مدونة / ???????? ????????? ????????? ??

‏الثلاثاء، 3 مارس 2009 في 14:09

???????? ????????? ????????? ?? ????? ??????? ?? ???? ???????
1- ????? ???????? ????????? ?????? ????????:-

???? ???? ??????? ?????? ????? ?????? ??????? ??? ??????? ????? ?? ???? ????? ??????? ?????? ?? ???? ??????? ??? ??????? ??? ??? ?????? ????? ????? ?? ??????? ??? ??????:
??? ?????? ????? ????? ?? ??? ?? ??????? ??? ?????? ????? ???? ??? ???? ????????? ???? ?????? ??????? ??? :-
????? ???????(????? ????:) ????? ???? ??????? ???? ( ????? ???:).
??? ???? ?????? ???? ?????? ??????? ??? ???? ??????? "?????" ?????? ????????? ?? ?????? ?????????? . ???????? ??????? ???? ??????? ?? ???? ??????? ??? ????????? ??? ????? ????.

????? ???????? ?????????:-
?? ??????? ???? ????? ?? ??? ????????? ???? ?????? ???? ??? ??????? ??? ????? ?????? ?? ????? ????? ??? ???? ?? ??????? ?????? ??? ??? ???? ??????? ??? ??????? ????? ????? ?????? ??????? ??????? ??? ????? ??????? ??? ????? ??????? ???????? ???? ????? ????? ??? ???? ?????? ???? ?????? ??????? ???????? ?? ???? ????????? ?? ????? ?????? ???????.
?? ???? ??? ?????? ??????? ??? ????????? ???? ????????? (Correlation ) ????? ?? ????? ?????? ?????? (prediction) ???????? ??? ??????? ?? ???? ?? ???? ?????? ???????? (Regression) ??? ?? ?? ???????? ????????? ????? ???? ?????? ????? ?? ?? ???? ?????? ?????? ??? ???? ???? ??? ??? ????? ???????? ????? ?????? ????.

??? ????????:
???? ?? ????? ??? ????? ????? ???? ??????? ???????? ??? ??????? ??????? ???????? ?????? ?? ???? ??? ???? ?? ???? ??????? ??????? ?? ?????? ?????? ?? ??? ???? ??????? ?????? ?? ?????? ?????? ?? ???? ?????? ???? ????? ??????? ????????? ????????? ??? X1,y1)), X2,Y2)).................Xn,Yn)) ??? ????? ??????? ????? ?????? ????? ????? ??????? ??? ????????? ?? ????.
????? ???? ???? ?? ????? ??? ??????? ??? ?????? ??? ??????? ???????? ??????? ?? ???? ????? ??????? ????? ??? ?? ????? ?????? ???? ?? ??? ???????:
Y ??????? ??? ???????

X
????? ???????
??? (1) ??????? ?????

??? ????? ?????? ???? ??????? ??? ?????? ???? ??????? ???? ??????? ?????? ?? ??? ??????. Y ?????? ?????????

???? ??????? X
??? (2) ??????? ?????

?????? ????? ???????? : Correlation Analysis
????? ???????? ??? ???????? ????????? ?????? ?????????? ???? ???? ???? ????? ?????? ?????? ??????? ??? ??????? ?? ???? ?????? ????? ???????? ?????? ??? ????? ???????? ????? ?????? ??? ?? ??? ???????? ??????? ?????? ??????? ??? ??????? ?????? ???????? ??????? ??? ???? ???????? ?? ????? ????? ????????? .
??? ?? ???? ???????? ??????? ???? ??? ??? ??????? ???????? (???,???? ????? ,???????,??????,?????,????:) ?? ????????? ??? (?????- ??? ????- ???..??:) ????? ?????? ????? ???????? ???? ????? ?????? ????? (????? ??????:) ??? ?? ??? ??????? ??????? ?? ???? ????? ?????? ?????? ?? :-
1. ????? ??????? ??? ????????? :- ?????? ??? ??????? ??? ??? ???????? ?????? ????? ?????? ???? ?? ?????? ?? ?????? ???? ???????? ??? ??? ??????? ???? ????.
2. ????? ??????? ?? ??? ????????? :- ?????? ??????? ???? ????????? ?? ?????? ???? ??? ????? ???? ????? ???????? ??????? ?? ????? ????? ?????????.
3. ??? ??????:- ???? ?????? ?????? ??? ?? ?????? ?? ???? ?? ????? ???????? ?? ??? ????? ?? ?????? ?? ????? ?? ???? ??? ????? ???????? ???? ??????? ??????? ??? ????? ??? ??????.
?????:- ???????? Correlation :-
1- ????? ???????? ?????? :- ???? ??? ??????? ???????? ??? ??????? ?? ??????? ????? ????? ?? ??????? ???????:-
??- ????? ??? ???????? ??? ????????? :- ?? ???? ?? ??? ??? ???????? ????? ?? ??????? ?? ?????? ?? ???????.
??- ????? ????? ??????? ??? ????????? :- ?? ???? ?? ??? ???? ??????? ????? (????:) ?? ?????( ????:).
??- ????? ????? ??????? ??? ?????????.
??- ????? ????? ???????? ?? ?????? ?????? ???? ????? ???? ?????? ?????? ?? ?????? ??????.
??????? ???? ????? ???????? ??? +1 ?-1 ????? ???? ??????? ???? ???? ????? ????? ???????? ?? -1 ?? +1 ????? ??????? ???? ???? ????? ???? ????? ???????? ????? ( ) ??? ????? ??????? ??? ????????? ??? ?????? ???? ??????? ?? ????? ????? ??????? ??? ????? ??????? ??? ????????? ???????? ??????? ????? ????? ???????? ???? ???? ????? ????? ????? ?????? ??????? ??????? ????? ????? ????? ??? ?????????.

????? ??? ??? ????? ??? ????? ????????.
??? ????? ???????? ??? ???????
??? ????
???
?????
????
???? ???? ?? 0.80????????????0.99
?? 0.60??????????????0.79
?? 0.40??????????????0.59
??0.20????????????????0.39
??0.01????????????????? 0.19

????? ??????? ??? ??? ?? ????? ?????? ?????? ???? ??? ??????? ?????? ?????? ???? ????? ????? ??? ??? ?? ???? ??? ???? ????? ???? ??? ???? ???? ??? ???? ????? ???? ???,?? ?? ???? ????? ???? ?? ??? ??? ???? ????? ??? ????.
????:-
?? ????? ????????? ????? ??????? ??? ??? ???????? ???? ??????? ??????? ?? ????? ????? ??????? ????? ?? 15 ????? ??????? ??????.
??? ???????? X 8 9 9 10 10 28 29 29
??? ????? ??????Y 8 13 17 15 23 56 46 60

??? ???????? X 30 30 48 48 49 50 50
??? ????? ??????Y 52 65 86 90 95 99 88

????:-
????:- ??? ????????
Y

X 50 45 40 35 30 25 20 15 10 5 0

?? ???? ????? ???? ??? ?? ???? ????? ???? (????:) ????? ??? ??????? ??????? (??? ???????:) ???????? ?????? (??? ????? ?????:) ?? ?? ??? ???????? ???? ???? ???? ???? ??????? ??? ????????? (X-Y) .

??????:- ???? ??? ???????
????? ????? ???????? ????? ?????? ?????? ??? ????????? ?????? ????????? ???????:

??? ?? :
( ) = ????? (???? ??? ??? ??????? X ?? ??? ??????? Y)
( ) = ????? ??? ??????? X
( ) = ????? ??? ??????? Y
( ) = ???? ????? ??? ??????? X
( ) = ????? ???? ???? ??? ??????? X
( ) = ???? ????? ??? ???????Y
( ) = ????? ???? ???? ??? ??????? Y
n = ??? ??????
= ????? ???????? ????? ?????? ??? ????????? X? Y

??????? ???????? ???????? ????? ????? ???????? ??? ??????? X ????? ???? ??? ???????? ?? ?? ????? ??????? ???????? Y ????? ???? ??? ??????? ??????? ?????? ?? ?? ????? ???? ?????? ??????:
X Y X2 Y2 YX
8 8 64 64 64
9 13 81 169 117
9 17 81 289 153
10 15 100 225 150
10 23 100 529 230
28 56 784 3135 1568
29 46 841 2116 1334
29 60 841 3600 1740
30 52 900 2704 1560
30 65 900 4225 1950
48 86 2304 7395 4128
48 90 2304 8100 4320
49 95 2401 9025 4655
50 99 2500 9801 4950
50 88 2500 7744 4400
437 813 16701 59122 31319

????? ??? ??????? ????? ????? ????.

????? ?????? ????? Rank correlation coefficient
?? ????? ???????? ????? ?????? ????? ?? ???? ??? ????????? ?? ????? ????? ???? ???? ??? ??????? ?? ????????? ?? ?????? ??????? ???? ???? ?? ????? ??????(??????? ?????:) ?????? ??????? ??????(?????- ??? ???? ??? ????? ???? ???? ???:) ?? ??????? ?????????(????? ????? ????:) ?? ??????? ???????? (??? ???? ????? ????? ????? ????? ???:) ?? ???? ???????? (????? ????? ????:) ?????.
??? ??? ??????? ???? ????? ????? ???????? ??? ??? ????????? ???? ????? ?????? ??????? ????? ???? ????? ????? ?????? ????? ?? ???? ????? ?? ?? ????????? ??????? ???????? ?? ???????? ?? ??? ??????? ???????? ?????? ???????? ???????:

??? ?? :
???? ????? ?????? ?????? ??? ??? ??? ????????? x?y
n ???? ??? ??????.

????:-
??? ???? ?????? ?????? ???? ????? ?? 11 ???? ????? ?????? ??????? ?? ???? ??????? ????? ????? ??????? ??? ???:
d d ??? Y ???X ????? ?????? ??????? Y ????? ?????? ?????? X
25 5 1.5 6.5 ???? ???? ???
64 8- 10.5 2.5 ????? ????
36 6- 10.5 4.5 ????? ?????
1 1- 7.5 6.5 ??? ???
30.25 5.5 5 10.5 ????? ?????
20.25 4.5- 9 4.5 ??? ???? ?????
16 4- 5 1 ????? ???? ????
30.25 5.5 3 8.5 ???? ??? ????
9 3 7.5 10.5 ??? ?????
1 1 1.5 2.5 ???? ???? ????
12.25 3.5 5 8.5 ????? ??? ????
d 245? 0

??????? ???? ??????? ??? ???? ?????? ?? ????????.

????:-
?????? ??? ??????? ?????? ????? ?????? ????? ?? ?? ???? ?????? ??????? ??????? ??? ???? ??????? ???????:
1- ???? ?????? ??? ??????? X ( ?????? ) ???????? ?? ???? ????? ????? ?????? ???? ??? ??? ????? ???? ???? ?????? 1 ??????? ???? ??? ??? ????? ???? 2 ???????? ????? ?????? 3 ???????? ??? ???? 4 ???????? ??? ???? 5 ???????? 6 ???? ????? ????? ???? ?? ??? ??? ???? ??? ???? ????? ???????? ?????? ??????? ???? ???? ?????? ????? ???? ????? ????? ???????? ????? ??? ????? ????? 2.5 ??????? ???? ??? ??? ?? ???????? ????? ????? ??? ????? ????? ??? ????? ??? ????? ????? ???????? ???? ?????? 4.5 ??? ????? ???? ???? ???? ???? ?????? 1 ????? ?? ????? ????? ????? ?????? ??????? ????? X ???? ????????? ??? ??????? ??? ??? ??????? ?????? y ??????? ?????? ???? ???:-
2- ???? ????? ??? ???? ?? ???? ?? ??? ??????? X ??????? ???????? ??? ?? ??????? ????? y ??? ?? ????? ?????? ????? ???.
3- ???? ?? ??? ?? ?????? ???????? ?? ?????? ???????.
4- ???? ???? ????? ???????? ?????? ?????? ???????? :-

?? ?? ??????? ??? ?????? ??????? ?????(????:) ??????.
??????:-
- ????? ??? X ) ):-
- ???? ???? ,???? , ???? , ????? , ????? , ??? , ??? , ??? ???? , ??? ????, ?????,?????
- (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)
- ????? ??? Y)):-
- ???? ????, ???? ????, ????, ????? ,?????, ????? ,???, ???, ??? ????, ?????,?????.
- (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)
????:-
???? ??? ??????? 6 ?? ???????? ?? ?????? ???????? ?? ??? ??????? ???????? ??????? ???????.
X Y ???X ??? Y d d
??? ????? 4 3 1 1
????? ??? 3 4 1- 1
???? ????? 1 2 1- 1
????? ???? 2 1 1 1
??? ???? ????? 5 6 1- 1
????? ??? ???? 6 5 1 1
0 6

???????? ????? (????:)?????.

?????? ????? ???????? Regression Analysis
?? ??????? ???????? ??????? ?????? ?????? ??????? ????? ??? ??? ???????? ?? ????? ????? ?? ????? ??????? ? ??? ????? ?? ????? ?????????? (?????:) ??? ????????? ? ?? ????? ?? ????? ???????? ??? ????????? ????????? ???????? ??????? ? ?? ????? ?? ?????? ?? ????? ?????. ??? ?????? ?? ????????? ??????? ???????? ????????? ?????? ?????????? ?? ????? ???????? ??? ??????? ??????? ??? ??? ???????? ??? ?????? ???????? ????????? ????????? ??????? ???? ??????? ???????.
??????? ?? ????? ??? ?????? ???????? ???????? ?????? ???????? ?????? ??????? ????????? ????? ??? ????? ???????. ??? ?? ???????? ?????? ????? ?????? ????? ????? ??? ??? ????? ?????? ??? ????? ?????? ??? ?????? ???? ????????? ??????? ?? ???? ????? ?????? ????? ???????.
?????? ???????? ?????? ?? ?????? ??? ????? ??????? ????? ?? ????? ???????? ??? ????? ????? ???? ??? ?? ??????? ????? ????? ????? ??? ??????? ??????? ???? ????? ??? ????? ??????? ??? ??? ????? ????? ???? ??????? ? ???? ???? ?????? ???? ????? ?????? ??? ????? ???? ????? ?????.
??? ????? ?????? ?? ???????? ?????? ?? ?????? ??? ????? ??????? ??????? ?????? ??? ??????? ??? ????? ????????? ??????? ?????? ?????? ?????? ?????????? ? ????? ?????? ?? ??? ??????? ?????? ??????? ?????? ?? ???????? ????? ????? ????? ????? ??????? ????? ?????? ?????.

????? ???????? The Regression Models Model
??? ????? ???????? ??? ????? ?? ???? ??????? ???????? ?? ????? ???? ??????? ??? ????? ?????? ???? ???? ???? ????? ???? ??? ????????? ????? ???? ????? ??? ????? ??? ????????? ?????? ??????? ????? . ????? ??????? ???? ???? ????? ????? ?????? ??? ????? ?????????? ?????? ???????? ?????? Dependent Variable ????? ??? ?? ????? ???? ?? ???? ??????? ?????? ??????? ??????? Variable Independent .
??????? ????? ???????? ?????? ?????? ?? ????? ??????? ??? ??????? ?? ???? ??? ??? ????? ????? ???? ?? ?????? ????? ?????? ?? ??? ????????? ??? ?????? ????? ?????????? ?????? ???? ?? ????? ??? ?????? ?????? ????? ??????? ?????? ?? ???? ????? ???? ????????? ?????? (????????? ???????:) ?????? ?? ???? ?? ????? ?? ?????? ????? ????? ???? ?????? ????? ???:) ???????? ???? ????? ?? ????? (??????? ??????? ????:) ???? ????? ??????? ?????? ??????? (??????? ??????? ?????:) ????? ????? ?? ????????? ???????? ???? ?? ??????? ??????.
????? ?? ???? ?????? ???????? ??? ??????? ???????? ???????? ???? ???? ???? ???? ???????? ??????? ???????? ?? ????????? ??????? ?? ???? ???????? ?????? ????? ???? ??????? ??? ??????? ???? ??? ????????? ???????? ???? ????:-
1- ????? ???????? ????? ??????. SIMPLE LINEAR REGRESSION
2- ????? ???????? ????? ???????. MALHIPLE LINEAR REGRESSION

????? ???????? ????? ?????? SIMPLE LINEAR REGRESSION MODEL
?? ????? ?????? ??? ???????
??? ????? ??? ????? ????? ???????? ??? ??????? ??? ?? ??????? ??????? ????? ???? ???? ? ????? ?????? ?? ??????.
????? ???????? ????? ??????:
?? ??? ???? ?? ????? ??? ??????? ??? ????? ?????? ??????? (????? ???:) ??????? ????????? ????? ????? ????? ??????? ?????? ?????? Y???????? ??????? ?????? X ????? ??????? ?? ??? ?????? ????? ?????? Y ??? X ??? ???????? ???? ?????? ?? ???? ??????? ????? ??? n ?? ????????? ??? ????????? X,Y ??? ?? ?? ?????? ??????:-

??? ???????? ??????? ?????? Y ??????? ???????X
1
2
3
.
.
.
.
n Y1
Y2
Y3
.
.
.
.
Yn X1
X2
X3
.
.
.
.
Xn

??? ????????: scatter diagram
?? ?????? ?????? ?? ???? ????? ???????? ?? ????? ??? ????? ???? ???? ???????? ???? ??? ????? ??? ?? ??? ?? ??????? ????????? X,Y (?Xn,YnX1,Y1) ?? ??? ???? ???? ?????? ??????? ??? ?????? ?????? ??????? ?????? ????? ?? ???? ?????? ?????? ?????? ??????? ?????? ??????? ?????? ??????? ??????? ??? ????? ??? ???????? ??? ????? ??? ???? ????? ?????? ??????? ??? ????????? ?????????? ?????? ????? ??? ????? ???? ?? ???? ????? ????? ??? ????????? ?????.
????? ????? ????? ???????? ????? ??????:-
??? ???? ??????? ???? ?? ????? ??????? ?????? ????? ???? ???????? ????????

??? ?? = = ????? ??????? ??????? = =????? ??????? ??????.

??????:- ???????? ????? ?????? simple linear regression
????? ????? ???????? ???? ????? ???? ?? ????? ?????? ??????? ??????? ????? ???????? ?? ??????? ??????? ????:-
1- ????? ??? ??????? ?????? ????? ?? ?????.
2- ??????? ???????.

??????? ??? ????? ?? ?????? ?? ???????? ????? ?????? ??????? Y "??? ??????? ??????? ?????? ?? ???????"??? ???????" ??? ????????" ????? ????? ?? ??? ?????? ???????:-
X 1.92+1.74- =
??? ????? ??? ??????? 1.92 ????? ?????? ???????? ????? ?? ?????? ?? ???? ????? ?????? ???????:-

=
=
??? ???? ??????? 1.74- ???? ???? ???????? ?? ????? ??????? ?? ?????? ?????? ?????? ???? ?? ?????? ???????:-

??? ?? ?? ????? ??????? ??????? X ?? ?? =
????? ?? ????? ??????? ?????? Y ?? ?? =
???? ?????? ?????? ??? :-

=54.2-55.92
=-1.74
???? ?? ??? ??? ??????? X ?? ????? ????? ??? ????? ????? ??????? ??? ?? ???? ????? ?? ??? ??????? ??? ????? ????? ???????? ( ) ?? ?????? ???? ???? ??? ???? ?? ????? ???? ???? ???? ?? ????? ???? ??? ????? ??????? 1.92 ?? ???? ??????? ?????? ?? ???????.
??????? ??????? :-
?????? ????? ?? ???????? ?????? ?? ????? ?????? ???????? ??????? Y ??? ???? ?????? ?? X ?????? ???? ??? ??? X ?? ?????? ???? ?? ???? ?????? ???? ??????? Y ?????? ?? ???? ????? ??? ?? ??????? ???? ???? ??? ???????? (X=48) ???? ????? ????? ??? ??????? ????????? ?????? ??:
?? ??? ??? ?????? 86 ?? ??? ????? ???? ???? ??????? X ?? ???? ?????? ??? ??? ?????? ???? ???? Y ???????? ??? ???? ???? ?????.
???? ?????? ?????? ???????? ?????????:-
?????? ???? ??????? ????? 8 ???? ???? ??????? ?????? ??????? ??? ??? ??????? ???? ?????? ?????? ?? ?????? ??????? ???????? ?? ??????? ???? ??????? ?????? ?? ?????? ??????? ?? ????? ??????? ?????? ????? ??????? ??? ???:-

4 1 5 8 2 3 7 6 X ??? ????? ????????
7 9 6 3 10 8 5 2 Y ?????? ?? ???????

- ?? ???? ????? ???? ??? ???? ???????? ???????? ??????? ??? ????? ???????? ??? ??? ??????.
- ???? ?????? ???? ??? ???? ????? ???? ???? ????????? 7 ????? .
????:-
????? ??? ????????:
??????? ??????? : ????? ????????
??????? ?????? : ??????? ??????
Y
-10
-8
-6
-4
-2
X 12 10 8 6 4 2
??????? ????? ??? ?????????.

?????? : ????? ????????:

Y2 X2 XY Y ?????? ?????? ????? ?? ???????? X ??? ????? ???????? ???????
04 36 12 2 6
25 49 35 5 7
64 09 24 8 3
100 04 20 10 2
09 64 24 3 8
36 25 30 6 5
81 01 09 9 1
49 16 28 7 4
368 204 182 50 36

0.96=
- ??? ??????? ?????? : ????? ?????.
- ??? ??????? ??????: ???? ????

1.024- =

?????? ???? ????? ?? ???????? ???? ??? ????? ?????? ?? ???????? ???? ????? ???????.


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