴﺚ ﺯﺍﺩ ﲟﻘﺪﺍﺭ ‪37‬‬ ‫ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﺍﻛﺘﺸﻔﻬﺎ ﺑﺎﳋﻄﺄ ﺃﻱ ﺍﻧﻪ ﺍﻛﺘﺸﻒ ﺑﻨﺴﺒﺔ ‪ %3.7‬ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﻣﻦ ﳎﻤﻮﻉ‬ ‫ﺍﳌﺸﺎﻫﺪﺍﺕ‪ .‬ﻭﻳﻼﺣﻆ ﻫﻨﺎ ﺍﻧﻪ ﺃﺳﻮﺀ ﻣﻦ ﺍﳌﻘﺎﻳﻴﺲ ﺍﻟﺴﺎﺑﻘﺔ ‪ Di‬ﻭ ‪ COVR‬ﻷﻧﻪ ﺍﻛﺘﺸﻒ‬ ‫‪ 25‬ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﺑﺎﳋﻄﺄ ﻏﲑ ﺍﻟﱵ ﺍﻛﺘﺸﻔﻬﺎ ﺍﳌﻘﺎﻳﻴﺲ ﺍﻟﺴﺎﺑﻘﺔ ﺃﻱ ﺍﻧﻪ ﺯﺍﺩ ﻋﻦ ﺍﳌﻘﺎﻳﻴﺲ‬ ‫ﺍﻟﺴﺎﺑﻘﺔ ﰲ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﺑﺎﳋﻄﺄ ﺑﻨﺴﺒﺔ ‪ %2.5‬ﻟﺬﻟﻚ ﺍﻋﺘﱪﻧﺎﻩ ﺃﺳﻮﺀ‪ .‬ﻭﺣﻴﺚ‬ ‫ﺗﻮﺯﻋﺖ ﻫﺬﻩ ﺍﳌﺸﺎﻫﺪﺍﺕ ﻋﻠﻰ ﺍﻟﺘﺠﺎﺭﺏ ﺑﺎﻟﺸﻜﻞ ﺍﻟﺘﺎﱄ‪ 64 :‬ﲡﺮﺑﺔ ﺃﻭ ‪ %46‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ‬ ‫ﺃﻛﺘﺸﻒ ‪‬ﺎ ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﻭﺍﺣﺪﺓ ﻓﻘﻂ ) ﻣﺸﺎﻫﺪﺓ ﺭﻗﻢ ‪ .(11‬ﻭ‪ 35‬ﲡﺮﺑﻪ ﺃﻭ ‪ %35‬ﻣﻦ‬ ‫ﺍﻟﺘﺠﺎﺭﺏ ﺍﻛﺘﺸﻒ ‪‬ﺎ ﻣﺸﺎﻫﺪﺗﲔ ﻣﺆﺛﺮﺓ‪ .‬ﻛﺬﻟﻚ ﰲ ﲡﺮﺑﺔ ﻭﺍﺣﺪﺓ ﺃﻭ ﺑﻨﺴﺒﺔ ‪ %1‬ﻣﻦ‬ ‫ﺍﻟﺘﺠﺎﺭﺏ ﺍﻛﺘﺸﻒ ﺛﻼﺙ ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ‪.‬‬ ‫ﻣﻘﻴﺎﺱ ‪ :DFBo‬ﻳﻌﺘﱪ ﻫﺬﺍ ﺍﳌﻘﻴﺎﺱ ﻫﻨﺎ ﻫﻮ ﺍﻷﺳﻮﺀ ﻣﻦ ﺍﳌﻘﺎﻳﻴﺲ ﲨﻴﻌﻬﺎ ﻻﻛﺘﺸﺎﻓﻪ ﻛﺜﲑ ﻣﻦ‬ ‫ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﺑﺎﳋﻄﺄ‪ .‬ﺣﻴﺚ ﺍﻛﺘﺸﻒ ‪ 148‬ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﻣﻦ ‪ 1000‬ﻣﺸﺎﻫﺪﺓ‬ ‫ﺑﻨﺴﺒﺔ ‪ %14.8‬ﻣﻦ ﳎﻤﻮﻉ ﺍﳌﺸﺎﻫﺪﺍﺕ ﻭﻳﻌﺘﱪ ﺣﱴ ﺍﻵﻥ ﻫﻮ ﺍﳌﻘﻴﺎﺱ ﺍﻟﺬﻱ ﺍﻛﺘﺸﻒ ﺍﻛﱪ‬ ‫ﻋﺪﺩ ﻣﻦ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﺑﺎﳋﻄﺄ‪ .‬ﻭﻳﻔﺼﻠﻪ ﻋﻦ ﻣﻘﻴﺎﺱ ﻣﺴﺎﻓﺔ ﻛﻮﻙ ‪ 36‬ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ‬

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‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫‬

‫ﺑﺎﳋﻄﺄ ﺃﻱ ﺍﻧﻪ ﻳﺰﻳﺪ ﺑﻨﺴﺒﺔ ‪ %3.6‬ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﺑﺎﳋﻄﺄ ﻋﻠﻰ ﻣﻘﻴﺎﺱ ﻣﺴﺎﻓﺔ ﻛﻮﻙ‪ .‬ﺣﻴﺚ‬ ‫ﺗﻮﺯﻋﺖ ﻣﺸﺎﻫﺪﺍﺕ ﻫﺬﺍ ﺍﳌﻘﻴﺎﺱ ﻋﻠﻰ ﺍﻟﺸﻜﻞ ﺍﻟﺘﺎﱄ‪ 56 :‬ﲡﺮﺑﺔ ﺃﻭ ‪ %56‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ ‪‬ﺎ‬ ‫ﻣﺸﺎﻫﺪﺓ ﻭﺍﺣﺪﺓ ﻭ‪ 40‬ﲡﺮﺑﺔ ﺍﻭ ‪ %40‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ ﺍﻛﺘﺸﻒ ‪‬ﺎ ﻣﺸﺎﻫﺪﺗﲔ ﻣﺆﺛﺮﺓ ﻭ ‪4‬‬ ‫ﲡﺎﺭﺏ ﺑﻨﺴﺒﺔ ‪ %4‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ ﺍﻛﺘﺸﻒ ‪‬ﺎ ﺛﻼﺙ ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ‪.‬‬ ‫ﻣﻘﻴﺎﺱ ‪ :DFB1‬ﺍﻛﺘﺸﻒ ﻫﺬﺍ ﺍﳌﻘﻴﺎﺱ ‪ 129‬ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﻣﻦ ‪ 1000‬ﻣﺸﺎﻫﺪﺓ ﻭﺗﻌﺘﱪ‬ ‫‪ 29‬ﻣﺸﺎﻫﺪﺓ ﻣﻦ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﺍﳋﺎﻃﺌﺔ ﺃﻭ ‪ %2.9‬ﻣﻦ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﻜﺘﺸﻔﺔ ﺑﺎﳋﻄﺄ‪.‬‬ ‫ﻭﻳﻔﺼﻠﻪ ﻋﻦ ﻣﻘﻴﺎﺱ ﻣﺴﺎﻓﺔ ﻛﻮﻙ ﺑﻌﺪﺩ ‪ 17‬ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﺍﻛﺘﺸﻔﺖ ﺑﺎﳋﻄﺄ ﺃﻱ ﺑﻨﺴﺒﺔ‬ ‫‪ %1.7‬ﺣﻴﺚ ﺗﻮﺯﻋﺖ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﻜﺘﺸﻔﺔ ﻛﺎﻟﺘﺎﱄ‪ 73 :‬ﲡﺮﺑﺔ ﺃﻭ ‪ %73‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ‬ ‫ﺍﻛﺘﺸﻒ ‪‬ﺎ ﻣﺸﺎﻫﺪﺓ ﻭﺍﺣﺪﺓ ﻭﻫﻲ ﺍﳌﺸﺎﻫﺪﺓ ﺭﻗﻢ ‪ 11‬ﻭ ‪ 25‬ﲡﺮﺑﺔ ﺃﻭ ‪ %25‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ‬ ‫ﺍﻛﺘﺸﻒ ‪‬ﺎ ﻣﺸﺎﻫﺪﺗﲔ ﻣﺆﺛﺮﺓ‪ .‬ﻭﲡﺮﺑﺘﲔ ﺃﻭ ‪ %2‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ ﺍﻛﺘﺸﻒ ‪‬ﺎ ‪ 3‬ﻣﺸﺎﻫﺪﺍﺕ‬ ‫ﻣﺆﺛﺮﺓ‪.‬‬

‫ﻭﺃﺧﲑﹰﺍ ﻳﻌﺘﱪ ﻣﻘﻴﺎﺱ ﻣﺴﺎﻓﺔ ﻛﻮﻙ ﻫﻮ ﺍﻷﻓﻀﻞ ﰲ ﻛﻠﺘﺎ ﺍﳊﺎﻟﺘﲔ ﺍﻟﺴﺎﺑﻘﺔ ﻋﻨﺪ ﺇﺿﺎﻓﺔ ﺍﳌﺸﺎﻫﺪﺓ‬ ‫ﺍﳌﺆﺛﺮﺓ ﺃﻭ ﻋﺪﻡ ﺇﺿﺎﻓﺘﻬﺎ ﻭﻳﻼﺣﻆ ﻣﻦ ﺧﻼﻝ ﺍﻟﺮﺳﻮﻣﺎﺕ ﺍﻧﻪ ﺗﻔﻮﻕ ﻋﻠﻰ ﲨﻴﻊ ﺍﳌﻘﺎﻳﻴﺲ ﰲ ﻗﻠﺔ ﺍﻛﺘﺸﺎﻓﻪ‬ ‫ﻟﻠﻤﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﺑﺎﳋﻄﺄ‪.‬‬ ‫ﺗﻄﺒﻴﻖ )‪-:(5-2‬‬ ‫ﺩﺍﻟﺔ ﺍﶈﺎﻛﺎﺓ ﺍﳌﺴﺘﺨﺪﻣﺔ ﺑﻮﺍﺳﻄﺔ ‪.SPSS‬‬ ‫‪COMPUTE Y=RV.NORMAL(5+2 * x,1).‬‬ ‫‪EXECUTE.‬‬

‫ﺃﻭ ﹰﻻ‪ :‬ﺍﶈﺎﻛﺎﺓ ﻟـ ‪ 100‬ﳕﻮﺫﺝ ﺍﻷﻭﱃ ﻋﻨﺪ ﻋﺪﻡ ﺇﺿﺎﻓﺔ ﺍﳌﺸﺎﻫﺪﺓ ﺍﳌﺆﺛﺮﺓ )ﻣﺸﺎﻫﺪﺓ ﺭﻗﻢ ‪: (11‬‬ ‫ﺗﻜﻮﻥ ﺍﳌﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﺣﺴﺐ ﺍﳌﻘﺎﻳﻴﺲ ﺍﻟﺘﺎﻟﻴﺔ‪:‬‬ ‫‪DFFITS i > 0.894427‬‬ ‫‪DFBETAS i > 0.632455‬‬ ‫‪Di > 0.5‬‬ ‫‪0.8 < COVRATIOi < 1.6‬‬

‫‪73‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫ﺟﺪﻭﻝ)‪ :(5-6‬ﻋﺪﺩ ﺍﳊﺎﻻﺕ ﺍﳌﻜﺘﺸﻔﺔ ﻛﺤﺎﻻﺕ ﻣﺆﺛﺮﺓ ﰲ ﻇﻞ ﻋﺪﻡ ﻭﺟﻮﺩ ﺣﺎﻻﺕ ﻣﺆﺛﺮﺓ‪.‬‬ ‫‪DFB1‬‬

‫‪DFBo‬‬

‫‪DFFITS‬‬

‫‪COVR‬‬

‫‪Di‬‬

‫ﺍﻟﺘﺠﺮﺑﺔ‬

‫‪0‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪3‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪3‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪3‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬

‫‪0‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪3‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪3‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪0‬‬

‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪3‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪3‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬

‫‪4‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪4‬‬ ‫‪6‬‬ ‫‪3‬‬ ‫‪3‬‬ ‫‪3‬‬ ‫‪3‬‬ ‫‪3‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪3‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪2‬‬ ‫‪5‬‬ ‫‪2‬‬ ‫‪4‬‬ ‫‪2‬‬ ‫‪4‬‬ ‫‪3‬‬ ‫‪3‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪4‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪4‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪2‬‬ ‫‪4‬‬ ‫‪5‬‬ ‫‪5‬‬ ‫‪5‬‬ ‫‪1‬‬ ‫‪5‬‬ ‫‪2‬‬ ‫‪4‬‬ ‫‪5‬‬

‫‪0‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪0‬‬

‫‪1‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪5‬‬ ‫‪6‬‬ ‫‪7‬‬ ‫‪8‬‬ ‫‪9‬‬ ‫‪10‬‬ ‫‪11‬‬ ‫‪12‬‬ ‫‪13‬‬ ‫‪14‬‬ ‫‪15‬‬ ‫‪16‬‬ ‫‪17‬‬ ‫‪18‬‬ ‫‪19‬‬ ‫‪20‬‬ ‫‪21‬‬ ‫‪22‬‬ ‫‪23‬‬ ‫‪24‬‬ ‫‪25‬‬ ‫‪26‬‬ ‫‪27‬‬ ‫‪28‬‬ ‫‪29‬‬ ‫‪30‬‬ ‫‪31‬‬ ‫‪32‬‬ ‫‪33‬‬ ‫‪34‬‬ ‫‪35‬‬ ‫‪36‬‬ ‫‪37‬‬ ‫‪38‬‬ ‫‪39‬‬ ‫‪40‬‬ ‫‪41‬‬ ‫‪42‬‬ ‫‪43‬‬ ‫‪44‬‬ ‫‪45‬‬ ‫‪46‬‬

‫‪74‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬ ‫‪DFB1‬‬

‫‪DFBo‬‬

‫‪DFFITS‬‬

‫‪COVR‬‬

‫‪Di‬‬

‫ﺍﻟﺘﺠﺮﺑﺔ‬

‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬

‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬

‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪3‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬

‫‪2‬‬ ‫‪3‬‬ ‫‪2‬‬ ‫‪4‬‬ ‫‪5‬‬ ‫‪4‬‬ ‫‪4‬‬ ‫‪4‬‬ ‫‪6‬‬ ‫‪5‬‬ ‫‪3‬‬ ‫‪5‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪4‬‬ ‫‪4‬‬ ‫‪4‬‬ ‫‪4‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪4‬‬ ‫‪4‬‬ ‫‪4‬‬ ‫‪4‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪3‬‬ ‫‪5‬‬ ‫‪4‬‬ ‫‪3‬‬ ‫‪5‬‬ ‫‪4‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪3‬‬ ‫‪5‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪2‬‬

‫‪0‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪0‬‬

‫‪47‬‬ ‫‪48‬‬ ‫‪49‬‬ ‫‪50‬‬ ‫‪51‬‬ ‫‪52‬‬ ‫‪53‬‬ ‫‪54‬‬ ‫‪55‬‬ ‫‪56‬‬ ‫‪57‬‬ ‫‪58‬‬ ‫‪59‬‬ ‫‪60‬‬ ‫‪61‬‬ ‫‪62‬‬ ‫‪63‬‬ ‫‪64‬‬ ‫‪65‬‬ ‫‪66‬‬ ‫‪67‬‬ ‫‪68‬‬ ‫‪69‬‬ ‫‪70‬‬ ‫‪71‬‬ ‫‪72‬‬ ‫‪73‬‬ ‫‪74‬‬ ‫‪75‬‬ ‫‪76‬‬ ‫‪77‬‬ ‫‪78‬‬ ‫‪79‬‬ ‫‪80‬‬ ‫‪81‬‬ ‫‪82‬‬ ‫‪83‬‬ ‫‪84‬‬ ‫‪85‬‬ ‫‪86‬‬ ‫‪87‬‬ ‫‪88‬‬ ‫‪89‬‬ ‫‪90‬‬ ‫‪91‬‬ ‫‪92‬‬ ‫‪93‬‬ ‫‪94‬‬

‫‪75‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬ ‫‪DFB1‬‬

‫‪DFBo‬‬

‫‪DFFITS‬‬

‫‪COVR‬‬

‫‪Di‬‬

‫ﺍﻟﺘﺠﺮﺑﺔ‬

‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪125‬‬ ‫‪12.5%‬‬

‫‪2‬‬ ‫‪2‬‬ ‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪117‬‬ ‫‪11.7%‬‬

‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪125‬‬ ‫‪12.5%‬‬

‫‪2‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪4‬‬ ‫‪3‬‬ ‫‪2‬‬ ‫‪330‬‬ ‫‪33%‬‬

‫‪0‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪63‬‬ ‫‪6.3%‬‬

‫‪95‬‬ ‫‪96‬‬ ‫‪97‬‬ ‫‪98‬‬ ‫‪99‬‬ ‫‪100‬‬ ‫=‪Total‬‬ ‫=‪Percent‬‬

‫ﺟﺪﻭﻝ )‪ :(5-7‬ﻣﻠﺨﺺ ﻋﺪﺩ ﺍﳊﺎﻻﺕ ﺍﳌﻜﺘﺸﻔﺔ ﻛﺤﺎﻻﺕ ﻣﺆﺛﺮﺓ )ﰲ ﺿﻞ ﻋﺪﻡ ﻭﺟﻮﺩ ﺣﺎﻻﺕ‬ ‫ﻣﺆﺛﺮﺓ(‪.‬‬ ‫‪Total‬‬

‫‪6‬‬

‫‪5‬‬

‫‪4‬‬

‫‪3‬‬

‫‪2‬‬

‫‪1‬‬

‫*‪0‬‬

‫ﺍﳌﻘﻴﺎﺱ‬

‫‪100‬‬

‫‪0‬‬

‫‪0‬‬

‫‪0‬‬

‫‪0‬‬

‫‪14‬‬

‫‪35‬‬

‫‪51‬‬

‫‪100‬‬

‫‪2‬‬

‫‪12‬‬

‫‪32‬‬

‫‪27‬‬

‫‪22‬‬

‫‪5‬‬

‫‪0‬‬

‫‪100‬‬

‫‪0‬‬

‫‪0‬‬

‫‪0‬‬

‫‪3‬‬

‫‪33‬‬

‫‪50‬‬

‫‪14‬‬

‫‪100‬‬

‫‪0‬‬

‫‪0‬‬

‫‪0‬‬

‫‪3‬‬

‫‪33‬‬

‫‪42‬‬

‫‪22‬‬

‫‪100‬‬

‫‪0‬‬

‫‪0‬‬

‫‪0‬‬

‫‪3‬‬

‫‪40‬‬

‫‪36‬‬

‫‪21‬‬

‫‪Di‬‬ ‫‪COVR‬‬ ‫‪DFFITS‬‬ ‫‪DFBo‬‬ ‫‪DFB1‬‬

‫ﺭﺳﻮﻣﺎﺕ ﺗﻮﺿﻴﺤﻴﺔ ﻟﻌﺪﺩ ﺍﳊﺎﻻﺕ ﺍﳌﻜﺘﺸﻔﺔ ﻛﺤﺎﻻﺕ ﻣﺆﺛﺮﺓ )ﰲ ﺿﻞ ﻋﺪﻡ ﻭﺟﻮﺩ ﺣﺎﻻﺕ ﻣﺆﺛﺮﺓ(‪.‬‬ ‫ﺷﻜﻞ )‪ :(5-8‬ﺭﺳﻢ ﳌﻘﻴﺎﺱ ﻣﺴﺎﻓﺔ ﻛﻮﻙ ﻭ ﻣﻘﻴﺎﺱ ‪:COVR‬‬

‫‪76‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫ﺷﻜﻞ )‪ :(5-9‬ﺭﺳﻢ ﳌﻘﻴﺎﺱ ‪ DFFITS‬ﻭ ‪:DFBo‬‬

‫ﺷﻜﻞ )‪ :(5-10‬ﺭﺳﻢ ﳌﻘﻴﺎﺱ ‪:DFB1‬‬

‫ﺍﻟﻨﺘﺎﺋﺞ )ﺑﺪﻭﻥ ﺇﺿﺎﻓﺔ ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ(‪:‬‬ ‫ﻳﻼﺣﻆ ﻋﺪﺓ ﻣﻼﺣﻈﺎﺕ‪:‬‬ ‫ ﻋﺪﺩ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﺍﻟﱵ ﺍﻛﺘﺸﻔﺘﻬﺎ ﺍﳌﻘﺎﻳﻴﺲ ﲨﻴﻌﻬﺎ ﻋﻨﺪ ﻋﺪﻡ ﺇﺿﺎﻓﺔ ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ‬ ‫)ﻣﺸﺎﻫﺪﺓ ﺭﻗﻢ ‪ (11‬ﻟﻨﻔﺲ ﺍﳌﻘﺪﺭﺍﺕ ﲞﻄﺄ ﻋﺸﻮﺍﺋﻲ ﻳﺘﺒﻊ ﺍﻟﺘﻮﺯﻳﻊ ﺍﻟﻄﺒﻴﻌﻲ ﲟﺘﻮﺳﻂ ﺻﻔﺮ‬ ‫ﻭﺗﺒﺎﻳﻦ ‪ . ε i ~ ! (0,1) 1‬ﺗﺴﺎﻭﻱ ‪ 760‬ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﻣﻦ ‪ 1000‬ﻣﺸﺎﻫﺪﺓ ﻣﻮﺯﻋﺔ ﻋﻠﻰ‬ ‫ﲨﻴﻊ ﺍﳌﻘﺎﻳﻴﺲ‪ ،‬ﻣﻦ ﳏﺎﻛﺎﺓ ‪ 100‬ﳕﻮﺫﺝ ﺍﳓﺪﺍﺭ ﺧﻄﻲ ﺑﺴﻴﻂ‪ .‬ﺑﻨﺴﺒﺔ ‪ %76‬ﻣﻦ ﳎﻤﻮﻉ‬ ‫ﺍﳌﺸﺎﻫﺪﺍﺕ‪ .‬ﲝﻴﺚ ﺗﻌﺘﱪ ﺍﻛﺘﺸﺎﻑ ﻫﺬﻩ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﻫﻨﺎ ﺑﺎﳋﻄﺄ ﻭﻣﻊ ﻣﻼﺣﻈﺔ ﺃﻥ ﻋﺪﺩ‬ ‫ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﻜﺘﺸﻔﺔ ﺑﺎﳋﻄﺄ ﻫﻨﺎ ﱂ ﺗﺒﺘﻌﺪ ﻛﺜﲑﹰﺍ ﻋﻦ ﺍﻟﺘﻄﺒﻴﻖ ﺍﻟﺴﺎﺑﻖ )ﺗﻄﺒﻴﻖ ‪ (5-1‬ﺣﻴﺚ‬ ‫ﻛﺎﻥ ﺍﻟﻔﺮﻕ ‪ 7‬ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ ﺑﺎﳋﻄﺄ ﻓﻘﻂ ﺃﻱ ﺃﻥ ﺍﻟﻔﺮﻕ ﺑﲔ ﻫﺬﺍ ﺍﻟﺘﻄﺒﻴﻖ ﻭﺍﻟﺘﻄﺒﻴﻖ ﺍﻟﺴﺎﺑﻖ‬ ‫)ﺗﻄﺒﻴﻖ ‪ (5-1‬ﺑﻨﺴﺒﺔ ‪ . %0.7‬ﻭﻣﻦ ﺧﻼﻝ ﺍﻟﺮﺳﻢ ﺍﻟﺘﻮﺿﻴﺤﻲ ﻳﻼﺣﻆ ﺗﺸﺎﺑﻪ ﺍﳌﻘﺎﻳﻴﺲ‬ ‫‪ DFFITS‬ﻭ ‪ DFBo‬ﺗﻘﺮﻳﺒﹰﺎ ﰲ ﻋﺪﺩ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﺑﺎﳋﻄﺄ‪ .‬ﻭﻳﺘﻢ ﺗﻮﺯﻳﻊ‬ ‫‪77‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫‬

‫‬

‫‬

‫ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﻜﺘﺸﻔﺔ ﻛﺎﻟﺘﺎﱄ‪:‬‬ ‫ﻣﻘﻴﺎﺱ ‪ :Di‬ﻣﻘﻴﺎﺱ ﻣﺴﺎﻓﺔ ﻛﻮﻙ ﻫﻨﺎ ﻳﻌﺘﱪ ﺃﻓﻀﻞ ﺍﳌﻘﺎﻳﻴﺲ ﲝﻴﺚ ﺍﻛﺘﺸﻒ ﺍﻗﻞ ﻋﺪﺩ ﻣﻦ‬ ‫ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﺑﺎﳋﻄﺄ‪ .‬ﻭﻛﺎﻧﺖ ﺑﻌﺪﺩ ‪ 63‬ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﺑﺎﳋﻄﺄ ﻣﻦ ‪ 1000‬ﻣﺸﺎﻫﺪﺓ‬ ‫ﺑﻨﺴﺒﺔ ‪ %6.3‬ﻭﻧﻼﺣﻆ ﻋﻨﺪﻣﺎ ﻗﻞ ﺍﻟﺘﺒﺎﻳﻦ ﺑﺎﻟﻨﺴﺒﺔ ﻟﻠﺘﻄﺒﻴﻖ ﺍﻟﺴﺎﺑﻖ ﺯﺍﺩﺕ ﻗﺪﺭﺕ ﻫﺬﺍ ﺍﳌﻘﻴﺎﺱ‬ ‫ﰲ ﻋﺪﻡ ﺍﻛﺘﺸﺎﻑ ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ ﺑﺎﳋﻄﺄ ﺣﻴﺚ ﺃﻥ ﺍﻟﻔﺮﻕ ﻳﺴﺎﻭﻱ ‪ 7‬ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ‬ ‫ﺑﺎﳋﻄﺄ ﻋﻦ ﺍﻟﺘﻄﺒﻴﻖ ﺍﻟﺴﺎﺑﻖ )ﺗﻄﺒﻴﻖ ‪ (5-1‬ﺑﻨﺴﺒﺔ ‪ %0.7‬ﻣﻊ ﻣﻼﺣﻈﺔ ﺍﻧﻪ ﺍﳌﻘﻴﺎﺱ ﺍﻟﺬﻱ ﺗﺄﺛﺮ‬ ‫ﺑﺎﺧﺘﻼﻑ ﺍﻟﺘﺒﺎﻳﻦ ﻣﻦ ‪ 2‬ﺇﱃ ‪ 1‬ﺑﺎﳌﻘﺎﺭﻧﺔ ﻣﻊ ﺍﻟﺘﻄﺒﻴﻖ ﺍﻟﺴﺎﺑﻖ‪ .‬ﺣﻴﺚ ﺗﻮﺯﻋﺖ ﺍﳌﺸﺎﻫﺪﺍﺕ‬ ‫ﺍﳌﺆﺛﺮﺓ ﻫﻨﺎ ﻋﻠﻰ ﺍﻟﺘﺠﺎﺭﺏ ﺑﺎﻟﺸﻜﻞ ﺍﻟﺘﺎﱄ‪ 35 :‬ﲡﺮﺑﺔ ﺃﻭ ‪ %35‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ ﺍﻛﺘﺸﻒ ‪‬ﺎ‬ ‫ﻣﺸﺎﻫﺪﺓ ﻭﺍﺣﺪﺓ ﻣﺆﺛﺮﺓ‪ .‬ﻭ‪ 14‬ﲡﺮﺑﻪ ﺃﻭ ‪ %14‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ ﺍﻛﺘﺸﻒ ‪‬ﺎ ﻣﺸﺎﻫﺪﺗﲔ ﻣﺆﺛﺮﺓ‪.‬‬ ‫ﻭ ‪ 51‬ﲡﺮﺑﺔ ﺍﻭ ‪ %51‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ ﱂ ﻳﻜﺘﺸﻒ ‪‬ﺎ ﺃﻱ ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ‪.‬‬ ‫ﻣﻘﻴﺎﺱ ‪ :COVR‬ﺍﻛﺘﺸﻒ ﻫﺬﺍ ﺍﳌﻘﻴﺎﺱ ﻋﺪﺩ ‪ 330‬ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﻣﻦ ‪ 1000‬ﻣﺸﺎﻫﺪﺓ‬ ‫ﺑﻨﺴﺒﺔ ‪ .%33‬ﲝﻴﺚ ﺃ‪‬ﺎ ﲨﻴﻌﹰﺎ ﺍﻛﺘﺸﻔﺖ ﺑﺎﳋﻄﺄ ﻛﻤﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ ﻭﻳﻌﺘﱪ ﻫﺬﺍ ﺍﳌﻘﻴﺎﺱ‬ ‫ﺳﻲﺀ ﺑﺎﻟﻨﺴﺒﺔ ﻟﻠﻤﻘﺎﻳﻴﺲ ﺍﻷﺧﺮﻯ‪ .‬ﻭﺗﻮﺯﻋﺖ ﻫﺬﻩ ﺍﳌﺸﺎﻫﺪﺍﺕ ﻋﻠﻰ ﺍﻟﺘﺠﺎﺭﺏ ﺑﺎﻟﺸﻜﻞ ﺍﻟﺘﺎﱄ‪:‬‬ ‫‪ 5‬ﲡﺎﺭﺏ ﺃﻭ ‪ %5‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ ﺍﻛﺘﺸﻒ ‪‬ﺎ ﻣﺸﺎﻫﺪﺓ ﻭﺍﺣﺪﺓ ﻣﺆﺛﺮﺓ‪ .‬ﻭ‪ 22‬ﲡﺮﺑﺔ ﺃﻭ ‪%22‬‬ ‫ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ ﺍﻛﺘﺸﻒ ‪‬ﺎ ﻣﺸﺎﻫﺪﺗﲔ ﻣﺆﺛﺮﺓ‪ .‬ﻭ ‪ 27‬ﲡﺮﺑﺔ ﺃﻭ ‪ %27‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ ﺍﻛﺘﺸﻒ‬ ‫‪‬ﺎ ‪ 3‬ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ ﻭ ‪ 32‬ﲡﺮﺑﺔ ﺃﻭ ‪ %32‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ ﺍﻛﺘﺸﻒ ‪‬ﺎ ‪ 4‬ﻣﺸﺎﻫﺪﺍﺕ‬ ‫ﻣﺆﺛﺮﺓ‪ .‬ﻭ‪ 12‬ﲡﺮﺑﺔ ﺃﻭ ‪ %12‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ ﺍﻛﺘﺸﻒ ‪‬ﺎ ‪ 5‬ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ ﻭ ﲡﺮﺑﺘﲔ ﺍﻭ‬ ‫‪ %2‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ ﺍﻛﺘﺸﻒ ‪‬ﺎ ‪ 6‬ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ‪ .‬ﺣﻴﺚ ﱂ ﻳﺴﻠﻢ ﺃﻱ ﳕﻮﺫﺝ ﻣﻦ ﻋﺪﻡ‬ ‫ﺍﻛﺘﺸﺎﻑ ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ ﺣﺴﺐ ﻣﺎ ﺃﻋﻄﻰ ﻣﻘﻴﺎﺱ ‪ COVR‬ﰲ ﺍﻟﻨﺘﺎﺋﺞ ﺍﻟﺴﺎﺑﻘﺔ‪.‬‬ ‫ﻣﻘﻴﺎﺱ ‪ :DFFITS‬ﺍﻛﺘﺸﻒ ﻫﺬﺍ ﺍﳌﻘﻴﺎﺱ ‪ 125‬ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﺑﺎﳋﻄﺄ ﻣﻦ ‪1000‬‬ ‫ﻣﺸﺎﻫﺪﺓ ﺑﻨﺴﺒﺔ ‪ %12.5‬ﻭﻛﺎﻧﺖ ﺍﳌﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ ﺍﳌﻜﺘﺸﻔﺔ ﺗﺘﻮﺯﻉ ﻋﻠﻰ ﺍﻟﺘﺠﺎﺭﺏ‬ ‫ﻛﺎﻟﺘﺎﱄ‪ 50 :‬ﲡﺮﺑﺔ ﺃﻭ ‪ %50‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ ﺍﻛﺘﺸﻒ ‪‬ﺎ ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﻭﺍﺣﺪﺓ ﻓﻘﻂ‪33 .‬‬ ‫ﲡﺮﺑﺔ ﺃﻭ ‪ %33‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ ﺍﻛﺘﺸﻒ ‪‬ﺎ ﻣﺸﺎﻫﺪﺗﲔ ﻣﺆﺛﺮﺓ‪ 3 .‬ﲡﺎﺭﺏ ﺃﻭ ‪ %3‬ﻣﻦ‬ ‫ﺍﻟﺘﺠﺎﺭﺏ ﺍﻛﺘﺸﻒ ‪‬ﺎ ‪ 3‬ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ‪ .‬ﻭﺃﻳﻀﹰﺎ ﻫﻨﺎﻙ ‪ 14‬ﲡﺮﺑﺔ ﺃﻭ ‪ %14‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ‬ ‫ﱂ ﻳﻜﺘﺸﻒ ‪‬ﺎ ﺃﻱ ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ‪.‬‬

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‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬ ‫‬

‫‬

‫ﻣﻘﻴﺎﺱ ‪ :DFBo‬ﻳﻌﺘﱪ ﻫﺬﺍ ﺍﳌﻘﻴﺎﺱ ﻫﻨﺎ ﺑﻌﺪ ﻣﻘﻴﺎﺱ ﻣﺴﺎﻓﺔ ﻛﻮﻙ ﰲ ﺍﻛﺘﺸﺎﻑ ﺍﻗﻞ‬ ‫ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﺑﺎﳋﻄﺄ ﲝﻴﺚ ﺍﻛﺘﺸﻒ ‪ 117‬ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﺑﺎﳋﻄﺄ ﻣﻦ ‪ 1000‬ﻣﺸﺎﻫﺪﺓ‬ ‫ﺑﻨﺴﺒﺔ ‪ %11.7‬ﺣﻴﺚ ﺗﺘﻮﺯﻉ ﻫﺬﻩ ﺍﳌﺸﺎﻫﺪﺍﺕ ﻋﻠﻰ ﺍﻟﺘﺠﺎﺭﺏ ﻛﺎﻟﺘﺎﱄ‪ :‬ﰲ ‪ 42‬ﲡﺮﺑﺔ ﺃﻭ‬ ‫‪ %42‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ ﺍﻛﺘﺸﻒ ‪‬ﺎ ﻣﺸﺎﻫﺪﺓ ﻭﺍﺣﺪﺓ ﻣﺆﺛﺮﺓ ﻓﻘﻂ‪ .‬ﻭ ‪ 33‬ﲡﺮﺑﺔ ﺃﻭ ‪ %33‬ﻣﻦ‬ ‫ﺍﻟﺘﺠﺎﺭﺏ ﺍﻛﺘﺸﻒ ‪‬ﺎ ﻣﺸﺎﻫﺪﺗﲔ ﻣﺆﺛﺮﺓ‪ .‬ﻭ‪ 3‬ﲡﺎﺭﺏ ﺃﻭ ‪ %3‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ ﺍﻛﺘﺸﻒ ‪‬ﺎ‬ ‫ﺛﻼﺙ ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ‪ .‬ﻭﻳﻼﺣﻆ ﺃﻥ ﰲ ‪ 22‬ﲡﺮﺑﺔ ﺃﻭ ‪ %22‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ ﱂ ﻳﻜﺘﺸﻒ‬ ‫ﺍﳌﻘﻴﺎﺱ ﺃﻱ ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ‪.‬‬ ‫ﻣﻘﻴﺎﺱ ‪ :DFB1‬ﺍﻛﺘﺸﻒ ﻫﺬﺍ ﺍﳌﻘﻴﺎﺱ ‪ 125‬ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﺑﺎﳋﻄﺄ ﻣﻦ ‪ 1000‬ﻣﺸﺎﻫﺪﺓ‬ ‫ﺑﻨﺴﺒﺔ ‪ %12.5‬ﲝﻴﺚ ﺗﻮﺯﻋﺖ ﻋﻠﻰ ﺍﻟﺘﺠﺎﺭﺏ ﻛﺎﻟﺘﺎﱄ‪ 36 :‬ﲡﺮﺑﻪ ﺃﻭ ‪ %36‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ‬ ‫ﺍﻛﺘﺸﻒ ‪‬ﺎ ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﻭﺍﺣﺪﺓ ﻓﻘﻂ‪ .‬ﻭ‪ 40‬ﲡﺮﺑﺔ ﺃﻭ ‪ %40‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ ﺍﻛﺘﺸﻒ ‪‬ﺎ‬ ‫ﻣﺸﺎﻫﺪﻳﻦ ﻣﺆﺛﺮﺓ‪ .‬ﻭ‪ 3‬ﲡﺎﺭﺏ ﺃﻭ ‪ %3‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ ﺍﻛﺘﺸﻒ ‪‬ﺎ ﺛﻼﺙ ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ‪.‬‬ ‫ﻭﻣﻊ ﻣﻼﺣﻈﺔ ﺍﻧﻪ ﰲ ‪ 21‬ﲡﺮﺑﺔ ﱂ ﻳﻜﺘﺸﻒ ﺃﻱ ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ ﺑﻨﺴﺒﺔ ‪.%21‬‬

‫ﺛﺎﻧﻴﹰﺎ‪ :‬ﺍﶈﺎﻛﺎﺓ ﻟـ ‪ 100‬ﳕﻮﺫﺝ ﻋﻨﺪ ﺇﺿﺎﻓﺔ ﺍﳌﺸﺎﻫﺪﺓ ﺍﳌﺆﺛﺮﺓ )ﻣﺸﺎﻫﺪﺓ ﺭﻗﻢ ‪ (11‬ﻟﻨﻔﺲ ﺍﻟﺒﻴﺎﻧﺎﺕ‬ ‫ﺍﻟﺴﺎﺑﻘﺔ ﲝﻴﺚ ﺗﻜﻮﻥ ﺍﳌﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﺣﺴﺐ ﺍﳌﻘﺎﻳﻴﺲ ﺍﻟﺘﺎﻟﻴﺔ‪:‬‬ ‫‪DFFITS i > 0.852802‬‬ ‫‪DFBETAS i > 0.603022‬‬ ‫‪Di > 0.44444‬‬ ‫‪0.4545 < COVRATIOi < 1.5454‬‬

‫ﺟﺪﻭﻝ)‪ :(5-8‬ﻋﺪﺩ ﺍﳊﺎﻻﺕ ﺍﳌﻜﺘﺸﻔﺔ ﻛﺤﺎﻻﺕ ﻣﺆﺛﺮﺓ ﰲ ﻇﻞ ﻭﺟﻮﺩ ﺣﺎﻻﺕ ﻣﺆﺛﺮﺓ‪.‬‬ ‫‪DFB1‬‬

‫‪DFBo‬‬

‫‪DFFITS‬‬

‫‪COVR‬‬

‫‪Di‬‬

‫ﺍﻟﺘﺠﺮﺑﺔ‬

‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬

‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬

‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬

‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬

‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬

‫‪1‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪4‬‬ ‫‪5‬‬ ‫‪6‬‬ ‫‪7‬‬ ‫‪8‬‬ ‫‪9‬‬ ‫‪10‬‬

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‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬ ‫‪DFB1‬‬

‫‪DFBo‬‬

‫‪DFFITS‬‬

‫‪COVR‬‬

‫‪Di‬‬

‫ﺍﻟﺘﺠﺮﺑﺔ‬

‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬

‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬

‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬

‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬

‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬

‫‪11‬‬ ‫‪12‬‬ ‫‪13‬‬ ‫‪14‬‬ ‫‪15‬‬ ‫‪16‬‬ ‫‪17‬‬ ‫‪18‬‬ ‫‪19‬‬ ‫‪20‬‬ ‫‪21‬‬ ‫‪22‬‬ ‫‪23‬‬ ‫‪24‬‬ ‫‪25‬‬ ‫‪26‬‬ ‫‪27‬‬ ‫‪28‬‬ ‫‪29‬‬ ‫‪30‬‬ ‫‪31‬‬ ‫‪32‬‬ ‫‪33‬‬ ‫‪34‬‬ ‫‪35‬‬ ‫‪36‬‬ ‫‪37‬‬ ‫‪38‬‬ ‫‪39‬‬ ‫‪40‬‬ ‫‪41‬‬ ‫‪42‬‬ ‫‪43‬‬ ‫‪44‬‬ ‫‪45‬‬ ‫‪46‬‬ ‫‪47‬‬ ‫‪48‬‬ ‫‪49‬‬ ‫‪50‬‬ ‫‪51‬‬ ‫‪52‬‬ ‫‪53‬‬ ‫‪54‬‬ ‫‪55‬‬ ‫‪56‬‬ ‫‪57‬‬ ‫‪58‬‬

‫‪80‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬ ‫‪DFB1‬‬

‫‪DFBo‬‬

‫‪DFFITS‬‬

‫‪COVR‬‬

‫‪Di‬‬

‫ﺍﻟﺘﺠﺮﺑﺔ‬

‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪101‬‬ ‫‪10.1%‬‬

‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪182‬‬ ‫‪18.2%‬‬

‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪100‬‬ ‫‪10%‬‬

‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪100‬‬ ‫‪10%‬‬

‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪100‬‬ ‫‪10%‬‬

‫‪59‬‬ ‫‪60‬‬ ‫‪61‬‬ ‫‪62‬‬ ‫‪63‬‬ ‫‪64‬‬ ‫‪65‬‬ ‫‪66‬‬ ‫‪67‬‬ ‫‪68‬‬ ‫‪69‬‬ ‫‪70‬‬ ‫‪71‬‬ ‫‪72‬‬ ‫‪73‬‬ ‫‪74‬‬ ‫‪75‬‬ ‫‪76‬‬ ‫‪77‬‬ ‫‪78‬‬ ‫‪79‬‬ ‫‪80‬‬ ‫‪81‬‬ ‫‪82‬‬ ‫‪83‬‬ ‫‪84‬‬ ‫‪85‬‬ ‫‪86‬‬ ‫‪87‬‬ ‫‪88‬‬ ‫‪89‬‬ ‫‪90‬‬ ‫‪91‬‬ ‫‪92‬‬ ‫‪93‬‬ ‫‪94‬‬ ‫‪95‬‬ ‫‪96‬‬ ‫‪97‬‬ ‫‪98‬‬ ‫‪99‬‬ ‫‪100‬‬ ‫=‪Total‬‬ ‫=‪Percent‬‬

‫‪81‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫ﺟﺪﻭﻝ)‪ :(5-9‬ﻣﻠﺨﺺ ﻋﺪﺩ ﺍﳊﺎﻻﺕ ﺍﳌﻜﺘﺸﻔﺔ ﻛﺤﺎﻻﺕ ﻣﺆﺛﺮﺓ )ﰲ ﺿﻞ ﻭﺟﻮﺩ ﺣﺎﻟﺔ ﻣﺆﺛﺮﺓ‬ ‫ﻭﺍﺣﺪﺓ(‪.‬‬ ‫‪Total‬‬

‫‪6‬‬

‫‪5‬‬

‫‪4‬‬

‫‪3‬‬

‫‪2‬‬

‫*‪1‬‬

‫‪0‬‬

‫ﺍﳌﻘﻴﺎﺱ‬

‫‪100‬‬

‫‪0‬‬

‫‪0‬‬

‫‪0‬‬

‫‪0‬‬

‫‪0‬‬

‫‪100‬‬

‫‪0‬‬

‫‪100‬‬

‫‪0‬‬

‫‪0‬‬

‫‪0‬‬

‫‪0‬‬

‫‪0‬‬

‫‪100‬‬

‫‪0‬‬

‫‪100‬‬

‫‪0‬‬

‫‪0‬‬

‫‪0‬‬

‫‪0‬‬

‫‪0‬‬

‫‪100‬‬

‫‪0‬‬

‫‪100‬‬

‫‪0‬‬

‫‪0‬‬

‫‪0‬‬

‫‪0‬‬

‫‪82‬‬

‫‪18‬‬

‫‪0‬‬

‫‪100‬‬

‫‪0‬‬

‫‪0‬‬

‫‪0‬‬

‫‪0‬‬

‫‪1‬‬

‫‪99‬‬

‫‪0‬‬

‫‪Di‬‬ ‫‪COVR‬‬ ‫‪DFFITS‬‬ ‫‪DFBo‬‬ ‫‪DFB1‬‬

‫ﺭﺳﻮﻣﺎﺕ ﺗﻮﺿﻴﺤﻴﺔ ﻟﻌﺪﺩ ﺍﳊﺎﻻﺕ ﺍﳌﻜﺘﺸﻔﺔ ﻛﺤﺎﻻﺕ ﻣﺆﺛﺮﺓ )ﰲ ﺿﻞ ﻭﺟﻮﺩ ﺣﺎﻟﺔ ﻣﺆﺛﺮﺓ ﻭﺍﺣﺪﺓ(‪.‬‬ ‫ﺷﻜﻞ )‪ :(5-11‬ﺭﺳﻢ ﳌﻘﻴﺎﺱ ﻣﺴﺎﻓﺔ ﻛﻮﻙ ﻭ ﻣﻘﻴﺎﺱ ‪:COVR‬‬

‫ﺷﻜﻞ )‪ :(5-12‬ﺭﺳﻢ ﳌﻘﻴﺎﺱ ‪ DFFITS‬ﻭ ‪:DFBo‬‬

‫‪82‬‬

‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

‫ﺷﻜﻞ )‪ :(5-13‬ﺭﺳﻢ ﳌﻘﻴﺎﺱ ‪:DFB1‬‬

‫ﺍﻟﻨﺘﺎﺋﺞ )ﻣﻊ ﺇﺿﺎﻓﺔ ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ(‪:‬‬ ‫ﻳﻼﺣﻆ ﻋﺪﺓ ﻣﻼﺣﻈﺎﺕ‪:‬‬ ‫ ﳎﻤﻮﻉ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﱵ ﺍﻛﺘﺸﻔﺘﻬﺎ ﲨﻴﻊ ﺍﳌﻘﺎﻳﻴﺲ ﻋﻨﺪ ﺇﺿﺎﻓﺔ ﺍﳌﺸﺎﻫﺪﺓ ﺍﳌﺆﺛﺮﺓ ﺗﺴﺎﻭﻱ ‪583‬‬ ‫ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﻣﻦ ‪ 1000‬ﻣﺸﺎﻫﺪﺓ ﻣﻮﺯﻋﺔ ﻋﻠﻰ ﲨﻴﻊ ﺍﳌﻘﺎﻳﻴﺲ‪ ،‬ﻟﻨﻔﺲ ﺍﳌﻘﺪﺭﺍﺕ ﲞﻄﺄ‬ ‫ﻋﺸﻮﺍﺋﻲ ﻳﺘﺒﻊ ﺍﻟﺘﻮﺯﻳﻊ ﺍﻟﻄﺒﻴﻌﻲ ﲟﺘﻮﺳﻂ ﺻﻔﺮ ﻭﺗﺒﺎﻳﻦ ‪ . ε i ~ ! (0,1) 1‬ﻣﻦ ﳏﺎﻛﺎﺓ ‪100‬‬ ‫ﳕﻮﺫﺝ ﺍﳓﺪﺍﺭ ﺧﻄﻲ ﺑﺴﻴﻂ‪ .‬ﺑﻨﺴﺒﺔ ‪ %58.3‬ﻣﻦ ﳎﻤﻮﻉ ﺍﳌﺸﺎﻫﺪﺍﺕ‪ .‬ﻭﻣﻦ ﺧﻼﻝ ﺍﻟﺮﺳﻢ‬ ‫ﺍﻟﺘﻮﺿﻴﺤﻲ ﻳﻼﺣﻆ ﺗﺸﺎﺑﻪ ﺍﳌﻘﺎﻳﻴﺲ ﺗﻘﺮﻳﺒﹰﺎ ﰲ ﻋﺪﺩ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﻭﻛﺬﻟﻚ‬ ‫ﻳﻼﺣﻆ ﺍﺧﺘﻼﻑ ﻣﻘﻴﺎﺱ ‪ DFBo‬ﻋﻦ ﺍﻟﺒﻘﻴﺔ‪ .‬ﻭﻳﺘﻢ ﺗﻮﺯﻳﻊ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﻜﺘﺸﻔﺔ ﻛﺎﻟﺘﺎﱄ‪:‬‬ ‫ ﻣﻘﻴﺎﺱ ‪ :Di‬ﱂ ﻳﻜﺘﺸﻒ ﻣﻘﻴﺎﺱ ﻣﺴﺎﻓﺔ ﻛﻮﻙ ﻋﻨﺪ ﺇﺿﺎﻓﺔ ﺍﳌﺸﺎﻫﺪﺓ ﺍﳌﺆﺛﺮﺓ )ﻣﺸﺎﻫﺪﺓ ﺭﻗﻢ‬ ‫‪ (11‬ﺇﻻ ﻫﺬﻩ ﺍﳌﺸﺎﻫﺪﺓ ﻓﻘﻂ ﻭﱂ ﻳﻜﺘﺸﻒ ﺃﻱ ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ ﺑﺎﳋﻄﺄ‪ .‬ﺃﻱ ﺍﻧﻪ ﺍﻛﺘﺸﻒ‬ ‫‪ 100‬ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﺣﻘﻴﻘﻴﺔ ﻣﻦ ‪ 1000‬ﻣﺸﺎﻫﺪﺓ ﻭﻫﻲ ﺍﳌﺸﺎﻫﺪﺓ ﺍﻟﱵ ﻗﻤﻨﺎ ﺑﺈﺿﺎﻓﺘﻬﺎ ﰲ‬ ‫ﺍﻟﻨﻤﻮﺫﺝ ﻭﺫﻟﻚ ﺑﻨﺴﺒﺔ ‪ %10‬ﻣﻦ ﳎﻤﻮﻉ ﺍﳌﺸﺎﻫﺪﺍﺕ ﻭﻳﻌﺘﱪ ﻫﺬﺍ ﺍﳌﻘﻴﺎﺱ ﻫﻮ ﺍﻷﻓﻀﻞ ﰲ‬ ‫ﺍﻛﺘﺸﺎﻑ ﺍﳊﺎﻻﺕ ﺍﳌﺆﺛﺮﺓ ﻋﻨﺪ ﻭﺟﻮﺩﻫﺎ‪.‬‬ ‫ ﻣﻘﻴﺎﺱ ‪ :COVR‬ﱂ ﳜﺘﻠﻒ ﻫﺬﺍ ﺍﳌﻘﻴﺎﺱ ﻛﺜﲑﹰﺍ ﻋﻦ ﻣﻘﻴﺎﺱ ﻣﺴﺎﻓﺔ ﻛﻮﻙ ﻓﻘﺪ ﺍﻛﺘﺸﻒ‬ ‫‪ 100‬ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﺃﻳﻀﹰﺎ ﻭﻫﻲ ﺍﻟﱵ ﺍﻛﺘﺸﻔﻬﺎ ﻣﻘﻴﺎﺱ ﻣﺴﺎﻓﺔ ﻛﻮﻙ ﻭﺍﻟﱵ ﻗﻤﻨﺎ ﺑﺈﺿﺎﻓﺘﻬﺎ‪.‬‬ ‫ ﻣﻘﻴﺎﺱ ‪ :DFFITS‬ﺍﻛﺘﺸﻒ ﻫﻮ ﺍﻵﺧﺮ ‪ 100‬ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﻣﻦ ‪ 1000‬ﻣﺸﺎﻫﺪﺓ ﻭﻫﻲ‬ ‫ﺍﻟﱵ ﺍﻛﺘﺸﻔﻬﺎ ﺍﳌﻘﺎﻳﻴﺲ ﺍﻷﺧﺮﻯ‪ .‬ﻭﱂ ﻳﻜﺘﺸﻒ ﻫﺬﺍ ﺍﳌﻘﻴﺎﺱ ﻫﻨﺎ ﺃﻱ ﻣﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ ﺑﺎﳋﻄﺄ‪.‬‬

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‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬ ‫‬

‫‬

‫ﻣﻘﻴﺎﺱ ‪ :DFBo‬ﺍﻛﺘﺸﻒ ﻫﺬﺍ ﺍﳌﻘﻴﺎﺱ ‪ 182‬ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﻣﻦ ‪ 1000‬ﻣﺸﺎﻫﺪﺓ ﺑﻨﺴﺒﺔ‬ ‫‪ %18.2‬ﻣﻨﻬﺎ ‪ 82‬ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﺍﻛﺘﺸﻔﻬﺎ ﺑﺎﳋﻄﺄ ﺑﻨﺴﺒﺔ ‪ %8.2‬ﻟﺬﻟﻚ ﻳﻌﺘﱪ ﻫﺬﺍ ﺍﳌﻘﻴﺎﺱ‬ ‫ﻏﲑ ﺟﻴﺪ ﻻﻛﺘﺸﺎﻑ ﺑﻌﺾ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﺑﺎﳋﻄﺄ ﰲ ﺣﺎﻝ ﻭﺟﻮﺩ ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﺣﻘﻴﻘﺔ‪.‬‬ ‫ﻭﻟﻘﺪ ﺗﻮﺯﻋﺖ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻟﺘﺠﺎﺭﺏ ﻛﺎﻟﺘﺎﱄ‪ 18 :‬ﲡﺮ‪‬ﺎ ﺍﻛﺘﺸﻒ ‪‬ﺎ ﻣﺸﺎﻫﺪﺓ‬ ‫ﻣﺆﺛﺮﺓ ﻭﺍﺣﺪﺓ ﻓﻘﻂ ﺑﻨﺴﺒﺔ ‪ . %18‬ﺑﻴﻨﻤﺎ ‪ 82‬ﲡﺮﺑﺔ ﺃﻭ ‪ %82‬ﻣﻦ ﺍﻟﺘﺠﺎﺭﺏ ﺍﻛﺘﺸﻒ ‪‬ﺎ‬ ‫ﻣﺸﺎﻫﺪﺗﲔ ﻣﺆﺛﺮﺓ ﻓﻘﻂ‪.‬‬ ‫ﻣﻘﻴﺎﺱ ‪ :DFB1‬ﱂ ﳜﺘﻠﻒ ﻫﺬﺍ ﺍﳌﻘﻴﺎﺱ ﻋﻦ ﺑﻘﻴﺔ ﺍﳌﻘﺎﻳﻴﺲ ﺍﻟﺴﺎﺑﻘﺔ ﻭﻟﻜﻨﻪ ﺍﻛﺘﺸﻒ ﻣﺸﺎﻫﺪﺓ‬ ‫ﻭﺍﺣﺪﺓ ﺑﺎﳋﻄﺄ ﰲ ﺍﻟﺘﺠﺮﺑﺔ ﺭﻗﻢ ‪ 30‬ﺃﻱ ﺍﻧﻪ ﺍﻛﺘﺸﻒ ‪ 101‬ﻣﺸﺎﻫﺪﺓ ﻣﺆﺛﺮﺓ ﻣﻨﻬﺎ ﻓﻘﻂ‬ ‫ﻣﺸﺎﻫﺪﺓ ﻭﺍﺣﺪﺓ ﺍﻛﺘﺸﻔﻬﺎ ﺑﺎﳋﻄﺄ ﻭﺫﻟﻚ ﺑﻨﺴﺒﺔ ‪ %10.1‬ﻣﻦ ‪ 1000‬ﻣﺸﺎﻫﺪﺓ‪.‬‬

‫ﺍﺳﺘﻨﺘﺎﺟﺎﺕ ﻭﺗﻮﺻﻴﺎﺕ‪:‬‬ ‫‪ (1‬ﻋﻨﺪ ﺇﺿﺎﻓﺔ ﺍﳌﺸﺎﻫﺪﺓ ﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﳕﺎﺫﺝ ﺍﻻﳓﺪﺍﺭ ﺍﶈﺎﻛﺎﺓ )ﻣﺸﺎﻫﺪﺓ ﺭﻗﻢ ‪ (11‬ﻭﻋﻨﺪﻣﺎ‬ ‫ﻳﻜﻮﻥ ﺍﻟﺘﺒﺎﻳﻦ ﺻﻐﲑﹰﺍ‪ ،‬ﻧﻼﺣﻆ ﺃﻥ ﺍﳌﻘﺎﻳﻴﺲ ﺗﻮﺣﺪﺕ ﺗﻘﺮﻳﺒﹰﺎ ﰲ ﺍﻛﺘﺸﺎﻑ ﻫﺬﻩ ﺍﳌﺸﺎﻫﺪﺓ ﺍﳌﺆﺛﺮﺓ ﻣﺎ ﻋﺪﻯ‬ ‫ﻣﻘﻴﺎﺱ ‪ DFBETAS‬ﻓﻘﺪ ﲣﻠﻒ ﻭﻟﻜﻨﻪ ﱂ ﻳﺘﺨﻠﻒ ﻛﺜﲑﹰﺍ ﻓﻘﻂ ﺳﺠﻞ ﺗﻘﺮﻳﺒﹰﺎ ﻧﻔﺲ ﺍﻟﻌﺪﺩ ﺑﺎﻟﻨﺴﺒﺔ‬ ‫ﻟﻌﺪﺩ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﻣﻌﻠﻤﺔ ﺍﻟﻨﻤﻮﺫﺝ ﺍﻟﺜﺎﻧﻴﺔ ‪ . β1‬ﻛﺬﻟﻚ ﺍﺗﻀﺢ ﺃﻥ ﻫﺬﻩ ﺍﳌﺸﺎﻫﺪﺓ )ﻣﺸﺎﻫﺪﺓ‬ ‫ﺭﻗﻢ ‪ (11‬ﺗﺴﻠﻂ ﺍﻷﺿﻮﺍﺀ ﻋﻠﻴﻬﺎ ﻭﺍﳌﻘﺎﻳﻴﺲ ﺗﻜﺘﺸﻔﻬﺎ ﻟﻮﺣﺪﻫﺎ ﺗﻘﺮﻳﺒﹰﺎ‪ ،‬ﻭﻛﺄﻥ ﺩﺍﺋﺮﺓ ﺍﻟﺘﺒﺎﻳﻦ ﻭﺍﻷﺧﻄﺎﺀ‬ ‫ﺍﻟﻌﺸﻮﺍﺋﻴﺔ ﺗﺘﺴﻊ ﺑﺴﺒﺐ ﻫﺬﻩ ﺍﻹﺿﺎﻓﺔ ﺍﳌﺆﺛﺮﺓ ﺣﻴﺚ ﺃﻥ ﺍﳌﻘﺎﻳﻴﺲ ﺍﻛﺘﺸﻔﺖ ﻛﺜﲑ ﻣﻦ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ‬ ‫)ﺑﺎﳋﻄﺄ( ﻭﻟﻜﻦ ﺑﻌﺪ ﺍﻹﺿﺎﻓﺔ ﱂ ﺗﻜﺘﺸﻔﻬﺎ ﺇﻻ ﰲ ﻣﻘﻴﺎﺱ ‪ ،DFBo‬ﻟﺬﻟﻚ ﻳﻨﺼﺢ ﺑﺒﻌﺾ ﺍﳋﻄﻮﺍﺕ‬ ‫ﻟﻠﺘﺄﻛﺪ ﻣﻦ ﺻﻼﺣﻴﺔ ﺍﻟﻨﻤﻮﺫﺝ ﻗﺒﻞ ﺍﻟﺘﻨﺒﺆ ﺑﺎﺳﺘﺨﺪﺍﻡ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ ﺃﻭ ﺍﲣﺎﺫ ﺃﻱ ﻗﺮﺍﺭ‪ ،‬ﻭﺗﺘﻠﺨﺺ ﺑﻌﺾ‬ ‫ﻫﺬﻩ ﺍﳋﻄﻮﺍﺕ ﻛﺎﻟﺘﺎﱄ‪:‬‬ ‫‬

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‫ﺑﻌﺪ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻋﻠﻰ ﺍﳌﺘﻐﲑﺍﺕ ﺍﳌﺴﺘﻘﻠﺔ ﻭﺍﳌﺘﻐﲑ ﺍﻟﺘﺎﺑﻊ ﻳﻨﺒﻐﻲ ﻣﺮﺍﻋﺎﺓ ﺍﻟﻔﺮﻭﻕ‬ ‫ﺑﲔ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﲢﺪﻳﺪ ﺃﻱ ﺍﳌﺸﺎﻫﺪﺍﺕ ﻣﺆﺛﺮﺓ‪.‬‬ ‫ﲢﺪﻳﺪ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻟﻨﻤﻮﺫﺝ ﻭﺗﻘﺴﻤﻬﺎ ﺇﱃ ﳎﻤﻮﻋﺎﺕ ﺃﻭ ﺩﺭﺟﺎﺕ ﺍﻷﻛﺜﺮ ﺃﺛﺮ ﻋﻠﻰ‬ ‫ﳕﻮﺫﺝ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ ﰒ ﺍﳌﺸﺎﻫﺪﺓ ﺍﳌﺆﺛﺮﺓ ﺍﻟﱵ ﺗﻠﻴﻬﺎ ﻭﻗﻴﺎﺱ ﻓﺮﻕ ﺍﻟﺘﺄﺛﲑ ﺑﻴﻨﻬﻤﺎ‪ ،‬ﻭﺍﺳﺘﺨﺪﺍﻡ‬

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‫ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ‪.‬‬

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‫ﻃﺮﻳﻘﺔ ﺗﺪﺭﳚﻴﺔ ﰲ ﺇﻟﻐﺎﺀ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ) ﻋﻨﺪ ﻭﺟﻮﺩ ﻣﱪﺭ ﻛﺎﰲ ﻹﻟﻐﺎﺋﻬﺎ ( ﺃﻭ ﺗﻘﻠﻴﻞ ﺃﺛﺮﻫﺎ‬ ‫ﻋﻠﻰ ﺍﻟﻨﻤﻮﺫﺝ ﻭﺍﻟﻘﻴﺎﺱ ﺑﺪﻭﻥ ﻫﺬﻩ ﺍﳌﺸﺎﻫﺪﺓ ﻭﻣﻘﺎﺭﻧﺔ ﺍﻟﻨﺘﺎﺋﺞ ﻗﺒﻞ ﻭﺑﻌﺪ ﺍﲣﺎﺫ ﻫﺬﺍ ﺍﻹﺟﺮﺍﺀ‪.‬‬ ‫ﺗﻜﺮﺍﺭ ﻫﺬﻩ ﺍﻟﻌﻤﻠﻴﺔ ﻣﻊ ﻣﺮﺍﻋﺎﺓ ﻋﺪﻡ ﺍﻟﻮﻗﻮﻉ ﰲ ﺗﺄﺛﲑﺍﺕ ﺃﺧﺮﻯ ﺣﱴ ﺍﻟﻮﺻﻮﻝ ﺇﱃ ﳕﻮﺫﺝ‬ ‫ﺍﳓﺪﺍﺭ ﻣﺮﺿﻲ ﳝﺘﺎﺯ ﺑﺼﻐﺮ ﺗﺒﺎﻳﻦ ﺍﻷﺧﻄﺎﺀ ﺍﻟﻌﺸﻮﺍﺋﻴﺔ‪.‬‬

‫‪ (2‬ﺃﻭﺿﺤﺖ ﻫﺬﻩ ﺍﻟﺪﺭﺍﺳﺔ ﺑﺄﻥ ﺍﳌﻘﻴﺎﺱ ‪ Di‬ﻣﻘﻴﺎﺱ ﻣﺴﺎﻓﺔ ﻛﻮﻙ ﻫﻮ ﺍﻷﻓﻀﻞ ﰲ ﻋﺪﻡ ﺍﻛﺘﺸﺎﻑ‬ ‫ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﳌﺆﺛﺮﺓ ﻏﲑ ﺍﳊﻘﻴﻘﻴﺔ ) ﺍﻹﻧﺬﺍﺭ ﺍﳋﺎﻃﺊ (‪ .‬ﻭﻫﻮ ﺃﻓﻀﻞ ﺍﳌﻘﺎﻳﻴﺲ ﰲ ﺍﻛﺘﺸﺎﻑ ﺍﳊﺎﻟﺔ‬ ‫ﺍﳌﺆﺛﺮﺓ ﻋﻨﺪ ﻭﺟﻮﺩﻫﺎ‪.‬‬

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‫ﺍﳌﺮﺍﺟﻊ‪:‬‬

‫‪.‬‬

‫ﺛﺎﻣﺮ ﻣﻨﺸﻲ‪ .‬ﺩﻫﺎﻡ ﺍﻟﺪﻫﺎﻡ‪ .‬ﻣﺸﺮﻭﻉ ﲝﺚ ﺑﺈﺷﺮﺍﻑ ﺩ‪.‬ﳏﻤﺪ ﻗﺎﻳﺪ‪ .‬ﺑﻌﻨﻮﺍﻥ "ﺃﺳﺎﺳﻴﺎﺕ ﺍﻟﻌﺮﺽ ﻭﺍﻟﺘﺤﻠﻴﻞ ﺍﻹﺣﺼﺎﺋﻲ‬

‫ﺑﺈﺳﺘﺨﺪﺍﻡ ‪ "Spsswin‬ﺍﳉﺰﺀ ﺍﻟﺜﺎﱐ‪ .‬ﺍﻟﺮﻳﺎﺽ‪ .‬ﺟﺎﻣﻌﺔ ﺍﳌﻠﻚ ﺳﻌﻮﺩ – ﻛﻠﻴﺔ ﺍﻟﻌﻠﻮﻡ – ﻗﺴﻢ ﺍﻹﺣﺼﺎﺀ ﻭﲝﻮﺙ ﺍﻟﻌﻤﻠﻴﺎﺕ‪.‬‬ ‫)‪1429‬ﻫـ( ‪.‬‬ ‫‪ .‬ﺟﻮﻥ ﻧﻴﺘﺮ ﻭﺁﺧﺮﻭﻥ "ﳕﺎﺫﺝ ﺇﺣﺼﺎﺋﻴﺔ ﺧﻄﻴﺔ ﺗﻄﺒﻴﻘﻴﺔ" ﺍﳉﺰﺀ ﺍﻷﻭﻝ )ﺍﻻﳓﺪﺍﺭ(‪ .‬ﻣﺘﺮﺟﻢ ﻟﻠﻌﺮﺑﻴﺔ ﺑﻮﺍﺳﻄﺔ ‪/‬ﺃ‪.‬ﺩ ﺃﻧﻴﺲ ﻛﻨﺠﻮ‬ ‫ﺃ‪.‬ﺩ ﻋﺒﺪﺍﳊﻤﻴﺪ ﺍﻟﺰﻳﺪ ﺩ‪.‬ﺇﺑﺮﺍﻫﻴﻢ ﺍﻟﻮﺍﺻﻞ ﺩ‪ .‬ﺍﳊﺴﻴﲏ ﺭﺍﺿﻲ‪ .‬ﺍﻟﺮﻳﺎﺽ‪ .‬ﺟﺎﻣﻌﺔ ﺍﳌﻠﻚ ﺳﻌﻮﺩ ﻗﺴﻢ ﺍﻹﺣﺼﺎﺀ ﻭﲝﻮﺙ‬ ‫ﺍﻟﻌﻤﻠﻴﺎﺕ – ﻛﻠﻴﺔ ﺍﻟﻌﻠﻮﻡ – )‪1421‬ﻫـ ‪2000 -‬ﻡ(‪.‬‬ ‫‪ .‬ﺩ‪ .‬ﻋﺪﻧﺎﻥ ﺑﺮﻱ "ﳕﺎﺫﺝ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ"‪ .‬ﺍﻟﻄﺒﻌﺔ ﺍﻷﻭﱃ‪ .‬ﺍﻟﺮﻳﺎﺽ‪ .‬ﺟﺎﻣﻌﺔ ﺍﳌﻠﻚ ﺳﻌﻮﺩ‪ .‬ﻗﺴﻢ ﺍﻹﺣﺼﺎﺀ ﻭﲝﻮﺙ ﺍﻟﻌﻤﻠﻴﺎﺕ‬ ‫– ﻛﻠﻴﺔ ﺍﻟﻌﻠﻮﻡ – ﻛﺘﺎﺏ ﺇﻟﻜﺘﺮﻭﱐ ﳌﻘﺮﺭ ‪ 335‬ﺇﺣﺺ‪1428) .‬ﻫـ(‪.‬‬ ‫‪ .‬ﺩ‪ .‬ﻋﺼﺎﻡ ﻭﺁﺧﺮﻭﻥ "ﺍﺳﺘﺨﺪﺍﻡ ﺍﶈﺎﻛﺎﺓ ﰲ ﺗﺪﺭﻳﺲ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ ﺍﻟﺒﺴﻴﻂ"‪ .‬ﲝﺚ ﻣﻨﺸﻮﺭ ﰲ ﳎﻠﺔ ﺟﺎﻣﻌﺔ ﺍﻻﻧﺒﺎﺭ‪ .‬ﺍﻟﻌﺪﺩ‬ ‫‪ .3‬ﳎﻠﺪ ‪.(2008) .2‬‬ ‫‪ .‬ﳏﻤﺪ ﺇﲰﺎﻋﻴﻞ " ﲢﻠﻴﻞ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ"‪ .‬ﺍﻟﻄﺒﻌﺔ ﺍﻷﻭﱃ‪ .‬ﺍﻟﺮﻳﺎﺽ‪ .‬ﻣﻌﻬﺪ ﺍﻹﺩﺍﺭﺓ ﺍﻟﻌﺎﻣﺔ‪1421) .‬ﻫـ ‪2000 -‬ﻡ(‪.‬‬

‫‪Reference.‬‬

‫‪. Belsley et all “Regression Diagnostics”. identifying influential data and‬‬ ‫‪sources of collinearity. (1980).‬‬

‫‪. Chatterjee. Ali S. Hadi “Sensitivity Analysis In Linear Regression”.‬‬ ‫‪New York (1988).‬‬

‫)‪. John Fox “Regression Diagnostics”. (1991‬‬ ‫‪. John Fox “Applied regression analysis, linear models, and related‬‬ ‫‪methods”. (1997).‬‬

‫‪. John Neter et all “Applied Linear Statistical Models”. Regression Analysis‬‬ ‫‪of Variance. And Experimental Designs. (3rd ed. 1990).‬‬

‫‪Web Sites:‬‬ ‫‪. Statisticians Arabs : http://www.arabicstat.com‬‬ ‫‪. Wikipedia : http://www.wikipedia.org‬‬

Statistic
Statistic

Abdulaziz Almutairi