library(ggplot2)

## Exercise 1

nb_cyl <- as.factor(mtcars$cyl)
ggplot(mtcars,aes(x=disp,y=mpg, colour=nb_cyl))+ 
  geom_point()

## Exercise 2

X <- seq(-2*pi,2*pi,by=0.1)
n <- length(X)
D <- data.frame(x=rep(X,2),
                type=c(rep("sine",n),rep("cosine",n)),f=c(sin(X),cos(X)))
ggplot(D,aes(x=x,y=f,colour=type))+
  geom_line()+
  geom_hline(yintercept=-1,size=2, colour="blue")+
  geom_hline(yintercept=1,size=2, colour="blue")+
  theme(legend.position="none")+
  facet_wrap(~type)

## Exercise 3

n <- 100
x <- runif(n)
y <- 3+x+rnorm(n,sd=0.2)
D <- data.frame(x=x,y=y)
model.reg <- lm(y~x,data=D)
D <- data.frame(x=x, y=y, yhat=model.reg$fitted.values)
ggplot(D,aes(x=x,y=y))+
  geom_point()+
  geom_segment(data=D, aes(x=x, y=y, xend=x, yend=yhat), color="red", alpha=0.5)+
  geom_abline(intercept=model.reg$coefficients[1],slope=model.reg$coefficients[2], color="blue")+
  theme_classic()

## Exercise 4

data(state)
states <- data.frame(state.x77,state.name=rownames(state.x77), state.region=state.region)

q1 <- quantile(states$Income,1/3,names=FALSE)
q2 <- quantile(states$Income,2/3,names=FALSE) 
states$revenu1 <- cut(states$Income,breaks=c(min(states$Income),q1,q2,max(states$Income)),labels=c("low","medium","high"),include.lowest=TRUE)

ggplot(states,aes(x=Population,y=Murder))+
  geom_smooth(method="lm",se=FALSE)+
  geom_point(aes(colour=state.region), size=0.3)+
  facet_wrap(~revenu1)+
  theme(axis.text.x = element_text(angle = 30))