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 ﺷﺄﺎ 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 ﺃﺎ 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 ﺃﺎ 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
R-Sq(adj) = 96.1%
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 ﺃﺎ 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
R-Sq(adj) = 77.0%
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%
R-Sq(adj) = 88.1%
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 ﺃﺎ 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
R-Sq(adj) = 94.1%
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
R-Sq(adj) = 94.3%
.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 ﺃﺎ 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 ﺃﺎ 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
R-Sq(adj) = 96.1%
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
R-Sq(adj) = 88.1%
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 ﺃﺎ 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
R-Sq(adj) = 94.3%
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 ﺣﺴﺎﺎ 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
= )DFBETASk(i
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
| DFBETASk(i) |> 2
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
Adjusted R Square .961
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
R-Sq(adj) = 96.1%
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
Adjusted R
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
R-Sq(adj) = 88.1%
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
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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 21ﻓﺄﺎ 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
Adjusted R Square
.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
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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
R-Sq(adj) = 94.3%
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
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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 1ﻓﺈﺎ ﺗﺆﺛﺮ ﻋﻠﻰ ﺍﳌﻌﺎﻣﻞ ﺍﻷﻭﻝ β 0ﻭﻛﺬﻟﻚ ﺍﳌﻌﺎﻣﻞ ﺍﻟﺜﺎﱐ . β1ﺃﻣﺎ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺭﻗﻢ 4,20,33ﻓﺈﺎ 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 ﻷﺎ 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 ﺍﳌﺎﻻﺎﻳﻪ .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 ﺃﺎ 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
66
ﺃﺳﺎﻟﻴﺐ ﺍﻛﺘﺸﺎﻑ ﺍﳌﺸﺎﻫﺪﺍﺕ ﺍﻟﺸﺎﺫﺓ ﻭﺍﳌﺆﺛﺮﺓ ﻋﻠﻰ ﺍﻻﳓﺪﺍﺭ ﺍﳋﻄﻲ.
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:
67
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.
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
72
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 ﺃﺎ 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.
78
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
79
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.
83
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 :ﲡﺮﺎ 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:
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.
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(.
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. 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).
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