chuong_4.pdf

36 Chng 6

B MN TON GVGD: Nguyn nh Huy

Chng 4

P DNG MS-EXCEL

TRONG PHN TCH

TNG QUAN V HI QUY

Phn tch tng quan

Phn tch hi quy

n gin

a tham s

37 Chng 6


A- PHN TCH TNG QUAN

6.1 Khi nim thng k

Hai bin s ngu nhin Y v X c th: lin quan tuyn tnh (a v b), c khuynh hng tuyn tnh

(c) hoc khng c lin quan (d v c).

H s tng quan Pearson:

,( , )

X Y

X X

COV X Y

; 2 2

1

1( )

N

X i X

i

XN

; 2 21

1( )

N

Y i Y

i

YN

S phn tch tng quan (correlation) kho st khuynh hng v mc ca s lin

quan, trong s phn tch hi quy(regrestion) xc nh s lin quan nh lng gia hai bin s

ngu nhin Y v X. H s tng quan c th c c tnh bi biu thc:

1

2 2

1 1

( )( )

( ) ( )

n

i i

iXY

n nXX YY

i i

i i

X X Y YS

RS S

X X Y Y

H s tng quan c dng trong vic nh gi mc lin quan:

Gi tr |R| Mc

38 Chng 6


6.2.1 Nhp d liu vo bng tnh

6.2.3 p dng Correlation

a- Nhp ln lt n lnh Tools v lnh Data Analysic

b- Chn phng trnh Correlation trong hp thoi Data Analysic ri nhp nt OK.

c- Trong hp Correlation, ln lt n nh cc chi tit:

Phm vi u vo (Input Range),

Cch xp xp theo hng hay ct (Group By),

Nhn d liu (Labels Fisrt Row/Column),

Phm vi u ra (Output Range)

Hp thoi Correlation

Kt qu

Cc h s tng quan: R (m/thi gian) = 0,97; R(nhit/thi gian) = 0,97 v R (m / nhit)

= 0,95

39 Chng 6


B- PHN TCH HI QUY

6.4 Khi nhim thng k

Php phm tch hi quy tuyn tnh (liner regression) hay c p dng trong khoa hc. Th

d, ng hi quy (regression line / line of best fit) thng dng d on v tui th hay hn

dng ca thuc

(L thuyt)

(c tnh)

Phng trnh hi quy c th c c

tnh bng phng php bnh phng

cc tiu (least-squares estimation).

40 Chng 6


C- HI QUY TUYN TNH N GIN

6.5 Phng trnh tng qut

| 0XY B BX

0B Y BX

/i i i i

i

X Y X Y N

BX X

Y: bin s ph thuc

(dependent / reponse variable)

X: l bin s c lp

(independent / predictor variable)

B0 v B l cc h s hi quy

(regression coefficients)

Bng ANOVA

Ngun

sai s

Bc

t do

Tng s bnh

phng

Bnh phng

trung bnh

Gi tr

thng k

Hi quy 1 ' ' 2( )iSSR Y Y MSR = SSR

MSRF

MSE

Sai s N 2 ' 2( )i iSSE Y Y MSE = SSE/(N-2)

Tng cng N 1

2( )iSST Y Y

= SSR + SSE

Gi tr thng k

Gi tr R bnh phng (R square):

SSR

RSST

(100R2: % ca bin i trn Y c gii thch bi X)

lch chun (Standard Error):

' 21

( )2

i iS Y YN

(S phn tn ca d liu cng t th gi

tr ca S cng gn zero)

Trc nghim thng k

i vi mt phng trnh hi quy, | 0XY B BX , ngha thng k ca cc h s Bi (B0

hay B) c nh gi bng trc nghim t (phn phi Student) trong khi tnh cht thch hp ca

phng trnh | ( )XY f X c nh gi bng trc nghim F (phn b Fischer)

Trc nghim t

- Gi thuyt:

41 Chng 6


H0: i = 0 H s hi quy khng c ngha

H0: i 0 H s hi quy c ngha

- Gi tr thng k:

2

i i

n

Bt

S

;

22

2( )n

i

SS

X X

2

n

B

S

Phn b Student = N-2

- Bin lun:

Nu t < t (N-2) Chp nhn gi thuyt H0 .

Trc nghim F

- Gi thuyt:

H0: i = 0 Phng trnh hi quy khng thch hp

H0: i 0 Phng trnh hi quy thch hp

- Gi tr thng k:MSR

FMSE

Phn b Fischer v1 = 1, v2 = N-2

- Kt lun:

Nu F < F (1,N-2) Chp nhn gi thuyt H0 .

42 Chng 6


D- HI QUY TUYN TNH A THAM S

Trong phng trnh hi quy tuyn tnh a tham s bin s ph thuc Y c lin quan n k

bin s c lp Xi (i = 1,2,k) thay v ch c mt nh trong hi quy tuyn tnh n gin.

Phng trnh tng qut : 0 1| , ,..., 0 1 1 2 2

...kX X X k k

Y B B X B X B X

Phng trnh hi quy a tham s c th c trnh by di dng ma trn:

Bng ANOVA

Ngun

sai s

Bc

t do

Tng s bnh

phng

Bnh phng

trung bnh

Gi tr thng k

Hi quy k SSR MSR = SSR/k MSR

FMSE

Sai s N k 1 SSE MSE = SSE/(N-k-1)

Tng cng N 1 SST= SSR + SSE

Gi tr thng k:

Gi tr R bnh phng:

Gi tr R2 c hiu chnh (Adjusted R Square)

2

( 1)

SSR kFR

SST N k kF

(R2 0,81 l kh tt)

Gi tr R2 c hiu chnh (Adjusted R square):

2 2

2 2( 1) (1 )

1 ( 1)ii

N R k k RR R

N k N k

( 2iiR s tr nn m hay khng xc nh nu R2 hay N nh)

43 Chng 6


lch chun:

( 1)

SSES

N k

(S 0,30 l kh tt)

Trc nghim thng k

Tng t hi quy n gin, song bn cn ch :

- Trong trc nghim t

H0: i = 0 Cc h s hi quy khng c ngha

H0: i 0 C t nht vi h s hi quy c ngha

Bc t do ca gi tr t: = N k 1.

2

i i

n

Bt

S

;

22

2( )n

i

SS

X X

- Trong trc nghim F:

H0: i = 0 Phng trnh hi quy khng thch hp

H0: i 0 Phng trnh hi quy thch hp vi t nht vi Bi .

Bc t do ca gi tr F: v1 = 1; v2 = N-k-1.

p dng MS-EXCEL

Th d 17: Ngi ta dng ba mc nhit gm 105, 120 v 1350C kt hp vi ba

khong thi gian l 15, 30 v 60 pht thc hin mt phn ng tng hp. Cc hiu sut ca

phn ng (%) c trnh by trong bng sau y:

Thi gian (pht) X1

Nhit (0C)

X2 Hiu sut (%)

Y

15 105 1.87

30 105 2.02

60 105 3.28

15 120 3.05

30 120 4.07

60 120 5.54

15 135 5.03

30 135 6.45

60 135 7.26

Hy cho bit yu t nhit v/ hoc yu t thi gian c lin quan tuyn tnh vi hiu sut

ca phn ng tng hp ? Nu c th iu kin nhit 1150C trong vng 50 pht th hiu sut

phn ng s l bao nhiu?

Nhp d liu vo bng tnh

D liu nht thit phi c nht thit c nhp theo ct:

44 Chng 6


S dng Regression

Nhn ln lt n lnh Tools v lnh Data Analysis.

Chn chng trnh Regression trong hp thoi Data Analysis ri nhp OK.

Trong hp thoi Regression, ln lt n nh cc chi tit:

Phm vi ca bin s Y (Input Y Range).

Phm vi ca bin s X (Input Y Range)

Nhn d liu (Labels)

Mc tin cy (Confidence Level)

Ta u ra (Output Range)

V mt s ty chn khc nh ng hi quy (Line Fit Plots), biu thc sai s

(Residuals Plots)

Hp thoi Regression

45 Chng 6


Phng trnh hi quy 1| 1

( )XY f X

1| 1

2,73 0,04XY X

(R2 = 0,21; S=1,81)

Regression Statistics

Multiple R 0.462512069

R Square 0.213917414

Adjusted R

Square 0.101619901

Standard Error 1.811191587

Observations 9

ANOVA

df SS MS F Significance F

Regression 1 6.24891746 6.24891746 1.904917 0.209994918

Residual 7 22.96290476 3.280414966

Total 8 29.21182222

Coefficients

Standard

Error t Stat P-value Lower 95%

Intercept 2.726666667 1.280705853 2.129034282 0.070771 -0.301721453

X1 0.044539683 0.032270754 1.38018722 0.209995 -0.031768525

t0 = 2,19 < t0,05 = 2,365 (Hay 2 0,071 0,05VP )

Chp nhn gi thuyt H0.

t1 = 1,38 < t0,05 = 2,365 (Hay 0,209 0,05VP )


30,051,905 5,590F F (Hay 4 0,209 0,05SF )


Vy c hai h s 2,37(B0) v 0,04(B1) ca phng trnh hi quy | 2,73 0,04iX iY X u

khng c ngha thng k. Ni mt cch khc, phng trnh hi quy ny khng thch hp.

Kt lun: Yu t thi gian khng c lin quan tuyn tnh vi hiu sut ca phn ng tng hp.

Phng trnh hi quy 2 2

( )XY f X

2| 2

2,73 0,04XY X

(R2 = 0,76; S=0,99)

46 Chng 6




R Square 0.76375984

Adjusted R

Square 0.730011246


Observations 9

ANOVA


Regression 1 22.31081667 22.31082 22.63086 0.002066188

Residual 7 6.901005556 0.985858

Total 8 29.21182222

Coefficients Standard Error t Stat P-value Lower 95%

Intercept -11.14111111 3.25965608 -3.41788 0.011168 -18.84897293

X2 0.128555556 0.027023418 4.757191 0.002066 0.064655325

t0 = 3,418 < t0,05 = 2,365 (Hay 0,011 0,05VP )

Bc b gi thuyt H0.

t2 = 4,757 < t0,05 = 2,365 (Hay 0,00206 0,05VP )

Bc b gi thuyt H0.

0,0522,631 5,590F F (Hay 0,00206 0,05SF )

Bc b gi thuyt H0.

Vy c hai h s -11,14(B0) v 0,13(B2) ca phng trnh hi quy 2| 2

11,14 0,13XY X

u c ngha thng k. Ni mt cch khc, phng trnh hi quy ny thch hp.

Kt lun: Yu t nhit c lin quan tuyn tnh vi hiu sut ca phn ng tng hp.

Phng trnh hi quy 1 2| , 1 2

( , )X XY f X X

1 2| , 1 2

12,70 0,04 0,13X XY X X

(R2 = 0,97; S=0,33)

47 Chng 6




R Square 0.977677254

Adjusted R

Square 0.970236338


Observations 9

ANOVA


Regression 2 28.55973413 14.27987 131.3921 1.11235E-05

Residual 6 0.652088095 0.108681

Total 8 29.21182222

Coefficients Standard Error t Stat P-value Lower 95%

Intercept -12.7 1.101638961 -11.5283 2.56E-05 -15.39561342

X1 0.044539683 0.005873842 7.582718 0.000274 0.03016691

X2 0.128555556 0.008972441 14.32782 7.23E-06 0.106600783

t0 = 11,528 > t0,05 = 2,365 (Hay 52,260.10 0,05VP )

Bc b gi thuyt H0.

t1 = 7,583 > t0,05 = 2,365 (Hay 0,00027 0,05VP )

Bc b gi thuyt H0.

t2 = 14,328 > t0,05 = 2,365 (Hay 67,233.10 0,05VP )

Bc b gi thuyt H0.

0,05131,392 5,140F F (Hay 51,112.10 0,05SF )

Bc b gi thuyt H0.

Vy c hai h s -12,70(B0), 0,04(B1) v 0,13(B2) ca phng trnh hi quy

1 2| , 1 212,70 0,04 0,13X XY X X u c ngha thng k. Ni mt cch khc, phng trnh

hi quy ny thch hp.

Kt lun: Hiu sut ca phn ng tng hp c lin quan tuyn tnh vi c hai yu t l thi

gian v nhit .

S tuyn tnh ca phng trnh 1 2| , 1 2

12,70 0,04 0,13X XY X X c th c trnh by

trn biu phn tn (scatterplots):

48 Chng 6


Mun d on hiu sut ca phn ng bng phng trnh hi quy

1 2| , 1 212,70 0,04 0,13X XY X X , bn ch cn chn mt , th d B21, sau nhp hm v

c kt qu nh sau:

B21 = B17 + B18 * 50 + B19 * 115

A B C D

17 Interrcept -12,7 1,101638961 -11,52827782

18 X1 0,044539683 0,005873842 7.582717626

19 X2 0,128555556 0,008972441 14,32782351

20

21 D on 4,310873016

Ghi ch: B17 ta ca B0, B18 ta ca B1, B19 ta ca B2, 50 l gi tr ca X1(thi gian)

v 115 l gi tr ca X2(nhit ).

PH LC:

Bng gi tr ti hn dng trong trc nghim loi gi tr bt thng:

Gi tr thng k

G1

S trng hp kho

st

N

Tr s ti hn

GP (P=0,01)

N=37 3 0,976

2 11

1N

Y YG

Y Y

4 0,846

5 0,729

6 0,644

7 0,586

N=813 8 0,780

3 12

1 1N

Y YG

Y Y

9 0,725

10 0,678

11 0,638

12 0,605

13 0,578

N=1424 14 0,602

3 13

2 1N

Y YG

Y Y

15 0,579

16 0,559

17 0,542

18 0,527

19 0,514

20 0,502

21 0,491

22 0,481

23 0,472

24 0,464

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