DocumentC2

CHNG 2: M HNH HI QUY BI

GV: Trng Bch Phng

I. MO HNH HOI QUY TUYEN TNH 3 BIEN1. M hnh hi quy 3 bin

iiii UXXY +++= 33221 Trong

Y l bin ph thucX2,X3 l cc bin c lpX2i, X3i l gi tr thc t ca X2, X3Ui l cc sai s ngu nhin

1.1. Hm hi quy tng th (PRF)

1.2. Cc gi thit ca m hnh

Gi tr trung bnh ca i lng ngu nhinUi bng 0 Phng sai ca Ui khng thay i

Khng c s tng quan gia cc Ui Khng c s tng quan (cng tuyn) giaX2 v X3 Khng c s tng quan gia cc Ui vX2,X3

1.3. c lng cc tham sChng ta s dng phng php bnh phng nh nht OLS

Hm hi quy mu tng ng s l :

iii XXY 33221 ++=iiii eXXYSRF +++= 33221 :

Hay:

iiii UXXYPRF +++= 33221:

I. Mo hnh hoi quy tuyen tnh 3 bien

iiiiii XXYYYe 33221 ==Theo phng php OLS th cc tham s

321,, c chn sao cho

( ) = min 2332212 iiii XXYe Nh vy , cng thc tnh ca cc tham s nh sau :


=2

=3

=1

K hiu: YYy ii =222 XXx ii =

333 XXx ii =


Ngi ta chng minh c

( )222222 XnXx ii =( )232323 XnXx ii =( )222 YnYy ii =

323232 XXnXXxx iiii =222 XYnXYxy iiii =333 XYnXYxy iiii =


V dBng di y cho cc s liu v doanh s bn(Y), chi ph cho hng (X2) v chi ph qung co(X3) ca mt cng tyHy c lng hm hi quy tuyn tnh ca doanhs bn theo chi ph cho hng v chi ph qungco


Ths. Tran Van Hoang

Doanh s bn Yi (tr) Chi ph cho hng X2 Chi ph qung co X3

1270 100 1801490 106 2481060 60 1901626 160 2401020 70 1501800 170 2601610 140 2501280 120 1601390 116 1701440 120 2301590 140 2201380 150 150

T s liu trn, ta tnh c cc tng nh sau :


1.4. H s xc nh ca m hnh

=TSS

=2R

=ESS

=RSS

=2R


i vi m hnh hi quy bi, ngi ta tnh R2 c hiu chnh nh sau :

k l s tham s trong m hnh


Khi k>1 th:

1.4. H s xc nh ca m hnhV d : Tnh h s xc nh ca m hnh hi quytheo s liu ca v d trc

1.5. Phng sai ca h s hi quyPhng sai ca cc tham s hi quy c tnhtheo cc cng thc sau:

( )

++=

232

23

22

323222

23

23

2222

211

iiii

iiii

xxxx

xxXXxXxXn

21 1

)(

=se


3 2

=

nRSSVi

( )

=

232

23

22

2322

2

iiii

i

xxxx

x

22 2

)(

=se


3 2

=

nRSSVi

1.5. Phng sai ca h s hi quy

( )

=

232

23

22

2222

3

iiii

i

xxxx

x

23 3

)(

=se

3 2

=

nRSSVi

I. Mo hnh hoi quy tuyen tnh 3 bien1.5. Phng sai ca h s hi quy

1.6. Khong tin cy ca cc h s hi quy

Khong tin cy ca 1

+ )();( 2

222

22 setset

Khong tin cy ca 2

+ )();( 1

211

21 setset

Vi tin cy l 1-



+ )();( 3

233

23 setset

Khong tin cy ca 3

Lu khi tra bng T-Student, trong trng hp hm hi quy 3 bin th bc t do l (n-3)



V d : Tnh khong tin cy ca 2 v 3 m hnh hi quy theo s liu ca v d trc vi tin cy 95%

1.7. Kim nh gi thit

a) Kim nh gi thit v 1, 2 3

Bc 1 : Lp khong tin cyBc 2 : Nu 0 thuc khong tin cy th chp nhn Ho. Nu 0 khng thuc khong tin cy th bc b Ho

V d : (theo s liu trc), yu cu kim nh cc gi thit 2 , 3 Vi tin cy 95%

Ho:i= oH1:i o


b) Kim nh gi thit v R2

Bc 1 : tnh

Ho:R2= 0H1:R2 0

Bc 2 : Tra bng tm F(2,n-3), mc ngha l

Bc 3 : Nu F>F(2,n-3) , bc b H0Nu FF(2,n-3) , chp nhn H0

1.7. Kim nh gi thit

b) Kim nh gi thit v R2

Ho:R2= 0H1:R2 0

tin cy l 95%

V d: Yu cu kim nh gi thit

1.7. Kim nh gi thit

Hm sn xut Cobb-Douglas c biu din nh sau:

iUiii eXXY 32 321=

Trong : Yi : sn lng ca doanh nghipX2i : lng vnX3i : lng lao ngUi : sai s ngu nhin

Hm sn xut Cobb-Douglas c th a c v dng tuyn tnh bng cch ly logarit hai v

2.1. Hm sn xut Cobb-Douglas

2. Mt s dng hm

2.1. Hm sn xut Cobb-Douglas

iiii UXXY +++= 33221 lnlnlnln

t

Dng tuyn tnh s l :

ii

ii

ii

XXXX

YY

3*3

2*2

1*1

*

lnlnlnln

====

iiii UXXY +++=*33

*22

*1

*

2. Mt s dng hm

2.2. Hm hi quy a thc bc 2

iiii UXXY +++=2

321

Mc d ch c mt bin c lp Xi nhng n xut hin vi cc lu tha khc nhau khin cho m hnh tr thnh hi quy ba bin

II. Mot so dang ham


1 2 2 3 3 ...i i i k ki iY X X X U = + + + + +

Trong Y l bin ph thucX2,X3,,Xk l cc bin c lpUi l cc sai s ngu nhin1 :H s t do

2, 3,, k l cc h s hi quy ring

3. HI QUY TUYN TNH K BIN

12

...

n

YY

Y

Y

=

1

2

...

k

=

1

2

...

n

UU

U

U

=

K hiu


21 31 1

22 32 2

2 3

1 ...1 ...... ... ... ... ...1 ...

k

k

n n kn

X X XX X X

X

X X X

=

V

III. HI QUY TUYN TNH K BIN3.1. Hm hi quy tng th (PRF)

.Y X U= +

Khi , h thng cc quan st c th c vit li di dng :

III. HI QUY TUYN TNH K BIN3.1. Hm hi quy tng th (PRF)

3.2. Cc gi thit ca m hnh hi quy k bin

Gi thit 1 : Cc bin c lp X1, X2,,Xk chov khng ngu nhinGi thit 2 : Cc sai s ngu nhin Ui c gi trtrung bnh bng 0 v c phng sai khng iGi thit 3: Khng c s tng quan gia cc sais Ui

III. HI QUY TUYN TNH K BIN

Gi thit 4 : Khng c hin tng cng tuyn gia cc bin c lp X2, X3,,XkGi thit 5 : Khng c tng quan gia cc bin c lp X2,X3,,Xk vi cc sai s ngu nhin Ui

1 2 2 3 3 ...i i i k ki iY X X X e = + + + + +SRF:

hoc:

Hm hi quy mu :

1 2 2 3 3 ...i i i k kiY X X X = + + + +

Hay : (Vit di dng ma trn )Y X e= +

III. HI QUY TUYN TNH K BIN3.2. Cc gi thit ca m hnh hi quy k bin

3.3. c lng cc tham s

Vi

1

2

...

n

ee

e

e

=

1

2

...

k

=


( )i i ie Y Y=

1 2 2 3 3 ...i i i k kiY X X X =

1 2 2 3 3 ...i i i k ki iY X X X e = + + + + +SRF:

hoc:1 2 2 3 3

...i i i k kiY X X X = + + + +

Khi


Theo phng php OLS th cc tham s

1 2 3 , , ,..., k c chn sao cho

( )22 i i ie Y Y= ( )21 2 2 3 3 ...i i i k kiY X X X =

min


Ta k hiu l cc ma trn, , ,T T T TX Y echuyn v ca , , ,X Y eTc l

( )1 2, ,...,T nY Y Y Y=( )1 2, ,...,T ne e e e=( )1 2 , ,...,T k =

21 22 23 2

1 2 3

1 1 1 ... 1...

... ... ... ... ......

n

k k k kn

X X X XX

X X X X

=


Khi :

1 ( )T TX X X Y =


2 32

2 2 2 3 2

22 3

...

...... ... ... ... ...

...

i i ki

i i i i i ki

ki ki i ki i ki

n X X XX X X X X X

X

X X X X X X

=

Trong (XTX) l ma trn c dng


V d minh hoBng di y cho cc s liu v lng hngbn c ca mt loi hng ha(Y), thu nhpca ngi tiu dng (X2) v gi bn ca loihng ny (X3)Tm hm hi quy tuyn tnh

1 2 2 3 3

i i iY X X = + +


Yi (tn/thng) X2 (triung/nm)

X3(ngn ng/kg)

20 8 218 7 319 8 418 8 417 6 517 6 516 5 615 5 713 4 812 3 8

Gii T s liu trn, ta tnh c cc tng nh sau:


2( )TTSS Y Y n Y=

=2R

2 ( )T TESS X Y n Y=

=RSS


3.5. Khong tin cy v kim nh gi thit

Gi cjj l phn t nm dng j ct j ca ma trn (XTX)-1

Khi : 2 2 2 . .j

jj jjc c =

Vi 2 RSS

n k =

(k l s tham s)

2

( )j

jse =


Khong tin cy ca j l

2 2

( ( ); ( ))j j j jt se t se +

Hoc tnh gi tr ti hn ca j l

*( )

j j

j

tse

= Bc t do l (n-k)


Kim nh gi thit v R2

Vi tin cy 1-

Bc 1 : tnh

Bc 2 : Tra bng tm F(k-1,n-k), mc ngha l Bc 3 : Nu F>F(k-1,n-k) , bc b H0 Nu FF(k-1,n-k) , chp nhn H0

( )2

2

( )( 1) 1

R n kFk R

=

Ho:R2= 0H1:R2 0

3.6. Vn d bo

Cho02

0

1

...o

n

XX

X

=

Yu cu d bo gi tr Y0 ca Y


D bo im :

0 0 00 0 2 2 3 3

... k kY X X X = + + + +D bo khong :

0 0 02 2

( ( ); ( ))jY t se Y t se Y +

Bc t do l (n-k)


3.6. Vn d bo

02 2 1 0 0 ( )

T TY X X X X

=

0

20( ) Yse Y =


3.6. Vn d bo

V d (s liu trc)V d : Tnh khong tin cy ca 2 theo s liu ca v d trc vi tin cy 95%


yu cu kim nh cc gi thit

Ho:2= 0H1:2 0

Vi tin cy 95%


V d (s liu trc)

Yu cu kim nh cc gi thit

Vi tin cy 95%

Ho:R2= 0H1:R2 0


V d (s liu trc)

Yu cu d bo gi tr ca Y khi X2=9 v X3=9 vi tin cy 95%


V d (s liu trc)

Y: Doanh thu, X2 Chi ph quang cao, X3= Lng nhanvien

Y X2 X3

126 17 11148 23 14105 18 9162 22 16101 14 9175 24 17

Y X2 X3

160 23 15127 15 11138 16 12143 21 14158 22 15137 13 13

1. Viet phng trnh hoi quy2. Tm R2 va R2 hieu chnh3. Tm khoang tin cay cua cac he so hoi quy4. Kiem nh gia thiet H0 1 = 0, H0 2 = 0 vi =5%5. D bao doanh thu cty neu lng 10tr, quang cao 100tr

Chng 2: M HNH HI QUY BIMo hnh hoi quy tuyen tnh 3 bienSlide Number 3Slide Number 4Slide Number 5Slide Number 6Slide Number 7Slide Number 8Slide Number 9Slide Number 10Slide Number 11Slide Number 12Slide Number 13Slide Number 14Slide Number 15Slide Number 16Slide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21Slide Number 22Slide Number 23Slide Number 24Slide Number 25Slide Number 26Slide Number 27Slide Number 28Slide Number 29Slide Number 30Slide Number 31Slide Number 32Slide Number 33Slide Number 34Slide Number 35Slide Number 36Slide Number 37Slide Number 38Slide Number 39Slide Number 40Slide Number 41Slide Number 42Slide Number 43Slide Number 44Slide Number 45Slide Number 46Slide Number 47Slide Number 48Slide Number 49Slide Number 50Slide Number 51Slide Number 52Slide Number 53Slide Number 54Slide Number 55Slide Number 56Slide Number 57Slide Number 58Slide Number 59

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