econometrie - autocorelare

*AUTOCORELAREA ERORILOR Modelul de regresie:Y=X

V=

Erorile sunt autocorelateij astfel nct Cov(i,j) 0. undeV=

*AUTOCORELAREA ERORILORProblemele ce se pun n acest caz sunt:1. Identificarea cauzelor de apariie a corelrii erorilor2. Testele statistice utilizate pentru depistarea autocorelrii3. Metode de estimare a parametrilor n cazul autocorelrii

*1. Cauzele de apariie a autocorelrii erorilor Absena uneia sau mai multor variabile explicative importanteneincluderea uneia sau mai multor variabile explicative importante poate genera autocorelarea erorilor.exemplu:variabila exogen x3 este omis variabilele reziduale sunt autocorelate i reziduul va fi explicitat prin intermediul acestei variabile omise:Modelul de regresie nu este corect specificat: fie modelul se exprim sub forma unei combinaii liniare de variabile n condiiile n care o specificare corect a modelului trebuie s fie exprimat printr-o combinaie liniar de logaritmi de variabile exogene etc.Au fost fcute transformri neadecvate sau interpolri n cadrul seriei de date

*2. Testele statistice utilizate pentru depistarea autocorelrii: Durbin WatsonVariabila rezidual satisface:Ipoteze: Ho: =0 Ha: 0

Statistica testului:

Numrtorul statisticii va fi scris sub forma echivalent:

Atunci statistica d va fi:

Dac seria de date este suficient de mare, vom neglija termenii extremi din seria reziduurilor, obinnd:

_1016449011.unknown

_1016449012.unknown

_1016449009.unknown

*d1 i d2 extrase din tabela Durbin Watson pentru , k i n:0 < DW < d1 autocorelare pozitiv a erorilord1 DW d2 indecizie, recomandat acceptarea autocorelrii pozitived2 < DW < 4-d2 erori independente4-d2 DW 4-d1 indecizie, recomandat acceptarea autocorelrii negative4-d1< DW

*Testul Durbin Watson

Testul Durbin-Watson pentru = 5 %.

n

k = 1

k = 2

k = 3

k = 4

k = 5

d1

d2

d1

d2

d1

d2

d1

d2

d1

d2

15

1,08

1,36

0,95

1,54

0,82

1,75

0,69

1,97

0,56

2,21

20

1,20

1,41

1,10

1,94

1,00

1,68

0,90

1,83

0,79

1,99

30

1,35

1,49

1,28

1,57

1,21

1,65

1,14

1,74

1,07

1,83

40

1,44

1,54

1,39

1,60

1,34

1,66

1,29

1,72

1,23

1,79

50

1,50

1,59

1,46

1, 63

1,42

1,67

1,38

1,72

1,34

1,77

100

1,65

1,69

1,63

1,72

1,61

1,74

1,59

1,76

1,37

1,78

*3. Metode de estimare a parametrilor n cazul autocorelrii Erorile prezint o autocorelare de un anumit ordin estimatorii parametrilor sunt nedeplasai i consisteni, dar nu sunt eficieni. 1. Se estimeaz parametrii modelului de regresie: Y=X prin metoda celor mai mici ptrate i se obine seria erorilor (ei)i=1,n2. Se consider c erorile urmeaz un proces autoregresiv de ordinul I:3. Notnd:

4. Se estimeaz parametrii noului model i apoi se revine la modelul iniial.

*HOMOSCEDASTICITATEA

Y=X

Problemele ce se pun n acest caz sunt:1. Testele statistice utilizate pentru depistarea heteroscedasticitii2. Metode de estimare a parametrilor n cazul heteroscedasticitii

xu

*1. Testele statistice utilizate pentru depistarea heteroscedasticitii - Testul White1. Se estimeaz parametrii modelului de regresie: Y=X prin metoda celor mai mici ptrate i se obine seria erorilor (ei)i=1,n2. Se expliciteaz seria (ei2)i=1,n n raport cu una sau mai multe variabile exogene i se definete modelul de regresie:1. 2. 3. Ipotezele testului:H0: a1=...=ak=b1=...=bk=0 model homoscedasticH1: a1 0 sau bj 0 model heteroscedastic4. Statistica testului:LM=nR2r2Observaie:o cretere a lui r conduce la diminuarea puterii testuluipentru un numr mare de variabile exogene se recomand modelul 1pentru un numr moderat de variabile exogene se recomand modelul 2

*2. Metode de estimare a parametrilor n cazul heteroscedasticitii n cazul n care heteroscedasticitatea este indus de o variabil exogen ntr-o manier multiplicativ:

Fenomenul de heteroscedasticitate se elimin prin transformarea modelului:

Notnd:

Modelul devine:

Dup estimarea parametrilor acestui model transformat se revine n modelul iniial cu estimatorii.

*MULTICOLINEARITATEAeste determinat de prezena corelrii ntre variabilele exogene determinantul matricei XX este zero, deci aceasta nu este inversabil.Se consider modelul centrat i redus, deci modelul de regresie fr termen liber:matricea de corelaie evaluat pentru variabilele exogene este 1/n(XX)-1variaia estimatorilor este 2R-1/n prezena corelrii variabilelor exogene conduce la creterea varianei acelor estimatori ai parametrilor modelului liniar de regresie ce corespund variabilelor exogene aflate ntr-o dependen liniar semnificativ, deci scderea performanelor modelului de regresie estimat prin forma clasic a metodei celor mai mici ptrate.

Problemele ce se pun n acest caz sunt:1. Indicatori pentru semnalarea coliniaritii2. nlturarea efectului de multicoliniaritate

*1. Indicatori pentru semnalarea coliniaritii Criteriul Kleinse determin raportul de corelaie Ry2 i coeficienii liniari de corelaie a variabilelor exogene , ij.dou variabile exogene Xi i Xj sunt coliniare dac:sunt identificate numai dependenele liniare dintre dou variabile exogene.Criteriul Belsleyse calculeaz valorile proprii ale matricei XX, deci soluii ale ecuaiei: XX-Ip=0. n cazul n care una sau mai multe valori proprii sunt zero sau aproximativ zero, fenomenul de colinearitate este semnificativ i va afecta ntr-o bun msur calitatea estimatorilor.se calculeaz indicatorul:dac valorile acestui indicator sunt superioare lui 1 colinearitatea o valoare cuprins ntre 20 i 30 sau mai mare, pentru datele reale, relev o colinearitate puternic a variabilelor exogene.

*2. nlturarea efectului de multicoliniaritate Estimarea prin partiionarea matricei X n dou blocuri de variabilese consider partiionarea matricei n dou submatrice ale cror coloane sunt liniar independente: X=(Xm, Xp-m)se estimeaz parametrii modelului de regresie: y=Xmm+mse calculeaz apoi: i se estimeaz parametrii modelului liniar de regresie: y*=Xrr+rEliminarea mecanic a coliniaritiidac dependena celor dou variabile exogene este: x2i=x1i + i cu

atunci se estimeaz modelul de regresie:

*ExempluDepartamentul de HR al unei mari companii care produce aparatur industrial de nalt precizie vrea s foloseasc modelele de regresie pentru fundamentarea deciziei de recrutare a directorilor de vnzri.Compania are 45 de regiuni de vnzare, fiecare fiind coordonat de ctre un director de vnzri(sales manager).Muli dintre directorii de vnzri au studii universitare n domeniul ingineriei electrice i datorit gradului nalt de specializare a produselor vndute, conducerea companiei crede c ar trebui acceptai pentru postul de director de vnzri doar candidaii cu studii tehnice.

*n timpul interviului pentru angajare, candidaii trebuie s susin dou tipuri de teste, specifice jobului: Strong-Campbell Interest Inventory Test i Wonderlic Personnel Test.

Din cauza timpului i a banilor cheltuii n procesul de testare, la nivelul conducerii snt discuii cu privire la eliminarea unuia sau a ambelor teste.

Pentru nceput, directorul HR adun informaii despre toi cei 45 de directori: anii de experien n vnzri, studii de inginerie, precum i punctajele de la cele dou teste.

*Variabila dependent este indicele vnzrilor(sales index), care este raportul dintre vnzrile actuale din regiunea respectiv i vnzrile planificate (actual/targeted sales).

Valorile target snt stabilite n fiecare an de ctre conducerea companiei, dup consultarea directorilor de vnzri, fiind bzate pe performanele anterioare i potenialul pieei din fiecare regiune.

*Datele

*Variabilele studiateSales raportul dintre vnzrile anuale i vnzrile planificate din fiecare regiune.Wonder scorul la testul Wonderlic Personnel Test. Cu ct punctajul este mai mare, cu att abilitile manageriale ale candidatului snt mai puternice.SC scorul la testul Strong-Campbell. Cu ct punctajul este mai mare, cu att candidatul este mai indicat pentru munca de vnzri.Experience - numrul de ani de experien n vnzri nainte de a deveni director.Engineer o variabil dummy, care ia valoarea 1 dac directorul de vnzri are studii tehnice i 0 altfel.

*Obiectivele studiuluin urma studiului trebuie realizat cel mai bun model de predicie a vnzrilor.

Studiul trebuie s rspund la urmtoarele ntrebri:Pe viitor ar trebui pstrate la angajare cele dou teste?Se susine ideea c a avea studii tehnice este un avantaj n munca de vnzri?Este realist ipoteza de a angaja numai ingineri pe poziiile de directori de vnzri?Ct de important este experiena anterioar?

*Formalizarea modeluluiY sales indexX1 scorul la testul Wonderlic Personnel (abiliti manageriale)X2 - scorul la testul Strong-Campbell (abiliti de vnzri)X3 numrul de ani de experien n vnzriX4 variabila indicator a studiilor tehnice

Modelul iniial:

*

DCII

SCExperienceEngineer

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17910

15290

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14530

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164110

13960

15220

17450

14590

16150

16680

14680

14650

16390

154110

146110

14930

16200

15750

14120

13490

15440

14880

15310

15450

13600

14980

156110

15540

143130

15050

14150

Residual Plot for X1

5.5077662589

-5.855508125

12.3639983434

8.0905471112

-11.2278156969

7.7363059153

-0.6494242566

7.0680913232

-11.5820568928

4.8485848549

1.6913943394

-12.81564796

11.0995802992

20.9782681715

4.485310471

-11.2861498727

-14.523722717

9.0097571475

13.5302220468

7.0995802992

-5.3984288123

9.485310471

17.0322129354

2.3281199555

3.144491875

-5.855508125

3.3505757434

-44.5820568928

9.4313657071

0.1220360871

5.6913943394

9.3954873193

1.135458687

-8.7656849733

-4.5820568928

-9.5371453169

-22.9543644647

-0.5820568928

-2.4473221652

-0.8779639129

-5.2636940847

-2.9228754888

2.4538214951

3.7812174911

0.8485848549

SC

Residuals

SC Residual Plot

DurbinWatson

Durbin-Watson Calculations

Sum of Squared Difference of Residuals11119.1329079039

Sum of Squared Residuals5528.9586593053

Durbin-Watson Statistic2.0110718117

5.5077662589

-5.855508125

12.3639983434

8.0905471112

-11.2278156969

7.7363059153

-0.6494242566

7.0680913232

-11.5820568928

4.8485848549

1.6913943394

-12.81564796

11.0995802992

20.9782681715

4.485310471

-11.2861498727

-14.523722717

9.0097571475

13.5302220468

7.0995802992

-5.3984288123

9.485310471

17.0322129354

2.3281199555

3.144491875

-5.855508125

3.3505757434

-44.5820568928

9.4313657071

0.1220360871

5.6913943394

9.3954873193

1.135458687

-8.7656849733

-4.5820568928

-9.5371453169

-22.9543644647

-0.5820568928

-2.4473221652

-0.8779639129

-5.2636940847

-2.9228754888

2.4538214951

3.7812174911

0.8485848549

Engineer

Residuals

Engineer Residual Plot

X1

Regression Analysis

SC and all other X

Regression Statistics

Multiple R0

R Square0

Adjusted R Square-0.0227272727

Standard Error9.6667711593

Observations45

VIF1

CPD Calculations

Regression Analysis

Coefficients of Partial Determination

Intermediate Calculations

SSR(X1,X2)8029.0413406947

SST13558

SSR(X2)-0SSR(X1 | X2)8029.0413406947

SSR(X1)7589.030720339SSR(X2 | X1)440.0106203557

Coefficients

r2 Y1.20.5921995383

r2 Y2.10.0737163486

NOTX2

Regression Analysis

All but Engineer

Multiple R0.7481614738

R Square0.5597455908

Adjusted R Square0.5495071162

Observations45

ANOVA

dfSSMSFSignificance F

Regression17589.0307203397589.03072033954.67079920930.0000000035

Residual435968.969279661138.8132390619

Total4413558

CoefficientsStandard Errort StatP-valueLower 95%Upper 95%

Intercept31.47457627129.69859035643.24527329380.002274888411.91550500651.0336475364

SC1.35858050850.18374167377.39397046310.00000000350.98803011311.7291309038

NOTX1

Regression Analysis

All but SC

Multiple R65535

R Square-0

Observations45

ANOVA

Regression1-0-001

Residual4413558308.1363636364

Total4513558

Intercept1022.616767996538.9793822519096.7262507024107.2737492976

Engineer006553500

MR

Regression Analysis

R Square0.5921995383

Observations45

ANOVA

Regression28029.04134069474014.520670347330.500.00

Residual425528.9586593053131.6418728406

Total4413558

Intercept26.8909788789.77183452752.75188643470.017.170618649246.6113391068

SC1.3408185960.17919606357.48241099750.000.97918630341.7024508886

Engineer7.28687383213.98571918121.82824566930.07-0.756633024515.3303806887

RESIDUAL OUTPUT

ObservationPredicted SalesResiduals

190.49223374115.5077662589

295.855508125-5.855508125

3100.636001656612.3639983434

489.90945288888.0905471112

587.2278156969-11.2278156969

6109.26369408477.7363059153

7118.6494242566-0.6494242566

893.93190867687.0680913232

9106.5820568928-11.5820568928

1089.15141514514.8485848549

11117.30860566061.6913943394

12132.81564796-12.81564796

13103.900419700811.0995802992

14110.021731828520.9782681715

1594.5146895294.485310471

16113.2861498727-11.2861498727

1780.523722717-14.523722717

18119.99024285259.0097571475

1986.469777953213.5302220468

20103.90041970087.0995802992

21133.3984288123-5.3984288123

2294.5146895299.485310471

23115.967787064617.0322129354

24122.67188004452.3281199555

2595.8555081253.144491875

2695.855508125-5.855508125

27118.64942425663.3505757434

28106.5820568928-44.5820568928

2988.56863429299.4313657071

3099.87796391290.1220360871

31117.30860566065.6913943394

32110.60451268079.3954873193

3381.8645413131.135458687

3479.7656849733-8.7656849733

35106.5820568928-4.5820568928

3698.5371453169-9.5371453169

3797.9543644647-22.9543644647

38106.5820568928-0.5820568928

3982.4473221652-2.4473221652

4099.8779639129-0.8779639129

41109.2636940847-5.2636940847

42107.9228754888-2.9228754888

4384.54617850492.4538214951

44101.21878250893.7812174911

4589.15141514510.8485848549

Residual Plot for X1 2

5.5077662589

-5.855508125

12.3639983434

8.0905471112

-11.2278156969

7.7363059153

-0.6494242566

7.0680913232

-11.5820568928

4.8485848549

1.6913943394

-12.81564796

11.0995802992

20.9782681715

4.485310471

-11.2861498727

-14.523722717

9.0097571475

13.5302220468

7.0995802992

-5.3984288123

9.485310471

17.0322129354

2.3281199555

3.144491875

-5.855508125

3.3505757434

-44.5820568928

9.4313657071

0.1220360871

5.6913943394

9.3954873193

1.135458687

-8.7656849733

-4.5820568928

-9.5371453169

-22.9543644647

-0.5820568928

-2.4473221652

-0.8779639129

-5.2636940847

-2.9228754888

2.4538214951

3.7812174911

0.8485848549

SC

Residuals

SC Residual Plot

DurbinWatson2

5.5077662589

-5.855508125

12.3639983434

8.0905471112

-11.2278156969

7.7363059153

-0.6494242566

7.0680913232

-11.5820568928

4.8485848549

1.6913943394

-12.81564796

11.0995802992

20.9782681715

4.485310471

-11.2861498727

-14.523722717

9.0097571475

13.5302220468

7.0995802992

-5.3984288123

9.485310471

17.0322129354

2.3281199555

3.144491875

-5.855508125

3.3505757434

-44.5820568928

9.4313657071

0.1220360871

5.6913943394

9.3954873193

1.135458687

-8.7656849733

-4.5820568928

-9.5371453169

-22.9543644647

-0.5820568928

-2.4473221652

-0.8779639129

-5.2636940847

-2.9228754888

2.4538214951

3.7812174911

0.8485848549

Engineer

Residuals

X12

Regression Analysis

SC and all other X

Multiple R0

R Square0

Observations45

VIF1

CPD Calculations2

Regression Analysis

SSR(X1,X2)8029.0413406947

SST13558

SSR(X2)-0SSR(X1 | X2)8029.0413406947

SSR(X1)7589.030720339SSR(X2 | X1)440.0106203557

Coefficients

r2 Y1.20.5921995383

r2 Y2.10.0737163486

NOTX22

Regression Analysis

All but Engineer

R Square0.5597455908

Observations45

ANOVA

Regression17589.0307203397589.03072033954.67079920930.0000000035

Residual435968.969279661138.8132390619

Total4413558

CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 90.0%Upper 90.0%

Intercept31.47457627129.69859035643.24527329380.002274888411.91550500651.033647536415.17056015647.7785923864

SC1.35858050850.18374167377.39397046310.00000000350.98803011311.72913090381.04969776371.6674632532

NOTX12

Regression Analysis

All but SC

Multiple R65535

R Square-0

Observations45

ANOVA

Regression1-0-001

Residual4413558308.1363636364

Total4513558

Intercept1022.616767996538.9793822519096.7262507024107.273749297697.6032279693106.3967720307

Engineer00655350000

Intervals

Confidence and Prediction Estimate Intervals

Data

Confidence Level90%

1

SC given value0

Engineer given value0

X'X4523360

23361253760

000

Inverse of X'X000

000

X'G times Inverse of X'X000

[X'G times Inverse of X'X] times XG0

t Statistic1.6819523579

Predicted Y (YHat)26.890978878

For Average Predicted Y (YHat)

Interval Half Width0

Confidence Interval Lower Limit0

Confidence Interval Upper Limit0

For Individual Response Y

Prediction Interval Lower Limit0

Prediction Interval Upper Limit0

PHStat2 User Note:

Enter the values for the given X'sin the cell range B6:B7.(You can interactively changethese values at any time.)

To delete this note:Select this note and thenselect Edit | Cut.

DCII2

SCEngineer

1420

1460

1550

1470

1450

1560

1630

1500

1540

1410

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1520

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1450

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MR2

Regression Analysis

R Square0.5921995383

Observations45

ANOVA

Regression28029.04134069474014.520670347330.49577299170.0000000066

Residual425528.9586593053131.6418728406

Total4413558

Intercept26.8909788789.77183452752.75188643470.00871033757.170618649246.611339106810.455218753143.3267390029

SC1.3408185960.17919606357.48241099750.0000000030.97918630341.70245088861.03941935451.6422178375

Engineer7.28687383213.98571918121.82824566930.0746210532-0.756633024515.33038068870.583084057313.990663607

RESIDUAL OUTPUT

190.49223374115.5077662589

295.855508125-5.855508125

3100.636001656612.3639983434

489.90945288888.0905471112

587.2278156969-11.2278156969

6109.26369408477.7363059153

7118.6494242566-0.6494242566

893.93190867687.0680913232

9106.5820568928-11.5820568928

1089.15141514514.8485848549

11117.30860566061.6913943394

12132.81564796-12.81564796

13103.900419700811.0995802992

14110.021731828520.9782681715

1594.5146895294.485310471

16113.2861498727-11.2861498727

1780.523722717-14.523722717

18119.99024285259.0097571475

1986.469777953213.5302220468

20103.90041970087.0995802992

21133.3984288123-5.3984288123

2294.5146895299.485310471

23115.967787064617.0322129354

24122.67188004452.3281199555

2595.8555081253.144491875

2695.855508125-5.855508125

27118.64942425663.3505757434

28106.5820568928-44.5820568928

2988.56863429299.4313657071

3099.87796391290.1220360871

31117.30860566065.6913943394

32110.60451268079.3954873193

3381.8645413131.135458687

3479.7656849733-8.7656849733

35106.5820568928-4.5820568928

3698.5371453169-9.5371453169

3797.9543644647-22.9543644647

38106.5820568928-0.5820568928

3982.4473221652-2.4473221652

4099.8779639129-0.8779639129

41109.2636940847-5.2636940847

42107.9228754888-2.9228754888

4384.54617850492.4538214951

44101.21878250893.7812174911

4589.15141514510.8485848549

DurbinWatson3

7.4650423729

-3.969279661

6.8034957627

2.6721398305

-16.6106991525

9.4449152542

0.9348516949

1.5963983051

-9.8379237288

6.8236228814

3.2934322034

-18.8024364407

12.8792372881

15.2934322034

6.3893008475

-9.6308262712

-19.8177966102

10.5762711864

15.5407838983

8.8792372881

-4.0095338983

11.3893008475

18.6520127119

3.8591101695

5.030720339

-3.969279661

4.9348516949

-42.8379237288

4.030720339

1.9549788136

7.2934322034

11.0863347458

-4.1763771186

-6.6663135593

-2.8379237288

-7.686440678

-28.4793432203

1.1620762712

-0.3834745763

0.9549788136

-3.5550847458

-1.1965042373

-2.8935381356

5.5963983051

2.8236228814

SC

Residuals

SC Residual Plot

NOTX13

SalesSC

9642

9046

11355

9847

7645

11756

11863

10150

9554

9441

11962

12079

11552

13162

9945

10259

6640

12964

10039

11152

12874

10445

13361

12566

9946

9046

12263

6254

9846

10049

12362

12057

8341

7134

10254

8948

7553

10654

8036

9949

10456

10555

8743

10550

9041

MR3

Regression Analysis

R Square0.5597455908

Observations45

ANOVA

Regression17589.0307203397589.03072033954.67079920930.0000000035

Residual435968.969279661138.8132390619

Total4413558

Intercept31.47457627129.69859035643.24527329380.002274888411.91550500651.0336475364

SC1.35858050850.18374167377.39397046310.00000000350.98803011311.7291309038

RESIDUAL OUTPUT

188.53495762717.4650423729

293.969279661-3.969279661

3106.19650423736.8034957627

495.32786016952.6721398305

592.6106991525-16.6106991525

6107.55508474589.4449152542

7117.06514830510.9348516949

899.40360169491.5963983051

9104.8379237288-9.8379237288

1087.17637711866.8236228814

11115.70656779663.2934322034

12138.8024364407-18.8024364407

13102.120762711912.8792372881

14115.706567796615.2934322034

1592.61069915256.3893008475

16111.6308262712-9.6308262712

1785.8177966102-19.8177966102

18118.423728813610.5762711864

1984.459216101715.5407838983

20102.12076271198.8792372881

21132.0095338983-4.0095338983

2292.610699152511.3893008475

23114.347987288118.6520127119

24121.14088983053.8591101695

2593.9692796615.030720339

2693.969279661-3.969279661

27117.06514830514.9348516949

28104.8379237288-42.8379237288

2993.9692796614.030720339

3098.04502118641.9549788136

31115.70656779667.2934322034

32108.913665254211.0863347458

3387.1763771186-4.1763771186

3477.6663135593-6.6663135593

35104.8379237288-2.8379237288

3696.686440678-7.686440678

37103.4793432203-28.4793432203

38104.83792372881.1620762712

3980.3834745763-0.3834745763

4098.04502118640.9549788136

41107.5550847458-3.5550847458

42106.1965042373-1.1965042373

4389.8935381356-2.8935381356

4499.40360169495.5963983051

4587.17637711862.8236228814

Scatter

96

90

113

98

76

117

118

101

95

94

119

120

115

131

99

102

66

129

100

111

128

104

133

125

99

90

122

62

98

100

123

120

83

71

102

89

75

106

80

99

104

105

87

105

90

Sales

X

Y

Scatter Diagram

DataCopy

SCSales

4296

4690

55113

4798

4576

56117

63118

50101

5495

4194

62119

79120

52115

62131

4599

59102

4066

64129

39100

52111

74128

45104

61133

66125

4699

4690

63122

5462

4698

49100

62123

57120

4183

3471

54102

4889

5375

54106

3680

4999

56104

55105

4387

50105

4190

DurbinWatson4

7.4650423729

-3.969279661

6.8034957627

2.6721398305

-16.6106991525

9.4449152542

0.9348516949

1.5963983051

-9.8379237288

6.8236228814

3.2934322034

-18.8024364407

12.8792372881

15.2934322034

6.3893008475

-9.6308262712

-19.8177966102

10.5762711864

15.5407838983

8.8792372881

-4.0095338983

11.3893008475

18.6520127119

3.8591101695

5.030720339

-3.969279661

4.9348516949

-42.8379237288

4.030720339

1.9549788136

7.2934322034

11.0863347458

-4.1763771186

-6.6663135593

-2.8379237288

-7.686440678

-28.4793432203

1.1620762712

-0.3834745763

0.9549788136

-3.5550847458

-1.1965042373

-2.8935381356

5.5963983051

2.8236228814

SC

Residuals

SC Residual Plot

SLR

Regression Analysis

R Square0.5597455908

Observations45

ANOVA

Regression17589.0307203397589.03072033954.670.0000000035

Residual435968.969279661138.8132390619

Total4413558

Intercept31.47457627129.69859035643.24527329380.0011.91550500651.0336475364

SC1.35858050850.18374167377.39397046310.000.98803011311.7291309038

RESIDUAL OUTPUT

188.53495762717.4650423729

293.969279661-3.969279661

3106.19650423736.8034957627

495.32786016952.6721398305

592.6106991525-16.6106991525

6107.55508474589.4449152542

7117.06514830510.9348516949

899.40360169491.5963983051

9104.8379237288-9.8379237288

1087.17637711866.8236228814

11115.70656779663.2934322034

12138.8024364407-18.8024364407

13102.120762711912.8792372881

14115.706567796615.2934322034

1592.61069915256.3893008475

16111.6308262712-9.6308262712

1785.8177966102-19.8177966102

18118.423728813610.5762711864

1984.459216101715.5407838983

20102.12076271198.8792372881

21132.0095338983-4.0095338983

2292.610699152511.3893008475

23114.347987288118.6520127119

24121.14088983053.8591101695

2593.9692796615.030720339

2693.969279661-3.969279661

27117.06514830514.9348516949

28104.8379237288-42.8379237288

2993.9692796614.030720339

3098.04502118641.9549788136

31115.70656779667.2934322034

32108.913665254211.0863347458

3387.1763771186-4.1763771186

3477.6663135593-6.6663135593

35104.8379237288-2.8379237288

3696.686440678-7.686440678

37103.4793432203-28.4793432203

38104.83792372881.1620762712

3980.3834745763-0.3834745763

4098.04502118640.9549788136

41107.5550847458-3.5550847458

42106.1965042373-1.1965042373

4389.8935381356-2.8935381356

4499.40360169495.5963983051

4587.17637711862.8236228814

Data

SalesWonderSCEngineerExperienceEngineerEngineer

962742151Yes

903546181Yes

1133055080No

982647020No

762845070No

11724561111Yes

1183563141Yes

1013350090No

952754141Yes

943841181Yes

1193162131Yes

1203179010No

1153252191Yes

1313162040No

993445131Yes

1022559101Yes

662640060No

12925641111Yes

1002539161Yes

1113352121Yes

1283974151Yes

1042845191Yes

1333361151Yes

1253766181Yes

992346181Yes

903146151Yes

1223663191Yes

6232541111Yes

9837460110No

1002549131Yes

1233062101Yes

1203657151Yes

832841020No

712434191Yes

1023454141Yes

893548181Yes

753153010No

1063054151Yes

803036101Yes

992549181Yes

10438561111Yes

1052655141Yes

8724430130No

1052650151Yes

903741151Yes

*

DCII

SCExperienceEngineer

14250

14680

15580

14720

14570

156110

16340

15090

15440

14180

16230

17910

15290

16240

14530

15900

14060

164110

13960

15220

17450

14590

16150

16680

14680

14650

16390

154110

146110

14930

16200

15750

14120

13490

15440

14880

15310

15450

13600

14980

156110

15540

143130

15050

14150

5.5077662589

-5.855508125

12.3639983434

8.0905471112

-11.2278156969

7.7363059153

-0.6494242566

7.0680913232

-11.5820568928

4.8485848549

1.6913943394

-12.81564796

11.0995802992

20.9782681715

4.485310471

-11.2861498727

-14.523722717

9.0097571475

13.5302220468

7.0995802992

-5.3984288123

9.485310471

17.0322129354

2.3281199555

3.144491875

-5.855508125

3.3505757434

-44.5820568928

9.4313657071

0.1220360871

5.6913943394

9.3954873193

1.135458687

-8.7656849733

-4.5820568928

-9.5371453169

-22.9543644647

-0.5820568928

-2.4473221652

-0.8779639129

-5.2636940847

-2.9228754888

2.4538214951

3.7812174911

0.8485848549

SC

Residuals

SC Residual Plot

DurbinWatson

5.5077662589

-5.855508125

12.3639983434

8.0905471112

-11.2278156969

7.7363059153

-0.6494242566

7.0680913232

-11.5820568928

4.8485848549

1.6913943394

-12.81564796

11.0995802992

20.9782681715

4.485310471

-11.2861498727

-14.523722717

9.0097571475

13.5302220468

7.0995802992

-5.3984288123

9.485310471

17.0322129354

2.3281199555

3.144491875

-5.855508125

3.3505757434

-44.5820568928

9.4313657071

0.1220360871

5.6913943394

9.3954873193

1.135458687

-8.7656849733

-4.5820568928

-9.5371453169

-22.9543644647

-0.5820568928

-2.4473221652

-0.8779639129

-5.2636940847

-2.9228754888

2.4538214951

3.7812174911

0.8485848549

Engineer

Residuals

X1

Regression Analysis

SC and all other X

Multiple R0

R Square0

Observations45

VIF1

CPD Calculations

Regression Analysis

SSR(X1,X2)8029.0413406947

SST13558

SSR(X2)-0SSR(X1 | X2)8029.0413406947

SSR(X1)7589.030720339SSR(X2 | X1)440.0106203557

Coefficients

r2 Y1.20.5921995383

r2 Y2.10.0737163486

NOTX2

Regression Analysis

All but Engineer

R Square0.5597455908

Observations45

ANOVA

Regression17589.0307203397589.03072033954.67079920930.0000000035

Residual435968.969279661138.8132390619

Total4413558

Intercept31.47457627129.69859035643.24527329380.002274888411.91550500651.0336475364

SC1.35858050850.18374167377.39397046310.00000000350.98803011311.7291309038

NOTX1

Regression Analysis

All but SC

Multiple R65535

R Square-0

Observations45

ANOVA

Regression1-0-001

Residual4413558308.1363636364

Total4513558

Intercept1022.616767996538.9793822519096.7262507024107.2737492976

Engineer006553500

MR

Regression Analysis

R Square0.5921995383

Observations45

ANOVA

Regression28029.04134069474014.520670347330.500.00

Residual425528.9586593053131.6418728406

Total4413558

Intercept26.8909788789.77183452752.75188643470.017.170618649246.6113391068

SC1.3408185960.17919606357.48241099750.000.97918630341.7024508886

Engineer7.28687383213.98571918121.82824566930.07-0.756633024515.3303806887

RESIDUAL OUTPUT

190.49223374115.5077662589

295.855508125-5.855508125

3100.636001656612.3639983434

489.90945288888.0905471112

587.2278156969-11.2278156969

6109.26369408477.7363059153

7118.6494242566-0.6494242566

893.93190867687.0680913232

9106.5820568928-11.5820568928

1089.15141514514.8485848549

11117.30860566061.6913943394

12132.81564796-12.81564796

13103.900419700811.0995802992

14110.021731828520.9782681715

1594.5146895294.485310471

16113.2861498727-11.2861498727

1780.523722717-14.523722717

18119.99024285259.0097571475

1986.469777953213.5302220468

20103.90041970087.0995802992

21133.3984288123-5.3984288123

2294.5146895299.485310471

23115.967787064617.0322129354

24122.67188004452.3281199555

2595.8555081253.144491875

2695.855508125-5.855508125

27118.64942425663.3505757434

28106.5820568928-44.5820568928

2988.56863429299.4313657071

3099.87796391290.1220360871

31117.30860566065.6913943394

32110.60451268079.3954873193

3381.8645413131.135458687

3479.7656849733-8.7656849733

35106.5820568928-4.5820568928

3698.5371453169-9.5371453169

3797.9543644647-22.9543644647

38106.5820568928-0.5820568928

3982.4473221652-2.4473221652

4099.8779639129-0.8779639129

41109.2636940847-5.2636940847

42107.9228754888-2.9228754888

4384.54617850492.4538214951

44101.21878250893.7812174911

4589.15141514510.8485848549

5.5077662589

-5.855508125

12.3639983434

8.0905471112

-11.2278156969

7.7363059153

-0.6494242566

7.0680913232

-11.5820568928

4.8485848549

1.6913943394

-12.81564796

11.0995802992

20.9782681715

4.485310471

-11.2861498727

-14.523722717

9.0097571475

13.5302220468

7.0995802992

-5.3984288123

9.485310471

17.0322129354

2.3281199555

3.144491875

-5.855508125

3.3505757434

-44.5820568928

9.4313657071

0.1220360871

5.6913943394

9.3954873193

1.135458687

-8.7656849733

-4.5820568928

-9.5371453169

-22.9543644647

-0.5820568928

-2.4473221652

-0.8779639129

-5.2636940847

-2.9228754888

2.4538214951

3.7812174911

0.8485848549

SC

Residuals

SC Residual Plot

DurbinWatson2

5.5077662589

-5.855508125

12.3639983434

8.0905471112

-11.2278156969

7.7363059153

-0.6494242566

7.0680913232

-11.5820568928

4.8485848549

1.6913943394

-12.81564796

11.0995802992

20.9782681715

4.485310471

-11.2861498727

-14.523722717

9.0097571475

13.5302220468

7.0995802992

-5.3984288123

9.485310471

17.0322129354

2.3281199555

3.144491875

-5.855508125

3.3505757434

-44.5820568928

9.4313657071

0.1220360871

5.6913943394

9.3954873193

1.135458687

-8.7656849733

-4.5820568928

-9.5371453169

-22.9543644647

-0.5820568928

-2.4473221652

-0.8779639129

-5.2636940847

-2.9228754888

2.4538214951

3.7812174911

0.8485848549

Engineer

Residuals

X12

Regression Analysis

SC and all other X

Multiple R0

R Square0

Observations45

VIF1

CPD Calculations2

Regression Analysis

SSR(X1,X2)8029.0413406947

SST13558

SSR(X2)-0SSR(X1 | X2)8029.0413406947

SSR(X1)7589.030720339SSR(X2 | X1)440.0106203557

Coefficients

r2 Y1.20.5921995383

r2 Y2.10.0737163486

NOTX22

Regression Analysis

All but Engineer

R Square0.5597455908

Observations45

ANOVA

Regression17589.0307203397589.03072033954.67079920930.0000000035

Residual435968.969279661138.8132390619

Total4413558

Intercept31.47457627129.69859035643.24527329380.002274888411.91550500651.033647536415.17056015647.7785923864

SC1.35858050850.18374167377.39397046310.00000000350.98803011311.72913090381.04969776371.6674632532

NOTX12

Regression Analysis

All but SC

Multiple R65535

R Square-0

Observations45

ANOVA

Regression1-0-001

Residual4413558308.1363636364

Total4513558

Intercept1022.616767996538.9793822519096.7262507024107.273749297697.6032279693106.3967720307

Engineer00655350000

Intervals

Confidence and Prediction Estimate Intervals

Data

Confidence Level90%

1

SC given value0

Engineer given value0

X'X4523360

23361253760

000

Inverse of X'X000

000

X'G times Inverse of X'X000

[X'G times Inverse of X'X] times XG0

t Statistic1.6819523579

Predicted Y (YHat)26.890978878

For Average Predicted Y (YHat)

Confidence Interval Lower Limit0

Confidence Interval Upper Limit0

For Individual Response Y

Prediction Interval Lower Limit0

Prediction Interval Upper Limit0

PHStat2 User Note:

Enter the values for the given X'sin the cell range B6:B7.(You can interactively changethese values at any time.)

To delete this note:Select this note and thenselect Edit | Cut.

DCII2

SCEngineer

1420

1460

1550

1470

1450

1560

1630

1500

1540

1410

1620

1790

1520

1620

1450

1590

1400

1640

1390

1520

1740

1450

1610

1660

1460

1630

1540

1460

1490

1620

1570

1410

1340

1540

1480

1530

1540

1360

1490

1560

1550

1430

1500

1410

MR2

Regression Analysis

R Square0.5921995383

Observations45

ANOVA

Regression28029.04134069474014.520670347330.49577299170.0000000066

Residual425528.9586593053131.6418728406

Total4413558

Intercept26.8909788789.77183452752.75188643470.00871033757.170618649246.611339106810.455218753143.3267390029

SC1.3408185960.17919606357.48241099750.0000000030.97918630341.70245088861.03941935451.6422178375

Engineer7.28687383213.98571918121.82824566930.0746210532-0.756633024515.33038068870.583084057313.990663607

RESIDUAL OUTPUT

190.49223374115.5077662589

295.855508125-5.855508125

3100.636001656612.3639983434

489.90945288888.0905471112

587.2278156969-11.2278156969

6109.26369408477.7363059153

7118.6494242566-0.6494242566

893.93190867687.0680913232

9106.5820568928-11.5820568928

1089.15141514514.8485848549

11117.30860566061.6913943394

12132.81564796-12.81564796

13103.900419700811.0995802992

14110.021731828520.9782681715

1594.5146895294.485310471

16113.2861498727-11.2861498727

1780.523722717-14.523722717

18119.99024285259.0097571475

1986.469777953213.5302220468

20103.90041970087.0995802992

21133.3984288123-5.3984288123

2294.5146895299.485310471

23115.967787064617.0322129354

24122.67188004452.3281199555

2595.8555081253.144491875

2695.855508125-5.855508125

27118.64942425663.3505757434

28106.5820568928-44.5820568928

2988.56863429299.4313657071

3099.87796391290.1220360871

31117.30860566065.6913943394

32110.60451268079.3954873193

3381.8645413131.135458687

3479.7656849733-8.7656849733

35106.5820568928-4.5820568928

3698.5371453169-9.5371453169

3797.9543644647-22.9543644647

38106.5820568928-0.5820568928

3982.4473221652-2.4473221652

4099.8779639129-0.8779639129

41109.2636940847-5.2636940847

42107.9228754888-2.9228754888

4384.54617850492.4538214951

44101.21878250893.7812174911

4589.15141514510.8485848549

DurbinWatson3

7.4650423729

-3.969279661

6.8034957627

2.6721398305

-16.6106991525

9.4449152542

0.9348516949

1.5963983051

-9.8379237288

6.8236228814

3.2934322034

-18.8024364407

12.8792372881

15.2934322034

6.3893008475

-9.6308262712

-19.8177966102

10.5762711864

15.5407838983

8.8792372881

-4.0095338983

11.3893008475

18.6520127119

3.8591101695

5.030720339

-3.969279661

4.9348516949

-42.8379237288

4.030720339

1.9549788136

7.2934322034

11.0863347458

-4.1763771186

-6.6663135593

-2.8379237288

-7.686440678

-28.4793432203

1.1620762712

-0.3834745763

0.9549788136

-3.5550847458

-1.1965042373

-2.8935381356

5.5963983051

2.8236228814

SC

Residuals

SC Residual Plot

NOTX13

SalesSC

9642

9046

11355

9847

7645

11756

11863

10150

9554

9441

11962

12079

11552

13162

9945

10259

6640

12964

10039

11152

12874

10445

13361

12566

9946

9046

12263

6254

9846

10049

12362

12057

8341

7134

10254

8948

7553

10654

8036

9949

10456

10555

8743

10550

9041

MR3

Regression Analysis

R Square0.5597455908

Observations45

ANOVA

Regression17589.0307203397589.03072033954.67079920930.0000000035

Residual435968.969279661138.8132390619

Total4413558

Intercept31.47457627129.69859035643.24527329380.002274888411.91550500651.0336475364

SC1.35858050850.18374167377.39397046310.00000000350.98803011311.7291309038

RESIDUAL OUTPUT

188.53495762717.4650423729

293.969279661-3.969279661

3106.19650423736.8034957627

495.32786016952.6721398305

592.6106991525-16.6106991525

6107.55508474589.4449152542

7117.06514830510.9348516949

899.40360169491.5963983051

9104.8379237288-9.8379237288

1087.17637711866.8236228814

11115.70656779663.2934322034

12138.8024364407-18.8024364407

13102.120762711912.8792372881

14115.706567796615.2934322034

1592.61069915256.3893008475

16111.6308262712-9.6308262712

1785.8177966102-19.8177966102

18118.423728813610.5762711864

1984.459216101715.5407838983

20102.12076271198.8792372881

21132.0095338983-4.0095338983

2292.610699152511.3893008475

23114.347987288118.6520127119

24121.14088983053.8591101695

2593.9692796615.030720339

2693.969279661-3.969279661

27117.06514830514.9348516949

28104.8379237288-42.8379237288

2993.9692796614.030720339

3098.04502118641.9549788136

31115.70656779667.2934322034

32108.913665254211.0863347458

3387.1763771186-4.1763771186

3477.6663135593-6.6663135593

35104.8379237288-2.8379237288

3696.686440678-7.686440678

37103.4793432203-28.4793432203

38104.83792372881.1620762712

3980.3834745763-0.3834745763

4098.04502118640.9549788136

41107.5550847458-3.5550847458

42106.1965042373-1.1965042373

4389.8935381356-2.8935381356

4499.40360169495.5963983051

4587.17637711862.8236228814

Scatter

96

90

113

98

76

117

118

101

95

94

119

120

115

131

99

102

66

129

100

111

128

104

133

125

99

90

122

62

98

100

123

120

83

71

102

89

75

106

80

99

104

105

87

105

90

Sales

X

Y

Scatter Diagram

DataCopy

SCSales

4296

4690

55113

4798

4576

56117

63118

50101

5495

4194

62119

79120

52115

62131

4599

59102

4066

64129

39100

52111

74128

45104

61133

66125

4699

4690

63122

5462

4698

49100

62123

57120

4183

3471

54102

4889

5375

54106

3680

4999

56104

55105

4387

50105

4190

DurbinWatson4

7.4650423729

-3.969279661

6.8034957627

2.6721398305

-16.6106991525

9.4449152542

0.9348516949

1.5963983051

-9.8379237288

6.8236228814

3.2934322034

-18.8024364407

12.8792372881

15.2934322034

6.3893008475

-9.6308262712

-19.8177966102

10.5762711864

15.5407838983

8.8792372881

-4.0095338983

11.3893008475

18.6520127119

3.8591101695

5.030720339

-3.969279661

4.9348516949

-42.8379237288

4.030720339

1.9549788136

7.2934322034

11.0863347458

-4.1763771186

-6.6663135593

-2.8379237288

-7.686440678

-28.4793432203

1.1620762712

-0.3834745763

0.9549788136

-3.5550847458

-1.1965042373

-2.8935381356

5.5963983051

2.8236228814

SC

Residuals

SC Residual Plot

SLR

Regression Analysis

R Square0.5597455908

Observations45

ANOVA

Regression17589.0307203397589.03072033954.670.0000000035

Residual435968.969279661138.8132390619

Total4413558

Intercept31.47457627129.69859035643.24527329380.0011.91550500651.0336475364

SC1.35858050850.18374167377.39397046310.000.98803011311.7291309038

RESIDUAL OUTPUT

188.53495762717.4650423729

293.969279661-3.969279661

3106.19650423736.8034957627

495.32786016952.6721398305

592.6106991525-16.6106991525

6107.55508474589.4449152542

7117.06514830510.9348516949

899.40360169491.5963983051

9104.8379237288-9.8379237288

1087.17637711866.8236228814

11115.70656779663.2934322034

12138.8024364407-18.8024364407

13102.120762711912.8792372881

14115.706567796615.2934322034

1592.61069915256.3893008475

16111.6308262712-9.6308262712

1785.8177966102-19.8177966102

18118.423728813610.5762711864

1984.459216101715.5407838983

20102.12076271198.8792372881

21132.0095338983-4.0095338983

2292.610699152511.3893008475

23114.347987288118.6520127119

24121.14088983053.8591101695

2593.9692796615.030720339

2693.969279661-3.969279661

27117.06514830514.9348516949

28104.8379237288-42.8379237288

2993.9692796614.030720339

3098.04502118641.9549788136

31115.70656779667.2934322034

32108.913665254211.0863347458

3387.1763771186-4.1763771186

3477.6663135593-6.6663135593

35104.8379237288-2.8379237288

3696.686440678-7.686440678

37103.4793432203-28.4793432203

38104.83792372881.1620762712

3980.3834745763-0.3834745763

4098.04502118640.9549788136

41107.5550847458-3.5550847458

42106.1965042373-1.1965042373

4389.8935381356-2.8935381356

4499.40360169495.5963983051

4587.17637711862.8236228814

Data

SalesWonderSCEngineerExperienceEngineerEngineer

962742151Yes

903546181Yes

1133055080No

982647020No

762845070No

11724561111Yes

1183563141Yes

1013350090No

952754141Yes

943841181Yes

1193162131Yes

1203179010No

1153252191Yes

1313162040No

993445131Yes

1022559101Yes

662640060No

12925641111Yes

1002539161Yes

1113352121Yes

1283974151Yes

1042845191Yes

1333361151Yes

1253766181Yes

992346181Yes

903146151Yes

1223663191Yes

6232541111Yes

9837460110No

1002549131Yes

1233062101Yes

1203657151Yes

832841020No

712434191Yes

1023454141Yes

893548181Yes

753153010No

1063054151Yes

803036101Yes

992549181Yes

10438561111Yes

1052655141Yes

8724430130No

1052650151Yes

903741151Yes

*ConcluziiSingurul factor semnificativ de influen asupra vnzrilor este rezultatul la testul SC( abiliti de vnzri)Este recomandat ca la angajare s fie eliminat testul Wonderlic Personnel(aptitudini manageriale)Experiena sau studiile tehnice nu trebuie sa fie un criteriu definitoriu la angajare.

econometrie - autocorelare

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