Statistical Modeling and Analysis of the Correlation between the Gross Domestic Product per Capita and the Life Expectancy

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Norah Manning
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1 Als of Dure de Jos Uerst of Glt Fsccle. Ecoocs d Appled fortcs Yers XX o /5 N-L N-Ole 44-44X 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 ,66 UNTED KNGDOM ,4 GERMANY ,44 AUTRA 5.7 8,7 NETHERLAND 5.7 8, U..A ,56 WEDEN ,89 DENMARK ,9 ource: EUROTAT Fcult of Ecoocs d Busess Adstrto, Dure de Jos Uerst of Glt, Ro. E-l ddress: gopt@ugl.ro (G. Opt

2 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, ,49 8,95554, JAPAN 6. 84, ,7 8,8665,6 FRANCE , ,8 8,754659,6 UNTED , ,6 8, ,4 KNGDOM GERMANY , ,6 8,889857,85 AUTRA 5.7 8, ,9 8,769487,6 NETHERLAND 5.7 8, ,76 8, ,6 U..A , , 8,9588,75 WEDEN , ,99 79, , DENMARK , ,76 79,475669,9 TOTAL , ,7 8, ,7 f we clculte the sttstcl dt for to djust the ler fucto, we ot for the preters d the lues: , ,7 87, ( , , ( Hece, the coeffcet of rto for the djusted ler fucto s:,976 t t 8,7 :,7% 8,44 5

3 - 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, , JAPAN 6, 84, , FRANCE 44,58 8, , UNTED 45,65 8, ,8 KNGDOM GERMANY 47,59 8, , 7479 AUTRA 5.7 8, ,9 744 NETHERLA 5,7 8, ,8 ND 576 U..A. 54,597 79, ,5 747 WEDEN 58,49 8, , DENMARK 6,564 79, , TOTAL 486,68 8, , , , , , , , , , , , , , , , , , ,69 49, , , , , , ,9 6,58899,96 99,9767 7,5,9497,5,584,6 97, , 97, , 85,7576 6, 6, ,97 46,746498,4 8, ,5 f we clculte the sttstcl dt for to djust the qudrtc fucto, we ot for the preters, d c the et lues: 54

4 , , , , , , , ,68 8,44 477, ,68 c c c 6, , 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

5 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, ,657 JAPAN 6. 84,46, ,869 FRANCE ,66, ,75 7 UNTED ,4, ,5858 KNGDOM GERMANY ,44, ,454 AUTRA 5.7 8,7, ,77 NETHERLA 5.7 8,, ,697 ND 6 U..A ,56, , 6 WEDEN ,89,987 96,786 9 DENMARK ,9, ,85 TOTAL ,44 9, ,49 6, ,986,, , ,6,945 8,78595,4, ,54444,, , ,8, ,759695,59, , ,6, , ,55, ,779844,, , ,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, , , , , ,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.

6 ,% < ep 4,89% < 4,44% 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, , ,49 JAPAN 6. 84, , ,7 FRANCE , , ,8 U. K , , ,6 GERMANY , , ,6 AUTRA 5.7 8, ,89 48,9 NETHERLAND 5.7 8, , ,76 U..A , , , WEDEN , , ,99 DENMARK , ,8 4796,76 TOTAL , , 96944,7 57

7 58 ] ( ][ ( [ r,74 ] (8, , ][ ( [ 8, ,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, , , , ,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 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, ( (

8 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, ,878958, , ,888888, , ,888888, , , , , ,785788, TOTAL.7 7, , ,4 f we clculte the sttstcl dt for to djust the ler fucto, we ot for the preters d the lues: 4.. 7, ( , (.7 Hece, the coeffcet of rto for the djusted ler fucto s:, ,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

9 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, , , , , , , , , , , , , , , TOTAL , ,97 f we clculte the sttstcl dt for to djust the qudrtc fucto, we ot for the preters, d c the et lues: c 7, c c ,47894, c, 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

10 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, ,59796, ,77884, ,98, ,69668, ,466489, ,, ,488, ,46689, ,45, ,49599, ,756677, ,69, ,5977, , ,74 TOTAL.7 7,8 9, , ,6 Cosequetl, f we clculte the sttstcl dt for to djust the epoetl fucto, we ot for the preters d the lues:, , ,

5 9,54655786.7 6.67,99986467,5858 5.7.7 4.

11 5 9, , , 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 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

12 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, , , , , , , , , , TOTAL.7 7, , r [ ( ][ ( ] ,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 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

CURVE FITTING LEAST SQUARES METHOD

CURVE FITTING LEAST SQUARES METHOD Nuercl Alss for Egeers Ger Jord Uverst CURVE FITTING Although, the for of fucto represetg phscl sste s kow, the fucto tself ot be kow. Therefore, t s frequetl desred to ft curve to set of dt pots the ssued