#reg-leverage.r
#Figure 2
dev.off()
#x is the absolute value of z=(x-mu_x)/sd_x, with mu_x and sd_x being robust estimate;
x=c(
 0.1039211,
 1.8050155,
 2.2116516,
 0.9233243,
 0.9738637,
 0.0179033,
 0.9965386,
 0.2395215,
 0.7409176,
 0.4815837,
 0.2564837,
 0.6747881,
 1.2017722,
  0.624243,
 0.7723846);
#y is the standardized residual following robust regression;
y=c(
 2.9665221,
  0.629598,
 -2.672544,
 -0.302395,
 -0.813451,
  0.603379,
 -0.952705,
  0.454144,
 -0.080149,
 0.1886351,
 0.7953704,
 -0.678748,
 -0.234016,
 0.5771241,
 -0.186778);

n=15

plot(x, y, type="p", lty=1, xlab="Robust M-distance of x", ylab="Residual of robust regression",  main="", col=1)

v_x2=qchisq(.95, 1, ncp=0, lower.tail = TRUE, log.p = FALSE);#quantile
v_x=sqrt(v_x2);
h_y=qnorm(.975, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE) #quantile;

abline(v=v_x)
abline(h=h_y)
abline(h=-h_y)

text(1.0,2.5,"A1")
text(1.0,-2.4,"A2")
text(2.12,2.5,"A3")
text(2.12,0,"A4")
text(2.12,-2.35,"A5")

text(1.0,h_y-.15, "a")
text(1.0, -h_y+.15, "b")
text(v_x-.05, 0, "c")

text(.02,2.95,"A")
text(1.74,.67,"B")
text(2.15,-2.63,"C")

#========================================;
#Figure 3;

#res_s=ordered y in Figure 2;
res_s=c(
 -2.672544,
 -0.952705,
 -0.813451,
 -0.678748,
 -0.302395,
 -0.234016,
 -0.186778,
 -0.080149,
 0.1886351,
  0.454144,
 0.5771241,
  0.603379,
  0.629598,
 0.7953704,
 2.9665221);


N=15;
library(plotrix)

x=matrix(0,N,1);
for (i in 1:N){
	p_i=i/(N+1);
	x[i]=qchisq(p_i, 1, ncp=0, lower.tail = TRUE, log.p = FALSE)
	#qnorm(p_i, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE) #quantile
	}
q_chi1=sqrt(x);
y=sort(abs(res_s));
plot(q_chi1,y,pch=16,cex=.5,cex.lab=1.3, xlab="Quantile of chi-distribution (df=1)",ylab="Absolute residual of robust regression");
text(1.81,2.95,"A")
text(1.48,2.65,"C")
draw.ellipse(x=1.65, y=2.8, a=.32, b=.1, border=1, angle=c(43), lty=1, lwd=.2)