How to plot regression or LOWESS lines over data i

Question

It is often helpful to plot a line (e.g., a fitted regression line or a non-parametric LOWESS line) over data. Likewise, when variables are confounded, it is often helpful to plot x1, y data stratified by x2. However, I can't quite figure out how to combine both using ?coplot. This ought to be quite natural in lattice, but I can't seem to figure out how to do it there, either.

The following provides some data to play with:

library(MASS)
set.seed(7422)
X <- mvrnorm(100, mu=c(5,5), Sigma=rbind(c(2.0, 1.9),
                                         c(1.9, 2.0) ) )
x1 <- X[,1];  x2 <- X[,2]
y <- 3 + .6*x1 - .4*x2 + rnorm(100)
m <- lm(y~x1+x2)
summary(m)$coefficients
#               Estimate Std. Error   t value     Pr(>|t|)
# (Intercept)  3.8281801  0.4022204  9.517619 1.476519e-15
# x1           0.5466495  0.2060269  2.653292 9.314673e-03
# x2          -0.4835804  0.2139542 -2.260205 2.604451e-02
windows()
  pairs(cbind(y, x1, x2))
xs <- seq(1.6, 9.2, by=.1)
windows()
  plot(y~x2)
  lines(xs, predict(m, data.frame(x1=5.2, x2=xs)), col="blue")
windows()
  coplot(y~x2|x1)
  ## doesn't work (lines on plot were drawn by hand)
  # lines(xs, predict(m, data.frame(x1=mean(x1[subscripts], x2=xs)), col="blue")
  # lines(lowess(y~x2, subset=x1[subscripts]), col="gray")

Scatterplot matrix of the raw data:

Here is a marginal plot of x2 vs y, with fitted the regression line and a marginal LOWESS line plotted on top of the data. This will look weird to people who aren't statistically savvy.

This is what I have in mind. It's a coplot, with the regression model and a LOWESS line fitted to each stratum of the data plotted inside each panel.

Answer 1

To do this with coplot, you need to define your own panel function. The default function is points which just plots the points, but you can add a regression line and a lowess curve with a simple function.

PointsWithReg = function(x, y, pch=20, col=1, ...) {
    points(x=x, y=y, col=col, pch=pch, type="p", ...)
    abline(lm(y ~ x))
    lines(lowess(x=x, y=y), col="blue")
}

coplot(y~x2|x1, panel=PointsWithReg, pch=16)