# Transformação na variável preditora
# Modelo original Y ~ X

rm(list=ls(all=TRUE))

X<-c(0.5,0.5,1,1,1.5,1.5,2,2,2.5,2.5)

Y<-c(42.5,50.6,68.5,80.7,89,99.6,105.3,111.8,112.3, 125.7)

par(pty="s")

par(mfrow=c(1,3))

plot(X,Y, pch=16)

abline(lm(Y~X), lwd=2)

par(new=TRUE)

plot(lowess(X,Y), type="l", ylim=range(Y), xlim=range(X), ylab="", xlab="",  lty=2)

legend(locator(1), c("modelo linear", "lowess"), lwd=c(2,1), lty=c(1,2))

fit.model <- lm(Y~X)

## Programa do Gilberto para resíduos padronizados
X <- model.matrix(fit.model)
n <- nrow(X)
p <- ncol(X)
H <- X%*%solve(t(X)%*%X)%*%t(X)
h <- diag(H)
lms <- summary(fit.model)
s <- lms$sigma
r <- resid(lms)
si <- lm.influence(fit.model)$sigma
tsi <- r/(si*sqrt(1-h))
a <- max(tsi)+1
b <- min(tsi)-1
plot(tsi, pch=16, ylab="resíduo padronizados", xlab="índices", ylim=range(a,b))
abline(2,0,lty=2)
abline(-2,0,lty=2)


qqnorm(tsi, pch=16, ylab="resíduos", xlab="índices")

abline(0,1)

library(alr3)

pureErrorAnova(fit.model)

source("d:\\fontes\\envel_norm.txt")



# Transformação na variável preditora
# Modelo original Y ~ log(X)

rm(list=ls(all=TRUE))

X<-c(0.5,0.5,1,1,1.5,1.5,2,2,2.5,2.5)

Y<-c(42.5,50.6,68.5,80.7,89,99.6,105.3,111.8,112.3, 125.7)

par(new=FALSE)

par(pty="s")

par(mfrow=c(1,3))

plot(sqrt(X),Y, pch=16, xlab=expression(sqrt(X)))

abline(lm(Y~sqrt(X)), lwd=2)

par(new=TRUE)

plot(lowess(sqrt(X),Y), type="l", ylim=range(Y), xlim=range(sqrt(X)), ylab="", xlab="", lty=2)

legend(locator(1), c("modelo linear", "lowess"), lwd=c(2,1), lty=c(1,2))

fit.model <- lm(Y~sqrt(X))

## Programa do Gilberto para resíduos padronizados
X <- model.matrix(fit.model)
n <- nrow(X)
p <- ncol(X)
H <- X%*%solve(t(X)%*%X)%*%t(X)
h <- diag(H)
lms <- summary(fit.model)
s <- lms$sigma
r <- resid(lms)
si <- lm.influence(fit.model)$sigma
tsi <- r/(si*sqrt(1-h))
a <- max(tsi)+1
b <- min(tsi)-1
plot(tsi, pch=16, ylab="resíduos padronizados", xlab="índices", ylim=range(a,b))
abline(2,0,lty=2)
abline(-2,0,lty=2)

abline(lm(Y~X))

library(alr3)

pureErrorAnova(fit.model)

qqnorm(tsi, pch=16, ylab="resíduos", xlab="índices")

abline(0,1)

source("d:\\fontes\\envel_norm.txt")




# Transformação na variável resposta
# Modelo original Y ~ X

rm(list=ls(all=TRUE))

dados<-read.table("d:\\dados\\poliamina.txt", header=TRUE)

attach(dados)

par(mfrow=c(1,3))

plot(X,Y, pch=16)

abline(lm(Y~X), lwd=2)

par(new=TRUE)

plot(lowess(X,Y), type="l", ylim=range(Y), xlim=range(X), ylab="", xlab="",  lty=2)

legend(locator(1), c("modelo linear", "lowess"), lwd=c(2,1), lty=c(1,2))

fit.model <-lm(Y~X)

## Programa do Gilberto para resíduos padronizados
X <- model.matrix(fit.model)
n <- nrow(X)
p <- ncol(X)
H <- X%*%solve(t(X)%*%X)%*%t(X)
h <- diag(H)
lms <- summary(fit.model)
s <- lms$sigma
r <- resid(lms)
si <- lm.influence(fit.model)$sigma
tsi <- r/(si*sqrt(1-h))
a <- max(tsi)+1
b <- min(tsi)-1
plot(tsi, pch=16, ylab="resíduos padronizados", xlab="índices", ylim=range(a,b))
abline(2,0,lty=2)
abline(-2,0,lty=2)

qqnorm(tsi, pch=16, ylab="resíduos", xlab="índices")

abline(0,1)

source("d:\\fontes\\envel_norm.txt")




# Transformação na variável preditora
# Modelo original log(Y) ~ X

rm(list=ls(all=TRUE))

dados<-read.table("d:\\dados\\poliamina.txt", header=TRUE)

attach(dados)

par(mfrow=c(1,3))

plot(X,log(Y), pch=16)

abline(lm(log(Y)~X), lwd=2)

par(new=TRUE)

plot(lowess(X,log(Y)), type="l", ylim=range(log(Y)), xlim=range(X), ylab="", xlab="",  lty=2)

legend(locator(1), c("modelo linear", "lowess"), lwd=c(2,1), lty=c(1,2))

fit.model <-lm(log(Y)~X)

## Programa do Gilberto para resíduos padronizados
X <- model.matrix(fit.model)
n <- nrow(X)
p <- ncol(X)
H <- X%*%solve(t(X)%*%X)%*%t(X)
h <- diag(H)
lms <- summary(fit.model)
s <- lms$sigma
r <- resid(lms)
si <- lm.influence(fit.model)$sigma
tsi <- r/(si*sqrt(1-h))
a <- max(tsi)+1
b <- min(tsi)-1
plot(tsi, pch=16, ylab="resíduos padronizados", xlab="índices", ylim=range(a,b))
abline(2,0,lty=2)
abline(-2,0,lty=2)

qqnorm(tsi, pch=16, ylab="resíduos", xlab="índices")

abline(0,1)

source("d:\\fontes\\envel_norm.txt")


# Transformação de Box-Cox

rm(list=ls(all=TRUE))

dados<-read.table("d:\\dados\\poliamina.txt", header=TRUE)

attach(dados)

boxcox(Y ~ X, lambda = seq(-2, 2, len = 20))

rm(list=ls(all=TRUE))

par(mfrow=c(1,3))

plot(X,1/sqrt(Y), pch=16)

abline(lm(1/sqrt(Y) ~ X), lwd=2)

par(new=TRUE)

plot(lowess(X,1/sqrt(Y)), type="l", ylim=range(log(Y)), xlim=range(X), ylab="", xlab="",  lty=2)

legend(locator(1), c("modelo linear", "lowess"), lwd=c(2,1), lty=c(1,2))

fit.model <-lm(1/sqrt(Y)~X)

## Programa do Gilberto para resíduos padronizados
X <- model.matrix(fit.model)
n <- nrow(X)
p <- ncol(X)
H <- X%*%solve(t(X)%*%X)%*%t(X)
h <- diag(H)
lms <- summary(fit.model)
s <- lms$sigma
r <- resid(lms)
si <- lm.influence(fit.model)$sigma
tsi <- r/(si*sqrt(1-h))
a <- max(tsi)+1
b <- min(tsi)-1
plot(tsi, pch=16, ylab="resíduos padronizados", xlab="índices", ylim=range(a,b))
abline(2,0,lty=2)
abline(-2,0,lty=2)

qqnorm(tsi, pch=16, ylab="resíduos", xlab="índices")

abline(0,1)


source("d:\\fontes\\envel_norm.txt")