randu dataset, part 2

In my last post I have plotted randu dataset to show that all its points lie on 15 parallel planes. But I was not fully satified with the solution and decided to show this numerically.

It can be done in four steps:

1. identifying four points lying on the same plane and finding its equation (we know that we have 15 planes so it is enough to check 15*3+1 points to find them);
2. applying the equation to all points in randu dataset to divide them into 15 classes;
3. veryfying that the classes separate points into 15 parallel planes;
4. plotting the solution changing colors for points on different planes.

Here is the code I used to do this:

library(rgl)

library(caTools)

# STEP 1

all.combs <- combs(1:46, 4)

i <- 1

repeat {

      model <- lm(z ~ x + y, data = randu[all.combs[i, ], ])

      if (summary(model)$r.squared > 0.99999) {

            break

      }

      i <- i + 1

}

# STEP 2

line.class <- predict(model, randu) - randu$z

line.class <- factor(round(line.class) + 10)

# STEP 3

summary(lm(z ~ x + y + line.class, data = randu))

# STEP 4

with(randu, plot3d(x, y, z, axes = FALSE, col = line.class,

       xlab = "", ylab = "", zlab = ""))

rgl.viewpoint(theta = -3.8, phi = 3.8, fov = 0, zoom = 0.7)

At step three we can see that the model obtains perfect fit. The final figure is plotted below: