quantitative reasoning ii - final project

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  • QuantitativeReasoningIIFinalProject

    HannahPierceandSarahLeeShanYunPreliminarystage

    Whatishumandevelopment?

    Humandevelopmentistheconceptandsubsequentstudyofhumanlongevityandwellbeingasafactorofnational(orglobal)developmentthattakesprecedentovermeasurementsofeconomicfactors,suchasGDP.Humandevelopmentpairseasilywithsocialjusticeinitiativesandplaysaroleinsocialresearch.Thisconceptmeasuresincreasedwellnessandopportunitiesasindicatorsofgrowth.Education,publichealth,andpublictransportationinfrastructureareallimportanttopicsthathumandevelopmentfocusesupon.Variables

    1. Urbanpopulation(%Urban) isdescribedasthepercentageofthepopulationlivingincitiesinagivenstate.Itismeasuredasapercentage(%)and iscalculatedusingWorldBankPopulation estimatesandurban ratiosfromtheUnitedNationsWorldUrbanizationProspects viastatisticalestimation.1

    2. Percentagepopulationwithlongcommutes(%LongCommute) measuresthepercentage(%)ofthepopulationwithcommutetimesthatare60minutesorlongerandisobtainedthroughsurveyingarepresentativeportionofeachstatespopulation.Thisdataincludesactivecommuters(bikers,walkers,etc.)aswellascommuterstakingpublictransportationorautomobiletransportation).

    3. Percentagepopulationwithabachelor'sdegree(%BA) measuresthepercentageofthepopulation(%)whoholdbachelorsdegreeleveleducation(BA)orhigher.TherewillbeahigherpercentageofBAdegreeholdersthanMAdegreeholdersbecauseaBAisrequiredbeforeanindividualcanpursueanMA.EducationattainmentiscalculatedthroughacensusofU.S.universitiesineachoftheU.S.states.

    4. Percentagepopulationwithagraduatedegree(%MA) measuresthepercentageofthepopulation(%)whoholdmastersdegreeleveleducation(MA)orhigher.EducationattainmentiscalculatedthroughacensusofU.S.universitiesineachoftheU.S.states.

    1"UrbanPopulationData."UrbanPopulationData.TheWorldBank,2015.Web.3Nov.2015.

  • PatternsacrossU.S.states

    Urbanpopulation(%Urban)TheDistrictofColumbiahasthehighesturbanpopulationat100%becausethestateconstitutesWashingtonD.C.ThestatewiththesecondhighesturbanpopulationisCaliforniaat95%.ThestatewiththelowestpercentageurbanpopulationisMaineatonly38.7%.ThemapshowsthepopulationdensityoftheU.S.bycountyin2010 .2

    Stateswiththehighesturbanpopulationstendtobesituatedalongtheeastandwestcoasts,whilstthemidwestconsistsofmoreruralpopulations.Percentagepopulationwithlongcommutes(%LongCommute)NewYorkhasthehighestpercentageoflongcommutersat16.6%.Northeasternstateshavesomeofthehighestpercentagesofcommutesoveronehour.SouthDakotahasthelowestpercentageoflongcommutersat2.6%.TheMidwest,intotheNorthwesthavethelowestpercentageofcommutetimesoveronehour.Percentagepopulationwithabachelorsdegree(%BA)WestVirginiahasthelowestpercentageofpeoplewithbachelorsdegreesat17.5%,whiletheDistrictofColumbiahasthehighestpercentageofcitizenswithbachelorsdegreesat50%,followedbyMassachusettsat39%.ItappearsthatSoutheasternstatestendtohavelowerpercentagesofpeoplethatholdabachelorsdegree,whilestatesintheNortheasthavethehighestpercentageofthoseholdingbachelorsdegrees.Percentagepopulationwithamastersdegree(%MA)ThestatewiththelowestpercentageofthepopulationwithamastersdegreeisArkansas,at6.3%.ThestatewiththehighestnumberofpeoplewithmastersdegreesistheDistrictofColumbia,at26.9%,followedbyMassachusettsat16.7%.Thehighandlowregionaltrendsaresimilartothemeasuresofbachelorsdegrees.

    2"ThematicMaps,Geography."U.S.CensusBureau.U.S.CensusBureau,2010.Web.12Nov.2015..

  • Possiblerelationshipsbetweenvariables/hypotheses

    Frominitialobservationsofthevariables,webelievethatthepercentpopulationwithlongcommuteswillhaveanegativelinearrelationshipwithpercentagepopulationwithabachelorsdegree andpercentagepopulationwithamastersdegree ,butapositivelinearrelationshipwithurbanpopulation .Forexample,stateswithahigherurbanpopulation aremorelikelytohaveahigherpercentpopulationwithlongcommutes.Wepredictthatstateswithhigherurbanpopulationswillhaveahigherpercentagepopulationwithbachelorsandmastersdegrees,andthatthoseholdingthosedegreesliveclosertoworkandarelesslikelytocommuteover60minutestowork.

  • StageOne:UnivariateAnalysis

    Percentagepopulationwithabachelor'sdegree(%BA)Summarystatistics

    Column n Mean Std.dev. Median Range Min Max Q1 Q3

    %BA 51 27.93333 5.723309 27.1 32.6 17.5 50.1 24.5 30.8

    Accordingtothedata,themedianpercentageofpopulationwithabachelorsdegreeis27.1%andthemeanisabout28%.41.1%ofU.S.statescontainpopulationswhere25%to30%ofpeoplehaveatleastabachelorsleveldegree.

    Thedistributionofthecurveispositively(right)skewedwithmoststateshavinga%BApopulationbelowthemean.About70%oftheU.S.stateshave%BApopulationsbetween17.5%to30%.Onlyabout30%ofU.S.stateshave%BApopulationsabove30%.

    1state,inparticular,TheDistrictofColumbiaisanoutlierinthedatawith50.1%ofthepopulationbeingbachelordegreelevelholdersandabove.Excludingtheoutlier,thedatafollowsanormaldistributionveryclosely.

    Onestandarddeviationfromthemeanis22.2%and33.7%.84.3%ofthedatafallswithinonestandarddeviationofthemean,suggestingthatthepercentageofcommutetimesover1hourdonotvarylargelybetweenregionsorstates.

  • Percentagepopulationwithamastersdegree(%MA)Summarystatistics

    Column n Mean Std.dev. Median Range Min Max Q1 Q3

    %MA 51 10.323529 3.4059705 9.4 20.6 6.3 26.9 8.1 11.3

    Accordingtothedata,themedian

    percentageofpopulationwithamastersdegreeis9.4%andthemeanis10.3%.51%ofU.S.statescontainpopulationswhere7.5%to10%ofpeoplehaveatleastamastersleveldegree.

    Thedistributionofthecurveispositively

    (right)skewedwithabout61%ofstateshavinga%MApopulationbelowthemean.MorethanhalfofU.S.stateshave%MApopulationsbetween7.5%to10%.Onlyabout38.5%ofU.S.stateshave%MApopulationsabove10%.

    Again,1state,inparticular,TheDistrict

    ofColumbiaisanoutlierinthedatawith26.9%ofthepopulationbeingmasterdegreelevelholdersandabove.Thedatawithouttheoutlierstillshowsapositive(right)skew.

    Onestandarddeviationfromthemeanis6.0%and12.8%.84.3%ofthedatafallswithinonestandarddeviationofthemean,suggestingthatthepercentageofcommutetimesover1hourdonotvarylargelybetweenregionsorstates.

  • Comparisonofpercentage%BAto%MA

    Overall,thereisamuchlowerpercentageofmastersgraduatesincomparisontobachelorsgraduatesintheU.S.population.Unlikethe%BApopulationdata,%MApopulationisstillpositively(rightskewed)afterexcludingtheoutlier,whichmeansthattherearemorestateswithlower%MApopulationsandverylittlestateswithhigh%MApopulationsrelativetothedataprovided.

  • Urbanpopulation(%Urban)

    Column n Mean Std.dev.

    Median Range Min Max Q1 Q3

    %Urban 51 74.104 14.887 74.2 61.3 38.7 100 64.8 87.9

    Accordingtothedistributionofthedata,

    themedianisanurbanpopulationof74.2%,whilethemeanisnotfaroff,at74.1%.

    Thedatacloselyfollowsanormal

    distribution.Theonlyoutlierforthedata,(bylessthan1%)isTheDistrictofColumbia(Washington,D.C.)withanurbanpopulationof100%.Itdoesnotmakemuchofadifferencetotheappearanceofthedistributionwhenithasbeenremoved,butthemeanandstandarddeviationdecreaseto73.586%and14.567%.Ifanything,thedatahasaslightnegativeskewtotheleft.

    Onestandarddeviationfromthemean

    is59.3%and89.1%.Exactly66.7%ofthedatafallswithinonestandarddeviationofthemean(34outof50statesand1district).

    Thefactthatthedatahasanearnormaldistributionseemslogical,giventhatitaccountsforverydifferentregionsofonecountry.TheEastCoasthaslargelyurbanpopulations,asthereisahigherpopulationdensityinthesestatesthaninmanyWesternstates.Thedistributionreflectsthistrend.

  • Percentagepopulationwithlongcommutes(%LongCommute)

    Column n Mean Std.dev.

    Median Range Min Max Q1 Q3

    %Long

    Commute

    51 6.806 2.851 5.8 14 2.6 16.6 4.9 8.3

    Themeanpercentageofastate

    populationwithcommutesover1hourindurationis6.81%,whilethemedianis5.8%ofastatespopulation.

    Thedistributionisskewedpositivelyto

    theright.Withtheremovaloftheoutliers(Maryland,13.9%,NewJersey,13.9%,andNewYork,16.6%),theskewisfarlessdrastic.Themeandecreasesto6.3%,whilethemediandecreasesto5.75%.

    Forthisdataset,onestandarddeviation

    fromthemeanis4.0%and9.7%.76.5%ofthedatafallswithinonestandarddeviationofthemean,suggestingthatthepercentageofcommutetimesover1hourdonotvarylargelybetweenregionsorstates.Tofurtherresearchthisdataset,itmaybeusefultoseparatestatesbythetypesoftransportationusedforcommutes,ortheaveragedistancetraveledtowork.

  • Stagetwo:bivariateanalysis

    Percentagepopulationwithabachelor'sdegree(%BA)VSurbanpopulation(%Urban)

    Thedatashowsapositiverelationship

    between%BAand%Urban.Asthepercentageofthepopulationwithbachelorsdegreesincreases,thepercentageofurbanpopulationincreasesaswell.

    Thecorrelationcoefficient( r )between%BAand%Urbanis+0.50.Thisshowsamoderatetostronglinearrelationship.

    Theequationfortheregressionlineofbestfitisy=37.88+1.30x.

    TheRsquaredvalue( r 2)between%BAand%Urbanis0.25indicatingthat25%ofthevariabilityofthe%Urbandatacanbeexplainedbythevariabilityofthe%BAdata.

    Percentagepopulationwithamastersdegree(%MA)VSurbanpopulation(%Urban)

    Thedatashowsapositiverelationshipbetween%BAand%Urban.Asthepercentageofthepopulationwithmastersdegreesincreases,thepercentageofurbanpopulationincreasesaswell.

    Thecorrelationcoefficient( r )between%BAand%Urbanis+0.48.Thisshowsamoderatetostronglinearrelationship.

    Theequationfortheregressionlineofbestfitisy=52.23+2.12x.

    TheRsquaredvalue( r 2)between%BAand%Urbanis0.23indicatingthat23%ofthevariabilityofthe%Urbandatacanbeexplainedbythevariabilityofthe%MAdata.

  • Aspredicted,thehigherboth%BAand%MApopulationsofthestate,thehighertheurbanpopulation.Thismightbebecauseastherearemorepeoplewithdegrees,therearemorepeopleintheworkforcewhotendtoliveandworkinmoredenselypopulatedurbancities.Companiesalsotendtocongregateinurbanareasandhirecollegegraduates.

    Percentagepopulationwithabachelor'sdegree(%BA)VSpercentagepopulationwithlongcommutes(%LongCommute)

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