Connecting dots to the 3d regression line

Question

This is the 3d version of this other question.

Consider the following data:

Income2<-structure(list(X = 1:30, Education = c(21.5862068965517, 18.2758620689655, 
12.0689655172414, 17.0344827586207, 19.9310344827586, 18.2758620689655, 
19.9310344827586, 21.1724137931034, 20.3448275862069, 10, 13.7241379310345, 
18.6896551724138, 11.6551724137931, 16.6206896551724, 10, 20.3448275862069, 
14.1379310344828, 16.6206896551724, 16.6206896551724, 20.3448275862069, 
18.2758620689655, 14.551724137931, 17.448275862069, 10.4137931034483, 
21.5862068965517, 11.2413793103448, 19.9310344827586, 11.6551724137931, 
12.0689655172414, 17.0344827586207), Seniority = c(113.103448275862, 
119.310344827586, 100.689655172414, 187.586206896552, 20, 26.2068965517241, 
150.344827586207, 82.0689655172414, 88.2758620689655, 113.103448275862, 
51.0344827586207, 144.137931034483, 20, 94.4827586206897, 187.586206896552, 
94.4827586206897, 20, 44.8275862068966, 175.172413793103, 187.586206896552, 
100.689655172414, 137.931034482759, 94.4827586206897, 32.4137931034483, 
20, 44.8275862068966, 168.965517241379, 57.2413793103448, 32.4137931034483, 
106.896551724138), Income = c(99.9171726114381, 92.579134855529, 
34.6787271520874, 78.7028062353695, 68.0099216471551, 71.5044853814318, 
87.9704669939115, 79.8110298331255, 90.00632710858, 45.6555294997364, 
31.9138079371295, 96.2829968022869, 27.9825049000603, 66.601792415137, 
41.5319924201478, 89.00070081522, 28.8163007592387, 57.6816942573605, 
70.1050960424457, 98.8340115435447, 74.7046991976891, 53.5321056283034, 
72.0789236655191, 18.5706650327685, 78.8057842852386, 21.388561306174, 
90.8140351180409, 22.6361626208955, 17.613593041445, 74.6109601985289
)), .Names = c("X", "Education", "Seniority", "Income"), class = "data.frame", row.names = c(NA, 
-30L))

How to make a 3d graph of a regression model, including the points, the hyperplane of the model and a line connecting the points to the hyperplane?

I’d like to see different ways of making this kind of graph, especially with base charts, lattice and rgl.

Based on my SOEN question.

Answer 1

Another solution, somewhat simpler and perhaps not so pretty graphically, is the function plotPlane package rockchalk. The advantage is that you can make a 3D chart with only one command line. Using the above data:

require(rockchalk)
model <- loess(Income ~ Education + Seniority, data = Income2)
plotPlane(model, plotx1 = "Education", plotx2 = "Seniority",
                 drawArrow = TRUE, pch = 20, pcol = 2,
                 npp = 100, theta = 20, phi = 30)

In which plotx is the variable on each of the axes, drawArrow lines, npp is the number of points for which the predicted values are calculated, and theta and phi are used to rotate the graph horizontally and vertically. The result is this:

Answer 2

Making with the base charts:

First, run the model:

model <- loess(Income ~Education + Seniority, data=Income2)

Create sequences of x and y:

x <-range(Income2$Education)
x <- seq(x[1], x[2], length.out=50)    
y <- range(Income2$Seniority)
y <- seq(y[1], y[2], length.out=50)

Create the values of z with all combinations of x and y:

z <- outer(x,y, 
           function(Education,Seniority)
                     predict(model, data.frame(Education,Seniority)))

Chart the template with persp:

p <- persp(x,y,z, theta=30, phi=30, 
           col="lightblue",expand = 0.5,shade = 0.2,
           xlab="Education", ylab="Seniority", zlab="Income")

Make a projection of the dots in 3d to 2d with trans3d and add the dots (with points) and segments (with segment):

obs <- trans3d(Income2$Education, Income2$Seniority,Income2$Income,p)
pred <- trans3d(Income2$Education, Income2$Seniority,fitted(model),p)
points(obs, col="red",pch=16)
segments(obs$x, obs$y, pred$x, pred$y)