## Regressione lineare semplice e multipla
## 20/05/2026
# dati "insulate.dat"

insulate<-read.table("Insulate.dat", col.names = c("when", "temp", "cons"))
insulate$when<-as.factor(insulate$when)
str(insulate)
summary(insulate)

attach(insulate)
plot(temp, cons, pch=19, col=4)

### funzione lm()
## stima modello lineare con y="cons" e x="temp"
ins.lm <- lm(cons ~ temp)  

ins.lm$coefficients  # stime coefficienti (beta1, beta2)
## oppure coef(ins.lm)
ins.lm$residuals[1]    # residui: valori oss. - val. stimati
ins.lm$fitted.values # fitted(ins.lm)
summary(ins.lm)

## retta stimata: cons=5.4862-0.2902*temp
plot(temp, cons, pch=19)
abline(ins.lm)

plot(ins.lm, which=1)
plot(ins.lm, which=2)

# predict: stima della media di Y
# oppure previsione in corrispondenza di un nuovo valore di x

ins.mean<-predict(ins.lm, interval="none")
plot(temp, cons, pch=19)
points(temp, ins.mean, pch=8, col=2)

## creo dei nuovi valori di temp
new.data<-data.frame(temp=seq(-5, 15))
## previsione per i nuovi valori di x
ins.mean.new<-predict(ins.lm, newdata = new.data, 
                      interval = "none")
plot(temp, cons, pch=19, xlim=range(new.data$temp))
points(new.data$temp, ins.mean.new, pch=8, col=2)
lines(new.data$temp, ins.mean.new, col=2)

## intervalli di confidenza e previsione

ins.confnew<-predict(ins.lm, newdata = new.data, 
                     interval = "confidence")
ins.prev<-predict(ins.lm, newdata = new.data, 
                     interval = "prediction")
matplot(new.data$temp, ins.prev, type="l", lty=c("solid","dashed","dashed"),
        col=c("red","purple","purple"), xlab="temp", ylab="predicted y")
matlines(new.data$temp, ins.confnew, type="l", lty=c("solid","dashed","dashed"),
         col=c("red","blue","blue"))
points(temp, cons)