stack.dat<-scan(what=list(x1=0,x2=0,x3=0,y=0))
80 27 89 42
80 27 88 37
75 25 90 37
62 24 87 28
62 22 87 18
62 23 87 18
62 24 93 19
62 24 93 20
58 23 87 15
58 18 80 14
58 18 89 14
58 17 88 13
58 18 82 11
58 19 93 12
50 18 89  8
50 18 86  7
50 19 72  8
50 19 79  8
50 20 80  9
56 20 82 15
70 20 91 15

attach(stack.dat)
y<-stack.dat$y
x1<-stack.dat$x1
x2<-stack.dat$x2
x3<-stack.dat$x3
n<-length(y)
Y<-cbind(y,x1,x2,x3)
pairs(Y)
stack.fit<-lm(y~x1+x2+x3)
stack.fit
lms<-summary(stack.fit)
lms
anova(stack.fit)
stack0.fit<-lm(y~x1+x2)
anova(stack0.fit,stack.fit)
fit.model<-stack0.fit
X<-model.matrix(fit.model)
p<-ncol(X)
n<-length(y)
s<-lms$sigma
r<-resid(lms)
h<-lm.influence(fit.model)$hat
ti<-r/(s*sqrt(1-h))
tsi<-ti*sqrt((n-p-1)/(n-p-ti^2))
yh<-fitted(fit.model)
###envelope####
###envelope####
form=y~1+x1+x2
envelope.normal(form,k=20,alfa=0.05)
win.graph()
par(mfrow=c(2,2))
#####grafico do residuos
plot(tsi,xlab="indice",ylab="Residuo Studentizado")
abline(-2,0,lty=2)
abline(2,0,lty=2)
identify(tsi)
plot(yh,tsi,xlab="Valores ajustados",ylab="Residuo Studentizado")
abline(-2,0,lty=2)
abline(2,0,lty=2)
identify(tsi,yh)
plot(x1,tsi,xlab="x1",ylab="Residuo Studentizado")
abline(-2,0,lty=2)
abline(2,0,lty=2)
identify(x1,tsi)
plot(x2,tsi,xlab="x2",ylab="Residuo Studentizado")
abline(-2,0,lty=2)
abline(2,0,lty=2)
identify(x2,tsi)

#####graficos de diagnosticos
 win.graph()
par(mfrow=c(2,2))
plot(h,xlab="indice",ylab="Leverage")
abline(2*p/n,0,lty=2)
abline(3*p/n,0,lty=3)
identify(h,n=2)
di<-(ti^2)*h/(p*(1-h))
plot(di,xlab="indice",ylab="DCook")
dfit<-abs(tsi)*sqrt(h/(1-h))
plot(dfit,xlab="indice",ylab="DFFITS")
abline(2*sqrt(p/(n-p)),0,lty=2)
identify(dfit)
#########Influencia Local
r<-resid(fit.model)
R<-diag(r)
X<-model.matrix(fit.model)
H<-X%*%solve(t(X)%*%X)%*%t(X)
A<-R%*%H%*%R
Lmax<-eigen(A)$val[1]
dmax<-eigen(A)$vec[,1]
dmax<-dmax/sqrt(Lmax)
dmax<-abs(dmax)
plot(dmax,xlab="indice",ylab="dmax")
identify(dmax)
#################grafico da variavel adicionada
fit<-lm(y~x2)
r<-resid(fit)
fit1<-lm(x1~x2)
v<-resid(fit1)
plot(v,r,xlab="residuo v",ylab="residuo r",main="var. adic x1")
abline(lm(r~v-1),lty=2)
#################grafico da variavel adicionada
fit<-lm(y~x1)
r<-resid(fit)
fit1<-lm(x2~x1)
v<-resid(fit1)
plot(v,r,xlab="residuo v",ylab="residuo r",main="var. adic x2")
abline(lm(r~v-1),lty=2)
###Calculando a variacao (%) quando retiramos o ponto
fit<-lm(y~x1+x2)
fit1<-lm(y~x1+x2,subset=-c(21))
sa<-100*((coef(fit1)-coef(fit)) /coef(fit)  )
sfit<-summary(fit)
sfit1<-summary(fit1)
sa1<-100*(sfit1$sigma*sqrt(diag(sfit1$cov.unscaled))-sfit$sigma*sqrt(diag(sfit$cov.unscaled)))/(sfit$sigma*sqrt(diag(sfit$cov.unscaled)))
round(sa,digits=2)
round(sa1,digits=2)