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Transcript of econometrie
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.