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تحليل الانحدار.pdf
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تحليل الانحدار.pdf
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Ayman Sobhy
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β 0 @$ A9& ε i + x i ( y i / 9& !* $ β1 < B+ x " !% * y " !* $ ; " . "#$ ,- B + x 9 9+ $ 9 ( D ( @* y ! C<
. ε i ∼ N ( 0, σ 2 ) !84 + -< F$ G84 . x " E#& : * ); ! .6 )$ 9 &+ $ !% < & Cars.sav ) + ) &+ 4 + + " ! "#$ 4 > ! C< . ) -< & &+ + 0+ % )9+ $+ ( % ! " :5 9& ! . $ & ; ! ! "#$ 9 +
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. 9& > 9& "#$ !% ! %A F ! ! "#$ H4 =I Graphs " ! Scatter 5 & ) @ + !% : (
: ( =I Define : * ; Simple 5 3 &
.. C* @@ : * + =I OK : *
2
!84 0 J "#* + 9& "#$ ; !% G + ! I# 5 &+ 9& . "#$ 2= K+ !% + 9&
( =I
3
. . =I OK : *
! 9& +< ,- B ANOVA J : * . B ) ! % DJ +< 9& ! F % @ 0) ( D &+ $ ANOVA J & . " @$ )4#& ! -< & / 0F H 0 : β1 = 0 H a : β1 ≠ 0
& F & !84 4 . -4 $ -4 !84 L+ J : * D . $ % β1 $ $ & ! ! "#$ $ 2 4 F & !84 0 + ! ;% 4 J * F & . $4 $ ( J $ & H 0 : β1 = 0; β 2 = 0;… ; β k = 0 H a : β1 ≠ 0; β 2 ≠ 0;…; β k ≠ 0
% $ & / $ & : $ -4 C4 4 N 4 0$ -4 C4 0&M !* < $ ! $ % .K+ > &+ ! : @
$ & J B+ B $ K+ !% G84 R2 =
SSR 461270.9 = = 0.807 SST 571435.9
4
! 19.3 ! 4 0( " 4 )4#& ! %80.7 +< !84 9& @$ A9& )@ 6 4$ . @* * ! J )4#& :B+ B Residuals " L< )$ 3 J 9+ &+ 0 MSE =
110165 = 283.20 389
= ! KJ G 0 9& ) D% : MSE " @ .@$ A9& ! : * % ( " ;A 0 $ $ T )& ( $ ) : * ; J B !84 : * 0 ( β1 = 0.329 ) " ( β0 = 40.434 ) " )% / : y = 40.434 + 0.329x
& / 0C$ =-$ !* < $ $ ; J & :! ! -< H 0 : β0 = 0
:5 -<
H a : β0 ≠ 0 H 0 : β1 = 0
; -<
H a : β1 ≠ 0
-< , :5 -< 4 $ -4 C4 !% G84 J . : * :B+ T & + ! / t* =
b0 = 22.52 s (b 0 )
; -< 4 $ -4 C4 !% G84 % .< B+ P-Value " :B+ T & + ! / -< , t* =
b1 = 40.36 s (b1 )
:5 -< & ! : @7 J G .< B+ P-Value " !% ! ! 4 4 K+ . ; -< C4 ! !% @ $ .5 4 "#$ K+ + : * D L+ @ + ( P 9& C* !% 5 & ; ) + 9 @ L+ @
5
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( B $ @$ A9& @ 4$ 4 - )9& ! .( N ;A 4# $ &+ 0 $ ( " ( =I Linear Regression ( 4 Plots D : * :
6
: . =I OK ; Continue : *
! : *
0< 9& J %@ @ $ " ! I# Histogram &+ F " ( D & L+ ( ! % !% 0 J .$ 9 ( D ( =A %A Normal probability plot
7
Multiple Linear Regression $ = 0F &+ 7 ) ;% ! $ $ % ) * ( % ! "#$ $ !% G84 0! + ! ( J C4 . + ) 6& : : * > y i = β 0 + β1x 1i + β 2 x 2i + ε i
@$ A9& ε i + ) ( x 1i ; x 2i ) ( y i /
( β1; β 2 ) < B+ ( x 1 ; x 2 ) " !% *
y " !* $ ; " β 0
9& ) -4 : . + ) )# $ !* $ ) ! 9 J * -4 : 4-7 $ : * + . + ( % ! + " ! "#* ! % ) + ) &+ + 5 &+ . + !D )9+ $+ ! + !
) 7 9& G#& ! !% B ( =I . 9 ) +
8
. . =I OK : * 9&
0 $ $ & ; J ! ! 4 $ 5 J & !% .< !* E & =$ J $ ! J 9& ! + !% : * % J ;A G !% 9 + 9& J 4- ! I# 4 E#& +< 4 J + < L< )$ 3 J + ) ! B" 9 J = ++5 K+ !% " .( ! 9 J ! %A !% .Multicollinearity 9& $ : + .F = ; + )
9
!% G : @
+ ) ! B 9 + ,- 9& $ %@ N " !% . <% ! !* + .9& $ & ; Linear Regression ( ! Statistics D : *
. ! - 9& $ & . =I 0OK ; Continue : * .
10
5 E 9 / 0) 4< 9 )+ L+ J ; + /; E 9 5 + ; E 9 ; Condition Index " )% ;Q 9& $ %@ $ .! ; .9& $ %@ J : * @Q =4 15 !* )D 84 0 % : I 021.454 B+ ; " !84 L+ J : I + !D ; + ! J 0; = + ) .)9+ $+ 5 + ! ! %88 + +
11
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