Als of Dure de Jos Uerst of Glt Fsccle. Ecoocs d Appled fortcs Yers XX o /5 N-L 584-49 N-Ole 44-44X www.e.fe.ugl.ro ttstcl Mode d Alss of the Correlto etwee the Gross Doestc Product per Cpt d the Lfe Epectc Grel OPAT ARTCLE NFO ABTRACT Artcle hstor: Accepted M 4 Alle ole 4 August 4 JEL Clssfcto C, C, C Kewords: Gross Doestc Product per cpt, Lfe Epectc, Lest qures Method Ths pper reflects the sttstcl ode of the treds cocerg the G.D.P. per cpt d the Lfe Epectc coutres, 4, respectel the G.D.P. per cpt d the Lfe Epectc Ro, etwee -4. Wth the help of the Lest qures Method, whch s ethod through we c to reflect the tred le of the est ft cocerg odel. Ths reserch reflects tht there s strog test regrdg the correlto etwee the G.D.P. per cpt d the Lfe Epectc the world. o, f eeroe s eeds of the people re stsfed, the crese G.D.P. per cpt would rel ffect lfe epectc. 5 EA. All rghts resered.. troducto ths reserch, preset persol cotruto whch reflects sttstcl lss of the treds odels etwee the Gross Doestc Product per cpt d the Lfe Epectc coutres, 4, respectel the Gross Doestc Product per cpt d the Lfe Epectc Ro, the perod - 4. The purpose of the reserch reflects the posslt for to epress the test of the correlto wth the help of the Perso correlto coeffcet. The sttstcl ethods used re the Coeffcets of Vrto Method, respectel the Lest qures Method ppled for to clculte the preters of the regresso equto d the Perso Method of Correlto used for to reflect the test of the correlto etwee the G.D.P. per cpt d the Lfe Epectc. The sectos, respectel the secto 4, preset the ethodolog for to chee the treds odels etwee the G.D.P. per cpt d the Lfe Epectc coutres, 4, respectel the G.D.P. per cpt d the Lfe Epectc Ro, the perod - 4, wth the help of the Lest qures Method. The secto, respectel the secto 5, reflect the test of the correlto etwee the G.D.P. per cpt d the Lfe Epectc, coutres, respectel Ro. The stte of the rt ths do s represeted the reserch elogs to Crl Frederch Guss, who creted the Lest qures Method d Krl Perso, who cheed the Perso correlto coeffcet [], [].. The ode of the tred etwee the G.D.P. per cpt d the Lfe Epectc 4, for coutres 4, we osere the et eoluto cocerg the G.D.P. per cpt d the Lfe Epectc coutres, ccordg to the tle o. : Tle The eoluto of the G.D.P. per cpt d the Lfe Epectc 4 COUNTRE GRO DOMETC PRODUCT LFE EXPECTANCY PER CAPTA N 4, ($ 4 TALY 5.8 8,6 JAPAN 6. 84,46 FRANCE 44.58 8,66 UNTED KNGDOM 45.65 8,4 GERMANY 47.59 8,44 AUTRA 5.7 8,7 NETHERLAND 5.7 8, U..A. 54.597 79,56 WEDEN 58.49 8,89 DENMARK 6.564 79,9 ource: EUROTAT Fcult of Ecoocs d Busess Adstrto, Dure de Jos Uerst of Glt, Ro. E-l ddress: gopt@ugl.ro (G. Opt
We wt to detf the tred odel etwee the G.D.P. per cpt d the Lfe Epectc for these coutres 4, usg the tle o.. - f we forulte the ull hpothess H : whch etos the ssupto of the estece for the odel of tedec cocerg Y fctor, where Y the Lfe Epectc, s eg the fucto t, the the preters d of the djusted ler fucto, c to e clculted es of the et sste []: Therefore, ( ( COUNTRE Tle The estte of the lue for the rto coeffcet the cse of the djusted ler fucto, the hpothess cocerg the ler eoluto of the correlto etwee the G.D.P. per cpt d the Lfe Epectc coutres, 4 G.D.P. per cpt LFE EXPECTANCY LNEAR TREND ($ 4 ( 4 ( TALY 5.8 8,6 8879 9654,49 8,95554, JAPAN 6. 84,46 44 686,7 8,8665,6 FRANCE 44.58 8,66 986444 6697,8 8,754659,6 UNTED 45.65 8,4 849649 6744,6 8,55969774,4 KNGDOM GERMANY 47.59 8,44 6488 889,6 8,889857,85 AUTRA 5.7 8,7 64849 48,9 8,769487,6 NETHERLAND 5.7 8, 69859 46777,76 8,7684454,6 U..A. 54.597 79,56 98849 4477, 8,9588,75 WEDEN 58.49 8,89 4978 478987,99 79,76555996, DENMARK 6.564 79,9 66799896 4796,76 79,475669,9 TOTAL 48668 8,44 47755747 96944,7 8,44776 8,7 f we clculte the sttstcl dt for to djust the ler fucto, we ot for the preters d the lues: 4.77.557.47 8,44 486.689.69.44,7 87,94487 4.77.557.47 (486.68 9.69.44,7 486.688,44 4.77.577.47 (486.68 Hece, the coeffcet of rto for the djusted ler fucto s:,976 t t 8,7 :,7% 8,44 5
- the stuto of the lterte hpothess H : whch specfes the ssupto of the estece for the odel of tedec regrdg Y fctor, where Y the Lfe Epectc, s eg the qudrtc fucto t c, the preters, ş c of the djusted qudrtc fucto, c to e clculted es of the sste []: ( t ( c Therefore, c ( ( ( c c c c c 4 c ( /( ( /( ( /( Tle The esttes of the lue for the rto coeffcet the cse of the djusted qudrtc fucto, the hpothess cocerg the prolc eoluto of the correlto etwee the G.D.P. per cpt d the Lfe Epectc coutres, 4 COUN- TRE G.D.P. per cpt ($ 4 ( Lfe Epec tc 4 ( PARABOLC TREND 4 c t t TALY 5,8 8,6 8879 4597, 986767 JAPAN 6, 84,46 44 47958,75 678668 FRANCE 44,58 8,66 986444 8847,6 6887 UNTED 45,65 8,4 849649 9549,8 KNGDOM 86677 GERMANY 47,59 8,44 6488 778, 7479 AUTRA 5.7 8,7 64849 56,9 744 NETHERLA 5,7 8, 69859 558,8 ND 576 U..A. 54,597 79,56 98849 6744,5 747 WEDEN 58,49 8,89 4978 9, 846477 DENMARK 6,564 79,9 66799896 48,6 66864 TOTAL 486,68 8,44 47755747 4855, 7897 64686,6 8779 7447,55 56 948,64 55 44874,67 884 5955,7 9856 69957,8 94 696598,4 547 88856,85 5447 74589,4 674 454, 59 64768,6 45987 68, 9957 488,4 594 698,57 74 676,75 78 88,6 564 4,69 49,697 66448 4,84 54 86,88 969 9,969 464 9488,65 997 57,74669 4,9 6,58899,96 99,9767 7,5,9497,5,584,6 97,866949 7, 97,65666 6, 85,7576 6, 6,99547 8,97 46,746498,4 8,4959 98,5 f we clculte the sttstcl dt for to djust the qudrtc fucto, we ot for the preters, d c the et lues: 54
55 9488,65997 64768,645987 4855,7897 477,55747 969,447 4855,7897 477,55747 486,68 8,44 477,55747 486,68 c c c 6,664 84647, 4674, c o, the coeffcet of rto for the djusted qudrtc fucto hs the lue: 4,44% 8,44 98,5 : t t - the cse of the lterte hpothess H : whch descres the supposto of the estece for the odel of tedec cocerg Y fctor, where Y the Lfe Epectc, s eg the epoetl fucto t, the the preters d of the djusted epoetl fucto, c to e clculted es of the et sste []: t ( ( /( ( ( /( ( ( Thus, d
Tle 4. The estte of the lue for the rto coeffcet the cse of the djusted epoetl fucto, the hpothess cocerg the epoetl eoluto of the correlto etwee the G.D.P. per cpt d the Lfe Epectc coutres 4 COUN- TRE G.D.P. per cpt ($ 4 ( Lfe Epec tc 4 ( EXPONENTAL TREND t TALY 5.8 8,6,97775 68677,657 JAPAN 6. 84,46,966577 69999,869 FRANCE 44.58 8,66,9976 8557,75 7 UNTED 45.65 8,4,956469 86985,5858 KNGDOM GERMANY 47.59 8,44,95476 968,454 AUTRA 5.7 8,7,94884 97689,77 NETHERLA 5.7 8,,99794 9877,697 ND 6 U..A. 54.597 79,56,9694774 77, 6 WEDEN 58.49 8,89,987 96,786 9 DENMARK 6.564 79,9,898576 4957,85 TOTAL 48668 8,44 9,984 9794,49 6,987776 8,986,,98857 8,85588968,6,945 8,78595,4,99454 8,54444,,99954885 8,7447784,8,979977 8,759695,59,98587 96,77646 5,6,98594 96,89958 7,55,98585 79,779844,,9969 79,4894778,4 9,7 Cosequetl, f we clculte the sttstcl dt for to djust the epoetl fucto, we ot for the preters d the lues: 9,984 9794,496 47755747,9455945 48668 48668 48668 47755747 48668 48668 9,984 9794,496 48668 47755747,744 Accordgl, the coeffcet of rto for the djusted epoetl fucto hs the et lue: ep ep t t 9,7 ep : 4,89% 8,44 We ppl the coeffcets of rto ethod s crtero of selecto for the est odel of tred. We otce tht: 56
,% < ep 4,89% < 4,44% 85 75 5 45 55 THE TREND MODEL BETWEEN THE LFE EXPECTANCY AND THE G.D.P. PER CAPTA N COUNTRE Fgure. The tred odel of the lues regrdg the correlto etwee the Lfe Epectc d the GDP per cpt cotres, 4 We osere tht, the cloud of pots whch reflects the lues of the Lfe Epectc fucto of the G.D.P. per cpt coutres, 4, t crrg roud ler odel of tred, ccordg to the tpe o.. o, the pth reflected the correlto etwee the Lfe Epectc d the G.D.P. per cpt these coutres, 4, s ler tred of the shpe t, wth other words t cofrs the hpothess H.. The test of the correlto etwee the G.D.P. per cpt d the Lfe Epectc 4, for coutres For to reflect the test of the ler correlto etwee the G.D.P. per cpt d the Lfe Epectc 4, for coutres, we use the Perso correlto coeffcet oted wth r []: Tle 5. The clculto of the lue for the correlto coeffcet the cse of the ler correlto etwee the G.D.P. per cpt d the Lfe Epectc 4, for coutres COUNTRE THE G.D.P. THE LFE PER CAPTA EXPECTANCY ( ( TALY 5.8 8,6 8879 687,769 9654,49 JAPAN 6. 84,46 44 7,496 686,7 FRANCE 44.58 8,66 986444 6668,556 6697,8 U. K. 45.65 8,4 849649 6467,764 6744,6 GERMANY 47.59 8,44 6488 647,596 889,6 AUTRA 5.7 8,7 64849 647,89 48,9 NETHERLAND 5.7 8, 69859 658,4544 46777,76 U..A. 54.597 79,56 98849 69,796 4477, WEDEN 58.49 8,89 4978 675,97 478987,99 DENMARK 6.564 79,9 66799896 655,8 4796,76 TOTAL 48668 8,44 47755747 65866, 96944,7 57
58 ] ( ][ ( [ r,74 ] (8,44 65.866, ][ (486.68 4.77.557.47 [ 8,44 486.68 9.69.44,7 cocluso, ecuse the lue of the Perso correlto coeffcet teds to -, there s strog test of the reltoshp etwee the G.D.P. per cpt d the Lfe Epectc 4, for respectel coutres. 4. The ode of the tred etwee the G.D.P. per cpt d the Lfe Epectc etwee - 4, for Ro the perod -4, we osere the et eoluto cocerg the G.D.P. per cpt d the Lfe Epectc Ro, ccordg to the tle o. 6: Tle 6 The eoluto of the G.D.P. per cpt d the Lfe Epectc etwee -4, Ro YEAR GRO DOMETC PRODUCT PER CAPTA N ROMANA (Euro LFE EXPECTANCY N ROMANA 6. 7,74 6.4 7,98 6.4 74, 6.7 74,45 4 6.9 74,69 The sourse: EUROTAT, CA World Fctook We wt to detf the tred odel etwee the G.D.P. per cpt d the Lfe Epectc for Ro, the perod -4, usg the tle o. 6. - f we forulte the ull hpothess H : whch etos the ssupto of the estece for the odel of tedec cocerg fctor, where the Lfe Epectc Ro, s eg the fucto t, the the preters d of the djusted ler fucto, c to e clculted es of the et sste []: Therefore, ( (
YEAR Tle 7 The estte of the lue for the rto coeffcet the cse of the djusted ler fucto, the hpothess cocerg the ler eoluto of the correlto etwee the G.D.P. per cpt Ro d the Lfe Epectc Ro, etwee -4 G.D.P. per cpt Ro (Euro ( LFE EXPECTANCY Ro ( LNEAR TREND 6. 7,74 9.69. 464.56 7,878958,4 6.4 7,98 4.96. 47.47 74,888888,4 6.4 74, 4.96. 475.8 74,888888, 6.7 74,45 44.89. 498.85 74,4469788, 4 6.9 74,69 47.6. 55.6 74,785788, TOTAL.7 7,8 4...47.8 7,79999795,4 f we clculte the sttstcl dt for to djust the ler fucto, we ot for the preters d the lues: 4.. 7,8.7.47.8 5 4.. (.7 5.47.8.7 7,8 5 4.. (.7 Hece, the coeffcet of rto for the djusted ler fucto s:,47965 65,8958,4 :,% 7,8 - the stuto of the lterte hpothess H : whch specfes the ssupto of the estece for the odel of tedec regrdg fctor, where the Lfe Epectc Ro, s eg the qudrtc fucto c, the preters, ş c of the djusted qudrtc fucto, c to e clculted es of the sste []: ( ( c c ( c ( /( ( c ( /( ( c ( /( 59
Therefore, c c 4 c Tle 8. The esttes of the lue for the rto coeffcet the cse of the djusted qudrtc fucto, the hpothess cocerg the prolc eoluto of the correlto etwee the GDP per cpt d the Lfe Epectc coutres, 4 YEAR G.D.P. per cpt Ro (Euro ( LFE EXPEC TANC Y Ro ( 4 PARABOLC TREND c 6. 7,74 5.47...575.96....96.74.6 77,4799464,68 6.4 7,98 6.44...677.7.6.....8 7,7466885, 6.4 74, 6.44...677.7.6.....8 7,7466885,47 6.7 74,45.76...5....4.6.5 7,68974 4,8 4 6.9 74,69 8.59...66.7....555.99.9 77,99556584, TOTAL.4.67.. 9..56.5.. 5.885..6 7,79999994,97 f we clculte the sttstcl dt for to djust the qudrtc fucto, we ot for the preters, d c the et lues: 5.7 4.. c 7,8.7 4...4.67.. c.47.8 4...4.67.. 9..56.5.. c 5.885..6 4.,47894, 599956 c, 954585 o, the coeffcet of rto for the djusted qudrtc fucto hs the lue:,97 :,77% 7,8 - the cse of the lterte hpothess H : whch descres the supposto the ssupto of the estece for the odel of tedec cocerg fctor, where the Lfe Epectc Ro, s eg the epoetl fucto, the the preters d of the djusted epoetl fucto, c to e clculted es of the et sste []: ( ( 6
6 /( ( ( /( ( ( Thus, d Tle 9 The estte of the lue for the rto coeffcet the cse of the djusted epoetl fucto, the hpothess cocerg the epoetl eoluto of the correlto etwee the G.D.P. per cpt Ro d the Lfe Epectc Ro EXPONENTAL TREND YEAR G.D.P. per cpt Ro (Euro ( Lfe Epec tc ( 6. 7,74,8677.766,59796,85567847 7,77884,7 6.4 7,98,86947.96,69668,8544487 7,466489,5 6.4 74,,87595.97,488,8544487 7,46689,75 6.7 74,45,878647.54,49599,8558585887 7,756677,69 4 6.9 74,69,8764594.95,5977,8579487 7,9497599,74 TOTAL.7 7,8 9,5465578 6.67,99986467,6 Cosequetl, f we clculte the sttstcl dt for to djust the epoetl fucto, we ot for the preters d the lues:,866887 4...7.7 5 4.. 6.67,99986467.7 9,54655786
5 9,54655786.7 6.67,99986467,5858 5.7.7 4.. Accordgl, the coeffcet of rto for the djusted epoetl fucto hs the et lue: ep ep,6 ep :,5% 7,8 We ppl the coeffcets of rto ethod s crtero of selecto for the est odel of tred. We otce tht:,% < ep,5% <,77% o, the pth reflected the correlto etwee the Lfe Epectc Ro d the G.D.P. per cpt Ro, etwee -4, s ler tred of the shpe, wth other words t cofrs the hpothess H. 7 6 7 THE TREND MODEL CONCERNNG THE LFE EXPECTANCY AND THE G.D.P. PER CAPTA N ROMANA, N THE PEROD -4 Fgure. The tred odel of the lues for the correlto etwee the Lfe Epectc d the G.D.P. per cpt Ro, the perod -4 We osere tht, the cloud of pots whch reflects the lues of the the Lfe Epectc Ro fucto of the G.D.P. per cpt Ro, etwee -4, t crrg roud ler odel of tred, ccordg to the tpe o.. 6
5. The test of the correlto etwee the G.D.P. per cpt Ro d the Lfe Epectc Ro, the perod -4 For to reflect the test of the ler correlto etwee the G.D.P. per cpt Ro d the Lfe Epectc Ro, etwee -4, we use the Perso correlto coeffcet oted wth r []: Tle The clculto of the lue for the correlto coeffcet the cse of the ler correlto etwee the G.D.P. per cpt Ro d the Lfe Epectc Ro, etwee -4 YEAR THE G.D.P. THE LFE PER CAPTA EXPECTANCY N ROMANA N ROMANA ( ( 6. 7,74 9.69. 5.47,5876 464.56 6.4 7,98 4.96. 5.47,44 47.47 6.4 74, 4.96. 5.58,684 475.8 6.7 74,45 44.89. 5.54,85 498.85 4 6.9 74,69 47.6. 5.578,596 55.6 TOTAL.7 7,8 4.. 7.54,65.47.8 r [ ( ][ ( ] 5.47.8 7,8.7 [5 4.. (.7 ][5 7.54,65 (7,8 ],94 cocluso, ecuse the lue of the Perso correlto coeffcet teds to, there s er strog test of the reltoshp etwee the G.D.P. per cpt Ro d the Lfe Epectc Ro, etwee -4. 6. Coclusos We c to sthesze tht, there s strog test of the correlto etwee the G.D.P. per cpt d the Lfe Epectc the respectel lsed coutres 4 d er strog test of the reltoshp etwee the G.D.P. per cpt d the Lfe Epectc Ro, the perod -4, ecuse the G.D.P. per cpt represets esure of the socetl progress d the effects of h deelopet c e osered o the Lfe Epectc. Refereces []. Guss C. F. - Theor Cotos Osertou Errorus Ms Ooe, Apud Hercu Deterch Pulsg House, Gottge, 8. []. Kr T., Kurt H. - Geerlzed Lest qures, Joh Wle&os Pulshg House, Hooke, 4. []. Perso K. - O the Geerl Theor of skew correlto d o-ler regresso, Dulu&Co Pulshg House, Lodo, 95. [4]. Ro Rdhkrsh C., Touteurg H., Feger A., Heu C., Ntter T., ched. - Ler Models: Lest qures d Altertes, prger eres ttstcs, prger-verlg New York Berl Hedelerg Pulshg House, New-York, 999. [5]. Wolerg J. - Dt Alss Usg the ethod of Lest qures: Etrctg the Most forto fro Eperets, prger-verlg New York Berl Hedelerg Pulshg House, New-York, 6. 6