names = c("state","county","community","communityname","fold","population","householdsize","racepctblack","racePctWhite","racePctAsian","racePctHisp","agePct12t21","agePct12t29","agePct16t24","agePct65up","numbUrban","pctUrban","medIncome","pctWWage","pctWFarmSelf","pctWInvInc","pctWSocSec","pctWPubAsst","pctWRetire","medFamInc","perCapInc","whitePerCap","blackPerCap","indianPerCap","AsianPerCap","OtherPerCap","HispPerCap","NumUnderPov","PctPopUnderPov","PctLess9thGrade","PctNotHSGrad","PctBSorMore","PctUnemployed","PctEmploy","PctEmplManu","PctEmplProfServ","PctOccupManu","PctOccupMgmtProf","MalePctDivorce","MalePctNevMarr","FemalePctDiv","TotalPctDiv","PersPerFam","PctFam2Par","PctKids2Par","PctYoungKids2Par","PctTeen2Par","PctWorkMomYoungKids","PctWorkMom","NumIlleg","PctIlleg","NumImmig","PctImmigRecent","PctImmigRec5","PctImmigRec8","PctImmigRec10","PctRecentImmig","PctRecImmig5","PctRecImmig8","PctRecImmig10","PctSpeakEnglOnly","PctNotSpeakEnglWell","PctLargHouseFam","PctLargHouseOccup","PersPerOccupHous","PersPerOwnOccHous","PersPerRentOccHous","PctPersOwnOccup","PctPersDenseHous","PctHousLess3BR","MedNumBR","HousVacant","PctHousOccup","PctHousOwnOcc","PctVacantBoarded","PctVacMore6Mos","MedYrHousBuilt","PctHousNoPhone","PctWOFullPlumb","OwnOccLowQuart","OwnOccMedVal","OwnOccHiQuart","RentLowQ","RentMedian","RentHighQ","MedRent","MedRentPctHousInc","MedOwnCostPctInc","MedOwnCostPctIncNoMtg","NumInShelters","NumStreet","PctForeignBorn","PctBornSameState","PctSameHouse85","PctSameCity85","PctSameState85","LemasSwornFT","LemasSwFTPerPop","LemasSwFTFieldOps","LemasSwFTFieldPerPop","LemasTotalReq","LemasTotReqPerPop","PolicReqPerOffic","PolicPerPop","RacialMatchCommPol","PctPolicWhite","PctPolicBlack","PctPolicHisp","PctPolicAsian","PctPolicMinor","OfficAssgnDrugUnits","NumKindsDrugsSeiz","PolicAveOTWorked","LandArea","PopDens","PctUsePubTrans","PolicCars","PolicOperBudg","LemasPctPolicOnPatr","LemasGangUnitDeploy","LemasPctOfficDrugUn","PolicBudgPerPop","ViolentCrimesPerPop")

data = read.csv("communities.data",header=FALSE)

missing = rep(0,128)
for (i in 1:128)
  missing[i] = sum(data[,i]=="?")
ind = 1:128
inds = ind[missing==0]
data = data[,inds]

y = data[,103]
X = as.matrix(data[,4:102])
names = names[inds][4:103]
p = ncol(X)
n = nrow(X)

r2adj = rep(0,p)
for (i in 1:p)
  r2adj[i] = summary(lm(y~X[,i]))$adj.r.squared

ord = order(r2adj,decreasing=TRUE)

plot(r2adj[ord])  

par(mfrow=c(2,5))
for (i in 1:10){
  plot(X[,ord[i]],y,xlab=names[ord[i]],ylab=names[100])
  title(paste("R2 adj=",round(100*r2adj[ord[i]],1),sep=""))
}  

par(mfrow=c(2,5))
for (i in 11:20){
  plot(X[,ord[i]],y,xlab=names[ord[i]],ylab=names[100])
  title(paste("R2 adj=",round(100*r2adj[ord[i]],1),sep=""))
}  

par(mfrow=c(2,5))
for (i in 21:30){
  plot(X[,ord[i]],y,xlab=names[ord[i]],ylab=names[100])
  title(paste("R2 adj=",round(100*r2adj[ord[i]],1),sep=""))
}  

par(mfrow=c(2,5))
for (i in 31:40){
  plot(X[,ord[i]],y,xlab=names[ord[i]],ylab=names[100])
  title(paste("R2 adj=",round(100*r2adj[ord[i]],1),sep=""))
}  

# Standardizing the variables
y   = (y - mean(y))/sqrt(var(y))
mX  = apply(X,2,mean)
sdX = sqrt(apply(X,2,var))
X   = (X-matrix(mX,n,p,byrow=TRUE))%*%diag(1/sdX)

reg = lm(y~X)
sde = sqrt(diag(summary(reg)$sigma*solve(t(X)%*%X)))
L = reg$coef[2:(p+1)]-2*sde
U = reg$coef[2:(p+1)]+2*sde

par(mfrow=c(1,1))
plot(reg$coef[2:(p+1)],pch=16,ylim=range(L,U),
     xlab="Regressor",ylab="Coefficient")
abline(h=0,lty=2)
for (i in 1:p)
  segments(i,L[i],i,U[i])
count = 0
ind = NULL
for (i in 1:p){
  if ((L[i]>0)|(U[i]<0)){
    text(i,1,i,col="2",cex=0.75)
    count = count + 1
    ind = c(ind,i)
  }
}


> names[ind]
 [1] "racepctblack"          "pctUrban"              "PctPopUnderPov"       
 [4] "PctEmploy"             "MalePctNevMarr"        "PctWorkMom"           
 [7] "PersPerRentOccHous"    "PctPersDenseHous"      "PctVacMore6Mos"       
[10] "RentLowQ"              "MedRent"               "MedOwnCostPctIncNoMtg"
[13] "NumStreet"  

#1.percentage of population that is african american
#2.percentage of people living in areas classified as urban
#3.percentage of people under the poverty level
#4.percentage of people 16 and over who are employed
#5.percentage of males who have never married
#6.percentage of moms of kids under 18 in labor force
#7.mean persons per rental household
#8.percent of persons in dense housing (more than 1 person per room)
#9.percent of vacant housing that has been vacant more than 6 months
#10.rental housing - lower quartile rent
#11.median gross rent (Census variable H43A from file STF3A - includes utilities)
#12.median owners cost as a percentage of household income - for owners without a mortgage
#13.number of homeless people counted in the street