library(faraway)
data(longley)
g <- lm(Employed ~ GNP + Population, longley)
summary(g,cor=T)
cor(longley$GNP,longley$Pop)
cor(residuals(g)[-1],residuals(g)[-16])
x <- model.matrix(g)
Sigma <- diag(16)
Sigma <- 0.31041^abs(row(Sigma)-col(Sigma))
Sigi <- solve(Sigma)
xtxi <- solve(t(x) %*% Sigi %*% x)
(beta <- solve(t(x) %*% Sigi %*% x,t(x) %*% Sigi %*% longley$Empl))
res <- longley$Empl - x %*% beta
(sig <- sqrt((t(res) %*% Sigi %*% res)/g$df))
sqrt(diag(xtxi))*sig
sm <- chol(Sigma)
smi <- solve(t(sm))
sx <- smi %*% x
sy <- smi %*% longley$Empl
summary(lm(sy ~ sx-1))
cor(res[-1],res[-16])
library(nlme)
g <- gls(Employed ~ GNP + Population,correlation=corAR1(form= ~Year), data=longley)
summary(g)
intervals(g)
data(fpe)
fpe
fpe$N <- fpe[,12]+fpe[,13]-apply(fpe[,2:11],1,sum)
g <- lm(A2 ~ A+B+C+D+E+F+G+H+J+K+N-1, fpe, weights=1/EI)
coef(g)
lm(A2 ~ A+B+C+D+E+F+G+H+J+K+N-1, fpe)$coef
lm(A2 ~ A+B+C+D+E+F+G+H+J+K+N-1, fpe, weights=53/EI)$coef
lm(A2 ~ offset(A+G+K)+C+D+E+F+N-1, fpe, weights=1/EI)$coef
data(corrosion)
plot(loss ~ Fe, corrosion,xlab="Iron content",ylab="Weight loss")
g <- lm(loss ~ Fe, corrosion)
summary(g)
abline(coef(g))
ga <- lm(loss ~ factor(Fe), corrosion)
points(corrosion$Fe,fitted(ga),pch=18)
anova(g,ga)
gp <- lm(loss ~ Fe+I(Fe^2)+I(Fe^3)+I(Fe^4)+I(Fe^5)+I(Fe^6),corrosion)
plot(loss ~ Fe, data=corrosion,ylim=c(60,130))
points(corrosion$Fe,fitted(ga),pch=18)
grid <- seq(0,2,len=50)
lines(grid,predict(gp,data.frame(Fe=grid)))
summary(gp)$r.squared
data(gala)
gl <- lm(Species ~ Area + Elevation + Nearest + Scruz + Adjacent,gala)
summary(gl)
library(MASS)
gr <- rlm(Species ~ Area + Elevation + Nearest + Scruz + Adjacent,gala)
summary(gr)
library(quantreg)
gq <- rq(Species ~Area+Elevation+Nearest+Scruz+Adjacent,data=gala)
summary(gq)
g <- ltsreg(Species ~ Area + Elevation + Nearest + Scruz + Adjacent,gala)
coef(g)
g <- ltsreg(Species ~ Area + Elevation + Nearest + Scruz + Adjacent,gala)
coef(g)
g <- ltsreg(Species ~ Area + Elevation + Nearest + Scruz + Adjacent, gala,nsamp="exact")
coef(g)
sample(10,rep=T)
residuals(g)[sample(30,rep=TRUE)]
x <- model.matrix( ~ Area+Elevation+Nearest+Scruz+Adjacent,gala)[,-1]
bcoef <- matrix(0,1000,6)
for(i in 1:1000){
newy <- predict(g) + residuals(g)[sample(30,rep=T)]
brg <- ltsreg(x,newy,nsamp="best")
bcoef[i,] <- brg$coef
}
quantile(bcoef[,2],c(0.025,0.975))
plot(density(bcoef[,2]),xlab="Coefficient of Area",main="")
abline(v=quantile(bcoef[,2],c(0.025,0.975)))
gli <- lm(Species ~ Area + Elevation + Nearest + Scruz + Adjacent,  gala,subset=(row.names(gala) != "Isabela"))
summary(gli)
data(star)
plot(light ~ temp, star)
gs1 <- lm(light ~ temp, star)
abline(coef(gs1))
gs2 <- rlm(light ~ temp, star)
abline(coef(gs2), lty=2)
gs3 <- ltsreg(light ~ temp, star, nsamp="exact")
abline(coef(gs3), lty=5)