<
]†Â<êÞ^nÖ]<Ø’ËÖ
Ù]<…]‚©÷]<tƒ^´<Øé× خ3ê
Linear Regression Analysis
.1 .12ﻣﻘﺪﻣﺔ .1 .1 .12اﻻﻧﺤﺪار اﻟﺨﻄﻲ اﻟﺒﺴﻴﻂ )ﺑﻴﻦ ﻣﺘﻐﻴﺮﻳﻦ( .2 .1 .12اﻻﻧﺤﺪار اﻟﻤﺘﻌﺪد .3 .1 .12اﻟﺒﻮاﻗﻲ )اﻷﺧﻄﺎء( .4 .1 .12ﻣﻌﺎﻣﻞ اﻻرﺗﺒﺎط اﻟﻤﺘﻌﺪد .5 .1 .12ﻓﺘﺢ ﻧﺎﻓﺬة ﺗﺤﻠﻴﻞ اﻻﻧﺤﺪار اﻟﺨﻄﻲ .2 .12اﻻﻧﺤﺪار اﻟﺨﻄﻲ اﻟﺒﺴﻴﻂ .3 .12اﻻﻧﺤﺪار اﻟﻤﺘﻌﺪد .4 .12ﺷﻜﻞ اﻻﻧﺘﺸﺎر وﺧﻂ اﻻﻧﺤﺪار
) (12ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
402
) (12ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
403
]†Â<êÞ^nÖ]<Ø’ËÖ Ù]<…]‚©÷]<tƒ^´<Øé× خê Linear Regression Analysis .1 .12ﻣﻘﺪﻣﺔ: ﺘﺤﺩﺜﻨﺎ ﻓﻲ ﺍﻟﻔﺼل ﺍﻟﺴﺎﺒﻕ ﻋﻥ ﻤﻘﺎﻴﻴﺱ ﺍﻻﺭﺘﺒﺎﻁ ﻭﻗﺩ ﻋﺎﻟﺠﻨﺎ ﺒﺎﻟﺘﻔﺼﻴل
ﺍﺴﺘﺨﺩﺍﻤﺎﺕ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺒﻴﺭﺴﻭﻥ ﻟﻘﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻜﻤﻴﺔ ﺍﻟﻘﻴﺎﺴﻴﺔ ،ﻭﻟﻜﻥ ﻫﻨﺎﻙ ﻭﺠﻪ ﺁﺨﺭ ﻟﻠﻌﻤل ﻫﻨﺎ ،ﻓﻌﻨﺩﻤﺎ ﻨﻌﻠﻡ ﺒﻭﺠﻭﺩ ﻋﻼﻗﺔ ﻗﻭﻴﺔ ﺒﻴﻥ ﻤﺘﻐﻴﺭﻴﻥ ﺃﻭ ﺃﻜﺜﺭ ﻻﺒﺩ ﻤﻥ ﻤﺤﺎﻭﻟﺔ ﻤﻌﺭﻓﺔ ﻁﺒﻴﻌﺔ ﺘﻠﻙ ﺍﻟﻌﻼﻗﺔ ﺒﺎﻟﺘﺤﺩﻴﺩ ،ﻓﺄﺴﻠﻭﺏ
ﺍﻻﻨﺤﺩﺍﺭ Regressionﻴﻬﺘﻡ ﺒﻤﺤﺎﻭﻟﺔ ﺘﺤﺩﻴﺩ ﻁﺒﻴﻌﺔ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﻭﺍﺴﺘﺨﺩﺍﻡ
ﺘﻠﻙ ﺍﻟﻌﻼﻗﺔ ﻓﻲ ﺍﻟﺘﻨﺒﺅ ﺒﻘﻴﻡ ﻤﺘﻐﻴﺭ ﻤﺎ )ﻭﻴﻁﻠﻕ ﻋﻠﻴﻪ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﺘﺎﺒﻊ Dependent
(Variableﺇﺫﺍ ﻋﻠﻤﺕ ﻗﻴﻤﺔ ﺍﻟﻤﺘﻐﻴﺭ )ﺃﻭ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ( ﺍﻵﺨﺭ )ﻭﻴﻁﻠﻕ ﻋﻠﻰ ﻫﺫﻩ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﻤﺘﻐﻴﺭﺍﺕ ﻤﺴﺘﻘﻠﺔ ،(Independent Variablesﻭﻫﺫﺍ ﺍﻟﻔﺼل ﻴﻬﺘﻡ ﺒﻤﻌﺎﻟﺠﺔ
ﺍﺴﺘﺨﺩﺍﻡ ﻨﻅﺎﻡ SPSSﻓﻲ ﺘﺤﻠﻴل ﺍﻟﻌﻼﻗﺎﺕ ﺒﻴﻥ ﺍﻟﻅﻭﺍﻫﺭ ﺍﻟﻜﻤﻴﺔ ﺒﺎﺴﺘﺨﺩﺍﻡ ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ .Regression Models
ﻭﺒﺎﺨﺘﺼﺎﺭ ،ﺒﻴﻨﻤﺎ ﺘﻬﺘﻡ ﺃﺴﺎﻟﻴﺏ ﺍﻻﺭﺘﺒﺎﻁ ﺒﺈﻴﺠﺎﺩ ﻤﻘﻴﺎﺱ ﻟﻘﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ
ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺒﻘﻴﻤﺔ ﻭﺤﻴﺩﺓ ﺘﻌﺭﻑ ﺒﻤﻌﺎﻤل ﺍﻻﺭﺘﺒﺎﻁ ﻴﻜﻭﻥ ﺍﻟﻐﺭﺽ ﻤﻥ ﺃﺴﺎﻟﻴﺏ ﺍﻻﻨﺤﺩﺍﺭ
ﻫﻭ ﺘﻘﺩﻴﺭ ﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺫﻱ ﻴﻤﺜل ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﻻﺴﺘﺨﺩﺍﻤﻬﺎ ﻓﻲ ﺍﻟﺘﻨﺒﺅ ﺍﻹﺤﺼﺎﺌﻲ.
) (12ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
404
.1 .1 .12اﻻﻧﺤﺪار اﻟﺨﻄﻲ اﻟﺒﺴﻴﻂ )ﺑﻴﻦ ﻣﺘﻐﻴﺮﻳﻦ( : Simple (two variable) Regression : ﻋﻨﺩﻤﺎ ﻨﻜﻭﻥ ﻤﻬﺘﻤﻴﻥ ﺒﺩﺭﺍﺴﺔ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﻤﺘﻐﻴﺭﻴﻥ ﻓﻘﻁ ﻓﺈﻨﻪ ﻴﻁﻠﻕ ﻋﻠﻰ ﻨﻤﻭﺫﺝ
ﺍﻻﻨﺤﺩﺍﺭ ﺒﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺒﺴﻴﻁ ،ﻭﻓﻲ ﻫﺫﻩ ﺍﻟﺤﺎﻻﺕ ﻴﻤﻜﻥ ﺘﻘﺩﻴﺭ ﻗﻴﻡ ﺃﺤﺩ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ
)ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﺘﺎﺒﻊ (Y ،ﻤﻥ ﻗﻴﻡ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻵﺨﺭ )ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﻤﺴﺘﻘل (X ،ﻤﻥ ﺨﻼل ﻤﻌﺎﺩﻟﺔ ﺨﻁﻴﺔ )ﻤﻥ ﺍﻟﺩﺭﺠﺔ ﺍﻷﻭﻟﻰ ﻓﻲ ﻜل ﻤﻥ Xﻭ (Yﺘﺄﺨﺫ ﺍﻟﺼﻭﺭﺓ ﺍﻟﻌﺎﻤﺔ : y = bo + b1 x ﺤﻴﺙ yﻫﻲ ﻗﻴﻤﺔ ﻤﻥ ﻗﻴﻡ ﺍﻟﻤﺘﻐﻴﺭ Yﻭ b1ﻫﻲ ﻤﻴل ﺍﻟﺨﻁ ﺍﻟﻤﺴﺘﻘﻴﻡ the slope
)ﻭﺘﻌﺭﻑ ﺒﻤﻌﺎﻤل ﺍﻻﻨﺤﺩﺍﺭ (the regression coefficientﻭ b0ﻫﻲ ﻤﻘﻁﻊ ﺍﻟﺨﻁ ﺍﻟﻤﺴﺘﻘﻴﻡ ) interceptﻭﺘﻌﺭﻑ ﺒﺜﺎﺒﺕ ﺍﻻﻨﺤﺩﺍﺭ .(regression constant
.2 .1 .12اﻻﻧﺤﺪار اﻟﻤﺘﻌﺪد :
Multiple regression
ﻓﻲ ﺤﺎﻟﺔ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﻤﺘﻌﺩﺩ ﻴﻤﻜﻥ ﺘﻘﺩﻴﺭ ﻗﻴﻡ ﺃﺤﺩ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ )ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﺘﺎﺒﻊ(Y ، ﻤﻥ ﻗﻴﻡ ﻤﺘﻐﻴﺭﻴﻥ ﺁﺨﺭﻴﻥ ﺃﻭ ﺃﻜﺜﺭ )ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻤﺴﺘﻘﻠﺔ (X1,X2,......,Xp ،ﻤﻥ ﺨﻼل
ﻤﻌﺎﺩﻟﺔ ﺨﻁﻴﺔ )ﻤﻥ ﺍﻟﺩﺭﺠﺔ ﺍﻷﻭﻟﻰ( ،ﻭﻫﺫﺍ ﻴﻤﻜﻥ ﺃﻥ ﻴﺘﻡ ﺒﺎﺴﺘﺨﺩﺍﻡ ﺍﻟﻤﻌﺎﺩﻟﺔ ﺍﻟﺨﻁﻴﺔ
ﻋﻠﻰ ﺍﻟﺼﻭﺭﺓ ﺍﻟﻌﺎﻤﺔ :
y = bo + b1 x1 + b2 x 2 + ............. + b p x p
ﺤﻴﺙ yﻫﻲ ﻗﻴﻤﺔ ﻤﻥ ﻗﻴﻡ ﺍﻟﻤﺘﻐﻴﺭ Yﻭ b1ﻭ b2ﻭ ....ﻭ bpﻫﻲ ﻤﻌﺎﻤﻼﺕ
ﺍﻻﻨﺤﺩﺍﺭ (the regression coefficientsﻭ b0ﻫﻲ ﺜﺎﺒﺕ ﺍﻻﻨﺤﺩﺍﺭ regression ، constantﻭﻫﺫﻩ ﺍﻟﻤﻌﺎﺩﻟﺔ ﺘﻌﺭﻑ ﺒﻤﻌﺎﺩﻟﺔ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ ﺍﻟﻤﺘﻌﺩﺩ Multiple
. regression equation of y upon x1,x2,.....,xp
) (12ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
.3 .1 .12اﻟﺒﻮاﻗﻲ )اﻷﺧﻄﺎء( :
405
Residuals
ﻋﻨﺩﻤﺎ ﺘﺴﺘﺨﺩﻡ ﻤﻌﺎﺩﻟﺔ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺘﻲ ﺘﻡ ﺘﻘﺩﻴﺭﻫﺎ ﻤﻥ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻓﻲ ﺘﻘﺩﻴﺭ ﻗﻴﻤﺔ
ﺍﻟﻤﺘﻐﻴﺭ Yﺒﺎﺴﺘﺨﺩﺍﻡ ﻗﻴﻡ ﻭﺍﺤﺩﹰﺍ ﺃﻭ ﺃﻜﺜﺭ ﻤﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻤﺴﺘﻘﻠﺔ Xﻓﺈﻥ ﻗﻴﻤﺔ ﺍﻟﻤﺘﻐﻴﺭ
Yﺍﻟﻤﻘﺩﺭﺓ ﺍﻟﻨﺎﺘﺠﺔ )ﻭﺍﻟﺘﻲ ﺴﻨﺭﻤﺯ ﻟﻬﺎ ﺒﺎﻟﺭﻤﺯ ˆ ( Yﻟﻥ ﺘﻜﻭﻥ ﺒﺎﻟﻀﺭﻭﺭﺓ ﻤﺴﺎﻭﻴﺔ ﻟﻘﻴﻤﺘﻬﺎ ﺍﻟﺤﻘﻴﻘﻴﺔ ،ﺒل ﻴﺘﻭﻗﻊ ﺃﻥ ﻴﻜﻭﻥ ﻫﻨﺎﻙ ﻓﺭﻕ ﺒﻴﻥ ﺍﻟﻘﻴﻤﺔ ﺍﻟﺤﻘﻴﻘﻴﺔ ﻭﺍﻟﻘﻴﻤﺔ ﺍﻟﻤﻘﺩﺭﺓ
) ˆ (Y- Yﻭﻫﺫﻩ ﺍﻟﻔﺭﻭﻕ ﻟﺠﻤﻴﻊ ﺍﻟﻘﻴﻡ ˆ Yﻴﻁﻠﻕ ﻋﻠﻴﻬﺎ ﺍﺴﻡ ﺍﻷﺨﻁﺎﺀ ﺃﻭ ﺍﻟﺒﻭﺍﻗﻲ ، residualsﻭﻫﺫﺍ ﻴﻌﻨﻲ ﻫﻨﺩﺴﻴﹰﺎ ﺃﻨﻪ ﻟﻥ ﺘﻘﻊ ﺒﺎﻟﻀﺭﻭﺭﺓ ﻗﻴﻡ ﺍﻟﻤﺘﻐﻴﺭ Yﻋﻠﻰ ﺍﻟﺨﻁ ﺍﻟﻤﺴﺘﻘﻴﻡ ﺃﻭ ﺍﻟﻤﻨﺤﻨﻰ ﺃﻭ ﺍﻟﻤﺴﺘﻭﻯ ﺍﻟﺫﻱ ﺘﻡ ﺘﻭﻓﻴﻘﻪ ﻤﻥ ﺍﻟﺒﻴﺎﻨﺎﺕ ﺒﺎﺴﺘﺨﺩﺍﻡ ﺃﺴﻠﻭﺏ
ﺍﻻﻨﺤﺩﺍﺭ ،ﻭﺩﺭﺍﺴﺔ ﻫﺫﻩ ﺍﻷﺨﻁﺎﺀ residualsﻟﻬﺎ ﺃﻫﻤﻴﺔ ﻜﺒﻴﺭﺓ ﻋﻨﺩ ﺍﺴﺘﺨﺩﺍﻡ ﻁﺭﻕ
ﺍﻻﻨﺤﺩﺍﺭ ﻷﻨﻬﺎ ﺘﻌﻁﻲ ﻤﺅﺸﺭﺍﺕ ﻭﻤﻘﺎﻴﻴﺱ ﻋﻥ ﻤﺩﻯ ﺍﻟﺩﻗﺔ ﻓﻲ ﺘﻘﺩﻴﺭ ﻤﻌﺎﺩﻟﺔ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﻨﺎﺘﺠﺔ ﻭﺇﻤﻜﺎﻨﻴﺎﺕ ﺍﺴﺘﺨﺩﺍﻡ ﻫﺫﻩ ﺍﻟﻤﻌﺎﺩﻟﺔ ﻓﻲ ﺘﻘﺩﻴﺭ ﻗﻴﻡ ﺍﻟﻤﺘﻐﻴﺭ Yﺍﻟﻤﺴﺘﻘﺒﻠﻴﺔ.
.4 .1 .12ﻣﻌﺎﻣﻞ اﻻرﺗﺒﺎط اﻟﻤﺘﻌﺪد : The multiple correlation coefficient : ﺃﺤﺩ ﺍﻟﻤﻘﺎﻴﻴﺱ ﺍﻟﺒﺴﻴﻁﺔ ﺍﻟﻤﺴﺘﺨﺩﻤﺔ ﻓﻲ ﻗﻴﺎﺱ ﺩﻗﺔ ﻤﻌﺎﺩﻟﺔ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺫﻱ ﺘﻡ
ﺘﻘﺩﻴﺭﻩ ﻓﻲ ﺍﻟﺘﻨﺒﺅ ﺒﻘﻴﻡ Yﻫﻭ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺒﻴﺭﺴﻭﻥ ﺒﻴﻥ ﺍﻟﻘﻴﻡ ﺍﻟﺤﻘﻴﻘﻴﺔ ﻟﻠﻤﺘﻐﻴﺭ Yﻭﻗﻴﻡ
ˆ Yﺍﻟﻤﻨﺎﻅﺭﺓ ﻟﻬﺎ ﻭﺍﻟﺘﻲ ﺘﻡ ﺘﻘﺩﻴﺭﻫﺎ ﺒﺎﺴﺘﺨﺩﺍﻡ ﻤﻌﺎﺩﻟﺔ ﺍﻻﻨﺤﺩﺍﺭ ﻋﻥ ﻁﺭﻴﻕ ﺍﻟﺘﻌﻭﻴﺽ
ﺒﻘﻴﻡ Xﻓﻲ ﺍﻟﻤﻌﺎﺩﻟﺔ ،ﻭﻴﻌﺭﻑ ﻤﻌﺎﻤل ﺍﻻﺭﺘﺒﺎﻁ ﺒﻴﻥ ﻗﻴﻡ Yﻭﻗﻴﻡ ˆ Yﺒﺎﺴﻡ ﻤﻌﺎﻤل
ﺍﻻﺭﺘﺒﺎﻁ ﺍﻟﻤﺘﻌﺩﺩ ، multiple correlation coefficient Rﻻﺤﻅ ﺃﻥ ﺍﻟﺤﺭﻑ R
ﺍﻟﻜﺒﻴﺭ ﻭﻟﻴﺱ rﻫﻭ ﺍﻟﻤﺴﺘﺨﺩﻡ ﻟﻠﺘﻌﺒﻴﺭ ﻋﻥ ﻤﻌﺎﻤل ﺍﻻﺭﺘﺒﺎﻁ ﺍﻟﻤﺘﻌﺩﺩ ﻟﻠﺘﻤﻴﻴﺯ ﺒﻴﻨﻪ ﻭﺒﻴﻥ
ﻤﻌﺎﻤل ﺍﻻﺭﺘﺒﺎﻁ ﺍﻟﺒﺴﻴﻁ rﻭﺍﻟﺫﻱ ﺘﻤﺕ ﻤﻨﺎﻗﺸﺘﻪ ﻓﻲ ﺍﻟﻔﺼل ﺍﻟﺴﺎﺒﻕ ،ﻭﻴﺠﺩﺭ ﺒﺎﻟﺫﻜﺭ ﻫﻨﺎ
ﺃﻥ ﻫﺫﺍ ﺍﻟﻤﻌﺎﻤل ﻻ ﻴﺄﺨﺫ ﻗﻴﻤﹰﺎ ﺴﺎﻟﺒﺔ ﺭﻏﻡ ﺃﻥ ﻗﻴﻤﺘﻪ ﺍﻟﻤﻁﻠﻘﺔ ﺴﺘﻜﻭﻥ ﻤﺴﺎﻭﻴﺔ ﻟﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺒﻴﺭﺴﻭﻥ )ﺍﻟﺒﺴﻴﻁ( ﻓﻲ ﺤﺎﻟﺔ ﻋﻨﺩﻤﺎ ﻴﻜﻭﻥ ﻫﻨﺎﻙ ﻤﺘﻐﻴﺭ ﻤﺴﺘﻘل ﻭﺍﺤﺩ .
) (12ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
406
.5 .1 .12ﻓﺘﺢ ﻧﺎﻓﺬة ﺗﺤﻠﻴﻞ اﻻﻧﺤﺪار اﻟﺨﻄﻲ : Linear Regression Dialog Box : ﻟﺘﻨﻔﻴﺫ ﺃﻱ ﺃﻤﺭ ﻴﺘﻌﻠﻕ ﺒﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﻓﻲ ﻫﺫﺍ ﺍﻟﻔﺼل ﻨﺤﺘﺎﺝ ﺇﻟﻰ ﻓﺘﺢ
ﻨﺎﻓﺫﺓ ﻭﺍﺤﺩﺓ ﻭﻫﻲ ﻨﺎﻓﺫﺓ ﺘﺤﻠﻴل ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ ، Linear Regressionﻭﻴﻤﻜﻥ ﺍﻟﻭﺼﻭل ﺇﻟﻰ ﻫﺫﻩ ﺍﻟﻨﺎﻓﺫﺓ ﻋﻥ ﻁﺭﻴﻕ ﺍﺨﺘﻴﺎﺭ ﺃﻤﺭ ﺍﻻﻨﺤﺩﺍﺭ Regressionﻤﻥ ﻗﺎﺌﻤﺔ
ﺍﻟﺘﺤﻠﻴل ﺍﻹﺤﺼﺎﺌﻲ ) Analyzeﺃﻭ Statisticsﻓﻲ ﺇﺼﺩﺍﺭ 8.0ﻤﻥ ﺍﻟﻨﻅﺎﻡ( ﻤﻥ ﺍﻟﻘﺎﺌﻤﺔ ﺍﻟﺭﺌﻴﺴﻴﺔ )ﺸﻜل ،(1-12ﻭﺴﻴﻔﺘﺢ ﺃﻤﺭ ﺍﻻﻨﺤﺩﺍﺭ Regressionﻗﺎﺌﻤﺔ ﺃﻭﺍﻤﺭ
ﺍﻻﻨﺤﺩﺍﺭ ﻭﻤﻨﻬﺎ ﻴﺘﻡ ﺍﺨﺘﻴﺎﺭ ﺃﻤﺭ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ Linearﻟﺘﻔﺘﺢ ﻨﺎﻓﺫﺓ ﺘﺤﻠﻴل ﺍﻻﻨﺤﺩﺍﺭ
ﺍﻟﺨﻁﻲ ) Linear Regressionﺸﻜل .(2-12 ﻭﺤﻴﺙ ﺃﻥ ﺘﺭﻜﻴﺯﻨﺎ ﻓﻲ ﻫﺫﺍ ﺍﻟﻔﺼل ﺴﻴﻜﻭﻥ ﻋﻠﻰ ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
ﺭﻏﻡ ﻭﺠﻭﺩ ﺃﻨﻭﺍﻉ ﺃﺨﺭﻯ ﻤﻥ ﺍﻻﻨﺤﺩﺍﺭ ﺴﻨﺘﺤﺩﺙ ﻋﻥ ﺒﻌﻀﻬﺎ ﻓﻲ ﺍﻟﻔﺼل ﺍﻟﺘﺎﻟﻲ ﻓﺈﻥ
ﻫﺫﻩ ﺍﻟﻨﺎﻓﺫﺓ ﺘﺤﺘﻭﻱ ﻋﻠﻰ ﺠﻤﻴﻊ ﺍﻹﺠﺭﺍﺀﺍﺕ ﺍﻟﻤﺘﻌﻠﻘﺔ ﺒﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
ﺍﻟﺨﺎﺼﺔ ﺒﻬﺫﺍ ﺍﻟﻔﺼل.
ﺸﻜل : 1-12ﺍﻟﻭﺼﻭل ﺇﻟﻰ ﻨﺎﻓﺫﺓ ﺘﺤﻠﻴل ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ .Linear Regression
) (12ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
407
ﺸﻜل : 2-12ﻨﺎﻓﺫﺓ ﺘﺤﻠﻴل ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ Linear Regression
.2 .12اﻻﻧﺤﺪار اﻟﺨﻄﻲ اﻟﺒﺴﻴﻂ Simple Regression : ﻓﻲ ﺇﺤﺩﻯ ﺍﻟﻜﻠﻴﺎﺕ ﺍﻟﻜﺒﺭﻯ ﻓﻲ ﺃﺤﺩ ﺍﻟﺠﺎﻤﻌﺎﺕ ﻟﻭﺤﻅ ﺃﻥ ﻫﻨﺎﻙ ﻤﺸﻜﻠﺔ ﻓﻲ
ﻤﻌﺎﻴﻴﺭ ﻗﺒﻭل ﺍﻟﻁﻠﺒﺔ ﻟﻬﺫﻩ ﺍﻟﻜﻠﻴﺔ ،ﻓﺎﻗﺘﺭﺡ ﻤﺠﻠﺱ ﻫﺫﻩ ﺍﻟﻜﻠﻴﺔ ﻨﻅﺎﻡ ﺍﻤﺘﺤﺎﻥ ﻟﻠﻘﺒﻭل ﻟﻬﺫﻩ ﺍﻟﻜﻠﻴﺔ ،ﻓﺘﻘﺭﺭ ﺃﻥ ﻴﺘﻡ ﺘﺠﺭﺒﺔ ﻫﺫﺍ ﺍﻟﻨﻅﺎﻡ ﻓﻲ ﻋﺎﻡ ﻤﻌﻴﻥ ﻋﻠﻰ ﺃﻥ ﻴﺘﻡ ﺍﻟﻌﻤل ﺒﻪ ﻓﻲ ﺤﺎﻟﺔ ﻨﺠﺎﺡ
ﺘﻠﻙ ﺍﻟﺘﺠﺭﺒﺔ ،ﻭﺍﺘﻔﻕ ﻋﻠﻰ ﺃﻥ ﻴﻜﻭﻥ ﻤﻌﻴﺎﺭ ﺍﻟﻨﺠﺎﺡ ﻟﻬﺫﺍ ﺍﻟﻨﻅﺎﻡ ﻫﻭ ﻗﺩﺭﺓ
ﻤﺠﻤﻭﻉ ﺍﻟﺩﺭﺠﺎﺕ ﺍﻟﺘﻲ ﻴﺤﺼل ﻋﻠﻴﻬﺎ ﺍﻟﻁﺎﻟﺏ ﻓﻲ ﺫﻟﻙ ﺍﻻﻤﺘﺤﺎﻥ ﻋﻠﻰ ﺍﻟﺘﻨﺒﺅ ﺒﻤﺴﺘﻭﻯ
ﺃﺩﺍﺀ ﺍﻟﻁﺎﻟﺏ ﻓﻲ ﺍﻟﻜﻠﻴﺔ.
ﻓﺈﺫﺍ ﺤﺼﻠﻨﺎ ﻋﻠﻰ ﻤﺠﻤﻭﻉ ﺍﻟﺩﺭﺠﺎﺕ ﺍﻟﺘﻲ ﺤﺼل ﻋﻠﻴﻬﺎ ﺍﻟﻁﺎﻟﺏ ﻓﻲ ﺍﻟﻔﺼل
ﺍﻷﻭل ﺒﺎﻟﻜﻠﻴﺔ yﻭﻤﺠﻤﻭﻉ ﺍﻟﺩﺭﺠﺎﺕ ﺍﻟﺘﻲ ﺤﺼل ﻋﻠﻴﻬﺎ ﻓﻲ ﺍﻤﺘﺤﺎﻥ ﺍﻟﻘﺒﻭل ﻟﻠﻜﻠﻴﺔ x
ﻓﺈﻨﻪ ﻴﻤﻜﻥ ﺤﺴﺎﺏ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺒﻴﺭﺴﻭﻥ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﻟﻘﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺍﻟﺨﻁﻴﺔ ﺒﻴﻨﻬﻤﺎ ،ﻭﻤﻥ ﺍﻟﻤﻤﻜﻥ ﺃﻴﻀﹰﺎ ﺍﺴﺘﺨﺩﺍﻡ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ ﺍﻟﺒﺴﻴﻁ ﻟﻠﺘﻨﺒﺅ ﺒﻤﺴﺘﻭﻯ ﺃﺩﺍﺀ
ﺍﻟﻁﺎﻟﺏ ﻓﻲ ﺍﻟﺠﺎﻤﻌﺔ ﻤﻥ ﺩﺭﺠﺎﺘﻪ ﻓﻲ ﺍﻤﺘﺤﺎﻥ ﺍﻟﻘﺒﻭل.
) (12ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
408
ﻭﻴﻤﻜﻥ ﺭﻴﺎﻀﻴﹰﺎ ﺃﻴﻀﹰﺎ ﺇﺜﺒﺎﺕ ﺃﻨﻪ ﻋﻨﺩﻤﺎ ﻴﺴﺘﺨﺩﻡ ﻤﺘﻐﻴﺭﻴﻥ ﻤﺴﺘﻘﻠﻴﻥ ﺃﻭ ﺃﻜﺜﺭ ﻓﻲ ﻤﻌﺎﺩﻟﺔ ﺍﻻﻨﺤﺩﺍﺭ ﻟﻠﺘﻨﺒﺅ ﺒﻘﻴﻡ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﺘﺎﺒﻊ yﻓﺈﻥ ﺍﻟﻘﻴﻡ ﺍﻟﻤﺘﻨﺒﺄ ﺒﻬﺎ ﺴﺘﻜﻭﻥ ﺃﺩﻕ ﻤﻤﺎ ﻟﻭ
ﺍﺴﺘﺨﺩﻡ ﻤﺘﻐﻴﺭ ﻤﺴﺘﻘل ﻭﺍﺤﺩ ﻭﻋﻠﻰ ﺍﻷﻗل ﺒﻨﻔﺱ ﺍﻟﺩﻗﺔ ،ﺒﻌﺒﺎﺭﺓ ﺃﺨﺭﻯ ﻻﺒﺩ ﺃﻥ ﻴﻜﻭﻥ
ﻤﻌﺎﻤل ﺍﻻﺭﺘﺒﺎﻁ ﺍﻟﻤﺘﻌﺩﺩ Rﻋﻠﻰ ﺍﻷﻗل ﻤﺴﺎﻭﻴﹰﺎ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺒﻴﺭﺴﻭﻥ ، rﻭﻓﻲ ﻫﺫﺍ
ﺍﻟﻘﺴﻡ ﺴﻭﻑ ﻨﻨﺎﻗﺵ ﺃﺴﻠﻭﺏ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺒﺴﻴﻁ ﻭﺴﻨﻨﺎﻗﺵ ﺃﺴﻠﻭﺏ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﻤﺘﻌﺩﺩ ﻓﻲ
ﺍﻟﻘﺴﻡ ﺍﻟﺘﺎﻟﻲ ﻤﻥ ﻫﺫﺍ ﺍﻟﻔﺼل .
ﻴﻌﺭﺽ ﺍﻟﺸﻜل 3-12ﺒﻴﺎﻨﺎﺕ ﻟﻌﻴﻨﺔ ﻋﺸﻭﺍﺌﻴﺔ ﻤﻜﻭﻨﺔ ﻤﻥ 34ﻤﻥ ﺍﻟﻁﻠﺒﺔ ﻋﻠﻰ ﺸﻜل ﺃﺯﻭﺍﺝ ﻤﻥ ﻗﻴﻡ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ) (x , yﺘﻤﺜل ﻤﺠﻤﻭﻉ ﺩﺭﺠﺎﺕ ﺍﻟﻁﺎﻟﺏ ﻓﻲ ﺍﻤﺘﺤﺎﻥ ﻼ ﺍﻟﻁﺎﻟﺏ ﺍﻟﻘﺒﻭل ﻟﻠﻜﻠﻴﺔ xﻭﻤﺠﻤﻭﻉ ﺩﺭﺠﺎﺘﻪ ﻓﻲ ﺍﻟﻔﺼل ﺍﻷﻭل ﻓﻲ ﺍﻟﻜﻠﻴﺔ ، yﻓﻤﺜ ﹰ ﺍﻷﻭل ﺤﺼل ﻋﻠﻰ ﺍﻟﻤﺠﻤﻭﻉ 44ﻓﻲ ﺍﻤﺘﺤﺎﻥ ﺍﻟﻘﺒﻭل ﻭﻋﻠﻰ ﺍﻟﻤﺠﻤﻭﻉ 38ﻓﻲ
ﺍﻤﺘﺤﺎﻨﺎﺕ ﺍﻟﻜﻠﻴﺔ ،ﻭﺒﺎﻟﻤﺜل ﺤﺼل ﺍﻟﻁﺎﻟﺏ ﺍﻷﺨﻴﺭ )ﺭﻗﻡ (34ﻋﻠﻰ ﺍﻟﻤﺠﻤﻭﻉ 49ﻓﻲ
ﺍﻤﺘﺤﺎﻥ ﺍﻟﻘﺒﻭل ﻭﻋﻠﻰ ﺍﻟﻤﺠﻤﻭﻉ 149ﻓﻲ ﺍﻟﻜﻠﻴﺔ ،ﻭﻫﻜﺫﺍ...
ﺸﻜل : 3-12ﺒﻴﺎﻨﺎﺕ ﻋﻥ ﻤﺠﻤﻭﻉ ﺩﺭﺠﺎﺕ ﺍﻟﻁﻠﺒﺔ ﻓﻲ ﺍﻻﻤﺘﺤﺎﻥ ﺍﻟﻨﻬﺎﺌﻲ Final Univ. Examﻓﻲ ﺍﻟﻜﻠﻴﺔ yﻭﻤﺠﻤﻭﻉ ﺩﺭﺠﺎﺘﻪ ﻓﻲ ﺍﻤﺘﺤﺎﻥ ﺍﻟﻘﺒﻭل Entrance Scoreﻟﻠﻜﻠﻴﺔ x y
x
y
x
y
x
y
x
y
x
60
145
49
112
40
98
37
76
44
38
55
150
46
114
37
100
41
78
40
49
54
152
41
114
48
100
53
81
43
61
58
164
49
117
48
103
47
86
42
65
62
169
63
125
43
105
45
91
44
69
49
195
52
140
55
106
41
94
46
73
56
142
48
107
39
95
34
74
ﻭﺒﺎﺴﺘﺨﺩﺍﻡ ﺍﻟﻁﺭﻕ ﺍﻟﺘﻲ ﺘﻤﺕ ﻤﻨﺎﻗﺸﺘﻬﺎ ﻓﻲ ﺍﻟﻔﺼل ﺍﻟﺜﺎﻨﻲ ﻟﺘﻌﺭﻴﻑ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
ﻭﺇﺩﺨﺎل ﺍﻟﺒﻴﺎﻨﺎﺕ ﻴﻤﻜﻨﻨﺎ ﺒﺴﻬﻭﻟﺔ ﺘﻌﺭﻴﻑ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ selectexﻭ finalexﺍﻟﺫﻴﻥ ﻴﺩﻻﻥ ﻋﻠﻰ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﻤﺠﻤﻭﻉ ﺩﺭﺠﺎﺕ ﺍﻟﻁﺎﻟﺏ ﻓﻲ ﺍﻤﺘﺤﺎﻥ ﺍﻟﻘﺒﻭل ﻟﻠﻜﻠﻴﺔ Entrance Exam
) (12ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
409
ﻭﻤﺠﻤﻭﻉ ﺩﺭﺠﺎﺘﻪ ﻓﻲ ﺍﻟﻔﺼل ﺍﻷﻭل ﻓﻲ ﺍﻟﻜﻠﻴﺔ ، University Examﺜﻡ ﻴﺘﻡ ﺇﺩﺨﺎل ﺍﻟﺒﻴﺎﻨﺎﺕ ﻜﻤﺎ ﻭﺭﺩﺕ ﻓﻲ ﺍﻟﺸﻜل 3-12ﻓﻲ ﻋﻤﻭﺩﻴﻥ ﻓﻘﻁ ﻓﻲ ﻤﺤﺭﺭ ﺍﻟﺒﻴﺎﻨﺎﺕ Data
Editorﻟﻨﻅﺎﻡ . SPSS
ﻭﻟﺘﺤﻠﻴل ﻫﺫﻩ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻻﺒﺩ ﻤﻥ ﺍﻟﻭﺼﻭل ﺇﻟﻰ ﻨﺎﻓﺫﺓ ﺘﺤﻠﻴل ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
Linear Regressionﺒﺎﻟﻁﺭﻴﻘﺔ ﺍﻟﺘﻲ ﺘﻡ ﺘﻭﻀﻴﺤﻬﺎ ﻓﻲ ﺍﻟﺒﻨﺩ .5 .1 .12ﻟﺘﻔﺘﺢ ﺘﻠﻙ ﺍﻟﻨﺎﻓﺫﺓ ،ﻭﻴﺘﻡ ﺒﻬﺎ ﺇﺩﺨﺎل ﺍﺴﻡ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﺘﺎﺒﻊ ﻭﻫﻭ ﻓﻲ ﻫﺫﻩ ﺍﻟﺤﺎﻟﺔ ﻨﺘﻴﺠﺔ ﺍﻤﺘﺤﺎﻥ ﺍﻟﺠﺎﻤﻌﺔ
University Examﻓﻲ ﻤﺭﺒﻊ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﺘﺎﺒﻊ ، Dependent Variableﻭﻴﺘﻡ ﺃﻴﻀﹰﺎ ﺇﺩﺨﺎل ﺍﺴﻡ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﻤﺴﺘﻘل ﻓﻲ ﻤﺭﺒﻊ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻤﺴﺘﻘﻠﺔ ) Independent(sﻭﻫﻭ
ﻓﻲ ﻫﺫﻩ ﺍﻟﺤﺎﻟﺔ ﻨﺘﻴﺠﺔ ﺍﻤﺘﺤﺎﻥ ﺍﻟﻘﺒﻭل Entrance Examﻟﺘﻅﻬﺭ ﺍﻟﻨﺎﻓﺫﺓ ﺘﻤﺎﻤﹰﺎ ﻜﻤﺎ ﻓﻲ ﺍﻟﺸﻜل . 2-12
ﻭﻴﻨﺼﺢ ﺩﺍﺌﻤﺎ ﺒﻁﻠﺏ ﺤﺴﺎﺏ ﺍﻟﻤﻘﺎﻴﻴﺱ ﺍﻟﻭﺼﻔﻴﺔ Descriptive Statistics
ﻼ ﻟﻸﺨﻁﺎﺀ ، residualsﻭﻴﻤﻜﻥ ﺍﻟﺤﺼﻭل ﻋﻠﻰ ﻟﻠﻤﺘﻐﻴﺭﺍﺕ ﻗﻴﺩ ﺍﻟﺩﺭﺍﺴﺔ ﻭﻜﺫﻟﻙ ﺘﺤﻠﻴ ﹰ ﺍﻟﻤﻘﺎﻴﻴﺱ ﺍﻟﻭﺼﻔﻴﺔ ﻤﻥ ﺨﻼل ﺍﻟﻀﻐﻁ ﻋﻠﻰ ﻤﺭﺒﻊ ﺤﻭﺍﺭ ﺍﻹﺤﺼﺎﺀﺍﺕ Statisticsﻓﻲ ﺃﺴﻔل ﺍﻟﻨﺎﻓﺫﺓ ﺍﻟﺴﺎﺒﻘﺔ ﻟﺘﻅﻬﺭ ﻨﺎﻓﺫﺓ ﺍﻹﺤﺼﺎﺀﺍﺕ Linear Regression: Statisticsﻜﻤﺎ
ﻓﻲ ﺍﻟﺸﻜل 4-12ﻓﻴﺘﻡ ﺍﺨﺘﻴﺎﺭ ﺍﻹﺤﺼﺎﺀﺍﺕ ﺍﻟﻤﻁﻠﻭﺒﺔ ﻭﺃﻫﻤﻬﺎ ﻓﻲ ﻫﺫﺍ ﺍﻟﻤﺜﺎل ﺍﻟﻤﻘﺎﻴﻴﺱ ﺍﻟﻭﺼﻔﻴﺔ Descriptive Statisticsﻭﺘﻘﺩﻴﺭ ﻟﻤﻌﺎﺩﻟﺔ ﺍﻻﻨﺤﺩﺍﺭ
Estimates
ﻭﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻼﺯﻤﺔ ﻻﺨﺘﺒﺎﺭ ﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ Model fitﺒﺎﻹﻀﺎﻓﺔ ﺇﻟﻰ ﻓﺤﺹ
ﺍﻷﺨﻁﺎﺀ Residualsﺒﻬﺩﻑ ﺍﺴﺘﻜﺸﺎﻑ ﺍﻟﻤﻔﺭﺩﺍﺕ ﺒﺤﺜﹰﺎ ﻋﻥ ﺃﻱ ﻋﺩﺩ ﻤﻥ ﺍﻟﻘﻴﻡ ﺍﻟﺸﺎﺫﺓ
،Outliersﺤﻴﺙ ﻴﺤﺩﺩ ﺘﻌﺭﻴﻑ ﻫﺫﻩ ﺍﻟﻘﻴﻡ ﺒﺤﻴﺙ ﺘﻜﻭﻥ ﺍﻟﻘﻴﻡ ﺍﻟﺘﻲ ﺘﺒﻌﺩ ﻋﻥ ﺍﻟﻭﺴﻁ ﺍﻟﺤﺴﺎﺒﻲ meanﺒﻤﻘﺩﺍﺭ ) (3ﺃﻀﻌﺎﻑ ﻗﻴﻤﺔ ﺍﻻﻨﺤﺭﺍﻑ ﺍﻟﻤﻌﻴﺎﺭﻱ
standard
deviationsﻤﻊ ﺇﻤﻜﺎﻨﻴﺔ ﺘﻐﻴﻴﺭ ﺍﻟﻘﻴﻤﺔ ، 3ﻭﻫﺫﺍ ﻴﺘﻡ ﻋﻥ ﻁﺭﻴﻕ ﺍﺨﺘﻴﺎﺭ ﻓﺤﺹ ﺍﻟﻤﻔﺭﺩﺍﺕ Casewise Diagnosticsﺘﺤﺕ ﺒﻨﺩ ﺍﻷﺨﻁﺎﺀ Residualsﻓﻲ ﺃﺴﻔل ﻨﺎﻓﺫﺓ ﺍﻹﺤﺼﺎﺀﺍﺕ ،ﻻﺤﻅ ﺃﻥ ﻫﻨﺎﻙ ﺃﻴﻀﺎ ﺇﺤﺼﺎﺀﺍﺕ ﺃﺨﺭﻯ ﻴﻤﻜﻥ ﺤﺴﺎﺒﻬﺎ ﻭﻟﻜﻨﻬﺎ ﻟﻴﺴﺕ
ﺫﺍﺕ ﺃﻫﻤﻴﺔ ﻜﺒﻴﺭﺓ ﻓﻲ ﺘﺤﻠﻴل ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ ﺍﻟﺒﺴﻴﻁ .
) (12ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
410
ﺸﻜل : 4-12ﻨﺎﻓﺫﺓ ﺍﻹﺤﺼﺎﺀﺍﺕ Statisticsﻓﻲ ﺘﺤﻠﻴل ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
ﺸﻜل : 5-12ﻨﺎﻓﺫﺓ ﺍﻟﺭﺴﻭﻤﺎﺕ ﺍﻟﺒﻴﺎﻨﻴﺔ Plotsﻓﻲ ﺘﺤﻠﻴل ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
ﻭﻴﻤﻜﻥ ﺍﻟﺤﺼﻭل ﻋﻠﻰ ﻤﻌﻠﻭﻤﺎﺕ ﺤﻭل ﺍﻷﺨﻁﺎﺀ residualsﻭﻜﺫﻟﻙ ﺤﻭل ﺍﻟﻘﻴﻡ
ﺍﻟﻤﺘﻭﻗﻌﺔ Fitted Valuesﻋﻥ ﻁﺭﻴﻕ ﺨﻴﺎﺭ ﺍﻟﺭﺴﻭﻤﺎﺕ ﺍﻟﺒﻴﺎﻨﻴﺔ Plotsﻓﻲ ﻨﺎﻓﺫﺓ ﺘﺤﻠﻴل
ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ ) Linear Regressionﺸﻜل ، (2-12ﻭﻤﻨﻬﺎ ﺘﻅﻬﺭ ﻨﺎﻓﺫﺓ ﺨﺎﺼﺔ
ﺒﺎﻟﺭﺴﻭﻤﺎﺕ ﺍﻟﺒﻴﺎﻨﻴﺔ ) Linear Regression: Plotsﺸﻜل (5-12ﻴﻤﻜﻨﻨﺎ ﻤﻥ ﺨﻼﻟﻬﺎ
ﺭﺴﻡ ﺃﻱ ﻤﻥ ﺍﻷﺨﻁﺎﺀ residualsﺃﻭ ﺍﻟﻘﻴﻡ ﺍﻟﻤﺘﻭﻗﻌﺔ fitted valuesﺃﻭ ﻜﻠﻴﻬﻤﺎ ﻤﻘﺎﺒل
) (12ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
411
ﻗﻴﻡ ﺃﻱ ﻤﺘﻐﻴﺭ ﺁﺨﺭ ﻤﻥ ﺒﻴﻥ ﻗﺎﺌﻤﺔ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﺘﻲ ﻗﺎﻡ ﺍﻟﻨﻅﺎﻡ ﺒﺤﺴﺎﺒﻬﺎ ﻋﻨﺩ ﺘﻘﺩﻴﺭ ﻤﻌﺎﺩﻟﺔ ﺍﻻﻨﺤﺩﺍﺭ ،ﻭﻓﻲ ﻤﺜل ﻫﺫﻩ ﺍﻟﺤﺎﻟﺔ ﻴﻜﻭﻥ ﻤﻥ ﺍﻟﻤﻔﻴﺩ ﺭﺴﻡ ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ ﻟﻠﻘﻴﻡ
ﺍﻟﻤﻌﻴﺎﺭﻴﺔ ﻟﻸﺨﻁﺎﺀ )ﻭﻴﺸﺎﺭ ﻟﻬﺎ ﻓﻲ ﻗﺎﺌﻤﺔ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﻓﻲ ﺍﻟﻨﺎﻓﺫﺓ ﺒﺎﻻﺴﻡ (*ZRESID ﻤﻘﺎﺒل ﺍﻟﻘﻴﻡ ﺍﻟﻤﻌﻴﺎﺭﻴﺔ ﻟﻠﻘﻴﻡ ﺍﻟﻤﺘﻭﻗﻌﺔ )ﻭﻴﺸﺎﺭ ﻟﻬﺎ ﻓﻲ ﻗﺎﺌﻤﺔ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﻓﻲ ﺍﻟﻨﺎﻓﺫﺓ
ﺒﺎﻻﺴﻡ (*ZPREDﻟﻠﺘﺄﻜﺩ ﻤﻥ ﺘﺤﻘﻕ ﺼﺤﺔ ﻓﺭﻀﻴﺘﻲ ﻋﺸﻭﺍﺌﻴﺔ ﺍﻷﺨﻁﺎﺀ ﻭﺘﺠﺎﻨﺱ
ﺘﺒﺎﻴﻨﻬﺎ ،ﻭﻜﺫﻟﻙ ﺭﺴﻡ ﺍﻟﺘﻭﺯﻴﻊ ﺍﻟﻁﺒﻴﻌﻲ ﻟﻸﺨﻁﺎﺀ Normal Probability Plotﻟﻠﺘﺤﻘﻕ ﻤﻥ ﺼﺤﺔ ﻓﺭﻀﻴﺔ ﺍﻟﺘﻭﺯﻴﻊ ﺍﻟﻁﺒﻴﻌﻲ ﻟﻸﺨﻁﺎﺀ ،ﻟﺘﻅﻬﺭ ﺍﻟﻨﺎﻓﺫﺓ ﺒﻌﺩ ﺇﺩﺨﺎل ﺍﻟﻤﻌﻠﻭﻤﺎﺕ
ﺍﻟﻤﻁﻠﻭﺒﺔ ﻜﻤﺎ ﻓﻲ ﺍﻟﺸﻜل ،5-12ﻓﺈﺫﺍ ﺘﺒﻴﻥ ﺃﻥ ﻫﻨﺎﻙ ﺍﺨﺘﺭﺍﻕ ﻜﺒﻴﺭ ﻷﻱ ﻓﺭﻀﻴﺔ ﻓﺈﻥ
ﺫﻟﻙ ﻴﻌﻨﻲ ﺃﻥ ﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺫﻱ ﺘﻡ ﺘﻁﺒﻴﻘﻪ ﻻ ﻴﺼﻠﺢ ﻟﻬﺫﻩ ﺍﻟﺒﻴﺎﻨﺎﺕ.
ﻭﻋﻨﺩ ﺘﻨﻔﻴﺫ ﺍﻷﻤﺭ ﺴﻭﻑ ﺘﻔﺘﺢ ﺸﺎﺸﺔ ﺍﻟﻨﺘﺎﺌﺞ Output Viewerﻟﺘﺨﺭﺝ ﻗﺎﺌﻤﺔ
ﻤﻥ ﺍﻟﺠﺩﺍﻭل ﻭﺍﻟﺭﺴﻭﻤﺎﺕ ﺍﻟﺒﻴﺎﻨﻴﺔ ﻓﻲ ﻫﺫﻩ ﺍﻟﺸﺎﺸﺔ ﻓﻲ ﺒﻨﻭﺩ ﺘﻅﻬﺭ ﺃﺴﻤﺎﺀﻫﺎ ﻓﻲ ﻗﺎﺌﻤﺔ
ﺒﻨﻭﺩ ﺍﻟﻨﺘﺎﺌﺞ ﻋﻠﻰ ﻴﺴﺎﺭ ﺍﻟﺸﺎﺸﺔ ﺘﺸﺒﻪ ﺍﻟﺸﻜل ،6-12ﻭﻴﻨﺼﺢ ﻓﻲ ﺍﻟﺒﺩﺍﻴﺔ ﺒﺎﻟﺒﺤﺙ ﻋﻥ ﺠﺩﻭل ﻓﺤﺹ ﺍﻟﺒﻴﺎﻨﺎﺕ Casewise Diagnosticsﺍﻟﺫﻱ ﻭﺠﻭﺩﻩ ﻴﻌﻨﻲ ﻭﺠﻭﺩ ﻗﻴﻡ ﺸﺎﺫﺓ
ﻗﺩ ﺘﺅﺩﻱ ﺇﻟﻰ ﺍﻟﺘﺄﺜﻴﺭ ﺒﺸﻜل ﺴﻠﺒﻲ ﻋﻠﻰ ﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﻤﺴﺘﺨﻠﺹ ،ﻓﻭﺠﻭﺩﻩ ﻴﻌﻨﻲ ﻭﺠﻭﺩ ﻗﻴﻤﹰﺎ ﺸﺎﺫﺓ Outliersﻓﻲ ﺍﻟﺒﻴﺎﻨﺎﺕ ،ﻭﻴﺘﻡ ﺍﻟﺒﺤﺙ ﻋﻥ ﻫﺫﺍ ﺍﻟﺠﺩﻭل ﻓﻲ ﺍﻟﻘﺎﺌﻤﺔ
ﻋﻠﻰ ﻴﺴﺎﺭ ﺍﻟﺸﺎﺸﺔ ﻋﻥ ﺒﻨﺩ ﻓﺤﺹ ﺍﻟﺒﻴﺎﻨﺎﺕ Casewise Diagnosticsﻭﺍﻟﻨﻅﺭ ﺇﻟﻰ
ﺍﻟﻨﺘﺎﺌﺞ ﺇﻥ ﻭﺠﺩ ﻫﺫﺍ ﺍﻟﺠﺩﻭل ،ﻭﻓﻲ ﻤﺜﺎﻟﻨﺎ )ﺸﻜل (7-12ﺴﻨﺠﺩ ﺃﻥ ﻫﻨﺎﻙ ﻗﻴﻤﺔ ﺸﺎﺫﺓ ﻭﺤﻴﺩﺓ ﻭﻫﻲ ﺍﻟﻤﻔﺭﺩﺓ ﺭﻗﻡ (49 ،195) 34ﺍﻷﻤﺭ ﺍﻟﺫﻱ ﻴﺴﺘﻭﺠﺏ ﺤﺫﻓﻬﺎ ﻤﻥ ﺍﻟﺒﻴﺎﻨﺎﺕ.
ﻭﻴﻤﻜﻥ ﺍﻻﻋﺘﻤﺎﺩ ﺃﻜﺜﺭ ﻋﻠﻰ ﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﻨﺎﺘﺞ ﺇﺫﺍ ﻟﻡ ﻴﺘﺨﻠل ﺍﻟﺒﻴﺎﻨﺎﺕ ﺃﻱ ﻗﻴﻤﺔ ﺸﺎﺫﺓ ﺘﻌﻜﺭ ﺼﻔﻭﻫﺎ ،ﻟﺫﺍ ﻓﺈﻥ ﺍﻟﻤﻔﺭﺩﺓ ﺭﻗﻡ 34ﻗﺩ ﺍﺴﺘﺒﻌﺩﺕ ﻤﻥ ﺍﻟﺒﻴﺎﻨﺎﺕ ،ﻭﻴﻤﻜﻥ ﺍﺴﺘﺒﻌﺎﺩ ﻗﻴﻤﺔ )ﺃﻭ ﺃﻜﺜﺭ( ﻤﻥ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻋﻥ ﻁﺭﻴﻕ ﺤﺫﻓﻬﺎ ﻨﻬﺎﺌﻴﹰﺎ ﺃﻭ ﻋﻥ ﻁﺭﻴﻕ ﺍﺴﺘﺨﺩﺍﻡ
ﺃﻤﺭ ﺍﺨﺘﻴﺎﺭ ﺍﻟﺒﻴﺎﻨﺎﺕ Select Casesﺍﻟﺫﻱ ﺘﻡ ﺍﻟﺘﻌﺎﻤل ﻤﻌﻪ ﻓﻲ ﺍﻟﻔﺼل ﺍﻟﺜﺎﻟﺙ ،ﻭﺒﻪ ﻴﺘﻡ
ﺍﺨﺘﻴﺎﺭ ﺠﻤﻴﻊ ﺍﻟﻤﻔﺭﺩﺍﺕ ﺫﺍﺕ ﻗﻴﻤﺔ ﻟﻤﺘﻐﻴﺭ ﺩﺭﺠﺎﺕ ﺍﻟﻁﺎﻟﺏ ﻓﻲ ﺍﻟﺠﺎﻤﻌﺔ Final Exam
ﻻ ﺘﺴﺎﻭﻱ 195ﻓﻲ ﻫﺫﻩ ﺍﻟﺤﺎﻟﺔ ﺃﻭ ﺃﺼﻐﺭ ﺃﻭ ﺃﻜﺒﺭ ﻤﻥ ﻗﻴﻤﺔ ﻤﻌﻴﻨﺔ ﻓﻲ ﺤﺎﻻﺕ ﺃﺨﺭﻯ.
( ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ12)
412
Linear Regression ﻗﺎﺌﻤﺔ ﺍﻟﻨﺘﺎﺌﺞ ﻤﻥ ﺘﻨﻔﻴﺫ ﺃﻤﺭ ﺘﺤﻠﻴل ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ:6-12 ﺸﻜل
ﻗﺒلLinear Regression ﺠﺎﻨﺏ ﻤﻥ ﻗﺎﺌﻤﺔ ﻨﺘﺎﺌﺞ ﺘﺤﻠﻴل ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ: 7-12 ﺸﻜل .Casewise Diagnostics ﻭﺍﻟﺨﺎﺹ ﺒﻔﺤﺹ ﺍﻟﺒﻴﺎﻨﺎﺕOutlier ﺤﺫﻑ ﺍﻟﻘﻴﻤﺔ ﺍﻟﺸﺎﺫﺓ Regression Variables Entered/Removedb
Model 1
Variables Entered
Variables Removed
Entrance a Exam
Method . Enter
a. All requested variables entered. b. Dependent Variable: University Exam
Casewise Diagnosticsa
Case Number 34
Std. Residual
University Exam
3.133
195
a. Dependent Variable: University Exam
Predicted Value 110.30
Residual 84.70
) (12ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
413
ﻭﻋﻨﺩﻤﺎ ﻴﺘﻡ ﺘﻨﻔﻴﺫ ﺃﻤﺭ ﺘﺤﻠﻴل ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ Linear Regressionﻤﺭﺓ ﺃﺨﺭﻯ ﺒﻌﺩ ﺍﺴﺘﺒﻌﺎﺩ ﺍﻟﻘﻴﻤﺔ ﺍﻟﺸﺎﺫﺓ ﻤﻥ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻟﻥ ﻴﻅﻬﺭ ﺍﻟﺠﺩﻭل ﺍﻟﺨﺎﺹ ﺒﻔﺤﺹ
ﺍﻟﺒﻴﺎﻨﺎﺕ Casewise Diagnosticsﻷﻨﻪ ﻟﻡ ﻴﺘﺒﻕ ﺃﻱ ﻗﻴﻡ ﺸﺎﺫﺓ ﻓﻲ ﺍﻟﺒﻴﺎﻨﺎﺕ ،ﻭﺒﻬﺫﺍ
ﻓﺈﻨﻪ ﻴﻤﻜﻨﻨﺎ ﺍﺴﺘﻜﻤﺎل ﻓﺤﺹ ﺍﻟﻨﻤﻭﺫﺝ ﻗﺒل ﺍﻻﻋﺘﻤﺎﺩ ﻋﻠﻴﻪ ﻋﻥ ﻁﺭﻴﻕ ﻓﺤﺹ ﺍﻟﺠﺩﺍﻭل ﻭﺍﻟﺭﺴﻭﻤﺎﺕ ﺍﻷﺨﺭﻯ ﺍﻟﻨﺎﺘﺠﺔ ،ﻭﺍﻟﺠﺯﺀ ﺍﻷﻭل ﻤﻥ ﻗﺎﺌﻤﺔ ﺍﻟﻨﺘﺎﺌﺞ ﻴﺘﻜﻭﻥ ﻤﻥ ﺠﺩﻭﻟﻴﻥ
ﺨﺎﺼﻴﻥ ﺒﺎﻟﻤﻘﺎﻴﻴﺱ ﺍﻟﻭﺼﻔﻴﺔ ﻟﻠﻤﺘﻐﻴﺭﺍﺕ ﻭﻤﻌﺎﻤل ﺍﻻﺭﺘﺒﺎﻁ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ rﻭﺫﻟﻙ ﺒﺎﺴﺘﺨﺩﺍﻡ 33ﻤﻔﺭﺩﺓ ﺍﻟﻤﺘﺒﻘﻴﺔ )ﺸﻜل .(8-12
ﻭﺍﻟﺠﺯﺀ ﺍﻟﺜﺎﻨﻲ ﻤﻥ ﺍﻟﻨﺘﺎﺌﺞ )ﺸﻜل (9-12ﻴﺤﺘﻭﻱ ﻋﻠﻰ ﻗﻴﻤﺔ ﺍﻻﺭﺘﺒﺎﻁ ﺍﻟﻤﺘﻌﺩﺩ
،Rﻭﺤﻴﺙ ﺃﻥ ﻫﻨﺎﻙ ﻤﺘﻐﻴﺭ ﻤﺴﺘﻘل ﻭﺍﺤﺩ ﻓﺈﻥ ﻗﻴﻤﺘﻪ ﻟﻥ ﺘﺨﺘﻠﻑ ﻋﻥ ﻗﻴﻤﺔ ﻤﻌﺎﻤل
ﺍﺭﺘﺒﺎﻁ ﺒﻴﺭﺴﻭﻥ rﻓﻲ ﺍﻟﺠﺩﻭل ﺍﻟﻤﺒﻴﻥ ﻓﻲ ﺸﻜل 8-12ﺍﻟﺴﺎﺒﻕ ،ﻭﺍﻹﺤﺼﺎﺀﺍﺕ ﺍﻷﺨﺭﻯ ﺍﻟﻤﺒﻴﻨﺔ ﻫﻲ ﻤﺭﺒﻊ ﻗﻴﻤﺔ ﻤﻌﺎﻤل ﺍﻻﺭﺘﺒﺎﻁ ﺍﻟﻤﺘﻌﺩﺩ (R2) R-Squareﻭﻫﻭ
ﻤﻌﺎﻤل ﻤﻭﺠﺏ ﺩﺍﺌﻤﺎ ﻭﻴﻭﻀﺢ ﻨﺴﺒﺔ ﺍﻟﺘﻐﻴﺭﺍﺕ ﻓﻲ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﺘﺎﺒﻊ yﺍﻟﺘﻲ ﺘﺸﺭﺤﻬﺎ
ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻤﺴﺘﻘﻠﺔ xﻤﻥ ﺨﻼل ﻤﻌﺎﺩﻟﺔ ﺍﻻﻨﺤﺩﺍﺭ ،ﻭﻫﻨﺎﻙ ﻗﻴﻤﺔ ﻤﻌﺩﻟﺔ ﻟﻬﺫﺍ ﺍﻟﻤﻌﺎﻤل ﺃﻴﻀﹰﺎ Adjusted R-Squareﻭﻫﻲ ﻟﺘﺼﺤﻴﺢ ﺍﻟﺘﺤﻴﺯ ﻓﻲ ﺍﻟﻤﻌﺎﻤل ﺍﻟﺴﺎﺒﻕ )ﻟﺫﺍ ﻓﻬﻲ
ﺃﻗل ﻤﻥ ﺍﻟﻘﻴﻤﺔ ﺍﻷﻭﻟﻰ( ،ﻭﻫﻨﺎﻙ ﺃﻴﻀ ﹰﺎ ﻗﻴﻤﺔ ﺍﻟﺨﻁﺄ ﺍﻟﻤﻌﻴﺎﺭﻱ Standard Error
ﻟﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺫﻱ ﺘﻡ ﺍﺴﺘﺨﻼﺼﻪ ،ﻭﻫﻭ ﻋﺒﺎﺭﺓ ﻋﻥ ﺍﻻﻨﺤﺭﺍﻑ ﺍﻟﻤﻌﻴﺎﺭﻱ
Standard Deviationﻟﻸﺨﻁﺎﺀ .
( ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ12)
414
Linear Regression ﺍﻟﺠﺯﺀ ﺍﻷﻭل ﻤﻥ ﻨﺘﺎﺌﺞ ﺘﺤﻠﻴل ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ: 8-12 ﺸﻜل Descriptive Statistics Mean
Std. Deviation
N
University Exam
102.82
32.63
33
Entrance Exam
47.27
7.54
33
Correlations
Pearson Correlation Sig. (1-tailed) N
University Exam
Entrance Exam
University Exam
1.000
.729
Entrance Exam
.729
1.000
University Exam
.
.000
Entrance Exam
.000
.
University Exam
33
33
Entrance Exam
33
33
Linear Regression ﺍﻟﺠﺯﺀ ﺍﻟﺜﺎﻨﻲ ﻤﻥ ﻨﺘﺎﺌﺞ ﺘﺤﻠﻴل ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ: 9-12 ﺸﻜل Model Summaryb
Model 1
R a
.729
R Square
Adjusted R Square
Std. Error of the Estimate
.531
.516
22.70
a. Predictors: (Constant), Entrance Exam b. Dependent Variable: University Exam
Regression ﻭﻴﺤﺘﻭﻱ ﺍﻟﺠﺯﺀ ﺍﻟﺜﺎﻟﺙ ﻤﻥ ﺍﻟﻨﺘﺎﺌﺞ ﻋﻠﻰ ﺠﺩﻭل ﺘﺤﻠﻴل ﺍﻟﺘﺒﺎﻴﻥ
( ﻭﺍﻟﺫﻱ ﻤﻥ ﺨﻼﻟﻪ ﻴﺘﻡ ﺍﺨﺘﺒﺎﺭ ﻓﺭﻀﻴﺔ ﻭﺠﻭﺩ ﻋﻼﻗﺔ ﺨﻁﻴﺔ10-12 )ﺸﻜلANOVA
ﻭﺍﻟﺘﻲ ﺘﻤﺜل ﺍﻟﻨﺴﺒﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁF ﺤﻘﻴﻘﻴﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺒﺎﺴﺘﺨﺩﺍﻡ ﺩﺍﻟﺔ ﺍﺨﺘﺒﺎﺭ
ﻟﺫﺍ ﻓﺈﻨﻪ ﻟﻜﻲ ﺘﻜﻭﻥ،ﺍﻟﻤﺭﺒﻌﺎﺕ ﺍﻟﺫﻱ ﻴﻌﺯﻯ ﻟﻼﻨﺤﺩﺍﺭ ﺇﻟﻰ ﻤﺘﻭﺴﻁ ﻤﺭﺒﻌﺎﺕ ﺍﻷﺨﻁﺎﺀ
. ﻜﺒﻴﺭﺓF ﺍﻟﻌﻼﻗﺔ ﺍﻟﺨﻁﻴﺔ ﺤﻘﻴﻘﻴﺔ ﻭﻤﻌﻨﻭﻴﺔ ﻴﺠﺏ ﺃﻥ ﺘﻜﻭﻥ ﻗﻴﻤﺔ
) (12ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
415
ﺸﻜل : 10-12ﺍﻟﺠﺯﺀ ﺍﻟﺜﺎﻟﺙ ﻤﻥ ﻨﺘﺎﺌﺞ ﺘﺤﻠﻴل ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ Linear Regression ANOVAb
Sig.
F
Mean Square
df
Sum of Squares
.000
35.104
18096.329
1
18096.329
Regression
515.503
31
15980.580
Residual
32
34076.909
Total
a
Model 1
a. Predictors: (Constant), Entrance Exam b. Dependent Variable: University Exam
ﻭﻓﻲ ﻫﺫﺍ ﺍﻟﻤﺜﺎل ﻴﺘﻀﺢ ﺃﻥ ﻗﻴﻤﺔ Fﻜﺒﻴﺭﺓ ﺠﺩﹰﺍ ﻭﻜﺫﻟﻙ ﻗﻴﻤﺔ (p-value) Sig. ﺼﻐﻴﺭﺓ ﺠﺩﹰﺍ )ﺃﻗل ﻤﻥ ،(0.0005ﻭﻫﺫﺍ ﻴﺩل ﻋﻠﻰ ﺃﻥ ﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
ﻤﻌﻨﻭﻱ ،ﺃﻱ ﺃﻥ ﻋﻼﻗﺔ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻴﺔ ﻤﻌﻨﻭﻴﺔ ) (p-value < 0.01ﻭﻟﻜﻥ ﻴﺠﺏ
ﺍﻟﺘﺄﻜﻴﺩ ﻋﻠﻰ ﺃﻨﻪ ﻻ ﻴﻤﻜﻨﻨﺎ ﺍﻟﺘﺄﻜﺩ ﻤﻥ ﺼﺤﺔ ﻭﺠﻭﺩ ﺍﻟﻌﻼﻗﺔ ﺍﻟﺨﻁﻴﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﺇﻻ
ﺇﺫﺍ ﺩﻋﻤﺕ ﻫﺫﻩ ﺍﻟﻨﺘﻴﺠﺔ ﺒﻌﻼﻗﺔ ﺨﻁﻴﺔ ﺤﻘﻴﻘﻴﺔ ﻭﺍﻀﺤﺔ ﻓﻲ ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ.
ﺸﻜل : 11-12ﺍﻟﺠﺯﺀ ﺍﻟﺭﺍﺒﻊ ﻤﻥ ﻨﺘﺎﺌﺞ ﺘﺤﻠﻴل ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ Linear Regression Coefficientsa Standardized Coefficients Sig.
t
.079
-1.817
.000
5.925
Beta
.729
Unstandardized Coefficients Std. Error
B
25.477
-46.305
.532
3.155
Model )(Constant Entrance Exam
a. Dependent Variable: University Exam
1
) (12ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
416
ﻭﻴﺒﻴﻥ ﺸﻜل 11-12ﻨﻭﺍﺓ ﺘﺤﻠﻴل ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ ﺤﻴﺙ ﺃﻨﻪ ﻴﺤﺘﻭﻱ ﻋﻠﻰ ﻤﻌﺎﺩﻟﺔ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻴﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ،ﻓﻘﻴﻤﺔ ﺜﺎﺒﺕ ﺍﻻﻨﺤﺩﺍﺭ constantﻭﻤﻌﺎﻤل ﺍﻻﻨﺤﺩﺍﺭ regression coefficientﻟﻤﺘﻐﻴﺭ ﺩﺭﺠﺎﺕ ﺍﻟﻁﺎﻟﺏ ﻓﻲ ﺍﻤﺘﺤﺎﻥ ﺍﻟﻘﺒﻭل
Entrance Examﻭﺫﻟﻙ ﻓﻲ ﺍﻟﻌﻤﻭﺩ ﺒﻌﻨﻭﺍﻥ Bﻓﻲ ﺍﻟﺠﺩﻭل ،ﻭﻤﻥ ﻫﺫﺍ ﺍﻟﺸﻜل ﻴﻤﻜﻥ ﻗﺭﺍﺀﺓ ﻤﻌﺎﺩﻟﺔ ﺍﻻﻨﺤﺩﺍﺭ ﻟﻠﻤﺜﺎل ﺍﻟﺤﺎﻟﻲ ﻜﻤﺎ ﻴﻠﻲ:
Y = 3.15 X - 46.30
ﺃﻭ : Predicted University Exam = 3.15 × (Entrance Exam) – 46.30
ﻭﺒﺎﻟﺘﺎﻟﻲ ﻓﺈﻨﻪ ﺇﺫﺍ ﺤﺼل ﻁﺎﻟﺏ ﻋﻠﻰ ﺩﺭﺠﺔ ﻓﻲ ﺍﻤﺘﺤﺎﻥ ﺍﻟﻘﺒﻭل ﻤﺴﺎﻭﻴﺔ 60ﻓﺈﻨﻪ ﻴﺘﻭﻗﻊ
ﺃﻥ ﺘﻜﻭﻥ ﺩﺭﺠﺎﺘﻪ ﻓﻲ ﺍﻟﻔﺼل ﺍﻷﻭل ﻓﻲ ﺍﻟﻜﻠﻴﺔ ﻤﺴﺎﻭﻴﺔ :
3.15 × 60 – 46.30 = 142.7 ~= 143
ﻻﺤﻅ ﺃﻨﻪ ﻤﻥ ﻭﺍﻗﻊ ﺍﻟﺒﻴﺎﻨﺎﺕ ﺍﻟﺤﻘﻴﻘﻴﺔ ﻴﺘﺒﻴﻥ ﺃﻥ ﺍﻟﻁﺎﻟﺏ ﺍﻟﺫﻱ ﺤﺼل ﻋﻠﻰ ﺩﺭﺠﺔ 60
ﻼ ﻋﻠﻰ ﺍﻟﺩﺭﺠﺔ 145ﻓﻲ ﺍﻟﻔﺼل ﺍﻷﻭل ﻓﻲ ﺍﻟﻜﻠﻴﺔ، ﻓﻲ ﺍﻤﺘﺤﺎﻥ ﺍﻟﻘﺒﻭل ﻗﺩ ﺤﺼل ﻓﻌ ﹰ ﻭﺒﺎﻟﺘﺎﻟﻲ ﻴﻜﻭﻥ ﺍﻟﺨﻁﺄ residualﻋﻨﺩ ﻫﺫﻩ ﺍﻟﻨﻘﻁﺔ ﻤﺴﺎﻭﻴﹰﺎ . 145-143= +2 :
ﻭﻫﻨﺎﻙ ﺇﺤﺼﺎﺀﺍﺕ ﺃﺨﺭﻯ ﻫﺎﻤﺔ ﺘﻡ ﺤﺴﺎﺒﻬﺎ ﻓﻲ ﻨﻔﺱ ﺍﻟﺠﺩﻭل ﻓﻲ ﺸﻜل 11-12
ﻭﻫﻲ ﺍﻟﺨﻁﺄ ﺍﻟﻤﻌﻴﺎﺭﻱ Std. Errorﻟﻜل ﻤﻥ ﺜﺎﺒﺕ ﺍﻻﻨﺤﺩﺍﺭ ﻭﻤﻌﺎﻤل ﺍﻻﻨﺤﺩﺍﺭ ﺒﺎﻹﻀﺎﻓﺔ ﺇﻟﻰ ﻗﻴﻤﺔ ﺩﺍﻟﺔ ﺍﻻﺨﺘﺒﺎﺭ tﻟﻜل ﻤﻨﻬﻤﺎ ﻭﻫﻤﺎ ﻻﺨﺘﺒﺎﺭ ﻤﻌﻨﻭﻴﺔ ﻜل ﻤﻥ ﺜﺎﺒﺕ
ﺍﻻﻨﺤﺩﺍﺭ ﻭﻤﻌﺎﻤل ﺍﻻﻨﺤﺩﺍﺭ ،ﻭﻜل ﻗﻴﻤﺔ ﻤﻥ ﻫﺎﺘﻴﻥ ﺍﻟﻘﻴﻤﺘﻴﻥ ﻴﺘﺒﻌﻬﺎ ﻤﺴﺘﻭﻯ ﺍﻟﻤﻌﻨﻭﻴﺔ
(p-value) Sig.ﺍﻟﺨﺎﺹ ﺒﻬﺎ ﻻﺨﺘﺒﺎﺭ ﺍﻟﻔﺭﻀﻴﺔ ﺍﻟﻌﺩﻤﻴﺔ ﺃﻥ ﺍﻟﻘﻴﻤﺔ ﺍﻟﺤﻘﻴﻘﻴﺔ ﻓﻲ ﺍﻟﻤﺠﺘﻤﻊ ﻤﺴﺎﻭﻴﺔ ﺍﻟﺼﻔﺭ ،ﻭﻤﻌﻨﻭﻴﺔ ﺍﻻﺨﺘﺒﺎﺭ ﻓﻲ ﻫﺫﻩ ﺍﻟﺤﺎﻟﺔ ﺘﻌﻨﻲ ﺃﻥ ﺍﻟﻘﻴﻤﺔ ﺍﻟﺤﻘﻴﻘﻴﺔ
ﻓﻲ ﺍﻟﻤﺠﺘﻤﻊ ﻻ ﺘﺴﺎﻭﻱ ﺍﻟﺼﻔﺭ ،ﻭﺍﻷﻜﺜﺭ ﺃﻫﻤﻴﺔ ﻫﻲ ﻤﻌﻨﻭﻴﺔ ﻤﻌﺎﻤل ﺍﻻﻨﺤﺩﺍﺭ ﺇﺫ ﺃﻥ ﻋﺩﻡ ﻤﻌﻨﻭﻴﺘﻪ ﻴﻌﻨﻲ ﻋﺩﻡ ﻭﺠﻭﺩ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﻏﻴﺭ ﺤﻘﻴﻘﻴﺔ ،ﻭﻓﻲ ﻫﺫﺍ ﺍﻟﻤﺜﺎل
ﻨﺠﺩ ﺃﻥ ﻤﻌﺎﻤل ﺍﻻﻨﺤﺩﺍﺭ ﻤﻌﻨﻭﻱ ) . ( t = 5.925; p-value < 0.01
) (12ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
417
ﺸﻜل :12-12ﺍﻟﺠﺯﺀ ﺍﻟﺨﺎﻤﺱ ﻤﻥ ﻨﺘﺎﺌﺞ ﺘﺤﻠﻴل ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ Linear Regression Residuals Statisticsa
N
Std. Deviation
Mean
Minimum Maximum
33
23.78
102.82
152.43
60.95
Predicted Value
33
22.35
1.3E-14
30.97
-54.49
Residual
33
1.000
.000
2.086
-1.761
Std. Predicted Value
33
.984
.000
1.364
-2.400
Std. Residual
a. Dependent Variable: University Exam
ﻻ ﻭﻴﺒﻴﻥ ﺍﻟﺠﺯﺀ ﺍﻟﺨﺎﻤﺱ ﻤﻥ ﻗﺎﺌﻤﺔ ﺍﻟﻨﺘﺎﺌﺞ ﻓﻲ ﺸﻜل 12-12ﺠﺩﻭ ﹰ
ﺒﺎﻹﺤﺼﺎﺀﺍﺕ ﺍﻟﻤﺘﻌﻠﻘﺔ ﺒﺎﻷﺨﻁﺎﺀ Residualsﻭﺘﺸﻤل ﺇﺤﺼﺎﺀﺍﺕ ﺘﺘﻌﻠﻕ ﺒﺎﻟﻘﻴﻡ ﺍﻟﻤﺘﻭﻗﻌﺔ
ﺍﻟﺨﺎﻡ Predicted Valueﻭﺍﻷﺨﻁﺎﺀ ﺍﻟﺨﺎﻡ Residualﻭﺍﻟﻘﻴﻡ ﺍﻟﻤﺘﻭﻗﻌﺔ ﺍﻟﻤﻌﻴﺎﺭﻴﺔ Std.
Predicted Valueﻭﺍﻷﺨﻁﺎﺀ ﺍﻟﻤﻌﻴﺎﺭﻴﺔ ،Std. Residualﻫﺫﻩ ﺍﻹﺤﺼﺎﺀﺍﺕ ﺘﺘﻀﻤﻥ ﺍﻟﻘﻴﻤﺘﻴﻥ ﺍﻟﺼﻐﺭﻯ ﻭﺍﻟﻜﺒﺭﻯ ﻭﺍﻟﻤﺘﻭﺴﻁ ﻭﺍﻻﻨﺤﺭﺍﻑ ﺍﻟﻤﻌﻴﺎﺭﻱ ﻟﻜل ﻤﻥ ﺍﻟﻘﻴﻡ ﺍﻟﺴﺎﺒﻘﺔ.
ﻭﻴﺒﻴﻥ ﺍﻟﺠﺯﺀ ﺍﻟﺴﺎﺩﺱ ﻤﻥ ﻗﺎﺌﻤﺔ ﺍﻟﻨﺘﺎﺌﺞ )ﺸﻜل (13-12ﺭﺴﻤﹰﺎ ﻟﻤﻘﺎﺭﻨﺔ ﻗﻴﻡ ﺍﻷﺨﻁﺎﺀ residualsﺒﺎﻟﺘﻭﺯﻴﻊ ﺍﻟﻁﺒﻴﻌﻲ ، Normal Probability Plotﻭﻤﻥ ﻫﺫﺍ
ﺍﻟﺸﻜل ﻴﻤﻜﻥ ﺍﺨﺘﺒﺎﺭ ﻤﺎ ﺇﺫﺍ ﻜﺎﻥ ﻫﻨﺎﻙ ﺍﺨﺘﺭﺍﻕ ﺨﻁﻴﺭ ﻟﻠﻔﺭﻀﻴﺔ ﺍﻷﺴﺎﺴﻴﺔ ﻟﺘﺤﻠﻴل ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ ﻭﻫﻲ ﻭﺠﻭﺏ ﺃﻥ ﺘﻜﻭﻥ ﺍﻷﺨﻁﺎﺀ ﻤﻭﺯﻋﺔ ﻁﺒﻘﹰﺎ ﻟﻠﺘﻭﺯﻴﻊ ﺍﻟﻁﺒﻴﻌﻲ،
ﻭﺍﺨﺘﺭﺍﻕ ﻫﺫﻩ ﺍﻟﻔﺭﻀﻴﺔ )ﺇﺫﺍ ﻜﺎﻥ ﻭﺍﻀﺤﹰﺎ( ﻴﻌﻨﻲ ﻋﺩﻡ ﺼﺤﺔ ﺍﻟﻨﻤﻭﺫﺝ ﺍﻟﻤﺴﺘﺨﺩﻡ
ﻭﻴﺠﺏ ﺘﺤﻭﻴل ﺍﻟﺒﻴﺎﻨﺎﺕ ﺒﺎﺴﺘﺨﺩﺍﻡ ﺼﻴﻐﺔ ﻤﺎ )ﻤﺜل (Cox and Box transformation
ﺍﻟﺘﻲ ﻤﻥ ﺸﺄﻨﻬﺎ ﺘﺤﻘﻴﻕ ﻫﺫﻩ ﺍﻟﻔﺭﻀﻴﺔ ،ﻭﻜﻠﻤﺎ ﻜﺎﻨﺕ ﺍﻟﻨﻘﺎﻁ ﻓﻲ ﺸﻜل ﺍﻟﺘﻭﺯﻴﻊ ﺍﻟﻁﺒﻴﻌﻲ ﻟﻠﺒﻴﺎﻨﺎﺕ Normal Probability Plotﻗﺭﻴﺒﺔ ﻤﻥ ﺍﻟﺨﻁ ﺍﻟﻤﺴﺘﻘﻴﻡ ﻜﻠﻤﺎ ﻜﺎﻥ ﺘﻭﺯﻴﻌﻬﺎ ﺍﻻﺤﺘﻤﺎﻟﻲ ﺃﻗﺭﺏ ﺇﻟﻰ ﺍﻟﺘﻭﺯﻴﻊ ﺍﻟﻁﺒﻴﻌﻲ ،ﻭﺍﻟﻤﻬﻡ ﻓﻲ ﻫﺫﺍ ﺍﻟﺸﻜل ﺃﻻ ﺘﻜﻭﻥ ﺍﻟﻨﻘﺎﻁ ﺒﻪ
ﺒﻌﻴﺩﺓ ﺠﺩﹰﺍ ﻋﻥ ﺍﻟﺨﻁ ﺍﻟﻤﺴﺘﻘﻴﻡ ﻟﻜﻲ ﻻ ﻨﺠﺯﻡ ﺒﺎﻥ ﻫﻨﺎﻙ ﺍﺨﺘﺭﺍﻕ ﺨﻁﻴﺭ ﻟﻠﻔﺭﻀﻴﺔ.
) (12ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
418
ﺸﻜل :13-12ﺍﻟﺠﺯﺀ ﺍﻟﺴﺎﺩﺱ ﻤﻥ ﻨﺘﺎﺌﺞ ﺘﺤﻠﻴل ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ Linear Regression Normal P-P Plot of Regression Standardized Residuals Dependent Variable: University Exam
.75
Expected Cum Prob
1.00
.50
.25
0.00 1.00
.75
.50
.25
0.00
Observed Cum Prob
ﺃﻤﺎ ﺍﻟﺠﺯﺀ ﺍﻟﺴﺎﺒﻊ ﻭﺍﻷﺨﻴﺭ )ﺸﻜل (14-12ﻤﻥ ﻗﺎﺌﻤﺔ ﺍﻟﻨﺘﺎﺌﺞ ﻓﻴﺤﺘﻭﻱ ﻋﻠﻰ
ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ Scatterplotﻟﻸﺨﻁﺎﺀ ﺍﻟﻤﻌﻴﺎﺭﻴﺔ Standardized Residuals
)ﻭﺍﻟﻤﻌﺭﻓﺔ ﺒﺎﻻﺴﻡ (*ZRESIDﻤﻘﺎﺒل ﺍﻟﻘﻴﻡ ﺍﻟﻤﺘﻭﻗﻌﺔ ﺍﻟﻤﻌﻴﺎﺭﻴﺔ Standardized
) Predicted Valuesﻭﺍﻟﻤﻌﺭﻓﺔ ﺒﺎﺴﻡ (*ZPREDﺒﻌﺩ ﺇﺠﺭﺍﺀ ﺘﻌﺩﻴﻼﺕ ﺸﻜﻠﻴﺔ ﻋﻠﻴﻪ،
ﻭﻴﻜﺸﻑ ﻫﺫﺍ ﺍﻟﺸﻜل ﻋﻥ ﺃﻱ ﺍﺘﺠﺎﻩ ﻓﻲ ﻗﻴﻡ ﺍﻷﺨﻁﺎﺀ ﺇﺫﺍ ﻜﺎﻥ ﺒﻴﻨﻬﺎ ﺃﻱ ﻋﻼﻗﺔ.
) (12ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
419
ﻭﻓﻲ ﺍﻟﻤﺜﺎل ﺍﻟﺤﺎﻟﻲ ﻻ ﻴﺒﺩﻭ ﺃﻥ ﻫﻨﺎﻙ ﺃﻱ ﻋﻼﻗﺔ ﻭﺍﻀﺤﺔ ﺒﻴﻥ ﻫﺫﻩ ﺍﻷﺨﻁﺎﺀ ﻭﻜﺫﻟﻙ ﻴﺘﻀﺢ ﺃﻥ ﻫﻨﺎﻙ ﺘﺠﺎﻨﺱ ﻓﻲ ﺘﺒﺎﻴﻥ ﺍﻷﺨﻁﺎﺀ ﻤﻤﺎ ﻴﺅﻜﺩ ﻋﺩﻡ ﻭﺠﻭﺩ ﺍﺨﺘﺭﺍﻕ
ﻟﻔﺭﻀﻴﺔ ﺃﻥ ﺍﻷﺨﻁﺎﺀ ﻫﻲ ﻤﺘﻐﻴﺭﺍﺕ ﻋﺸﻭﺍﺌﻴﺔ ﺘﺘﺒﻊ ﺍﻟﺘﻭﺯﻴﻊ ﺍﻟﻁﺒﻴﻌﻲ ﻭﺒﺘﺒﺎﻴﻥ ﺜﺎﺒﺕ،
ﻓﻠﻭ ﺍﺘﻀﺢ ﻤﻥ ﻫﺫﺍ ﺍﻟﺸﻜل ﺃﻥ ﺍﻷﺨﻁﺎﺀ ﺘﺄﻜل ﺸﻜل ﺍﻟﻘﻤﻊ ﺃﻭ ﻫﻼﻟﻴﺔ ﺍﻟﺸﻜل ﺒﻤﻌﻨﻰ ﺃﻥ ﺘﺒﺎﻴﻨﻬﺎ ﻤﺘﺯﺍﻴﺩ ﺃﻭ ﻤﺘﻨﺎﻗﺹ ﻓﺈﻥ ﻫﺫﺍ ﻴﺘﻁﻠﺏ ﺇﻋﺎﺩﺓ ﺍﻟﺘﺤﻠﻴل ﺒﻌﺩ ﺇﺠﺭﺍﺀ ﺒﻌﺽ ﺃﺤﺩ
ﺍﻟﺘﺤﻭﻴﻼﺕ ﻋﻠﻰ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﻟﺘﺜﺒﻴﺕ ﺍﻟﺘﺒﺎﻴﻥ.
ﺸﻜل : 14-12ﺍﻟﺠﺯﺀ ﺍﻟﺴﺎﺒﻊ ﻤﻥ ﻨﺘﺎﺌﺞ ﺘﺤﻠﻴل ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ Linear Regression Edited Scatterplot of Residuals against Predicted Values
1
0
-1
-2
Regression Standardized Residual
2
-3 3
2
1
0
-1
-2
Regression Standardized Predicted Value
ﻭﻫﻨﺎﻙ ﺃﺩﻭﺍﺕ ﺃﺨﺭﻯ ﻟﻠﺘﺤﻘﻕ ﻤﻥ ﺘﻭﻓﺭ ﺍﻟﺸﺭﻭﻁ ﺍﻟﻼﺯﻤﺔ ﻹﺜﺒﺎﺕ ﺼﺤﺔ
ﻭﺍﻻﻋﺘﻤﺎﺩ ﻋﻠﻰ ﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺫﻱ ﺘﻡ ﺘﻘﺩﻴﺭﻩ ،ﻤﻥ ﺒﻴﻥ ﻫﺫﻩ ﺍﻷﺩﻭﺍﺕ ﺸﻜل ﺍﻟﻤﺩﺭﺝ
ﺍﻟﺘﻜﺭﺍﺭﻱ Histogramﻟﻸﺨﻁﺎﺀ ﺍﻟﻤﻌﻴﺎﺭﻴﺔ Standardized Residualsﻓﻴﺠﺏ ﺃﻥ ﻴﻜﻭﻥ ﺘﻭﺯﻴﻌﻬﺎ ﻤﻌﺘﺩل ﻭﻤﺘﻤﺎﺜل ﻭﻗﺭﻴﺏ ﻤﻥ ﺍﻟﺘﻭﺯﻴﻊ ﺍﻟﻁﺒﻴﻌﻲ ،ﻭﻴﻤﻜﻥ ﺍﻟﺤﺼﻭل ﻋﻠﻴﻪ ﻤﻥ ﻨﺎﻓﺫﺓ ﺍﻟﺭﺴﻭﻤﺎﺕ ﺍﻟﺒﻴﺎﻨﻴﺔ ) Linear Regression: Plotsﺸﻜل .(5-12
) (12ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
420
.3 .12اﻻﻧﺤﺪار اﻟﻤﺘﻌﺪد Multiple Regression : ﺇﻥ ﻋﻤﻠﻴﺔ ﺒﻨﺎﺀ ﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ ﺍﻟﺘﻲ ﻴﻤﻜﻥ ﺃﻥ ﺘﺴﺘﺨﺩﻡ ﻓﻲ ﺘﻘﺩﻴﺭ ﻗﻴﻡ
ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﺘﺎﺒﻊ ﻤﻥ ﺨﻼل ﻗﻴﻡ ﻤﺤﺩﺩﺓ ﻟﻠﻤﺘﻐﻴﺭ ﺍﻟﻤﺴﺘﻘل ﻴﻤﻜﻥ ﺘﻌﻤﻴﻤﻬﺎ ﻟﻠﺤﺎﻻﺕ ﺍﻟﺘﻲ
ﻴﻜﻭﻥ ﻤﺘﺎﺤﹰﺎ ﻟﺩﻴﻨﺎ ﺒﻬﺎ ﻤﻌﻠﻭﻤﺎﺕ ﻋﻥ ﻤﺘﻐﻴﺭﻴﻥ ﻤﺴﺘﻘﻠﻴﻥ ﺃﻭ ﺃﻜﺜﺭ ،ﻓﻌﻤﻠﻴﺔ ﺒﻨﺎﺀ ﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﻋﻨﺩﻤﺎ ﻴﻜﻭﻥ ﻟﺩﻴﻨﺎ ﻤﺘﻐﻴﺭ ﺘﺎﺒﻊ ﻭﺍﺤﺩ ﻭﻤﺘﻐﻴﺭﻴﻥ ﻤﺴﺘﻘﻠﻴﻥ ﺃﻭ ﺃﻜﺜﺭ ﺘﻌﺭﻑ ﺒﺎﺴﻡ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﻤﺘﻌﺩﺩ . Multiple Regression ﻭﻟﺘﻭﻀﻴﺢ ﻓﻜﺭﺓ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﻤﺘﻌﺩﺩ ﻭﻁﺭﻴﻘﺔ ﺒﻨﺎﺀ ﺍﻟﻨﻤﻭﺫﺝ ﺒﺎﺴﺘﺨﺩﺍﻡ ﻨﻅﺎﻡ SPSS
ﺴﻨﻔﺘﺭﺽ ﺃﻥ ﻟﺩﻴﻨﺎ ﺒﻴﺎﻨﺎﺕ ﻋﻥ ﻤﺘﻐﻴﺭﻴﻥ ﺇﻀﺎﻓﻴﻴﻥ ﺒﺎﻹﻀﺎﻓﺔ ﺇﻟﻰ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﺘﺎﺒﻊ ﻭﻫﻭ
ﺩﺭﺠﺎﺕ ﺍﻟﻁﺎﻟﺏ ﻓﻲ ﺍﻟﻜﻠﻴﺔ Final Examﻭﺩﺭﺠﺎﺘﻪ ﻓﻲ ﺍﻤﺘﺤﺎﻥ ﺍﻟﻘﺒﻭل Entrance
Examﻓﻲ ﺸﻜل 3-12ﻓﻲ ﺍﻟﻤﺜﺎل ﺍﻟﺴﺎﺒﻕ ،ﻫﺫﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﻫﻤﺎ ﻋﻤﺭ ﺍﻟﻁﺎﻟﺏ Age
ﻭﺩﺭﺠﺎﺘﻪ ﻓﻲ ﻤﺸﺭﻭﻉ ﺃﻜﺎﺩﻴﻤﻲ ، Projectﻋﻠﻤﹰﺎ ﺒﺄﻥ ﺍﻟﻘﻴﻤﺔ ﺍﻟﺸﺎﺫﺓ ﺍﻟﺘﻲ ﺘﻡ ﺍﻜﺘﺸﺎﻓﻬﺎ
ﺨﻼل ﺘﺤﻠﻴل ﺍﻟﺒﻴﺎﻨﺎﺕ ﻓﻲ ﺍﻟﻤﺜﺎل ﺍﻟﺴﺎﺒﻕ ﻗﺩ ﺘﻡ ﺍﺴﺘﺒﻌﺎﺩﻫﺎ ﻭﻴﺘﺒﻘﻰ ﻟﺩﻴﻨﺎ ﺒﻴﺎﻨﺎﺕ ﻜﺎﻤﻠﺔ
ﻋﻥ 33ﻤﻔﺭﺩﺓ ،ﻫﺫﻩ ﺍﻟﺒﻴﺎﻨﺎﺕ ﺘﻅﻬﺭ ﻓﻲ ﺸﻜل .15-12
ﻭﻓﻲ ﺍﻟﻤﻨﺎﻗﺸﺔ ﺍﻟﺘﺎﻟﻴﺔ ﺴﻭﻑ ﻨﻬﺘﻡ ﺒﺠﺎﻨﺒﻴﻥ ﺃﺴﺎﺴﻴﻴﻥ ﻫﻤﺎ: .1ﻫل ﻴﺤﺴﻥ ﺇﻀﺎﻓﺔ ﻤﺘﻐﻴﺭﺍﺕ ﻤﺴﺘﻘﻠﺔ ﺠﺩﻴﺩﺓ ﺇﻟﻰ ﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﻤﻥ ﺩﺭﺠﺔ ﺍﻟﺩﻗﺔ ﻓﻲ ﺍﻟﺘﻨﺒﺅ ﺒﻘﻴﻡ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﺘﺎﺒﻊ ﺩﺭﺠﺎﺕ ﺍﻟﻁﺎل ﻓﻲ ﺍﻟﺠﺎﻤﻌﺔ؟
.2ﻤﺒﻴﻥ ﺒﻴﻥ ﻫﺅﻻﺀ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻤﺴﺘﻘﻠﺔ ﺍﻟﺠﺩﻴﺩﺓ ﻫل ﻫﻨﺎﻙ ﻤﺘﻐﻴﺭﺍﺕ ﺃﻜﺜﺭ ﻓﺎﺌﺩﺓ ﻤﻥ ﺍﻷﺨﺭﻯ ﻓﻲ ﺘﺤﺴﻴﻥ ﺍﻟﺩﻗﺔ ﻓﻲ ﺍﻟﺘﻨﺒﺅ؟
ﻭﺴﻭﻑ ﻨﺭﻯ ﺃﻥ ﺍﻹﺠﺎﺒﺔ ﻋﻠﻰ ﺍﻟﺴﺅﺍل ﺍﻷﻭل ﺩﺍﺌﻤﹰﺎ ﻫﻭ ﺍﻹﻴﺠﺎﺏ ،ﺒﻴﻨﻤﺎ ﺍﻹﺠﺎﺒﺔ
ﻋﻠﻰ ﺍﻟﺴﺅﺍل ﺍﻟﺜﺎﻨﻲ ﻴﺸﻭﺒﻪ ﺍﻟﺨﻼﻑ ،ﻓﻼ ﻴﻭﺠﺩ ﺃﻱ ﻤﻥ ﺍﻟﻁﺭﻕ ﺍﻟﻤﺘﺎﺤﺔ ﻤﺎ ﻴﻤﻜﻨﻬﺎ ﻤﻥ ﺇﻋﻁﺎﺀ ﺇﺠﺎﺒﺔ ﺩﻗﻴﻘﺔ ﻭﺸﺎﻓﻴﻪ ﻋﻠﻴﻪ.
) (12ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
421
ﺸﻜل : 15-12ﺒﻴﺎﻨﺎﺕ ﻋﻥ ﻤﺠﻤﻭﻉ ﺩﺭﺠﺎﺕ ﺍﻟﻁﻠﺒﺔ ﻓﻲ ﺍﻻﻤﺘﺤﺎﻥ ﺍﻟﻨﻬﺎﺌﻲ Final Univ. Examﻓﻲ ﺍﻟﻜﻠﻴﺔ ﻭﻤﺠﻤﻭﻉ ﺩﺭﺠﺎﺘﻬﻡ ﻓﻲ ﺍﻤﺘﺤﺎﻥ ﺍﻟﻘﺒﻭل Entrance Scoreﻟﻠﻜﻠﻴﺔ ﻭﺃﻋﻤﺎﺭﻫﻡ Ageﻭﻜﺫﻟﻙ ﺩﺭﺠﺎﺘﻬﻡ ﻓﻲ ﺃﺤﺩ ﺍﻟﻤﺸﺎﺭﻴﻊ ﺍﻷﻜﺎﺩﻴﻤﻴﺔ Project
Final Final Entrance Age Project Entrance Age Project Exam Exam
53
22.3
48
103
50
21.9
44
38
72
21.8
43
105
75
22.6
40
49
69
21.4
55
106
54
21.8
43
61
50
21.6
48
107
60
22.5
42
65
68
22.8
49
112
82
21.9
44
69
72
22.1
46
114
65
21.8
46
73
60
21.9
41
114
61
22.2
34
74
74
22.5
49
117
68
22.5
37
76
70
21.9
63
125
60
21.5
41
78
77
22.2
52
140
69
22.4
53
81
79
21.4
56
142
64
21.9
47
86
84
21.6
60
145
78
22.0
45
91
60
22.1
55
150
68
22.2
41
94
76
21.9
54
152
70
21.7
39
95
84
23.0
58
164
65
22.2
40
98
65
21.2
62
169
75
39.3
37
100
65
21.0
48
100
) (12ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
422
ﻫﻨﺎﻙ ﺍﻟﻌﺩﻴﺩ ﻤﻥ ﺍﻟﻤﺸﺎﻜل ﻓﻲ ﻫﺫﺍ ﺍﻟﺴﻴﺎﻕ ،ﻭﻟﻜﻥ ﻤﻌﻅﻤﻬﺎ ﻴﻤﻜﻥ ﺇﺠﻤﺎﻟﻪ ﻓﻲ ﺍﻟﻌﺒﺎﺭﺓ ﺍﻟﺸﻬﻴﺭﺓ ﺍﻟﺘﺎﻟﻴﺔ :ﺍﻻﺭﺘﺒﺎﻁ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﻻ ﻴﻌﻨﻲ ﺒﺎﻟﻀﺭﻭﺭﺓ ﺍﻟﺴﺒﺒﻴﺔ ،ﻭﻓﻲ ﺍﻟﺤﺎﻻﺕ ﺍﻟﺘﻲ ﻴﺭﺘﺒﻁ ﻓﻴﻬﺎ ﻜل ﻤﺘﻐﻴﺭ ﻤﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻤﺴﺘﻘﻠﺔ ﺒﺠﻤﻴﻊ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
ﺍﻷﺨﺭﻯ ﻻ ﻴﻤﻜﻥ ﺃﻥ ﻴﻌﺯﻯ ﺍﻟﺘﻐﻴﺭ ﻓﻲ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﺘﺎﺒﻊ ﺒﻭﻀﻭﺡ ﺇﻟﻰ ﺃﻱ ﻤﺘﻐﻴﺭ ﺒﻌﻴﻨﻪ
ﻤﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻤﺴﺘﻘﻠﺔ.
ﻓﻲ ﻤﻌﺎﺩﻟﺔ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﻤﺘﻌﺩﺩ ﻴﻁﻠﻕ ﻋﻠﻰ ﻤﻌﺎﻤﻼﺕ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻤﺴﺘﻘﻠﺔ ﺍﺴﻡ ﻤﻌﺎﻤﻼﺕ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺠﺯﺌﻴﺔ ، partial regression coefficientsﻭﻴﻌﻨﻲ ﺃﻨﻬﺎ ﺘﻌﺒﺭ
ﻋﻥ ﺍﻹﻀﺎﻓﺔ ﻓﻲ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﺘﺎﺒﻊ ﺍﻟﻨﺎﺘﺠﺔ ﻋﻥ ﺇﻀﺎﻓﺔ ﻭﺤﺩﺓ ﻭﺍﺤﺩﺓ ﻤﻭﺠﺒﺔ ﻓﻲ ﺫﻟﻙ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﻤﺴﺘﻘل ﻤﻊ ﺍﻓﺘﺭﺍﺽ ﺜﺒﺎﺕ ﺃﺜﺭ ﺠﻤﻴﻊ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻤﺴﺘﻘﻠﺔ ﺍﻷﺨﺭﻯ ﻋﻠﻰ ﻜل ﻤﻥ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﺘﺎﺒﻊ ﻭﺫﻟﻙ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﻤﺴﺘﻘل.
ﺇﺫﺍ ﺘﻡ ﺇﻴﺠﺎﺩ ﺍﻟﻘﻴﻡ ﺍﻟﻤﻌﻴﺎﺭﻴﺔ ﻟﺠﻤﻴﻊ ﺍﻟﻘﻴﻡ ﻓﻲ ﺠﻤﻴﻊ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﻓﻲ ﻤﻌﺎﺩﻟﺔ
ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﻤﺘﻌﺩﺩ )ﺒﻁﺭﺡ ﻤﺘﻭﺴﻁ ﺍﻟﻤﺘﻐﻴﺭ ﻤﻥ ﻜل ﻗﻴﻤﺔ ﻤﻥ ﻗﻴﻤﻪ ﻭﻗﺴﻤﺔ ﺍﻟﻨﺎﺘﺞ ﻋﻠﻰ ﺍﻻﻨﺤﺭﺍﻑ ﺍﻟﻤﻌﻴﺎﺭﻱ ﻟﺫﻟﻙ ﺍﻟﻤﺘﻐﻴﺭ( ﻓﺈﻥ ﺜﺎﺒﺕ ﺍﻻﻨﺤﺩﺍﺭ ﺴﻭﻑ ﻴﺨﺘﻔﻲ ﻤﻥ ﺍﻟﻤﻌﺎﺩﻟﺔ
ﻭﺴﻭﻑ ﻴﺸﺎﺭ ﻟﻜل ﻤﻌﺎﻤل ﺍﻨﺤﺩﺍﺭ ﻓﻲ ﻫﺫﻩ ﺍﻟﺤﺎﻟﺔ ﺒﺎﻟﻭﺯﻥ ﺒﻴﺘﺎ beta weightﻟﺘﻌﺒﺭ
ﻋﻥ ﺍﻟﺘﻐﻴﺭ ﻓﻲ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﺘﺎﺒﻊ )ﻤﻘﺎﺴﹰﺎ ﺒﻤﻀﺎﻋﻔﺎﺕ ﺍﻨﺤﺭﺍﻓﻪ ﺍﻟﻤﻌﻴﺎﺭﻱ( ﺍﻟﻨﺎﺘﺞ ﻋﻥ ﺇﻀﺎﻓﺔ ﻭﺤﺩﺓ ﺍﻨﺤﺭﺍﻑ ﻤﻌﻴﺎﺭﻱ ﻤﻭﺠﺒﺔ ﻭﺍﺤﺩﺓ ﻤﻥ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﻤﺴﺘﻘل ﻗﻴﺩ ﺍﻻﻫﺘﻤﺎﻡ.
ﻓﻲ ﻫﺫﺍ ﺍﻟﻘﺴﻡ ﺴﻭﻑ ﻨﻬﺘﻡ ﺒﻁﺭﻴﻘﺘﻴﻥ ﻤﻥ ﻁﺭﻕ ﺍﺨﺘﻴﺎﺭ ﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ
ﺍﻟﻤﺘﻌﺩﺩ ،ﻭﻜل ﻤﻥ ﻫﺎﺘﻴﻥ ﺍﻟﻁﺭﻴﻘﺘﻴﻥ )ﺒﺎﻹﻀﺎﻓﺔ ﺇﻟﻰ ﺍﻟﻁﺭﻕ ﺍﻷﺨﺭﻯ ﺍﻟﻤﺘﺎﺤﺔ( ﻴﺸﻭﺒﻪ ﺍﻟﻌﺩﻴﺩ ﻤﻥ ﺍﻟﻤﺸﺎﻜل ﺤﻴﺙ ﻻ ﻴﻭﺠﺩ ﻁﺭﻴﻘﺔ ﻤﺤﺩﺩﺓ ﺘﺼﻠﺢ ﻟﻜل ﺍﻟﺤﺎﻻﺕ ،ﻓﻔﻲ ﺍﻟﻁﺭﻴﻘﺔ
ﺍﻷﻭﻟﻰ ﻭﻫﻲ ﻁﺭﻴﻘﺔ ﺍﻹﺩﺨﺎل ﺍﻟﻤﺘﺯﺍﻤﻥ Simultaneous Selection Procedure
ﺘﺩﺨل ﺠﻤﻴﻊ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻤﺴﺘﻘل ﺇﻟﻰ ﻤﻌﺎﺩﻟﺔ ﺍﻻﻨﺤﺩﺍﺭ ﻤﺒﺎﺸﺭﺓ ،ﻭﻓﻲ ﺍﻟﻁﺭﻴﻘﺔ ﺍﻟﺜﺎﻨﻴﺔ
ﻭﻫﻲ ﻁﺭﻴﻘﺔ ﺍﻻﺨﺘﻴﺎﺭ ﺍﻟﺘﺩﺭﻴﺠﻲ Stepwise Selection Procedureﺘﺩﺨل
ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻤﺴﺘﻘﻠﺔ ﺇﻟﻰ ﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ )ﻭﺘﺤﺫﻑ( ﻭﺍﺤﺩﺍ ﺘﻠﻭ ﺍﻵﺨﺭ ،ﻭﻴﻜﻭﻥ ﺘﺭﺘﻴﺏ
) (12ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
423
ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﻓﻲ ﺍﻟﺩﺨﻭل ﺇﻟﻰ ﺍﻟﻨﻤﻭﺫﺝ ﺘﺒﻌﹰﺎ ﻻﻋﺘﺒﺎﺭﺍﺕ ﺇﺤﺼﺎﺌﻴﺔ ،ﻭﻋﻠﻰ ﺍﻟﺭﻏﻡ ﻤﻥ ﺃﻥ ﺍﻟﻁﺭﻴﻘﺔ ﺍﻟﺜﺎﻨﻴﺔ ﺘﺒﺩﻭ ﺃﻜﺜﺭ ﻤﻨﻁﻘﻴﺔ ﺇﻻ ﺃﻥ ﻫﻨﺎﻙ ﺍﻨﺘﻘﺎﺩﺍﺕ ﺘﺘﻌﻠﻕ ﺒﺤﻘﻴﻘﺔ ﺃﻥ ﺍﻟﻤﺘﻐﻴﺭ
ﺍﻟﺫﻱ ﻴﻀﺎﻑ ﺇﻟﻰ ﺍﻟﻨﻤﻭﺫﺝ ﺴﻴﻜﻭﻥ ﻟﻪ ﺃﺜﺭ ﻋﻠﻰ ﺘﺄﺜﻴﺭ ﺠﻤﻴﻊ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻤﻭﺠﻭﺩﺓ ﻤﺴﺒﻘﹰﺎ ﻓﻲ ﺍﻟﻨﻤﻭﺫﺝ ﻋﻠﻰ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﺘﺎﺒﻊ.
ﻭﻋﻭﺩﺓ ﺇﻟﻰ ﺍﻟﻤﺜﺎل ﺍﻟﺤﺎﻟﻲ ﻭﺍﻟﻤﺘﻌﻠﻕ ﺒﺎﻟﺒﻴﺎﻨﺎﺕ ﻓﻲ ﺸﻜل ،15-12ﻓﻨﻌﻠﻡ ﺍﻵﻥ
ﻜﻴﻑ ﻴﻤﻜﻥ ﺇﺩﺨﺎل ﻫﺫﻩ ﺍﻟﺒﻴﺎﻨﺎﺕ ﺇﻟﻰ ﻤﺤﺭﺭ ﺍﻟﺒﻴﺎﻨﺎﺕ Data Editorﻭﺤﻔﻅﻬﺎ )ﻜﻤﺎ ﺘﻡ
ﺘﻭﻀﻴﺤﻪ ﻓﻲ ﺍﻟﻔﺼل ﺍﻟﺜﺎﻨﻲ( ﻭﺴﻨﻔﺘﺭﺽ ﺍﻵﻥ ﺃﻥ ﻫﺫﻩ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻗﺩ ﺠﻬﺯﺕ ﻟﻠﺘﺤﻠﻴل ﺍﻹﺤﺼﺎﺌﻲ ،ﻭﺒﻬﺫﺍ ﻴﻤﻜﻨﻨﺎ ﺃﻴﻀﹰﺎ ﻓﺘﺢ ﻨﺎﻓﺫﺓ ﺘﺤﻠﻴل ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
Linear
Regressionﻜﻤﺎ ﺘﻡ ﻭﺼﻔﻪ ﻓﻲ ﺍﻟﻘﺴﻡ .5.1.12ﻓﻲ ﺒﺩﺍﻴﺔ ﻫﺫﺍ ﺍﻟﻔﺼل ،ﻭﺴﻨﺒﺩﺃ ﺍﻵﻥ ﺍﻟﺘﺤﻠﻴل ﺒﺎﺴﺘﺨﺩﺍﻡ ﻁﺭﻴﻘﺔ ﺍﻹﺩﺨﺎل ﺍﻟﻤﺘﺯﺍﻤﻥ
Simultaneous Selection
Procedureﻜﻤﺎ ﻴﻠﻲ:
ﻓﻲ ﻨﺎﻓﺫﺓ ﺘﺤﻠﻴل ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ ) Linear Regressionﺸﻜل (2-12ﺍﻨﻘل
ﺃﺴﻤﺎﺀ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻤﺘﺤﺎﻥ ﺍﻟﻘﺒﻭل Entrance Examﻭﺍﻟﻌﻤﺭ Ageﻭﺩﺭﺠﺔ ﺍﻟﻤﺸﺭﻭﻉ Project Markﺇﻟﻰ ﻤﺭﺒﻊ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻤﺴﺘﻘﻠﺔ Independent Variablesﻭﺍﻨﻘل ﻜﺫﻟﻙ ﺍﺴﻡ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﺘﺎﺒﻊ ﺍﻤﺘﺤﺎﻥ ﺍﻟﻜﻠﻴﺔ University Examﺇﻟﻰ ﻤﺭﺒﻊ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﺘﺎﺒﻊ
، Dependent Variableﻭﻻﺤﻅ ﻭﺠﻭﺩ ﻜﻠﻤﺔ ﺩﺨﻭل Enterﺍﻟﻤﻌﺒﺭﺓ ﻋﻥ ﻁﺭﻴﻘﺔ ﺍﻹﺩﺨﺎل ﺍﻟﻤﺘﺯﺍﻤﻥ ﻓﻲ ﻤﺭﺒﻊ ﺤﻭﺍﺭ ﺍﻟﻁﺭﻴﻘﺔ ، Methodﺜﻡ ﺍﻀﻐﻁ ﻋﻠﻰ ﻤﻔﺘﺎﺡ ﺍﻟﺘﻨﻔﻴﺫ
OKﻟﺘﻨﻔﻴﺫ ﺍﻷﻤﺭ.
ﻭﻴﺒﻴﻥ ﺸﻜل 16-12ﺍﻟﺠﺯﺀ ﺍﻷﻭل ﻤﻥ ﻗﺎﺌﻤﺔ ﻨﺘﺎﺌﺞ ﺘﺤﻠﻴل ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﻤﺘﻌﺩﺩ ﺒﺎﺴﺘﺨﺩﺍﻡ ﻁﺭﻴﻘﺔ ﺍﻹﺩﺨﺎل ﺍﻟﻤﺘﺯﺍﻤﻥ ،ﻭﻴﺒﻴﻥ ﻫﺫﺍ ﺍﻟﺸﻜل ﺃﻥ ﻗﻴﻤﺔ ﻤﻌﺎﻤل ﺍﻻﺭﺘﺒﺎﻁ
ﺍﻟﻤﺘﻌﺩﺩ ) (Rﻤﺴﺎﻭﻴﺔ . 0.77
( ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ12)
424
Multiple Regression ﺍﻟﺠﺯﺀ ﺍﻷﻭل ﻤﻥ ﻨﺘﺎﺌﺞ ﺘﺤﻠﻴل ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﻤﺘﻌﺩﺩ:16-12 ﺸﻜل Simultaneous Selection Procedure ﺒﺎﺴﺘﺨﺩﺍﻡ ﻁﺭﻴﻘﺔ ﺍﻹﺩﺨﺎل ﺍﻟﻤﺘﺯﺍﻤﻥ Variables Entered/Removedb Model 1
Variables Entered
Variables Removed
Project Mark, Age, a Entrance Exam
Method . Enter
a. All requested variables entered. b. Dependent Variable: University Exam
Model Summary
Model 1
R .766
R Square
Adjusted R Square
Std. Error of the Estimate
.587
.544
22.03
a
a. Predictors: (Constant), Project Mark, Age, Entrance Exam
Multiple Regression ﺍﻟﺠﺯﺀ ﺍﻟﺜﺎﻨﻲ ﻤﻥ ﻨﺘﺎﺌﺞ ﺘﺤﻠﻴل ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﻤﺘﻌﺩﺩ:17-12 ﺸﻜل
Simultaneous Selection Procedure ﺒﺎﺴﺘﺨﺩﺍﻡ ﻁﺭﻴﻘﺔ ﺍﻹﺩﺨﺎل ﺍﻟﻤﺘﺯﺍﻤﻥ Coefficientsa Unstandardized Coefficients Model 1
(Constant)
B
Std. Error
-117.9
46.421
Standardized Coefficients Beta
t
Sig.
-2.540
.017
Entrance Exam 3.089
.573
.714
5.387
.000
Age
1.423
1.376
.133
1.035
.309
Project Mark
.628
.461
.176
1.363
.183
a. Dependent Variable: University Exam
) (12ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
425
ﻭﺇﺫﺍ ﺘﺫﻜﺭﻨﺎ ﺃﻨﻪ ﻋﻨﺩﻤﺎ ﺍﺴﺘﺨﺩﻡ ﻤﺘﻐﻴﺭ ﻤﺴﺘﻘل ﻭﺍﺤﺩ ﻭﻫﻭ ﺩﺭﺠﺎﺕ ﺍﻟﻁﺎﻟﺏ ﻓﻲ ﺍﻤﺘﺤﺎﻥ ﺍﻟﻘﺒﻭل Entrance Examﻓﻲ ﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﻟﻠﺘﻨﺒﺅ ﺒﺎﻟﻤﺘﻐﻴﺭ ﺍﻟﺘﺎﺒﻊ ﺩﺭﺠﺎﺕ
ﺍﻟﻁﺎﻟﺏ ﻓﻲ ﺍﻟﺠﺎﻤﻌﺔ University Examﻜﺎﻨﺕ ﻗﻴﻤﺔ ﻤﻌﺎﻤل ﺍﻻﺭﺘﺒﺎﻁ ﺍﻟﻤﺘﻌﺩﺩ )(R ﻤﺴﺎﻭﻴﺔ ، 0.73ﻭﺒﻘﻴﻤﺔ ) (Rﻤﺴﺎﻭﻴﺔ 0.77ﺴﺘﻜﻭﻥ ﺍﻹﺠﺎﺒﺔ ﻋﻠﻰ ﺍﻟﺴﺅﺍل ﺍﻟﻤﺘﻌﻠﻕ ﺒﻤﺎ
ﺇﺫﺍ ﻜﺎﻥ ﺇﻀﺎﻓﺔ ﻤﺘﻐﻴﺭﺍﺕ ﻤﺴﺘﻘﻠﺔ ﺃﺨﺭﻯ ﺴﻴﻀﻴﻑ ﺇﻟﻰ ﻗﻭﺓ ﺍﻟﺘﻨﺒﺅ ﻟﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﻫﻲ ﺍﻹﻴﺠﺎﺏ ﺭﻏﻡ ﺃﻥ ﻫﺫﻩ ﺍﻹﻀﺎﻓﺔ ﻓﻲ ﻫﺫﺍ ﺍﻟﻤﺜﺎل ﻟﻴﺴﺕ ﻋﻅﻴﻤﺔ.
ﻭﻟﻜﻥ ﻤﺎﺫﺍ ﺒﺎﻟﻨﺴﺒﺔ ﻟﻠﺴﺅﺍل ﺍﻟﺜﺎﻨﻲ؟ ﻫل ﻜﻼ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﻴﺴﺎﻫﻤﺎﻥ ﻓﻲ ﺯﻴﺎﺩﺓ ﻗﻭﺓ ﺍﻟﺘﻨﺒﺅ ﻟﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺃﻭ ﺃﻨﻪ ﻴﻤﻜﻥ ﺍﻻﺴﺘﻐﻨﺎﺀ ﻋﻥ ﺃﻱ ﻤﻨﻬﻤﺎ؟ ﻤﻥ ﺍﻟﻌﻤﻭﺩ ﺒﻌﻨﻭﺍﻥ Bﻓﻲ ﺍﻟﻘﺴﻡ ﺒﻌﻨﻭﺍﻥ ﺍﻟﻤﻌﺎﻤﻼﺕ ﻏﻴﺭ ﺍﻟﻤﻌﻴﺎﺭﻴﺔ
Unstandardized Coefficientsﻓﻲ ﺠﺩﻭل ﺍﻟﺨﺎﺹ ﺒﻤﻌﺎﻤﻼﺕ ﺍﻻﻨﺤﺩﺍﺭ ﻓﻲ ﻗﺎﺌﻤﺔ
ﺍﻟﻨﺘﺎﺌﺞ ﻓﻲ ﺸﻜل 17-12ﻴﻤﻜﻨﻨﺎ ﺍﺴﺘﻨﺒﺎﻁ ﻤﻌﺎﺩﻟﺔ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﻤﺘﻌﺩﺩ ﻟﻤﺘﻐﻴﺭ ﺍﻟﺩﺭﺠﺔ ﻓﻲ
ﺍﻟﺠﺎﻤﻌﺔ ) (Yﻋﻠﻰ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺩﺭﺠﺔ ﺍﻤﺘﺤﺎﻥ ﺍﻟﻘﺒﻭل ) (X1ﻭﺩﺭﺠﺔ ﺍﻟﻤﺸﺭﻭﻉ )(X2 ﻭﺍﻟﻌﻤﺭ ) (X3ﻋﻠﻰ ﺍﻟﺼﻭﺭﺓ :
Y’ = 3.09 X1 + 0.63 X2 + 1.42 X3 –117.91
ﺤﻴﺙ ' Yﻫﻲ ﺍﻟﻘﻴﻤﺔ ﺍﻟﻤﺘﻭﻗﻌﺔ ﻟﺩﺭﺠﺔ ﺍﻟﻁﺎﻟﺏ ﻓﻲ ﺍﻟﺠﺎﻤﻌﺔ. ﻭﻓﻲ ﺍﻟﻘﺴﻡ ﺒﻌﻨﻭﺍﻥ ﺍﻟﻤﻌﺎﻤﻼﺕ ﺍﻟﻤﻌﻴﺎﺭﻴﺔ Standardized Coefficientsﻓﻲ
ﺍﻟﺠﺩﻭل )ﻓﻲ ﺍﻟﻌﻤﻭﺩ ﺒﻌﻨﻭﺍﻥ ﺃﻭﺯﺍﻥ ﺒﻴﺘﺎ (Betaﻴﻤﻜﻥ ﺍﺴﺘﻨﺒﺎﻁ ﺒﻌﺽ ﺍﻟﻤﻌﻠﻭﻤﺎﺕ
ﺍﻹﻀﺎﻓﻴﺔ ،ﺇﺫ ﺘﻭﻀﺢ ﻫﺫﻩ ﺍﻟﻘﻴﻡ ﺃﻥ ﺩﺭﺠﺔ ﺍﻟﻁﺎﻟﺏ ﻓﻲ ﺍﻤﺘﺤﺎﻥ ﺍﻟﻘﺒﻭل Entrance
Examﺘﻘﺩﻡ ﺃﻜﺜﺭ ﺇﻀﺎﻓﺔ ﻓﻲ ﺸﺭﺡ ﺍﻟﺘﻐﻴﺭﺍﺕ ﻓﻲ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﺘﺎﺒﻊ ،ﺇﺫ ﻜﻤﺎ ﺃﺴﻠﻔﻨﺎ ﻓﺈﻥ
ﻫﺫﻩ ﺍﻟﻘﻴﻡ ﺍﻟﻤﻌﻴﺎﺭﻴﺔ ﺘﻌﻨﻲ ﺃﻥ ﺘﻐﻴﺭﹰﺍ ﺒﻤﻘﺩﺍﺭ ﺍﻨﺤﺭﺍﻑ ﻤﻌﻴﺎﺭﻱ ﻭﺍﺤﺩ ﻓﻲ ﻤﺘﻐﻴﺭ ﺩﺭﺠﺔ
ﺍﻤﺘﺤﺎﻥ ﺍﻟﻘﺒﻭل ﺴﻭﻑ ﻴﻨﺘﺞ ﻋﻨﻪ ﺘﻐﻴﺭﹰﺍ ﻓﻲ ﻤﺘﻐﻴﺭ ﺩﺭﺠﺔ ﺍﻟﻁﺎﻟﺏ ﻓﻲ ﺍﻟﺠﺎﻤﻌﺔ ﺒﻤﻘﺩﺍﺭ
0.71ﻤﻥ ﺍﻻﻨﺤﺭﺍﻑ ﺍﻟﻤﻌﻴﺎﺭﻱ ﻟﻤﺘﻐﻴﺭ ﺩﺭﺠﺔ ﺍﻟﻁﺎﻟﺏ ﻓﻲ ﺍﻟﺠﺎﻤﻌﺔ ،ﺒﻴﻨﻤﺎ ﺘﻐﻴﺭﹰﺍ
ﺒﻤﻘﺩﺍﺭ ﺍﻨﺤﺭﺍﻑ ﻤﻌﻴﺎﺭﻱ ﻭﺍﺤﺩ ﻓﻲ ﺩﺭﺠﺔ ﺍﻟﻤﺸﺭﻭﻉ ﺴﻭﻑ ﻴﻨﺘﺞ ﻋﻨﻪ ﺘﻐﻴﺭﹰﺍ ﻓﻲ ﻤﺘﻐﻴﺭ
) (12ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
426
ﺩﺭﺠﺔ ﺍﻟﻁﺎﻟﺏ ﻓﻲ ﺍﻟﺠﺎﻤﻌﺔ ﺒﻤﻘﺩﺍﺭ 0.18ﻤﻥ ﺍﻻﻨﺤﺭﺍﻑ ﺍﻟﻤﻌﻴﺎﺭﻱ ﻟﻤﺘﻐﻴﺭ ﺩﺭﺠﺔ ﺍﻟﻁﺎﻟﺏ ﻓﻲ ﺍﻟﺠﺎﻤﻌﺔ ،ﻭﻫﻜﺫﺍ ﻓﺈﻥ ﺘﻐﻴﺭﹰﺍ ﺒﻤﻘﺩﺍﺭ ﺍﻨﺤﺭﺍﻑ ﻤﻌﻴﺎﺭﻱ ﻭﺍﺤﺩ ﻓﻲ ﻋﻤﺭ
ﺍﻟﻁﺎﻟﺏ ﺴﻭﻑ ﻴﻨﺘﺞ ﻋﻨﻪ ﺘﻐﻴﺭﹰﺍ ﻓﻲ ﻤﺘﻐﻴﺭ ﺩﺭﺠﺔ ﺍﻟﻁﺎﻟﺏ ﻓﻲ ﺍﻟﺠﺎﻤﻌﺔ ﺒﻤﻘﺩﺍﺭ 0.13 ﻤﻥ ﺍﻻﻨﺤﺭﺍﻑ ﺍﻟﻤﻌﻴﺎﺭﻱ ﻟﻤﺘﻐﻴﺭ ﺩﺭﺠﺔ ﺍﻟﻁﺎﻟﺏ ﻓﻲ ﺍﻟﺠﺎﻤﻌﺔ ،ﻫﺫﺍ ﺍﻟﺘﺭﺘﻴﺏ ﻟﻘﻴﻡ ﺃﻭﺯﺍﻥ
ﺒﻴﺘﺎ ﺘﺅﻜﺩﻩ ﻗﻴﻡ ﻤﻌﺎﻤﻼﺕ ﺍﻻﺭﺘﺒﺎﻁ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﺘﺎﺒﻊ ﻭﻜل ﻤﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻤﺴﺘﻘﻠﺔ
ﺍﻟﺜﻼﺜﺔ ﻓﻲ ﺠﺩﻭل ﻤﻌﺎﻤﻼﺕ ﺍﻻﺭﺘﺒﺎﻁ ﻓﻲ ﺸﻜل . 18-12
ﻓﺸﻜل 18-2ﻴﺒﻴﻥ ﻗﻴﻡ ﻤﻌﺎﻤل ﺍﻻﺭﺘﺒﺎﻁ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﺘﺎﺒﻊ ﺩﺭﺠﺔ ﺍﻟﻁﺎﻟﺏ ﻓﻲ ﺍﻟﺠﺎﻤﻌﺔ ﻭﻜل ﻤﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻤﺴﺘﻘﻠﺔ :ﺍﻟﺩﺭﺠﺔ ﻓﻲ ﺍﻤﺘﺤﺎﻥ ﺍﻟﻘﺒﻭل ﻭﺩﺭﺠﺔ ﺍﻟﻤﺸﺭﻭﻉ
ﻭﺍﻟﻌﻤﺭ ،ﻭﻫﻲ ﻋﻠﻰ ﺍﻟﺘﺭﺘﻴﺏ ﺍﻟﺘﺎﻟﻲ 0.73ﻭ 0.41ﻭ ، -0.03ﺃﻱ ﺃﻥ ﻫﺫﻩ
ﺍﻟﻤﻌﺎﻤﻼﺕ ﻟﻬﺎ ﻨﻔﺱ ﺘﺭﺘﻴﺏ ﻗﻴﻡ ﺃﻭﺯﺍﻥ ﺒﻴﺘﺎ .
ﺸﻜل :18-12ﺍﻟﺠﺯﺀ ﺍﻟﺜﺎﻟﺙ ﻤﻥ ﻨﺘﺎﺌﺞ ﺘﺤﻠﻴل ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﻤﺘﻌﺩﺩ Multiple Regression
ﺒﺎﺴﺘﺨﺩﺍﻡ ﻁﺭﻴﻘﺔ ﺍﻹﺩﺨﺎل ﺍﻟﻤﺘﺯﺍﻤﻥ Simultaneous Selection Procedure Correlations University Exam 1.000 .729 -.033 .405 .
University Exam
Pearson Correlation
Entrance Exam Age Project Mark University Exam
.000
Entrance Exam
.428
Age
.010
Project Mark
)Sig. (1-tailed
) (12ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
ﻭﺍﻵﻥ ﻴﻤﻜﻨﻨﺎ ﺃﻴﻀﹰﺎ ﺍﺴﺘﺨﺩﺍﻡ ﻁﺭﻴﻘﺔ ﺍﻻﺨﺘﻴﺎﺭ ﺍﻟﺘﺩﺭﻴﺠﻲ
427
Stepwise
Selection Procedureﻓﻲ ﺘﺤﻠﻴل ﺍﻟﺒﻴﺎﻨﺎﺕ ﺍﻟﺴﺎﺒﻘﺔ ﻭﺍﺴﺘﻨﺒﺎﻁ ﺃﻓﻀل ﻨﻤﻭﺫﺝ ﺍﻨﺤﺩﺍﺭ
ﺒﻬﺫﻩ ﺍﻟﻁﺭﻴﻘﺔ ،ﻭﺘﺤﻠﻴل ﺍﻟﺒﻴﺎﻨﺎﺕ ﺒﻬﺫﻩ ﺍﻟﻁﺭﻴﻘﺔ ﺒﺎﺴﺘﺨﺩﺍﻡ ﻨﻅﺎﻡ SPSSﻴﺘﻡ ﺒﻨﻔﺱ ﺍﻟﻁﺭﻴﻘﺔ ﺍﻟﺴﺎﺒﻘﺔ ﺘﻤﺎﻤﹰﺎ ﺒﺎﺴﺘﺜﻨﺎﺀ ﺃﻨﻪ ﻓﻲ ﻤﺭﺒﻊ ﺤﻭﺍﺭ ﺍﻟﻁﺭﻴﻘﺔ Methodﻓﻲ ﻨﺎﻓﺫﺓ
ﺘﺤﻠﻴل ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ ) Linear Regressionﺸﻜل (2-12ﻻﺒﺩ ﻤﻥ ﺍﺨﺘﻴﺎﺭ ﻁﺭﻴﻘﺔ ﻻ ﻤﻥ ﻁﺭﻴﻘﺔ ﺍﻹﺩﺨﺎل ﺍﻟﻤﺘﺯﺍﻤﻥ ، Enterﻭﻓﻲ ﻫﺫﻩ ﺍﻻﺨﺘﻴﺎﺭ ﺍﻟﺘﺩﺭﻴﺠﻲ Stepwiseﺒﺩ ﹰ
ﺍﻟﻁﺭﻴﻘﺔ ﺘﻀﺎﻑ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻤﺴﺘﻘﻠﺔ ﻭﺍﺤﺩﹰﺍ ﺘﻠﻭ ﺍﻵﺨﺭ ﻭﻴﻤﻜﻥ ﺃﻥ ﺘﺤﺫﻑ ﺒﺎﻟﺘﺘﺎﻟﻲ ﺃﻴﻀﹰﺎ ﺇﺫﺍ ﺘﺒﻴﻥ ﺃﻥ ﻤﺴﺎﻫﻤﺘﻬﺎ ﻟﻘﻭﺓ ﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﻏﻴﺭ ﻤﻌﻨﻭﻴﺔ) ،ﻻﺤﻅ ﺃﻥ ﻫﻨﺎﻙ
ﺃﻴﻀﹰﺎ ﻁﺭﻴﻘﺔ ﺨﻠﻔﻴﺔ Backward Selection Procedureﻻﺨﺘﻴﺎﺭ ﺃﻓﻀل ﻨﻤﻭﺫﺝ
ﺍﻨﺤﺩﺍﺭ ﻭﺘﺘﻀﻤﻥ ﺒﻨﺎﺀ ﻨﻤﻭﺫﺝ ﻜﺎﻤل ﺒﻜل ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻤﺴﺘﻘﻠﺔ ﻭﺤﺫﻑ ﺘﻠﻙ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
ﺫﺍﺕ ﺍﻟﻤﺴﺎﻫﻤﺔ ﻏﻴﺭ ﺍﻟﻤﻌﻨﻭﻴﺔ ﻭﺍﺤﺩﹰﺍ ﺘﻠﻭ ﺍﻵﺨﺭ ،ﻭﻫﻨﺎﻙ ﺃﻴﻀﹰﺎ ﻁﺭﻴﻘﺔ ﺃﻤﺎﻤﻴﺔ Forward Selection Procedureﻻﺨﺘﻴﺎﺭ ﺃﻓﻀل ﻨﻤﻭﺫﺝ ﺍﻨﺤﺩﺍﺭ ﺤﻴﺙ ﺘﻀﺎﻑ
ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻤﺴﺘﻘﻠﺔ ﺇﻟﻰ ﺍﻟﻨﻤﻭﺫﺝ ﺒﺎﻟﺘﺘﺎﻟﻲ ﻁﺎﻟﻤﺎ ﺘﺤﻘﻕ ﺸﺭﻁ ﺇﺤﺼﺎﺌﻲ ﻤﻌﻴﻥ ﻭﺘﺴﺘﻘﺭ
ﺒﻌﺩ ﺫﻟﻙ ﻓﻲ ﺍﻟﻨﻤﻭﺫﺝ ﺩﻭﻥ ﺤﺫﻑ( ،ﻭﺒﺫﻟﻙ ﺘﻜﻭﻥ ﻁﺭﻴﻘﺔ ﺍﻻﺨﺘﻴﺎﺭ ﺍﻟﺘﺩﺭﻴﺠﻲ Stepwise Selection Procedureﻋﺒﺎﺭﺓ ﻋﻥ ﻤﺯﻴﺞ ﻤﻥ ﺍﻟﻁﺭﻴﻘﺘﻴﻥ ﺍﻟﺴﺎﺒﻘﺘﻴﻥ(.
ﻭﺍﻟﺸﻜﻠﻴﻥ 19-12ﻭ 20-12ﻴﻭﻀﺤﺎﻥ ﺍﻷﺠﺯﺍﺀ ﺍﻟﻤﻬﻤﺔ ﻤﻥ ﻨﺘﺎﺌﺞ ﺘﻁﺒﻴﻕ
ﻁﺭﻴﻘﺔ ﺍﻻﺨﺘﻴﺎﺭ ﺍﻟﺘﺩﺭﻴﺠﻲ Stepwise Selection Procedureﻋﻠﻰ ﺒﻴﺎﻨﺎﺕ ﺍﻟﻤﺜﺎل
ﺍﻟﺴﺎﺒﻕ ،ﻭﺃﻜﺜﺭ ﺍﻟﻨﺘﺎﺌﺞ ﻭﻀﻭﺤﹰﺎ ﻫﻲ ﻗﻴﻤﺔ ﻤﻌﺎﻤل ﺍﻻﺭﺘﺒﺎﻁ ﺍﻟﻤﺘﻌﺩﺩ ﻟﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ
ﺍﻟﻨﺎﺘﺞ ﺒﻬﺫﻩ ﺍﻟﻁﺭﻴﻘﺔ ﻭﺍﻟﺫﻱ ﻴﺴﺎﻭﻱ ، 0.729ﻭﻫﻲ ﻗﻴﻤﺔ ﺍﻗل ﻤﻥ ﺍﻟﻘﻴﻤﺔ ﺍﻟﺘﻲ ﺤﺼﻠﻨﺎ
ﻋﻠﻴﻬﺎ ﺒﺎﻟﻁﺭﻴﻘﺔ ﺍﻟﺴﺎﺒﻘﺔ ) (0.77ﺤﻴﺙ ﺍﺤﺘﻭﻯ ﺍﻟﻨﻤﻭﺫﺝ ﺍﻟﻤﺴﺘﻨﺒﻁ ﺒﺎﻟﻁﺭﻴﻘﺔ ﺍﻟﺴﺎﺒﻘﺔ
ﻋﻠﻰ ﺠﻤﻴﻊ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻤﺴﺘﻘﻠﺔ ،ﻭﻫﺫﺍ ﻴﺩل ﻋﻠﻰ ﺃﻥ ﺇﻀﺎﻓﺔ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﺩﺭﺠﺔ ﺍﻟﻤﺸﺭﻭﻉ ﻭﺍﻟﻌﻤﺭ ﻻ ﻴﺴﺎﻫﻤﺎﻥ ﻤﻌﻨﻭﻴﹰﺎ ﻓﻲ ﻗﻴﻤﺔ ﻤﻌﺎﻤل ﺍﻻﺭﺘﺒﺎﻁ ﺍﻟﻤﺘﻌﺩﺩ ) ،(Rﻭﻟﺫﺍ
ﺘﻘﺭﺭ ﺍﺴﺘﺒﻌﺎﺩﻫﻤﺎ ﻤﻥ ﺍﻟﻨﻤﻭﺫﺝ ﺍﻟﻨﻬﺎﺌﻲ.
( ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ12)
428
Multiple Regression ﺍﻟﺠﺯﺀ ﺍﻷﻭل ﻤﻥ ﻨﺘﺎﺌﺞ ﺘﺤﻠﻴل ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﻤﺘﻌﺩﺩ:19-12 ﺸﻜل Stepwise Selection Procedure ﺒﺎﺴﺘﺨﺩﺍﻡ ﻁﺭﻴﻘﺔ ﺍﻻﺨﺘﻴﺎﺭ ﺍﻟﺘﺩﺭﻴﺠﻲ Model Summary
Model 1
R
R Square
Adjusted R Square
Std. Error of the Estimate
.531
.516
22.70
a
.729
a. Predictors: (Constant), Entrance Exam
Coefficientsa Unstandardized Coefficients
(Constant) Entrance Exam
B
Std. Error
-46.305
25.477
3.155
.532
Standardized Coefficients Beta .729
t
Sig.
-1.817
.079
5.925
.000
a. Dependent Variable: University Exam
Multipl Regression ﺍﻟﺠﺯﺀ ﺍﻟﺜﺎﻨﻲ ﻤﻥ ﻨﺘﺎﺌﺞ ﺘﺤﻠﻴل ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﻤﺘﻌﺩﺩ:20-12 ﺸﻜل Stepwise Selection Procedure ﺒﺎﺴﺘﺨﺩﺍﻡ ﻁﺭﻴﻘﺔ ﺍﻻﺨﺘﻴﺎﺭ ﺍﻟﺘﺩﺭﻴﺠﻲ Excluded Variablesb
Model 1
t
Sig.
Partial Correlation
a
1.416
.167
.250
.926
a
1.686
.102
.294
.915
Beta In Age Project Mark
Collinearit y Statistics
.178 .211
a. Predictors in the Model: (Constant), Entrance Exam b. Dependent Variable: University Exam
Tolerance
) (12ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
429
ﻭﻤﻥ ﺘﻠﻙ ﺍﻟﻨﺘﺎﺌﺞ ﻴﺘﻀﺢ ﺃﻥ ﺃﻓﻀل ﻨﻤﻭﺫﺝ ﺍﻨﺤﺩﺍﺭ ﻴﻤﻜﻥ ﺍﺴﺘﻨﺒﺎﻁﻪ ﺒﻁﺭﻴﻘﺔ ﺍﻻﺨﺘﻴﺎﺭ ﺍﻟﺘﺩﺭﻴﺠﻲ Stepwise Selection Procedureﻗﺩ ﺍﺸﺘﻤل ﻋﻠﻰ ﻤﺘﻐﻴﺭ ﻤﺴﺘﻘل
ﻭﺍﺤﺩ ﻭﻫﻭ ﺩﺭﺠﺔ ﺍﻟﻁﺎﻟﺏ ﻓﻲ ﺍﻤﺘﺤﺎﻥ ﺍﻟﻘﺒﻭل Entrance Examﻭﺫﻟﻙ ﻟﻠﺘﻨﺒﺅ ﺒﺩﺭﺠﺎﺕ ﺍﻟﻁﺎﻟﺏ ﻓﻲ ﺍﻟﺠﺎﻤﻌﺔ ، University Examﻭﻜﺎﻥ ﺍﻟﻘﺭﺍﺭ ﺒﺎﺴﺘﺒﻌﺎﺩ ﻜﻼ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ
ﺩﺭﺠﺔ ﺍﻟﻤﺸﺭﻭﻉ ﻭﺍﻟﻌﻤﺭ ﻷﻥ ﻗﻴﻤﺔ p-valueﻓﻲ ﺍﻟﻌﻤﻭﺩ ﺒﻌﻨﻭﺍﻥ Sig.ﺍﻟﻤﻘﺎﺒﻠﺔ ﻟﻬﻤﺎ
ﺃﻜﺒﺭ ﻤﻥ ) 0.05ﺸﻜل ،(20-12ﻭﺒﺎﻟﺘﺎﻟﻲ ﻨﺴﺘﻨﺘﺞ ﺃﻥ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﻭﺤﻴﺩ ﺍﻟﺫﻱ ﻴﻤﻜﻥ
ﺍﻻﻋﺘﻤﺎﺩ ﻋﻠﻴﻪ ﻓﻲ ﺍﻟﺘﻨﺒﺅ ﺒﻘﻴﻡ ﺩﺭﺠﺎﺕ ﺍﻟﻁﺎﻟﺏ ﻓﻲ ﺍﻟﺠﺎﻤﻌﺔ ﻫﻭ ﻤﺘﻐﻴﺭ ﺩﺭﺠﺎﺕ ﺍﻟﻁﺎﻟﺏ
ﻓﻲ ﺍﻤﺘﺤﺎﻥ ﺍﻟﻘﺒﻭل. ﻭﺍﻵﻥ ،ﻟﻨﻔﺘﺭﺽ ﺃﻥ ﺍﻟﺒﺎﺤﺙ ﺍﻋﺘﻘﺩ ﺃﻥ ﻫﻨﺎﻙ ﻤﺘﻐﻴﺭﺍﺕ ﺃﺨﺭﻯ ﻴﻤﻜﻥ ﺇﺩﺨﺎﻟﻬﺎ ﻓﻲ
ﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﻭﺭﺒﻤﺎ ﺘﻤﻜﻥ ﻤﻥ ﺍﻟﺤﺼﻭل ﻋﻠﻰ ﻨﻤﻭﺫﺝ ﺍﻨﺤﺩﺍﺭ ﺃﻜﺜﺭ ﻗﻭﺓ ﻓﻲ ﺍﻟﺘﻨﺒﺅ
ﺒﻘﻴﻡ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﺘﺎﺒﻊ ﻤﻥ ﺍﻟﻨﻤﻭﺫﺝ ﺍﻟﺴﺎﺒﻕ ،ﻭﺘﻤﻜﻥ ﻤﻥ ﺠﻤﻊ ﺒﻴﺎﻨﺎﺕ ﻋﻥ ﻤﺘﻐﻴﺭ ﺠﺩﻴﺩ
ﻭﻫﻭ ﻨﺘﻴﺠﺔ ﺍﻤﺘﺤﺎﻥ ﺍﻟﺠﺯﺀ ﺍﻟﺸﻔﻭﻱ ﻤﻥ ﺍﺨﺘﺒﺎﺭ ﺍﻟﺫﻜﺎﺀ ﺍﻟﻤﺴﻤﻰ IQﻟﺠﻤﻴﻊ ﺍﻟﻁﻼﺏ ﻓﻲ
ﺍﻟﻌﻴﻨﺔ ﻭﺘﻡ ﺭﺼﺩﻫﺎ ﻓﻲ ﺸﻜل ،21-12ﻭﻴﺘﻭﻗﻊ ﺃﻥ ﺇﻀﺎﻓﺔ ﻫﺫﺍ ﺍﻟﻤﺘﻐﻴﺭ )ﺍﻟﺫﻱ ﺴﻨﻁﻠﻕ ﻋﻠﻴﻪ (IQﺴﻭﻑ ﻴﺤﺴﻥ ﻤﻥ ﺩﻗﺔ ﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﻤﺘﻌﺩﺩ ﻓﻲ ﺍﻟﺘﻨﺒﺅ ﺒﻘﻴﻡ ﺩﺭﺠﺎﺕ
ﺍﻟﻁﺎﻟﺏ ﻓﻲ ﺍﻟﺠﺎﻤﻌﺔ ،ﻭﻋﻨﺩ ﺇﻀﺎﻓﺔ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﺠﺩﻴﺩ ﺇﻟﻰ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻤﺴﺘﻘﻠﺔ ﺍﻟﻤﻭﺠﻭﺩﺓ
ﻤﺴﺒﻘﹰﺎ ﻭﺇﻋﺎﺩﺓ ﺒﻨﺎﺀ ﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﻤﺘﻌﺩﺩ ﻴﺭﻏﺏ ﺍﻟﺒﺎﺤﺙ ﻓﻲ ﺍﺨﺘﺒﺎﺭ ﺍﻟﻔﺭﻀﻴﺔ ﺃﻥ
ﺍﻟﻤﺘﻐﻴﺭ IQﻴﺤﺴﻥ ﻤﻥ ﺩﻗﺔ ﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﻤﺘﻌﺩﺩ ﻓﻲ ﺍﻟﺘﻨﺒﺅ ﺒﻘﻴﻡ ﺩﺭﺠﺎﺕ ﺍﻟﻁﺎﻟﺏ
ﻓﻲ ﺍﻟﺠﺎﻤﻌﺔ.
ﻭﻴﻤﻜﻥ ﻟﻠﻘﺎﺭﺉ ﺍﻟﺘﺩﺭﺏ ﻋﻠﻰ ﺇﺩﺨﺎل ﺍﻟﺒﻴﺎﻨﺎﺕ ﺍﻟﺠﺩﻴﺩﺓ )ﻜﻤﺎ ﻓﻲ ﺠﺩﻭل (21-12 ﻭﺇﻋﺎﺩﺓ ﺍﻟﺘﺤﻠﻴل ﺒﻁﺭﻴﻘﺘﻲ ﺍﻹﺩﺨﺎل ﺍﻟﻤﺘﺯﺍﻤﻥ Simultaneous Selection Procedure
ﻭﺍﻻﺨﺘﻴﺎﺭ ﺍﻟﺘﺩﺭﻴﺠﻲ ،Stepwise Selection Procedureﻭﺴﻴﺠﺩ ﺃﺠﺯﺍﺀ ﻤﺨﺘﺎﺭﺓ
ﻫﺎﻤﺔ ﻤﻥ ﻨﺘﺎﺌﺞ ﻫﺫﺍ ﺍﻟﺘﺤﻠﻴل ﻓﻲ ﺍﻷﺸﻜﺎل 22-12ﻭ 23-12ﻭ 24-12ﻭ .25-12
) (12ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
430
ﺸﻜل : 21-12ﺒﻴﺎﻨﺎﺕ ﻋﻥ ﻤﺠﻤﻭﻉ ﺩﺭﺠﺎﺕ ﺍﻟﻁﻠﺒﺔ ﻓﻲ ﺍﻻﻤﺘﺤﺎﻥ ﺍﻟﻨﻬﺎﺌﻲ Final Exam ﻓﻲ ﺍﻟﻜﻠﻴﺔ ﻭﻤﺠﻤﻭﻉ ﺩﺭﺠﺎﺘﻬﻡ ﻓﻲ ﺍﻤﺘﺤﺎﻥ ﺍﻟﻘﺒﻭل ﻟﻠﻜﻠﻴﺔ Entrance Scoreﻭﺃﻋﻤﺎﺭﻫﻡ
Ageﻭﺩﺭﺠﺎﺘﻬﻡ ﻓﻲ ﺃﺤﺩ ﺍﻟﻤﺸﺎﺭﻴﻊ ﺍﻷﻜﺎﺩﻴﻤﻴﺔ Projectﻭﺩﺭﺠﺎﺘﻬﻡ ﻓﻲ ﺍﺨﺘﺒﺎﺭ ﺍﻟﺫﻜﺎﺀ IQ IQ
Final Entr. Age Proj. Exam
IQ
Final Entr. Age Proj. Exam
134
53
22.3
48
103
110
50
21.9
44
38
140
72
21.8
43
105
120
75
22.6
40
49
127
69
21.4
55
106
119
54
21.8
43
61
135
50
21.6
48
107
125
60
22.5
42
65
132
68
22.8
49
112
121
82
21.9
44
69
135
72
22.1
46
114
140
65
21.8
46
73
135
60
21.9
41
114
122
61
22.2
34
74
129
74
22.5
49
117
123
68
22.5
37
76
140
70
21.9
63
125
133
60
21.5
41
78
134
77
22.2
52
140
100
69
22.4
53
81
134
79
21.4
56
142
120
64
21.9
47
86
132
84
21.6
60
145
115
78
22.0
45
91
135
60
22.1
55
150
124
68
22.2
41
94
135
76
21.9
54
152
135
70
21.7
39
95
149
84
23.0
58
164
132
65
22.2
40
98
135
65
21.2
62
169
128
75
39.3
37
100
130
65
21.0
48
100
( ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ12)
431
ﺒﺎﺴﺘﺨﺩﺍﻡ ﻁﺭﻴﻘﺔR ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﺘﻲ ﺍﺸﺘﻤل ﻋﻠﻴﻬﺎ ﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﻭﻗﻴﻤﺔ: 22-12 ﺸﻜل . 21-12 ﻟﺒﻴﺎﻨﺎﺕ ﺸﻜلSimultaneous Selection Procedure ﺍﻹﺩﺨﺎل ﺍﻟﻤﺘﺯﺍﻤﻥ Variables Entered/Removedb Model 1
Variables Entered
Variables Removed
IQ, Age, Projecta Mark, Entrance Exam
Method . Enter
a. All requested variables entered. b. Dependent Variable: University Exam
Model Summary
Model 1
R
R Square
Adjusted R Square
Std. Error of the Estimate
.765
.731
16.92
a
.874
a. Predictors: (Constant), IQ, Age, Project Mark, Entrance Exam
ﺒﺎﺴﺘﺨﺩﺍﻡ ﻁﺭﻴﻘﺔRegression coefficients ﻤﻌﺎﻤﻼﺕ ﺍﻻﻨﺤﺩﺍﺭ: 23-12 ﺸﻜل . 21-12 ﻟﺒﻴﺎﻨﺎﺕ ﺸﻜلSimultaneous Selection Procedure ﺍﻹﺩﺨﺎل ﺍﻟﻤﺘﺯﺍﻤﻥ Coefficientsa Unstandardized Coefficients Model 1
B
Std. Error
(Constant)
-272.1
48.936
Entrance Exam
2.494
.459
Age
1.244
Project Mark IQ
Standardized Coefficients t
Sig.
-5.561
.000
.576
5.434
.000
1.057
.116
1.177
.249
.504
.355
.141
1.419
.167
1.510
.328
.447
4.601
.000
a. Dependent Variable: University Exam
Beta
) (12ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
432
ﻭﻴﻤﻜﻨﻨﺎ ﺃﻥ ﻨﻼﺤﻅ ﻤﻥ ﺍﻟﺸﻜل 22-12ﺃﻥ ﺇﻀﺎﻓﺔ ﺍﻟﻤﺘﻐﻴﺭ IQﻗﺩ ﺤﺴﻥ ﻤﻥ ﻗﻭﺓ ﺍﻟﺘﻨﺒﺅ ﻟﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﻤﺘﻌﺩﺩ ،ﺤﻴﺙ ﺃﻋﻁﻰ ﻗﻴﻤﺔ ﻟﻤﻌﺎﻤل ﺍﻻﻨﺤﺩﺍﺭ Rﻤﺴﺎﻭﻴﺔ
0.87ﻭﺍﻟﺘﻲ ﺘﺯﻴﺩ ﺒﺸﻜل ﻤﻠﺤﻭﻅ ﻋﻥ ﺴﺎﺒﻘﺘﻬﺎ ﺒﺩﻭﻥ ﺇﺩﺨﺎل ﺫﻟﻙ ﺍﻟﻤﺘﻐﻴﺭ )ﺤﻴﺙ ﻜﺎﻨﺕ 0.77ﺒﺩﻭﻥ ﺍﻟﻤﺘﻐﻴﺭ .(IQ
ﻭﺒﺎﻟﻨﻅﺭ ﺇﻟﻰ ﺍﻟﻤﻌﺎﻤﻼﺕ ﺍﻟﻤﻌﻴﺎﺭﻴﺔ ) Standardized coefficientsﺃﻭﺯﺍﻥ
ﺒﻴﺘﺎ (Beta weightsﻓﻲ ﻗﺎﺌﻤﺔ ﺍﻟﻨﺘﺎﺌﺞ ﻓﻲ ﺸﻜل 23-12ﺴﻭﻑ ﻨﻼﺤﻅ ﺃﻥ ﺇﻀﺎﻓﺔ
ﺒﻤﻘﺩﺍﺭ ﺍﻨﺤﺭﺍﻑ ﻤﻌﻴﺎﺭﻱ ﻭﺍﺤﺩ ﺇﻟﻰ ﻤﺘﻐﻴﺭ ﻨﺘﻴﺠﺔ ﺍﻤﺘﺤﺎﻥ ﺍﻟﺩﺨﻭل ﺴﻭﻑ ﻴﻨﺘﺞ ﻋﻨﻬﺎ ﺇﻀﺎﻓﺔ ﺒﻤﻘﺩﺍﺭ 0.58ﻤﻥ ﺍﻻﻨﺤﺭﺍﻑ ﺍﻟﻤﻌﻴﺎﺭﻱ ﻟﻤﺘﻐﻴﺭ ﻨﺘﻴﺠﺔ ﺍﻤﺘﺤﺎﻥ ﺍﻟﺠﺎﻤﻌﺔ ،ﻭﻜﺫﻟﻙ
ﺇﻀﺎﻓﺔ ﻤﻘﺩﺍﺭ ﺍﻨﺤﺭﺍﻑ ﻤﻌﻴﺎﺭﻱ ﻭﺍﺤﺩ ﺇﻟﻰ ﻤﺘﻐﻴﺭ ﻨﺘﻴﺠﺔ ﺍﻤﺘﺤﺎﻥ ﺍﻟﺩﺨﻭل ﺴﻭﻑ ﻴﻨﺘﺞ
ﻋﻨﻬﺎ ﺇﻀﺎﻓﺔ ﺒﻤﻘﺩﺍﺭ 0.45ﻤﻥ ﺍﻻﻨﺤﺭﺍﻑ ﺍﻟﻤﻌﻴﺎﺭﻱ ﻟﻠﻤﺘﻐﻴﺭ ، IQﻭﻫﺫﻩ ﺘﻌﺩ ﺇﻀﺎﻓﺔ
ﺠﻭﻫﺭﻴﺔ ﻤﻘﺎﺭﻨﺔ ﺒﺎﻹﻀﺎﻓﺔ ﺍﻟﺘﻲ ﻴﻘﺩﻤﻬﺎ ﻜل ﻤﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﺩﺭﺠﺔ ﺍﻟﻤﺸﺭﻭﻉ ﻭﺍﻟﻌﻤﺭ.
ﻻ ﺒﺎﻟﻤﺘﻐﻴﺭﻴﻥ ﻭﻜﺫﻟﻙ ﺒﺎﻟﻘﺎﻋﺩﺓ ﺍﻹﺤﺼﺎﺌﻴﺔ ﻹﺩﺨﺎل ﻭﻴﻘﺩﻡ ﺸﻜل 24-12ﺠﺩﻭ ﹰ
ﻜل ﻤﻨﻬﻤﺎ )ﻨﻤﻭﺫﺝ 1ﻭ (2ﻟﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﻤﺘﻌﺩﺩ ﺒﺎﺴﺘﺨﺩﺍﻡ ﻁﺭﻴﻘﺔ ﺍﻻﺨﺘﻴﺎﺭ ﺍﻟﺘﺩﺭﻴﺠﻲ ﻟﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ . Stepwise Selection Procedure ﺸﻜل : 24-12ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﺍﻟﺫﻴﻥ ﺍﺸﺘﻤل ﻋﻠﻴﻬﻤﺎ ﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﻤﺘﻌﺩﺩ ﺒﺎﺴﺘﺨﺩﺍﻡ ﻁﺭﻴﻘﺔ ﺍﻻﺨﺘﻴﺎﺭ ﺍﻟﺘﺩﺭﻴﺠﻲ Stepwise Selection Procedureﻟﺒﻴﺎﻨﺎﺕ ﺸﻜل . 21-12 Variables Entered/Removeda Variables Removed
Method
Variables Entered
Stepwise (Criteria: . Probability-of-F-to-enter <= .050, Probability-of-F-to-remove >= .100).
Entrance Exam
Stepwise (Criteria: . Probability-of-F-to-enter <= .050, Probability-of-F-to-remove >= .100).
IQ
Model 1
2
a. Dependent Variable: University Exam
) (12ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
433
ﻭﻴﺒﻴﻥ ﺍﻟﺸﻜل ﺍﻟﺴﺎﺒﻕ ) (24-12ﺃﻥ ﺍﻟﺨﻁﻭﺓ ﺍﻷﻭﻟﻰ )ﺍﻟﻨﻤﻭﺫﺝ (1ﻜﺎﻨﺕ ﺇﺩﺨﺎل ﺍﻟﻤﺘﻐﻴﺭ ﻨﺘﻴﺠﺔ ﺍﻤﺘﺤﺎﻥ ﺍﻟﻘﺒﻭل Entrance Examﺇﻟﻰ ﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﻭﺘﺒﻌﻪ ﺇﺩﺨﺎل
ﺍﻟﻤﺘﻐﻴﺭ IQﻜﺨﻁﻭﺓ ﺜﺎﻨﻴﺔ )ﺍﻟﻨﻤﻭﺫﺝ ،(2ﻻﺤﻅ ﺃﻥ ﻁﺭﻴﻘﺔ ﺍﻻﺨﺘﻴﺎﺭ ﺍﻟﺘﺩﺭﻴﺠﻲ ﻗﺩ ﺘﻭﻗﻔﺕ ﺤﻴﻨﺌ ٍﺫ ﻭﺒﺩﻭﻥ ﻤﺤﺎﻭﻟﺔ ﺇﺩﺨﺎل ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﻨﺘﻴﺠﺔ ﺍﻟﻤﺸﺭﻭﻉ ﻭﺍﻟﻌﻤﺭ.
ﻭﻴﻭﻀﺢ ﺍﻟﺸﻜل 25-12ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﺘﻲ ﺍﺴﺘﺒﻌﺩﺕ ﻓﻲ ﻜل ﺨﻁﻭﺓ ﻤﻥ
ﺍﻟﺨﻁﻭﺍﺕ ﺍﻟﺴﺎﺒﻘﺔ ،ﻓﻔﻲ ﺍﻟﺨﻁﻭﺓ ﺍﻷﻭﻟﻰ )ﺍﻟﻨﻤﻭﺫﺝ (1ﻗﺩ ﺩﺨل ﻤﺘﻐﻴﺭ ﻤﺴﺘﻘل ﻭﺍﺤﺩ
ﻭﺍﺴﺘﺒﻌﺩﺕ ﺜﻼﺙ ﻤﺘﻐﻴﺭﺍﺕ ﻭﻫﻡ ﺍﻟﻌﻤﺭ ﻭﺩﺭﺠﺔ ﺍﻟﻤﺸﺭﻭﻉ ﻭ ، IQﻭﻟﻜﻥ ﺤﻴﺙ ﺃﻥ ﻗﻴﻤﺔ
ﻼ p-valueﻟﻤﻌﻨﻭﻴﺔ ﺍﻟﻤﺘﻐﻴﺭ IQﺃﺼﻐﺭ ﻤﻥ 0.05ﻓﺈﻥ ﻫﺫﺍ ﺍﻟﻤﺘﻐﻴﺭ ﺃﺼﺒﺢ ﻤﺅﻫ ﹰ ﻟﻠﺩﺨﻭل ﻓﻲ ﺍﻟﺨﻁﻭﺓ ﺍﻟﺜﺎﻨﻴﺔ )ﺍﻟﻨﻤﻭﺫﺝ ،(2ﻭﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﺘﻲ ﺍﺴﺘﺒﻌﺩﺕ ﻓﻲ ﺍﻟﺨﻁﻭﺓ
ﺍﻟﺜﺎﻨﻴﺔ )ﺍﻟﻨﻤﻭﺫﺝ (2ﻭﻫﻤﺎ ﺍﻟﻌﻤﺭ ﻭﺩﺭﺠﺔ ﺍﻟﻤﺸﺭﻭﻉ ﺒﻘﻴﺎ ﻤﺴﺘﺒﻌﺩﻴﻥ ﻷﻥ ﻗﻴﻤﺔ p-value
ﻟﻤﻌﻨﻭﻴﺘﻬﻤﺎ ﺒﻘﻴﺘﺎ ﺃﻜﺒﺭ ﻤﻥ ، 0.05ﻭﻟﻬﺫﺍ ﺘﻭﻗﻑ ﺍﻟﻨﻤﻭﺫﺝ ﻫﻨﺎ.
ﺸﻜل : 25-12ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻤﺴﺘﺒﻌﺩﺓ ﻤﻥ ﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﻤﺘﻌﺩﺩ ﻨﺘﻴﺠﺔ ﻻﺴﺘﺨﺩﺍﻡ ﻁﺭﻴﻘﺔ ﺍﻻﺨﺘﻴﺎﺭ ﺍﻟﺘﺩﺭﻴﺠﻲ Stepwise Selection Procedureﻟﺒﻴﺎﻨﺎﺕ ﺸﻜل . 21-12 Excluded Variablesc Collinearit y Statistics
Partial Correlation
Sig.
t
.926
.250
.167
1.416
a
.915
.294
.102
1.686
a
.898
.646
.000
4.631
a
.923
.279
.129
1.565
b
.908
.312
.088
1.766
b
Tolerance
Beta In .178 .211 .467 .152 .171
Age
Model 1
Project Mark IQ Age Project Mark IQ
a. Predictors in the Model: (Constant), Entrance Exam b. Predictors in the Model: (Constant), Entrance Exam, IQ c. Dependent Variable: University Exam
2
) (12ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
434
ﺇﻥ ﺍﻻﻓﺘﻘﺎﺭ ﺇﻟﻰ ﺃﻫﻤﻴﺔ ﻨﺴﺒﻴﺔ ﻟﻠﻤﺘﻐﻴﺭﻴﻥ ﺍﻟﺫﻴﻥ ﺘﻡ ﺍﺴﺘﺒﻌﺎﺩﻫﻤﺎ ﻤﻥ ﻨﺎﺤﻴﺔ ﺃﺜﺭﻫﻤﺎ ﻋﻠﻰ ﻗﻭﺓ ﺍﻟﺘﻨﺒﺅ ﺒﺎﻟﻤﺘﻐﻴﺭ ﺍﻟﺘﺎﺒﻊ ﺩﺭﺠﺎﺕ ﺍﻟﻁﺎﻟﺏ ﻓﻲ ﺍﻤﺘﺤﺎﻥ ﺍﻟﺠﺎﻤﻌﺔ ﻗﺩ ﺃﻜﺩﺘﻬﺎ ﻗﻴﻡ ﻜل ﻤﻥ ﻤﻌﺎﻤل ﺍﻻﺭﺘﺒﺎﻁ Rﻭﻤﺭﺒﻌﻪ ) R2ﺍﻟﺫﻱ ﻴﻁﻠﻕ ﻋﻠﻴﻪ ﻤﻌﺎﻤل ﺍﻟﺘﺤﺩﻴﺩ Coefficient
(of Determinationﻭﺍﻟﻠﺘﺎﻥ ﺘﺘﻀﺤﺎﻥ ﻤﻥ ﺸﻜل ،26-12ﻓﻘﻴﻤﺔ Rﻗﺩ ﺃﺼﺒﺤﺕ
) 0.852ﺍﻟﻨﻤﻭﺫﺝ (2ﻭﻫﻲ ﻗﺭﻴﺒﺔ ﻤﻥ ﺍﻟﻘﻴﻤﺔ 0.874ﺍﻟﺘﻲ ﺤﺼﻠﻨﺎ ﻋﻠﻴﻬﺎ ﻤﻥ ﺇﺩﺨﺎل ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻤﺴﺘﻘﻠﺔ ﺍﻷﺭﺒﻊ ﺠﻤﻴﻌﻬﺎ )ﺸﻜل .(22-12
ﺸﻜل : 26-12ﻗﻴﻤﺘﻲ Rﻭ R2ﻟﻠﺨﻁﻭﺘﻴﻥ )ﻓﻲ ﺍﻟﻨﻤﻭﺫﺠﻴﻥ 1ﻭ (2ﺒﺎﺴﺘﺨﺩﺍﻡ ﻁﺭﻴﻘﺔ ﺍﻻﺨﺘﻴﺎﺭ ﺍﻟﺘﺩﺭﻴﺠﻲ Stepwise Selection Procedureﻟﺒﻴﺎﻨﺎﺕ ﺸﻜل . 21-12 Model Summary Std. Error of the Estimate
Adjusted R Square
R Square
22.70
.516
.531
a
17.62
.708
.727
b
R
Model
.729 .852
1 2
a. Predictors: (Constant), Entrance Exam b. Predictors: (Constant), Entrance Exam, IQ
ﻭﺸﻜل 27-12ﻴﻌﺭﺽ ﻗﻴﻡ ﻤﻌﺎﻤﻼﺕ ﺍﻻﻨﺤﺩﺍﺭ Regression Coefficients
ﻟﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻷﻭﻟﻲ )ﺍﻟﻨﻤﻭﺫﺝ (1ﻭﺍﻟﻨﻬﺎﺌﻲ )ﺍﻟﻨﻤﻭﺫﺝ (2ﺍﻟﺫﻴﻥ ﺘﻡ ﺘﻭﻓﻴﻘﻬﻤﺎ ﺒﺎﺴﺘﺨﺩﺍﻡ ﻁﺭﻴﻘﺔ ﺍﻻﺨﺘﻴﺎﺭ ﺍﻟﺘﺩﺭﻴﺠﻲ . Stepwise Selection Procedure
ﻭﺃﺨﻴﺭﹰﺍ ،ﺘﺒﺭﺯ ﺍﻟﻨﺘﺎﺌﺞ ﺍﻟﺴﺎﺒﻘﺔ ﻤﻼﺤﻅﺔ ﻫﺎﻤﺔ ﺘﺘﻌﻠﻕ ﺒﺎﺴﺘﺨﺩﺍﻤﺎﺕ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﻤﺘﻌﺩﺩ ﻜﻭﺴﻴﻠﺔ ﻟﻠﺒﺤﺙ ،ﻓﺈﻀﺎﻓﺔ ﻤﺘﻐﻴﺭﺍﺕ ﻤﺴﺘﻘﻠﺔ ﺠﺩﻴﺩﺓ ﻟﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﻴﻤﻜﻥ ﺃﻥ
ﻴﺅﺜﺭ ﺒﺸﺩﺓ ﻋﻠﻰ ﺍﻷﻫﻤﻴﺔ ﺍﻟﻨﺴﺒﻴﺔ ﻟﻠﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻤﺴﺘﻘﻠﺔ ﺍﻟﻤﻭﺠﻭﺩﺓ ﻤﺴﺒﻘﹰﺎ ،ﻓﻌﻨﺩ ﺍﻟﺘﺨﻁﻴﻁ ﻟﺒﻨﺎﺀ ﻨﻤﻭﺫﺝ ﺍﻨﺤﺩﺍﺭ ﻤﺘﻌﺩﺩ ﻭﺍﺨﺘﻴﺎﺭ ﻤﺘﻐﻴﺭﺍﺕ ﻤﺴﺘﻘﻠﺔ ﻻﺒﺩ ﺃﻥ ﻴﺄﺨﺫ ﺍﻟﺒﺎﺤﺙ ﻓﻲ ﺍﻋﺘﺒﺎﺭﻩ ﺍﻷﺴﺱ ﺍﻟﻨﻅﺭﻴﺔ ﺍﻷﺴﺎﺴﻴﺔ ﻟﻤﻭﻀﻭﻉ ﺍﻟﺒﺤﺙ ،ﺇﺫ ﻻ ﻴﻤﻜﻥ ﻟﻠﻨﻤﻭﺫﺝ ﺍﻹﺤﺼﺎﺌﻲ
ﺒﻤﻔﺭﺩﻩ ﺘﺭﺠﻤﺔ ﻨﺘﺎﺌﺞ ﻨﻤﻭﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺩﻭﻥ ﺍﻷﺨﺫ ﻓﻲ ﺍﻻﻋﺘﺒﺎﺭ ﺍﻟﻌﻼﻗﺎﺕ ﺍﻟﺴﺒﺒﻴﺔ.
) (12ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
435
ﺸﻜل : 27-12ﻤﻌﺎﻤﻼﺕ ﺍﻻﻨﺤﺩﺍﺭ Regression coefficientsﺒﺎﺴﺘﺨﺩﺍﻡ ﻁﺭﻴﻘﺔ ﺍﻻﺨﺘﻴﺎﺭ ﺍﻟﺘﺩﺭﻴﺠﻲ Stepwise Selection Procedureﻟﺒﻴﺎﻨﺎﺕ ﺸﻜل . 21-12 Coefficientsa Standardized Coefficients Beta
Sig.
t
.079
-1.817
.000
5.925
.000
-5.188
.000
5.750
.579
.000
4.631
.467
.729
Unstandardized Coefficients Std. Error
B
25.477
-46.305
.532
3.155
42.225
-219.068
.436
2.508
Entrance Exam
.340
1.576
IQ
)(Constant
Model 1
Entrance Exam IQ )(Constant
2
a. Dependent Variable: University Exam
.4 .12ﺷﻜﻞ اﻻﻧﺘﺸﺎر وﺧﻂ اﻻﻧﺤﺪار : Scatterplots and Regression Lines : ﻭﻴﻤﻜﻥ ﺭﺴﻡ ﺨﻁ ﺍﻻﻨﺤﺩﺍﺭ ﺒﺴﻬﻭﻟﺔ ﻓﻲ ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ Scatter plotﺍﻟﺫﻱ ﺘﻡ
ﺍﻟﺘﻌﺭﻑ ﻋﻠﻰ ﺃﻫﻤﻴﺘﻪ ﻓﻲ ﺘﺤﻠﻴل ﺍﻻﺭﺘﺒﺎﻁ ﻭﺍﻻﻨﺤﺩﺍﺭ ﻭﻁﺭﻴﻘﺔ ﺭﺴﻤﻪ ﻓﻲ ﺍﻟﻔﺼل ﺍﻟﺴﺎﺒﻕ ﻭﺫﻟﻙ ﻜﻤﺎ ﻴﻠﻲ :
• ﺒﻌﺩ ﺭﺴﻡ ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ ﺒﺎﻟﻁﺭﻴﻘﺔ ﺍﻟﻤﻌﺭﻭﻓﺔ ﺒﺈﺩﺨﺎل ﺍﻟﻤﻌﻠﻭﻤﺎﺕ ﺍﻟﻤﻁﻠﻭﺒﺔ ﻟﻨﺎﻓﺫﺓ ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ ﺍﻟﺒﺴﻴﻁ Simple Scatterplotﻴﻤﻜﻥ ﻓﻲ ﺸﺎﺸﺔ ﺍﻟﻨﺘﺎﺌﺞ
Output Viewerﺍﻟﻨﻘﺭ ﺍﻟﻤﺯﺩﻭﺝ ﻭﺍﻟﻤﺘﺘﺎﻟﻲ ﺒﺎﻟﻔﺄﺭﺓ ﻓﻲ ﺃﻱ ﻤﻜﺎﻥ ﻋﻠﻰ ﺍﻟﺭﺴﻡ ﺍﻟﻨﺎﺘﺞ ﻟﺘﻔﻌﻴل ﻤﺤﺭﺭ ﺍﻟﺭﺴﻭﻤﺎﺕ .Chart Editor
• ﻴﻤﻜﻥ ﺘﻌﺩﻴل ﺍﻟﺸﻜل ﺒﺎﻟﻁﺭﻴﻘﺔ ﺍﻟﻤﺭﻏﻭﺒﺔ )ﻤﺜل ﺘﻐﻴﻴﺭ ﺍﻷﻟﻭﺍﻥ ﺃﻭ ﺍﻟﻌﻨﻭﺍﻥ ﺃﻭ ﺤﺠﻡ ﺍﻟﺨﻁ(.
) (12ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
436
• ﻹﻀﺎﻓﺔ ﺨﻁ ﺍﻻﻨﺤﺩﺍﺭ ﺇﻟﻰ ﺍﻟﺸﻜل ﺍﻟﻨﺎﺘﺞ ﺍﺫﻫﺏ ﺇﻟﻰ ﻗﺎﺌﻤﺔ ﺍﻟﺭﺴﻭﻤﺎﺕ Chartﻭﻤﻨﻬﺎ ﺃﻤﺭ ﺍﻟﺨﻴﺎﺭﺍﺕ Optionsﻟﻔﺘﺢ ﻨﺎﻓﺫﺓ ﺨﻴﺎﺭﺍﺕ ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ
) Scatterplot Optionsﺸﻜل (28-12ﻭﺤﺩﺩ ﺨﻴﺎﺭ ﺍﻟﻤﺠﻤﻭﻉ Totalﻓﻲ ﻫﺫﻩ ﺍﻟﻨﺎﻓﺫﺓ ﻓﻲ ﻗﺴﻡ ﺘﻭﻓﻴﻕ ﺍﻟﺨﻁ ﺍﻟﻤﺴﺘﻘﻴﻡ Fit Lineﻭﺒﺎﻟﻨﻘﺭ ﻋﻠﻰ ﻤﺭﺒﻊ
ﺨﻴﺎﺭﺍﺕ ﺍﻟﺘﻭﻓﻴﻕ Fit Optionsﺴﻭﻑ ﻴﺘﻡ ﺘﻔﻌﻴل ﻨﺎﻓﺫﺓ ﺨﻴﺎﺭﺍﺕ ﺍﻟﺘﻭﻓﻴﻕ Fit
. Options
ﺸﻜل : 28-12ﻨﺎﻓﺫﺓ ﺍﻟﺨﻴﺎﺭﺍﺕ Optionsﻓﻲ ﺃﻤﺭ ﺭﺴﻡ ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ Scatterplot ﻭﺒﺎﺨﺘﻴﺎﺭ ﺍﻟﻤﺠﻤﻭﻉ Totalﻓﻲ ﺨﻴﺎﺭﺍﺕ ﺭﺴﻡ ﺍﻟﺨﻁ ﺍﻟﻤﺴﺘﻘﻴﻡ ﺃﻭ ﺍﻟﻤﻨﺤﻨﻰ .Fit Options
• ﺍﻟﻀﻐﻁ ﻋﻠﻰ ﻤﺭﺒﻊ ﺨﻴﺎﺭﺍﺕ ﺍﻟﺘﻭﻓﻴﻕ Fit Optionsﺴﻴﻔﺘﺢ ﻨﺎﻓﺫﺓ ﺨﻴﺎﺭﺍﺕ ﺍﻟﺨﻁ ﺍﻟﻤﺴﺘﻘﻴﻡ ) Fit Lineﺸﻜل . (29-12
• ﻫﻨﺎ ﻴﻤﻜﻥ ﺍﺨﺘﻴﺎﺭ ﺸﻜل ﺍﻟﺨﻁ ﺍﻟﻤﺴﺘﻘﻴﻡ ﺃﻭ ﺸﻜل ﻤﻨﺤﻨﻰ ﻤﻥ ﺩﺭﺠﺔ ﺃﻋﻠﻰ ﻤﻥ ﺨﻼل ﻤﺭﺒﻊ ﻁﺭﻴﻘﺔ ﺍﻟﺘﻭﻓﻴﻕ Fit Methodﻓﻲ ﻫﺫﻩ ﺍﻟﻨﺎﻓﺫﺓ ،ﻜﺫﻟﻙ ﻴﻤﻜﻥ
ﺍﺨﺘﻴﺎﺭ ﺭﺴﻡ ﺤﺩﻭﺩ ﺍﻟﺜﻘﺔ Confidence Limitsﻟﻤﺘﻭﺴﻁﺎﺕ ﺍﻟﻘﻴﻡ ﺃﻭ ﺍﻟﻘﻴﻡ
ﺍﻟﻤﺘﻭﻗﻌﺔ ﻤﻥ ﺨﻼل ﻤﺭﺒﻊ ﺨﻁﻭﻁ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﻤﺘﻭﻗﻌﺔ
Regression
) (12ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
437
، Prediction Linesﻭﻴﻤﻜﻥ ﺃﻴﻀﹰﺎ ﻜﺘﺎﺒﺔ ﻗﻴﻤﺔ ﻤﻌﺎﻤل ﺍﻟﺘﺤﺩﻴﺩ ) Coefficient of determination (R2ﺒﺠﺎﻨﺏ ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ ﻋﻥ ﻁﺭﻴﻕ
ﺍﻟﻀﻐﻁ ﻋﻠﻰ ﻤﺭﺒﻊ ﺇﻅﻬﺎﺭ ﻗﻴﻤﺔ ﻤﻌﺎﻤل ﺍﻟﺘﺤﺩﻴﺩ ﻓﻲ ﺨﺭﻴﻁﺔ ﺍﻟﺸﻜل Display
. R-squared in legend
ﺸﻜل : 29-12ﻨﺎﻓﺫﺓ ﺨﻴﺎﺭﺍﺕ ﺭﺴﻡ ﺍﻟﻤﻨﺤﻨﻰ)ﺃﻭ ﺍﻟﺨﻁ ﺍﻟﻤﺴﺘﻘﻴﻡ( Fit Lineﻓﻲ ﺃﻤﺭ ﺭﺴﻡ ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ Scatterplotﻭﺒﺎﺨﺘﻴﺎﺭ ﺍﻟﺨﻁ ﺍﻟﻤﺴﺘﻘﻴﻡ . Linear Regression
• ﻭﺃﺨﻴﺭﹰﺍ ﺍﻀﻐﻁ ﻋﻠﻰ ﺃﻤﺭ ﺍﻻﺴﺘﻤﺭﺍﺭ Continueﻓﻲ ﻫﺫﻩ ﺍﻟﻨﺎﻓﺫﺓ ﻹﻏﻼﻗﻬﺎ ﻭﻤﻥ ﺜﻡ ﻋﻠﻰ ﺃﻤﺭ ﺍﻟﺘﻨﻔﻴﺫ OKﻓﻲ ﻨﺎﻓﺫﺓ ﺨﻴﺎﺭﺍﺕ ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ
Scatterplot Optionsﻟﺘﻨﻔﻴﺫ ﺍﻷﻤﺭ ﻭﻅﻬﻭﺭ ﺍﻟﺨﻁ ﺍﻟﻤﺴﺘﻘﻴﻡ ﻓﻲ ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ ﻜﻤﺎ ﻓﻲ ﺍﻟﺸﻜل 30-12ﺃﺩﻨﺎﻩ.
) (12ﺘﺤﻠﻴل ﻨﻤﺎﺫﺝ ﺍﻻﻨﺤﺩﺍﺭ ﺍﻟﺨﻁﻲ
438
ﺸﻜل : 30-12ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ Scatter Plotﻭﺒﺈﻀﺎﻓﺔ ﺍﻟﺨﻁ ﺍﻟﻤﺴﺘﻘﻴﻡ ﻟﻠﺒﻴﺎﻨﺎﺕ .
160 140 120 100 80 60 40 20 70
60
Entrance Exam
50
40
30
University Exam
180