# rm(list=ls())  
options(OutDec = ",") 
#============================================================================
# Exemplo sobre a variancia do estimador do coeficiente angular do 
# modelo de regressao: y = beta0 + beta1*x + epsilon,
# para tamanhos de amostra 1000
# aula_01.pdf
#============================================================================
set.seed(12345)
n       <- 1000    # Tamanho de cada amostra
beta0   <- 0.5     # Intercepto
beta1   <- 0.5     # Coeficiente angular
sigma   <- 0.5     # Desvio padrao do erro
epsilon <- rnorm(n,0,sigma)
# primeira regressao, variancia de x "pequena"
x1      <- rnorm(n,0,1)
y1      <- beta0 + beta1*x1 + epsilon
# segunda regressao, variancia de x "grande"
x2      <- rnorm(n,0,2)
y2      <- beta0 + beta1*x2 + epsilon
xseq    <- seq(-6.5,6.5,length=500)
yseq    <- beta0 + beta1*xseq

par(mfrow=c(1,1),lwd=2.0,cex.lab=1.5,cex.axis=1.3,lab=c(10,10,5),
     mar=c(5,5,2,2.5),cex.main=2.0,bty="n")
plot(x1,y1,pch="*",xlab=expression(x),ylab=expression(y),
     xlim=c(-6.5,6.5),ylim=c(-4,4))
lines(xseq,yseq,col=2,lwd=2)
text(-5,3,"n = 1000")

par(mfrow=c(1,1),lwd=2.0,cex.lab=1.5,cex.axis=1.3,lab=c(10,10,5),
     mar=c(5,5,2,2.5),cex.main=2.0,bty="n")
plot(x2,y2,pch="*",xlab=expression(x),ylab=expression(y),
     xlim=c(-6.5,6.5),ylim=c(-4,4))
lines(xseq,yseq,col=2,lwd=2)
text(-5,3,"n = 1000")

# Somas de quadrados
print(sum((x1-mean(x1))^2))
print(sum((x2-mean(x2))^2))

[1] 1015,759
[1] 3657,902

#============================================================================
# Fim
#============================================================================