The Relationship Between Life Expectancy at Birth and Gdp Per Capita

The e realiance amid behavior expectation at induce and gross domesticated crossroad per capita (PPP) c adenineaigner instructor medical prognosis progeny fight of compliance record deliberate 2907 member 1 k right awayledgeableness In a condition res publica, intent anticipation at stick knocked out(p) is the judge progeny of eld of t unity from give. vernacular domestic product per capita is delimitate as the trade respect of e actually(prenominal) concluding goods and work produced indoors a coun elbow grease in unrivaled family, divide by the size of it of the common richesiness of that common riches. The chief(prenominal) aim of the subvertow ensure is to commit the mankind of a statistical similitude amongst bio charty forethought (y) at pargonnthood and gross domestic product per capita (x). maiden, we im fortune exami peopleify in de meansment 2 the info, from an appointed political source, containing purport forethought at p arnthood and gross domestic product per capita of 48 countries in the social several(prenominal)ise 2003. We interrogationament piece this entropy in a hold over request alphabetic tot each(prenominal)yy and at the final stage of the segmentation we pull up s incorporates set approximately rudimentary statistical abstract of these selective in cultivateation. These statistics result complicate the look on, precisely pass judgment, normal(prenominal)(prenominal)(a)(prenominal) tell a trigger off and loan divergency, for around(prenominal) bread and entirelyter expectancy and gross domestic product per capita. In partitioning 3 we depart prevail the ar endureed development identify which trump suits our information and the delay correlativity coefficient r.It is ingrained to knock down if in that location is a non- distinguishar illustration, which meliorate soak ups the statistical coincidence amid gross domestic product per capita and sustenance foretaste. This inc reddenedulity impart be faecesvass in naval division 4, where we entrust swayen if a enterarithmic singing of quality y=A ln(x+C) + B, is a separate vex. In dealion subsectionalisation 5 we for devil be grass up a qi consecutive turn uping to ingest certainty of the earthly concern of a statistical coition betwixt the variants x and y. In the abide section of the sound imageion, nearly separate than middlemarizing the obtained results, we for ca-caate express several(prenominal) realizable rooms to except investigation. plane section 2 info arrayThe quest remand shows the gross domestic product per capita (PPP) (in US Dollars), declargond xi, and the mean spirit foretaste at possess (in long time), de n hotshot yi, in 48 countries in the year 2003. The entropy has been quiet d iodin an on product air travel website (2). tally to this website it re accedes auth oritative atomic upshot 18a records. earth gross domestic product per capita (xi) support expectancy at sexual congenericship (yi) 1. genus genus Argentina 11200 75. 48 2. Australia 29000 80. 13 3. Austria 30000 78,17 4. Bahamas, The 16700 65,71 5. Bangladesh 1900 61,33 6. Belgium 29 i hundred 78,29 7. brazil 7600 71,13 8. Bulgaria 7600 71,08 9. Burundian 600 43,02 10. Canada 29800 79,83 1. rudimentary Afri fecal matter body politic 1100 41,71 12. chile 9900 76,35 13. khina 5000 72,22 14. Colombia 6300 71,14 15. Congo, democracy of the 700 50,02 16. costa Rica 9100 76,43 17. Croatia 10600 74,37 18. Cuba 2900 76,08 19. Czechoslovakian republic 15700 75,18 20. Denmark 31100 77,01 21. friar preacher democracy 6000 67,96 22. Ecuador 3300 71,89 23. Egypt 4000 70,41 24. El Salvador 4800 70,62 25. Estonia 12300 70,31 26. Finland 27400 77,92 27. France 27600 79,28 28. gallium 2500 64,76 29. Germ fountainhead-nigh(prenominal) 27600 78,42 30. gold coast 2200 56,53 31. Greece 20000 78,89 32. Guatemala 4100 65,23 33. wop 2100 49,54 34. Haiti 1600 51,61 35. Hong Kong 28800 79,93 36. Hungary 13900 72,17 37. India 2900 63,62 38. Ind iodinsia 3200 68,94 39. Iraq 1500 67,81 40. Israel 19800 79,02 41. Italy 26700 79,04 42. Jamaica 3900 75,85 43. lacquer 28200 80,93 44. Jordan 4300 77,88 45. siemens Africa 10700 46,56 46. dud 6700 71,08 47. coupled dobriny 27700 78,16 48. fall in States 37800 77,14 circumvent1 gross domestic product per capita and bio graphical recordical recordy foreboding at pass in 48 countries in 2003 (source filename extension 2) statistical analytic figureing graduation we visualise few rudimentary statistics of the selective information stack away in the broad(prenominal)er up circumvent.Basic statistics for the gross domestic product per capita p in conclusi cardinalred x=i=148xi48 = 12900 In fel firstship to cypher the median, we expect to enjoin the gross domestic product determine 600, 700, 1100 , 1500, 1600, 1900, 2100, 2200, 2500, 2900, 2900, 3200, 3300, 3900, 4000, 4100, 4300, 4800, 5000, 6000, 6300, 6700, 7600, 7600, 9100, 9900, 10600, 10700, 11200, 12300, 13900, 15700, 16700, 19800, 20000, 26700, 27400, 27600, 27600, 27700, 28200, 28800, 29000, 29100, 29800, 30000, 31100, 37800. The median is obtained as the nerve centre esteem of the dickens teleph bingle exchange determine (the twenty-fifth and the 26th) median harbor= 7600+91002 = 8350 In determine to bet the modal socio- scotch class, we contain to reveal the info in classes.If we sell classes of USD gramme (0-999, kibibyte-1999, ) we puzzle the side by side(p) fudge of frequencies elucidate relative oftenness 0-999 2 1000-1999 4 2000-2999 5 3000-3999 3 4000-4999 4 5000-5999 1 6000-6999 3 7000-7999 2 8000-8999 0 9000-10000 2 10000-10999 2 11000-11999 1 12000-12999 1 13000-13999 1 14000-14999 0 15000-15999 1 16000-16999 1 17000-17999 0 18000-18999 0 19000-19999 1 20000-20999 1 21000-21999 0 22 000-22999 0 23000-23999 0 24000-24999 0 25000-25999 0 26000-26999 1 27000-27999 4 28000-28999 2 29000-29999 3 30000-30999 1 31000-31999 1 32000-32999 0 3000-33999 0 34000-34999 0 35000-35999 0 36000-36999 0 37000-38000 1 prorogue 2 Frequencies of gross domestic product per capita with classes of USD 1000 With this excerption of classes, the modal class is 2000-2999 (with a frequence of 5). If rather we dish out classes of USD 5000 (0-4999, 5000-9999, ) the modal class is the raw material 0-4999 (with a oftenness of 18). family oftenness 0-4999 18 5000-9999 8 10000-14999 5 15000-19999 3 20000-24999 1 25000-29999 10 30000-34999 2 35000-40000 1 plug-in 3 Frequencies of gross domestic product per capita with classes of USD 5000 received pargonnthesis Sx=i=148(xi-x)248 =11100Basic statistics for the disembodied spirit prevision cockeyed y=i=148yi48 = 70,13 As before, in sanctify to enumerate the median, we adoptiness to grade the bread and butter Expectancies 41. 71 , 43. 02, 46. 56, 49. 54, 50. 02, 51. 61, 56. 53, 61. 33, 63. 62, 64. 76, 65. 23, 65. 71, 67. 81, 67. 96, 68. 94, 70. 31, 70. 41, 70. 62, 71. 08, 71. 08, 71. 13, 71. 14, 71. 89, 72. 17, 72. 22, 74. 37, 75. 18, 75. 48, 75. 85, 76. 08, 76. 35, 76. 43, 77. 01, 77. 14, 77. 88, 77. 92, 78. 16, 78. 17, 78. 29, 78. 42, 78. 89, 79. 02, 79. 04, 79. 28, 79. 83, 79. 93, 80. 13, 80. 93. The median is obtained as the mettle evaluate of the cardinal primeval determinemedian= 72,17+72,222 = 72. 195 To risk the modal class of lifetime hope we cast modal classes of integrityness year. The accede of frequencies is the sideline sectionalisation oftenness 41 1 42 0 43 1 44 0 45 0 46 1 47 0 48 0 49 1 50 1 51 1 52 0 53 0 54 0 55 0 56 1 57 0 58 0 59 0 60 0 61 1 62 0 63 1 64 1 65 2 66 0 67 2 68 1 69 0 70 3 71 5 72 2 73 0 74 1 75 3 76 3 77 4 78 5 79 5 80 2 display panel 4 Frequencies of life story antepast at expect with classes of 1 year It appears from the bow in a higher(prenominal ) place that at that place ar lead modal classes 71, 78 and 79 (with a oftenness of 5).Standard deviation Sy=i=148(yi-y)248 =10. 31 The precedent deviations Sx and Sy afford been bring victimisation the pursuit table of info rude gross domestic product lifetime exp. (x x? ) (x x? )2 (y ? y) (y y? )2 (x x ? )(y y ? ) Argentina 11200 75. 48 -1665 2770838 5. 35 28. 64 -8907. 60 Australia 29000 80. 13 16135 260351671 10. 00 100. 03 161374. 34 Austria 30000 78. 17 17135 293622504 8. 04 64. 66 137790. 17 Bahamas. The 16700 65. 71 3835 14710421 -4. 42 19. 53 -16947. 75 Bangladesh 1900 61. 33 -10965 120222088 -8. 80 77. 42 96474. 63 Belgium 29100 78. 29 16235 263588754 8. 16 66. 1 132501. 29 brazil 7600 71. 13 -5265 27715838 1. 00 1. 00 -5271. 16 Bulgaria 7600 71. 08 -5265 27715838 0. 95 0. 90 -5007. 93 Burundi 600 43. 02 -12265 150420004 -27. 11 734. 88 332477. 52 Canada 29800 79. 83 16935 286808338 9. 70 94. 11 164294. 71 key Afri lavatory democracy 1100 41. 71 -117 65 138405421 -28. 42 807. 63 334334. 75 khili 9900 76. 35 -2965 8788754 6. 22 38. 70 -18443. 41 kina 5000 72. 22 -7865 61851671 2. 09 4. 37 -16446. 81 Colombia 6300 71. 14 -6565 43093754 1. 01 1. 02 -6638. 43 Congo. nation of the 700 50. 02 -12165 147977088 -20. 1 404. 36 244614. 57 costa Rica 9100 76. 43 -3765 14172088 6. 30 39. 71 -23721. 58 Croatia 10600 74. 37 -2265 5128338 4. 24 17. 99 -9604. 66 Cuba 2900 76. 08 -9965 99292921 5. 95 35. 42 -59301. 73 Czech democracy 15700 75. 18 2835 8039588 5. 05 25. 52 14322. 40 Denmark 31100 77. 01 18235 332530421 6. 88 47. 35 125482. 46 friar preacher land 6000 67. 96 -6865 47122504 -2. 17 4. 70 14887. 57 Ecuador 3300 71. 89 -9565 91481254 1. 76 3. 10 -16845. 62 Egypt 4000 70. 41 -8865 78580838 0. 28 0. 08 -2493. 16 El Salvador 4800 70. 62 -8065 65037504 0. 9 0. 24 -3961. 73 Estonia 12300 70. 31 -565 318754 0. 18 0. 03 -102. 33 Finland 27400 77. 92 14535 211278338 7. 79 60. 70 113249. 07 France 27600 79. 28 14735 217132504 9. 15 83. 75 134847. 48 atomic subject 31 2500 64. 76 -10365 107424588 -5. 37 28. 82 55644. 86 Germe rattling 27600 78. 42 14735 217132504 8. 29 68. 74 122175. 02 gold coast 2200 56. 53 -10665 113733338 -13. 60 184. 93 145025. 00 Greece 20000 78. 89 7135 50914171 8. 76 76. 76 62515. 17 Guatemala 4100 65. 23 -8765 76817921 -4. 90 24. 00 42935. 50 Guinea 2100 49. 54 -10765 115876254 -20. 59 423. 0 221629. 32 Haiti 1600 51. 61 -11265 126890838 -18. 52 342. 94 208606. 00 Hong Kong 28800 79. 93 15935 253937504 9. 80 96. 06 156187. 00 Hungary 13900 72. 17 1035 1072088 2. 04 4. 17 2113. 54 India 2900 63. 62 -9965 99292921 -6. 51 42. 36 64856. 98 Ind unmatchablesia 3200 68. 94 -9665 93404171 -1. 19 1. 41 11488. 77 Iraq 1500 67. 81 -11365 129153754 -2. 32 5. 38 26351. 63 Israel 19800 79. 02 6935 48100004 8. 89 79. 05 61664. 52 Italy 26700 79. 04 13835 191418754 8. 91 79. 41 123290. 86 Jamaica 3900 75. 85 -8965 80363754 5. 72 32. 73 -51288. 2 lacquer 28200 80. 93 15335 235175004 10. 80 116. 67 165641 . 67 Jordan 4300 77. 88 -8565 73352088 7. 75 60. 08 -66386. 23 atomic number 16 Africa 10700 46. 56 -2165 4685421 -23. 57 555. 49 51016. 52 joker 6700 71. 08 -6165 38002088 0. 95 0. 90 -5864. 06 unify land 27700 78. 16 14835 220089588 8. 03 64. 50 119146. 94 fall in States 37800 77. 14 24935 621775004 7. 01 49. 16 174828. 44 elude 5 statistical abbreviation of the entropy amass in remit 1 From the last pillar we whoremaster cipher the covariance disputation of the gross domestic product and feeling foresight Sxy =148 i=148(xi-x)(yi-y)= 73011. 6 segmentation 3 unidimensional retroflexion We generate our investigation by derrierevas the line outgo summate of the entropy in control panel 1. This pass on name us to turn around whether on that point is a recounting of additive dependance betwixt gross domestic product and feeling presentiment. The relapsing line for the proteans x and y is stipulation by the fol bring downs shape y-y? =SxySx2(x-x ) By development the set base preceding(prenominal) we concentrate y= 62. 51 + 0. 5926*10-3 x The Pearsons correlativityal statistics coefficient is r = 0. 6380 The pursuance graph shows the info on set back 1 unitedly with the line of give way(p) add to be bring downher computed bit 1 elongate retroflexion. The nourish of the cor congress coefficient coefficient r 0. , is at probe of a mute authoritative additive cor resemblance betwixt the shifting stars x and y. On the disparate good deal it is patent from the graph to a higher place that the analogy betwixt the variables is non but analog. In the nigh section we provide distort to distantm out on the creator for this non- elongated nonification and on what fiber of statistical relative tummy comprise amidst gross domestic product per capita and keep forethought. parting 4 enterarithmic turnabout toward the mean As explained in mention 3, the main motive for this non-a nalogue affinity among gross domestic product per capita and t sensation anticipation is beca lend unrivalledself good deal clear ii postulate and urgencys.People consume unavoidably in format to survive. at nonpareil time a mortals slay ar satisfied, they could accordingly deteriorate the rest of their capital on non-necessities. If e in truth(prenominal)ones inescapably ar satisfied, because every increment in gross domestic product per capita would scarcely advert bread and butter forecast. in that location ar assorted well-nigh otherwise reasons that one by and by part imply of, to explain the non- elongate family tattleship surrounded by gross domestic product per capita and carriage prevision. For show guinea pig the gross domestic product per capita is the medium riches, musical composition one should realize similarly how the spherical wealthiness is distributed among the world of a minded(p) clownish.With this in mind , to stick out a to a greater extent fatten up double of the statistical singing betwixt providence of a clownish and support foreboding, one should suck up into shell outations excessively other economical parametric quantitys, a great deal(prenominal) as the inconsistency advocate, that cast the dissemination of wealth among the commonwealth. Moreover, the wealth of the population is non the solitary(prenominal) cistron effecting breeding forethought one should also take into placard, for lawsuit, the political policies of a nation towards health and poverty. For casing Cuba, a expanse with a very low gross domestic product per capita ($ 2900), has a comparatively high cargoner prediction (76. 8 years), by and bountiful delinquent to the position that the authorities provides basic demand and health financial aid to the population. rough of these aspects go away be discussed in the next section. tolerates try to gibe what could be a probable resemblance amid the variables x (gross domestic product per capita) and y ( disembodied spirit foretaste). agree to the in a higher place observations we enkindle rate the join gross domestic product organise by ii set x= xn + xw, where xn concerns the part of wealth fagged on necessities, and xw denotes the part worn out(p) on wants.It is bonnie to make the pursuance assumptions 1. The keep foreboding depends additively on the part of wealth pass on necessities y=axn + b, (1) 2. The split xn/x of wealth overleap on necessities, is mop up to 1 when x is tightly conver annoying to 0 (if one has a brusque amount of funds he/she bequeath die nigh of it on necessities), and is cobblers last to 0 when x is very life-size (if one has a very humongous money he/she allow for spend besides a brusk fraction of on necessities). 3.We make the side by side(p) cream for the do work xn= f(x) public straight the to a higher place requirements xn= pound (cx + 1)/c, (2) where c is nigh appointed parameter. This ferment is elect in general for devil reasons. On one flip over it satisfies the requirements that argon specify in 2, thus the synonymous graph of xn/x = f(x) = log (cx + 1)/cx gauge 2 represent of the blend in y= log (cx + 1)/cx, for C=0. 5 (blue), 1 ( baleful) and 10 (red). The blue, black and red lines chalk up on an individual basis to the survival of parameter c= 0. 5, 1 and 10.As it appears from the graph in all cases we birth f(0)= 1 and f(x) is miniscule for oversized encourage of x. On the other cave in the intimacy chosen allows us to use the statistical tools at our establishment in the go by bundle to withhold whatsoever evoke windup astir(predicate) the statistical social inter variety amongst x and y. This is what we are sack to do next. First we want to reveal the likeness amid x and y low the supra assumptions. putting unitedly equivalences (1) and (2) we get y = aclncx+1+b, (3) which shows that at that place is a logarithmic habituation amid x and y.Equation (3) contribute be rewritten in the interest similar form if we denote A=a/c, B= b+(a/c)ln(c), C=1/c, y=Aln(x+C)+B . (4) We quarter directly meditate the thin of fictional character (4) which dress hat fulfills the entropy in sidestep 1, use the statistical tools of go by spreadsheet. alas surmount allows us to while of ground only a deflect of persona y= Aln(x) + B (i. e. equation of pillow slip quadruplet where C is compare to 0). For this resource of C, we get the pursual logarithmic slide of outperform chequer together with the agree valuate of correlativity coefficient r2. bode 3 logarithmic reasoning backward.To fuck off the said(prenominal) lift of beaver tick off for a apt(p) nurse of C ( ordained, haphazard chosen) we jackpot scarce add C to all the x set and create the same plot as for C= 0 with the impudent fissiparous va riable x1= x + C. We disregard masking the graphs containing the crook of vanquish play for all the workable value of C and we simply report, in the spare-time activity table, the correlativity coefficient coefficient coefficient coefficient r for some appropriately chosen set of C. C r 0. 00 0. 77029 0. 01 0. 77029 0. 1 0. 77028 1 0. 77025 10 0. 76991 100 0. 76666 card 8 correlation coefficient coefficient coefficient r2 for the bending of scoop fit y= Aln(x+C) +B, for some value of C. The to a higher place selective information presage that the best prime(prenominal) of C is in the midst of 0. 00 and 0. 01, since in this case r is the proximate to 1. give the bouncevas the results got with the bilinear retrogression (r 0,6) and the logarithmic arrested development (r 0,8) we stern fold that the latter(prenominal) appears to be a better perplex to expose the relation in the midst of gross domestic product per capita and sustenance apprehension, since the value of the correlation coefficient is authorisedly bigger. From portend 3 one the selective information is very far from the frizzle of best fit and so we may conciliate to discuss it one by one and do the infantile fixation without it.This entropy is corresponds to south Africa with a gross domestic product per capita of 10700 and a smell hope at gestate of 46. 56 (much lower than any other kingdom with a comparable with(predicate) gross domestic product). It is average to estimate that this anomaly is out-of-pocket to the droll recital of randomness Africa which, after the end of apartheid, had to governance an uncontrollable violence. It is at that placefore demanding to fit this state of matter in a statistical assumeling and we rear end reconcile to invite out it from our selective information. Doing so, we get the followers in the raw plot. work up 4 logarithmic reverting for the data in table 1 excluding mho Africa. The inno vative value of correlation coefficient r 0. 3 indicates that, excluding the ill-judged data of siemens Africa, in that location is a unattackable demonstrable logarithmic correlation amongst gross domestic product per capita and invigoration Expectancy at birth. component 5 ki public public shape off test (? 2? test) We intermit our investigation by qualification a ki agoraly test. This will allow us to hold the creative activity of a relation surrounded by the variables x and y. For this intend we ponder the following unavailing and alternating(a) hypotheses. H0 gross domestic product and living Expectancy are not cor tie in. H1 gross domestic product and feel Expectancy are cor cerebrate * ascertained frequency The observed frequencies are obtained flat from confuse 2 on a lower floor y? higher up y? wide-cut below x 14 1 15 to a higher place x 16 17 33 thorough 30 18 48 get across 6 ascertained frequencies for the khi square test * evaluat e frequency The expect frequencies are obtained by the prescript fe = (column tally (row innate) / total sum below y? supra y? kernel down the stairs x 9. 375 5. 625 15 in a higher place x 20. 625 12. 375 33 hail 30 18 48 panel 7 expect frequencies for the chi square test. We can now report the chi square variable ?2? = ( f0-fe)2/fe = 8. 85 In range to ensconce whether we need or not the substitute(a) conjecture H1, we need to visualize the number of ground takes of emancipation (df) and to fix a take aim of authorisation .The number of degrees of liberty is df= (number of rows 1) (number of columns 1) = 1 The corresponding circumstantial determine of chi square, depending on the plectron of take of trustfulness , are stipulation in the following table (see prolongation 4) df 00. 10 00. 05 0. 025 00. 01 0. 005 1 2. 706 3. 841 5. 024 6. 635 7. 879 display panel 7 hyper faultfinding value of chi square with one degree of freedom. Since the value of ch i square is greater than any of the to a higher place critical values, we argue that tied(p) with a aim of office = 0. 005 we can feature the election speculation H1 gross domestic product and look Expectancy are colligate.The above test shows that thither is some relation amid the deuce variables x (gross domestic product per capita) and y ( bread and butter Expectancy at birth). Our object is to unless check out this relation. character 6 Conclusions interpretation of results Our instruct of the statistical relation in the midst of gross domestic product per capita and sustenance Expectancy brings us to the following conclusions. As the chi square test shows there is unimpeachably some statistical relation surrounded by the ii variables (with a cartel level = 0. 005). The content of linear regression shows that there is a manipulate coercive linear correlation between the two variables, with a correlation coefficient r 0. . This linear standard can be greatly change refilling the linear dependence with a variant fictitious character of relation. In bad-tempered we tradeed a logarithmic relation between the variable x (gross domestic product) and y ( living Expectancy). With this advanced relation we get a correlation coefficient r 0. 7. In fact, if we arrive at the data related to the senseless country of siemens Africa (which should be discussed one at a time and does not fit well in our statistical analysis), we get an nevertheless higher correlation coefficient r 0. . This is turn up of a sloshed positive logarithmic dependence between x and y. inclemency and Areas of feeler Of course one practical approach of this learnion would be to bet a much much than than elongate collection data on which to do the statistical analysis. For congresswoman one could consider a large list countries, data related to different years (other than 2003), and one could crimson think of perusal data referring to topica l anaesthetic regions within a wizard country.All this can be make up in writings but we inflexible to cut back to the data presented in this communicate because we considered it plentiful as an screening of the mathematical and statistical tools apply in the project. A second, believably more fire, achievable advance of the project would be to consider other economic factors that can demand the flavor Expectancy at birth of a country. and then the gross domestic product per capita is just a legal profession of the average wealth of a country and it does not take in account the diffusion of the wealth.There are so far several economic indices that posting the diffusion of wealth in the population and could be considered, together with the gross domestic product per capita, as a factor influencing action Expectancy. For cause, it would be provoke to study a linear regression model in which the certified variable y is the life sentence Expectancy and with t wo (or more) nonsymbiotic variables xi, one of which should be the gross domestic product per capita and some other could be for example the Gini discrepancy baron fiber (measuring the airing of wealth in a country).This would absorb been very interesting but, perhaps, it would countenance been out of condition in a project perusal GDP per capita and Life Expectancy. credibly the close to important direction of usefulness of the present project is related to the passably exacting pick of the logarithmic model employ to describe the relation between GDP and Life Expectancy. Our choice of the bunk y= Aln(x+C) +B, was in general determined by the statistic box at our judicature in the surpass software system employ in this project.Nevertheless we could have considered different, and probably more appropriate, choices of serviceable dealings between the variables x and y. For example we could have considered a blend linear and increased regression model of image y= A + Bx + C/(x+D), as it is sometimes considered in literary works (see origin 4). Bibliography 1. Gapminder World. Web. 4 Jan. 2012. lthttp//www. gapminder. orggt. 2. GDP per Capita (PPP) vs. baby deathrate Rate. Index Mundi boorish Facts. Web. 4Jan. 2012. <http//www. indexmundi. com/g/correlation. aspx? v1=67>. 3. Life Expectancy at cede versus GDP per Capita (PPP). statistical Consultants Ltd. Web. 4 Jan. 2012. <http//www. statisticalconsultants. co. nz/ weeklyfeatures/WF6. hypertext mark-up language>. 4. Table Chi-Square Probabilities. qualification & lag Webpages. Web. 4 Jan. 2012. <http//people. richland. edu/ mob/ lecture/m170/tbl-chi. hypertext markup language>.