Proiectul urmarete realizarea unui model econometric referitor la datele despre suprafata locuibila, populatie, PIB, salariu si numarul salariatilor la nivel de jude,in anul 2009.

JudetSuprafata locuibila PopulatiePIBSalariuNr Salariati

Bihor754459305512751.31025159047

Bistrita53553172056028.1111556798

Cluj667469022920326.11387187236

Maramures63045113118219.6104691900

Satu Mare44183649386181.9106475732

Salaj38642418404393.2115243903

Alba6242373755839.1114283830

Brasov5363597439164431323150855

Covasna37102227104030.3103748089

Harghita66393246385975.1109962983

Mures6714580815108541207124747

Sibiu543242513711406.91311115929

Bacau662171617611784.81319110753

Botosani49864484235530112255511

Iasi547682997314806.31310153433

Neamt58965624897403.2108081943

Suceava855370672010066.6111799779

Vaslui53814502694817.5112655182

Braila47663601916870.2118071500

Buzau61034826847297116681600

Constanta707172236019553.11391187134

Galati44666094809686.81254117780

Tulcea84992474443921.9118043817

Vrancea48573905965377109155469

Arges682664087117545.51374136440

Calarasi50883128794255.5112043985

Dambovita40545303549154.5123279849

Giurgiu35262812073905.6126533413

Ialomita44532877804550.8113147783

Prahova471681565720061.51403180022

Teleorman57904024625668.4112253669

Ilfov158331231712913.91697106110

Bucuresti2381944426111374.91831886480

Dolj741470534513355.21302129976

Gorj56023777188764.2149080285

Mehedinti49332929714359.8129645837

Olt54984668216080.7126366726

Valcea57654077647386.9117679306

Arad775445595210774.51215110826

Caras Severin85203229416409.6114858694

Hunedoara70634647399301.71231118140

Timis869767806822714.41357202772

Presupunnd c ntre cele 5 variabile exist o dependen liniar, se cere:a) s se estimeze parametrii modelului de regresie;b) s se determine erorile reziduale;c) s se msoare intensitatea legturii dintre producie i cele dou variabile;d) s se testeze validitatea modelului de regresie folosit.

Rezolvare:Notm cu:y = suprafata locuibila;x1 = populatia;x2 = PIB;x3=salariu;x4=nr salariatiEcuaia de regresie este:

= b0 + b1x1 + b2x2 + b3 x3 + b4x4

unde reprezint valorile ajustate sau teoretice ale variabilei y n funcie de cele patru variabile factoriale x1,x2,x3,x4.

Rezultatele obinute cu ajutorul EXCEL-ului sunt:

SUMMARY OUTPUT

Regression Statistics

Multiple R0,623124601

R Square0,388284268

Adjusted R Square0,322152838

Standard Error1430,824358

Observations42

ANOVA

dfSSMSFSignificance F

Regression448081113,7912020278,455,8714030,000920651

Residual3775748558,692047258,343

Total41123829672,5

CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Upper 95,0%

Intercept9847,8709432332,553114,22192790,0001515121,66941214574,0724714574,07247

X Variable 10,0037094680,0023035991,61029240,115834-0,0009580670,0083770030,008377003

X Variable 20,1177820930,0456693312,57901940,0140190,0252472380,2103169480,210316948

X Variable 3-4,7896829791,923131127-2,4905650,017369-8,686316774-0,89304918-0,893049185

X Variable 4-0,0096426860,00531573-1,8139910,077795-0,0204133790,0011280060,001128006

RESIDUAL OUTPUT

ObservationPredicted YResiduals

17106,563555437,4364452

25846,341372-491,3413721

36353,543826320,4561739

46816,442481-512,4424808

56103,125276-1685,125276

65321,327765-1457,327765

75054,9579681187,042032

84466,169734896,830266

95722,849683-2012,849683

105884,666309754,3336911

116296,748879417,2511212

125371,18421360,81578719

135394,0583821226,941618

146253,317219-1267,317219

156916,51989-1440,51989

166525,326803-629,3268035

176176,7645032376,235497

186160,199977-779,1999771

195651,872916-885,8729164

206126,214163-23,21416335

216363,512007707,4879931

226107,576791-1641,576791

235153,2406243345,759376

246169,674318-1312,674318

256394,975683431,024317

265718,473262-630,4732616

276222,531117-2168,531117

284969,798335-1443,798335

295573,402233-1120,402233

304448,444698267,5553025

316116,842118-326,8421176

323376,043554-1793,043554

331082,352296-844,3522964

347026,788752387,2112484

354335,1206941266,879306

364798,628678134,3713219

375602,856134-104,8561344

386080,60219-315,60219

395920,0693821833,930618

405736,1517862783,848214

414646,17382416,8262

427062,5466341634,453366

Explicitarea datelor din tabelele de mai sus:SUMMARY OUTPUT

Regression Statistics

Multiple RRaportul de corelatie (R)0,623124601

R SquareCoeficientul(gradul ) de determinaie0,388284268

Adjusted R SquareValoarea ajustat a coeficientului de determinaie0,3221528380,3221528380,322152838

1430,824358

Standard ErrorAbaterea medie ptratic a erorilor n eantion1430,824358

ObservationsNumrul observaiilor (n)42

Tabel 2.

ANOVA

Sursa variaieidf(grade de libertate)SS (variana)(suma ptratelor)MS =SS/df(media ptratelor)(dispersia corectat)FSignificanceF

Regression (variaiadatorat regresiei)4 (k)SSR=

= 48081113,78=12020278,447TestulF= 5,87140

F=/0,0009206 < 0.05(resping H0 model valid)

Residual(variaia rezidual)37 (n-k-1)SSE=

= 75748558,6880=2047258,3429

Total (variaia total)41 (n-1)SST=

=123829672,4 SST=SSR + SSE

Tabel 3Coefficients(Coeficieni)Standard Error(Abaterea mediepatratic)t StatP-valueLower95%Upper95%

Limita inf. a intervalului de ncredereLimita sup. a intervalului de ncredere

Intercept(termenul liber)a0=9847,87094334549 =2332,5531=4,221920,0001509 0,05-0,00095800,0083770

PIBa2 =0,11778209=0,045669331=2,579010,0140190 0,05 nseamn c acest coeficient este nesemnificativ. Intervalul de ncredere pentru acest parametru este

-0,000958067 0,008377003. Coeficientul a2 este 0,117782093, ceea ce nsemn c la cresterea PIB cu o sut, suprafata locuibila va crete cu 0,117782093 km patrati. Deoarece = 2,579019439 iar pragul de semnificaie P-value este 0,014019063 < 0,05 nseamn c acest coeficient este semnificativ.

Coeficientul a3 este -4,789682979, ceea ce nsemn c la cresterea salariului cu o sut, suprafata locuibila va scade cu 4,789682979 km patrati. Deoarece = -2,49056495iar pragul de semnificaie P-value este 0,017369 0,05 nseamn c acest coeficient este nesemnificativ.