#Simulate Residual patterns
set.seed(10101)

pdf('ResidualPatternsNew.pdf',height=11,width=8)
par(mfrow=c(2,1))
n<-1000		
x<-runif(1000,0,100)
beta0<-30
beta1<-1.5
y1<-beta0+beta1*x+rnorm(n)*10
plot(x,y1,pch=3,cex=0.6);title('Original data')
summary(lm(y1~x))
abline(coef(lm(y1~x)),col='red',lwd=2)
e1<-residuals(lm(y1~x))
plot(x,e1,pch=19,cex=0.6,ylab='residuals')
title('Residuals show no pattern vs x \n Straight line assumption correct')
abline(h=0,lty=2)

y2<-beta0+beta1*x+0.02*x^2+rnorm(n)*10
plot(x,y2,pch=3,cex=0.6);title('Original data')
summary(lm(y2~x))
abline(coef(lm(y2~x)),col='red',lwd=2)
e2<-residuals(lm(y2~x))
plot(x,e2,pch=19,cex=0.6,ylab='residuals')
title('Residuals show parabolic pattern vs x \n Incorrect straight line assumption')
abline(h=0,lty=2)

y3<-beta0+beta1*x+0.01*exp(x/11)+rnorm(n)*10
plot(x,y3,pch=3,cex=0.6);title('Original data')
summary(lm(y3~x))
abline(coef(lm(y3~x)),col='red',lwd=2)
e3<-residuals(lm(y3~x))
plot(x,e3,pch=19,cex=0.6,ylab='residuals')
title('Residuals show curvilinear pattern vs x \n Incorrect straight line assumption')
abline(h=0,lty=2)

y4<-beta0+beta1*x+rnorm(n)*(x*(1000-x)/1000+10)
plot(x,y4,pch=3,cex=0.6);title('Original data')
summary(lm(y4~x))
abline(coef(lm(y4~x)),col='red',lwd=2)
e4<-residuals(lm(y4~x))
plot(x,e4,pch=19,cex=0.6,ylab='residuals')
title('Residuals show parabolic pattern vs x \n Incorrect constant variance assumption')
abline(h=0,lty=2)

y5<-beta0+beta1*x+rnorm(n)*(x*(100-x)/100+10)
plot(x,y5,pch=3,cex=0.6);title('Original data')
summary(lm(y5~x))
abline(coef(lm(y5~x)),col='red',lwd=2)
e5<-residuals(lm(y5~x))
plot(x,e5,pch=19,cex=0.6,ylab='residuals')
title('Residuals show non-constant variance pattern vs x \n Incorrect constant variance assumption')

x<-rnorm(n,50,100/sqrt(12))
beta0<-30
beta1<-1.5
y6<-beta0+beta1*x+rnorm(n)*10
plot(x,y6,pch=3,cex=0.6,xlim=range(0,100));title('Original data')
summary(lm(y6~x))
abline(coef(lm(y6~x)),col='red',lwd=2)
e6<-residuals(lm(y6~x))
plot(x,e6,pch=19,cex=0.6,ylab='residuals')
title('Residuals show no pattern vs x \n Straight line assumption correct')
abline(h=0,lty=2)

n<-50000
x<-runif(n,0,100)

xlabs<-paste(10*c(0:9),"-",10+10*c(0:9),sep='')

class.7<-cut(x,breaks=seq(0,100,by=10),labels=FALSE)

y7<-beta0+beta1*x+rnorm(n)*(x*(100-x)/100+10)
e7<-residuals(lm(y7~x))
plot(x,e7,pch=19,cex=0.6,ylab='residuals')
title('Larger sample size (50000) \n Incorrect constant variance assumption')
boxplot(e7~class.7,col='gray',names=xlabs)
title('Residuals show non-constant variance pattern in boxplot')

x<-rnorm(n,50,100/sqrt(12))
class.8<-cut(x,breaks=seq(0,100,by=10),labels=FALSE)
beta0<-30
beta1<-1.5
y8<-beta0+beta1*x+rnorm(n)*10
e8<-residuals(lm(y8~x))
plot(x,e8,pch=19,cex=0.6,ylab='residuals')
title('Larger sample size (50000) \n Straight line assumption correct')
abline(h=0,lty=2)
boxplot(e8~class.8,col='gray',names=xlabs)
title('Residuals show constant variance pattern in boxplot')

dev.off()