# grafico della retta dei minimi quadrati
plot(cars$speed, cars$dist, ylab = "dist", xlab="speed")
abline(lm(dist ~ speed), col = "red")

# con ggplot2
library(ggplot2)

ggplot(cars, aes(speed, dist)) +
  geom_point() +
  geom_smooth(method = "lm")

# lm  
res <- lm(dist ~ speed, data = cars)
summary(res)

# intervalli di confidenza
confint(res)

# errore standard dei residui
sigma(res)

# regressione e correlazione
cov(cars$speed, cars$dist) / var(cars$speed)
cov(cars$speed, cars$dist) / var(cars$dist)
3.932409 * 0.1655676
sqrt(3.932409 * 0.1655676)