fat <- read.table("DATA/fat.txt",header=T)
summary(fat)

plot(fat$hip.F, fat$body.W, xlab='Tloustka kozni rasy (mm)', ylab='Telesna hmotnost (kg)')

m.weight <- lm(body.W ~ hip.F, data=fat)
par(mfrow=c(2,2))
plot(m.weight)

shapiro.test(m.weight$residuals)

t.test(m.weight$residuals)

library(car)

durbinWatsonTest(m.weight)

summary(m.weight)

confint(m.weight)

100 * mean(abs(m.weight$residuals/fat$body.W))

predict(m.weight, newdata=data.frame(hip.F=20))

xx <- seq(min(fat$hip.F), max(fat$hip.F), length=300)
interval.spol <- predict(m.weight,newdata=data.frame(hip.F=xx),interval='confidence')
pred.interval <- predict(m.weight,newdata=data.frame(hip.F=xx),interval='predict')
plot(fat$hip.F, fat$body.W, xlab='Tloustka kozni rasy (mm)', ylab='Telesna hmotnost (kg)')
lines(xx,interval.spol[,1],col='red')
lines(xx,interval.spol[,2], col='red', lty=2)
lines(xx,interval.spol[,3], col='red', lty=2)
lines(xx,pred.interval[,2], col='blue', lty=2)
lines(xx,pred.interval[,3], col='blue', lty=2)
legend("topleft",c('model','IS','pred. int.'), lty=c(1,2,2),
       col=c('red', 'red', 'blue'))

m.weight.2 <- lm(body.W ~ hip.F + I(hip.F^2), data=fat)
par(mfrow=c(2,2))
plot(m.weight.2)

shapiro.test(m.weight.2$residuals)

t.test(m.weight.2$residuals)

durbinWatsonTest(m.weight.2)

summary(m.weight.2)

#parabola
100 * mean(abs(m.weight.2$residuals/fat$body.W))