How to change the color of points in a specific quadrant?

Question

I have a scatter plot of data points, and I am able to use abline to create the quadrant lines. Now I'm trying to color the points of those in quadrant 1 and quadrant 3. I am going to plot all the points first, and then plot only those in quadrant one in red, and those in quadrant three in blue. They will be superimposed on the old ones. However, I don't know how to plot points by quadrant. Thank you.

"write the R code to plot the points that are in the(Q1,Q1) quadrant of(waiting, eruption) in Red, AND the points that are in the(Q3,Q3) Quadrant of(waiting, eruption) in blue, everything else in black, use a pch=19 and cex=0.5. (Hint, plot everything with pch=19, col="black" first, then add the conditional points with the required colors, they will be superimposed on the old ones, whatever left stays in black)."

This is my foundation:

plot(faithful$waiting, faithful$eruptions, pch=19, cex=0.5, col="black")

I realize I somehow need to plot only those in quadrant 1 in a color and then plot those in quadrant 3 in another color, and run that code after my foundation. But I'm not sure how. Thanks.

The dput(faithful) is:

structure(list(eruptions = c(3.6, 1.8, 3.333, 2.283, 4.533, 2.883, 
4.7, 3.6, 1.95, 4.35, 1.833, 3.917, 4.2, 1.75, 4.7, 2.167, 1.75, 
4.8, 1.6, 4.25, 1.8, 1.75, 3.45, 3.067, 4.533, 3.6, 1.967, 4.083, 
3.85, 4.433, 4.3, 4.467, 3.367, 4.033, 3.833, 2.017, 1.867, 4.833, 
1.833, 4.783, 4.35, 1.883, 4.567, 1.75, 4.533, 3.317, 3.833, 
2.1, 4.633, 2, 4.8, 4.716, 1.833, 4.833, 1.733, 4.883, 3.717, 
1.667, 4.567, 4.317, 2.233, 4.5, 1.75, 4.8, 1.817, 4.4, 4.167, 
4.7, 2.067, 4.7, 4.033, 1.967, 4.5, 4, 1.983, 5.067, 2.017, 4.567, 
3.883, 3.6, 4.133, 4.333, 4.1, 2.633, 4.067, 4.933, 3.95, 4.517, 
2.167, 4, 2.2, 4.333, 1.867, 4.817, 1.833, 4.3, 4.667, 3.75, 
1.867, 4.9, 2.483, 4.367, 2.1, 4.5, 4.05, 1.867, 4.7, 1.783, 
4.85, 3.683, 4.733, 2.3, 4.9, 4.417, 1.7, 4.633, 2.317, 4.6, 
1.817, 4.417, 2.617, 4.067, 4.25, 1.967, 4.6, 3.767, 1.917, 4.5, 
2.267, 4.65, 1.867, 4.167, 2.8, 4.333, 1.833, 4.383, 1.883, 4.933, 
2.033, 3.733, 4.233, 2.233, 4.533, 4.817, 4.333, 1.983, 4.633, 
2.017, 5.1, 1.8, 5.033, 4, 2.4, 4.6, 3.567, 4, 4.5, 4.083, 1.8, 
3.967, 2.2, 4.15, 2, 3.833, 3.5, 4.583, 2.367, 5, 1.933, 4.617, 
1.917, 2.083, 4.583, 3.333, 4.167, 4.333, 4.5, 2.417, 4, 4.167, 
1.883, 4.583, 4.25, 3.767, 2.033, 4.433, 4.083, 1.833, 4.417, 
2.183, 4.8, 1.833, 4.8, 4.1, 3.966, 4.233, 3.5, 4.366, 2.25, 
4.667, 2.1, 4.35, 4.133, 1.867, 4.6, 1.783, 4.367, 3.85, 1.933, 
4.5, 2.383, 4.7, 1.867, 3.833, 3.417, 4.233, 2.4, 4.8, 2, 4.15, 
1.867, 4.267, 1.75, 4.483, 4, 4.117, 4.083, 4.267, 3.917, 4.55, 
4.083, 2.417, 4.183, 2.217, 4.45, 1.883, 1.85, 4.283, 3.95, 2.333, 
4.15, 2.35, 4.933, 2.9, 4.583, 3.833, 2.083, 4.367, 2.133, 4.35, 
2.2, 4.45, 3.567, 4.5, 4.15, 3.817, 3.917, 4.45, 2, 4.283, 4.767, 
4.533, 1.85, 4.25, 1.983, 2.25, 4.75, 4.117, 2.15, 4.417, 1.817, 
4.467), waiting = c(79, 54, 74, 62, 85, 55, 88, 85, 51, 85, 54, 
84, 78, 47, 83, 52, 62, 84, 52, 79, 51, 47, 78, 69, 74, 83, 55, 
76, 78, 79, 73, 77, 66, 80, 74, 52, 48, 80, 59, 90, 80, 58, 84, 
58, 73, 83, 64, 53, 82, 59, 75, 90, 54, 80, 54, 83, 71, 64, 77, 
81, 59, 84, 48, 82, 60, 92, 78, 78, 65, 73, 82, 56, 79, 71, 62, 
76, 60, 78, 76, 83, 75, 82, 70, 65, 73, 88, 76, 80, 48, 86, 60, 
90, 50, 78, 63, 72, 84, 75, 51, 82, 62, 88, 49, 83, 81, 47, 84, 
52, 86, 81, 75, 59, 89, 79, 59, 81, 50, 85, 59, 87, 53, 69, 77, 
56, 88, 81, 45, 82, 55, 90, 45, 83, 56, 89, 46, 82, 51, 86, 53, 
79, 81, 60, 82, 77, 76, 59, 80, 49, 96, 53, 77, 77, 65, 81, 71, 
70, 81, 93, 53, 89, 45, 86, 58, 78, 66, 76, 63, 88, 52, 93, 49, 
57, 77, 68, 81, 81, 73, 50, 85, 74, 55, 77, 83, 83, 51, 78, 84, 
46, 83, 55, 81, 57, 76, 84, 77, 81, 87, 77, 51, 78, 60, 82, 91, 
53, 78, 46, 77, 84, 49, 83, 71, 80, 49, 75, 64, 76, 53, 94, 55, 
76, 50, 82, 54, 75, 78, 79, 78, 78, 70, 79, 70, 54, 86, 50, 90, 
54, 54, 77, 79, 64, 75, 47, 86, 63, 85, 82, 57, 82, 67, 74, 54, 
83, 73, 73, 88, 80, 71, 83, 56, 79, 78, 84, 58, 83, 43, 60, 75, 
81, 46, 90, 46, 74)), row.names = c(NA, 272L), class = "data.frame")

And how I defined my quadrants:

plot(faithful$waiting, faithful$eruptions, pch=19, cex=0.5, col="green")
abline(v=quantile(faithful$waiting, 0.75), col="red")
abline(h=quantile(faithful$eruptions,0.75),col="red")  
abline(v=quantile(faithful$waiting, 0.25), col="red")
abline(h=quantile(faithful$eruptions,0.25),col="red")  

mtext("Q1", side=1, at=quantile(faithful$waiting, 0.25), col="red")
mtext("Q1", side=2, at=quantile(faithful$eruptions, 0.25), col="red")
mtext("Q3", side=2, at=quantile(faithful$eruptions, 0.75), col="red")
mtext("Q3", side=1, at=quantile(faithful$waiting, 0.75), col="red")

What I've been trying, when using a grouping:

faithful$color<- 'black'

q1<-quantile(faithful$waiting, 0.25)  #how do I assign the quantiles
q3<-quantile(faithful$waiting, 0.75)

faithful$color[faithful$waiting  ]="red"    #how do I then assign the quantiles a color
faithful$color[faithful$waiting  ]="blue"

Answer 1

We can cut both variables into quantiles and paste the levels together to obtain a group for each quadrant.

faithful <- within(faithful, {
  e.qtl <- as.integer(cut(faithful$eruptions, 
                          quantile(faithful$eruptions, c(0, .25, .75, 1)), 
                          include.lowest=TRUE))
  w.qtl <- as.integer(cut(faithful$waiting, 
                          quantile(faithful$waiting, c(0, .25, .75, 1)), 
                          include.lowest=TRUE))
  qtl <- as.integer(as.factor(with(faithful, 
                                   paste0(e.qtl, w.qtl))))
})

Then we can easily plot the data assigning color for each group.

colors <- rainbow(length(unique(faithful$qtl)))  # create colors

# plot
plot(faithful$waiting, faithful$eruptions, type="n")  # empty plot here
with(faithful, points(waiting, eruptions, col=colors[qtl], pch=19, cex=0.5))

After that add your ablines and mtext.

abline(v=quantile(faithful$waiting, 0.75), col="red")
abline(h=quantile(faithful$eruptions, 0.75),col="red")  
abline(v=quantile(faithful$waiting, 0.25), col="red")
abline(h=quantile(faithful$eruptions, 0.25),col="red")  
mtext("Q1", side=1, at=quantile(faithful$waiting, 0.25), col="red")
mtext("Q1", side=2, at=quantile(faithful$eruptions, 0.25), col="red")
mtext("Q3", side=2, at=quantile(faithful$eruptions, 0.75), col="red")
mtext("Q3", side=1, at=quantile(faithful$waiting, 0.75), col="red")

Result