October 5, 2012

Three first axes of our PCA: Variables Point of View

Circle Correlation analysis extracted from the Principal Component analysis.

The circles griven from our last analysis permit to see the structure or our variables. on the contrary of our individuals analysis we cans see that some groups can be explained easily.

This kind of information permit to extract some groups and give some information to treat different variables as a group and not individually.

The first two axes we can see it in this figure:

Group enumeration and description
  •  PctSpeakEnglOnly : this is an unique element in this class. Apparently the comportment of people whose talking English is independent from the rest of the variables.
  • racePctWhite  ,PctPersOwnOccup ,MedNumBR and  PctHouseOwnOccup compose a class that describes the race white, the owned occupation of the house and the median number of bedrooms. The last element is interesting because in grouping this value with the others we can conclude that the evolution of the number of bed is really connected to the percentage of white people in a community.
  • PctSameHouse85, PctWorkMom and PctWRetire combine the people whose leaving on the same house since 1985, have moms of kids under 18 in labor force and retired. Interesting , we describe a certain stability on the house.
  • PctBornSameState,pctWSocSec,agePct65up and PctVacMore6Mo describe the people whose born on the same state , with social security income, 65 and over in age and housing vacant more than 6 months. Clearly we describe a peaceful state where retired people born in the state live with social income with abandoned house.
  • PctSameState85,PctWorkMomYoungKids, PctSameCity85 and PctEmplManu group the people whose living in the same state, moms of kids 6 and under in labor force, living on the same city and manual employment. We describe a perfect industrial emplacement where people live near their work with moms working with young kids.
  • MedOwnCostPctInc, pctWFarmSelf and PctEmplProfServ describe the people whose are median owners cost as a percentage of household income with a mortgage, with farm or self employment income and employed in professional services. We can summarize in describing a farm with people employed near the farm and living in acceptable but difficult conditions. 
  • PctOccupManu,PctHousNoPhone, MalePctDivorce, TotalPctDiv, PctNotHSGrad, PctPopUnderPov, racepctblack, PctVacantBoarded, FemalePctDiv, PctLess9thGrade, PctUnemployed, pctWPubAsst, PctWOFullPlumb, PctHousLess3BR, PctIlleg and ViolentCrimesPerPop describe the people in social and economics difficulties. I can't describe totally each of this variables but each describe a particular and hard existence. Our variable to determine complete completely this view. We can see with a hard opinion that the social and economic level is really indicate the level of crimes. I don't know,if it s because we have a crime and poverty concentration, that the level of crimes are very important. But we can easily understood that to obtain a more low level crime in a country the most effect that a society can do is to furnish more services to this kind of people in terms of social help to obtain by example a free phone in the house or in adding more help to train and to direct people to new jobs. I can than in having amelioration in social relation we can obtain a better value. I don't talk about the race black because for me it's just a consequence of long social difficulties in US.
  • pctWInvInc,PctKids2Par,PctTeen2Par,PctFam2Par and PctYoungKids2Par correspond on people whose invest in household and having a young family with two kids and one less than 4 years. We understand a perfect family group searching some family stability who paying to loan their house
  • PctHouseOccup,HispPerCap and AsianPerCap appear sufficiently independent to not be considered in a group. 
  • medFamInc,medIncome,perCapInc,PctOccuptMgmtProf,PctEmploy,PctBSorMore,blackPerCap and white per cap describe median family whose working , having higher education and having a good income. This is a perfect family . We can see that black and white are represented in this family. This group is at the opposite of the our variable to predict( the violent crimes). Some stability in social and economic life can reduce considerably the crimes , this is the result of this short study.
  • pctWWage is alone and not linked directly to an other variable
  • pctUrban is not considered in a group.
  • MedRent,RentMedian,RenLowQ,RentHighQ the renting people
  • OwnOccLowQuart, OwnOccHiQuart and OwnOccMedVal are considered on a group whose considering owner occupied housing on low,median and high quartile. 
  • PctUsePubTrans,PersPerOwnOccHous,PersPerOccupHous and householdsize corresponding to people using public transport with a strong house occupation and size. The Big family.
  • MedOwnCostPctInc and racePctAsian correspond to asian whose leaving in a house with mortgage.
  • PersPerFam,PopDens and NumImmig correspond to the immigration and population density. 
  • PctForreignBorn,PctRecentImmig,PctRecImmig5,PctRecImmig8 and PctRecImmig10. Correspond to immigrant from all generation and not born in US
Second and third axes conform on this description

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