### 21/05/2026

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

# modello con interazione "temp*when"

contrasts(when)
# 1= when:prima
# 0= when:dopo
## stima modello lineare con y="cons" e x="temp"
ins.lm <- lm(cons ~ temp)  # y=beta1+beta2*x

ins.lm.w<-lm(cons ~ temp*when) 
summary(ins.lm.w)

## when=prima (z=1) y=(beta1+beta3)+(beta2+beta4)*x
## when=dopo (z=0) y=beta1+beta2*x
# x=4 --> media(Y)|prima = 5.28, media(Y)|dopo = 3.61

plot(temp, cons, pch=19)
# when="prima"
abline(ins.lm.w$coefficients[1]+ins.lm.w$coefficients[3], 
       ins.lm.w$coefficients[2]+ins.lm.w$coefficients[4], 
       col=2, lwd=2)
# when="dopo"
abline(ins.lm.w$coefficients[1], 
       ins.lm.w$coefficients[2],
       col=3, lwd=2)
legend("topright", c("prima", "dopo"), 
       lty=1, col=c(2,3), lwd=c(2,2))

anova(ins.lm, ins.lm.w)
detach(insulate)

## Esempio dati "orange Juice"

oj<-read.csv("oj.csv")
View(oj)
oj$brand<-as.factor(oj$brand)
oj$feat<-as.factor(oj$feat)
#str(oj)
bcol<-c("green", "red", "cyan")

plot(sales~price, data=oj, col=bcol[oj$brand])
#levels(oj$brand)

plot(log(sales)~log(price), 
     data=oj, col=bcol[oj$brand])
plot(log(price)~brand,data=oj, col=bcol)

# Modello 1: Y=log(sales); x=log(price)
## log(sales)=beta1+beta2*log(price) + epsilon
m1<-lm(log(sales)~log(price), data=oj)
summary(m1)

# Modello 2: Y=log(sales); x2=log(price); x3= brand 
## log(sales)=beta1+beta2*log(price) + beta3*brand(MM)+beta4*brand(TR) 
m2<-lm(log(sales)~log(price)+brand, data=oj)
summary(m2)

## DOM. log(sales)=beta1+beta2*log(price)
## MM. log(sales)=(beta1+beta3)+beta2*log(price)