Chng trnh Ging dy Kinh t Fulbright Nm hc 2013-2014

Cc Phng Php nh Lng

Gi gii Bi tp 7

inh Hong Thng 1

Chng Trnh Ging Dy Kinh t Fulbright

Hc k Thu nm 2013

Cc Phng Php Phn Tch nh Lng

Gi gii Bi tp 7

HI QUY N BIN (TIP THEO)

Ngy Pht: Th ba 26/11/2013 Ngy Np: Th ba 3/12/2013 Bn in np lc 8h20 sng, ti Hp np bi tp trong phng Lab Bn in t gi theo hng dn ca tr ging.

Bi 1 (50 im)

Bn hy s dng file d liu Employee Data.xls Bi tp 4 phn thng k ng dng. File ny c cc bin sau

id s th t

age tui

Gender 1: Nam, 2:n

Jobcat (v tr cng vic) 1: nhn vin, 2: trng nhm/t trng/Qun c , 3:qun l

educ s nm i hc

prevexp s thng i lm

salary tin lng hin ti trong mt nm (USD)

salbegin tin lng khi im trong mt nm (USD)

a. S dng Excel (SPSS, Eviews hoc Stata), hy c lng hm hi quy mu:

salaryi= 1+

2 educi+ui

S dng Excel, chy hi quy bng hm Regression trong Data Analysis ta c:

SUMMARY OUTPUT

Regression Statistics

Multiple R 0,66055891

R Square 0,43633807

Adjusted R Square 0,43514387

Standard Error 12833,5397

Observations 474

ANOVA

df SS MS F Significance F

Regression 1 6,0178E+10 6,0178E+10 365,381375 9,6397E-61

Residual 472 7,7738E+10 164699741

Total 473 1,3792E+11

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

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Intercept -18331,178 2821,91156 -6,4960144 2,0963E-10 -23876,242 -12786,115 -23876,2 -12786,1

educ 3909,90671 204,547037 19,1149516 9,6397E-61 3507,97125 4311,84216 3507,971 4311,842

Vy hm hi quy mu c dng:

salaryi= -18331,178+3909,90671 educi +ui

hay

Thc hin cc thao tc trn Eview, ta cng c cc kt qu tng t:

Dependent Variable: SALARY

Method: Least Squares Date: 11/27/13 Time: 09:58

Sample: 1 474

Included observations: 474 Variable Coefficient Std. Error t-Statistic Prob. C -18331,18 2821,912 -6,496014 0,0000

EDUC 3909,907 204,5470 19,11495 0,0000 R-squared 0,436338 Mean dependent var 34419,57

Adjusted R-squared 0,435144 S,D, dependent var 17075,66

S.E. of regression 12833,54 Akaike info criterion 21,76172 Sum squared resid 7,77E+10 Schwarz criterion 21,77928

Log likelihood -5155,528 Hannan-Quinn criter, 21,76863

F-statistic 365,3814 Durbin-Watson stat 1,862914

Prob(F-statistic) 0,000000

Thao tc trn Stata

Kt qu tng t cng c c khi thc hin trn SPSS

Model Summary

Model R R Square Adjusted R

Square

Std. Error of the

Estimate

1 .661a .436 .435 12833.540

a. Predictors: (Constant), educ

ANOVAa

Model Sum of Squares df Mean Square F Sig.

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1

Regression 60178217760.00

0 1

60178217760.00

0 365.381 .000

b

Residual 77738277676.34

0 472 164699740.840

Total 137916495436.3

40 473

a. Dependent Variable: salary

b. Predictors: (Constant), educ

Coefficientsa

Model Unstandardized Coefficients Standardized

Coefficients

t Sig. 95.0% Confidence Interval for B

B Std. Error Beta Lower Bound Upper Bound

1 (Constant) -18331.178 2821.912 -6.496 .000 -23876.242 -12786.114

educ 3909.907 204.547 .661 19.115 .000 3507.971 4311.842

a. Dependent Variable: salary

b. Bn hy cho bit ngha kinh t ca h s hi quy2

Cn phn bit ngha kinh t v ngha kinh t lng:

ngha kinh t: H s hi quy 2

=3909,907 cho bit tc ng bin ca S nm

i hc (EDUC) ln Tin lng hin ti trong 1 nm (SALARY), thng thng khi s nm i hc ca mt ngi tng ln th tin lng ca ngi cng s tng theo. Con s 3909,907 cho bit khi S nm i hc tng thm 1 nm th Tin lng hin ti trong 1 nm s tng 3909,907 USD v ngc li.

ngha kinh t lng: Trong iu kin cc yu t khc khng i, nu S nm i hc tng thm 1 nm th v mt trung bnh Tin lng hin ti trong 1 nm s tng 3909,907 USD v ngc li.

c. Bn hy cho bit khong tin cy 95% ca h s 2. S dng khong tin cy ny kim nh gi thuyt cho rng educ khng nh hng n salary.

Khong tin cy ca 95% ca h s 2:

][2)(,

2

22

stkn

vi 2

t =1,965002595 (s dng lnh TINV trong excel vi

mc ngha 5% v bc t do l 472)

=> 2[3909,9071,965002595 * 204,5470]

=> 2[3507,971249; 4311,842164]

Kim nh gi thuyt cho rng educ khng nh hng n salary

Ta c cp gi thuyt:

H0: 2 = 0

Ha: 2 0

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Khong tin cy (va tnh c trn): [3507,971249; 4311,842164]

Do 0 [3507,971249; 4311,842164] nn ta bc b gi thuyt H0 ; chp nhn Ha

Vy, vi mc ngha 5%, c c s cho rng, 2 khc 0; tc educ c nh hng n salary

d. Kim nh gi thuyt cp cu c bng cch s dng thng k t.

H0: 2 = 0 Ha: 2 0 Tr kim nh thng k

2

02

st

=

204,547037

3909,907=19,11495161

Vi mc ngha 5%, )2474(,

2

05,0)(,

2

ttkn

=1,965002595 (s dng lnh TINV trong

excel vi mc ngha 5% v bc t do l 472)

Do t> )(,

2kn

t

nn ta bc b gi thuyt H0 ; chp nhn Ha

Vy, vi mc ngha 5%, c c s cho rng, 2 khc 0; tc educ c nh hng n salary

e. Kim nh gi thuyt cp cu c bng cch s dng P-value

H0: 2 = 0 Ha: 2 0 Tr kim nh thng k

2

02

st

=

204,547037

3909,907=19,11495161

Vi mc ngha 5%, Pvalue=9,63974E-61 (s dng lnh TDIST(19,11495161,472,2) trong excel)

Do Pvalue < mc ngha =5% nn ta bc b gi thuyt H0 ; chp nhn Ha

Vy, vi mc ngha 5%, c c s cho rng, 2 khc 0; tc educ c nh hng n salary.

f. Kim nh gi thuyt cp cu c bng cch s dng thng k F

H0: 2 = 0 Ha: 2 0 Tr kim nh thng k

2

222

2

2

)2/(

1/

)/(

)1/(

i

i

i x

nu

y

knRSS

kESS

MSR

MSEF

=>F 22

22

22

22

)(2

tsxi

=>F =19,114951612=365,3813749

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Tra bng phn phi Fisher (df1=1;df2=472) hoc s dng lnh =FINV(5%,1,472) ta c F=3,861235197

Do F> F nn ta bc b gi thuyt H0; chp nhn Ha

Vy, vi mc ngha 5%, c c s cho rng, 2 khc 0; tc educ c nh hng n salary.

g. Mt ngi c s nm i hc l 16 nm, bn s d on mc lng trung bnh ca ngi ny l bao nhiu USD mt nm? (S dng gi tr d bo im, gi tr d bo khong cho gi tr trung bnh tin cy 95%)

Cch 1: Tnh bng tay kt hp vi Excel

Mt ngi c s nm i hc l Educ0 = 16

Gi tr d bo im cho gi tr trung bnh:

E(Salary|Educ=16)= -18331,178+3909,90671 * 16 = 44227,32927 (USD)

Gi tr d bo khong cho gi tr trung bnh tin cy 95%

tin cy 95%=>)2474(,

2

05,0)(,

2

ttkn

= 1,965

2

2)16(1

i

ryaSalx

cued

nS

vi

2

2

2

n

ui

v cuededucx ii

Tnh ton trn Excel ta c:1

2

2

2

n

ui

=77.738.277.676,340 / (474-2) = 164.699.740,840

=>

=12.833,540

2ix =3.936,4662

=> ryaSalS 3.936,4662

)13,491616(

474

1 0,840164.699.74

2 =781,4940692

Vy khong tin cy ca gi tr trung bnh tin cy 95% l:

[ 0ryaSal

2

t * ryaSalS ] hay [44227,329271,965*781,4940692]

Hay [42.691,69342; 45.762,96512]

1 Hc vin nn a bng tnh Excel vo minh ha

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Cch 2: Thc hin trn Stata, ta cng c kt qu tng t

h. Theo bn, m hnh gii thch c bao nhiu % bin thin ca bin salary?

M hnh c R-squared = 0,436338 => Bin educ c th gii thch c 43,6338% s bin thin ca bin Salary v mt trung bnh.2

i. C ngi cho rng trong iu kin cc yu t khc khng i, khi s nm i hc tng ln (hoc gim xung) 1 nm th trung bnh mc lng hng nm ca ngi lao ng tng ln (hoc gim xung) 4400 USD. Bn c nhn xt g v pht biu ny.

Ta tin hnh kim nh gi thuyt i vi pht biu trn, vi gi thuyt Ha rng con s thc t l nh hn so vi pht biu trn.

H0: 2 = 4400 Ha: 2 < 4400 Tr kim nh thng k

2 Hc vin cng c th dng Adjusted R-Squared gii thch.

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2

44002

st

=

204,547037

4400-3909,907=-2,395993125

Vi mc ngha 5%, )(, knt =1,648 (s dng lnh TINV trong excel vi mc

ngha 5%*2 v bc t do l 472)

Do t3000

Tr kim nh thng k

2

30002

st

=

204,547037

3000-3909,907= 4,448398381

Vi mc ngha 5%, )(, knt =1,648 (s dng lnh TINV trong excel vi mc

ngha 5%*2 v bc t do l 472)

Do t> )(, knt nn ta bc b gi thuyt H0 ; chp nhn Ha

Vy, vi mc ngha 5%, c c s cho rng 2>3000, tc l trong iu kin cc yu t khc khng i, khi s nm i hc tng ln (hoc gim xung) 1 nm th trung bnh mc lng hng nm ca ngi lao ng tng ln (hoc gim xung) ln hn 3000 USD.

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