delivery.dat<-scan(what=list(y=0,x1=0,x2=0))
16.68  7  560 
11.50  3  220 
12.03  3  340 
14.88  4   80 
13.75  6  150 
18.11  7  330 
 8.00  2  110 
17.83  7  210
79.24 30 1460
21.50  5  605 
40.33 16  688 
21.00 10  215 
13.50  4  255 
19.75  6  462 
24.00  9  448 
29.00 10  776 
15.35  6  200 
19.00  7  132 
 9.50  3   36 
35.10 17  770 
17.90 10  140
52.32 26  810
18.75  9  450 
19.83  8  635 
10.75  4  150 

attach(delivery.dat)
y<-delivery.dat$y
x1<-delivery.dat$x1
x2<-delivery.dat$x2
X<-cbind(1,x1,x2)
Y<-cbind(y,x1,x2)
pairs(Y)
delivery<-data.frame(y,x1,x2)
fit.model<-lm(y~1+x1+x2)
fit.model
lms<-summary(fit.model)
lms
anova(fit.model)
p<-2
n<-length(y)
s<-lms$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(22))
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)