data = read.csv("http://hedibert.org/wp-content/uploads/2014/04/dadosmunicipais.csv",header=TRUE)

attach(data)


y = log(rendapercapita[sigla=="MG"])

n = length(y)

x = analfabeto[sigla=="MG"]



pdf(file="renda-anafalbetismo-MG-2010.pdf",width=9,height=6)
par(mfrow=c(1,1))
hist(y,prob=TRUE,xlab="Renda per capita (log)",main="")
title("851 municipios de MG\n Censo 2010")
box()

mean(y)

var(y)


par(mfrow=c(1,1))
boxplot(y,y[x<10],y[(x>=10)&(x<15)],y[(x>=15)&(x<20)],y[(x>=20)&(x<25)],
        y[(x>=25)&(x<30)],y[(x>=30)&(x<35)],y[(x>=35)],ylab="Renda per capita (log)",
        names=c("Todos","x<10","[10,15)","[15,20)","[20,25)","[25,30)","[30,35)","x>=35"),
        xlab="x=taxa de analfabetismo",ylim=c(min(y),max(y)+0.25),main="")
title("851 municipios de MG\n Censo 2010")
text(1,6.5,round(sqrt(var(y)),2),col=4)
text(2,6.5,round(sqrt(var(y[x<10])),2),col=2)
text(3,6.5,round(sqrt(var(y[(x>=10)&(x<15)])),2),col=2)
text(4,6.5,round(sqrt(var(y[(x>=15)&(x<20)])),2),col=2)
text(5,6.5,round(sqrt(var(y[(x>=20)&(x<25)])),2),col=2)
text(6,6.5,round(sqrt(var(y[(x>=25)&(x<30)])),2),col=2)
text(7,6.5,round(sqrt(var(y[(x>=30)&(x<35)])),2),col=2)
text(8,6.5,round(sqrt(var(y[(x>=35)])),2),col=2)



par(mfrow=c(1,1))
plot(x,y,xlab="Taxa de analfabetismo",ylab="Renda per capita (log)",
     main="Minas Gerais")

reg = lm(y~x)


summary(reg)

abline(reg$coef,col=2,lwd=3)


yhat = reg$coef[1]+reg$coef[2]*x

ehat = y - yhat


R2 = 1 - sum(ehat^2)/sum((y-mean(y))^2)

R2

summary(reg)$r.sq


text(30,6,"yhat = 5.88 - 0.043*X",col=2)
text(35,5.7,"SSR = 45.13",col=2)
text(35,5.5,"SST = 149.53",col=2)
text(35,5.3,"R2 = 0.698",col=2)

dev.off()