# Simulate Residual Plots

par(mfrow=c(3,3))
for (i in 1:9) plot(1:50, rnorm(50))
for (i in 1:9) plot(1:50, (1:50)*rnorm(50))
for (i in 1:9) plot(1:50, sqrt(1:50)*rnorm(50))
for (i in 1:9) plot(1:50, cos((1:50)*pi/25+rnorm(50)))
par(mfrow=c(1,1))



par(mfrow=c(3,3))
for (i in 1:9) plot(1:50, rt(50,df=2),ylim=c(-6,6))
for (i in 1:9) hist(rt(50,df=2))
for (i in 1:9) plot(1:50, rchisq(50,df=2),ylim=c(0,12))
for (i in 1:9) hist(rchisq(50,df=2))
for (i in 1:9) plot(1:50, 2+3*rnorm(50))
for (i in 1:9) hist(2+3*rnorm(50))
par(mfrow=c(1,1))


# Simulations-homework

x1<-seq(from=-3,to=3,by=0.2)
x2<-x1+0.8*rnorm(length(x1)) # add some random scatter to x1

plot(x1,x2)  



a<-seq(from=-3,to=3,by=0.2)
a1<-rep(a,length(a))
a2<-rep(a,each=length(a))
x<-cbind(a1,a2) # Create grid
s<-sample(seq(1:length(a1)),size=length(a),replace=FALSE) # Choose random points from the grid
x<-x[s,]
x1<-x[,1]
x1<-x[,2]

plot(x1,x2)